Limited-memory fast gradient descent method for graph regularized nonnegative matrix factorization.

PubMed

Guan, Naiyang; Wei, Lei; Luo, Zhigang; Tao, Dacheng

2013-01-01

Graph regularized nonnegative matrix factorization (GNMF) decomposes a nonnegative data matrix X[Symbol:see text]R(m x n) to the product of two lower-rank nonnegative factor matrices, i.e.,W[Symbol:see text]R(m x r) and H[Symbol:see text]R(r x n) (r < min {m,n}) and aims to preserve the local geometric structure of the dataset by minimizing squared Euclidean distance or Kullback-Leibler (KL) divergence between X and WH. The multiplicative update rule (MUR) is usually applied to optimize GNMF, but it suffers from the drawback of slow-convergence because it intrinsically advances one step along the rescaled negative gradient direction with a non-optimal step size. Recently, a multiple step-sizes fast gradient descent (MFGD) method has been proposed for optimizing NMF which accelerates MUR by searching the optimal step-size along the rescaled negative gradient direction with Newton's method. However, the computational cost of MFGD is high because 1) the high-dimensional Hessian matrix is dense and costs too much memory; and 2) the Hessian inverse operator and its multiplication with gradient cost too much time. To overcome these deficiencies of MFGD, we propose an efficient limited-memory FGD (L-FGD) method for optimizing GNMF. In particular, we apply the limited-memory BFGS (L-BFGS) method to directly approximate the multiplication of the inverse Hessian and the gradient for searching the optimal step size in MFGD. The preliminary results on real-world datasets show that L-FGD is more efficient than both MFGD and MUR. To evaluate the effectiveness of L-FGD, we validate its clustering performance for optimizing KL-divergence based GNMF on two popular face image datasets including ORL and PIE and two text corpora including Reuters and TDT2. The experimental results confirm the effectiveness of L-FGD by comparing it with the representative GNMF solvers.

Real time on-chip sequential adaptive principal component analysis for data feature extraction and image compression

NASA Technical Reports Server (NTRS)

Duong, T. A.

2004-01-01

In this paper, we present a new, simple, and optimized hardware architecture sequential learning technique for adaptive Principle Component Analysis (PCA) which will help optimize the hardware implementation in VLSI and to overcome the difficulties of the traditional gradient descent in learning convergence and hardware implementation.

A gradient system solution to Potts mean field equations and its electronic implementation.

PubMed

Urahama, K; Ueno, S

1993-03-01

A gradient system solution method is presented for solving Potts mean field equations for combinatorial optimization problems subject to winner-take-all constraints. In the proposed solution method the optimum solution is searched by using gradient descent differential equations whose trajectory is confined within the feasible solution space of optimization problems. This gradient system is proven theoretically to always produce a legal local optimum solution of combinatorial optimization problems. An elementary analog electronic circuit implementing the presented method is designed on the basis of current-mode subthreshold MOS technologies. The core constituent of the circuit is the winner-take-all circuit developed by Lazzaro et al. Correct functioning of the presented circuit is exemplified with simulations of the circuits implementing the scheme for solving the shortest path problems.

A conjugate gradient method with descent properties under strong Wolfe line search

NASA Astrophysics Data System (ADS)

Zull, N.; ‘Aini, N.; Shoid, S.; Ghani, N. H. A.; Mohamed, N. S.; Rivaie, M.; Mamat, M.

2017-09-01

The conjugate gradient (CG) method is one of the optimization methods that are often used in practical applications. The continuous and numerous studies conducted on the CG method have led to vast improvements in its convergence properties and efficiency. In this paper, a new CG method possessing the sufficient descent and global convergence properties is proposed. The efficiency of the new CG algorithm relative to the existing CG methods is evaluated by testing them all on a set of test functions using MATLAB. The tests are measured in terms of iteration numbers and CPU time under strong Wolfe line search. Overall, this new method performs efficiently and comparable to the other famous methods.

Policy Gradient Adaptive Dynamic Programming for Data-Based Optimal Control.

PubMed

Luo, Biao; Liu, Derong; Wu, Huai-Ning; Wang, Ding; Lewis, Frank L

2017-10-01

The model-free optimal control problem of general discrete-time nonlinear systems is considered in this paper, and a data-based policy gradient adaptive dynamic programming (PGADP) algorithm is developed to design an adaptive optimal controller method. By using offline and online data rather than the mathematical system model, the PGADP algorithm improves control policy with a gradient descent scheme. The convergence of the PGADP algorithm is proved by demonstrating that the constructed Q -function sequence converges to the optimal Q -function. Based on the PGADP algorithm, the adaptive control method is developed with an actor-critic structure and the method of weighted residuals. Its convergence properties are analyzed, where the approximate Q -function converges to its optimum. Computer simulation results demonstrate the effectiveness of the PGADP-based adaptive control method.

Hybrid DFP-CG method for solving unconstrained optimization problems

NASA Astrophysics Data System (ADS)

Osman, Wan Farah Hanan Wan; Asrul Hery Ibrahim, Mohd; Mamat, Mustafa

2017-09-01

The conjugate gradient (CG) method and quasi-Newton method are both well known method for solving unconstrained optimization method. In this paper, we proposed a new method by combining the search direction between conjugate gradient method and quasi-Newton method based on BFGS-CG method developed by Ibrahim et al. The Davidon-Fletcher-Powell (DFP) update formula is used as an approximation of Hessian for this new hybrid algorithm. Numerical result showed that the new algorithm perform well than the ordinary DFP method and proven to posses both sufficient descent and global convergence properties.

Machine learning for inverse lithography: using stochastic gradient descent for robust photomask synthesis

NASA Astrophysics Data System (ADS)

Jia, Ningning; Y Lam, Edmund

2010-04-01

Inverse lithography technology (ILT) synthesizes photomasks by solving an inverse imaging problem through optimization of an appropriate functional. Much effort on ILT is dedicated to deriving superior masks at a nominal process condition. However, the lower k1 factor causes the mask to be more sensitive to process variations. Robustness to major process variations, such as focus and dose variations, is desired. In this paper, we consider the focus variation as a stochastic variable, and treat the mask design as a machine learning problem. The stochastic gradient descent approach, which is a useful tool in machine learning, is adopted to train the mask design. Compared with previous work, simulation shows that the proposed algorithm is effective in producing robust masks.

A modified three-term PRP conjugate gradient algorithm for optimization models.

PubMed

Wu, Yanlin

2017-01-01

The nonlinear conjugate gradient (CG) algorithm is a very effective method for optimization, especially for large-scale problems, because of its low memory requirement and simplicity. Zhang et al. (IMA J. Numer. Anal. 26:629-649, 2006) firstly propose a three-term CG algorithm based on the well known Polak-Ribière-Polyak (PRP) formula for unconstrained optimization, where their method has the sufficient descent property without any line search technique. They proved the global convergence of the Armijo line search but this fails for the Wolfe line search technique. Inspired by their method, we will make a further study and give a modified three-term PRP CG algorithm. The presented method possesses the following features: (1) The sufficient descent property also holds without any line search technique; (2) the trust region property of the search direction is automatically satisfied; (3) the steplengh is bounded from below; (4) the global convergence will be established under the Wolfe line search. Numerical results show that the new algorithm is more effective than that of the normal method.

Mini-batch optimized full waveform inversion with geological constrained gradient filtering

NASA Astrophysics Data System (ADS)

Yang, Hui; Jia, Junxiong; Wu, Bangyu; Gao, Jinghuai

2018-05-01

High computation cost and generating solutions without geological sense have hindered the wide application of Full Waveform Inversion (FWI). Source encoding technique is a way to dramatically reduce the cost of FWI but subject to fix-spread acquisition setup requirement and slow convergence for the suppression of cross-talk. Traditionally, gradient regularization or preconditioning is applied to mitigate the ill-posedness. An isotropic smoothing filter applied on gradients generally gives non-geological inversion results, and could also introduce artifacts. In this work, we propose to address both the efficiency and ill-posedness of FWI by a geological constrained mini-batch gradient optimization method. The mini-batch gradient descent optimization is adopted to reduce the computation time by choosing a subset of entire shots for each iteration. By jointly applying the structure-oriented smoothing to the mini-batch gradient, the inversion converges faster and gives results with more geological meaning. Stylized Marmousi model is used to show the performance of the proposed method on realistic synthetic model.

A multi-resolution approach for optimal mass transport

NASA Astrophysics Data System (ADS)

Dominitz, Ayelet; Angenent, Sigurd; Tannenbaum, Allen

2007-09-01

Optimal mass transport is an important technique with numerous applications in econometrics, fluid dynamics, automatic control, statistical physics, shape optimization, expert systems, and meteorology. Motivated by certain problems in image registration and medical image visualization, in this note, we describe a simple gradient descent methodology for computing the optimal L2 transport mapping which may be easily implemented using a multiresolution scheme. We also indicate how the optimal transport map may be computed on the sphere. A numerical example is presented illustrating our ideas.

Concurrent Monte Carlo transport and fluence optimization with fluence adjusting scalable transport Monte Carlo

PubMed Central

Svatos, M.; Zankowski, C.; Bednarz, B.

2016-01-01

Purpose: The future of radiation therapy will require advanced inverse planning solutions to support single-arc, multiple-arc, and “4π” delivery modes, which present unique challenges in finding an optimal treatment plan over a vast search space, while still preserving dosimetric accuracy. The successful clinical implementation of such methods would benefit from Monte Carlo (MC) based dose calculation methods, which can offer improvements in dosimetric accuracy when compared to deterministic methods. The standard method for MC based treatment planning optimization leverages the accuracy of the MC dose calculation and efficiency of well-developed optimization methods, by precalculating the fluence to dose relationship within a patient with MC methods and subsequently optimizing the fluence weights. However, the sequential nature of this implementation is computationally time consuming and memory intensive. Methods to reduce the overhead of the MC precalculation have been explored in the past, demonstrating promising reductions of computational time overhead, but with limited impact on the memory overhead due to the sequential nature of the dose calculation and fluence optimization. The authors propose an entirely new form of “concurrent” Monte Carlo treat plan optimization: a platform which optimizes the fluence during the dose calculation, reduces wasted computation time being spent on beamlets that weakly contribute to the final dose distribution, and requires only a low memory footprint to function. In this initial investigation, the authors explore the key theoretical and practical considerations of optimizing fluence in such a manner. Methods: The authors present a novel derivation and implementation of a gradient descent algorithm that allows for optimization during MC particle transport, based on highly stochastic information generated through particle transport of very few histories. A gradient rescaling and renormalization algorithm, and the concept of momentum from stochastic gradient descent were used to address obstacles unique to performing gradient descent fluence optimization during MC particle transport. The authors have applied their method to two simple geometrical phantoms, and one clinical patient geometry to examine the capability of this platform to generate conformal plans as well as assess its computational scaling and efficiency, respectively. Results: The authors obtain a reduction of at least 50% in total histories transported in their investigation compared to a theoretical unweighted beamlet calculation and subsequent fluence optimization method, and observe a roughly fixed optimization time overhead consisting of ∼10% of the total computation time in all cases. Finally, the authors demonstrate a negligible increase in memory overhead of ∼7–8 MB to allow for optimization of a clinical patient geometry surrounded by 36 beams using their platform. Conclusions: This study demonstrates a fluence optimization approach, which could significantly improve the development of next generation radiation therapy solutions while incurring minimal additional computational overhead. PMID:27277051

14 CFR 23.69 - Enroute climb/descent.

Code of Federal Regulations, 2010 CFR

2010-01-01

... climb/descent. (a) All engines operating. The steady gradient and rate of climb must be determined at.... The steady gradient and rate of climb/descent must be determined at each weight, altitude, and ambient...

Performance comparison of a new hybrid conjugate gradient method under exact and inexact line searches

NASA Astrophysics Data System (ADS)

Ghani, N. H. A.; Mohamed, N. S.; Zull, N.; Shoid, S.; Rivaie, M.; Mamat, M.

2017-09-01

Conjugate gradient (CG) method is one of iterative techniques prominently used in solving unconstrained optimization problems due to its simplicity, low memory storage, and good convergence analysis. This paper presents a new hybrid conjugate gradient method, named NRM1 method. The method is analyzed under the exact and inexact line searches in given conditions. Theoretically, proofs show that the NRM1 method satisfies the sufficient descent condition with both line searches. The computational result indicates that NRM1 method is capable in solving the standard unconstrained optimization problems used. On the other hand, the NRM1 method performs better under inexact line search compared with exact line search.

DOE Office of Scientific and Technical Information (OSTI.GOV)

Yang, Y. M., E-mail: ymingy@gmail.com; Bednarz, B.; Svatos, M.

Purpose: The future of radiation therapy will require advanced inverse planning solutions to support single-arc, multiple-arc, and “4π” delivery modes, which present unique challenges in finding an optimal treatment plan over a vast search space, while still preserving dosimetric accuracy. The successful clinical implementation of such methods would benefit from Monte Carlo (MC) based dose calculation methods, which can offer improvements in dosimetric accuracy when compared to deterministic methods. The standard method for MC based treatment planning optimization leverages the accuracy of the MC dose calculation and efficiency of well-developed optimization methods, by precalculating the fluence to dose relationship withinmore » a patient with MC methods and subsequently optimizing the fluence weights. However, the sequential nature of this implementation is computationally time consuming and memory intensive. Methods to reduce the overhead of the MC precalculation have been explored in the past, demonstrating promising reductions of computational time overhead, but with limited impact on the memory overhead due to the sequential nature of the dose calculation and fluence optimization. The authors propose an entirely new form of “concurrent” Monte Carlo treat plan optimization: a platform which optimizes the fluence during the dose calculation, reduces wasted computation time being spent on beamlets that weakly contribute to the final dose distribution, and requires only a low memory footprint to function. In this initial investigation, the authors explore the key theoretical and practical considerations of optimizing fluence in such a manner. Methods: The authors present a novel derivation and implementation of a gradient descent algorithm that allows for optimization during MC particle transport, based on highly stochastic information generated through particle transport of very few histories. A gradient rescaling and renormalization algorithm, and the concept of momentum from stochastic gradient descent were used to address obstacles unique to performing gradient descent fluence optimization during MC particle transport. The authors have applied their method to two simple geometrical phantoms, and one clinical patient geometry to examine the capability of this platform to generate conformal plans as well as assess its computational scaling and efficiency, respectively. Results: The authors obtain a reduction of at least 50% in total histories transported in their investigation compared to a theoretical unweighted beamlet calculation and subsequent fluence optimization method, and observe a roughly fixed optimization time overhead consisting of ∼10% of the total computation time in all cases. Finally, the authors demonstrate a negligible increase in memory overhead of ∼7–8 MB to allow for optimization of a clinical patient geometry surrounded by 36 beams using their platform. Conclusions: This study demonstrates a fluence optimization approach, which could significantly improve the development of next generation radiation therapy solutions while incurring minimal additional computational overhead.« less

Algorithms for accelerated convergence of adaptive PCA.

PubMed

Chatterjee, C; Kang, Z; Roychowdhury, V P

2000-01-01

We derive and discuss new adaptive algorithms for principal component analysis (PCA) that are shown to converge faster than the traditional PCA algorithms due to Oja, Sanger, and Xu. It is well known that traditional PCA algorithms that are derived by using gradient descent on an objective function are slow to converge. Furthermore, the convergence of these algorithms depends on appropriate choices of the gain sequences. Since online applications demand faster convergence and an automatic selection of gains, we present new adaptive algorithms to solve these problems. We first present an unconstrained objective function, which can be minimized to obtain the principal components. We derive adaptive algorithms from this objective function by using: 1) gradient descent; 2) steepest descent; 3) conjugate direction; and 4) Newton-Raphson methods. Although gradient descent produces Xu's LMSER algorithm, the steepest descent, conjugate direction, and Newton-Raphson methods produce new adaptive algorithms for PCA. We also provide a discussion on the landscape of the objective function, and present a global convergence proof of the adaptive gradient descent PCA algorithm using stochastic approximation theory. Extensive experiments with stationary and nonstationary multidimensional Gaussian sequences show faster convergence of the new algorithms over the traditional gradient descent methods.We also compare the steepest descent adaptive algorithm with state-of-the-art methods on stationary and nonstationary sequences.

A mesh gradient technique for numerical optimization

NASA Technical Reports Server (NTRS)

Willis, E. A., Jr.

1973-01-01

A class of successive-improvement optimization methods in which directions of descent are defined in the state space along each trial trajectory are considered. The given problem is first decomposed into two discrete levels by imposing mesh points. Level 1 consists of running optimal subarcs between each successive pair of mesh points. For normal systems, these optimal two-point boundary value problems can be solved by following a routine prescription if the mesh spacing is sufficiently close. A spacing criterion is given. Under appropriate conditions, the criterion value depends only on the coordinates of the mesh points, and its gradient with respect to those coordinates may be defined by interpreting the adjoint variables as partial derivatives of the criterion value function. In level 2, the gradient data is used to generate improvement steps or search directions in the state space which satisfy the boundary values and constraints of the given problem.

A modified conjugate gradient coefficient with inexact line search for unconstrained optimization

NASA Astrophysics Data System (ADS)

Aini, Nurul; Rivaie, Mohd; Mamat, Mustafa

2016-11-01

Conjugate gradient (CG) method is a line search algorithm mostly known for its wide application in solving unconstrained optimization problems. Its low memory requirements and global convergence properties makes it one of the most preferred method in real life application such as in engineering and business. In this paper, we present a new CG method based on AMR* and CD method for solving unconstrained optimization functions. The resulting algorithm is proven to have both the sufficient descent and global convergence properties under inexact line search. Numerical tests are conducted to assess the effectiveness of the new method in comparison to some previous CG methods. The results obtained indicate that our method is indeed superior.

Product Distribution Theory for Control of Multi-Agent Systems

NASA Technical Reports Server (NTRS)

Lee, Chia Fan; Wolpert, David H.

2004-01-01

Product Distribution (PD) theory is a new framework for controlling Multi-Agent Systems (MAS's). First we review one motivation of PD theory, as the information-theoretic extension of conventional full-rationality game theory to the case of bounded rational agents. In this extension the equilibrium of the game is the optimizer of a Lagrangian of the (probability distribution of) the joint stare of the agents. Accordingly we can consider a team game in which the shared utility is a performance measure of the behavior of the MAS. For such a scenario the game is at equilibrium - the Lagrangian is optimized - when the joint distribution of the agents optimizes the system's expected performance. One common way to find that equilibrium is to have each agent run a reinforcement learning algorithm. Here we investigate the alternative of exploiting PD theory to run gradient descent on the Lagrangian. We present computer experiments validating some of the predictions of PD theory for how best to do that gradient descent. We also demonstrate how PD theory can improve performance even when we are not allowed to rerun the MAS from different initial conditions, a requirement implicit in some previous work.

Understanding and Optimizing Asynchronous Low-Precision Stochastic Gradient Descent

PubMed Central

De Sa, Christopher; Feldman, Matthew; Ré, Christopher; Olukotun, Kunle

2018-01-01

Stochastic gradient descent (SGD) is one of the most popular numerical algorithms used in machine learning and other domains. Since this is likely to continue for the foreseeable future, it is important to study techniques that can make it run fast on parallel hardware. In this paper, we provide the first analysis of a technique called Buckwild! that uses both asynchronous execution and low-precision computation. We introduce the DMGC model, the first conceptualization of the parameter space that exists when implementing low-precision SGD, and show that it provides a way to both classify these algorithms and model their performance. We leverage this insight to propose and analyze techniques to improve the speed of low-precision SGD. First, we propose software optimizations that can increase throughput on existing CPUs by up to 11×. Second, we propose architectural changes, including a new cache technique we call an obstinate cache, that increase throughput beyond the limits of current-generation hardware. We also implement and analyze low-precision SGD on the FPGA, which is a promising alternative to the CPU for future SGD systems. PMID:29391770

Optimal control of switching time in switched stochastic systems with multi-switching times and different costs

NASA Astrophysics Data System (ADS)

Liu, Xiaomei; Li, Shengtao; Zhang, Kanjian

2017-08-01

In this paper, we solve an optimal control problem for a class of time-invariant switched stochastic systems with multi-switching times, where the objective is to minimise a cost functional with different costs defined on the states. In particular, we focus on problems in which a pre-specified sequence of active subsystems is given and the switching times are the only control variables. Based on the calculus of variation, we derive the gradient of the cost functional with respect to the switching times on an especially simple form, which can be directly used in gradient descent algorithms to locate the optimal switching instants. Finally, a numerical example is given, highlighting the validity of the proposed methodology.

Steepest descent with momentum for quadratic functions is a version of the conjugate gradient method.

PubMed

Bhaya, Amit; Kaszkurewicz, Eugenius

2004-01-01

It is pointed out that the so called momentum method, much used in the neural network literature as an acceleration of the backpropagation method, is a stationary version of the conjugate gradient method. Connections with the continuous optimization method known as heavy ball with friction are also made. In both cases, adaptive (dynamic) choices of the so called learning rate and momentum parameters are obtained using a control Liapunov function analysis of the system.

Two New PRP Conjugate Gradient Algorithms for Minimization Optimization Models.

PubMed

Yuan, Gonglin; Duan, Xiabin; Liu, Wenjie; Wang, Xiaoliang; Cui, Zengru; Sheng, Zhou

2015-01-01

Two new PRP conjugate Algorithms are proposed in this paper based on two modified PRP conjugate gradient methods: the first algorithm is proposed for solving unconstrained optimization problems, and the second algorithm is proposed for solving nonlinear equations. The first method contains two aspects of information: function value and gradient value. The two methods both possess some good properties, as follows: 1) βk ≥ 0 2) the search direction has the trust region property without the use of any line search method 3) the search direction has sufficient descent property without the use of any line search method. Under some suitable conditions, we establish the global convergence of the two algorithms. We conduct numerical experiments to evaluate our algorithms. The numerical results indicate that the first algorithm is effective and competitive for solving unconstrained optimization problems and that the second algorithm is effective for solving large-scale nonlinear equations.

Two New PRP Conjugate Gradient Algorithms for Minimization Optimization Models

PubMed Central

Yuan, Gonglin; Duan, Xiabin; Liu, Wenjie; Wang, Xiaoliang; Cui, Zengru; Sheng, Zhou

2015-01-01

Two new PRP conjugate Algorithms are proposed in this paper based on two modified PRP conjugate gradient methods: the first algorithm is proposed for solving unconstrained optimization problems, and the second algorithm is proposed for solving nonlinear equations. The first method contains two aspects of information: function value and gradient value. The two methods both possess some good properties, as follows: 1)β k ≥ 0 2) the search direction has the trust region property without the use of any line search method 3) the search direction has sufficient descent property without the use of any line search method. Under some suitable conditions, we establish the global convergence of the two algorithms. We conduct numerical experiments to evaluate our algorithms. The numerical results indicate that the first algorithm is effective and competitive for solving unconstrained optimization problems and that the second algorithm is effective for solving large-scale nonlinear equations. PMID:26502409

Online learning in optical tomography: a stochastic approach

NASA Astrophysics Data System (ADS)

Chen, Ke; Li, Qin; Liu, Jian-Guo

2018-07-01

We study the inverse problem of radiative transfer equation (RTE) using stochastic gradient descent method (SGD) in this paper. Mathematically, optical tomography amounts to recovering the optical parameters in RTE using the incoming–outgoing pair of light intensity. We formulate it as a PDE-constraint optimization problem, where the mismatch of computed and measured outgoing data is minimized with same initial data and RTE constraint. The memory and computation cost it requires, however, is typically prohibitive, especially in high dimensional space. Smart iterative solvers that only use partial information in each step is called for thereafter. Stochastic gradient descent method is an online learning algorithm that randomly selects data for minimizing the mismatch. It requires minimum memory and computation, and advances fast, therefore perfectly serves the purpose. In this paper we formulate the problem, in both nonlinear and its linearized setting, apply SGD algorithm and analyze the convergence performance.

An Approach to Stable Gradient-Descent Adaptation of Higher Order Neural Units.

PubMed

Bukovsky, Ivo; Homma, Noriyasu

2017-09-01

Stability evaluation of a weight-update system of higher order neural units (HONUs) with polynomial aggregation of neural inputs (also known as classes of polynomial neural networks) for adaptation of both feedforward and recurrent HONUs by a gradient descent method is introduced. An essential core of the approach is based on the spectral radius of a weight-update system, and it allows stability monitoring and its maintenance at every adaptation step individually. Assuring the stability of the weight-update system (at every single adaptation step) naturally results in the adaptation stability of the whole neural architecture that adapts to the target data. As an aside, the used approach highlights the fact that the weight optimization of HONU is a linear problem, so the proposed approach can be generally extended to any neural architecture that is linear in its adaptable parameters.

Optimization for high-dose-rate brachytherapy of cervical cancer with adaptive simulated annealing and gradient descent.

PubMed

Yao, Rui; Templeton, Alistair K; Liao, Yixiang; Turian, Julius V; Kiel, Krystyna D; Chu, James C H

2014-01-01

To validate an in-house optimization program that uses adaptive simulated annealing (ASA) and gradient descent (GD) algorithms and investigate features of physical dose and generalized equivalent uniform dose (gEUD)-based objective functions in high-dose-rate (HDR) brachytherapy for cervical cancer. Eight Syed/Neblett template-based cervical cancer HDR interstitial brachytherapy cases were used for this study. Brachytherapy treatment plans were first generated using inverse planning simulated annealing (IPSA). Using the same dwell positions designated in IPSA, plans were then optimized with both physical dose and gEUD-based objective functions, using both ASA and GD algorithms. Comparisons were made between plans both qualitatively and based on dose-volume parameters, evaluating each optimization method and objective function. A hybrid objective function was also designed and implemented in the in-house program. The ASA plans are higher on bladder V75% and D2cc (p=0.034) and lower on rectum V75% and D2cc (p=0.034) than the IPSA plans. The ASA and GD plans are not significantly different. The gEUD-based plans have higher homogeneity index (p=0.034), lower overdose index (p=0.005), and lower rectum gEUD and normal tissue complication probability (p=0.005) than the physical dose-based plans. The hybrid function can produce a plan with dosimetric parameters between the physical dose-based and gEUD-based plans. The optimized plans with the same objective value and dose-volume histogram could have different dose distributions. Our optimization program based on ASA and GD algorithms is flexible on objective functions, optimization parameters, and can generate optimized plans comparable with IPSA. Copyright © 2014 American Brachytherapy Society. Published by Elsevier Inc. All rights reserved.

Error measure comparison of currently employed dose-modulation schemes for e-beam proximity effect control

NASA Astrophysics Data System (ADS)

Peckerar, Martin C.; Marrian, Christie R.

1995-05-01

Standard matrix inversion methods of e-beam proximity correction are compared with a variety of pseudoinverse approaches based on gradient descent. It is shown that the gradient descent methods can be modified using 'regularizers' (terms added to the cost function minimized during gradient descent). This modification solves the 'negative dose' problem in a mathematically sound way. Different techniques are contrasted using a weighted error measure approach. It is shown that the regularization approach leads to the highest quality images. In some cases, ignoring negative doses yields results which are worse than employing an uncorrected dose file.

Manifold regularized discriminative nonnegative matrix factorization with fast gradient descent.

PubMed

Guan, Naiyang; Tao, Dacheng; Luo, Zhigang; Yuan, Bo

2011-07-01

Nonnegative matrix factorization (NMF) has become a popular data-representation method and has been widely used in image processing and pattern-recognition problems. This is because the learned bases can be interpreted as a natural parts-based representation of data and this interpretation is consistent with the psychological intuition of combining parts to form a whole. For practical classification tasks, however, NMF ignores both the local geometry of data and the discriminative information of different classes. In addition, existing research results show that the learned basis is unnecessarily parts-based because there is neither explicit nor implicit constraint to ensure the representation parts-based. In this paper, we introduce the manifold regularization and the margin maximization to NMF and obtain the manifold regularized discriminative NMF (MD-NMF) to overcome the aforementioned problems. The multiplicative update rule (MUR) can be applied to optimizing MD-NMF, but it converges slowly. In this paper, we propose a fast gradient descent (FGD) to optimize MD-NMF. FGD contains a Newton method that searches the optimal step length, and thus, FGD converges much faster than MUR. In addition, FGD includes MUR as a special case and can be applied to optimizing NMF and its variants. For a problem with 165 samples in R(1600), FGD converges in 28 s, while MUR requires 282 s. We also apply FGD in a variant of MD-NMF and experimental results confirm its efficiency. Experimental results on several face image datasets suggest the effectiveness of MD-NMF.

Convergence Rates of Finite Difference Stochastic Approximation Algorithms

DTIC Science & Technology

2016-06-01

dfferences as gradient approximations. It is shown that the convergence of these algorithms can be accelerated by controlling the implementation of the...descent algorithm, under various updating schemes using finite dfferences as gradient approximations. It is shown that the convergence of these...the Kiefer-Wolfowitz algorithm and the mirror descent algorithm, under various updating schemes using finite differences as gradient approximations. It

A Fast Deep Learning System Using GPU

DTIC Science & Technology

2014-06-01

hour per response, including the time for reviewing instructions, searching existing data sources, gathering and maintaining the data needed, and...widely used in data modeling until three decades later when efficient training algorithm for RBM is invented by Hinton [3] and the computing power is...be trained using most of optimization algorithms , such as BP, conjugate gradient descent (CGD) or Levenberg-Marquardt (LM). The advantage of this

Development of gradient descent adaptive algorithms to remove common mode artifact for improvement of cardiovascular signal quality.

PubMed

Ciaccio, Edward J; Micheli-Tzanakou, Evangelia

2007-07-01

Common-mode noise degrades cardiovascular signal quality and diminishes measurement accuracy. Filtering to remove noise components in the frequency domain often distorts the signal. Two adaptive noise canceling (ANC) algorithms were tested to adjust weighted reference signals for optimal subtraction from a primary signal. Update of weight w was based upon the gradient term of the steepest descent equation: [see text], where the error epsilon is the difference between primary and weighted reference signals. nabla was estimated from Deltaepsilon(2) and Deltaw without using a variable Deltaw in the denominator which can cause instability. The Parallel Comparison (PC) algorithm computed Deltaepsilon(2) using fixed finite differences +/- Deltaw in parallel during each discrete time k. The ALOPEX algorithm computed Deltaepsilon(2)x Deltaw from time k to k + 1 to estimate nabla, with a random number added to account for Deltaepsilon(2) . Deltaw--> 0 near the optimal weighting. Using simulated data, both algorithms stably converged to the optimal weighting within 50-2000 discrete sample points k even with a SNR = 1:8 and weights which were initialized far from the optimal. Using a sharply pulsatile cardiac electrogram signal with added noise so that the SNR = 1:5, both algorithms exhibited stable convergence within 100 ms (100 sample points). Fourier spectral analysis revealed minimal distortion when comparing the signal without added noise to the ANC restored signal. ANC algorithms based upon difference calculations can rapidly and stably converge to the optimal weighting in simulated and real cardiovascular data. Signal quality is restored with minimal distortion, increasing the accuracy of biophysical measurement.

Large Airborne Full Tensor Gradient Data Inversion Based on a Non-Monotone Gradient Method

NASA Astrophysics Data System (ADS)

Sun, Yong; Meng, Zhaohai; Li, Fengting

2018-03-01

Following the development of gravity gradiometer instrument technology, the full tensor gravity (FTG) data can be acquired on airborne and marine platforms. Large-scale geophysical data can be obtained using these methods, making such data sets a number of the "big data" category. Therefore, a fast and effective inversion method is developed to solve the large-scale FTG data inversion problem. Many algorithms are available to accelerate the FTG data inversion, such as conjugate gradient method. However, the conventional conjugate gradient method takes a long time to complete data processing. Thus, a fast and effective iterative algorithm is necessary to improve the utilization of FTG data. Generally, inversion processing is formulated by incorporating regularizing constraints, followed by the introduction of a non-monotone gradient-descent method to accelerate the convergence rate of FTG data inversion. Compared with the conventional gradient method, the steepest descent gradient algorithm, and the conjugate gradient algorithm, there are clear advantages of the non-monotone iterative gradient-descent algorithm. Simulated and field FTG data were applied to show the application value of this new fast inversion method.

Stochastic parallel gradient descent based adaptive optics used for a high contrast imaging coronagraph

NASA Astrophysics Data System (ADS)

Dong, Bing; Ren, De-Qing; Zhang, Xi

2011-08-01

An adaptive optics (AO) system based on a stochastic parallel gradient descent (SPGD) algorithm is proposed to reduce the speckle noises in the optical system of a stellar coronagraph in order to further improve the contrast. The principle of the SPGD algorithm is described briefly and a metric suitable for point source imaging optimization is given. The feasibility and good performance of the SPGD algorithm is demonstrated by an experimental system featured with a 140-actuator deformable mirror and a Hartmann-Shark wavefront sensor. Then the SPGD based AO is applied to a liquid crystal array (LCA) based coronagraph to improve the contrast. The LCA can modulate the incoming light to generate a pupil apodization mask of any pattern. A circular stepped pattern is used in our preliminary experiment and the image contrast shows improvement from 10-3 to 10-4.5 at an angular distance of 2λ/D after being corrected by SPGD based AO.

Cosmic Microwave Background Mapmaking with a Messenger Field

NASA Astrophysics Data System (ADS)

Huffenberger, Kevin M.; Næss, Sigurd K.

2018-01-01

We apply a messenger field method to solve the linear minimum-variance mapmaking equation in the context of Cosmic Microwave Background (CMB) observations. In simulations, the method produces sky maps that converge significantly faster than those from a conjugate gradient descent algorithm with a diagonal preconditioner, even though the computational cost per iteration is similar. The messenger method recovers large scales in the map better than conjugate gradient descent, and yields a lower overall χ2. In the single, pencil beam approximation, each iteration of the messenger mapmaking procedure produces an unbiased map, and the iterations become more optimal as they proceed. A variant of the method can handle differential data or perform deconvolution mapmaking. The messenger method requires no preconditioner, but a high-quality solution needs a cooling parameter to control the convergence. We study the convergence properties of this new method and discuss how the algorithm is feasible for the large data sets of current and future CMB experiments.

Gradient descent learning algorithm overview: a general dynamical systems perspective.

PubMed

Baldi, P

1995-01-01

Gives a unified treatment of gradient descent learning algorithms for neural networks using a general framework of dynamical systems. This general approach organizes and simplifies all the known algorithms and results which have been originally derived for different problems (fixed point/trajectory learning), for different models (discrete/continuous), for different architectures (forward/recurrent), and using different techniques (backpropagation, variational calculus, adjoint methods, etc.). The general approach can also be applied to derive new algorithms. The author then briefly examines some of the complexity issues and limitations intrinsic to gradient descent learning. Throughout the paper, the author focuses on the problem of trajectory learning.

Adaptive ISAR Imaging of Maneuvering Targets Based on a Modified Fourier Transform.

PubMed

Wang, Binbin; Xu, Shiyou; Wu, Wenzhen; Hu, Pengjiang; Chen, Zengping

2018-04-27

Focusing on the inverse synthetic aperture radar (ISAR) imaging of maneuvering targets, this paper presents a new imaging method which works well when the target's maneuvering is not too severe. After translational motion compensation, we describe the equivalent rotation of maneuvering targets by two variables-the relative chirp rate of the linear frequency modulated (LFM) signal and the Doppler focus shift. The first variable indicates the target's motion status, and the second one represents the possible residual error of the translational motion compensation. With them, a modified Fourier transform matrix is constructed and then used for cross-range compression. Consequently, the imaging of maneuvering is converted into a two-dimensional parameter optimization problem in which a stable and clear ISAR image is guaranteed. A gradient descent optimization scheme is employed to obtain the accurate relative chirp rate and Doppler focus shift. Moreover, we designed an efficient and robust initialization process for the gradient descent method, thus, the well-focused ISAR images of maneuvering targets can be achieved adaptively. Human intervention is not needed, and it is quite convenient for practical ISAR imaging systems. Compared to precedent imaging methods, the new method achieves better imaging quality under reasonable computational cost. Simulation results are provided to validate the effectiveness and advantages of the proposed method.

An image morphing technique based on optimal mass preserving mapping.

PubMed

Zhu, Lei; Yang, Yan; Haker, Steven; Tannenbaum, Allen

2007-06-01

Image morphing, or image interpolation in the time domain, deals with the metamorphosis of one image into another. In this paper, a new class of image morphing algorithms is proposed based on the theory of optimal mass transport. The L(2) mass moving energy functional is modified by adding an intensity penalizing term, in order to reduce the undesired double exposure effect. It is an intensity-based approach and, thus, is parameter free. The optimal warping function is computed using an iterative gradient descent approach. This proposed morphing method is also extended to doubly connected domains using a harmonic parameterization technique, along with finite-element methods.

An Image Morphing Technique Based on Optimal Mass Preserving Mapping

PubMed Central

Zhu, Lei; Yang, Yan; Haker, Steven; Tannenbaum, Allen

2013-01-01

Image morphing, or image interpolation in the time domain, deals with the metamorphosis of one image into another. In this paper, a new class of image morphing algorithms is proposed based on the theory of optimal mass transport. The L2 mass moving energy functional is modified by adding an intensity penalizing term, in order to reduce the undesired double exposure effect. It is an intensity-based approach and, thus, is parameter free. The optimal warping function is computed using an iterative gradient descent approach. This proposed morphing method is also extended to doubly connected domains using a harmonic parameterization technique, along with finite-element methods. PMID:17547128

An approach to multiobjective optimization of rotational therapy. II. Pareto optimal surfaces and linear combinations of modulated blocked arcs for a prostate geometry.

PubMed

Pardo-Montero, Juan; Fenwick, John D

2010-06-01

The purpose of this work is twofold: To further develop an approach to multiobjective optimization of rotational therapy treatments recently introduced by the authors [J. Pardo-Montero and J. D. Fenwick, "An approach to multiobjective optimization of rotational therapy," Med. Phys. 36, 3292-3303 (2009)], especially regarding its application to realistic geometries, and to study the quality (Pareto optimality) of plans obtained using such an approach by comparing them with Pareto optimal plans obtained through inverse planning. In the previous work of the authors, a methodology is proposed for constructing a large number of plans, with different compromises between the objectives involved, from a small number of geometrically based arcs, each arc prioritizing different objectives. Here, this method has been further developed and studied. Two different techniques for constructing these arcs are investigated, one based on image-reconstruction algorithms and the other based on more common gradient-descent algorithms. The difficulty of dealing with organs abutting the target, briefly reported in previous work of the authors, has been investigated using partial OAR unblocking. Optimality of the solutions has been investigated by comparison with a Pareto front obtained from inverse planning. A relative Euclidean distance has been used to measure the distance of these plans to the Pareto front, and dose volume histogram comparisons have been used to gauge the clinical impact of these distances. A prostate geometry has been used for the study. For geometries where a blocked OAR abuts the target, moderate OAR unblocking can substantially improve target dose distribution and minimize hot spots while not overly compromising dose sparing of the organ. Image-reconstruction type and gradient-descent blocked-arc computations generate similar results. The Pareto front for the prostate geometry, reconstructed using a large number of inverse plans, presents a hockey-stick shape comprising two regions: One where the dose to the target is close to prescription and trade-offs can be made between doses to the organs at risk and (small) changes in target dose, and one where very substantial rectal sparing is achieved at the cost of large target underdosage. Plans computed following the approach using a conformal arc and four blocked arcs generally lie close to the Pareto front, although distances of some plans from high gradient regions of the Pareto front can be greater. Only around 12% of plans lie a relative Euclidean distance of 0.15 or greater from the Pareto front. Using the alternative distance measure of Craft ["Calculating and controlling the error of discrete representations of Pareto surfaces in convex multi-criteria optimization," Phys. Medica (to be published)], around 2/5 of plans lie more than 0.05 from the front. Computation of blocked arcs is quite fast, the algorithms requiring 35%-80% of the running time per iteration needed for conventional inverse plan computation. The geometry-based arc approach to multicriteria optimization of rotational therapy allows solutions to be obtained that lie close to the Pareto front. Both the image-reconstruction type and gradient-descent algorithms produce similar modulated arcs, the latter one perhaps being preferred because it is more easily implementable in standard treatment planning systems. Moderate unblocking provides a good way of dealing with OARs which abut the PTV. Optimization of geometry-based arcs is faster than usual inverse optimization of treatment plans, making this approach more rapid than an inverse-based Pareto front reconstruction.

Multigrid one shot methods for optimal control problems: Infinite dimensional control

NASA Technical Reports Server (NTRS)

Arian, Eyal; Taasan, Shlomo

1994-01-01

The multigrid one shot method for optimal control problems, governed by elliptic systems, is introduced for the infinite dimensional control space. ln this case, the control variable is a function whose discrete representation involves_an increasing number of variables with grid refinement. The minimization algorithm uses Lagrange multipliers to calculate sensitivity gradients. A preconditioned gradient descent algorithm is accelerated by a set of coarse grids. It optimizes for different scales in the representation of the control variable on different discretization levels. An analysis which reduces the problem to the boundary is introduced. It is used to approximate the two level asymptotic convergence rate, to determine the amplitude of the minimization steps, and the choice of a high pass filter to be used when necessary. The effectiveness of the method is demonstrated on a series of test problems. The new method enables the solutions of optimal control problems at the same cost of solving the corresponding analysis problems just a few times.

Application of Artificial Neural Networks in the Design and Optimization of a Nanoparticulate Fingolimod Delivery System Based on Biodegradable Poly(3-Hydroxybutyrate-Co-3-Hydroxyvalerate).

PubMed

Shahsavari, Shadab; Rezaie Shirmard, Leila; Amini, Mohsen; Abedin Dokoosh, Farid

2017-01-01

Formulation of a nanoparticulate Fingolimod delivery system based on biodegradable poly(3-hydroxybutyrate-co-3-hydroxyvalerate) was optimized according to artificial neural networks (ANNs). Concentration of poly(3-hydroxybutyrate-co-3-hydroxyvalerate), PVA and amount of Fingolimod is considered as the input value, and the particle size, polydispersity index, loading capacity, and entrapment efficacy as output data in experimental design study. In vitro release study was carried out for best formulation according to statistical analysis. ANNs are employed to generate the best model to determine the relationships between various values. In order to specify the model with the best accuracy and proficiency for the in vitro release, a multilayer percepteron with different training algorithm has been examined. Three training model formulations including Levenberg-Marquardt (LM), gradient descent, and Bayesian regularization were employed for training the ANN models. It is demonstrated that the predictive ability of each training algorithm is in the order of LM > gradient descent > Bayesian regularization. Also, optimum formulation was achieved by LM training function with 15 hidden layers and 20 neurons. The transfer function of the hidden layer for this formulation and the output layer were tansig and purlin, respectively. Also, the optimization process was developed by minimizing the error among the predicted and observed values of training algorithm (about 0.0341). Copyright © 2016 American Pharmacists Association®. Published by Elsevier Inc. All rights reserved.

Piecewise convexity of artificial neural networks.

PubMed

Rister, Blaine; Rubin, Daniel L

2017-10-01

Although artificial neural networks have shown great promise in applications including computer vision and speech recognition, there remains considerable practical and theoretical difficulty in optimizing their parameters. The seemingly unreasonable success of gradient descent methods in minimizing these non-convex functions remains poorly understood. In this work we offer some theoretical guarantees for networks with piecewise affine activation functions, which have in recent years become the norm. We prove three main results. First, that the network is piecewise convex as a function of the input data. Second, that the network, considered as a function of the parameters in a single layer, all others held constant, is again piecewise convex. Third, that the network as a function of all its parameters is piecewise multi-convex, a generalization of biconvexity. From here we characterize the local minima and stationary points of the training objective, showing that they minimize the objective on certain subsets of the parameter space. We then analyze the performance of two optimization algorithms on multi-convex problems: gradient descent, and a method which repeatedly solves a number of convex sub-problems. We prove necessary convergence conditions for the first algorithm and both necessary and sufficient conditions for the second, after introducing regularization to the objective. Finally, we remark on the remaining difficulty of the global optimization problem. Under the squared error objective, we show that by varying the training data, a single rectifier neuron admits local minima arbitrarily far apart, both in objective value and parameter space. Copyright © 2017 Elsevier Ltd. All rights reserved.

Fourier ptychographic reconstruction using Poisson maximum likelihood and truncated Wirtinger gradient.

PubMed

Bian, Liheng; Suo, Jinli; Chung, Jaebum; Ou, Xiaoze; Yang, Changhuei; Chen, Feng; Dai, Qionghai

2016-06-10

Fourier ptychographic microscopy (FPM) is a novel computational coherent imaging technique for high space-bandwidth product imaging. Mathematically, Fourier ptychographic (FP) reconstruction can be implemented as a phase retrieval optimization process, in which we only obtain low resolution intensity images corresponding to the sub-bands of the sample's high resolution (HR) spatial spectrum, and aim to retrieve the complex HR spectrum. In real setups, the measurements always suffer from various degenerations such as Gaussian noise, Poisson noise, speckle noise and pupil location error, which would largely degrade the reconstruction. To efficiently address these degenerations, we propose a novel FP reconstruction method under a gradient descent optimization framework in this paper. The technique utilizes Poisson maximum likelihood for better signal modeling, and truncated Wirtinger gradient for effective error removal. Results on both simulated data and real data captured using our laser-illuminated FPM setup show that the proposed method outperforms other state-of-the-art algorithms. Also, we have released our source code for non-commercial use.

New hybrid conjugate gradient methods with the generalized Wolfe line search.

PubMed

Xu, Xiao; Kong, Fan-Yu

2016-01-01

The conjugate gradient method was an efficient technique for solving the unconstrained optimization problem. In this paper, we made a linear combination with parameters β k of the DY method and the HS method, and putted forward the hybrid method of DY and HS. We also proposed the hybrid of FR and PRP by the same mean. Additionally, to present the two hybrid methods, we promoted the Wolfe line search respectively to compute the step size α k of the two hybrid methods. With the new Wolfe line search, the two hybrid methods had descent property and global convergence property of the two hybrid methods that can also be proved.

Geodesic regression on orientation distribution functions with its application to an aging study.

PubMed

Du, Jia; Goh, Alvina; Kushnarev, Sergey; Qiu, Anqi

2014-02-15

In this paper, we treat orientation distribution functions (ODFs) derived from high angular resolution diffusion imaging (HARDI) as elements of a Riemannian manifold and present a method for geodesic regression on this manifold. In order to find the optimal regression model, we pose this as a least-squares problem involving the sum-of-squared geodesic distances between observed ODFs and their model fitted data. We derive the appropriate gradient terms and employ gradient descent to find the minimizer of this least-squares optimization problem. In addition, we show how to perform statistical testing for determining the significance of the relationship between the manifold-valued regressors and the real-valued regressands. Experiments on both synthetic and real human data are presented. In particular, we examine aging effects on HARDI via geodesic regression of ODFs in normal adults aged 22 years old and above. © 2013 Elsevier Inc. All rights reserved.

Comparison of SIRT and SQS for Regularized Weighted Least Squares Image Reconstruction

PubMed Central

Gregor, Jens; Fessler, Jeffrey A.

2015-01-01

Tomographic image reconstruction is often formulated as a regularized weighted least squares (RWLS) problem optimized by iterative algorithms that are either inherently algebraic or derived from a statistical point of view. This paper compares a modified version of SIRT (Simultaneous Iterative Reconstruction Technique), which is of the former type, with a version of SQS (Separable Quadratic Surrogates), which is of the latter type. We show that the two algorithms minimize the same criterion function using similar forms of preconditioned gradient descent. We present near-optimal relaxation for both based on eigenvalue bounds and include a heuristic extension for use with ordered subsets. We provide empirical evidence that SIRT and SQS converge at the same rate for all intents and purposes. For context, we compare their performance with an implementation of preconditioned conjugate gradient. The illustrative application is X-ray CT of luggage for aviation security. PMID:26478906

Accelerating deep neural network training with inconsistent stochastic gradient descent.

PubMed

Wang, Linnan; Yang, Yi; Min, Renqiang; Chakradhar, Srimat

2017-09-01

Stochastic Gradient Descent (SGD) updates Convolutional Neural Network (CNN) with a noisy gradient computed from a random batch, and each batch evenly updates the network once in an epoch. This model applies the same training effort to each batch, but it overlooks the fact that the gradient variance, induced by Sampling Bias and Intrinsic Image Difference, renders different training dynamics on batches. In this paper, we develop a new training strategy for SGD, referred to as Inconsistent Stochastic Gradient Descent (ISGD) to address this problem. The core concept of ISGD is the inconsistent training, which dynamically adjusts the training effort w.r.t the loss. ISGD models the training as a stochastic process that gradually reduces down the mean of batch's loss, and it utilizes a dynamic upper control limit to identify a large loss batch on the fly. ISGD stays on the identified batch to accelerate the training with additional gradient updates, and it also has a constraint to penalize drastic parameter changes. ISGD is straightforward, computationally efficient and without requiring auxiliary memories. A series of empirical evaluations on real world datasets and networks demonstrate the promising performance of inconsistent training. Copyright © 2017 Elsevier Ltd. All rights reserved.

Algorithms for the optimization of RBE-weighted dose in particle therapy.

PubMed

Horcicka, M; Meyer, C; Buschbacher, A; Durante, M; Krämer, M

2013-01-21

We report on various algorithms used for the nonlinear optimization of RBE-weighted dose in particle therapy. Concerning the dose calculation carbon ions are considered and biological effects are calculated by the Local Effect Model. Taking biological effects fully into account requires iterative methods to solve the optimization problem. We implemented several additional algorithms into GSI's treatment planning system TRiP98, like the BFGS-algorithm and the method of conjugated gradients, in order to investigate their computational performance. We modified textbook iteration procedures to improve the convergence speed. The performance of the algorithms is presented by convergence in terms of iterations and computation time. We found that the Fletcher-Reeves variant of the method of conjugated gradients is the algorithm with the best computational performance. With this algorithm we could speed up computation times by a factor of 4 compared to the method of steepest descent, which was used before. With our new methods it is possible to optimize complex treatment plans in a few minutes leading to good dose distributions. At the end we discuss future goals concerning dose optimization issues in particle therapy which might benefit from fast optimization solvers.

Algorithms for the optimization of RBE-weighted dose in particle therapy

NASA Astrophysics Data System (ADS)

Horcicka, M.; Meyer, C.; Buschbacher, A.; Durante, M.; Krämer, M.

2013-01-01

We report on various algorithms used for the nonlinear optimization of RBE-weighted dose in particle therapy. Concerning the dose calculation carbon ions are considered and biological effects are calculated by the Local Effect Model. Taking biological effects fully into account requires iterative methods to solve the optimization problem. We implemented several additional algorithms into GSI's treatment planning system TRiP98, like the BFGS-algorithm and the method of conjugated gradients, in order to investigate their computational performance. We modified textbook iteration procedures to improve the convergence speed. The performance of the algorithms is presented by convergence in terms of iterations and computation time. We found that the Fletcher-Reeves variant of the method of conjugated gradients is the algorithm with the best computational performance. With this algorithm we could speed up computation times by a factor of 4 compared to the method of steepest descent, which was used before. With our new methods it is possible to optimize complex treatment plans in a few minutes leading to good dose distributions. At the end we discuss future goals concerning dose optimization issues in particle therapy which might benefit from fast optimization solvers.

A Comparative Study of Probability Collectives Based Multi-agent Systems and Genetic Algorithms

NASA Technical Reports Server (NTRS)

Huang, Chien-Feng; Wolpert, David H.; Bieniawski, Stefan; Strauss, Charles E. M.

2005-01-01

We compare Genetic Algorithms (GA's) with Probability Collectives (PC), a new framework for distributed optimization and control. In contrast to GA's, PC-based methods do not update populations of solutions. Instead they update an explicitly parameterized probability distribution p over the space of solutions. That updating of p arises as the optimization of a functional of p. The functional is chosen so that any p that optimizes it should be p peaked about good solutions. The PC approach works in both continuous and discrete problems. It does not suffer from the resolution limitation of the finite bit length encoding of parameters into GA alleles. It also has deep connections with both game theory and statistical physics. We review the PC approach using its motivation as the information theoretic formulation of bounded rationality for multi-agent systems. It is then compared with GA's on a diverse set of problems. To handle high dimensional surfaces, in the PC method investigated here p is restricted to a product distribution. Each distribution in that product is controlled by a separate agent. The test functions were selected for their difficulty using either traditional gradient descent or genetic algorithms. On those functions the PC-based approach significantly outperforms traditional GA's in both rate of descent, trapping in false minima, and long term optimization.

Adjoint shape optimization for fluid-structure interaction of ducted flows

NASA Astrophysics Data System (ADS)

Heners, J. P.; Radtke, L.; Hinze, M.; Düster, A.

2018-03-01

Based on the coupled problem of time-dependent fluid-structure interaction, equations for an appropriate adjoint problem are derived by the consequent use of the formal Lagrange calculus. Solutions of both primal and adjoint equations are computed in a partitioned fashion and enable the formulation of a surface sensitivity. This sensitivity is used in the context of a steepest descent algorithm for the computation of the required gradient of an appropriate cost functional. The efficiency of the developed optimization approach is demonstrated by minimization of the pressure drop in a simple two-dimensional channel flow and in a three-dimensional ducted flow surrounded by a thin-walled structure.

A Gradient Taguchi Method for Engineering Optimization

NASA Astrophysics Data System (ADS)

Hwang, Shun-Fa; Wu, Jen-Chih; He, Rong-Song

2017-10-01

To balance the robustness and the convergence speed of optimization, a novel hybrid algorithm consisting of Taguchi method and the steepest descent method is proposed in this work. Taguchi method using orthogonal arrays could quickly find the optimum combination of the levels of various factors, even when the number of level and/or factor is quite large. This algorithm is applied to the inverse determination of elastic constants of three composite plates by combining numerical method and vibration testing. For these problems, the proposed algorithm could find better elastic constants in less computation cost. Therefore, the proposed algorithm has nice robustness and fast convergence speed as compared to some hybrid genetic algorithms.

LASER APPLICATIONS AND OTHER TOPICS IN QUANTUM ELECTRONICS: Application of the stochastic parallel gradient descent algorithm for numerical simulation and analysis of the coherent summation of radiation from fibre amplifiers

NASA Astrophysics Data System (ADS)

Zhou, Pu; Wang, Xiaolin; Li, Xiao; Chen, Zilum; Xu, Xiaojun; Liu, Zejin

2009-10-01

Coherent summation of fibre laser beams, which can be scaled to a relatively large number of elements, is simulated by using the stochastic parallel gradient descent (SPGD) algorithm. The applicability of this algorithm for coherent summation is analysed and its optimisaton parameters and bandwidth limitations are studied.

Programmed gradient descent biosorption of strontium ions by Saccaromyces cerevisiae and ashing analysis: A decrement solution for nuclide and heavy metal disposal.

PubMed

Liu, Mingxue; Dong, Faqin; Zhang, Wei; Nie, Xiaoqin; Sun, Shiyong; Wei, Hongfu; Luo, Lang; Xiang, Sha; Zhang, Gege

2016-08-15

One of the waste disposal principles is decrement. The programmed gradient descent biosorption of strontium ions by Saccaromyces cerevisiae regarding bioremoval and ashing process for decrement were studied in present research. The results indicated that S. cerevisiae cells showed valid biosorption for strontium ions with greater than 90% bioremoval efficiency for high concentration strontium ions under batch culture conditions. The S. cerevisiae cells bioaccumulated approximately 10% of strontium ions in the cytoplasm besides adsorbing 90% strontium ions on cell wall. The programmed gradient descent biosorption presented good performance with a nearly 100% bioremoval ratio for low concentration strontium ions after 3 cycles. The ashing process resulted in a huge volume and weight reduction ratio as well as enrichment for strontium in the ash. XRD results showed that SrSO4 existed in ash. Simulated experiments proved that sulfate could adjust the precipitation of strontium ions. Finally, we proposed a technological flow process that combined the programmed gradient descent biosorption and ashing, which could yield great decrement and allow the supernatant to meet discharge standard. This technological flow process may be beneficial for nuclides and heavy metal disposal treatment in many fields. Copyright © 2016 Elsevier B.V. All rights reserved.

Rapid Generation of Optimal Asteroid Powered Descent Trajectories Via Convex Optimization

NASA Technical Reports Server (NTRS)

Pinson, Robin; Lu, Ping

2015-01-01

This paper investigates a convex optimization based method that can rapidly generate the fuel optimal asteroid powered descent trajectory. The ultimate goal is to autonomously design the optimal powered descent trajectory on-board the spacecraft immediately prior to the descent burn. Compared to a planetary powered landing problem, the major difficulty is the complex gravity field near the surface of an asteroid that cannot be approximated by a constant gravity field. This paper uses relaxation techniques and a successive solution process that seeks the solution to the original nonlinear, nonconvex problem through the solutions to a sequence of convex optimal control problems.

Optimal landing of a helicopter in autorotation

NASA Technical Reports Server (NTRS)

Lee, A. Y. N.

1985-01-01

Gliding descent in autorotation is a maneuver used by helicopter pilots in case of engine failure. The landing of a helicopter in autorotation is formulated as a nonlinear optimal control problem. The OH-58A helicopter was used. Helicopter vertical and horizontal velocities, vertical and horizontal displacement, and the rotor angle speed were modeled. An empirical approximation for the induced veloctiy in the vortex-ring state were provided. The cost function of the optimal control problem is a weighted sum of the squared horizontal and vertical components of the helicopter velocity at touchdown. Optimal trajectories are calculated for entry conditions well within the horizontal-vertical restriction curve, with the helicopter initially in hover or forwared flight. The resultant two-point boundary value problem with path equality constraints was successfully solved using the Sequential Gradient Restoration Technique.

Aeroassisted orbital maneuvering using Lyapunov optimal feedback control

NASA Technical Reports Server (NTRS)

Grantham, Walter J.; Lee, Byoung-Soo

1987-01-01

A Liapunov optimal feedback controller incorporating a preferred direction of motion at each state of the system which is opposite to the gradient of a specified descent function is developed for aeroassisted orbital transfer from high-earth orbit to LEO. The performances of the Liapunov controller and a calculus-of-variations open-loop minimum-fuel controller, both of which are based on the 1962 U.S. Standard Atmosphere, are simulated using both the 1962 U.S. Standard Atmosphere and an atmosphere corresponding to the STS-6 Space Shuttle flight. In the STS-6 atmosphere, the calculus-of-variations open-loop controller fails to exit the atmosphere, while the Liapunov controller achieves the optimal minimum-fuel conditions, despite the + or - 40 percent fluctuations in the STS-6 atmosphere.

Medial-based deformable models in nonconvex shape-spaces for medical image segmentation.

PubMed

McIntosh, Chris; Hamarneh, Ghassan

2012-01-01

We explore the application of genetic algorithms (GA) to deformable models through the proposition of a novel method for medical image segmentation that combines GA with nonconvex, localized, medial-based shape statistics. We replace the more typical gradient descent optimizer used in deformable models with GA, and the convex, implicit, global shape statistics with nonconvex, explicit, localized ones. Specifically, we propose GA to reduce typical deformable model weaknesses pertaining to model initialization, pose estimation and local minima, through the simultaneous evolution of a large number of models. Furthermore, we constrain the evolution, and thus reduce the size of the search-space, by using statistically-based deformable models whose deformations are intuitive (stretch, bulge, bend) and are driven in terms of localized principal modes of variation, instead of modes of variation across the entire shape that often fail to capture localized shape changes. Although GA are not guaranteed to achieve the global optima, our method compares favorably to the prevalent optimization techniques, convex/nonconvex gradient-based optimizers and to globally optimal graph-theoretic combinatorial optimization techniques, when applied to the task of corpus callosum segmentation in 50 mid-sagittal brain magnetic resonance images.

Recursive inverse kinematics for robot arms via Kalman filtering and Bryson-Frazier smoothing

NASA Technical Reports Server (NTRS)

Rodriguez, G.; Scheid, R. E., Jr.

1987-01-01

This paper applies linear filtering and smoothing theory to solve recursively the inverse kinematics problem for serial multilink manipulators. This problem is to find a set of joint angles that achieve a prescribed tip position and/or orientation. A widely applicable numerical search solution is presented. The approach finds the minimum of a generalized distance between the desired and the actual manipulator tip position and/or orientation. Both a first-order steepest-descent gradient search and a second-order Newton-Raphson search are developed. The optimal relaxation factor required for the steepest descent method is computed recursively using an outward/inward procedure similar to those used typically for recursive inverse dynamics calculations. The second-order search requires evaluation of a gradient and an approximate Hessian. A Gauss-Markov approach is used to approximate the Hessian matrix in terms of products of first-order derivatives. This matrix is inverted recursively using a two-stage process of inward Kalman filtering followed by outward smoothing. This two-stage process is analogous to that recently developed by the author to solve by means of spatial filtering and smoothing the forward dynamics problem for serial manipulators.

Fast Optimization for Aircraft Descent and Approach Trajectory

NASA Technical Reports Server (NTRS)

Luchinsky, Dmitry G.; Schuet, Stefan; Brenton, J.; Timucin, Dogan; Smith, David; Kaneshige, John

2017-01-01

We address problem of on-line scheduling of the aircraft descent and approach trajectory. We formulate a general multiphase optimal control problem for optimization of the descent trajectory and review available methods of its solution. We develop a fast algorithm for solution of this problem using two key components: (i) fast inference of the dynamical and control variables of the descending trajectory from the low dimensional flight profile data and (ii) efficient local search for the resulting reduced dimensionality non-linear optimization problem. We compare the performance of the proposed algorithm with numerical solution obtained using optimal control toolbox General Pseudospectral Optimal Control Software. We present results of the solution of the scheduling problem for aircraft descent using novel fast algorithm and discuss its future applications.

Optimal control of a variable spin speed CMG system for space vehicles. [Control Moment Gyros

NASA Technical Reports Server (NTRS)

Liu, T. C.; Chubb, W. B.; Seltzer, S. M.; Thompson, Z.

1973-01-01

Many future NASA programs require very high accurate pointing stability. These pointing requirements are well beyond anything attempted to date. This paper suggests a control system which has the capability of meeting these requirements. An optimal control law for the suggested system is specified. However, since no direct method of solution is known for this complicated system, a computation technique using successive approximations is used to develop the required solution. The method of calculus of variations is applied for estimating the changes of index of performance as well as those constraints of inequality of state variables and terminal conditions. Thus, an algorithm is obtained by the steepest descent method and/or conjugate gradient method. Numerical examples are given to show the optimal controls.

A dynamical regularization algorithm for solving inverse source problems of elliptic partial differential equations

NASA Astrophysics Data System (ADS)

Zhang, Ye; Gong, Rongfang; Cheng, Xiaoliang; Gulliksson, Mårten

2018-06-01

This study considers the inverse source problem for elliptic partial differential equations with both Dirichlet and Neumann boundary data. The unknown source term is to be determined by additional boundary conditions. Unlike the existing methods found in the literature, which usually employ the first-order in time gradient-like system (such as the steepest descent methods) for numerically solving the regularized optimization problem with a fixed regularization parameter, we propose a novel method with a second-order in time dissipative gradient-like system and a dynamical selected regularization parameter. A damped symplectic scheme is proposed for the numerical solution. Theoretical analysis is given for both the continuous model and the numerical algorithm. Several numerical examples are provided to show the robustness of the proposed algorithm.

An optimization-based framework for anisotropic simplex mesh adaptation

NASA Astrophysics Data System (ADS)

Yano, Masayuki; Darmofal, David L.

2012-09-01

We present a general framework for anisotropic h-adaptation of simplex meshes. Given a discretization and any element-wise, localizable error estimate, our adaptive method iterates toward a mesh that minimizes error for a given degrees of freedom. Utilizing mesh-metric duality, we consider a continuous optimization problem of the Riemannian metric tensor field that provides an anisotropic description of element sizes. First, our method performs a series of local solves to survey the behavior of the local error function. This information is then synthesized using an affine-invariant tensor manipulation framework to reconstruct an approximate gradient of the error function with respect to the metric tensor field. Finally, we perform gradient descent in the metric space to drive the mesh toward optimality. The method is first demonstrated to produce optimal anisotropic meshes minimizing the L2 projection error for a pair of canonical problems containing a singularity and a singular perturbation. The effectiveness of the framework is then demonstrated in the context of output-based adaptation for the advection-diffusion equation using a high-order discontinuous Galerkin discretization and the dual-weighted residual (DWR) error estimate. The method presented provides a unified framework for optimizing both the element size and anisotropy distribution using an a posteriori error estimate and enables efficient adaptation of anisotropic simplex meshes for high-order discretizations.

Analysis of Online Composite Mirror Descent Algorithm.

PubMed

Lei, Yunwen; Zhou, Ding-Xuan

2017-03-01

We study the convergence of the online composite mirror descent algorithm, which involves a mirror map to reflect the geometry of the data and a convex objective function consisting of a loss and a regularizer possibly inducing sparsity. Our error analysis provides convergence rates in terms of properties of the strongly convex differentiable mirror map and the objective function. For a class of objective functions with Hölder continuous gradients, the convergence rates of the excess (regularized) risk under polynomially decaying step sizes have the order [Formula: see text] after [Formula: see text] iterates. Our results improve the existing error analysis for the online composite mirror descent algorithm by avoiding averaging and removing boundedness assumptions, and they sharpen the existing convergence rates of the last iterate for online gradient descent without any boundedness assumptions. Our methodology mainly depends on a novel error decomposition in terms of an excess Bregman distance, refined analysis of self-bounding properties of the objective function, and the resulting one-step progress bounds.

Pixel-based OPC optimization based on conjugate gradients.

PubMed

Ma, Xu; Arce, Gonzalo R

2011-01-31

Optical proximity correction (OPC) methods are resolution enhancement techniques (RET) used extensively in the semiconductor industry to improve the resolution and pattern fidelity of optical lithography. In pixel-based OPC (PBOPC), the mask is divided into small pixels, each of which is modified during the optimization process. Two critical issues in PBOPC are the required computational complexity of the optimization process, and the manufacturability of the optimized mask. Most current OPC optimization methods apply the steepest descent (SD) algorithm to improve image fidelity augmented by regularization penalties to reduce the complexity of the mask. Although simple to implement, the SD algorithm converges slowly. The existing regularization penalties, however, fall short in meeting the mask rule check (MRC) requirements often used in semiconductor manufacturing. This paper focuses on developing OPC optimization algorithms based on the conjugate gradient (CG) method which exhibits much faster convergence than the SD algorithm. The imaging formation process is represented by the Fourier series expansion model which approximates the partially coherent system as a sum of coherent systems. In order to obtain more desirable manufacturability properties of the mask pattern, a MRC penalty is proposed to enlarge the linear size of the sub-resolution assistant features (SRAFs), as well as the distances between the SRAFs and the main body of the mask. Finally, a projection method is developed to further reduce the complexity of the optimized mask pattern.

Separating figure from ground with a parallel network.

PubMed

Kienker, P K; Sejnowski, T J; Hinton, G E; Schumacher, L E

1986-01-01

The differentiation of figure from ground plays an important role in the perceptual organization of visual stimuli. The rapidity with which we can discriminate the inside from the outside of a figure suggests that at least this step in the process may be performed in visual cortex by a large number of neurons in several different areas working together in parallel. We have attempted to simulate this collective computation by designing a network of simple processing units that receives two types of information: bottom-up input from the image containing the outlines of a figure, which may be incomplete, and a top-down attentional input that biases one part of the image to be the inside of the figure. No presegmentation of the image was assumed. Two methods for performing the computation were explored: gradient descent, which seeks locally optimal states, and simulated annealing, which attempts to find globally optimal states by introducing noise into the computation. For complete outlines, gradient descent was faster, but the range of input parameters leading to successful performance was very narrow. In contrast, simulated annealing was more robust: it worked over a wider range of attention parameters and a wider range of outlines, including incomplete ones. Our network model is too simplified to serve as a model of human performance, but it does demonstrate that one global property of outlines can be computed through local interactions in a parallel network. Some features of the model, such as the role of noise in escaping from nonglobal optima, may generalize to more realistic models.

A pipeline leakage locating method based on the gradient descent algorithm

NASA Astrophysics Data System (ADS)

Li, Yulong; Yang, Fan; Ni, Na

2018-04-01

A pipeline leakage locating method based on the gradient descent algorithm is proposed in this paper. The method has low computing complexity, which is suitable for practical application. We have built experimental environment in real underground pipeline network. A lot of real data has been gathered in the past three months. Every leak point has been certificated by excavation. Results show that positioning error is within 0.4 meter. Rate of false alarm and missing alarm are both under 20%. The calculating time is not above 5 seconds.

Speckle-metric-optimization-based adaptive optics for laser beam projection and coherent beam combining.

PubMed

Vorontsov, Mikhail; Weyrauch, Thomas; Lachinova, Svetlana; Gatz, Micah; Carhart, Gary

2012-07-15

Maximization of a projected laser beam's power density at a remotely located extended object (speckle target) can be achieved by using an adaptive optics (AO) technique based on sensing and optimization of the target-return speckle field's statistical characteristics, referred to here as speckle metrics (SM). SM AO was demonstrated in a target-in-the-loop coherent beam combining experiment using a bistatic laser beam projection system composed of a coherent fiber-array transmitter and a power-in-the-bucket receiver. SM sensing utilized a 50 MHz rate dithering of the projected beam that provided a stair-mode approximation of the outgoing combined beam's wavefront tip and tilt with subaperture piston phases. Fiber-integrated phase shifters were used for both the dithering and SM optimization with stochastic parallel gradient descent control.

14 CFR 23.69 - Enroute climb/descent.

Code of Federal Regulations, 2013 CFR

2013-01-01

... inoperative and its propeller in the minimum drag position; (2) The remaining engine(s) at not more than... climb/descent. (a) All engines operating. The steady gradient and rate of climb must be determined at... applicant with— (1) Not more than maximum continuous power on each engine; (2) The landing gear retracted...

14 CFR 23.69 - Enroute climb/descent.

Code of Federal Regulations, 2014 CFR

2014-01-01

... inoperative and its propeller in the minimum drag position; (2) The remaining engine(s) at not more than... climb/descent. (a) All engines operating. The steady gradient and rate of climb must be determined at... applicant with— (1) Not more than maximum continuous power on each engine; (2) The landing gear retracted...

14 CFR 23.69 - Enroute climb/descent.

Code of Federal Regulations, 2012 CFR

2012-01-01

... inoperative and its propeller in the minimum drag position; (2) The remaining engine(s) at not more than... climb/descent. (a) All engines operating. The steady gradient and rate of climb must be determined at... applicant with— (1) Not more than maximum continuous power on each engine; (2) The landing gear retracted...

14 CFR 23.69 - Enroute climb/descent.

Code of Federal Regulations, 2011 CFR

2011-01-01

... inoperative and its propeller in the minimum drag position; (2) The remaining engine(s) at not more than... climb/descent. (a) All engines operating. The steady gradient and rate of climb must be determined at... applicant with— (1) Not more than maximum continuous power on each engine; (2) The landing gear retracted...

Planning fuel-conservative descents in an airline environmental using a small programmable calculator: Algorithm development and flight test results

NASA Technical Reports Server (NTRS)

Knox, C. E.; Vicroy, D. D.; Simmon, D. A.

1985-01-01

A simple, airborne, flight-management descent algorithm was developed and programmed into a small programmable calculator. The algorithm may be operated in either a time mode or speed mode. The time mode was designed to aid the pilot in planning and executing a fuel-conservative descent to arrive at a metering fix at a time designated by the air traffic control system. The speed model was designed for planning fuel-conservative descents when time is not a consideration. The descent path for both modes was calculated for a constant with considerations given for the descent Mach/airspeed schedule, gross weight, wind, wind gradient, and nonstandard temperature effects. Flight tests, using the algorithm on the programmable calculator, showed that the open-loop guidance could be useful to airline flight crews for planning and executing fuel-conservative descents.

Planning fuel-conservative descents in an airline environmental using a small programmable calculator: algorithm development and flight test results

DOE Office of Scientific and Technical Information (OSTI.GOV)

Knox, C.E.; Vicroy, D.D.; Simmon, D.A.

A simple, airborne, flight-management descent algorithm was developed and programmed into a small programmable calculator. The algorithm may be operated in either a time mode or speed mode. The time mode was designed to aid the pilot in planning and executing a fuel-conservative descent to arrive at a metering fix at a time designated by the air traffic control system. The speed model was designed for planning fuel-conservative descents when time is not a consideration. The descent path for both modes was calculated for a constant with considerations given for the descent Mach/airspeed schedule, gross weight, wind, wind gradient, andmore » nonstandard temperature effects. Flight tests, using the algorithm on the programmable calculator, showed that the open-loop guidance could be useful to airline flight crews for planning and executing fuel-conservative descents.« less

Deep kernel learning method for SAR image target recognition

NASA Astrophysics Data System (ADS)

Chen, Xiuyuan; Peng, Xiyuan; Duan, Ran; Li, Junbao

2017-10-01

With the development of deep learning, research on image target recognition has made great progress in recent years. Remote sensing detection urgently requires target recognition for military, geographic, and other scientific research. This paper aims to solve the synthetic aperture radar image target recognition problem by combining deep and kernel learning. The model, which has a multilayer multiple kernel structure, is optimized layer by layer with the parameters of Support Vector Machine and a gradient descent algorithm. This new deep kernel learning method improves accuracy and achieves competitive recognition results compared with other learning methods.

Fractional-order gradient descent learning of BP neural networks with Caputo derivative.

PubMed

Wang, Jian; Wen, Yanqing; Gou, Yida; Ye, Zhenyun; Chen, Hua

2017-05-01

Fractional calculus has been found to be a promising area of research for information processing and modeling of some physical systems. In this paper, we propose a fractional gradient descent method for the backpropagation (BP) training of neural networks. In particular, the Caputo derivative is employed to evaluate the fractional-order gradient of the error defined as the traditional quadratic energy function. The monotonicity and weak (strong) convergence of the proposed approach are proved in detail. Two simulations have been implemented to illustrate the performance of presented fractional-order BP algorithm on three small datasets and one large dataset. The numerical simulations effectively verify the theoretical observations of this paper as well. Copyright © 2017 Elsevier Ltd. All rights reserved.

GPU-based stochastic-gradient optimization for non-rigid medical image registration in time-critical applications

NASA Astrophysics Data System (ADS)

Bhosale, Parag; Staring, Marius; Al-Ars, Zaid; Berendsen, Floris F.

2018-03-01

Currently, non-rigid image registration algorithms are too computationally intensive to use in time-critical applications. Existing implementations that focus on speed typically address this by either parallelization on GPU-hardware, or by introducing methodically novel techniques into CPU-oriented algorithms. Stochastic gradient descent (SGD) optimization and variations thereof have proven to drastically reduce the computational burden for CPU-based image registration, but have not been successfully applied in GPU hardware due to its stochastic nature. This paper proposes 1) NiftyRegSGD, a SGD optimization for the GPU-based image registration tool NiftyReg, 2) random chunk sampler, a new random sampling strategy that better utilizes the memory bandwidth of GPU hardware. Experiments have been performed on 3D lung CT data of 19 patients, which compared NiftyRegSGD (with and without random chunk sampler) with CPU-based elastix Fast Adaptive SGD (FASGD) and NiftyReg. The registration runtime was 21.5s, 4.4s and 2.8s for elastix-FASGD, NiftyRegSGD without, and NiftyRegSGD with random chunk sampling, respectively, while similar accuracy was obtained. Our method is publicly available at https://github.com/SuperElastix/NiftyRegSGD.

Algorithm for Training a Recurrent Multilayer Perceptron

NASA Technical Reports Server (NTRS)

Parlos, Alexander G.; Rais, Omar T.; Menon, Sunil K.; Atiya, Amir F.

2004-01-01

An improved algorithm has been devised for training a recurrent multilayer perceptron (RMLP) for optimal performance in predicting the behavior of a complex, dynamic, and noisy system multiple time steps into the future. [An RMLP is a computational neural network with self-feedback and cross-talk (both delayed by one time step) among neurons in hidden layers]. Like other neural-network-training algorithms, this algorithm adjusts network biases and synaptic-connection weights according to a gradient-descent rule. The distinguishing feature of this algorithm is a combination of global feedback (the use of predictions as well as the current output value in computing the gradient at each time step) and recursiveness. The recursive aspect of the algorithm lies in the inclusion of the gradient of predictions at each time step with respect to the predictions at the preceding time step; this recursion enables the RMLP to learn the dynamics. It has been conjectured that carrying the recursion to even earlier time steps would enable the RMLP to represent a noisier, more complex system.

Adaptive critic designs for optimal control of uncertain nonlinear systems with unmatched interconnections.

PubMed

Yang, Xiong; He, Haibo

2018-05-26

In this paper, we develop a novel optimal control strategy for a class of uncertain nonlinear systems with unmatched interconnections. To begin with, we present a stabilizing feedback controller for the interconnected nonlinear systems by modifying an array of optimal control laws of auxiliary subsystems. We also prove that this feedback controller ensures a specified cost function to achieve optimality. Then, under the framework of adaptive critic designs, we use critic networks to solve the Hamilton-Jacobi-Bellman equations associated with auxiliary subsystem optimal control laws. The critic network weights are tuned through the gradient descent method combined with an additional stabilizing term. By using the newly established weight tuning rules, we no longer need the initial admissible control condition. In addition, we demonstrate that all signals in the closed-loop auxiliary subsystems are stable in the sense of uniform ultimate boundedness by using classic Lyapunov techniques. Finally, we provide an interconnected nonlinear plant to validate the present control scheme. Copyright © 2018 Elsevier Ltd. All rights reserved.

Stochastic Spectral Descent for Discrete Graphical Models

DOE PAGES

Carlson, David; Hsieh, Ya-Ping; Collins, Edo; ...

2015-12-14

Interest in deep probabilistic graphical models has in-creased in recent years, due to their state-of-the-art performance on many machine learning applications. Such models are typically trained with the stochastic gradient method, which can take a significant number of iterations to converge. Since the computational cost of gradient estimation is prohibitive even for modestly sized models, training becomes slow and practically usable models are kept small. In this paper we propose a new, largely tuning-free algorithm to address this problem. Our approach derives novel majorization bounds based on the Schatten- norm. Intriguingly, the minimizers of these bounds can be interpreted asmore » gradient methods in a non-Euclidean space. We thus propose using a stochastic gradient method in non-Euclidean space. We both provide simple conditions under which our algorithm is guaranteed to converge, and demonstrate empirically that our algorithm leads to dramatically faster training and improved predictive ability compared to stochastic gradient descent for both directed and undirected graphical models.« less

14 CFR 23.75 - Landing distance.

Code of Federal Regulations, 2010 CFR

2010-01-01

... to the 50 foot height and— (1) The steady approach must be at a gradient of descent not greater than... tests that a maximum steady approach gradient steeper than 5.2 percent, down to the 50-foot height, is safe. The gradient must be established as an operating limitation and the information necessary to...

A ℓ2, 1 norm regularized multi-kernel learning for false positive reduction in Lung nodule CAD.

PubMed

Cao, Peng; Liu, Xiaoli; Zhang, Jian; Li, Wei; Zhao, Dazhe; Huang, Min; Zaiane, Osmar

2017-03-01

The aim of this paper is to describe a novel algorithm for False Positive Reduction in lung nodule Computer Aided Detection(CAD). In this paper, we describes a new CT lung CAD method which aims to detect solid nodules. Specially, we proposed a multi-kernel classifier with a ℓ 2, 1 norm regularizer for heterogeneous feature fusion and selection from the feature subset level, and designed two efficient strategies to optimize the parameters of kernel weights in non-smooth ℓ 2, 1 regularized multiple kernel learning algorithm. The first optimization algorithm adapts a proximal gradient method for solving the ℓ 2, 1 norm of kernel weights, and use an accelerated method based on FISTA; the second one employs an iterative scheme based on an approximate gradient descent method. The results demonstrates that the FISTA-style accelerated proximal descent method is efficient for the ℓ 2, 1 norm formulation of multiple kernel learning with the theoretical guarantee of the convergence rate. Moreover, the experimental results demonstrate the effectiveness of the proposed methods in terms of Geometric mean (G-mean) and Area under the ROC curve (AUC), and significantly outperforms the competing methods. The proposed approach exhibits some remarkable advantages both in heterogeneous feature subsets fusion and classification phases. Compared with the fusion strategies of feature-level and decision level, the proposed ℓ 2, 1 norm multi-kernel learning algorithm is able to accurately fuse the complementary and heterogeneous feature sets, and automatically prune the irrelevant and redundant feature subsets to form a more discriminative feature set, leading a promising classification performance. Moreover, the proposed algorithm consistently outperforms the comparable classification approaches in the literature. Copyright © 2016 Elsevier Ireland Ltd. All rights reserved.

Optimized computational imaging methods for small-target sensing in lens-free holographic microscopy

NASA Astrophysics Data System (ADS)

Xiong, Zhen; Engle, Isaiah; Garan, Jacob; Melzer, Jeffrey E.; McLeod, Euan

2018-02-01

Lens-free holographic microscopy is a promising diagnostic approach because it is cost-effective, compact, and suitable for point-of-care applications, while providing high resolution together with an ultra-large field-of-view. It has been applied to biomedical sensing, where larger targets like eukaryotic cells, bacteria, or viruses can be directly imaged without labels, and smaller targets like proteins or DNA strands can be detected via scattering labels like micro- or nano-spheres. Automated image processing routines can count objects and infer target concentrations. In these sensing applications, sensitivity and specificity are critically affected by image resolution and signal-to-noise ratio (SNR). Pixel super-resolution approaches have been shown to boost resolution and SNR by synthesizing a high-resolution image from multiple, partially redundant, low-resolution images. However, there are several computational methods that can be used to synthesize the high-resolution image, and previously, it has been unclear which methods work best for the particular case of small-particle sensing. Here, we quantify the SNR achieved in small-particle sensing using regularized gradient-descent optimization method, where the regularization is based on cardinal-neighbor differences, Bayer-pattern noise reduction, or sparsity in the image. In particular, we find that gradient-descent with sparsity-based regularization works best for small-particle sensing. These computational approaches were evaluated on images acquired using a lens-free microscope that we assembled from an off-the-shelf LED array and color image sensor. Compared to other lens-free imaging systems, our hardware integration, calibration, and sample preparation are particularly simple. We believe our results will help to enable the best performance in lens-free holographic sensing.

Medical image registration by combining global and local information: a chain-type diffeomorphic demons algorithm.

PubMed

Liu, Xiaozheng; Yuan, Zhenming; Zhu, Junming; Xu, Dongrong

2013-12-07

The demons algorithm is a popular algorithm for non-rigid image registration because of its computational efficiency and simple implementation. The deformation forces of the classic demons algorithm were derived from image gradients by considering the deformation to decrease the intensity dissimilarity between images. However, the methods using the difference of image intensity for medical image registration are easily affected by image artifacts, such as image noise, non-uniform imaging and partial volume effects. The gradient magnitude image is constructed from the local information of an image, so the difference in a gradient magnitude image can be regarded as more reliable and robust for these artifacts. Then, registering medical images by considering the differences in both image intensity and gradient magnitude is a straightforward selection. In this paper, based on a diffeomorphic demons algorithm, we propose a chain-type diffeomorphic demons algorithm by combining the differences in both image intensity and gradient magnitude for medical image registration. Previous work had shown that the classic demons algorithm can be considered as an approximation of a second order gradient descent on the sum of the squared intensity differences. By optimizing the new dissimilarity criteria, we also present a set of new demons forces which were derived from the gradients of the image and gradient magnitude image. We show that, in controlled experiments, this advantage is confirmed, and yields a fast convergence.

Transmit Designs for the MIMO Broadcast Channel With Statistical CSI

NASA Astrophysics Data System (ADS)

Wu, Yongpeng; Jin, Shi; Gao, Xiqi; McKay, Matthew R.; Xiao, Chengshan

2014-09-01

We investigate the multiple-input multiple-output broadcast channel with statistical channel state information available at the transmitter. The so-called linear assignment operation is employed, and necessary conditions are derived for the optimal transmit design under general fading conditions. Based on this, we introduce an iterative algorithm to maximize the linear assignment weighted sum-rate by applying a gradient descent method. To reduce complexity, we derive an upper bound of the linear assignment achievable rate of each receiver, from which a simplified closed-form expression for a near-optimal linear assignment matrix is derived. This reveals an interesting construction analogous to that of dirty-paper coding. In light of this, a low complexity transmission scheme is provided. Numerical examples illustrate the significant performance of the proposed low complexity scheme.

Regularized Dual Averaging Image Reconstruction for Full-Wave Ultrasound Computed Tomography.

PubMed

Matthews, Thomas P; Wang, Kun; Li, Cuiping; Duric, Neb; Anastasio, Mark A

2017-05-01

Ultrasound computed tomography (USCT) holds great promise for breast cancer screening. Waveform inversion-based image reconstruction methods account for higher order diffraction effects and can produce high-resolution USCT images, but are computationally demanding. Recently, a source encoding technique has been combined with stochastic gradient descent (SGD) to greatly reduce image reconstruction times. However, this method bundles the stochastic data fidelity term with the deterministic regularization term. This limitation can be overcome by replacing SGD with a structured optimization method, such as the regularized dual averaging method, that exploits knowledge of the composition of the cost function. In this paper, the dual averaging method is combined with source encoding techniques to improve the effectiveness of regularization while maintaining the reduced reconstruction times afforded by source encoding. It is demonstrated that each iteration can be decomposed into a gradient descent step based on the data fidelity term and a proximal update step corresponding to the regularization term. Furthermore, the regularization term is never explicitly differentiated, allowing nonsmooth regularization penalties to be naturally incorporated. The wave equation is solved by the use of a time-domain method. The effectiveness of this approach is demonstrated through computer simulation and experimental studies. The results suggest that the dual averaging method can produce images with less noise and comparable resolution to those obtained by the use of SGD.

Human-in-the-loop Bayesian optimization of wearable device parameters

PubMed Central

Malcolm, Philippe; Speeckaert, Jozefien; Siviy, Christoper J.; Walsh, Conor J.; Kuindersma, Scott

2017-01-01

The increasing capabilities of exoskeletons and powered prosthetics for walking assistance have paved the way for more sophisticated and individualized control strategies. In response to this opportunity, recent work on human-in-the-loop optimization has considered the problem of automatically tuning control parameters based on realtime physiological measurements. However, the common use of metabolic cost as a performance metric creates significant experimental challenges due to its long measurement times and low signal-to-noise ratio. We evaluate the use of Bayesian optimization—a family of sample-efficient, noise-tolerant, and global optimization methods—for quickly identifying near-optimal control parameters. To manage experimental complexity and provide comparisons against related work, we consider the task of minimizing metabolic cost by optimizing walking step frequencies in unaided human subjects. Compared to an existing approach based on gradient descent, Bayesian optimization identified a near-optimal step frequency with a faster time to convergence (12 minutes, p < 0.01), smaller inter-subject variability in convergence time (± 2 minutes, p < 0.01), and lower overall energy expenditure (p < 0.01). PMID:28926613

Output Feedback Stabilization for a Class of Multi-Variable Bilinear Stochastic Systems with Stochastic Coupling Attenuation

DOE Office of Scientific and Technical Information (OSTI.GOV)

Zhang, Qichun; Zhou, Jinglin; Wang, Hong

In this paper, stochastic coupling attenuation is investigated for a class of multi-variable bilinear stochastic systems and a novel output feedback m-block backstepping controller with linear estimator is designed, where gradient descent optimization is used to tune the design parameters of the controller. It has been shown that the trajectories of the closed-loop stochastic systems are bounded in probability sense and the stochastic coupling of the system outputs can be effectively attenuated by the proposed control algorithm. Moreover, the stability of the stochastic systems is analyzed and the effectiveness of the proposed method has been demonstrated using a simulated example.

Topology optimization of hyperelastic structures using a level set method

NASA Astrophysics Data System (ADS)

Chen, Feifei; Wang, Yiqiang; Wang, Michael Yu; Zhang, Y. F.

2017-12-01

Soft rubberlike materials, due to their inherent compliance, are finding widespread implementation in a variety of applications ranging from assistive wearable technologies to soft material robots. Structural design of such soft and rubbery materials necessitates the consideration of large nonlinear deformations and hyperelastic material models to accurately predict their mechanical behaviour. In this paper, we present an effective level set-based topology optimization method for the design of hyperelastic structures that undergo large deformations. The method incorporates both geometric and material nonlinearities where the strain and stress measures are defined within the total Lagrange framework and the hyperelasticity is characterized by the widely-adopted Mooney-Rivlin material model. A shape sensitivity analysis is carried out, in the strict sense of the material derivative, where the high-order terms involving the displacement gradient are retained to ensure the descent direction. As the design velocity enters into the shape derivative in terms of its gradient and divergence terms, we develop a discrete velocity selection strategy. The whole optimization implementation undergoes a two-step process, where the linear optimization is first performed and its optimized solution serves as the initial design for the subsequent nonlinear optimization. It turns out that this operation could efficiently alleviate the numerical instability and facilitate the optimization process. To demonstrate the validity and effectiveness of the proposed method, three compliance minimization problems are studied and their optimized solutions present significant mechanical benefits of incorporating the nonlinearities, in terms of remarkable enhancement in not only the structural stiffness but also the critical buckling load.

Method of Real-Time Principal-Component Analysis

NASA Technical Reports Server (NTRS)

Duong, Tuan; Duong, Vu

2005-01-01

Dominant-element-based gradient descent and dynamic initial learning rate (DOGEDYN) is a method of sequential principal-component analysis (PCA) that is well suited for such applications as data compression and extraction of features from sets of data. In comparison with a prior method of gradient-descent-based sequential PCA, this method offers a greater rate of learning convergence. Like the prior method, DOGEDYN can be implemented in software. However, the main advantage of DOGEDYN over the prior method lies in the facts that it requires less computation and can be implemented in simpler hardware. It should be possible to implement DOGEDYN in compact, low-power, very-large-scale integrated (VLSI) circuitry that could process data in real time.

Minimum-fuel turning climbout and descent guidance of transport jets

NASA Technical Reports Server (NTRS)

Neuman, F.; Kreindler, E.

1983-01-01

The complete flightpath optimization problem for minimum fuel consumption from takeoff to landing including the initial and final turns from and to the runway heading is solved. However, only the initial and final segments which contain the turns are treated, since the straight-line climbout, cruise, and descent problems have already been solved. The paths are derived by generating fields of extremals, using the necessary conditions of optimal control together with singular arcs and state constraints. Results show that the speed profiles for straight flight and turning flight are essentially identical except for the final horizontal accelerating or decelerating turns. The optimal turns require no abrupt maneuvers, and an approximation of the optimal turns could be easily integrated with present straight-line climb-cruise-descent fuel-optimization algorithms. Climbout at the optimal IAS rather than the 250-knot terminal-area speed limit would save 36 lb of fuel for the 727-100 aircraft.

Sparse Representation with Spatio-Temporal Online Dictionary Learning for Efficient Video Coding.

PubMed

Dai, Wenrui; Shen, Yangmei; Tang, Xin; Zou, Junni; Xiong, Hongkai; Chen, Chang Wen

2016-07-27

Classical dictionary learning methods for video coding suer from high computational complexity and interfered coding eciency by disregarding its underlying distribution. This paper proposes a spatio-temporal online dictionary learning (STOL) algorithm to speed up the convergence rate of dictionary learning with a guarantee of approximation error. The proposed algorithm incorporates stochastic gradient descents to form a dictionary of pairs of 3-D low-frequency and highfrequency spatio-temporal volumes. In each iteration of the learning process, it randomly selects one sample volume and updates the atoms of dictionary by minimizing the expected cost, rather than optimizes empirical cost over the complete training data like batch learning methods, e.g. K-SVD. Since the selected volumes are supposed to be i.i.d. samples from the underlying distribution, decomposition coecients attained from the trained dictionary are desirable for sparse representation. Theoretically, it is proved that the proposed STOL could achieve better approximation for sparse representation than K-SVD and maintain both structured sparsity and hierarchical sparsity. It is shown to outperform batch gradient descent methods (K-SVD) in the sense of convergence speed and computational complexity, and its upper bound for prediction error is asymptotically equal to the training error. With lower computational complexity, extensive experiments validate that the STOL based coding scheme achieves performance improvements than H.264/AVC or HEVC as well as existing super-resolution based methods in ratedistortion performance and visual quality.

Selecting registration schemes in case of interstitial lung disease follow-up in CT

DOE Office of Scientific and Technical Information (OSTI.GOV)

Vlachopoulos, Georgios; Korfiatis, Panayiotis; Skiadopoulos, Spyros

Purpose: Primary goal of this study is to select optimal registration schemes in the framework of interstitial lung disease (ILD) follow-up analysis in CT. Methods: A set of 128 multiresolution schemes composed of multiresolution nonrigid and combinations of rigid and nonrigid registration schemes are evaluated, utilizing ten artificially warped ILD follow-up volumes, originating from ten clinical volumetric CT scans of ILD affected patients, to select candidate optimal schemes. Specifically, all combinations of four transformation models (three rigid: rigid, similarity, affine and one nonrigid: third order B-spline), four cost functions (sum-of-square distances, normalized correlation coefficient, mutual information, and normalized mutual information),more » four gradient descent optimizers (standard, regular step, adaptive stochastic, and finite difference), and two types of pyramids (recursive and Gaussian-smoothing) were considered. The selection process involves two stages. The first stage involves identification of schemes with deformation field singularities, according to the determinant of the Jacobian matrix. In the second stage, evaluation methodology is based on distance between corresponding landmark points in both normal lung parenchyma (NLP) and ILD affected regions. Statistical analysis was performed in order to select near optimal registration schemes per evaluation metric. Performance of the candidate registration schemes was verified on a case sample of ten clinical follow-up CT scans to obtain the selected registration schemes. Results: By considering near optimal schemes common to all ranking lists, 16 out of 128 registration schemes were initially selected. These schemes obtained submillimeter registration accuracies in terms of average distance errors 0.18 ± 0.01 mm for NLP and 0.20 ± 0.01 mm for ILD, in case of artificially generated follow-up data. Registration accuracy in terms of average distance error in clinical follow-up data was in the range of 1.985–2.156 mm and 1.966–2.234 mm, for NLP and ILD affected regions, respectively, excluding schemes with statistically significant lower performance (Wilcoxon signed-ranks test, p < 0.05), resulting in 13 finally selected registration schemes. Conclusions: Selected registration schemes in case of ILD CT follow-up analysis indicate the significance of adaptive stochastic gradient descent optimizer, as well as the importance of combined rigid and nonrigid schemes providing high accuracy and time efficiency. The selected optimal deformable registration schemes are equivalent in terms of their accuracy and thus compatible in terms of their clinical outcome.« less

Reconstructing the Surface Permittivity Distribution from Data Measured by the CONSERT Instrument aboard Rosetta: Method and Simulations

NASA Astrophysics Data System (ADS)

Plettemeier, D.; Statz, C.; Hegler, S.; Herique, A.; Kofman, W. W.

2014-12-01

One of the main scientific objectives of the Comet Nucleus Sounding Experiment by Radiowave Transmission (CONSERT) aboard Rosetta is to perform a dielectric characterization of comet 67P/Chuyurmov-Gerasimenko's nucleus by means of a bi-static sounding between the lander Philae launched onto the comet's surface and the orbiter Rosetta. For the sounding, the lander part of CONSERT will receive and process the radio signal emitted by the orbiter part of the instrument and transmit a signal to the orbiter to be received by CONSERT. CONSERT will also be operated as bi-static RADAR during the descent of the lander Philae onto the comet's surface. From data measured during the descent, we aim at reconstructing a surface permittivity map of the comet at the landing site and along the path below the descent trajectory. This surface permittivity map will give information on the bulk material right below and around the landing site and the surface roughness in areas covered by the instrument along the descent. The proposed method to estimate the surface permittivity distribution is based on a least-squares based inversion approach in frequency domain. The direct problem of simulating the wave-propagation between lander and orbiter at line-of-sight and the signal reflected on the comet's surface is modelled using a dielectric physical optics approximation. Restrictions on the measurement positions by the descent orbitography and limitations on the instrument dynamic range will be dealt with by application of a regularization technique where the surface permittivity distribution and the gradient with regard to the permittivity is projected in a domain defined by a viable model of the spatial material and roughness distribution. The least-squares optimization step of the reconstruction is performed in such domain on a reduced set of parameters yielding stable results. The viability of the proposed method is demonstrated by reconstruction results based on simulated data.

Region Segmentation in the Frequency Domain Applied to Upper Airway Real-Time Magnetic Resonance Images

PubMed Central

Narayanan, Shrikanth

2009-01-01

We describe a method for unsupervised region segmentation of an image using its spatial frequency domain representation. The algorithm was designed to process large sequences of real-time magnetic resonance (MR) images containing the 2-D midsagittal view of a human vocal tract airway. The segmentation algorithm uses an anatomically informed object model, whose fit to the observed image data is hierarchically optimized using a gradient descent procedure. The goal of the algorithm is to automatically extract the time-varying vocal tract outline and the position of the articulators to facilitate the study of the shaping of the vocal tract during speech production. PMID:19244005

Simultaneous digital super-resolution and nonuniformity correction for infrared imaging systems.

PubMed

Meza, Pablo; Machuca, Guillermo; Torres, Sergio; Martin, Cesar San; Vera, Esteban

2015-07-20

In this article, we present a novel algorithm to achieve simultaneous digital super-resolution and nonuniformity correction from a sequence of infrared images. We propose to use spatial regularization terms that exploit nonlocal means and the absence of spatial correlation between the scene and the nonuniformity noise sources. We derive an iterative optimization algorithm based on a gradient descent minimization strategy. Results from infrared image sequences corrupted with simulated and real fixed-pattern noise show a competitive performance compared with state-of-the-art methods. A qualitative analysis on the experimental results obtained with images from a variety of infrared cameras indicates that the proposed method provides super-resolution images with significantly less fixed-pattern noise.

CP decomposition approach to blind separation for DS-CDMA system using a new performance index

NASA Astrophysics Data System (ADS)

Rouijel, Awatif; Minaoui, Khalid; Comon, Pierre; Aboutajdine, Driss

2014-12-01

In this paper, we present a canonical polyadic (CP) tensor decomposition isolating the scaling matrix. This has two major implications: (i) the problem conditioning shows up explicitly and could be controlled through a constraint on the so-called coherences and (ii) a performance criterion concerning the factor matrices can be exactly calculated and is more realistic than performance metrics used in the literature. Two new algorithms optimizing the CP decomposition based on gradient descent are proposed. This decomposition is illustrated by an application to direct-sequence code division multiplexing access (DS-CDMA) systems; computer simulations are provided and demonstrate the good behavior of these algorithms, compared to others in the literature.

Nonconvex Sparse Logistic Regression With Weakly Convex Regularization

NASA Astrophysics Data System (ADS)

Shen, Xinyue; Gu, Yuantao

2018-06-01

In this work we propose to fit a sparse logistic regression model by a weakly convex regularized nonconvex optimization problem. The idea is based on the finding that a weakly convex function as an approximation of the $\\ell_0$ pseudo norm is able to better induce sparsity than the commonly used $\\ell_1$ norm. For a class of weakly convex sparsity inducing functions, we prove the nonconvexity of the corresponding sparse logistic regression problem, and study its local optimality conditions and the choice of the regularization parameter to exclude trivial solutions. Despite the nonconvexity, a method based on proximal gradient descent is used to solve the general weakly convex sparse logistic regression, and its convergence behavior is studied theoretically. Then the general framework is applied to a specific weakly convex function, and a necessary and sufficient local optimality condition is provided. The solution method is instantiated in this case as an iterative firm-shrinkage algorithm, and its effectiveness is demonstrated in numerical experiments by both randomly generated and real datasets.

Peak-Seeking Control For Reduced Fuel Consumption: Flight-Test Results For The Full-Scale Advanced Systems Testbed FA-18 Airplane

NASA Technical Reports Server (NTRS)

Brown, Nelson

2013-01-01

A peak-seeking control algorithm for real-time trim optimization for reduced fuel consumption has been developed by researchers at the National Aeronautics and Space Administration (NASA) Dryden Flight Research Center to address the goals of the NASA Environmentally Responsible Aviation project to reduce fuel burn and emissions. The peak-seeking control algorithm is based on a steepest-descent algorithm using a time-varying Kalman filter to estimate the gradient of a performance function of fuel flow versus control surface positions. In real-time operation, deflections of symmetric ailerons, trailing-edge flaps, and leading-edge flaps of an F/A-18 airplane are used for optimization of fuel flow. Results from six research flights are presented herein. The optimization algorithm found a trim configuration that required approximately 3 percent less fuel flow than the baseline trim at the same flight condition. This presentation also focuses on the design of the flight experiment and the practical challenges of conducting the experiment.

Small-Tip-Angle Spokes Pulse Design Using Interleaved Greedy and Local Optimization Methods

PubMed Central

Grissom, William A.; Khalighi, Mohammad-Mehdi; Sacolick, Laura I.; Rutt, Brian K.; Vogel, Mika W.

2013-01-01

Current spokes pulse design methods can be grouped into methods based either on sparse approximation or on iterative local (gradient descent-based) optimization of the transverse-plane spatial frequency locations visited by the spokes. These two classes of methods have complementary strengths and weaknesses: sparse approximation-based methods perform an efficient search over a large swath of candidate spatial frequency locations but most are incompatible with off-resonance compensation, multifrequency designs, and target phase relaxation, while local methods can accommodate off-resonance and target phase relaxation but are sensitive to initialization and suboptimal local cost function minima. This article introduces a method that interleaves local iterations, which optimize the radiofrequency pulses, target phase patterns, and spatial frequency locations, with a greedy method to choose new locations. Simulations and experiments at 3 and 7 T show that the method consistently produces single- and multifrequency spokes pulses with lower flip angle inhomogeneity compared to current methods. PMID:22392822

Variational stereo imaging of oceanic waves with statistical constraints.

PubMed

Gallego, Guillermo; Yezzi, Anthony; Fedele, Francesco; Benetazzo, Alvise

2013-11-01

An image processing observational technique for the stereoscopic reconstruction of the waveform of oceanic sea states is developed. The technique incorporates the enforcement of any given statistical wave law modeling the quasi-Gaussianity of oceanic waves observed in nature. The problem is posed in a variational optimization framework, where the desired waveform is obtained as the minimizer of a cost functional that combines image observations, smoothness priors and a weak statistical constraint. The minimizer is obtained by combining gradient descent and multigrid methods on the necessary optimality equations of the cost functional. Robust photometric error criteria and a spatial intensity compensation model are also developed to improve the performance of the presented image matching strategy. The weak statistical constraint is thoroughly evaluated in combination with other elements presented to reconstruct and enforce constraints on experimental stereo data, demonstrating the improvement in the estimation of the observed ocean surface.

Asynchronous Incremental Stochastic Dual Descent Algorithm for Network Resource Allocation

NASA Astrophysics Data System (ADS)

Bedi, Amrit Singh; Rajawat, Ketan

2018-05-01

Stochastic network optimization problems entail finding resource allocation policies that are optimum on an average but must be designed in an online fashion. Such problems are ubiquitous in communication networks, where resources such as energy and bandwidth are divided among nodes to satisfy certain long-term objectives. This paper proposes an asynchronous incremental dual decent resource allocation algorithm that utilizes delayed stochastic {gradients} for carrying out its updates. The proposed algorithm is well-suited to heterogeneous networks as it allows the computationally-challenged or energy-starved nodes to, at times, postpone the updates. The asymptotic analysis of the proposed algorithm is carried out, establishing dual convergence under both, constant and diminishing step sizes. It is also shown that with constant step size, the proposed resource allocation policy is asymptotically near-optimal. An application involving multi-cell coordinated beamforming is detailed, demonstrating the usefulness of the proposed algorithm.

Learning and optimization with cascaded VLSI neural network building-block chips

NASA Technical Reports Server (NTRS)

Duong, T.; Eberhardt, S. P.; Tran, M.; Daud, T.; Thakoor, A. P.

1992-01-01

To demonstrate the versatility of the building-block approach, two neural network applications were implemented on cascaded analog VLSI chips. Weights were implemented using 7-b multiplying digital-to-analog converter (MDAC) synapse circuits, with 31 x 32 and 32 x 32 synapses per chip. A novel learning algorithm compatible with analog VLSI was applied to the two-input parity problem. The algorithm combines dynamically evolving architecture with limited gradient-descent backpropagation for efficient and versatile supervised learning. To implement the learning algorithm in hardware, synapse circuits were paralleled for additional quantization levels. The hardware-in-the-loop learning system allocated 2-5 hidden neurons for parity problems. Also, a 7 x 7 assignment problem was mapped onto a cascaded 64-neuron fully connected feedback network. In 100 randomly selected problems, the network found optimal or good solutions in most cases, with settling times in the range of 7-100 microseconds.

Computational trigonometry

DOE Office of Scientific and Technical Information (OSTI.GOV)

Gustafson, K.

1994-12-31

By means of the author`s earlier theory of antieigenvalues and antieigenvectors, a new computational approach to iterative methods is presented. This enables an explicit trigonometric understanding of iterative convergence and provides new insights into the sharpness of error bounds. Direct applications to Gradient descent, Conjugate gradient, GCR(k), Orthomin, CGN, GMRES, CGS, and other matrix iterative schemes will be given.

On the boundary conditions on a shock wave for hypersonic flow around a descent vehicle

NASA Astrophysics Data System (ADS)

Golomazov, M. M.; Ivankov, A. A.

2013-12-01

Stationary hypersonic flow around a descent vehicle is examined by considering equilibrium and nonequilibrium reactions. We study how physical-chemical processes and shock wave conditions for gas species influence the shock-layer structure. It is shown that conservation conditions of species on the shock wave cause high-temperature and concentration gradients in the shock layer when we calculate spacecraft deceleration trajectory in the atmosphere at 75 km altitude.

Peak-Seeking Optimization of Trim for Reduced Fuel Consumption: Flight-Test Results

NASA Technical Reports Server (NTRS)

Brown, Nelson Andrew; Schaefer, Jacob Robert

2013-01-01

A peak-seeking control algorithm for real-time trim optimization for reduced fuel consumption has been developed by researchers at the National Aeronautics and Space Administration (NASA) Dryden Flight Research Center to address the goals of the NASA Environmentally Responsible Aviation project to reduce fuel burn and emissions. The peak-seeking control algorithm is based on a steepest-descent algorithm using a time-varying Kalman filter to estimate the gradient of a performance function of fuel flow versus control surface positions. In real-time operation, deflections of symmetric ailerons, trailing-edge flaps, and leading-edge flaps of an F/A-18 airplane (McDonnell Douglas, now The Boeing Company, Chicago, Illinois) are used for optimization of fuel flow. Results from six research flights are presented herein. The optimization algorithm found a trim configuration that required approximately 3 percent less fuel flow than the baseline trim at the same flight condition. The algorithm consistently rediscovered the solution from several initial conditions. These results show that the algorithm has good performance in a relevant environment.

Peak-Seeking Optimization of Trim for Reduced Fuel Consumption: Flight-test Results

NASA Technical Reports Server (NTRS)

Brown, Nelson Andrew; Schaefer, Jacob Robert

2013-01-01

A peak-seeking control algorithm for real-time trim optimization for reduced fuel consumption has been developed by researchers at the National Aeronautics and Space Administration (NASA) Dryden Flight Research Center to address the goals of the NASA Environmentally Responsible Aviation project to reduce fuel burn and emissions. The peak-seeking control algorithm is based on a steepest-descent algorithm using a time-varying Kalman filter to estimate the gradient of a performance function of fuel flow versus control surface positions. In real-time operation, deflections of symmetric ailerons, trailing-edge flaps, and leading-edge flaps of an F/A-18 airplane (McDonnell Douglas, now The Boeing Company, Chicago, Illinois) are used for optimization of fuel flow. Results from six research flights are presented herein. The optimization algorithm found a trim configuration that required approximately 3 percent less fuel flow than the baseline trim at the same flight condition. The algorithm consistently rediscovered the solution from several initial conditions. These results show that the algorithm has good performance in a relevant environment.

Optimization of rotational arc station parameter optimized radiation therapy.

PubMed

Dong, P; Ungun, B; Boyd, S; Xing, L

2016-09-01

To develop a fast optimization method for station parameter optimized radiation therapy (SPORT) and show that SPORT is capable of matching VMAT in both plan quality and delivery efficiency by using three clinical cases of different disease sites. The angular space from 0° to 360° was divided into 180 station points (SPs). A candidate aperture was assigned to each of the SPs based on the calculation results using a column generation algorithm. The weights of the apertures were then obtained by optimizing the objective function using a state-of-the-art GPU based proximal operator graph solver. To avoid being trapped in a local minimum in beamlet-based aperture selection using the gradient descent algorithm, a stochastic gradient descent was employed here. Apertures with zero or low weight were thrown out. To find out whether there was room to further improve the plan by adding more apertures or SPs, the authors repeated the above procedure with consideration of the existing dose distribution from the last iteration. At the end of the second iteration, the weights of all the apertures were reoptimized, including those of the first iteration. The above procedure was repeated until the plan could not be improved any further. The optimization technique was assessed by using three clinical cases (prostate, head and neck, and brain) with the results compared to that obtained using conventional VMAT in terms of dosimetric properties, treatment time, and total MU. Marked dosimetric quality improvement was demonstrated in the SPORT plans for all three studied cases. For the prostate case, the volume of the 50% prescription dose was decreased by 22% for the rectum and 6% for the bladder. For the head and neck case, SPORT improved the mean dose for the left and right parotids by 15% each. The maximum dose was lowered from 72.7 to 71.7 Gy for the mandible, and from 30.7 to 27.3 Gy for the spinal cord. The mean dose for the pharynx and larynx was reduced by 8% and 6%, respectively. For the brain case, the doses to the eyes, chiasm, and inner ears were all improved. SPORT shortened the treatment time by ∼1 min for the prostate case, ∼0.5 min for brain case, and ∼0.2 min for the head and neck case. The dosimetric quality and delivery efficiency presented here indicate that SPORT is an intriguing alternative treatment modality. With the widespread adoption of digital linac, SPORT should lead to improved patient care in the future.

Optimization of rotational arc station parameter optimized radiation therapy

PubMed Central

Dong, P.; Ungun, B.; Boyd, S.; Xing, L.

2016-01-01

Purpose: To develop a fast optimization method for station parameter optimized radiation therapy (SPORT) and show that SPORT is capable of matching VMAT in both plan quality and delivery efficiency by using three clinical cases of different disease sites. Methods: The angular space from 0° to 360° was divided into 180 station points (SPs). A candidate aperture was assigned to each of the SPs based on the calculation results using a column generation algorithm. The weights of the apertures were then obtained by optimizing the objective function using a state-of-the-art GPU based proximal operator graph solver. To avoid being trapped in a local minimum in beamlet-based aperture selection using the gradient descent algorithm, a stochastic gradient descent was employed here. Apertures with zero or low weight were thrown out. To find out whether there was room to further improve the plan by adding more apertures or SPs, the authors repeated the above procedure with consideration of the existing dose distribution from the last iteration. At the end of the second iteration, the weights of all the apertures were reoptimized, including those of the first iteration. The above procedure was repeated until the plan could not be improved any further. The optimization technique was assessed by using three clinical cases (prostate, head and neck, and brain) with the results compared to that obtained using conventional VMAT in terms of dosimetric properties, treatment time, and total MU. Results: Marked dosimetric quality improvement was demonstrated in the SPORT plans for all three studied cases. For the prostate case, the volume of the 50% prescription dose was decreased by 22% for the rectum and 6% for the bladder. For the head and neck case, SPORT improved the mean dose for the left and right parotids by 15% each. The maximum dose was lowered from 72.7 to 71.7 Gy for the mandible, and from 30.7 to 27.3 Gy for the spinal cord. The mean dose for the pharynx and larynx was reduced by 8% and 6%, respectively. For the brain case, the doses to the eyes, chiasm, and inner ears were all improved. SPORT shortened the treatment time by ∼1 min for the prostate case, ∼0.5 min for brain case, and ∼0.2 min for the head and neck case. Conclusions: The dosimetric quality and delivery efficiency presented here indicate that SPORT is an intriguing alternative treatment modality. With the widespread adoption of digital linac, SPORT should lead to improved patient care in the future. PMID:27587028

Optimization of rotational arc station parameter optimized radiation therapy

DOE Office of Scientific and Technical Information (OSTI.GOV)

Dong, P.; Ungun, B.

Purpose: To develop a fast optimization method for station parameter optimized radiation therapy (SPORT) and show that SPORT is capable of matching VMAT in both plan quality and delivery efficiency by using three clinical cases of different disease sites. Methods: The angular space from 0° to 360° was divided into 180 station points (SPs). A candidate aperture was assigned to each of the SPs based on the calculation results using a column generation algorithm. The weights of the apertures were then obtained by optimizing the objective function using a state-of-the-art GPU based proximal operator graph solver. To avoid being trappedmore » in a local minimum in beamlet-based aperture selection using the gradient descent algorithm, a stochastic gradient descent was employed here. Apertures with zero or low weight were thrown out. To find out whether there was room to further improve the plan by adding more apertures or SPs, the authors repeated the above procedure with consideration of the existing dose distribution from the last iteration. At the end of the second iteration, the weights of all the apertures were reoptimized, including those of the first iteration. The above procedure was repeated until the plan could not be improved any further. The optimization technique was assessed by using three clinical cases (prostate, head and neck, and brain) with the results compared to that obtained using conventional VMAT in terms of dosimetric properties, treatment time, and total MU. Results: Marked dosimetric quality improvement was demonstrated in the SPORT plans for all three studied cases. For the prostate case, the volume of the 50% prescription dose was decreased by 22% for the rectum and 6% for the bladder. For the head and neck case, SPORT improved the mean dose for the left and right parotids by 15% each. The maximum dose was lowered from 72.7 to 71.7 Gy for the mandible, and from 30.7 to 27.3 Gy for the spinal cord. The mean dose for the pharynx and larynx was reduced by 8% and 6%, respectively. For the brain case, the doses to the eyes, chiasm, and inner ears were all improved. SPORT shortened the treatment time by ∼1 min for the prostate case, ∼0.5 min for brain case, and ∼0.2 min for the head and neck case. Conclusions: The dosimetric quality and delivery efficiency presented here indicate that SPORT is an intriguing alternative treatment modality. With the widespread adoption of digital linac, SPORT should lead to improved patient care in the future.« less

A new modified conjugate gradient coefficient for solving system of linear equations

NASA Astrophysics Data System (ADS)

Hajar, N.; ‘Aini, N.; Shapiee, N.; Abidin, Z. Z.; Khadijah, W.; Rivaie, M.; Mamat, M.

2017-09-01

Conjugate gradient (CG) method is an evolution of computational method in solving unconstrained optimization problems. This approach is easy to implement due to its simplicity and has been proven to be effective in solving real-life application. Although this field has received copious amount of attentions in recent years, some of the new approaches of CG algorithm cannot surpass the efficiency of the previous versions. Therefore, in this paper, a new CG coefficient which retains the sufficient descent and global convergence properties of the original CG methods is proposed. This new CG is tested on a set of test functions under exact line search. Its performance is then compared to that of some of the well-known previous CG methods based on number of iterations and CPU time. The results show that the new CG algorithm has the best efficiency amongst all the methods tested. This paper also includes an application of the new CG algorithm for solving large system of linear equations

An Adaptive Orientation Estimation Method for Magnetic and Inertial Sensors in the Presence of Magnetic Disturbances

PubMed Central

Fan, Bingfei; Li, Qingguo; Wang, Chao; Liu, Tao

2017-01-01

Magnetic and inertial sensors have been widely used to estimate the orientation of human segments due to their low cost, compact size and light weight. However, the accuracy of the estimated orientation is easily affected by external factors, especially when the sensor is used in an environment with magnetic disturbances. In this paper, we propose an adaptive method to improve the accuracy of orientation estimations in the presence of magnetic disturbances. The method is based on existing gradient descent algorithms, and it is performed prior to sensor fusion algorithms. The proposed method includes stationary state detection and magnetic disturbance severity determination. The stationary state detection makes this method immune to magnetic disturbances in stationary state, while the magnetic disturbance severity determination helps to determine the credibility of magnetometer data under dynamic conditions, so as to mitigate the negative effect of the magnetic disturbances. The proposed method was validated through experiments performed on a customized three-axis instrumented gimbal with known orientations. The error of the proposed method and the original gradient descent algorithms were calculated and compared. Experimental results demonstrate that in stationary state, the proposed method is completely immune to magnetic disturbances, and in dynamic conditions, the error caused by magnetic disturbance is reduced by 51.2% compared with original MIMU gradient descent algorithm. PMID:28534858

14 CFR 23.75 - Landing distance.

Code of Federal Regulations, 2012 CFR

2012-01-01

... to the 50 foot height and— (1) The steady approach must be at a gradient of descent not greater than 5.2 percent (3 degrees) down to the 50-foot height. (2) In addition, an applicant may demonstrate by tests that a maximum steady approach gradient steeper than 5.2 percent, down to the 50-foot height, is...

14 CFR 23.75 - Landing distance.

Code of Federal Regulations, 2014 CFR

2014-01-01

... to the 50 foot height and— (1) The steady approach must be at a gradient of descent not greater than 5.2 percent (3 degrees) down to the 50-foot height. (2) In addition, an applicant may demonstrate by tests that a maximum steady approach gradient steeper than 5.2 percent, down to the 50-foot height, is...

14 CFR 23.75 - Landing distance.

Code of Federal Regulations, 2013 CFR

2013-01-01

... to the 50 foot height and— (1) The steady approach must be at a gradient of descent not greater than 5.2 percent (3 degrees) down to the 50-foot height. (2) In addition, an applicant may demonstrate by tests that a maximum steady approach gradient steeper than 5.2 percent, down to the 50-foot height, is...

Coordinated Beamforming for MISO Interference Channel: Complexity Analysis and Efficient Algorithms

DTIC Science & Technology

2010-01-01

Algorithm The cyclic coordinate descent algorithm is also known as the nonlinear Gauss - Seidel iteration [32]. There are several studies of this type of...vkρ(vi−1). It can be shown that the above BB gradient projection direction is always a descent direction. The R-linear convergence of the BB method has...KKT solution ) of the inexact pricing algorithm for MISO interference channel. The latter is interesting since the convergence of the original pricing

Error analysis of stochastic gradient descent ranking.

PubMed

Chen, Hong; Tang, Yi; Li, Luoqing; Yuan, Yuan; Li, Xuelong; Tang, Yuanyan

2013-06-01

Ranking is always an important task in machine learning and information retrieval, e.g., collaborative filtering, recommender systems, drug discovery, etc. A kernel-based stochastic gradient descent algorithm with the least squares loss is proposed for ranking in this paper. The implementation of this algorithm is simple, and an expression of the solution is derived via a sampling operator and an integral operator. An explicit convergence rate for leaning a ranking function is given in terms of the suitable choices of the step size and the regularization parameter. The analysis technique used here is capacity independent and is novel in error analysis of ranking learning. Experimental results on real-world data have shown the effectiveness of the proposed algorithm in ranking tasks, which verifies the theoretical analysis in ranking error.

Vectorial mask optimization methods for robust optical lithography

NASA Astrophysics Data System (ADS)

Ma, Xu; Li, Yanqiu; Guo, Xuejia; Dong, Lisong; Arce, Gonzalo R.

2012-10-01

Continuous shrinkage of critical dimension in an integrated circuit impels the development of resolution enhancement techniques for low k1 lithography. Recently, several pixelated optical proximity correction (OPC) and phase-shifting mask (PSM) approaches were developed under scalar imaging models to account for the process variations. However, the lithography systems with larger-NA (NA>0.6) are predominant for current technology nodes, rendering the scalar models inadequate to describe the vector nature of the electromagnetic field that propagates through the optical lithography system. In addition, OPC and PSM algorithms based on scalar models can compensate for wavefront aberrations, but are incapable of mitigating polarization aberrations in practical lithography systems, which can only be dealt with under the vector model. To this end, we focus on developing robust pixelated gradient-based OPC and PSM optimization algorithms aimed at canceling defocus, dose variation, wavefront and polarization aberrations under a vector model. First, an integrative and analytic vector imaging model is applied to formulate the optimization problem, where the effects of process variations are explicitly incorporated in the optimization framework. A steepest descent algorithm is then used to iteratively optimize the mask patterns. Simulations show that the proposed algorithms can effectively improve the process windows of the optical lithography systems.

WS-BP: An efficient wolf search based back-propagation algorithm

NASA Astrophysics Data System (ADS)

Nawi, Nazri Mohd; Rehman, M. Z.; Khan, Abdullah

2015-05-01

Wolf Search (WS) is a heuristic based optimization algorithm. Inspired by the preying and survival capabilities of the wolves, this algorithm is highly capable to search large spaces in the candidate solutions. This paper investigates the use of WS algorithm in combination with back-propagation neural network (BPNN) algorithm to overcome the local minima problem and to improve convergence in gradient descent. The performance of the proposed Wolf Search based Back-Propagation (WS-BP) algorithm is compared with Artificial Bee Colony Back-Propagation (ABC-BP), Bat Based Back-Propagation (Bat-BP), and conventional BPNN algorithms. Specifically, OR and XOR datasets are used for training the network. The simulation results show that the WS-BP algorithm effectively avoids the local minima and converge to global minima.

An evaluation of descent strategies for TNAV-equipped aircraft in an advanced metering environment

NASA Technical Reports Server (NTRS)

Izumi, K. H.; Schwab, R. W.; Groce, J. L.; Coote, M. A.

1986-01-01

Investigated were the effects on system throughput and fleet fuel usage of arrival aircraft utilizing three 4D RNAV descent strategies (cost optimal, clean-idle Mach/CAS and constant descent angle Mach/CAS), both individually and in combination, in an advanced air traffic control metering environment. Results are presented for all mixtures of arrival traffic consisting of three Boeing commercial jet types and for all combinations of the three descent strategies for a typical en route metering airport arrival distribution.

Autonomous optimal trajectory design employing convex optimization for powered descent on an asteroid

NASA Astrophysics Data System (ADS)

Pinson, Robin Marie

Mission proposals that land spacecraft on asteroids are becoming increasingly popular. However, in order to have a successful mission the spacecraft must reliably and softly land at the intended landing site with pinpoint precision. The problem under investigation is how to design a propellant (fuel) optimal powered descent trajectory that can be quickly computed onboard the spacecraft, without interaction from ground control. The goal is to autonomously design the optimal powered descent trajectory onboard the spacecraft immediately prior to the descent burn for use during the burn. Compared to a planetary powered landing problem, the challenges that arise from designing an asteroid powered descent trajectory include complicated nonlinear gravity fields, small rotating bodies, and low thrust vehicles. The nonlinear gravity fields cannot be represented by a constant gravity model nor a Newtonian model. The trajectory design algorithm needs to be robust and efficient to guarantee a designed trajectory and complete the calculations in a reasonable time frame. This research investigates the following questions: Can convex optimization be used to design the minimum propellant powered descent trajectory for a soft landing on an asteroid? Is this method robust and reliable to allow autonomy onboard the spacecraft without interaction from ground control? This research designed a convex optimization based method that rapidly generates the propellant optimal asteroid powered descent trajectory. The solution to the convex optimization problem is the thrust magnitude and direction, which designs and determines the trajectory. The propellant optimal problem was formulated as a second order cone program, a subset of convex optimization, through relaxation techniques by including a slack variable, change of variables, and incorporation of the successive solution method. Convex optimization solvers, especially second order cone programs, are robust, reliable, and are guaranteed to find the global minimum provided one exists. In addition, an outer optimization loop using Brent's method determines the optimal flight time corresponding to the minimum propellant usage over all flight times. Inclusion of additional trajectory constraints, solely vertical motion near the landing site and glide slope, were evaluated. Through a theoretical proof involving the Minimum Principle from Optimal Control Theory and the Karush-Kuhn-Tucker conditions it was shown that the relaxed problem is identical to the original problem at the minimum point. Therefore, the optimal solution of the relaxed problem is an optimal solution of the original problem, referred to as lossless convexification. A key finding is that this holds for all levels of gravity model fidelity. The designed thrust magnitude profiles were the bang-bang predicted by Optimal Control Theory. The first high fidelity gravity model employed was the 2x2 spherical harmonics model assuming a perfect triaxial ellipsoid and placement of the coordinate frame at the asteroid's center of mass and aligned with the semi-major axes. The spherical harmonics model is not valid inside the Brillouin sphere and this becomes relevant for irregularly shaped asteroids. Then, a higher fidelity model was implemented combining the 4x4 spherical harmonics gravity model with the interior spherical Bessel gravity model. All gravitational terms in the equations of motion are evaluated with the position vector from the previous iteration, creating the successive solution method. Methodology success was shown by applying the algorithm to three triaxial ellipsoidal asteroids with four different rotation speeds using the 2x2 gravity model. Finally, the algorithm was tested using the irregularly shaped asteroid, Castalia.

Application of the method of steepest descent to laminated shield weight optimization with several constraints: Theory

NASA Technical Reports Server (NTRS)

Lahti, G. P.

1971-01-01

The method of steepest descent used in optimizing one-dimensional layered radiation shields is extended to multidimensional, multiconstraint situations. The multidimensional optimization algorithm and equations are developed for the case of a dose constraint in any one direction being dependent only on the shield thicknesses in that direction and independent of shield thicknesses in other directions. Expressions are derived for one-, two-, and three-dimensional cases (one, two, and three constraints). The precedure is applicable to the optimization of shields where there are different dose constraints and layering arrangements in the principal directions.

Adaptive distance metric learning for diffusion tensor image segmentation.

PubMed

Kong, Youyong; Wang, Defeng; Shi, Lin; Hui, Steve C N; Chu, Winnie C W

2014-01-01

High quality segmentation of diffusion tensor images (DTI) is of key interest in biomedical research and clinical application. In previous studies, most efforts have been made to construct predefined metrics for different DTI segmentation tasks. These methods require adequate prior knowledge and tuning parameters. To overcome these disadvantages, we proposed to automatically learn an adaptive distance metric by a graph based semi-supervised learning model for DTI segmentation. An original discriminative distance vector was first formulated by combining both geometry and orientation distances derived from diffusion tensors. The kernel metric over the original distance and labels of all voxels were then simultaneously optimized in a graph based semi-supervised learning approach. Finally, the optimization task was efficiently solved with an iterative gradient descent method to achieve the optimal solution. With our approach, an adaptive distance metric could be available for each specific segmentation task. Experiments on synthetic and real brain DTI datasets were performed to demonstrate the effectiveness and robustness of the proposed distance metric learning approach. The performance of our approach was compared with three classical metrics in the graph based semi-supervised learning framework.

Adaptive Distance Metric Learning for Diffusion Tensor Image Segmentation

PubMed Central

Kong, Youyong; Wang, Defeng; Shi, Lin; Hui, Steve C. N.; Chu, Winnie C. W.

2014-01-01

High quality segmentation of diffusion tensor images (DTI) is of key interest in biomedical research and clinical application. In previous studies, most efforts have been made to construct predefined metrics for different DTI segmentation tasks. These methods require adequate prior knowledge and tuning parameters. To overcome these disadvantages, we proposed to automatically learn an adaptive distance metric by a graph based semi-supervised learning model for DTI segmentation. An original discriminative distance vector was first formulated by combining both geometry and orientation distances derived from diffusion tensors. The kernel metric over the original distance and labels of all voxels were then simultaneously optimized in a graph based semi-supervised learning approach. Finally, the optimization task was efficiently solved with an iterative gradient descent method to achieve the optimal solution. With our approach, an adaptive distance metric could be available for each specific segmentation task. Experiments on synthetic and real brain DTI datasets were performed to demonstrate the effectiveness and robustness of the proposed distance metric learning approach. The performance of our approach was compared with three classical metrics in the graph based semi-supervised learning framework. PMID:24651858

Inherent smoothness of intensity patterns for intensity modulated radiation therapy generated by simultaneous projection algorithms

NASA Astrophysics Data System (ADS)

Xiao, Ying; Michalski, Darek; Censor, Yair; Galvin, James M.

2004-07-01

The efficient delivery of intensity modulated radiation therapy (IMRT) depends on finding optimized beam intensity patterns that produce dose distributions, which meet given constraints for the tumour as well as any critical organs to be spared. Many optimization algorithms that are used for beamlet-based inverse planning are susceptible to large variations of neighbouring intensities. Accurately delivering an intensity pattern with a large number of extrema can prove impossible given the mechanical limitations of standard multileaf collimator (MLC) delivery systems. In this study, we apply Cimmino's simultaneous projection algorithm to the beamlet-based inverse planning problem, modelled mathematically as a system of linear inequalities. We show that using this method allows us to arrive at a smoother intensity pattern. Including nonlinear terms in the simultaneous projection algorithm to deal with dose-volume histogram (DVH) constraints does not compromise this property from our experimental observation. The smoothness properties are compared with those from other optimization algorithms which include simulated annealing and the gradient descent method. The simultaneous property of these algorithms is ideally suited to parallel computing technologies.

A New Efficient Hybrid Intelligent Model for Biodegradation Process of DMP with Fuzzy Wavelet Neural Networks

NASA Astrophysics Data System (ADS)

Huang, Mingzhi; Zhang, Tao; Ruan, Jujun; Chen, Xiaohong

2017-01-01

A new efficient hybrid intelligent approach based on fuzzy wavelet neural network (FWNN) was proposed for effectively modeling and simulating biodegradation process of Dimethyl phthalate (DMP) in an anaerobic/anoxic/oxic (AAO) wastewater treatment process. With the self learning and memory abilities of neural networks (NN), handling uncertainty capacity of fuzzy logic (FL), analyzing local details superiority of wavelet transform (WT) and global search of genetic algorithm (GA), the proposed hybrid intelligent model can extract the dynamic behavior and complex interrelationships from various water quality variables. For finding the optimal values for parameters of the proposed FWNN, a hybrid learning algorithm integrating an improved genetic optimization and gradient descent algorithm is employed. The results show, compared with NN model (optimized by GA) and kinetic model, the proposed FWNN model have the quicker convergence speed, the higher prediction performance, and smaller RMSE (0.080), MSE (0.0064), MAPE (1.8158) and higher R2 (0.9851) values. which illustrates FWNN model simulates effluent DMP more accurately than the mechanism model.

A New Efficient Hybrid Intelligent Model for Biodegradation Process of DMP with Fuzzy Wavelet Neural Networks

PubMed Central

Huang, Mingzhi; Zhang, Tao; Ruan, Jujun; Chen, Xiaohong

2017-01-01

A new efficient hybrid intelligent approach based on fuzzy wavelet neural network (FWNN) was proposed for effectively modeling and simulating biodegradation process of Dimethyl phthalate (DMP) in an anaerobic/anoxic/oxic (AAO) wastewater treatment process. With the self learning and memory abilities of neural networks (NN), handling uncertainty capacity of fuzzy logic (FL), analyzing local details superiority of wavelet transform (WT) and global search of genetic algorithm (GA), the proposed hybrid intelligent model can extract the dynamic behavior and complex interrelationships from various water quality variables. For finding the optimal values for parameters of the proposed FWNN, a hybrid learning algorithm integrating an improved genetic optimization and gradient descent algorithm is employed. The results show, compared with NN model (optimized by GA) and kinetic model, the proposed FWNN model have the quicker convergence speed, the higher prediction performance, and smaller RMSE (0.080), MSE (0.0064), MAPE (1.8158) and higher R2 (0.9851) values. which illustrates FWNN model simulates effluent DMP more accurately than the mechanism model. PMID:28120889

Neuro-fuzzy and neural network techniques for forecasting sea level in Darwin Harbor, Australia

NASA Astrophysics Data System (ADS)

Karimi, Sepideh; Kisi, Ozgur; Shiri, Jalal; Makarynskyy, Oleg

2013-03-01

Accurate predictions of sea level with different forecast horizons are important for coastal and ocean engineering applications, as well as in land drainage and reclamation studies. The methodology of tidal harmonic analysis, which is generally used for obtaining a mathematical description of the tides, is data demanding requiring processing of tidal observation collected over several years. In the present study, hourly sea levels for Darwin Harbor, Australia were predicted using two different, data driven techniques, adaptive neuro-fuzzy inference system (ANFIS) and artificial neural network (ANN). Multi linear regression (MLR) technique was used for selecting the optimal input combinations (lag times) of hourly sea level. The input combination comprises current sea level as well as five previous level values found to be optimal. For the ANFIS models, five different membership functions namely triangular, trapezoidal, generalized bell, Gaussian and two Gaussian membership function were tested and employed for predicting sea level for the next 1 h, 24 h, 48 h and 72 h. The used ANN models were trained using three different algorithms, namely, Levenberg-Marquardt, conjugate gradient and gradient descent. Predictions of optimal ANFIS and ANN models were compared with those of the optimal auto-regressive moving average (ARMA) models. The coefficient of determination, root mean square error and variance account statistics were used as comparison criteria. The obtained results indicated that triangular membership function was optimal for predictions with the ANFIS models while adaptive learning rate and Levenberg-Marquardt were most suitable for training the ANN models. Consequently, ANFIS and ANN models gave similar forecasts and performed better than the developed for the same purpose ARMA models for all the prediction intervals.

Optimal Control-Based Adaptive NN Design for a Class of Nonlinear Discrete-Time Block-Triangular Systems.

PubMed

Liu, Yan-Jun; Tong, Shaocheng

2016-11-01

In this paper, we propose an optimal control scheme-based adaptive neural network design for a class of unknown nonlinear discrete-time systems. The controlled systems are in a block-triangular multi-input-multi-output pure-feedback structure, i.e., there are both state and input couplings and nonaffine functions to be included in every equation of each subsystem. The design objective is to provide a control scheme, which not only guarantees the stability of the systems, but also achieves optimal control performance. The main contribution of this paper is that it is for the first time to achieve the optimal performance for such a class of systems. Owing to the interactions among subsystems, making an optimal control signal is a difficult task. The design ideas are that: 1) the systems are transformed into an output predictor form; 2) for the output predictor, the ideal control signal and the strategic utility function can be approximated by using an action network and a critic network, respectively; and 3) an optimal control signal is constructed with the weight update rules to be designed based on a gradient descent method. The stability of the systems can be proved based on the difference Lyapunov method. Finally, a numerical simulation is given to illustrate the performance of the proposed scheme.

Predictability of Top of Descent Location for Operational Idle-Thrust Descents

NASA Technical Reports Server (NTRS)

Stell, Laurel L.

2010-01-01

To enable arriving aircraft to fly optimized descents computed by the flight management system (FMS) in congested airspace, ground automation must accurately predict descent trajectories. To support development of the trajectory predictor and its uncertainty models, commercial flights executed idle-thrust descents at a specified descent speed, and the recorded data included the specified descent speed profile, aircraft weight, and the winds entered into the FMS as well as the radar data. The FMS computed the intended descent path assuming idle thrust after top of descent (TOD), and the controllers and pilots then endeavored to allow the FMS to fly the descent to the meter fix with minimal human intervention. The horizontal flight path, cruise and meter fix altitudes, and actual TOD location were extracted from the radar data. Using approximately 70 descents each in Boeing 757 and Airbus 319/320 aircraft, multiple regression estimated TOD location as a linear function of the available predictive factors. The cruise and meter fix altitudes, descent speed, and wind clearly improve goodness of fit. The aircraft weight improves fit for the Airbus descents but not for the B757. Except for a few statistical outliers, the residuals have absolute value less than 5 nmi. Thus, these predictive factors adequately explain the TOD location, which indicates the data do not include excessive noise.

On the efficiency of a randomized mirror descent algorithm in online optimization problems

NASA Astrophysics Data System (ADS)

Gasnikov, A. V.; Nesterov, Yu. E.; Spokoiny, V. G.

2015-04-01

A randomized online version of the mirror descent method is proposed. It differs from the existing versions by the randomization method. Randomization is performed at the stage of the projection of a subgradient of the function being optimized onto the unit simplex rather than at the stage of the computation of a subgradient, which is common practice. As a result, a componentwise subgradient descent with a randomly chosen component is obtained, which admits an online interpretation. This observation, for example, has made it possible to uniformly interpret results on weighting expert decisions and propose the most efficient method for searching for an equilibrium in a zero-sum two-person matrix game with sparse matrix.

Model-Free Optimal Tracking Control via Critic-Only Q-Learning.

PubMed

Luo, Biao; Liu, Derong; Huang, Tingwen; Wang, Ding

2016-10-01

Model-free control is an important and promising topic in control fields, which has attracted extensive attention in the past few years. In this paper, we aim to solve the model-free optimal tracking control problem of nonaffine nonlinear discrete-time systems. A critic-only Q-learning (CoQL) method is developed, which learns the optimal tracking control from real system data, and thus avoids solving the tracking Hamilton-Jacobi-Bellman equation. First, the Q-learning algorithm is proposed based on the augmented system, and its convergence is established. Using only one neural network for approximating the Q-function, the CoQL method is developed to implement the Q-learning algorithm. Furthermore, the convergence of the CoQL method is proved with the consideration of neural network approximation error. With the convergent Q-function obtained from the CoQL method, the adaptive optimal tracking control is designed based on the gradient descent scheme. Finally, the effectiveness of the developed CoQL method is demonstrated through simulation studies. The developed CoQL method learns with off-policy data and implements with a critic-only structure, thus it is easy to realize and overcome the inadequate exploration problem.

Graph Matching: Relax at Your Own Risk.

PubMed

Lyzinski, Vince; Fishkind, Donniell E; Fiori, Marcelo; Vogelstein, Joshua T; Priebe, Carey E; Sapiro, Guillermo

2016-01-01

Graph matching-aligning a pair of graphs to minimize their edge disagreements-has received wide-spread attention from both theoretical and applied communities over the past several decades, including combinatorics, computer vision, and connectomics. Its attention can be partially attributed to its computational difficulty. Although many heuristics have previously been proposed in the literature to approximately solve graph matching, very few have any theoretical support for their performance. A common technique is to relax the discrete problem to a continuous problem, therefore enabling practitioners to bring gradient-descent-type algorithms to bear. We prove that an indefinite relaxation (when solved exactly) almost always discovers the optimal permutation, while a common convex relaxation almost always fails to discover the optimal permutation. These theoretical results suggest that initializing the indefinite algorithm with the convex optimum might yield improved practical performance. Indeed, experimental results illuminate and corroborate these theoretical findings, demonstrating that excellent results are achieved in both benchmark and real data problems by amalgamating the two approaches.

Trajectory Design Employing Convex Optimization for Landing on Irregularly Shaped Asteroids

NASA Technical Reports Server (NTRS)

Pinson, Robin M.; Lu, Ping

2016-01-01

Mission proposals that land on asteroids are becoming popular. However, in order to have a successful mission the spacecraft must reliably and softly land at the intended landing site. The problem under investigation is how to design a fuel-optimal powered descent trajectory that can be quickly computed on- board the spacecraft, without interaction from ground control. An optimal trajectory designed immediately prior to the descent burn has many advantages. These advantages include the ability to use the actual vehicle starting state as the initial condition in the trajectory design and the ease of updating the landing target site if the original landing site is no longer viable. For long trajectories, the trajectory can be updated periodically by a redesign of the optimal trajectory based on current vehicle conditions to improve the guidance performance. One of the key drivers for being completely autonomous is the infrequent and delayed communication between ground control and the vehicle. Challenges that arise from designing an asteroid powered descent trajectory include complicated nonlinear gravity fields, small rotating bodies and low thrust vehicles. There are two previous studies that form the background to the current investigation. The first set looked in-depth at applying convex optimization to a powered descent trajectory on Mars with promising results.1, 2 This showed that the powered descent equations of motion can be relaxed and formed into a convex optimization problem and that the optimal solution of the relaxed problem is indeed a feasible solution to the original problem. This analysis used a constant gravity field. The second area applied a successive solution process to formulate a second order cone program that designs rendezvous and proximity operations trajectories.3, 4 These trajectories included a Newtonian gravity model. The equivalence of the solutions between the relaxed and the original problem is theoretically established. The proposed solution for designing the asteroid powered descent trajectory is to use convex optimization, a gravity model with higher fidelity than Newtonian, and an iterative solution process to design the fuel optimal trajectory. The solution to the convex optimization problem is the thrust profile, magnitude and direction, that will yield the minimum fuel trajectory for a soft landing at the target site, subject to various mission and operational constraints. The equations of motion are formulated in a rotating coordinate system and includes a high fidelity gravity model. The vehicle's thrust magnitude can vary between maximum and minimum bounds during the burn. Also, constraints are included to ensure that the vehicle does not run out of propellant, or go below the asteroid's surface, and any vehicle pointing requirements. The equations of motion are discretized and propagated with the trapezoidal rule in order to produce equality constraints for the optimization problem. These equality constraints allow the optimization algorithm to solve the entire problem, without including a propagator inside the optimization algorithm.

Taming the Wild: A Unified Analysis of Hogwild!-Style Algorithms.

PubMed

De Sa, Christopher; Zhang, Ce; Olukotun, Kunle; Ré, Christopher

2015-12-01

Stochastic gradient descent (SGD) is a ubiquitous algorithm for a variety of machine learning problems. Researchers and industry have developed several techniques to optimize SGD's runtime performance, including asynchronous execution and reduced precision. Our main result is a martingale-based analysis that enables us to capture the rich noise models that may arise from such techniques. Specifically, we use our new analysis in three ways: (1) we derive convergence rates for the convex case (Hogwild!) with relaxed assumptions on the sparsity of the problem; (2) we analyze asynchronous SGD algorithms for non-convex matrix problems including matrix completion; and (3) we design and analyze an asynchronous SGD algorithm, called Buckwild!, that uses lower-precision arithmetic. We show experimentally that our algorithms run efficiently for a variety of problems on modern hardware.

A hybrid neural network model for noisy data regression.

PubMed

Lee, Eric W M; Lim, Chee Peng; Yuen, Richard K K; Lo, S M

2004-04-01

A hybrid neural network model, based on the fusion of fuzzy adaptive resonance theory (FA ART) and the general regression neural network (GRNN), is proposed in this paper. Both FA and the GRNN are incremental learning systems and are very fast in network training. The proposed hybrid model, denoted as GRNNFA, is able to retain these advantages and, at the same time, to reduce the computational requirements in calculating and storing information of the kernels. A clustering version of the GRNN is designed with data compression by FA for noise removal. An adaptive gradient-based kernel width optimization algorithm has also been devised. Convergence of the gradient descent algorithm can be accelerated by the geometric incremental growth of the updating factor. A series of experiments with four benchmark datasets have been conducted to assess and compare effectiveness of GRNNFA with other approaches. The GRNNFA model is also employed in a novel application task for predicting the evacuation time of patrons at typical karaoke centers in Hong Kong in the event of fire. The results positively demonstrate the applicability of GRNNFA in noisy data regression problems.

Performance of Optimized Actuator and Sensor Arrays in an Active Noise Control System

NASA Technical Reports Server (NTRS)

Palumbo, D. L.; Padula, S. L.; Lyle, K. H.; Cline, J. H.; Cabell, R. H.

1996-01-01

Experiments have been conducted in NASA Langley's Acoustics and Dynamics Laboratory to determine the effectiveness of optimized actuator/sensor architectures and controller algorithms for active control of harmonic interior noise. Tests were conducted in a large scale fuselage model - a composite cylinder which simulates a commuter class aircraft fuselage with three sections of trim panel and a floor. Using an optimization technique based on the component transfer functions, combinations of 4 out of 8 piezoceramic actuators and 8 out of 462 microphone locations were evaluated against predicted performance. A combinatorial optimization technique called tabu search was employed to select the optimum transducer arrays. Three test frequencies represent the cases of a strong acoustic and strong structural response, a weak acoustic and strong structural response and a strong acoustic and weak structural response. Noise reduction was obtained using a Time Averaged/Gradient Descent (TAGD) controller. Results indicate that the optimization technique successfully predicted best and worst case performance. An enhancement of the TAGD control algorithm was also evaluated. The principal components of the actuator/sensor transfer functions were used in the PC-TAGD controller. The principal components are shown to be independent of each other while providing control as effective as the standard TAGD.

Robust resolution enhancement optimization methods to process variations based on vector imaging model

NASA Astrophysics Data System (ADS)

Ma, Xu; Li, Yanqiu; Guo, Xuejia; Dong, Lisong

2012-03-01

Optical proximity correction (OPC) and phase shifting mask (PSM) are the most widely used resolution enhancement techniques (RET) in the semiconductor industry. Recently, a set of OPC and PSM optimization algorithms have been developed to solve for the inverse lithography problem, which are only designed for the nominal imaging parameters without giving sufficient attention to the process variations due to the aberrations, defocus and dose variation. However, the effects of process variations existing in the practical optical lithography systems become more pronounced as the critical dimension (CD) continuously shrinks. On the other hand, the lithography systems with larger NA (NA>0.6) are now extensively used, rendering the scalar imaging models inadequate to describe the vector nature of the electromagnetic field in the current optical lithography systems. In order to tackle the above problems, this paper focuses on developing robust gradient-based OPC and PSM optimization algorithms to the process variations under a vector imaging model. To achieve this goal, an integrative and analytic vector imaging model is applied to formulate the optimization problem, where the effects of process variations are explicitly incorporated in the optimization framework. The steepest descent algorithm is used to optimize the mask iteratively. In order to improve the efficiency of the proposed algorithms, a set of algorithm acceleration techniques (AAT) are exploited during the optimization procedure.

Iterative free-energy optimization for recurrent neural networks (INFERNO).

PubMed

Pitti, Alexandre; Gaussier, Philippe; Quoy, Mathias

2017-01-01

The intra-parietal lobe coupled with the Basal Ganglia forms a working memory that demonstrates strong planning capabilities for generating robust yet flexible neuronal sequences. Neurocomputational models however, often fails to control long range neural synchrony in recurrent spiking networks due to spontaneous activity. As a novel framework based on the free-energy principle, we propose to see the problem of spikes' synchrony as an optimization problem of the neurons sub-threshold activity for the generation of long neuronal chains. Using a stochastic gradient descent, a reinforcement signal (presumably dopaminergic) evaluates the quality of one input vector to move the recurrent neural network to a desired activity; depending on the error made, this input vector is strengthened to hill-climb the gradient or elicited to search for another solution. This vector can be learned then by one associative memory as a model of the basal-ganglia to control the recurrent neural network. Experiments on habit learning and on sequence retrieving demonstrate the capabilities of the dual system to generate very long and precise spatio-temporal sequences, above two hundred iterations. Its features are applied then to the sequential planning of arm movements. In line with neurobiological theories, we discuss its relevance for modeling the cortico-basal working memory to initiate flexible goal-directed neuronal chains of causation and its relation to novel architectures such as Deep Networks, Neural Turing Machines and the Free-Energy Principle.

A guidance law for hypersonic descent to a point

DOE Office of Scientific and Technical Information (OSTI.GOV)

Eisler, G.R.; Hull, D.G.

1992-05-01

A neighboring external control problem is formulated for a hypersonic glider to execute a maximum-terminal-velocity descent to a stationary target. The resulting two-part, feedback control scheme initially solves a nonlinear algebraic problem to generate a nominal trajectory to the target altitude. Secondly, a neighboring optimal path computation about the nominal provides a lift and side-force perturbations necessary to achieve the target downrange and crossrange. On-line feedback simulations of the proposed scheme and a form of proportional navigation are compared with an off-line parameter optimization method. The neighboring optimal terminal velocity compares very well with the parameter optimization solution and ismore » far superior to proportional navigation. 8 refs.« less

A guidance law for hypersonic descent to a point

DOE Office of Scientific and Technical Information (OSTI.GOV)

Eisler, G.R.; Hull, D.G.

1992-01-01

A neighboring external control problem is formulated for a hypersonic glider to execute a maximum-terminal-velocity descent to a stationary target. The resulting two-part, feedback control scheme initially solves a nonlinear algebraic problem to generate a nominal trajectory to the target altitude. Secondly, a neighboring optimal path computation about the nominal provides a lift and side-force perturbations necessary to achieve the target downrange and crossrange. On-line feedback simulations of the proposed scheme and a form of proportional navigation are compared with an off-line parameter optimization method. The neighboring optimal terminal velocity compares very well with the parameter optimization solution and ismore » far superior to proportional navigation. 8 refs.« less

Implementation of a Balance Operator in NCOM

DTIC Science & Technology

2016-04-07

the background temperature Tb and salinity Sb fields do), f is the Coriolis parameter, k is the vertical unit vector, ∇ is the horizontal gradient, p... effectively used as a natural metric in the space of cost function gradients. The associated geometry inhibits descent in the unbalanced directions...28) where f is the local Coriolis parameter, ∆yv is the local grid spacing in the y direction at a v point, and the overbars indicates horizontal

Enhancements on the Convex Programming Based Powered Descent Guidance Algorithm for Mars Landing

NASA Technical Reports Server (NTRS)

Acikmese, Behcet; Blackmore, Lars; Scharf, Daniel P.; Wolf, Aron

2008-01-01

In this paper, we present enhancements on the powered descent guidance algorithm developed for Mars pinpoint landing. The guidance algorithm solves the powered descent minimum fuel trajectory optimization problem via a direct numerical method. Our main contribution is to formulate the trajectory optimization problem, which has nonconvex control constraints, as a finite dimensional convex optimization problem, specifically as a finite dimensional second order cone programming (SOCP) problem. SOCP is a subclass of convex programming, and there are efficient SOCP solvers with deterministic convergence properties. Hence, the resulting guidance algorithm can potentially be implemented onboard a spacecraft for real-time applications. Particularly, this paper discusses the algorithmic improvements obtained by: (i) Using an efficient approach to choose the optimal time-of-flight; (ii) Using a computationally inexpensive way to detect the feasibility/ infeasibility of the problem due to the thrust-to-weight constraint; (iii) Incorporating the rotation rate of the planet into the problem formulation; (iv) Developing additional constraints on the position and velocity to guarantee no-subsurface flight between the time samples of the temporal discretization; (v) Developing a fuel-limited targeting algorithm; (vi) Initial result on developing an onboard table lookup method to obtain almost fuel optimal solutions in real-time.

Adaptive Constrained Optimal Control Design for Data-Based Nonlinear Discrete-Time Systems With Critic-Only Structure.

PubMed

Luo, Biao; Liu, Derong; Wu, Huai-Ning

2018-06-01

Reinforcement learning has proved to be a powerful tool to solve optimal control problems over the past few years. However, the data-based constrained optimal control problem of nonaffine nonlinear discrete-time systems has rarely been studied yet. To solve this problem, an adaptive optimal control approach is developed by using the value iteration-based Q-learning (VIQL) with the critic-only structure. Most of the existing constrained control methods require the use of a certain performance index and only suit for linear or affine nonlinear systems, which is unreasonable in practice. To overcome this problem, the system transformation is first introduced with the general performance index. Then, the constrained optimal control problem is converted to an unconstrained optimal control problem. By introducing the action-state value function, i.e., Q-function, the VIQL algorithm is proposed to learn the optimal Q-function of the data-based unconstrained optimal control problem. The convergence results of the VIQL algorithm are established with an easy-to-realize initial condition . To implement the VIQL algorithm, the critic-only structure is developed, where only one neural network is required to approximate the Q-function. The converged Q-function obtained from the critic-only VIQL method is employed to design the adaptive constrained optimal controller based on the gradient descent scheme. Finally, the effectiveness of the developed adaptive control method is tested on three examples with computer simulation.

Algorithm based on the Thomson problem for determination of equilibrium structures of metal nanoclusters

NASA Astrophysics Data System (ADS)

Arias, E.; Florez, E.; Pérez-Torres, J. F.

2017-06-01

A new algorithm for the determination of equilibrium structures suitable for metal nanoclusters is proposed. The algorithm performs a stochastic search of the minima associated with the nuclear potential energy function restricted to a sphere (similar to the Thomson problem), in order to guess configurations of the nuclear positions. Subsequently, the guessed configurations are further optimized driven by the total energy function using the conventional gradient descent method. This methodology is equivalent to using the valence shell electron pair repulsion model in guessing initial configurations in the traditional molecular quantum chemistry. The framework is illustrated in several clusters of increasing complexity: Cu7, Cu9, and Cu11 as benchmark systems, and Cu38 and Ni9 as novel systems. New equilibrium structures for Cu9, Cu11, Cu38, and Ni9 are reported.

Hybrid preconditioning for iterative diagonalization of ill-conditioned generalized eigenvalue problems in electronic structure calculations

DOE Office of Scientific and Technical Information (OSTI.GOV)

Cai, Yunfeng, E-mail: yfcai@math.pku.edu.cn; Department of Computer Science, University of California, Davis 95616; Bai, Zhaojun, E-mail: bai@cs.ucdavis.edu

2013-12-15

The iterative diagonalization of a sequence of large ill-conditioned generalized eigenvalue problems is a computational bottleneck in quantum mechanical methods employing a nonorthogonal basis for ab initio electronic structure calculations. We propose a hybrid preconditioning scheme to effectively combine global and locally accelerated preconditioners for rapid iterative diagonalization of such eigenvalue problems. In partition-of-unity finite-element (PUFE) pseudopotential density-functional calculations, employing a nonorthogonal basis, we show that the hybrid preconditioned block steepest descent method is a cost-effective eigensolver, outperforming current state-of-the-art global preconditioning schemes, and comparably efficient for the ill-conditioned generalized eigenvalue problems produced by PUFE as the locally optimal blockmore » preconditioned conjugate-gradient method for the well-conditioned standard eigenvalue problems produced by planewave methods.« less

Algorithm based on the Thomson problem for determination of equilibrium structures of metal nanoclusters.

PubMed

Arias, E; Florez, E; Pérez-Torres, J F

2017-06-28

A new algorithm for the determination of equilibrium structures suitable for metal nanoclusters is proposed. The algorithm performs a stochastic search of the minima associated with the nuclear potential energy function restricted to a sphere (similar to the Thomson problem), in order to guess configurations of the nuclear positions. Subsequently, the guessed configurations are further optimized driven by the total energy function using the conventional gradient descent method. This methodology is equivalent to using the valence shell electron pair repulsion model in guessing initial configurations in the traditional molecular quantum chemistry. The framework is illustrated in several clusters of increasing complexity: Cu 7 , Cu 9 , and Cu 11 as benchmark systems, and Cu 38 and Ni 9 as novel systems. New equilibrium structures for Cu 9 , Cu 11 , Cu 38 , and Ni 9 are reported.

Radial basis function network learns ceramic processing and predicts related strength and density

NASA Technical Reports Server (NTRS)

Cios, Krzysztof J.; Baaklini, George Y.; Vary, Alex; Tjia, Robert E.

1993-01-01

Radial basis function (RBF) neural networks were trained using the data from 273 Si3N4 modulus of rupture (MOR) bars which were tested at room temperature and 135 MOR bars which were tested at 1370 C. Milling time, sintering time, and sintering gas pressure were the processing parameters used as the input features. Flexural strength and density were the outputs by which the RBF networks were assessed. The 'nodes-at-data-points' method was used to set the hidden layer centers and output layer training used the gradient descent method. The RBF network predicted strength with an average error of less than 12 percent and density with an average error of less than 2 percent. Further, the RBF network demonstrated a potential for optimizing and accelerating the development and processing of ceramic materials.

Approximate solution of the p-median minimization problem

NASA Astrophysics Data System (ADS)

Il'ev, V. P.; Il'eva, S. D.; Navrotskaya, A. A.

2016-09-01

A version of the facility location problem (the well-known p-median minimization problem) and its generalization—the problem of minimizing a supermodular set function—is studied. These problems are NP-hard, and they are approximately solved by a gradient algorithm that is a discrete analog of the steepest descent algorithm. A priori bounds on the worst-case behavior of the gradient algorithm for the problems under consideration are obtained. As a consequence, a bound on the performance guarantee of the gradient algorithm for the p-median minimization problem in terms of the production and transportation cost matrix is obtained.

Flight Management System Execution of Idle-Thrust Descents in Operations

NASA Technical Reports Server (NTRS)

Stell, Laurel L.

2011-01-01

To enable arriving aircraft to fly optimized descents computed by the flight management system (FMS) in congested airspace, ground automation must accurately predict descent trajectories. To support development of the trajectory predictor and its error models, commercial flights executed idle-thrust descents, and the recorded data includes the target speed profile and FMS intent trajectories. The FMS computes the intended descent path assuming idle thrust after top of descent (TOD), and any intervention by the controllers that alters the FMS execution of the descent is recorded so that such flights are discarded from the analysis. The horizontal flight path, cruise and meter fix altitudes, and actual TOD location are extracted from the radar data. Using more than 60 descents in Boeing 777 aircraft, the actual speeds are compared to the intended descent speed profile. In addition, three aspects of the accuracy of the FMS intent trajectory are analyzed: the meter fix crossing time, the TOD location, and the altitude at the meter fix. The actual TOD location is within 5 nmi of the intent location for over 95% of the descents. Roughly 90% of the time, the airspeed is within 0.01 of the target Mach number and within 10 KCAS of the target descent CAS, but the meter fix crossing time is only within 50 sec of the time computed by the FMS. Overall, the aircraft seem to be executing the descents as intended by the designers of the onboard automation.

Implementation of a Balance Operator in NCOM

DTIC Science & Technology

2016-04-07

the background temperature Tb and salinity Sb fields do), f is the Coriolis parameter, k is the vertical unit vector, ∇ is the horizontal gradient, p... effectively used as a natural metric in the space of cost function gradients. The associated geometry inhibits descent in the unbalanced directions and...28) where f is the local Coriolis parameter, ∆yv is the local grid spacing in the y direction at a v point, and the overbars indicates horizontal

Truncated Conjugate Gradient: An Optimal Strategy for the Analytical Evaluation of the Many-Body Polarization Energy and Forces in Molecular Simulations.

PubMed

Aviat, Félix; Levitt, Antoine; Stamm, Benjamin; Maday, Yvon; Ren, Pengyu; Ponder, Jay W; Lagardère, Louis; Piquemal, Jean-Philip

2017-01-10

We introduce a new class of methods, denoted as Truncated Conjugate Gradient(TCG), to solve the many-body polarization energy and its associated forces in molecular simulations (i.e. molecular dynamics (MD) and Monte Carlo). The method consists in a fixed number of Conjugate Gradient (CG) iterations. TCG approaches provide a scalable solution to the polarization problem at a user-chosen cost and a corresponding optimal accuracy. The optimality of the CG-method guarantees that the number of the required matrix-vector products are reduced to a minimum compared to other iterative methods. This family of methods is non-empirical, fully adaptive, and provides analytical gradients, avoiding therefore any energy drift in MD as compared to popular iterative solvers. Besides speed, one great advantage of this class of approximate methods is that their accuracy is systematically improvable. Indeed, as the CG-method is a Krylov subspace method, the associated error is monotonically reduced at each iteration. On top of that, two improvements can be proposed at virtually no cost: (i) the use of preconditioners can be employed, which leads to the Truncated Preconditioned Conjugate Gradient (TPCG); (ii) since the residual of the final step of the CG-method is available, one additional Picard fixed point iteration ("peek"), equivalent to one step of Jacobi Over Relaxation (JOR) with relaxation parameter ω, can be made at almost no cost. This method is denoted by TCG-n(ω). Black-box adaptive methods to find good choices of ω are provided and discussed. Results show that TPCG-3(ω) is converged to high accuracy (a few kcal/mol) for various types of systems including proteins and highly charged systems at the fixed cost of four matrix-vector products: three CG iterations plus the initial CG descent direction. Alternatively, T(P)CG-2(ω) provides robust results at a reduced cost (three matrix-vector products) and offers new perspectives for long polarizable MD as a production algorithm. The T(P)CG-1(ω) level provides less accurate solutions for inhomogeneous systems, but its applicability to well-conditioned problems such as water is remarkable, with only two matrix-vector product evaluations.

Truncated Conjugate Gradient: An Optimal Strategy for the Analytical Evaluation of the Many-Body Polarization Energy and Forces in Molecular Simulations

PubMed Central

2016-01-01

We introduce a new class of methods, denoted as Truncated Conjugate Gradient(TCG), to solve the many-body polarization energy and its associated forces in molecular simulations (i.e. molecular dynamics (MD) and Monte Carlo). The method consists in a fixed number of Conjugate Gradient (CG) iterations. TCG approaches provide a scalable solution to the polarization problem at a user-chosen cost and a corresponding optimal accuracy. The optimality of the CG-method guarantees that the number of the required matrix-vector products are reduced to a minimum compared to other iterative methods. This family of methods is non-empirical, fully adaptive, and provides analytical gradients, avoiding therefore any energy drift in MD as compared to popular iterative solvers. Besides speed, one great advantage of this class of approximate methods is that their accuracy is systematically improvable. Indeed, as the CG-method is a Krylov subspace method, the associated error is monotonically reduced at each iteration. On top of that, two improvements can be proposed at virtually no cost: (i) the use of preconditioners can be employed, which leads to the Truncated Preconditioned Conjugate Gradient (TPCG); (ii) since the residual of the final step of the CG-method is available, one additional Picard fixed point iteration (“peek”), equivalent to one step of Jacobi Over Relaxation (JOR) with relaxation parameter ω, can be made at almost no cost. This method is denoted by TCG-n(ω). Black-box adaptive methods to find good choices of ω are provided and discussed. Results show that TPCG-3(ω) is converged to high accuracy (a few kcal/mol) for various types of systems including proteins and highly charged systems at the fixed cost of four matrix-vector products: three CG iterations plus the initial CG descent direction. Alternatively, T(P)CG-2(ω) provides robust results at a reduced cost (three matrix-vector products) and offers new perspectives for long polarizable MD as a production algorithm. The T(P)CG-1(ω) level provides less accurate solutions for inhomogeneous systems, but its applicability to well-conditioned problems such as water is remarkable, with only two matrix-vector product evaluations. PMID:28068773

Linear feasibility algorithms for treatment planning in interstitial photodynamic therapy

NASA Astrophysics Data System (ADS)

Rendon, A.; Beck, J. C.; Lilge, Lothar

2008-02-01

Interstitial Photodynamic therapy (IPDT) has been under intense investigation in recent years, with multiple clinical trials underway. This effort has demanded the development of optimization strategies that determine the best locations and output powers for light sources (cylindrical or point diffusers) to achieve an optimal light delivery. Furthermore, we have recently introduced cylindrical diffusers with customizable emission profiles, placing additional requirements on the optimization algorithms, particularly in terms of the stability of the inverse problem. Here, we present a general class of linear feasibility algorithms and their properties. Moreover, we compare two particular instances of these algorithms, which are been used in the context of IPDT: the Cimmino algorithm and a weighted gradient descent (WGD) algorithm. The algorithms were compared in terms of their convergence properties, the cost function they minimize in the infeasible case, their ability to regularize the inverse problem, and the resulting optimal light dose distributions. Our results show that the WGD algorithm overall performs slightly better than the Cimmino algorithm and that it converges to a minimizer of a clinically relevant cost function in the infeasible case. Interestingly however, treatment plans resulting from either algorithms were very similar in terms of the resulting fluence maps and dose volume histograms, once the diffuser powers adjusted to achieve equal prostate coverage.

ATMOS/ATLAS-3 Observations of Long-Lived Tracers and Descent in the Antarctic Vortex in November 1994

NASA Technical Reports Server (NTRS)

Abrams, M. C.; Manney, G. L.; Gunson, M. R.; Abbas, M. M.; Chang, A. Y.; Goldman, A.; Irion, F. W.; Michelsen, H. A.; Newchurch, M. J.; Rinsland, C. P.;

OPTIMAL AIRCRAFT TRAJECTORIES FOR SPECIFIED RANGE

NASA Technical Reports Server (NTRS)

Lee, H.

1994-01-01

For an aircraft operating over a fixed range, the operating costs are basically a sum of fuel cost and time cost. While minimum fuel and minimum time trajectories are relatively easy to calculate, the determination of a minimum cost trajectory can be a complex undertaking. This computer program was developed to optimize trajectories with respect to a cost function based on a weighted sum of fuel cost and time cost. As a research tool, the program could be used to study various characteristics of optimum trajectories and their comparison to standard trajectories. It might also be used to generate a model for the development of an airborne trajectory optimization system. The program could be incorporated into an airline flight planning system, with optimum flight plans determined at takeoff time for the prevailing flight conditions. The use of trajectory optimization could significantly reduce the cost for a given aircraft mission. The algorithm incorporated in the program assumes that a trajectory consists of climb, cruise, and descent segments. The optimization of each segment is not done independently, as in classical procedures, but is performed in a manner which accounts for interaction between the segments. This is accomplished by the application of optimal control theory. The climb and descent profiles are generated by integrating a set of kinematic and dynamic equations, where the total energy of the aircraft is the independent variable. At each energy level of the climb and descent profiles, the air speed and power setting necessary for an optimal trajectory are determined. The variational Hamiltonian of the problem consists of the rate of change of cost with respect to total energy and a term dependent on the adjoint variable, which is identical to the optimum cruise cost at a specified altitude. This variable uniquely specifies the optimal cruise energy, cruise altitude, cruise Mach number, and, indirectly, the climb and descent profiles. If the optimum cruise cost is specified, an optimum trajectory can easily be generated; however, the range obtained for a particular optimum cruise cost is not known a priori. For short range flights, the program iteratively varies the optimum cruise cost until the computed range converges to the specified range. For long-range flights, iteration is unnecessary since the specified range can be divided into a cruise segment distance and full climb and descent distances. The user must supply the program with engine fuel flow rate coefficients and an aircraft aerodynamic model. The program currently includes coefficients for the Pratt-Whitney JT8D-7 engine and an aerodynamic model for the Boeing 727. Input to the program consists of the flight range to be covered and the prevailing flight conditions including pressure, temperature, and wind profiles. Information output by the program includes: optimum cruise tables at selected weights, optimal cruise quantities as a function of cruise weight and cruise distance, climb and descent profiles, and a summary of the complete synthesized optimal trajectory. This program is written in FORTRAN IV for batch execution and has been implemented on a CDC 6000 series computer with a central memory requirement of approximately 100K (octal) of 60 bit words. This aircraft trajectory optimization program was developed in 1979.

A conflict analysis of 4D descent strategies in a metered, multiple-arrival route environment

NASA Technical Reports Server (NTRS)

Izumi, K. H.; Harris, C. S.

1990-01-01

A conflict analysis was performed on multiple arrival traffic at a typical metered airport. The Flow Management Evaluation Model (FMEM) was used to simulate arrival operations using Denver Stapleton's arrival route structure. Sensitivities of conflict performance to three different 4-D descent strategies (clear-idle Mach/Constant AirSpeed (CAS), constant descent angle Mach/CAS and energy optimal) were examined for three traffic mixes represented by those found at Denver Stapleton, John F. Kennedy and typical en route metering (ERM) airports. The Monte Carlo technique was used to generate simulation entry point times. Analysis results indicate that the clean-idle descent strategy offers the best compromise in overall performance. Performance measures primarily include susceptibility to conflict and conflict severity. Fuel usage performance is extrapolated from previous descent strategy studies.

Fuel-Efficient Descent and Landing Guidance Logic for a Safe Lunar Touchdown

NASA Technical Reports Server (NTRS)

Lee, Allan Y.

2011-01-01

The landing of a crewed lunar lander on the surface of the Moon will be the climax of any Moon mission. At touchdown, the landing mechanism must absorb the load imparted on the lander due to the vertical component of the lander's touchdown velocity. Also, a large horizontal velocity must be avoided because it could cause the lander to tip over, risking the life of the crew. To be conservative, the worst-case lander's touchdown velocity is always assumed in designing the landing mechanism, making it very heavy. Fuel-optimal guidance algorithms for soft planetary landing have been studied extensively. In most of these studies, the lander is constrained to touchdown with zero velocity. With bounds imposed on the magnitude of the engine thrust, the optimal control solutions typically have a "bang-bang" thrust profile: the thrust magnitude "bangs" instantaneously between its maximum and minimum magnitudes. But the descent engine might not be able to throttle between its extremes instantaneously. There is also a concern about the acceptability of "bang-bang" control to the crew. In our study, the optimal control of a lander is formulated with a cost function that penalizes both the touchdown velocity and the fuel cost of the descent engine. In this formulation, there is not a requirement to achieve a zero touchdown velocity. Only a touchdown velocity that is consistent with the capability of the landing gear design is required. Also, since the nominal throttle level for the terminal descent sub-phase is well below the peak engine thrust, no bound on the engine thrust is used in our formulated problem. Instead of bangbang type solution, the optimal thrust generated is a continuous function of time. With this formulation, we can easily derive analytical expressions for the optimal thrust vector, touchdown velocity components, and other system variables. These expressions provide insights into the "physics" of the optimal landing and terminal descent maneuver. These insights could help engineers to achieve a better "balance" between the conflicting needs of achieving a safe touchdown velocity, a low-weight landing mechanism, low engine fuel cost, and other design goals. In comparing the computed optimal control results with the preflight landing trajectory design of the Apollo-11 mission, we noted interesting similarities between the two missions.

14 CFR 23.253 - High speed characteristics.

Code of Federal Regulations, 2013 CFR

2013-01-01

... and characteristics include gust upsets, inadvertent control movements, low stick force gradients in relation to control friction, passenger movement, leveling off from climb, and descent from Mach to... normal attitude and its speed reduced to VMO/MMO, without— (1) Exceptional piloting strength or skill; (2...

14 CFR 23.253 - High speed characteristics.

Code of Federal Regulations, 2014 CFR

2014-01-01

... and characteristics include gust upsets, inadvertent control movements, low stick force gradients in relation to control friction, passenger movement, leveling off from climb, and descent from Mach to... normal attitude and its speed reduced to VMO/MMO, without— (1) Exceptional piloting strength or skill; (2...

Using a Gradient Vector to Find Multiple Periodic Oscillations in Suspension Bridge Models

ERIC Educational Resources Information Center

Humphreys, L. D.; McKenna, P. J.

2005-01-01

This paper describes how the method of steepest descent can be used to find periodic solutions of differential equations. Applications to two suspension bridge models are discussed, and the method is used to find non-obvious large-amplitude solutions.

Nonuniformity correction for an infrared focal plane array based on diamond search block matching.

PubMed

Sheng-Hui, Rong; Hui-Xin, Zhou; Han-Lin, Qin; Rui, Lai; Kun, Qian

2016-05-01

In scene-based nonuniformity correction algorithms, artificial ghosting and image blurring degrade the correction quality severely. In this paper, an improved algorithm based on the diamond search block matching algorithm and the adaptive learning rate is proposed. First, accurate transform pairs between two adjacent frames are estimated by the diamond search block matching algorithm. Then, based on the error between the corresponding transform pairs, the gradient descent algorithm is applied to update correction parameters. During the process of gradient descent, the local standard deviation and a threshold are utilized to control the learning rate to avoid the accumulation of matching error. Finally, the nonuniformity correction would be realized by a linear model with updated correction parameters. The performance of the proposed algorithm is thoroughly studied with four real infrared image sequences. Experimental results indicate that the proposed algorithm can reduce the nonuniformity with less ghosting artifacts in moving areas and can also overcome the problem of image blurring in static areas.

3D-Web-GIS RFID location sensing system for construction objects.

PubMed

Ko, Chien-Ho

2013-01-01

Construction site managers could benefit from being able to visualize on-site construction objects. Radio frequency identification (RFID) technology has been shown to improve the efficiency of construction object management. The objective of this study is to develop a 3D-Web-GIS RFID location sensing system for construction objects. An RFID 3D location sensing algorithm combining Simulated Annealing (SA) and a gradient descent method is proposed to determine target object location. In the algorithm, SA is used to stabilize the search process and the gradient descent method is used to reduce errors. The locations of the analyzed objects are visualized using the 3D-Web-GIS system. A real construction site is used to validate the applicability of the proposed method, with results indicating that the proposed approach can provide faster, more accurate, and more stable 3D positioning results than other location sensing algorithms. The proposed system allows construction managers to better understand worksite status, thus enhancing managerial efficiency.

3D-Web-GIS RFID Location Sensing System for Construction Objects

PubMed Central

2013-01-01

Construction site managers could benefit from being able to visualize on-site construction objects. Radio frequency identification (RFID) technology has been shown to improve the efficiency of construction object management. The objective of this study is to develop a 3D-Web-GIS RFID location sensing system for construction objects. An RFID 3D location sensing algorithm combining Simulated Annealing (SA) and a gradient descent method is proposed to determine target object location. In the algorithm, SA is used to stabilize the search process and the gradient descent method is used to reduce errors. The locations of the analyzed objects are visualized using the 3D-Web-GIS system. A real construction site is used to validate the applicability of the proposed method, with results indicating that the proposed approach can provide faster, more accurate, and more stable 3D positioning results than other location sensing algorithms. The proposed system allows construction managers to better understand worksite status, thus enhancing managerial efficiency. PMID:23864821

A General Method for Solving Systems of Non-Linear Equations

NASA Technical Reports Server (NTRS)

Nachtsheim, Philip R.; Deiss, Ron (Technical Monitor)

1995-01-01

The method of steepest descent is modified so that accelerated convergence is achieved near a root. It is assumed that the function of interest can be approximated near a root by a quadratic form. An eigenvector of the quadratic form is found by evaluating the function and its gradient at an arbitrary point and another suitably selected point. The terminal point of the eigenvector is chosen to lie on the line segment joining the two points. The terminal point found lies on an axis of the quadratic form. The selection of a suitable step size at this point leads directly to the root in the direction of steepest descent in a single step. Newton's root finding method not infrequently diverges if the starting point is far from the root. However, the current method in these regions merely reverts to the method of steepest descent with an adaptive step size. The current method's performance should match that of the Levenberg-Marquardt root finding method since they both share the ability to converge from a starting point far from the root and both exhibit quadratic convergence near a root. The Levenberg-Marquardt method requires storage for coefficients of linear equations. The current method which does not require the solution of linear equations requires more time for additional function and gradient evaluations. The classic trade off of time for space separates the two methods.

Dynamic Aberration Correction for Conformal Window of High-Speed Aircraft Using Optimized Model-Based Wavefront Sensorless Adaptive Optics.

PubMed

Dong, Bing; Li, Yan; Han, Xin-Li; Hu, Bin

2016-09-02

For high-speed aircraft, a conformal window is used to optimize the aerodynamic performance. However, the local shape of the conformal window leads to large amounts of dynamic aberrations varying with look angle. In this paper, deformable mirror (DM) and model-based wavefront sensorless adaptive optics (WSLAO) are used for dynamic aberration correction of an infrared remote sensor equipped with a conformal window and scanning mirror. In model-based WSLAO, aberration is captured using Lukosz mode, and we use the low spatial frequency content of the image spectral density as the metric function. Simulations show that aberrations induced by the conformal window are dominated by some low-order Lukosz modes. To optimize the dynamic correction, we can only correct dominant Lukosz modes and the image size can be minimized to reduce the time required to compute the metric function. In our experiment, a 37-channel DM is used to mimic the dynamic aberration of conformal window with scanning rate of 10 degrees per second. A 52-channel DM is used for correction. For a 128 × 128 image, the mean value of image sharpness during dynamic correction is 1.436 × 10(-5) in optimized correction and is 1.427 × 10(-5) in un-optimized correction. We also demonstrated that model-based WSLAO can achieve convergence two times faster than traditional stochastic parallel gradient descent (SPGD) method.

Multigrid optimal mass transport for image registration and morphing

NASA Astrophysics Data System (ADS)

Rehman, Tauseef ur; Tannenbaum, Allen

2007-02-01

In this paper we present a computationally efficient Optimal Mass Transport algorithm. This method is based on the Monge-Kantorovich theory and is used for computing elastic registration and warping maps in image registration and morphing applications. This is a parameter free method which utilizes all of the grayscale data in an image pair in a symmetric fashion. No landmarks need to be specified for correspondence. In our work, we demonstrate significant improvement in computation time when our algorithm is applied as compared to the originally proposed method by Haker et al [1]. The original algorithm was based on a gradient descent method for removing the curl from an initial mass preserving map regarded as 2D vector field. This involves inverting the Laplacian in each iteration which is now computed using full multigrid technique resulting in an improvement in computational time by a factor of two. Greater improvement is achieved by decimating the curl in a multi-resolutional framework. The algorithm was applied to 2D short axis cardiac MRI images and brain MRI images for testing and comparison.

Spatiotemporal topology and temporal sequence identification with an adaptive time-delay neural network

NASA Astrophysics Data System (ADS)

Lin, Daw-Tung; Ligomenides, Panos A.; Dayhoff, Judith E.

1993-08-01

Inspired from the time delays that occur in neurobiological signal transmission, we describe an adaptive time delay neural network (ATNN) which is a powerful dynamic learning technique for spatiotemporal pattern transformation and temporal sequence identification. The dynamic properties of this network are formulated through the adaptation of time-delays and synapse weights, which are adjusted on-line based on gradient descent rules according to the evolution of observed inputs and outputs. We have applied the ATNN to examples that possess spatiotemporal complexity, with temporal sequences that are completed by the network. The ATNN is able to be applied to pattern completion. Simulation results show that the ATNN learns the topology of a circular and figure eight trajectories within 500 on-line training iterations, and reproduces the trajectory dynamically with very high accuracy. The ATNN was also trained to model the Fourier series expansion of the sum of different odd harmonics. The resulting network provides more flexibility and efficiency than the TDNN and allows the network to seek optimal values for time-delays as well as optimal synapse weights.

Towards exaggerated emphysema stereotypes

NASA Astrophysics Data System (ADS)

Chen, C.; Sørensen, L.; Lauze, F.; Igel, C.; Loog, M.; Feragen, A.; de Bruijne, M.; Nielsen, M.

2012-03-01

Classification is widely used in the context of medical image analysis and in order to illustrate the mechanism of a classifier, we introduce the notion of an exaggerated image stereotype based on training data and trained classifier. The stereotype of some image class of interest should emphasize/exaggerate the characteristic patterns in an image class and visualize the information the employed classifier relies on. This is useful for gaining insight into the classification and serves for comparison with the biological models of disease. In this work, we build exaggerated image stereotypes by optimizing an objective function which consists of a discriminative term based on the classification accuracy, and a generative term based on the class distributions. A gradient descent method based on iterated conditional modes (ICM) is employed for optimization. We use this idea with Fisher's linear discriminant rule and assume a multivariate normal distribution for samples within a class. The proposed framework is applied to computed tomography (CT) images of lung tissue with emphysema. The synthesized stereotypes illustrate the exaggerated patterns of lung tissue with emphysema, which is underpinned by three different quantitative evaluation methods.

Efficient Online Learning Algorithms Based on LSTM Neural Networks.

PubMed

Ergen, Tolga; Kozat, Suleyman Serdar

2017-09-13

We investigate online nonlinear regression and introduce novel regression structures based on the long short term memory (LSTM) networks. For the introduced structures, we also provide highly efficient and effective online training methods. To train these novel LSTM-based structures, we put the underlying architecture in a state space form and introduce highly efficient and effective particle filtering (PF)-based updates. We also provide stochastic gradient descent and extended Kalman filter-based updates. Our PF-based training method guarantees convergence to the optimal parameter estimation in the mean square error sense provided that we have a sufficient number of particles and satisfy certain technical conditions. More importantly, we achieve this performance with a computational complexity in the order of the first-order gradient-based methods by controlling the number of particles. Since our approach is generic, we also introduce a gated recurrent unit (GRU)-based approach by directly replacing the LSTM architecture with the GRU architecture, where we demonstrate the superiority of our LSTM-based approach in the sequential prediction task via different real life data sets. In addition, the experimental results illustrate significant performance improvements achieved by the introduced algorithms with respect to the conventional methods over several different benchmark real life data sets.

Statistical Physics for Adaptive Distributed Control

NASA Technical Reports Server (NTRS)

Wolpert, David H.

2005-01-01

A viewgraph presentation on statistical physics for distributed adaptive control is shown. The topics include: 1) The Golden Rule; 2) Advantages; 3) Roadmap; 4) What is Distributed Control? 5) Review of Information Theory; 6) Iterative Distributed Control; 7) Minimizing L(q) Via Gradient Descent; and 8) Adaptive Distributed Control.

Powered Descent Guidance with General Thrust-Pointing Constraints

NASA Technical Reports Server (NTRS)

Carson, John M., III; Acikmese, Behcet; Blackmore, Lars

2013-01-01

The Powered Descent Guidance (PDG) algorithm and software for generating Mars pinpoint or precision landing guidance profiles has been enhanced to incorporate thrust-pointing constraints. Pointing constraints would typically be needed for onboard sensor and navigation systems that have specific field-of-view requirements to generate valid ground proximity and terrain-relative state measurements. The original PDG algorithm was designed to enforce both control and state constraints, including maximum and minimum thrust bounds, avoidance of the ground or descent within a glide slope cone, and maximum speed limits. The thrust-bound and thrust-pointing constraints within PDG are non-convex, which in general requires nonlinear optimization methods to generate solutions. The short duration of Mars powered descent requires guaranteed PDG convergence to a solution within a finite time; however, nonlinear optimization methods have no guarantees of convergence to the global optimal or convergence within finite computation time. A lossless convexification developed for the original PDG algorithm relaxed the non-convex thrust bound constraints. This relaxation was theoretically proven to provide valid and optimal solutions for the original, non-convex problem within a convex framework. As with the thrust bound constraint, a relaxation of the thrust-pointing constraint also provides a lossless convexification that ensures the enhanced relaxed PDG algorithm remains convex and retains validity for the original nonconvex problem. The enhanced PDG algorithm provides guidance profiles for pinpoint and precision landing that minimize fuel usage, minimize landing error to the target, and ensure satisfaction of all position and control constraints, including thrust bounds and now thrust-pointing constraints.

Conjugate gradient filtering of instantaneous normal modes, saddles on the energy landscape, and diffusion in liquids.

PubMed

Chowdhary, J; Keyes, T

2002-02-01

Instantaneous normal modes (INM's) are calculated during a conjugate-gradient (CG) descent of the potential energy landscape, starting from an equilibrium configuration of a liquid or crystal. A small number (approximately equal to 4) of CG steps removes all the Im-omega modes in the crystal and leaves the liquid with diffusive Im-omega which accurately represent the self-diffusion constant D. Conjugate gradient filtering appears to be a promising method, applicable to any system, of obtaining diffusive modes and facilitating INM theory of D. The relation of the CG-step dependent INM quantities to the landscape and its saddles is discussed.

Advances in POST2 End-to-End Descent and Landing Simulation for the ALHAT Project

NASA Technical Reports Server (NTRS)

Davis, Jody L.; Striepe, Scott A.; Maddock, Robert W.; Hines, Glenn D.; Paschall, Stephen, II; Cohanim, Babak E.; Fill, Thomas; Johnson, Michael C.; Bishop, Robert H.; DeMars, Kyle J.;

Wavefront sensorless adaptive optics ophthalmoscopy in the human eye

PubMed Central

Hofer, Heidi; Sredar, Nripun; Queener, Hope; Li, Chaohong; Porter, Jason

2011-01-01

Wavefront sensor noise and fidelity place a fundamental limit on achievable image quality in current adaptive optics ophthalmoscopes. Additionally, the wavefront sensor ‘beacon’ can interfere with visual experiments. We demonstrate real-time (25 Hz), wavefront sensorless adaptive optics imaging in the living human eye with image quality rivaling that of wavefront sensor based control in the same system. A stochastic parallel gradient descent algorithm directly optimized the mean intensity in retinal image frames acquired with a confocal adaptive optics scanning laser ophthalmoscope (AOSLO). When imaging through natural, undilated pupils, both control methods resulted in comparable mean image intensities. However, when imaging through dilated pupils, image intensity was generally higher following wavefront sensor-based control. Despite the typically reduced intensity, image contrast was higher, on average, with sensorless control. Wavefront sensorless control is a viable option for imaging the living human eye and future refinements of this technique may result in even greater optical gains. PMID:21934779

Adaptive beam shaping for improving the power coupling of a two-Cassegrain-telescope

NASA Astrophysics Data System (ADS)

Ma, Haotong; Hu, Haojun; Xie, Wenke; Zhao, Haichuan; Xu, Xiaojun; Chen, Jinbao

2013-08-01

We demonstrate the adaptive beam shaping for improving the power coupling of a two-Cassegrain-telescope based on the stochastic parallel gradient descent (SPGD) algorithm and dual phase only liquid crystal spatial light modulators (LC-SLMs). Adaptive pre-compensation the wavefront of projected laser beam at the transmitter telescope is chosen to improve the power coupling efficiency. One phase only LC-SLM adaptively optimizes phase distribution of the projected laser beam and the other generates turbulence phase screen. The intensity distributions of the dark hollow beam after passing through the turbulent atmosphere with and without adaptive beam shaping are analyzed in detail. The influence of propagation distance and aperture size of the Cassegrain-telescope on coupling efficiency are investigated theoretically and experimentally. These studies show that the power coupling can be significantly improved by adaptive beam shaping. The technique can be used in optical communication, deep space optical communication and relay mirror.

Multi-Sensor Registration of Earth Remotely Sensed Imagery

NASA Technical Reports Server (NTRS)

LeMoigne, Jacqueline; Cole-Rhodes, Arlene; Eastman, Roger; Johnson, Kisha; Morisette, Jeffrey; Netanyahu, Nathan S.; Stone, Harold S.; Zavorin, Ilya; Zukor, Dorothy (Technical Monitor)

2001-01-01

Assuming that approximate registration is given within a few pixels by a systematic correction system, we develop automatic image registration methods for multi-sensor data with the goal of achieving sub-pixel accuracy. Automatic image registration is usually defined by three steps; feature extraction, feature matching, and data resampling or fusion. Our previous work focused on image correlation methods based on the use of different features. In this paper, we study different feature matching techniques and present five algorithms where the features are either original gray levels or wavelet-like features, and the feature matching is based on gradient descent optimization, statistical robust matching, and mutual information. These algorithms are tested and compared on several multi-sensor datasets covering one of the EOS Core Sites, the Konza Prairie in Kansas, from four different sensors: IKONOS (4m), Landsat-7/ETM+ (30m), MODIS (500m), and SeaWIFS (1000m).

Efficient numerical calculation of MHD equilibria with magnetic islands, with particular application to saturated neoclassical tearing modes

NASA Astrophysics Data System (ADS)

Raburn, Daniel Louis

We have developed a preconditioned, globalized Jacobian-free Newton-Krylov (JFNK) solver for calculating equilibria with magnetic islands. The solver has been developed in conjunction with the Princeton Iterative Equilibrium Solver (PIES) and includes two notable enhancements over a traditional JFNK scheme: (1) globalization of the algorithm by a sophisticated backtracking scheme, which optimizes between the Newton and steepest-descent directions; and, (2) adaptive preconditioning, wherein information regarding the system Jacobian is reused between Newton iterations to form a preconditioner for our GMRES-like linear solver. We have developed a formulation for calculating saturated neoclassical tearing modes (NTMs) which accounts for the incomplete loss of a bootstrap current due to gradients of multiple physical quantities. We have applied the coupled PIES-JFNK solver to calculate saturated island widths on several shots from the Tokamak Fusion Test Reactor (TFTR) and have found reasonable agreement with experimental measurement.

Minimum-Cost Aircraft Descent Trajectories with a Constrained Altitude Profile

NASA Technical Reports Server (NTRS)

Wu, Minghong G.; Sadovsky, Alexander V.

2015-01-01

An analytical formula for solving the speed profile that accrues minimum cost during an aircraft descent with a constrained altitude profile is derived. The optimal speed profile first reaches a certain speed, called the minimum-cost speed, as quickly as possible using an appropriate extreme value of thrust. The speed profile then stays on the minimum-cost speed as long as possible, before switching to an extreme value of thrust for the rest of the descent. The formula is applied to an actual arrival route and its sensitivity to winds and airlines' business objectives is analyzed.

Feedback control for fuel-optimal descents using singular perturbation techniques

NASA Technical Reports Server (NTRS)

Price, D. B.

1984-01-01

In response to rising fuel costs and reduced profit margins for the airline companies, the optimization of the paths flown by transport aircraft has been considered. It was found that application of optimal control theory to the considered problem can result in savings in fuel, time, and direct operating costs. The best solution to the aircraft trajectory problem is an onboard real-time feedback control law. The present paper presents a technique which shows promise of becoming a part of a complete solution. The application of singular perturbation techniques to the problem is discussed, taking into account the benefits and some problems associated with them. A different technique for handling the descent part of a trajectory is also discussed.

The DOPEX code: An application of the method of steepest descent to laminated-shield-weight optimization with several constraints

NASA Technical Reports Server (NTRS)

Lahti, G. P.

1972-01-01

A two- or three-constraint, two-dimensional radiation shield weight optimization procedure and a computer program, DOPEX, is described. The DOPEX code uses the steepest descent method to alter a set of initial (input) thicknesses for a shield configuration to achieve a minimum weight while simultaneously satisfying dose constaints. The code assumes an exponential dose-shield thickness relation with parameters specified by the user. The code also assumes that dose rates in each principal direction are dependent only on thicknesses in that direction. Code input instructions, FORTRAN 4 listing, and a sample problem are given. Typical computer time required to optimize a seven-layer shield is about 0.1 minute on an IBM 7094-2.

Toward a Caribbean psychology: an African-centered approach.

PubMed

Sutherland, Marcia Elizabeth

2011-01-01

Although the Americas and Caribbean region are purported to comprise different ethnic groups, this article’s focus is on people of African descent, who represent the largest ethnic group in many countries. The emphasis on people of African descent is related to their family structure, ethnic identity, cultural, psychohistorical, and contemporary psychosocial realities. This article discusses the limitations of Western psychology for theory, research, and applied work on people of African descent in the Americas and Caribbean region. In view of the adaptations that some people of African descent have made to slavery, colonialism, and more contemporary forms of cultural intrusions, it is argued that when necessary, notwithstanding Western psychology’s limitations, Caribbean psychologists should reconstruct mainstream psychology to address the psychological needs of these Caribbean people. The relationship between theory and psychological interventions for the optimal development of people of African descent is emphasized throughout this article. In this regard, the African-centered and constructionist viewpoint is argued to be of utility in addressing the psychological growth and development of people of African descent living in the Americas and Caribbean region.

Deep neural mapping support vector machines.

PubMed

Li, Yujian; Zhang, Ting

2017-09-01

The choice of kernel has an important effect on the performance of a support vector machine (SVM). The effect could be reduced by NEUROSVM, an architecture using multilayer perceptron for feature extraction and SVM for classification. In binary classification, a general linear kernel NEUROSVM can be theoretically simplified as an input layer, many hidden layers, and an SVM output layer. As a feature extractor, the sub-network composed of the input and hidden layers is first trained together with a virtual ordinary output layer by backpropagation, then with the output of its last hidden layer taken as input of the SVM classifier for further training separately. By taking the sub-network as a kernel mapping from the original input space into a feature space, we present a novel model, called deep neural mapping support vector machine (DNMSVM), from the viewpoint of deep learning. This model is also a new and general kernel learning method, where the kernel mapping is indeed an explicit function expressed as a sub-network, different from an implicit function induced by a kernel function traditionally. Moreover, we exploit a two-stage procedure of contrastive divergence learning and gradient descent for DNMSVM to jointly training an adaptive kernel mapping instead of a kernel function, without requirement of kernel tricks. As a whole of the sub-network and the SVM classifier, the joint training of DNMSVM is done by using gradient descent to optimize the objective function with the sub-network layer-wise pre-trained via contrastive divergence learning of restricted Boltzmann machines. Compared to the separate training of NEUROSVM, the joint training is a new algorithm for DNMSVM to have advantages over NEUROSVM. Experimental results show that DNMSVM can outperform NEUROSVM and RBFSVM (i.e., SVM with the kernel of radial basis function), demonstrating its effectiveness. Copyright © 2017 Elsevier Ltd. All rights reserved.

Reinforcement learning design-based adaptive tracking control with less learning parameters for nonlinear discrete-time MIMO systems.

PubMed

Liu, Yan-Jun; Tang, Li; Tong, Shaocheng; Chen, C L Philip; Li, Dong-Juan

2015-01-01

Based on the neural network (NN) approximator, an online reinforcement learning algorithm is proposed for a class of affine multiple input and multiple output (MIMO) nonlinear discrete-time systems with unknown functions and disturbances. In the design procedure, two networks are provided where one is an action network to generate an optimal control signal and the other is a critic network to approximate the cost function. An optimal control signal and adaptation laws can be generated based on two NNs. In the previous approaches, the weights of critic and action networks are updated based on the gradient descent rule and the estimations of optimal weight vectors are directly adjusted in the design. Consequently, compared with the existing results, the main contributions of this paper are: 1) only two parameters are needed to be adjusted, and thus the number of the adaptation laws is smaller than the previous results and 2) the updating parameters do not depend on the number of the subsystems for MIMO systems and the tuning rules are replaced by adjusting the norms on optimal weight vectors in both action and critic networks. It is proven that the tracking errors, the adaptation laws, and the control inputs are uniformly bounded using Lyapunov analysis method. The simulation examples are employed to illustrate the effectiveness of the proposed algorithm.

A Convex Formulation for Learning a Shared Predictive Structure from Multiple Tasks

PubMed Central

Chen, Jianhui; Tang, Lei; Liu, Jun; Ye, Jieping

2013-01-01

In this paper, we consider the problem of learning from multiple related tasks for improved generalization performance by extracting their shared structures. The alternating structure optimization (ASO) algorithm, which couples all tasks using a shared feature representation, has been successfully applied in various multitask learning problems. However, ASO is nonconvex and the alternating algorithm only finds a local solution. We first present an improved ASO formulation (iASO) for multitask learning based on a new regularizer. We then convert iASO, a nonconvex formulation, into a relaxed convex one (rASO). Interestingly, our theoretical analysis reveals that rASO finds a globally optimal solution to its nonconvex counterpart iASO under certain conditions. rASO can be equivalently reformulated as a semidefinite program (SDP), which is, however, not scalable to large datasets. We propose to employ the block coordinate descent (BCD) method and the accelerated projected gradient (APG) algorithm separately to find the globally optimal solution to rASO; we also develop efficient algorithms for solving the key subproblems involved in BCD and APG. The experiments on the Yahoo webpages datasets and the Drosophila gene expression pattern images datasets demonstrate the effectiveness and efficiency of the proposed algorithms and confirm our theoretical analysis. PMID:23520249

Trajectory Design Employing Convex Optimization for Landing on Irregularly Shaped Asteroids

NASA Technical Reports Server (NTRS)

Pinson, Robin M.; Lu, Ping

2016-01-01

Mission proposals that land spacecraft on asteroids are becoming increasingly popular. However, in order to have a successful mission the spacecraft must reliably and softly land at the intended landing site with pinpoint precision. The problem under investigation is how to design a propellant optimal powered descent trajectory that can be quickly computed onboard the spacecraft, without interaction from the ground control. The propellant optimal control problem in this work is to determine the optimal finite thrust vector to land the spacecraft at a specified location, in the presence of a highly nonlinear gravity field, subject to various mission and operational constraints. The proposed solution uses convex optimization, a gravity model with higher fidelity than Newtonian, and an iterative solution process for a fixed final time problem. In addition, a second optimization method is wrapped around the convex optimization problem to determine the optimal flight time that yields the lowest propellant usage over all flight times. Gravity models designed for irregularly shaped asteroids are investigated. Success of the algorithm is demonstrated by designing powered descent trajectories for the elongated binary asteroid Castalia.

Neural networks applications to control and computations

NASA Technical Reports Server (NTRS)

Luxemburg, Leon A.

1994-01-01

Several interrelated problems in the area of neural network computations are described. First an interpolation problem is considered, then a control problem is reduced to a problem of interpolation by a neural network via Lyapunov function approach, and finally a new, faster method of learning as compared with the gradient descent method, was introduced.

North Pacific Cloud Feedbacks Inferred from Synoptic-Scale Dynamic and Thermodynamic Relationships

NASA Technical Reports Server (NTRS)

Norris, Joel R.; Iacobellis, Sam F.

2005-01-01

This study analyzed daily satellite cloud observations and reanalysis dynamical parameters to determine how mid-tropospheric vertical velocity and advection over the sea surface temperature gradient control midlatitude North Pacific cloud properties. Optically thick clouds with high tops are generated by synoptic ascent, but two different cloud regimes occur under synoptic descent. When vertical motion is downward during summer, extensive stratocumulus cloudiness is associated with near surface northerly wind, while frequent cloudless pixels occur with southerly wind. Examinations of ship-reported cloud types indicates that midlatitude stratocumulus breaks up as the the boundary level decouples when it is advected equatorward over warmer water. Cumulus is prevalent under conditions of synoptic descent and cold advection during winter. Poleward advection of subtropical air over colder water causes stratification of the near-surface layer that inhibits upward mixing of moisture and suppresses cloudiness until a fog eventually forms. Averaging of cloud and radiation data into intervals of 500-hPa vertical velocity and advection over the SST gradient enables the cloud response to changes in temperature and the stratification of the lower troposphere to be investigated independent of the dynamics.

Optimizing wavefront-guided corrections for highly aberrated eyes in the presence of registration uncertainty

PubMed Central

Shi, Yue; Queener, Hope M.; Marsack, Jason D.; Ravikumar, Ayeswarya; Bedell, Harold E.; Applegate, Raymond A.

2013-01-01

Dynamic registration uncertainty of a wavefront-guided correction with respect to underlying wavefront error (WFE) inevitably decreases retinal image quality. A partial correction may improve average retinal image quality and visual acuity in the presence of registration uncertainties. The purpose of this paper is to (a) develop an algorithm to optimize wavefront-guided correction that improves visual acuity given registration uncertainty and (b) test the hypothesis that these corrections provide improved visual performance in the presence of these uncertainties as compared to a full-magnitude correction or a correction by Guirao, Cox, and Williams (2002). A stochastic parallel gradient descent (SPGD) algorithm was used to optimize the partial-magnitude correction for three keratoconic eyes based on measured scleral contact lens movement. Given its high correlation with logMAR acuity, the retinal image quality metric log visual Strehl was used as a predictor of visual acuity. Predicted values of visual acuity with the optimized corrections were validated by regressing measured acuity loss against predicted loss. Measured loss was obtained from normal subjects viewing acuity charts that were degraded by the residual aberrations generated by the movement of the full-magnitude correction, the correction by Guirao, and optimized SPGD correction. Partial-magnitude corrections optimized with an SPGD algorithm provide at least one line improvement of average visual acuity over the full magnitude and the correction by Guirao given the registration uncertainty. This study demonstrates that it is possible to improve the average visual acuity by optimizing wavefront-guided correction in the presence of registration uncertainty. PMID:23757512

Inversion of geothermal heat flux in a thermomechanically coupled nonlinear Stokes ice sheet model

DOE Office of Scientific and Technical Information (OSTI.GOV)

Zhu, Hongyu; Petra, Noemi; Stadler, Georg

We address the inverse problem of inferring the basal geothermal heat flux from surface velocity observations using a steady-state thermomechanically coupled nonlinear Stokes ice flow model. This is a challenging inverse problem since the map from basal heat flux to surface velocity observables is indirect: the heat flux is a boundary condition for the thermal advection–diffusion equation, which couples to the nonlinear Stokes ice flow equations; together they determine the surface ice flow velocity. This multiphysics inverse problem is formulated as a nonlinear least-squares optimization problem with a cost functional that includes the data misfit between surface velocity observations andmore » model predictions. A Tikhonov regularization term is added to render the problem well posed. We derive adjoint-based gradient and Hessian expressions for the resulting partial differential equation (PDE)-constrained optimization problem and propose an inexact Newton method for its solution. As a consequence of the Petrov–Galerkin discretization of the energy equation, we show that discretization and differentiation do not commute; that is, the order in which we discretize the cost functional and differentiate it affects the correctness of the gradient. Using two- and three-dimensional model problems, we study the prospects for and limitations of the inference of the geothermal heat flux field from surface velocity observations. The results show that the reconstruction improves as the noise level in the observations decreases and that short-wavelength variations in the geothermal heat flux are difficult to recover. We analyze the ill-posedness of the inverse problem as a function of the number of observations by examining the spectrum of the Hessian of the cost functional. Motivated by the popularity of operator-split or staggered solvers for forward multiphysics problems – i.e., those that drop two-way coupling terms to yield a one-way coupled forward Jacobian – we study the effect on the inversion of a one-way coupling of the adjoint energy and Stokes equations. Here, we show that taking such a one-way coupled approach for the adjoint equations can lead to an incorrect gradient and premature termination of optimization iterations. This is due to loss of a descent direction stemming from inconsistency of the gradient with the contours of the cost functional. Nevertheless, one may still obtain a reasonable approximate inverse solution particularly if important features of the reconstructed solution emerge early in optimization iterations, before the premature termination.« less

Inversion of geothermal heat flux in a thermomechanically coupled nonlinear Stokes ice sheet model

DOE PAGES

Zhu, Hongyu; Petra, Noemi; Stadler, Georg; ...

2016-07-13

We address the inverse problem of inferring the basal geothermal heat flux from surface velocity observations using a steady-state thermomechanically coupled nonlinear Stokes ice flow model. This is a challenging inverse problem since the map from basal heat flux to surface velocity observables is indirect: the heat flux is a boundary condition for the thermal advection–diffusion equation, which couples to the nonlinear Stokes ice flow equations; together they determine the surface ice flow velocity. This multiphysics inverse problem is formulated as a nonlinear least-squares optimization problem with a cost functional that includes the data misfit between surface velocity observations andmore » model predictions. A Tikhonov regularization term is added to render the problem well posed. We derive adjoint-based gradient and Hessian expressions for the resulting partial differential equation (PDE)-constrained optimization problem and propose an inexact Newton method for its solution. As a consequence of the Petrov–Galerkin discretization of the energy equation, we show that discretization and differentiation do not commute; that is, the order in which we discretize the cost functional and differentiate it affects the correctness of the gradient. Using two- and three-dimensional model problems, we study the prospects for and limitations of the inference of the geothermal heat flux field from surface velocity observations. The results show that the reconstruction improves as the noise level in the observations decreases and that short-wavelength variations in the geothermal heat flux are difficult to recover. We analyze the ill-posedness of the inverse problem as a function of the number of observations by examining the spectrum of the Hessian of the cost functional. Motivated by the popularity of operator-split or staggered solvers for forward multiphysics problems – i.e., those that drop two-way coupling terms to yield a one-way coupled forward Jacobian – we study the effect on the inversion of a one-way coupling of the adjoint energy and Stokes equations. Here, we show that taking such a one-way coupled approach for the adjoint equations can lead to an incorrect gradient and premature termination of optimization iterations. This is due to loss of a descent direction stemming from inconsistency of the gradient with the contours of the cost functional. Nevertheless, one may still obtain a reasonable approximate inverse solution particularly if important features of the reconstructed solution emerge early in optimization iterations, before the premature termination.« less

Inversion of geothermal heat flux in a thermomechanically coupled nonlinear Stokes ice sheet model

NASA Astrophysics Data System (ADS)

Zhu, Hongyu; Petra, Noemi; Stadler, Georg; Isaac, Tobin; Hughes, Thomas J. R.; Ghattas, Omar

2016-07-01

We address the inverse problem of inferring the basal geothermal heat flux from surface velocity observations using a steady-state thermomechanically coupled nonlinear Stokes ice flow model. This is a challenging inverse problem since the map from basal heat flux to surface velocity observables is indirect: the heat flux is a boundary condition for the thermal advection-diffusion equation, which couples to the nonlinear Stokes ice flow equations; together they determine the surface ice flow velocity. This multiphysics inverse problem is formulated as a nonlinear least-squares optimization problem with a cost functional that includes the data misfit between surface velocity observations and model predictions. A Tikhonov regularization term is added to render the problem well posed. We derive adjoint-based gradient and Hessian expressions for the resulting partial differential equation (PDE)-constrained optimization problem and propose an inexact Newton method for its solution. As a consequence of the Petrov-Galerkin discretization of the energy equation, we show that discretization and differentiation do not commute; that is, the order in which we discretize the cost functional and differentiate it affects the correctness of the gradient. Using two- and three-dimensional model problems, we study the prospects for and limitations of the inference of the geothermal heat flux field from surface velocity observations. The results show that the reconstruction improves as the noise level in the observations decreases and that short-wavelength variations in the geothermal heat flux are difficult to recover. We analyze the ill-posedness of the inverse problem as a function of the number of observations by examining the spectrum of the Hessian of the cost functional. Motivated by the popularity of operator-split or staggered solvers for forward multiphysics problems - i.e., those that drop two-way coupling terms to yield a one-way coupled forward Jacobian - we study the effect on the inversion of a one-way coupling of the adjoint energy and Stokes equations. We show that taking such a one-way coupled approach for the adjoint equations can lead to an incorrect gradient and premature termination of optimization iterations. This is due to loss of a descent direction stemming from inconsistency of the gradient with the contours of the cost functional. Nevertheless, one may still obtain a reasonable approximate inverse solution particularly if important features of the reconstructed solution emerge early in optimization iterations, before the premature termination.

Dynamic Aberration Correction for Conformal Window of High-Speed Aircraft Using Optimized Model-Based Wavefront Sensorless Adaptive Optics

PubMed Central

Dong, Bing; Li, Yan; Han, Xin-li; Hu, Bin

2016-01-01

For high-speed aircraft, a conformal window is used to optimize the aerodynamic performance. However, the local shape of the conformal window leads to large amounts of dynamic aberrations varying with look angle. In this paper, deformable mirror (DM) and model-based wavefront sensorless adaptive optics (WSLAO) are used for dynamic aberration correction of an infrared remote sensor equipped with a conformal window and scanning mirror. In model-based WSLAO, aberration is captured using Lukosz mode, and we use the low spatial frequency content of the image spectral density as the metric function. Simulations show that aberrations induced by the conformal window are dominated by some low-order Lukosz modes. To optimize the dynamic correction, we can only correct dominant Lukosz modes and the image size can be minimized to reduce the time required to compute the metric function. In our experiment, a 37-channel DM is used to mimic the dynamic aberration of conformal window with scanning rate of 10 degrees per second. A 52-channel DM is used for correction. For a 128 × 128 image, the mean value of image sharpness during dynamic correction is 1.436 × 10−5 in optimized correction and is 1.427 × 10−5 in un-optimized correction. We also demonstrated that model-based WSLAO can achieve convergence two times faster than traditional stochastic parallel gradient descent (SPGD) method. PMID:27598161

Mars Smart Lander Simulations for Entry, Descent, and Landing

NASA Technical Reports Server (NTRS)

Striepe, S. A.; Way, D. W.; Balaram, J.

2002-01-01

Two primary simulations have been developed and are being updated for the Mars Smart Lander Entry, Descent, and Landing (EDL). The high fidelity engineering end-to-end EDL simulation that is based on NASA Langley's Program to Optimize Simulated Trajectories (POST) and the end-to-end real-time, hardware-in-the-loop simulation testbed, which is based on NASA JPL's (Jet Propulsion Laboratory) Dynamics Simulator for Entry, Descent and Surface landing (DSENDS). This paper presents the status of these Mars Smart Lander EDL end-to-end simulations at this time. Various models, capabilities, as well as validation and verification for these simulations are discussed.

Implementation of neural network for color properties of polycarbonates

NASA Astrophysics Data System (ADS)

Saeed, U.; Ahmad, S.; Alsadi, J.; Ross, D.; Rizvi, G.

2014-05-01

In present paper, the applicability of artificial neural networks (ANN) is investigated for color properties of plastics. The neural networks toolbox of Matlab 6.5 is used to develop and test the ANN model on a personal computer. An optimal design is completed for 10, 12, 14,16,18 & 20 hidden neurons on single hidden layer with five different algorithms: batch gradient descent (GD), batch variable learning rate (GDX), resilient back-propagation (RP), scaled conjugate gradient (SCG), levenberg-marquardt (LM) in the feed forward back-propagation neural network model. The training data for ANN is obtained from experimental measurements. There were twenty two inputs including resins, additives & pigments while three tristimulus color values L*, a* and b* were used as output layer. Statistical analysis in terms of Root-Mean-Squared (RMS), absolute fraction of variance (R squared), as well as mean square error is used to investigate the performance of ANN. LM algorithm with fourteen neurons on hidden layer in Feed Forward Back-Propagation of ANN model has shown best result in the present study. The degree of accuracy of the ANN model in reduction of errors is proven acceptable in all statistical analysis and shown in results. However, it was concluded that ANN provides a feasible method in error reduction in specific color tristimulus values.

An approach to unbiased subsample interpolation for motion tracking.

PubMed

McCormick, Matthew M; Varghese, Tomy

2013-04-01

Accurate subsample displacement estimation is necessary for ultrasound elastography because of the small deformations that occur and the subsequent application of a derivative operation on local displacements. Many of the commonly used subsample estimation techniques introduce significant bias errors. This article addresses a reduced bias approach to subsample displacement estimations that consists of a two-dimensional windowed-sinc interpolation with numerical optimization. It is shown that a Welch or Lanczos window with a Nelder-Mead simplex or regular-step gradient-descent optimization is well suited for this purpose. Little improvement results from a sinc window radius greater than four data samples. The strain signal-to-noise ratio (SNR) obtained in a uniformly elastic phantom is compared with other parabolic and cosine interpolation methods; it is found that the strain SNR ratio is improved over parabolic interpolation from 11.0 to 13.6 in the axial direction and 0.7 to 1.1 in the lateral direction for an applied 1% axial deformation. The improvement was most significant for small strains and displacement tracking in the lateral direction. This approach does not rely on special properties of the image or similarity function, which is demonstrated by its effectiveness with the application of a previously described regularization technique.

Soil quality assessment using weighted fuzzy association rules

USGS Publications Warehouse

Xue, Yue-Ju; Liu, Shu-Guang; Hu, Yue-Ming; Yang, Jing-Feng

2010-01-01

Fuzzy association rules (FARs) can be powerful in assessing regional soil quality, a critical step prior to land planning and utilization; however, traditional FARs mined from soil quality database, ignoring the importance variability of the rules, can be redundant and far from optimal. In this study, we developed a method applying different weights to traditional FARs to improve accuracy of soil quality assessment. After the FARs for soil quality assessment were mined, redundant rules were eliminated according to whether the rules were significant or not in reducing the complexity of the soil quality assessment models and in improving the comprehensibility of FARs. The global weights, each representing the importance of a FAR in soil quality assessment, were then introduced and refined using a gradient descent optimization method. This method was applied to the assessment of soil resources conditions in Guangdong Province, China. The new approach had an accuracy of 87%, when 15 rules were mined, as compared with 76% from the traditional approach. The accuracy increased to 96% when 32 rules were mined, in contrast to 88% from the traditional approach. These results demonstrated an improved comprehensibility of FARs and a high accuracy of the proposed method.

SYNCHRONIZATION OF HETEROGENEOUS OSCILLATORS UNDER NETWORK MODIFICATIONS: PERTURBATION AND OPTIMIZATION OF THE SYNCHRONY ALIGNMENT FUNCTION

PubMed Central

Taylor, Dane; Skardal, Per Sebastian; Sun, Jie

2016-01-01

Synchronization is central to many complex systems in engineering physics (e.g., the power-grid, Josephson junction circuits, and electro-chemical oscillators) and biology (e.g., neuronal, circadian, and cardiac rhythms). Despite these widespread applications—for which proper functionality depends sensitively on the extent of synchronization—there remains a lack of understanding for how systems can best evolve and adapt to enhance or inhibit synchronization. We study how network modifications affect the synchronization properties of network-coupled dynamical systems that have heterogeneous node dynamics (e.g., phase oscillators with non-identical frequencies), which is often the case for real-world systems. Our approach relies on a synchrony alignment function (SAF) that quantifies the interplay between heterogeneity of the network and of the oscillators and provides an objective measure for a system’s ability to synchronize. We conduct a spectral perturbation analysis of the SAF for structural network modifications including the addition and removal of edges, which subsequently ranks the edges according to their importance to synchronization. Based on this analysis, we develop gradient-descent algorithms to efficiently solve optimization problems that aim to maximize phase synchronization via network modifications. We support these and other results with numerical experiments. PMID:27872501

Experimental demonstration of using divergence cost-function in SPGD algorithm for coherent beam combining with tip/tilt control.

PubMed

Geng, Chao; Luo, Wen; Tan, Yi; Liu, Hongmei; Mu, Jinbo; Li, Xinyang

2013-10-21

A novel approach of tip/tilt control by using divergence cost function in stochastic parallel gradient descent (SPGD) algorithm for coherent beam combining (CBC) is proposed and demonstrated experimentally in a seven-channel 2-W fiber amplifier array with both phase-locking and tip/tilt control, for the first time to our best knowledge. Compared with the conventional power-in-the-bucket (PIB) cost function for SPGD optimization, the tip/tilt control using divergence cost function ensures wider correction range, automatic switching control of program, and freedom of camera's intensity-saturation. Homemade piezoelectric-ring phase-modulator (PZT PM) and adaptive fiber-optics collimator (AFOC) are developed to correct piston- and tip/tilt-type aberrations, respectively. The PIB cost function is employed for phase-locking via maximization of SPGD optimization, while the divergence cost function is used for tip/tilt control via minimization. An average of 432-μrad of divergence metrics in open loop has decreased to 89-μrad when tip/tilt control implemented. In CBC, the power in the full width at half maximum (FWHM) of the main lobe increases by 32 times, and the phase residual error is less than λ/15.

Power Control and Optimization of Photovoltaic and Wind Energy Conversion Systems

NASA Astrophysics Data System (ADS)

Ghaffari, Azad

Power map and Maximum Power Point (MPP) of Photovoltaic (PV) and Wind Energy Conversion Systems (WECS) highly depend on system dynamics and environmental parameters, e.g., solar irradiance, temperature, and wind speed. Power optimization algorithms for PV systems and WECS are collectively known as Maximum Power Point Tracking (MPPT) algorithm. Gradient-based Extremum Seeking (ES), as a non-model-based MPPT algorithm, governs the system to its peak point on the steepest descent curve regardless of changes of the system dynamics and variations of the environmental parameters. Since the power map shape defines the gradient vector, then a close estimate of the power map shape is needed to create user assignable transients in the MPPT algorithm. The Hessian gives a precise estimate of the power map in a neighborhood around the MPP. The estimate of the inverse of the Hessian in combination with the estimate of the gradient vector are the key parts to implement the Newton-based ES algorithm. Hence, we generate an estimate of the Hessian using our proposed perturbation matrix. Also, we introduce a dynamic estimator to calculate the inverse of the Hessian which is an essential part of our algorithm. We present various simulations and experiments on the micro-converter PV systems to verify the validity of our proposed algorithm. The ES scheme can also be used in combination with other control algorithms to achieve desired closed-loop performance. The WECS dynamics is slow which causes even slower response time for the MPPT based on the ES. Hence, we present a control scheme, extended from Field-Oriented Control (FOC), in combination with feedback linearization to reduce the convergence time of the closed-loop system. Furthermore, the nonlinear control prevents magnetic saturation of the stator of the Induction Generator (IG). The proposed control algorithm in combination with the ES guarantees the closed-loop system robustness with respect to high level parameter uncertainty in the IG dynamics. The simulation results verify the effectiveness of the proposed algorithm.

POST2 End-To-End Descent and Landing Simulation for the Autonomous Landing and Hazard Avoidance Technology Project

NASA Technical Reports Server (NTRS)

Fisher, Jody l.; Striepe, Scott A.

2007-01-01

The Program to Optimize Simulated Trajectories II (POST2) is used as a basis for an end-to-end descent and landing trajectory simulation that is essential in determining the design and performance capability of lunar descent and landing system models and lunar environment models for the Autonomous Landing and Hazard Avoidance Technology (ALHAT) project. This POST2-based ALHAT simulation provides descent and landing simulation capability by integrating lunar environment and lander system models (including terrain, sensor, guidance, navigation, and control models), along with the data necessary to design and operate a landing system for robotic, human, and cargo lunar-landing success. This paper presents the current and planned development and model validation of the POST2-based end-to-end trajectory simulation used for the testing, performance and evaluation of ALHAT project system and models.

Fundamental limitations on V/STOL terminal guidance due to aircraft characteristics

NASA Technical Reports Server (NTRS)

Wolkovitch, J.; Lamont, C. W.; Lochtie, D. W.

1971-01-01

A review is given of limitations on approach flight paths of V/STOL aircraft, including limits on descent angle due to maximum drag/lift ratio. A method of calculating maximum drag/lift ratio of tilt-wing and deflected slipstream aircraft is presented. Derivatives and transfer functions for the CL-84 tilt-wing and X-22A tilt-duct aircraft are presented. For the unaugmented CL-84 in steep descents the transfer function relating descent angle to thrust contains a right-half plane zero. Using optimal control theory, it is shown that this zero causes a serious degradation in the accuracy with which steep flight paths can be followed in the presence of gusts.

A study on the performance comparison of metaheuristic algorithms on the learning of neural networks

NASA Astrophysics Data System (ADS)

Lai, Kee Huong; Zainuddin, Zarita; Ong, Pauline

2017-08-01

The learning or training process of neural networks entails the task of finding the most optimal set of parameters, which includes translation vectors, dilation parameter, synaptic weights, and bias terms. Apart from the traditional gradient descent-based methods, metaheuristic methods can also be used for this learning purpose. Since the inception of genetic algorithm half a century ago, the last decade witnessed the explosion of a variety of novel metaheuristic algorithms, such as harmony search algorithm, bat algorithm, and whale optimization algorithm. Despite the proof of the no free lunch theorem in the discipline of optimization, a survey in the literature of machine learning gives contrasting results. Some researchers report that certain metaheuristic algorithms are superior to the others, whereas some others argue that different metaheuristic algorithms give comparable performance. As such, this paper aims to investigate if a certain metaheuristic algorithm will outperform the other algorithms. In this work, three metaheuristic algorithms, namely genetic algorithms, particle swarm optimization, and harmony search algorithm are considered. The algorithms are incorporated in the learning of neural networks and their classification results on the benchmark UCI machine learning data sets are compared. It is found that all three metaheuristic algorithms give similar and comparable performance, as captured in the average overall classification accuracy. The results corroborate the findings reported in the works done by previous researchers. Several recommendations are given, which include the need of statistical analysis to verify the results and further theoretical works to support the obtained empirical results.

Support Vector Machines Trained with Evolutionary Algorithms Employing Kernel Adatron for Large Scale Classification of Protein Structures.

PubMed

Arana-Daniel, Nancy; Gallegos, Alberto A; López-Franco, Carlos; Alanís, Alma Y; Morales, Jacob; López-Franco, Adriana

2016-01-01

With the increasing power of computers, the amount of data that can be processed in small periods of time has grown exponentially, as has the importance of classifying large-scale data efficiently. Support vector machines have shown good results classifying large amounts of high-dimensional data, such as data generated by protein structure prediction, spam recognition, medical diagnosis, optical character recognition and text classification, etc. Most state of the art approaches for large-scale learning use traditional optimization methods, such as quadratic programming or gradient descent, which makes the use of evolutionary algorithms for training support vector machines an area to be explored. The present paper proposes an approach that is simple to implement based on evolutionary algorithms and Kernel-Adatron for solving large-scale classification problems, focusing on protein structure prediction. The functional properties of proteins depend upon their three-dimensional structures. Knowing the structures of proteins is crucial for biology and can lead to improvements in areas such as medicine, agriculture and biofuels.

Accurate modeling of switched reluctance machine based on hybrid trained WNN

DOE Office of Scientific and Technical Information (OSTI.GOV)

Song, Shoujun, E-mail: sunnyway@nwpu.edu.cn; Ge, Lefei; Ma, Shaojie

2014-04-15

According to the strong nonlinear electromagnetic characteristics of switched reluctance machine (SRM), a novel accurate modeling method is proposed based on hybrid trained wavelet neural network (WNN) which combines improved genetic algorithm (GA) with gradient descent (GD) method to train the network. In the novel method, WNN is trained by GD method based on the initial weights obtained per improved GA optimization, and the global parallel searching capability of stochastic algorithm and local convergence speed of deterministic algorithm are combined to enhance the training accuracy, stability and speed. Based on the measured electromagnetic characteristics of a 3-phase 12/8-pole SRM, themore » nonlinear simulation model is built by hybrid trained WNN in Matlab. The phase current and mechanical characteristics from simulation under different working conditions meet well with those from experiments, which indicates the accuracy of the model for dynamic and static performance evaluation of SRM and verifies the effectiveness of the proposed modeling method.« less

Using Inspiration from Synaptic Plasticity Rules to Optimize Traffic Flow in Distributed Engineered Networks.

PubMed

Suen, Jonathan Y; Navlakha, Saket

2017-05-01

Controlling the flow and routing of data is a fundamental problem in many distributed networks, including transportation systems, integrated circuits, and the Internet. In the brain, synaptic plasticity rules have been discovered that regulate network activity in response to environmental inputs, which enable circuits to be stable yet flexible. Here, we develop a new neuro-inspired model for network flow control that depends only on modifying edge weights in an activity-dependent manner. We show how two fundamental plasticity rules, long-term potentiation and long-term depression, can be cast as a distributed gradient descent algorithm for regulating traffic flow in engineered networks. We then characterize, both by simulation and analytically, how different forms of edge-weight-update rules affect network routing efficiency and robustness. We find a close correspondence between certain classes of synaptic weight update rules derived experimentally in the brain and rules commonly used in engineering, suggesting common principles to both.

Multiclass Reduced-Set Support Vector Machines

NASA Technical Reports Server (NTRS)

Tang, Benyang; Mazzoni, Dominic

2006-01-01

There are well-established methods for reducing the number of support vectors in a trained binary support vector machine, often with minimal impact on accuracy. We show how reduced-set methods can be applied to multiclass SVMs made up of several binary SVMs, with significantly better results than reducing each binary SVM independently. Our approach is based on Burges' approach that constructs each reduced-set vector as the pre-image of a vector in kernel space, but we extend this by recomputing the SVM weights and bias optimally using the original SVM objective function. This leads to greater accuracy for a binary reduced-set SVM, and also allows vectors to be 'shared' between multiple binary SVMs for greater multiclass accuracy with fewer reduced-set vectors. We also propose computing pre-images using differential evolution, which we have found to be more robust than gradient descent alone. We show experimental results on a variety of problems and find that this new approach is consistently better than previous multiclass reduced-set methods, sometimes with a dramatic difference.

Controlling bridging and pinching with pixel-based mask for inverse lithography

NASA Astrophysics Data System (ADS)

Kobelkov, Sergey; Tritchkov, Alexander; Han, JiWan

2016-03-01

Inverse Lithography Technology (ILT) has become a viable computational lithography candidate in recent years as it can produce mask output that results in process latitude and CD control in the fab that is hard to match with conventional OPC/SRAF insertion approaches. An approach to solving the inverse lithography problem as a nonlinear, constrained minimization problem over a domain mask pixels was suggested in the paper by Y. Granik "Fast pixel-based mask optimization for inverse lithography" in 2006. The present paper extends this method to satisfy bridging and pinching constraints imposed on print contours. Namely, there are suggested objective functions expressing penalty for constraints violations, and their minimization with gradient descent methods is considered. This approach has been tested with an ILT-based Local Printability Enhancement (LPTM) tool in an automated flow to eliminate hotspots that can be present on the full chip after conventional SRAF placement/OPC and has been applied in 14nm, 10nm node production, single and multiple-patterning flows.

Training feed-forward neural networks with gain constraints

PubMed

Hartman

2000-04-01

Inaccurate input-output gains (partial derivatives of outputs with respect to inputs) are common in neural network models when input variables are correlated or when data are incomplete or inaccurate. Accurate gains are essential for optimization, control, and other purposes. We develop and explore a method for training feedforward neural networks subject to inequality or equality-bound constraints on the gains of the learned mapping. Gain constraints are implemented as penalty terms added to the objective function, and training is done using gradient descent. Adaptive and robust procedures are devised for balancing the relative strengths of the various terms in the objective function, which is essential when the constraints are inconsistent with the data. The approach has the virtue that the model domain of validity can be extended via extrapolation training, which can dramatically improve generalization. The algorithm is demonstrated here on artificial and real-world problems with very good results and has been advantageously applied to dozens of models currently in commercial use.

A Space Affine Matching Approach to fMRI Time Series Analysis.

PubMed

Chen, Liang; Zhang, Weishi; Liu, Hongbo; Feng, Shigang; Chen, C L Philip; Wang, Huili

2016-07-01

For fMRI time series analysis, an important challenge is to overcome the potential delay between hemodynamic response signal and cognitive stimuli signal, namely the same frequency but different phase (SFDP) problem. In this paper, a novel space affine matching feature is presented by introducing the time domain and frequency domain features. The time domain feature is used to discern different stimuli, while the frequency domain feature to eliminate the delay. And then we propose a space affine matching (SAM) algorithm to match fMRI time series by our affine feature, in which a normal vector is estimated using gradient descent to explore the time series matching optimally. The experimental results illustrate that the SAM algorithm is insensitive to the delay between the hemodynamic response signal and the cognitive stimuli signal. Our approach significantly outperforms GLM method while there exists the delay. The approach can help us solve the SFDP problem in fMRI time series matching and thus of great promise to reveal brain dynamics.

Ptychographic overlap constraint errors and the limits of their numerical recovery using conjugate gradient descent methods.

PubMed

Tripathi, Ashish; McNulty, Ian; Shpyrko, Oleg G

2014-01-27

Ptychographic coherent x-ray diffractive imaging is a form of scanning microscopy that does not require optics to image a sample. A series of scanned coherent diffraction patterns recorded from multiple overlapping illuminated regions on the sample are inverted numerically to retrieve its image. The technique recovers the phase lost by detecting the diffraction patterns by using experimentally known constraints, in this case the measured diffraction intensities and the assumed scan positions on the sample. The spatial resolution of the recovered image of the sample is limited by the angular extent over which the diffraction patterns are recorded and how well these constraints are known. Here, we explore how reconstruction quality degrades with uncertainties in the scan positions. We show experimentally that large errors in the assumed scan positions on the sample can be numerically determined and corrected using conjugate gradient descent methods. We also explore in simulations the limits, based on the signal to noise of the diffraction patterns and amount of overlap between adjacent scan positions, of just how large these errors can be and still be rendered tractable by this method.

Fault-tolerant nonlinear adaptive flight control using sliding mode online learning.

PubMed

Krüger, Thomas; Schnetter, Philipp; Placzek, Robin; Vörsmann, Peter

2012-08-01

An expanded nonlinear model inversion flight control strategy using sliding mode online learning for neural networks is presented. The proposed control strategy is implemented for a small unmanned aircraft system (UAS). This class of aircraft is very susceptible towards nonlinearities like atmospheric turbulence, model uncertainties and of course system failures. Therefore, these systems mark a sensible testbed to evaluate fault-tolerant, adaptive flight control strategies. Within this work the concept of feedback linearization is combined with feed forward neural networks to compensate for inversion errors and other nonlinear effects. Backpropagation-based adaption laws of the network weights are used for online training. Within these adaption laws the standard gradient descent backpropagation algorithm is augmented with the concept of sliding mode control (SMC). Implemented as a learning algorithm, this nonlinear control strategy treats the neural network as a controlled system and allows a stable, dynamic calculation of the learning rates. While considering the system's stability, this robust online learning method therefore offers a higher speed of convergence, especially in the presence of external disturbances. The SMC-based flight controller is tested and compared with the standard gradient descent backpropagation algorithm in the presence of system failures. Copyright © 2012 Elsevier Ltd. All rights reserved.

An online supervised learning method based on gradient descent for spiking neurons.

PubMed

Xu, Yan; Yang, Jing; Zhong, Shuiming

2017-09-01

The purpose of supervised learning with temporal encoding for spiking neurons is to make the neurons emit a specific spike train encoded by precise firing times of spikes. The gradient-descent-based (GDB) learning methods are widely used and verified in the current research. Although the existing GDB multi-spike learning (or spike sequence learning) methods have good performance, they work in an offline manner and still have some limitations. This paper proposes an online GDB spike sequence learning method for spiking neurons that is based on the online adjustment mechanism of real biological neuron synapses. The method constructs error function and calculates the adjustment of synaptic weights as soon as the neurons emit a spike during their running process. We analyze and synthesize desired and actual output spikes to select appropriate input spikes in the calculation of weight adjustment in this paper. The experimental results show that our method obviously improves learning performance compared with the offline learning manner and has certain advantage on learning accuracy compared with other learning methods. Stronger learning ability determines that the method has large pattern storage capacity. Copyright © 2017 Elsevier Ltd. All rights reserved.

On the Convergence Analysis of the Optimized Gradient Method.

PubMed

Kim, Donghwan; Fessler, Jeffrey A

2017-01-01

This paper considers the problem of unconstrained minimization of smooth convex functions having Lipschitz continuous gradients with known Lipschitz constant. We recently proposed the optimized gradient method for this problem and showed that it has a worst-case convergence bound for the cost function decrease that is twice as small as that of Nesterov's fast gradient method, yet has a similarly efficient practical implementation. Drori showed recently that the optimized gradient method has optimal complexity for the cost function decrease over the general class of first-order methods. This optimality makes it important to study fully the convergence properties of the optimized gradient method. The previous worst-case convergence bound for the optimized gradient method was derived for only the last iterate of a secondary sequence. This paper provides an analytic convergence bound for the primary sequence generated by the optimized gradient method. We then discuss additional convergence properties of the optimized gradient method, including the interesting fact that the optimized gradient method has two types of worstcase functions: a piecewise affine-quadratic function and a quadratic function. These results help complete the theory of an optimal first-order method for smooth convex minimization.

On the Convergence Analysis of the Optimized Gradient Method

PubMed Central

Kim, Donghwan; Fessler, Jeffrey A.

2016-01-01

This paper considers the problem of unconstrained minimization of smooth convex functions having Lipschitz continuous gradients with known Lipschitz constant. We recently proposed the optimized gradient method for this problem and showed that it has a worst-case convergence bound for the cost function decrease that is twice as small as that of Nesterov’s fast gradient method, yet has a similarly efficient practical implementation. Drori showed recently that the optimized gradient method has optimal complexity for the cost function decrease over the general class of first-order methods. This optimality makes it important to study fully the convergence properties of the optimized gradient method. The previous worst-case convergence bound for the optimized gradient method was derived for only the last iterate of a secondary sequence. This paper provides an analytic convergence bound for the primary sequence generated by the optimized gradient method. We then discuss additional convergence properties of the optimized gradient method, including the interesting fact that the optimized gradient method has two types of worstcase functions: a piecewise affine-quadratic function and a quadratic function. These results help complete the theory of an optimal first-order method for smooth convex minimization. PMID:28461707

Modeling level change in Lake Urmia using hybrid artificial intelligence approaches

NASA Astrophysics Data System (ADS)

Esbati, M.; Ahmadieh Khanesar, M.; Shahzadi, Ali

2017-06-01

The investigation of water level fluctuations in lakes for protecting them regarding the importance of these water complexes in national and regional scales has found a special place among countries in recent years. The importance of the prediction of water level balance in Lake Urmia is necessary due to several-meter fluctuations in the last decade which help the prevention from possible future losses. For this purpose, in this paper, the performance of adaptive neuro-fuzzy inference system (ANFIS) for predicting the lake water level balance has been studied. In addition, for the training of the adaptive neuro-fuzzy inference system, particle swarm optimization (PSO) and hybrid backpropagation-recursive least square method algorithm have been used. Moreover, a hybrid method based on particle swarm optimization and recursive least square (PSO-RLS) training algorithm for the training of ANFIS structure is introduced. In order to have a more fare comparison, hybrid particle swarm optimization and gradient descent are also applied. The models have been trained, tested, and validated based on lake level data between 1991 and 2014. For performance evaluation, a comparison is made between these methods. Numerical results obtained show that the proposed methods with a reasonable error have a good performance in water level balance prediction. It is also clear that with continuing the current trend, Lake Urmia will experience more drop in the water level balance in the upcoming years.

Peak-Seeking Optimization of Trim for Reduced Fuel Consumption: Architecture and Performance Predictions

NASA Technical Reports Server (NTRS)

Schaefer, Jacob; Brown, Nelson

2013-01-01

A peak-seeking control approach for real-time trim configuration optimization for reduced fuel consumption has been developed by researchers at the National Aeronautics and Space Administration (NASA) Dryden Flight Research Center to address the goals of the NASA Environmentally Responsible Aviation project to reduce fuel burn and emissions. The peak-seeking control approach is based on a steepest-descent algorithm using a time-varying Kalman filter to estimate the gradient of a performance function of fuel flow versus control surface positions. In real-time operation, deflections of symmetric ailerons, trailing-edge flaps, and leading-edge flaps of an FA-18 airplane (McDonnell Douglas, now The Boeing Company, Chicago, Illinois) are controlled for optimization of fuel flow. This presentation presents the design and integration of this peak-seeking controller on a modified NASA FA-18 airplane with research flight control computers. A research flight was performed to collect data to build a realistic model of the performance function and characterize measurement noise. This model was then implemented into a nonlinear six-degree-of-freedom FA-18 simulation along with the peak-seeking control algorithm. With the goal of eventual flight tests, the algorithm was first evaluated in the improved simulation environment. Results from the simulation predict good convergence on minimum fuel flow with a 2.5-percent reduction in fuel flow relative to the baseline trim of the aircraft.

High resolution quantitative phase imaging of live cells with constrained optimization approach

NASA Astrophysics Data System (ADS)

Pandiyan, Vimal Prabhu; Khare, Kedar; John, Renu

2016-03-01

Quantitative phase imaging (QPI) aims at studying weakly scattering and absorbing biological specimens with subwavelength accuracy without any external staining mechanisms. Use of a reference beam at an angle is one of the necessary criteria for recording of high resolution holograms in most of the interferometric methods used for quantitative phase imaging. The spatial separation of the dc and twin images is decided by the reference beam angle and Fourier-filtered reconstructed image will have a very poor resolution if hologram is recorded below a minimum reference angle condition. However, it is always inconvenient to have a large reference beam angle while performing high resolution microscopy of live cells and biological specimens with nanometric features. In this paper, we treat reconstruction of digital holographic microscopy images as a constrained optimization problem with smoothness constraint in order to recover only complex object field in hologram plane even with overlapping dc and twin image terms. We solve this optimization problem by gradient descent approach iteratively and the smoothness constraint is implemented by spatial averaging with appropriate size. This approach will give excellent high resolution image recovery compared to Fourier filtering while keeping a very small reference angle. We demonstrate this approach on digital holographic microscopy of live cells by recovering the quantitative phase of live cells from a hologram recorded with nearly zero reference angle.

Efficient methods for overlapping group lasso.

PubMed

Yuan, Lei; Liu, Jun; Ye, Jieping

2013-09-01

The group Lasso is an extension of the Lasso for feature selection on (predefined) nonoverlapping groups of features. The nonoverlapping group structure limits its applicability in practice. There have been several recent attempts to study a more general formulation where groups of features are given, potentially with overlaps between the groups. The resulting optimization is, however, much more challenging to solve due to the group overlaps. In this paper, we consider the efficient optimization of the overlapping group Lasso penalized problem. We reveal several key properties of the proximal operator associated with the overlapping group Lasso, and compute the proximal operator by solving the smooth and convex dual problem, which allows the use of the gradient descent type of algorithms for the optimization. Our methods and theoretical results are then generalized to tackle the general overlapping group Lasso formulation based on the l(q) norm. We further extend our algorithm to solve a nonconvex overlapping group Lasso formulation based on the capped norm regularization, which reduces the estimation bias introduced by the convex penalty. We have performed empirical evaluations using both a synthetic and the breast cancer gene expression dataset, which consists of 8,141 genes organized into (overlapping) gene sets. Experimental results show that the proposed algorithm is more efficient than existing state-of-the-art algorithms. Results also demonstrate the effectiveness of the nonconvex formulation for overlapping group Lasso.

Peak-Seeking Optimization of Trim for Reduced Fuel Consumption: Architecture and Performance Predictions

NASA Technical Reports Server (NTRS)

Schaefer, Jacob; Brown, Nelson A.

2013-01-01

A peak-seeking control approach for real-time trim configuration optimization for reduced fuel consumption has been developed by researchers at the National Aeronautics and Space Administration (NASA) Dryden Flight Research Center to address the goals of the NASA Environmentally Responsible Aviation project to reduce fuel burn and emissions. The peak-seeking control approach is based on a steepest-descent algorithm using a time-varying Kalman filter to estimate the gradient of a performance function of fuel flow versus control surface positions. In real-time operation, deflections of symmetric ailerons, trailing-edge flaps, and leading-edge flaps of an F/A-18 airplane (McDonnell Douglas, now The Boeing Company, Chicago, Illinois) are controlled for optimization of fuel flow. This paper presents the design and integration of this peak-seeking controller on a modified NASA F/A-18 airplane with research flight control computers. A research flight was performed to collect data to build a realistic model of the performance function and characterize measurement noise. This model was then implemented into a nonlinear six-degree-of-freedom F/A-18 simulation along with the peak-seeking control algorithm. With the goal of eventual flight tests, the algorithm was first evaluated in the improved simulation environment. Results from the simulation predict good convergence on minimum fuel flow with a 2.5-percent reduction in fuel flow relative to the baseline trim of the aircraft.

Design and simulation of a descent controller for strategic four-dimensional aircraft navigation. M.S. Thesis

NASA Technical Reports Server (NTRS)

Lax, F. M.

1975-01-01

A time-controlled navigation system applicable to the descent phase of flight for airline transport aircraft was developed and simulated. The design incorporates the linear discrete-time sampled-data version of the linearized continuous-time system describing the aircraft's aerodynamics. Using optimal linear quadratic control techniques, an optimal deterministic control regulator which is implementable on an airborne computer is designed. The navigation controller assists the pilot in complying with assigned times of arrival along a four-dimensional flight path in the presence of wind disturbances. The strategic air traffic control concept is also described, followed by the design of a strategic control descent path. A strategy for determining possible times of arrival at specified waypoints along the descent path and for generating the corresponding route-time profiles that are within the performance capabilities of the aircraft is presented. Using a mathematical model of the Boeing 707-320B aircraft along with a Boeing 707 cockpit simulator interfaced with an Adage AGT-30 digital computer, a real-time simulation of the complete aircraft aerodynamics was achieved. The strategic four-dimensional navigation controller for longitudinal dynamics was tested on the nonlinear aircraft model in the presence of 15, 30, and 45 knot head-winds. The results indicate that the controller preserved the desired accuracy and precision of a time-controlled aircraft navigation system.

Regression Analysis of Top of Descent Location for Idle-thrust Descents

NASA Technical Reports Server (NTRS)

Stell, Laurel; Bronsvoort, Jesper; McDonald, Greg

2013-01-01

In this paper, multiple regression analysis is used to model the top of descent (TOD) location of user-preferred descent trajectories computed by the flight management system (FMS) on over 1000 commercial flights into Melbourne, Australia. The independent variables cruise altitude, final altitude, cruise Mach, descent speed, wind, and engine type were also recorded or computed post-operations. Both first-order and second-order models are considered, where cross-validation, hypothesis testing, and additional analysis are used to compare models. This identifies the models that should give the smallest errors if used to predict TOD location for new data in the future. A model that is linear in TOD altitude, final altitude, descent speed, and wind gives an estimated standard deviation of 3.9 nmi for TOD location given the trajec- tory parameters, which means about 80% of predictions would have error less than 5 nmi in absolute value. This accuracy is better than demonstrated by other ground automation predictions using kinetic models. Furthermore, this approach would enable online learning of the model. Additional data or further knowl- edge of algorithms is necessary to conclude definitively that no second-order terms are appropriate. Possible applications of the linear model are described, including enabling arriving aircraft to fly optimized descents computed by the FMS even in congested airspace. In particular, a model for TOD location that is linear in the independent variables would enable decision support tool human-machine interfaces for which a kinetic approach would be computationally too slow.

Adaptive Laplacian filtering for sensorimotor rhythm-based brain-computer interfaces.

PubMed

Lu, Jun; McFarland, Dennis J; Wolpaw, Jonathan R

2013-02-01

Sensorimotor rhythms (SMRs) are 8-30 Hz oscillations in the electroencephalogram (EEG) recorded from the scalp over sensorimotor cortex that change with movement and/or movement imagery. Many brain-computer interface (BCI) studies have shown that people can learn to control SMR amplitudes and can use that control to move cursors and other objects in one, two or three dimensions. At the same time, if SMR-based BCIs are to be useful for people with neuromuscular disabilities, their accuracy and reliability must be improved substantially. These BCIs often use spatial filtering methods such as common average reference (CAR), Laplacian (LAP) filter or common spatial pattern (CSP) filter to enhance the signal-to-noise ratio of EEG. Here, we test the hypothesis that a new filter design, called an 'adaptive Laplacian (ALAP) filter', can provide better performance for SMR-based BCIs. An ALAP filter employs a Gaussian kernel to construct a smooth spatial gradient of channel weights and then simultaneously seeks the optimal kernel radius of this spatial filter and the regularization parameter of linear ridge regression. This optimization is based on minimizing the leave-one-out cross-validation error through a gradient descent method and is computationally feasible. Using a variety of kinds of BCI data from a total of 22 individuals, we compare the performances of ALAP filter to CAR, small LAP, large LAP and CSP filters. With a large number of channels and limited data, ALAP performs significantly better than CSP, CAR, small LAP and large LAP both in classification accuracy and in mean-squared error. Using fewer channels restricted to motor areas, ALAP is still superior to CAR, small LAP and large LAP, but equally matched to CSP. Thus, ALAP may help to improve the accuracy and robustness of SMR-based BCIs.

Adaptive Laplacian filtering for sensorimotor rhythm-based brain-computer interfaces

NASA Astrophysics Data System (ADS)

Lu, Jun; McFarland, Dennis J.; Wolpaw, Jonathan R.

2013-02-01

Objective. Sensorimotor rhythms (SMRs) are 8-30 Hz oscillations in the electroencephalogram (EEG) recorded from the scalp over sensorimotor cortex that change with movement and/or movement imagery. Many brain-computer interface (BCI) studies have shown that people can learn to control SMR amplitudes and can use that control to move cursors and other objects in one, two or three dimensions. At the same time, if SMR-based BCIs are to be useful for people with neuromuscular disabilities, their accuracy and reliability must be improved substantially. These BCIs often use spatial filtering methods such as common average reference (CAR), Laplacian (LAP) filter or common spatial pattern (CSP) filter to enhance the signal-to-noise ratio of EEG. Here, we test the hypothesis that a new filter design, called an ‘adaptive Laplacian (ALAP) filter’, can provide better performance for SMR-based BCIs. Approach. An ALAP filter employs a Gaussian kernel to construct a smooth spatial gradient of channel weights and then simultaneously seeks the optimal kernel radius of this spatial filter and the regularization parameter of linear ridge regression. This optimization is based on minimizing the leave-one-out cross-validation error through a gradient descent method and is computationally feasible. Main results. Using a variety of kinds of BCI data from a total of 22 individuals, we compare the performances of ALAP filter to CAR, small LAP, large LAP and CSP filters. With a large number of channels and limited data, ALAP performs significantly better than CSP, CAR, small LAP and large LAP both in classification accuracy and in mean-squared error. Using fewer channels restricted to motor areas, ALAP is still superior to CAR, small LAP and large LAP, but equally matched to CSP. Significance. Thus, ALAP may help to improve the accuracy and robustness of SMR-based BCIs.

Sparse Recovery via l1 and L1 Optimization

DTIC Science & Technology

2014-11-01

problem, with t being the descent direc- tion, obtaining ut = uxx + f − 1 µ p(u) (6) as an evolution equation. We can hope that these L1 regularized (or...implementation. He considered a wide class of second–order elliptic equations and, with Friedman [14], an extension to parabolic equa- tions. In [15, 16...obtaining an elliptic PDE, or by gradi- ent descent to obtain a parabolic PDE. Addition- ally, some PDEs can be rewritten using the L1 subgradient such as the

Design optimization of single mixed refrigerant LNG process using a hybrid modified coordinate descent algorithm

NASA Astrophysics Data System (ADS)

Qyyum, Muhammad Abdul; Long, Nguyen Van Duc; Minh, Le Quang; Lee, Moonyong

2018-01-01

Design optimization of the single mixed refrigerant (SMR) natural gas liquefaction (LNG) process involves highly non-linear interactions between decision variables, constraints, and the objective function. These non-linear interactions lead to an irreversibility, which deteriorates the energy efficiency of the LNG process. In this study, a simple and highly efficient hybrid modified coordinate descent (HMCD) algorithm was proposed to cope with the optimization of the natural gas liquefaction process. The single mixed refrigerant process was modeled in Aspen Hysys® and then connected to a Microsoft Visual Studio environment. The proposed optimization algorithm provided an improved result compared to the other existing methodologies to find the optimal condition of the complex mixed refrigerant natural gas liquefaction process. By applying the proposed optimization algorithm, the SMR process can be designed with the 0.2555 kW specific compression power which is equivalent to 44.3% energy saving as compared to the base case. Furthermore, in terms of coefficient of performance (COP), it can be enhanced up to 34.7% as compared to the base case. The proposed optimization algorithm provides a deep understanding of the optimization of the liquefaction process in both technical and numerical perspectives. In addition, the HMCD algorithm can be employed to any mixed refrigerant based liquefaction process in the natural gas industry.

Risk-Constrained Dynamic Programming for Optimal Mars Entry, Descent, and Landing

NASA Technical Reports Server (NTRS)

Ono, Masahiro; Kuwata, Yoshiaki

2013-01-01

A chance-constrained dynamic programming algorithm was developed that is capable of making optimal sequential decisions within a user-specified risk bound. This work handles stochastic uncertainties over multiple stages in the CEMAT (Combined EDL-Mobility Analyses Tool) framework. It was demonstrated by a simulation of Mars entry, descent, and landing (EDL) using real landscape data obtained from the Mars Reconnaissance Orbiter. Although standard dynamic programming (DP) provides a general framework for optimal sequential decisionmaking under uncertainty, it typically achieves risk aversion by imposing an arbitrary penalty on failure states. Such a penalty-based approach cannot explicitly bound the probability of mission failure. A key idea behind the new approach is called risk allocation, which decomposes a joint chance constraint into a set of individual chance constraints and distributes risk over them. The joint chance constraint was reformulated into a constraint on an expectation over a sum of an indicator function, which can be incorporated into the cost function by dualizing the optimization problem. As a result, the chance-constraint optimization problem can be turned into an unconstrained optimization over a Lagrangian, which can be solved efficiently using a standard DP approach.

Shape regularized active contour based on dynamic programming for anatomical structure segmentation

NASA Astrophysics Data System (ADS)

Yu, Tianli; Luo, Jiebo; Singhal, Amit; Ahuja, Narendra

2005-04-01

We present a method to incorporate nonlinear shape prior constraints into segmenting different anatomical structures in medical images. Kernel space density estimation (KSDE) is used to derive the nonlinear shape statistics and enable building a single model for a class of objects with nonlinearly varying shapes. The object contour is coerced by image-based energy into the correct shape sub-distribution (e.g., left or right lung), without the need for model selection. In contrast to an earlier algorithm that uses a local gradient-descent search (susceptible to local minima), we propose an algorithm that iterates between dynamic programming (DP) and shape regularization. DP is capable of finding an optimal contour in the search space that maximizes a cost function related to the difference between the interior and exterior of the object. To enforce the nonlinear shape prior, we propose two shape regularization methods, global and local regularization. Global regularization is applied after each DP search to move the entire shape vector in the shape space in a gradient descent fashion to the position of probable shapes learned from training. The regularized shape is used as the starting shape for the next iteration. Local regularization is accomplished through modifying the search space of the DP. The modified search space only allows a certain amount of deformation of the local shape from the starting shape. Both regularization methods ensure the consistency between the resulted shape with the training shapes, while still preserving DP"s ability to search over a large range and avoid local minima. Our algorithm was applied to two different segmentation tasks for radiographic images: lung field and clavicle segmentation. Both applications have shown that our method is effective and versatile in segmenting various anatomical structures under prior shape constraints; and it is robust to noise and local minima caused by clutter (e.g., blood vessels) and other similar structures (e.g., ribs). We believe that the proposed algorithm represents a major step in the paradigm shift to object segmentation under nonlinear shape constraints.

An Approach to Unbiased Subsample Interpolation for Motion Tracking

PubMed Central

McCormick, Matthew M.; Varghese, Tomy

2013-01-01

Accurate subsample displacement estimation is necessary for ultrasound elastography because of the small deformations that occur and the subsequent application of a derivative operation on local displacements. Many of the commonly used subsample estimation techniques introduce significant bias errors. This article addresses a reduced bias approach to subsample displacement estimations that consists of a two-dimensional windowed-sinc interpolation with numerical optimization. It is shown that a Welch or Lanczos window with a Nelder–Mead simplex or regular-step gradient-descent optimization is well suited for this purpose. Little improvement results from a sinc window radius greater than four data samples. The strain signal-to-noise ratio (SNR) obtained in a uniformly elastic phantom is compared with other parabolic and cosine interpolation methods; it is found that the strain SNR ratio is improved over parabolic interpolation from 11.0 to 13.6 in the axial direction and 0.7 to 1.1 in the lateral direction for an applied 1% axial deformation. The improvement was most significant for small strains and displacement tracking in the lateral direction. This approach does not rely on special properties of the image or similarity function, which is demonstrated by its effectiveness with the application of a previously described regularization technique. PMID:23493609

Adaptive Batch Mode Active Learning.

PubMed

Chakraborty, Shayok; Balasubramanian, Vineeth; Panchanathan, Sethuraman

2015-08-01

Active learning techniques have gained popularity to reduce human effort in labeling data instances for inducing a classifier. When faced with large amounts of unlabeled data, such algorithms automatically identify the exemplar and representative instances to be selected for manual annotation. More recently, there have been attempts toward a batch mode form of active learning, where a batch of data points is simultaneously selected from an unlabeled set. Real-world applications require adaptive approaches for batch selection in active learning, depending on the complexity of the data stream in question. However, the existing work in this field has primarily focused on static or heuristic batch size selection. In this paper, we propose two novel optimization-based frameworks for adaptive batch mode active learning (BMAL), where the batch size as well as the selection criteria are combined in a single formulation. We exploit gradient-descent-based optimization strategies as well as properties of submodular functions to derive the adaptive BMAL algorithms. The solution procedures have the same computational complexity as existing state-of-the-art static BMAL techniques. Our empirical results on the widely used VidTIMIT and the mobile biometric (MOBIO) data sets portray the efficacy of the proposed frameworks and also certify the potential of these approaches in being used for real-world biometric recognition applications.

PSO-Assisted Development of New Transferable Coarse-Grained Water Models.

PubMed

Bejagam, Karteek K; Singh, Samrendra; An, Yaxin; Berry, Carter; Deshmukh, Sanket A

2018-02-15

We have employed two-to-one mapping scheme to develop three coarse-grained (CG) water models, namely, 1-, 2-, and 3-site CG models. Here, for the first time, particle swarm optimization (PSO) and gradient descent methods were coupled to optimize the force-field parameters of the CG models to reproduce the density, self-diffusion coefficient, and dielectric constant of real water at 300 K. The CG MD simulations of these new models conducted with various timesteps, for different system sizes, and at a range of different temperatures are able to predict the density, self-diffusion coefficient, dielectric constant, surface tension, heat of vaporization, hydration free energy, and isothermal compressibility of real water with excellent accuracy. The 1-site model is ∼3 and ∼4.5 times computationally more efficient than 2- and 3-site models, respectively. To utilize the speed of 1-site model and electrostatic interactions offered by 2- and 3-site models, CG MD simulations of 1:1 combination of 1- and 2-/3-site models were performed at 300 K. These mixture simulations could also predict the properties of real water with good accuracy. Two new CG models of benzene, consisting of beads with and without partial charges, were developed. All three water models showed good capacity to solvate these benzene models.

A finite-element toolbox for the stationary Gross-Pitaevskii equation with rotation

NASA Astrophysics Data System (ADS)

Vergez, Guillaume; Danaila, Ionut; Auliac, Sylvain; Hecht, Frédéric

2016-12-01

We present a new numerical system using classical finite elements with mesh adaptivity for computing stationary solutions of the Gross-Pitaevskii equation. The programs are written as a toolbox for FreeFem++ (www.freefem.org), a free finite-element software available for all existing operating systems. This offers the advantage to hide all technical issues related to the implementation of the finite element method, allowing to easily code various numerical algorithms. Two robust and optimized numerical methods were implemented to minimize the Gross-Pitaevskii energy: a steepest descent method based on Sobolev gradients and a minimization algorithm based on the state-of-the-art optimization library Ipopt. For both methods, mesh adaptivity strategies are used to reduce the computational time and increase the local spatial accuracy when vortices are present. Different run cases are made available for 2D and 3D configurations of Bose-Einstein condensates in rotation. An optional graphical user interface is also provided, allowing to easily run predefined cases or with user-defined parameter files. We also provide several post-processing tools (like the identification of quantized vortices) that could help in extracting physical features from the simulations. The toolbox is extremely versatile and can be easily adapted to deal with different physical models.

Distributed Method to Optimal Profile Descent

NASA Astrophysics Data System (ADS)

Kim, Geun I.

Current ground automation tools for Optimal Profile Descent (OPD) procedures utilize path stretching and speed profile change to maintain proper merging and spacing requirements at high traffic terminal area. However, low predictability of aircraft's vertical profile and path deviation during decent add uncertainty to computing estimated time of arrival, a key information that enables the ground control center to manage airspace traffic effectively. This paper uses an OPD procedure that is based on a constant flight path angle to increase the predictability of the vertical profile and defines an OPD optimization problem that uses both path stretching and speed profile change while largely maintaining the original OPD procedure. This problem minimizes the cumulative cost of performing OPD procedures for a group of aircraft by assigning a time cost function to each aircraft and a separation cost function to a pair of aircraft. The OPD optimization problem is then solved in a decentralized manner using dual decomposition techniques under inter-aircraft ADS-B mechanism. This method divides the optimization problem into more manageable sub-problems which are then distributed to the group of aircraft. Each aircraft solves its assigned sub-problem and communicate the solutions to other aircraft in an iterative process until an optimal solution is achieved thus decentralizing the computation of the optimization problem.

Analysis of Flight Management System Predictions of Idle-Thrust Descents

NASA Technical Reports Server (NTRS)

Stell, Laurel

2010-01-01

To enable arriving aircraft to fly optimized descents computed by the flight management system (FMS) in congested airspace, ground automation must accurately predict descent trajectories. To support development of the predictor and its uncertainty models, descents from cruise to the meter fix were executed using vertical navigation in a B737-700 simulator and a B777-200 simulator, both with commercial FMSs. For both aircraft types, the FMS computed the intended descent path for a specified speed profile assuming idle thrust after top of descent (TOD), and then it controlled the avionics without human intervention. The test matrix varied aircraft weight, descent speed, and wind conditions. The first analysis in this paper determined the effect of the test matrix parameters on the FMS computation of TOD location, and it compared the results to those for the current ground predictor in the Efficient Descent Advisor (EDA). The second analysis was similar but considered the time to fly a specified distance to the meter fix. The effects of the test matrix variables together with the accuracy requirements for the predictor will determine the allowable error for the predictor inputs. For the B737, the EDA prediction of meter fix crossing time agreed well with the FMS; but its prediction of TOD location probably was not sufficiently accurate to enable idle-thrust descents in congested airspace, even though the FMS and EDA gave similar shapes for TOD location as a function of the test matrix variables. For the B777, the FMS and EDA gave different shapes for the TOD location function, and the EDA prediction of the TOD location is not accurate enough to fully enable the concept. Furthermore, the differences between the FMS and EDA predictions of meter fix crossing time for the B777 indicated that at least one of them was not sufficiently accurate.

Flight Testing of Terrain-Relative Navigation and Large-Divert Guidance on a VTVL Rocket

NASA Technical Reports Server (NTRS)

Trawny, Nikolas; Benito, Joel; Tweddle, Brent; Bergh, Charles F.; Khanoyan, Garen; Vaughan, Geoffrey M.; Zheng, Jason X.; Villalpando, Carlos Y.; Cheng, Yang; Scharf, Daniel P.;

Nonlinear Performance Seeking Control using Fuzzy Model Reference Learning Control and the Method of Steepest Descent

NASA Technical Reports Server (NTRS)

Kopasakis, George

1997-01-01

Performance Seeking Control (PSC) attempts to find and control the process at the operating condition that will generate maximum performance. In this paper a nonlinear multivariable PSC methodology will be developed, utilizing the Fuzzy Model Reference Learning Control (FMRLC) and the method of Steepest Descent or Gradient (SDG). This PSC control methodology employs the SDG method to find the operating condition that will generate maximum performance. This operating condition is in turn passed to the FMRLC controller as a set point for the control of the process. The conventional SDG algorithm is modified in this paper in order for convergence to occur monotonically. For the FMRLC control, the conventional fuzzy model reference learning control methodology is utilized, with guidelines generated here for effective tuning of the FMRLC controller.

Recursive least-squares learning algorithms for neural networks

NASA Astrophysics Data System (ADS)

Lewis, Paul S.; Hwang, Jenq N.

1990-11-01

This paper presents the development of a pair of recursive least squares (ItLS) algorithms for online training of multilayer perceptrons which are a class of feedforward artificial neural networks. These algorithms incorporate second order information about the training error surface in order to achieve faster learning rates than are possible using first order gradient descent algorithms such as the generalized delta rule. A least squares formulation is derived from a linearization of the training error function. Individual training pattern errors are linearized about the network parameters that were in effect when the pattern was presented. This permits the recursive solution of the least squares approximation either via conventional RLS recursions or by recursive QR decomposition-based techniques. The computational complexity of the update is 0(N2) where N is the number of network parameters. This is due to the estimation of the N x N inverse Hessian matrix. Less computationally intensive approximations of the ilLS algorithms can be easily derived by using only block diagonal elements of this matrix thereby partitioning the learning into independent sets. A simulation example is presented in which a neural network is trained to approximate a two dimensional Gaussian bump. In this example RLS training required an order of magnitude fewer iterations on average (527) than did training with the generalized delta rule (6 1 BACKGROUND Artificial neural networks (ANNs) offer an interesting and potentially useful paradigm for signal processing and pattern recognition. The majority of ANN applications employ the feed-forward multilayer perceptron (MLP) network architecture in which network parameters are " trained" by a supervised learning algorithm employing the generalized delta rule (GDIt) [1 2]. The GDR algorithm approximates a fixed step steepest descent algorithm using derivatives computed by error backpropagatiori. The GDII algorithm is sometimes referred to as the backpropagation algorithm. However in this paper we will use the term backpropagation to refer only to the process of computing error derivatives. While multilayer perceptrons provide a very powerful nonlinear modeling capability GDR training can be very slow and inefficient. In linear adaptive filtering the analog of the GDR algorithm is the leastmean- squares (LMS) algorithm. Steepest descent-based algorithms such as GDR or LMS are first order because they use only first derivative or gradient information about the training error to be minimized. To speed up the training process second order algorithms may be employed that take advantage of second derivative or Hessian matrix information. Second order information can be incorporated into MLP training in different ways. In many applications especially in the area of pattern recognition the training set is finite. In these cases block learning can be applied using standard nonlinear optimization techniques [3 4 5].

SU-E-T-503: IMRT Optimization Using Monte Carlo Dose Engine: The Effect of Statistical Uncertainty.

PubMed

Tian, Z; Jia, X; Graves, Y; Uribe-Sanchez, A; Jiang, S

2012-06-01

With the development of ultra-fast GPU-based Monte Carlo (MC) dose engine, it becomes clinically realistic to compute the dose-deposition coefficients (DDC) for IMRT optimization using MC simulation. However, it is still time-consuming if we want to compute DDC with small statistical uncertainty. This work studies the effects of the statistical error in DDC matrix on IMRT optimization. The MC-computed DDC matrices are simulated here by adding statistical uncertainties at a desired level to the ones generated with a finite-size pencil beam algorithm. A statistical uncertainty model for MC dose calculation is employed. We adopt a penalty-based quadratic optimization model and gradient descent method to optimize fluence map and then recalculate the corresponding actual dose distribution using the noise-free DDC matrix. The impacts of DDC noise are assessed in terms of the deviation of the resulted dose distributions. We have also used a stochastic perturbation theory to theoretically estimate the statistical errors of dose distributions on a simplified optimization model. A head-and-neck case is used to investigate the perturbation to IMRT plan due to MC's statistical uncertainty. The relative errors of the final dose distributions of the optimized IMRT are found to be much smaller than those in the DDC matrix, which is consistent with our theoretical estimation. When history number is decreased from 108 to 106, the dose-volume-histograms are still very similar to the error-free DVHs while the error in DDC is about 3.8%. The results illustrate that the statistical errors in the DDC matrix have a relatively small effect on IMRT optimization in dose domain. This indicates we can use relatively small number of histories to obtain the DDC matrix with MC simulation within a reasonable amount of time, without considerably compromising the accuracy of the optimized treatment plan. This work is supported by Varian Medical Systems through a Master Research Agreement. © 2012 American Association of Physicists in Medicine.

Analysis of a New Variational Model to Restore Point-Like and Curve-Like Singularities in Imaging

DOE Office of Scientific and Technical Information (OSTI.GOV)

Aubert, Gilles, E-mail: gaubert@unice.fr; Blanc-Feraud, Laure, E-mail: Laure.Blanc-Feraud@inria.fr; Graziani, Daniele, E-mail: Daniele.Graziani@inria.fr

2013-02-15

The paper is concerned with the analysis of a new variational model to restore point-like and curve-like singularities in biological images. To this aim we investigate the variational properties of a suitable energy which governs these pathologies. Finally in order to realize numerical experiments we minimize, in the discrete setting, a regularized version of this functional by fast descent gradient scheme.

On Nonconvex Decentralized Gradient Descent

DTIC Science & Technology

2016-08-01

and J. Bolte, On the convergence of the proximal algorithm for nonsmooth functions involving analytic features, Math . Program., 116: 5-16, 2009. [2] H...splitting, and regularized Gauss-Seidel methods, Math . Pro- gram., Ser. A, 137: 91-129, 2013. [3] P. Bianchi and J. Jakubowicz, Convergence of a multi-agent...subgradient method under random communication topologies , IEEE J. Sel. Top. Signal Process., 5:754-771, 2011. [11] A. Nedic and A. Ozdaglar, Distributed

Understanding the Convolutional Neural Networks with Gradient Descent and Backpropagation

NASA Astrophysics Data System (ADS)

Zhou, XueFei

2018-04-01

With the development of computer technology, the applications of machine learning are more and more extensive. And machine learning is providing endless opportunities to develop new applications. One of those applications is image recognition by using Convolutional Neural Networks (CNNs). CNN is one of the most common algorithms in image recognition. It is significant to understand its theory and structure for every scholar who is interested in this field. CNN is mainly used in computer identification, especially in voice, text recognition and other aspects of the application. It utilizes hierarchical structure with different layers to accelerate computing speed. In addition, the greatest features of CNNs are the weight sharing and dimension reduction. And all of these consolidate the high effectiveness and efficiency of CNNs with idea computing speed and error rate. With the help of other learning altruisms, CNNs could be used in several scenarios for machine learning, especially for deep learning. Based on the general introduction to the background and the core solution CNN, this paper is going to focus on summarizing how Gradient Descent and Backpropagation work, and how they contribute to the high performances of CNNs. Also, some practical applications will be discussed in the following parts. The last section exhibits the conclusion and some perspectives of future work.

Applying Gradient Descent in Convolutional Neural Networks

NASA Astrophysics Data System (ADS)

Cui, Nan

2018-04-01

With the development of the integrated circuit and computer science, people become caring more about solving practical issues via information technologies. Along with that, a new subject called Artificial Intelligent (AI) comes up. One popular research interest of AI is about recognition algorithm. In this paper, one of the most common algorithms, Convolutional Neural Networks (CNNs) will be introduced, for image recognition. Understanding its theory and structure is of great significance for every scholar who is interested in this field. Convolution Neural Network is an artificial neural network which combines the mathematical method of convolution and neural network. The hieratical structure of CNN provides it reliable computer speed and reasonable error rate. The most significant characteristics of CNNs are feature extraction, weight sharing and dimension reduction. Meanwhile, combining with the Back Propagation (BP) mechanism and the Gradient Descent (GD) method, CNNs has the ability to self-study and in-depth learning. Basically, BP provides an opportunity for backwardfeedback for enhancing reliability and GD is used for self-training process. This paper mainly discusses the CNN and the related BP and GD algorithms, including the basic structure and function of CNN, details of each layer, the principles and features of BP and GD, and some examples in practice with a summary in the end.

A Dictionary Learning Approach with Overlap for the Low Dose Computed Tomography Reconstruction and Its Vectorial Application to Differential Phase Tomography

PubMed Central

Mirone, Alessandro; Brun, Emmanuel; Coan, Paola

2014-01-01

X-ray based Phase-Contrast Imaging (PCI) techniques have been demonstrated to enhance the visualization of soft tissues in comparison to conventional imaging methods. Nevertheless the delivered dose as reported in the literature of biomedical PCI applications often equals or exceeds the limits prescribed in clinical diagnostics. The optimization of new computed tomography strategies which include the development and implementation of advanced image reconstruction procedures is thus a key aspect. In this scenario, we implemented a dictionary learning method with a new form of convex functional. This functional contains in addition to the usual sparsity inducing and fidelity terms, a new term which forces similarity between overlapping patches in the superimposed regions. The functional depends on two free regularization parameters: a coefficient multiplying the sparsity-inducing norm of the patch basis functions coefficients, and a coefficient multiplying the norm of the differences between patches in the overlapping regions. The solution is found by applying the iterative proximal gradient descent method with FISTA acceleration. The gradient is computed by calculating projection of the solution and its error backprojection at each iterative step. We study the quality of the solution, as a function of the regularization parameters and noise, on synthetic data for which the solution is a-priori known. We apply the method on experimental data in the case of Differential Phase Tomography. For this case we use an original approach which consists in using vectorial patches, each patch having two components: one per each gradient component. The resulting algorithm, implemented in the European Synchrotron Radiation Facility tomography reconstruction code PyHST, has proven to be efficient and well-adapted to strongly reduce the required dose and the number of projections in medical tomography. PMID:25531987

A dictionary learning approach with overlap for the low dose computed tomography reconstruction and its vectorial application to differential phase tomography.

PubMed

Mirone, Alessandro; Brun, Emmanuel; Coan, Paola

2014-01-01

X-ray based Phase-Contrast Imaging (PCI) techniques have been demonstrated to enhance the visualization of soft tissues in comparison to conventional imaging methods. Nevertheless the delivered dose as reported in the literature of biomedical PCI applications often equals or exceeds the limits prescribed in clinical diagnostics. The optimization of new computed tomography strategies which include the development and implementation of advanced image reconstruction procedures is thus a key aspect. In this scenario, we implemented a dictionary learning method with a new form of convex functional. This functional contains in addition to the usual sparsity inducing and fidelity terms, a new term which forces similarity between overlapping patches in the superimposed regions. The functional depends on two free regularization parameters: a coefficient multiplying the sparsity-inducing L1 norm of the patch basis functions coefficients, and a coefficient multiplying the L2 norm of the differences between patches in the overlapping regions. The solution is found by applying the iterative proximal gradient descent method with FISTA acceleration. The gradient is computed by calculating projection of the solution and its error backprojection at each iterative step. We study the quality of the solution, as a function of the regularization parameters and noise, on synthetic data for which the solution is a-priori known. We apply the method on experimental data in the case of Differential Phase Tomography. For this case we use an original approach which consists in using vectorial patches, each patch having two components: one per each gradient component. The resulting algorithm, implemented in the European Synchrotron Radiation Facility tomography reconstruction code PyHST, has proven to be efficient and well-adapted to strongly reduce the required dose and the number of projections in medical tomography.

Evaluation of vertical profiles to design continuous descent approach procedure

NASA Astrophysics Data System (ADS)

Pradeep, Priyank

The current research focuses on predictability, variability and operational feasibility aspect of Continuous Descent Approach (CDA), which is among the key concepts of the Next Generation Air Transportation System (NextGen). The idle-thrust CDA is a fuel economical, noise and emission abatement procedure, but requires increased separation to accommodate for variability and uncertainties in vertical and speed profiles of arriving aircraft. Although a considerable amount of researches have been devoted to the estimation of potential benefits of the CDA, only few have attempted to explain the predictability, variability and operational feasibility aspect of CDA. The analytical equations derived using flight dynamics and Base of Aircraft and Data (BADA) Total Energy Model (TEM) in this research gives insight into dependency of vertical profile of CDA on various factors like wind speed and gradient, weight, aircraft type and configuration, thrust settings, atmospheric factors (deviation from ISA (DISA), pressure and density of the air) and descent speed profile. Application of the derived equations to idle-thrust CDA gives an insight into sensitivity of its vertical profile to multiple factors. This suggests fixed geometric flight path angle (FPA) CDA has higher degree of predictability and lesser variability at the cost of non-idle and low thrust engine settings. However, with optimized design this impact can be overall minimized. The CDA simulations were performed using Future ATM Concept Evaluation Tool (FACET) based on radar-track and aircraft type data (BADA) of the real air-traffic to some of the busiest airports in the USA (ATL, SFO and New York Metroplex (JFK, EWR and LGA)). The statistical analysis of the vertical profiles of CDA shows 1) mean geometric FPAs derived from various simulated vertical profiles are consistently shallower than 3° glideslope angle and 2) high level of variability in vertical profiles of idle-thrust CDA even in absence of uncertainties in external factors. Analysis from operational feasibility perspective suggests that two key features of the performance based Flight Management System (FMS) i.e. required time of arrival (RTA) and geometric descent path would help in reduction of unpredictability associated with arrival time and vertical profile of aircraft guided by the FMS coupled with auto-pilot (AP) and auto-throttle (AT). The statistical analysis of the vertical profiles of CDA also suggests that for procedure design window type, 'AT or above' and 'AT or below' altitude and FPA constraints are more realistic and useful compared to obsolete 'AT' type altitude constraint.

Improving the FLORIS wind plant model for compatibility with gradient-based optimization

DOE Office of Scientific and Technical Information (OSTI.GOV)

Thomas, Jared J.; Gebraad, Pieter MO; Ning, Andrew

The FLORIS (FLOw Redirection and Induction in Steady-state) model, a parametric wind turbine wake model that predicts steady-state wake characteristics based on wind turbine position and yaw angle, was developed for optimization of control settings and turbine locations. This article provides details on changes made to the FLORIS model to make the model more suitable for gradient-based optimization. Changes to the FLORIS model were made to remove discontinuities and add curvature to regions of non-physical zero gradient. Exact gradients for the FLORIS model were obtained using algorithmic differentiation. A set of three case studies demonstrate that using exact gradients withmore » gradient-based optimization reduces the number of function calls by several orders of magnitude. The case studies also show that adding curvature improves convergence behavior, allowing gradient-based optimization algorithms used with the FLORIS model to more reliably find better solutions to wind farm optimization problems.« less

Scalable Nonparametric Low-Rank Kernel Learning Using Block Coordinate Descent.

PubMed

Hu, En-Liang; Kwok, James T

2015-09-01

Nonparametric kernel learning (NPKL) is a flexible approach to learn the kernel matrix directly without assuming any parametric form. It can be naturally formulated as a semidefinite program (SDP), which, however, is not very scalable. To address this problem, we propose the combined use of low-rank approximation and block coordinate descent (BCD). Low-rank approximation avoids the expensive positive semidefinite constraint in the SDP by replacing the kernel matrix variable with V(T)V, where V is a low-rank matrix. The resultant nonlinear optimization problem is then solved by BCD, which optimizes each column of V sequentially. It can be shown that the proposed algorithm has nice convergence properties and low computational complexities. Experiments on a number of real-world data sets show that the proposed algorithm outperforms state-of-the-art NPKL solvers.

River suspended sediment estimation by climatic variables implication: Comparative study among soft computing techniques

NASA Astrophysics Data System (ADS)

Kisi, Ozgur; Shiri, Jalal

2012-06-01

Estimating sediment volume carried by a river is an important issue in water resources engineering. This paper compares the accuracy of three different soft computing methods, Artificial Neural Networks (ANNs), Adaptive Neuro-Fuzzy Inference System (ANFIS), and Gene Expression Programming (GEP), in estimating daily suspended sediment concentration on rivers by using hydro-meteorological data. The daily rainfall, streamflow and suspended sediment concentration data from Eel River near Dos Rios, at California, USA are used as a case study. The comparison results indicate that the GEP model performs better than the other models in daily suspended sediment concentration estimation for the particular data sets used in this study. Levenberg-Marquardt, conjugate gradient and gradient descent training algorithms were used for the ANN models. Out of three algorithms, the Conjugate gradient algorithm was found to be better than the others.

Learning Structured Classifiers with Dual Coordinate Ascent

DTIC Science & Technology

2010-06-01

stochastic gradient descent (SGD) [LeCun et al., 1998], and the margin infused relaxed algorithm (MIRA) [ Crammer et al., 2006]. This paper presents a...evaluate these methods on the Prague Dependency Treebank us- ing online large-margin learning tech- niques ( Crammer et al., 2003; McDonald et al., 2005...between two kinds of factors: hard constraint factors, which are used to rule out forbidden par- tial assignments by mapping them to zero potential values

A network of spiking neurons for computing sparse representations in an energy efficient way

PubMed Central

Hu, Tao; Genkin, Alexander; Chklovskii, Dmitri B.

2013-01-01

Computing sparse redundant representations is an important problem both in applied mathematics and neuroscience. In many applications, this problem must be solved in an energy efficient way. Here, we propose a hybrid distributed algorithm (HDA), which solves this problem on a network of simple nodes communicating via low-bandwidth channels. HDA nodes perform both gradient-descent-like steps on analog internal variables and coordinate-descent-like steps via quantized external variables communicated to each other. Interestingly, such operation is equivalent to a network of integrate-and-fire neurons, suggesting that HDA may serve as a model of neural computation. We compare the numerical performance of HDA with existing algorithms and show that in the asymptotic regime the representation error of HDA decays with time, t, as 1/t. We show that HDA is stable against time-varying noise, specifically, the representation error decays as 1/t for Gaussian white noise. PMID:22920853

A network of spiking neurons for computing sparse representations in an energy-efficient way.

PubMed

Hu, Tao; Genkin, Alexander; Chklovskii, Dmitri B

2012-11-01

Computing sparse redundant representations is an important problem in both applied mathematics and neuroscience. In many applications, this problem must be solved in an energy-efficient way. Here, we propose a hybrid distributed algorithm (HDA), which solves this problem on a network of simple nodes communicating by low-bandwidth channels. HDA nodes perform both gradient-descent-like steps on analog internal variables and coordinate-descent-like steps via quantized external variables communicated to each other. Interestingly, the operation is equivalent to a network of integrate-and-fire neurons, suggesting that HDA may serve as a model of neural computation. We show that the numerical performance of HDA is on par with existing algorithms. In the asymptotic regime, the representation error of HDA decays with time, t, as 1/t. HDA is stable against time-varying noise; specifically, the representation error decays as 1/√t for gaussian white noise.

Live Speech Driven Head-and-Eye Motion Generators.

PubMed

Le, Binh H; Ma, Xiaohan; Deng, Zhigang

2012-11-01

This paper describes a fully automated framework to generate realistic head motion, eye gaze, and eyelid motion simultaneously based on live (or recorded) speech input. Its central idea is to learn separate yet interrelated statistical models for each component (head motion, gaze, or eyelid motion) from a prerecorded facial motion data set: 1) Gaussian Mixture Models and gradient descent optimization algorithm are employed to generate head motion from speech features; 2) Nonlinear Dynamic Canonical Correlation Analysis model is used to synthesize eye gaze from head motion and speech features, and 3) nonnegative linear regression is used to model voluntary eye lid motion and log-normal distribution is used to describe involuntary eye blinks. Several user studies are conducted to evaluate the effectiveness of the proposed speech-driven head and eye motion generator using the well-established paired comparison methodology. Our evaluation results clearly show that this approach can significantly outperform the state-of-the-art head and eye motion generation algorithms. In addition, a novel mocap+video hybrid data acquisition technique is introduced to record high-fidelity head movement, eye gaze, and eyelid motion simultaneously.

Identification and control of plasma vertical position using neural network in Damavand tokamak.

PubMed

Rasouli, H; Rasouli, C; Koohi, A

2013-02-01

In this work, a nonlinear model is introduced to determine the vertical position of the plasma column in Damavand tokamak. Using this model as a simulator, a nonlinear neural network controller has been designed. In the first stage, the electronic drive and sensory circuits of Damavand tokamak are modified. These circuits can control the vertical position of the plasma column inside the vacuum vessel. Since the vertical position of plasma is an unstable parameter, a direct closed loop system identification algorithm is performed. In the second stage, a nonlinear model is identified for plasma vertical position, based on the multilayer perceptron (MLP) neural network (NN) structure. Estimation of simulator parameters has been performed by back-propagation error algorithm using Levenberg-Marquardt gradient descent optimization technique. The model is verified through simulation of the whole closed loop system using both simulator and actual plant in similar conditions. As the final stage, a MLP neural network controller is designed for simulator model. In the last step, online training is performed to tune the controller parameters. Simulation results justify using of the NN controller for the actual plant.

Approximate N-Player Nonzero-Sum Game Solution for an Uncertain Continuous Nonlinear System.

PubMed

Johnson, Marcus; Kamalapurkar, Rushikesh; Bhasin, Shubhendu; Dixon, Warren E

2015-08-01

An approximate online equilibrium solution is developed for an N -player nonzero-sum game subject to continuous-time nonlinear unknown dynamics and an infinite horizon quadratic cost. A novel actor-critic-identifier structure is used, wherein a robust dynamic neural network is used to asymptotically identify the uncertain system with additive disturbances, and a set of critic and actor NNs are used to approximate the value functions and equilibrium policies, respectively. The weight update laws for the actor neural networks (NNs) are generated using a gradient-descent method, and the critic NNs are generated by least square regression, which are both based on the modified Bellman error that is independent of the system dynamics. A Lyapunov-based stability analysis shows that uniformly ultimately bounded tracking is achieved, and a convergence analysis demonstrates that the approximate control policies converge to a neighborhood of the optimal solutions. The actor, critic, and identifier structures are implemented in real time continuously and simultaneously. Simulations on two and three player games illustrate the performance of the developed method.

Waveform inversion with source encoding for breast sound speed reconstruction in ultrasound computed tomography.

PubMed

Wang, Kun; Matthews, Thomas; Anis, Fatima; Li, Cuiping; Duric, Neb; Anastasio, Mark A

2015-03-01

Ultrasound computed tomography (USCT) holds great promise for improving the detection and management of breast cancer. Because they are based on the acoustic wave equation, waveform inversion-based reconstruction methods can produce images that possess improved spatial resolution properties over those produced by ray-based methods. However, waveform inversion methods are computationally demanding and have not been applied widely in USCT breast imaging. In this work, source encoding concepts are employed to develop an accelerated USCT reconstruction method that circumvents the large computational burden of conventional waveform inversion methods. This method, referred to as the waveform inversion with source encoding (WISE) method, encodes the measurement data using a random encoding vector and determines an estimate of the sound speed distribution by solving a stochastic optimization problem by use of a stochastic gradient descent algorithm. Both computer simulation and experimental phantom studies are conducted to demonstrate the use of the WISE method. The results suggest that the WISE method maintains the high spatial resolution of waveform inversion methods while significantly reducing the computational burden.

A new fitting method for measurement of the curvature radius of a short arc with high precision

NASA Astrophysics Data System (ADS)

Tao, Wei; Zhong, Hong; Chen, Xiao; Selami, Yassine; Zhao, Hui

2018-07-01

The measurement of an object with a short arc is widely encountered in scientific research and industrial production. As the most classic method of arc fitting, the least squares fitting method suffers from low precision when it is used for measurement of arcs with smaller central angles and fewer sampling points. The shorter the arc, the lower is the measurement accuracy. In order to improve the measurement precision of short arcs, a parameter constrained fitting method based on a four-parameter circle equation is proposed in this paper. The generalized Lagrange function was introduced together with the optimization by gradient descent method to reduce the influence from noise. The simulation and experimental results showed that the proposed method has high precision even when the central angle drops below 4° and it has good robustness when the noise standard deviation rises to 0.4 mm. This new fitting method is suitable for the high precision measurement of short arcs with smaller central angles without any prior information.

Quaternion-valued echo state networks.

PubMed

Xia, Yili; Jahanchahi, Cyrus; Mandic, Danilo P

2015-04-01

Quaternion-valued echo state networks (QESNs) are introduced to cater for 3-D and 4-D processes, such as those observed in the context of renewable energy (3-D wind modeling) and human centered computing (3-D inertial body sensors). The introduction of QESNs is made possible by the recent emergence of quaternion nonlinear activation functions with local analytic properties, required by nonlinear gradient descent training algorithms. To make QENSs second-order optimal for the generality of quaternion signals (both circular and noncircular), we employ augmented quaternion statistics to introduce widely linear QESNs. To that end, the standard widely linear model is modified so as to suit the properties of dynamical reservoir, typically realized by recurrent neural networks. This allows for a full exploitation of second-order information in the data, contained both in the covariance and pseudocovariances, and a rigorous account of second-order noncircularity (improperness), and the corresponding power mismatch and coupling between the data components. Simulations in the prediction setting on both benchmark circular and noncircular signals and on noncircular real-world 3-D body motion data support the analysis.

Control optimization, stabilization and computer algorithms for aircraft applications

NASA Technical Reports Server (NTRS)

1975-01-01

Research related to reliable aircraft design is summarized. Topics discussed include systems reliability optimization, failure detection algorithms, analysis of nonlinear filters, design of compensators incorporating time delays, digital compensator design, estimation for systems with echoes, low-order compensator design, descent-phase controller for 4-D navigation, infinite dimensional mathematical programming problems and optimal control problems with constraints, robust compensator design, numerical methods for the Lyapunov equations, and perturbation methods in linear filtering and control.

Incorporating uncertainty and motion in Intensity Modulated Radiation Therapy treatment planning

NASA Astrophysics Data System (ADS)

Martin, Benjamin Charles

In radiation therapy, one seeks to destroy a tumor while minimizing the damage to surrounding healthy tissue. Intensity Modulated Radiation Therapy (IMRT) uses overlapping beams of x-rays that add up to a high dose within the target and a lower dose in the surrounding healthy tissue. IMRT relies on optimization techniques to create high quality treatments. Unfortunately, the possible conformality is limited by the need to ensure coverage even if there is organ movement or deformation. Currently, margins are added around the tumor to ensure coverage based on an assumed motion range. This approach does not ensure high quality treatments. In the standard IMRT optimization problem, an objective function measures the deviation of the dose from the clinical goals. The optimization then finds the beamlet intensities that minimize the objective function. When modeling uncertainty, the dose delivered from a given set of beamlet intensities is a random variable. Thus the objective function is also a random variable. In our stochastic formulation we minimize the expected value of this objective function. We developed a problem formulation that is both flexible and fast enough for use on real clinical cases. While working on accelerating the stochastic optimization, we developed a technique of voxel sampling. Voxel sampling is a randomized algorithms approach to a steepest descent problem based on estimating the gradient by only calculating the dose to a fraction of the voxels within the patient. When combined with an automatic sampling rate adaptation technique, voxel sampling produced an order of magnitude speed up in IMRT optimization. We also develop extensions of our results to Intensity Modulated Proton Therapy (IMPT). Due to the physics of proton beams the stochastic formulation yields visibly different and better plans than normal optimization. The results of our research have been incorporated into a software package OPT4D, which is an IMRT and IMPT optimization tool that we developed.

Study of fail-safe abort system for an actively cooled hypersonic aircraft, volume 2

NASA Technical Reports Server (NTRS)

Peeples, M. E.; Herring, R. L.

1976-01-01

Conceptual designs of a fail-safe abort system for hydrogen fueled actively cooled high speed aircraft are examined. The fail-safe concept depends on basically three factors: (1) a reliable method of detecting a failure or malfunction in the active cooling system, (2) the optimization of abort trajectories which minimize the descent heat load to the aircraft, and (3) fail-safe thermostructural concepts to minimize both the weight and the maximum temperature the structure will reach during descent. These factors are examined and promising approaches are evaluated based on weight, reliability, ease of manufacture and cost.

Dynamic metrology and data processing for precision freeform optics fabrication and testing

NASA Astrophysics Data System (ADS)

Aftab, Maham; Trumper, Isaac; Huang, Lei; Choi, Heejoo; Zhao, Wenchuan; Graves, Logan; Oh, Chang Jin; Kim, Dae Wook

2017-06-01

Dynamic metrology holds the key to overcoming several challenging limitations of conventional optical metrology, especially with regards to precision freeform optical elements. We present two dynamic metrology systems: 1) adaptive interferometric null testing; and 2) instantaneous phase shifting deflectometry, along with an overview of a gradient data processing and surface reconstruction technique. The adaptive null testing method, utilizing a deformable mirror, adopts a stochastic parallel gradient descent search algorithm in order to dynamically create a null testing condition for unknown freeform optics. The single-shot deflectometry system implemented on an iPhone uses a multiplexed display pattern to enable dynamic measurements of time-varying optical components or optics in vibration. Experimental data, measurement accuracy / precision, and data processing algorithms are discussed.

Structural optimization with approximate sensitivities

NASA Technical Reports Server (NTRS)

Patnaik, S. N.; Hopkins, D. A.; Coroneos, R.

1994-01-01

Computational efficiency in structural optimization can be enhanced if the intensive computations associated with the calculation of the sensitivities, that is, gradients of the behavior constraints, are reduced. Approximation to gradients of the behavior constraints that can be generated with small amount of numerical calculations is proposed. Structural optimization with these approximate sensitivities produced correct optimum solution. Approximate gradients performed well for different nonlinear programming methods, such as the sequence of unconstrained minimization technique, method of feasible directions, sequence of quadratic programming, and sequence of linear programming. Structural optimization with approximate gradients can reduce by one third the CPU time that would otherwise be required to solve the problem with explicit closed-form gradients. The proposed gradient approximation shows potential to reduce intensive computation that has been associated with traditional structural optimization.

A Relation Between the Eikonal Equation Associated to a Potential Energy Surface and a Hyperbolic Wave Equation.

PubMed

Bofill, Josep Maria; Quapp, Wolfgang; Caballero, Marc

2012-12-11

The potential energy surface (PES) of a molecule can be decomposed into equipotential hypersurfaces. We show in this article that the hypersurfaces are the wave fronts of a certain hyperbolic partial differential equation, a wave equation. It is connected with the gradient lines, or the steepest descent, or the steepest ascent lines of the PES. The energy seen as a reaction coordinate plays the central role in this treatment.

Fast and Accurate Poisson Denoising With Trainable Nonlinear Diffusion.

PubMed

Feng, Wensen; Qiao, Peng; Chen, Yunjin; Wensen Feng; Peng Qiao; Yunjin Chen; Feng, Wensen; Chen, Yunjin; Qiao, Peng

2018-06-01

The degradation of the acquired signal by Poisson noise is a common problem for various imaging applications, such as medical imaging, night vision, and microscopy. Up to now, many state-of-the-art Poisson denoising techniques mainly concentrate on achieving utmost performance, with little consideration for the computation efficiency. Therefore, in this paper we aim to propose an efficient Poisson denoising model with both high computational efficiency and recovery quality. To this end, we exploit the newly developed trainable nonlinear reaction diffusion (TNRD) model which has proven an extremely fast image restoration approach with performance surpassing recent state-of-the-arts. However, the straightforward direct gradient descent employed in the original TNRD-based denoising task is not applicable in this paper. To solve this problem, we resort to the proximal gradient descent method. We retrain the model parameters, including the linear filters and influence functions by taking into account the Poisson noise statistics, and end up with a well-trained nonlinear diffusion model specialized for Poisson denoising. The trained model provides strongly competitive results against state-of-the-art approaches, meanwhile bearing the properties of simple structure and high efficiency. Furthermore, our proposed model comes along with an additional advantage, that the diffusion process is well-suited for parallel computation on graphics processing units (GPUs). For images of size , our GPU implementation takes less than 0.1 s to produce state-of-the-art Poisson denoising performance.

Quantitative assessment in thermal image segmentation for artistic objects

NASA Astrophysics Data System (ADS)

Yousefi, Bardia; Sfarra, Stefano; Maldague, Xavier P. V.

2017-07-01

The application of the thermal and infrared technology in different areas of research is considerably increasing. These applications involve Non-destructive Testing (NDT), Medical analysis (Computer Aid Diagnosis/Detection- CAD), Arts and Archaeology among many others. In the arts and archaeology field, infrared technology provides significant contributions in term of finding defects of possible impaired regions. This has been done through a wide range of different thermographic experiments and infrared methods. The proposed approach here focuses on application of some known factor analysis methods such as standard Non-Negative Matrix Factorization (NMF) optimized by gradient-descent-based multiplicative rules (SNMF1) and standard NMF optimized by Non-negative least squares (NNLS) active-set algorithm (SNMF2) and eigen decomposition approaches such as Principal Component Thermography (PCT), Candid Covariance-Free Incremental Principal Component Thermography (CCIPCT) to obtain the thermal features. On one hand, these methods are usually applied as preprocessing before clustering for the purpose of segmentation of possible defects. On the other hand, a wavelet based data fusion combines the data of each method with PCT to increase the accuracy of the algorithm. The quantitative assessment of these approaches indicates considerable segmentation along with the reasonable computational complexity. It shows the promising performance and demonstrated a confirmation for the outlined properties. In particular, a polychromatic wooden statue and a fresco were analyzed using the above mentioned methods and interesting results were obtained.

A different approach to estimate nonlinear regression model using numerical methods

NASA Astrophysics Data System (ADS)

Mahaboob, B.; Venkateswarlu, B.; Mokeshrayalu, G.; Balasiddamuni, P.

2017-11-01

This research paper concerns with the computational methods namely the Gauss-Newton method, Gradient algorithm methods (Newton-Raphson method, Steepest Descent or Steepest Ascent algorithm method, the Method of Scoring, the Method of Quadratic Hill-Climbing) based on numerical analysis to estimate parameters of nonlinear regression model in a very different way. Principles of matrix calculus have been used to discuss the Gradient-Algorithm methods. Yonathan Bard [1] discussed a comparison of gradient methods for the solution of nonlinear parameter estimation problems. However this article discusses an analytical approach to the gradient algorithm methods in a different way. This paper describes a new iterative technique namely Gauss-Newton method which differs from the iterative technique proposed by Gorden K. Smyth [2]. Hans Georg Bock et.al [10] proposed numerical methods for parameter estimation in DAE’s (Differential algebraic equation). Isabel Reis Dos Santos et al [11], Introduced weighted least squares procedure for estimating the unknown parameters of a nonlinear regression metamodel. For large-scale non smooth convex minimization the Hager and Zhang (HZ) conjugate gradient Method and the modified HZ (MHZ) method were presented by Gonglin Yuan et al [12].

Flight-Deck Strategies and Outcomes When Flying Schedule-Matching Descents

NASA Technical Reports Server (NTRS)

Kaneshige, John T.; Sharma, Shivanjli; Martin Lynne; Lozito, Sandra; Dulchinos, Victoria

2013-01-01

Recent studies at NASA Ames Research Center have investigated the development and use of ground-based (air traffic controller) tools to manage and schedule air traffic in future terminal airspace. An exploratory study was undertaken to investigate the impacts that such tools (and concepts) could have on the flight-deck. Ten Boeing 747-400 crews flew eight optimized profile descents in the Los Angeles terminal airspace, while receiving scripted current day and futuristic speed clearances, to ascertain their ability to fly schedulematching descents without prior training. Although the study was exploratory in nature, four variables were manipulated: route constraints, winds, speed changes, and clearance phraseology. Despite flying the same scenarios with the same events and timing, there were significant differences in the time it took crews to fly the approaches. This variation is the product of a number of factors but highlights potential difficulties for scheduling tools that would have to accommodate this amount of natural variation in descent times. The focus of this paper is the examination of the crews' aircraft management strategies and outcomes. This includes potentially problematic human-automation interaction issues that may negatively impact arrival times, speed and altitude constraint compliance, and energy management efficiency.

77 FR 71735 - Minimum Altitudes for Use of Autopilots

Federal Register 2010, 2011, 2012, 2013, 2014

2012-12-04

... Generation Air Transportation System (NextGen) technologies and procedures (Optimized Profile Descents... altitudes for use of autopilots were unduly restrictive and would limit the ability to use new technologies..., including the rise of new technologies.'' [[Page 71736

WE-AB-209-09: Optimization of Rotational Arc Station Parameter Optimized Radiation Therapy

DOE Office of Scientific and Technical Information (OSTI.GOV)

Dong, P; Xing, L; Ungun, B

Purpose: To develop a fast optimization method for station parameter optimized radiation therapy (SPORT) and show that SPORT is capable of improving VMAT in both plan quality and delivery efficiency. Methods: The angular space from 0° to 360° was divided into 180 station points (SPs). A candidate aperture was assigned to each of the SPs based on the calculation results using a column generation algorithm. The weights of the apertures were then obtained by optimizing the objective function using a state-of-the-art GPU based Proximal Operator Graph Solver (POGS) within seconds. Apertures with zero or low weight were thrown out. Tomore » avoid being trapped in a local minimum, a stochastic gradient descent method was employed which also greatly increased the convergence rate of the objective function. The above procedure repeated until the plan could not be improved any further. A weighting factor associated with the total plan MU also indirectly controlled the complexities of aperture shapes. The number of apertures for VMAT and SPORT was confined to 180. The SPORT allowed the coexistence of multiple apertures in a single SP. The optimization technique was assessed by using three clinical cases (prostate, H&N and brain). Results: Marked dosimetric quality improvement was demonstrated in the SPORT plans for all three studied cases. Prostate case: the volume of the 50% prescription dose was decreased by 22% for the rectum. H&N case: SPORT improved the mean dose for the left and right parotids by 15% each. Brain case: the doses to the eyes, chiasm and inner ears were all improved. SPORT shortened the treatment time by ∼1 min for the prostate case, ∼0.5 min for brain case, and ∼0.2 min for the H&N case. Conclusion: The superior dosimetric quality and delivery efficiency presented here indicates that SPORT is an intriguing alternative treatment modality.« less

Fast and robust estimation of spectro-temporal receptive fields using stochastic approximations.

PubMed

Meyer, Arne F; Diepenbrock, Jan-Philipp; Ohl, Frank W; Anemüller, Jörn

2015-05-15

The receptive field (RF) represents the signal preferences of sensory neurons and is the primary analysis method for understanding sensory coding. While it is essential to estimate a neuron's RF, finding numerical solutions to increasingly complex RF models can become computationally intensive, in particular for high-dimensional stimuli or when many neurons are involved. Here we propose an optimization scheme based on stochastic approximations that facilitate this task. The basic idea is to derive solutions on a random subset rather than computing the full solution on the available data set. To test this, we applied different optimization schemes based on stochastic gradient descent (SGD) to both the generalized linear model (GLM) and a recently developed classification-based RF estimation approach. Using simulated and recorded responses, we demonstrate that RF parameter optimization based on state-of-the-art SGD algorithms produces robust estimates of the spectro-temporal receptive field (STRF). Results on recordings from the auditory midbrain demonstrate that stochastic approximations preserve both predictive power and tuning properties of STRFs. A correlation of 0.93 with the STRF derived from the full solution may be obtained in less than 10% of the full solution's estimation time. We also present an on-line algorithm that allows simultaneous monitoring of STRF properties of more than 30 neurons on a single computer. The proposed approach may not only prove helpful for large-scale recordings but also provides a more comprehensive characterization of neural tuning in experiments than standard tuning curves. Copyright © 2015 Elsevier B.V. All rights reserved.

Modeling error PDF optimization based wavelet neural network modeling of dynamic system and its application in blast furnace ironmaking

DOE Office of Scientific and Technical Information (OSTI.GOV)

Zhou, Ping; Wang, Chenyu; Li, Mingjie

In general, the modeling errors of dynamic system model are a set of random variables. The traditional performance index of modeling such as means square error (MSE) and root means square error (RMSE) can not fully express the connotation of modeling errors with stochastic characteristics both in the dimension of time domain and space domain. Therefore, the probability density function (PDF) is introduced to completely describe the modeling errors in both time scales and space scales. Based on it, a novel wavelet neural network (WNN) modeling method is proposed by minimizing the two-dimensional (2D) PDF shaping of modeling errors. First,more » the modeling error PDF by the tradional WNN is estimated using data-driven kernel density estimation (KDE) technique. Then, the quadratic sum of 2D deviation between the modeling error PDF and the target PDF is utilized as performance index to optimize the WNN model parameters by gradient descent method. Since the WNN has strong nonlinear approximation and adaptive capability, and all the parameters are well optimized by the proposed method, the developed WNN model can make the modeling error PDF track the target PDF, eventually. Simulation example and application in a blast furnace ironmaking process show that the proposed method has a higher modeling precision and better generalization ability compared with the conventional WNN modeling based on MSE criteria. Furthermore, the proposed method has more desirable estimation for modeling error PDF that approximates to a Gaussian distribution whose shape is high and narrow.« less

Modeling error PDF optimization based wavelet neural network modeling of dynamic system and its application in blast furnace ironmaking

DOE Office of Scientific and Technical Information (OSTI.GOV)

Zhou, Ping; Wang, Chenyu; Li, Mingjie

In general, the modeling errors of dynamic system model are a set of random variables. The traditional performance index of modeling such as means square error (MSE) and root means square error (RMSE) cannot fully express the connotation of modeling errors with stochastic characteristics both in the dimension of time domain and space domain. Therefore, the probability density function (PDF) is introduced to completely describe the modeling errors in both time scales and space scales. Based on it, a novel wavelet neural network (WNN) modeling method is proposed by minimizing the two-dimensional (2D) PDF shaping of modeling errors. First, themore » modeling error PDF by the traditional WNN is estimated using data-driven kernel density estimation (KDE) technique. Then, the quadratic sum of 2D deviation between the modeling error PDF and the target PDF is utilized as performance index to optimize the WNN model parameters by gradient descent method. Since the WNN has strong nonlinear approximation and adaptive capability, and all the parameters are well optimized by the proposed method, the developed WNN model can make the modeling error PDF track the target PDF, eventually. Simulation example and application in a blast furnace ironmaking process show that the proposed method has a higher modeling precision and better generalization ability compared with the conventional WNN modeling based on MSE criteria. However, the proposed method has more desirable estimation for modeling error PDF that approximates to a Gaussian distribution whose shape is high and narrow.« less

Modeling error PDF optimization based wavelet neural network modeling of dynamic system and its application in blast furnace ironmaking

DOE PAGES

Zhou, Ping; Wang, Chenyu; Li, Mingjie; ...

2018-01-31

In general, the modeling errors of dynamic system model are a set of random variables. The traditional performance index of modeling such as means square error (MSE) and root means square error (RMSE) cannot fully express the connotation of modeling errors with stochastic characteristics both in the dimension of time domain and space domain. Therefore, the probability density function (PDF) is introduced to completely describe the modeling errors in both time scales and space scales. Based on it, a novel wavelet neural network (WNN) modeling method is proposed by minimizing the two-dimensional (2D) PDF shaping of modeling errors. First, themore » modeling error PDF by the traditional WNN is estimated using data-driven kernel density estimation (KDE) technique. Then, the quadratic sum of 2D deviation between the modeling error PDF and the target PDF is utilized as performance index to optimize the WNN model parameters by gradient descent method. Since the WNN has strong nonlinear approximation and adaptive capability, and all the parameters are well optimized by the proposed method, the developed WNN model can make the modeling error PDF track the target PDF, eventually. Simulation example and application in a blast furnace ironmaking process show that the proposed method has a higher modeling precision and better generalization ability compared with the conventional WNN modeling based on MSE criteria. However, the proposed method has more desirable estimation for modeling error PDF that approximates to a Gaussian distribution whose shape is high and narrow.« less

Flight Planning

NASA Technical Reports Server (NTRS)

1991-01-01

Seagull Technology, Inc., Sunnyvale, CA, produced a computer program under a Langley Research Center Small Business Innovation Research (SBIR) grant called STAFPLAN (Seagull Technology Advanced Flight Plan) that plans optimal trajectory routes for small to medium sized airlines to minimize direct operating costs while complying with various airline operating constraints. STAFPLAN incorporates four input databases, weather, route data, aircraft performance, and flight-specific information (times, payload, crew, fuel cost) to provide the correct amount of fuel optimal cruise altitude, climb and descent points, optimal cruise speed, and flight path.

Optimal autorotational descent of a helicopter with control and state inequality constraints

NASA Technical Reports Server (NTRS)

Lee, Allan Y.

1990-01-01

A point-mass model of the OH-58A helicopter has been used to ascertain the autorotation profiles which minimize helicopter impact velocity while remaining within the bounds of the main rotor's collective pitch and angular speed. The optimal control strategies are comparable to those employed by pilots in autorotational landings. It is noted that a possibility exists for the reduction of the height-sink rate restriction zone of OH-58A helicopters, using optimal energy-management techniques.

The Double Star Orbit Initial Value Problem

NASA Astrophysics Data System (ADS)

Hensley, Hagan

2018-04-01

Many precise algorithms exist to find a best-fit orbital solution for a double star system given a good enough initial value. Desmos is an online graphing calculator tool with extensive capabilities to support animations and defining functions. It can provide a useful visual means of analyzing double star data to arrive at a best guess approximation of the orbital solution. This is a necessary requirement before using a gradient-descent algorithm to find the best-fit orbital solution for a binary system.

Learning in Modular Systems

DTIC Science & Technology

2010-05-07

important for deep modular systems is that taking a series of small update steps and stopping before convergence, so called early stopping, is a form of regu...larization around the initial parameters of the system . For example, the stochastic gradient descent 5 1 u + 1 v = 1 6‖x2‖q = ‖x‖22q 22 Chapter 2...Aside from the overall speed of the classifier, no quantitative performance analysis was given, and the role played by the features in the larger system

Dynamic load balancing algorithm for molecular dynamics based on Voronoi cells domain decompositions

DOE Office of Scientific and Technical Information (OSTI.GOV)

Fattebert, J.-L.; Richards, D.F.; Glosli, J.N.

2012-12-01

We present a new algorithm for automatic parallel load balancing in classical molecular dynamics. It assumes a spatial domain decomposition of particles into Voronoi cells. It is a gradient method which attempts to minimize a cost function by displacing Voronoi sites associated with each processor/sub-domain along steepest descent directions. Excellent load balance has been obtained for quasi-2D and 3D practical applications, with up to 440·10 6 particles on 65,536 MPI tasks.

Differential Frequency Hopping (DFH) Modulation for Underwater Acoustic Communications and Networking

DTIC Science & Technology

2009-10-09

trains the coefficients c of a finite impulse response (FIR) filter by gradient descent. The coefficients at iteration k + 1 are computed with the update... absorption . Figure 9 shows the reflection loss as a function of grazing angle for this bottom model. Note that below 30◦ this bottom model predicts...less than 1 dB loss per ray bounce. 11 Figure 9: Jackson bottom reflection loss for sand at 15 kHz Absorption Loss The absorption loss in the medium was

Study of a fail-safe abort system for an actively cooled hypersonic aircraft. Volume 1: Technical summary

NASA Technical Reports Server (NTRS)

Pirello, C. J.; Herring, R. L.

1976-01-01

Conceptual designs of a fail-safe abort system for hydrogen fueled actively cooled high speed aircraft are examined. The fail-safe concept depends on basically three factors: (1) a reliable method of detecting a failure or malfunction in the active cooling system, (2) the optimization of abort trajectories which minimize the descent heat load to the aircraft, and (3) fail-safe thermostructural concepts to minimize both the weight and the maximum temperature the structure will reach during descent. These factors are examined and promising approaches are evaluated based on weight, reliability, ease of manufacture and cost.

On the usefulness of gradient information in multi-objective deformable image registration using a B-spline-based dual-dynamic transformation model: comparison of three optimization algorithms

NASA Astrophysics Data System (ADS)

Pirpinia, Kleopatra; Bosman, Peter A. N.; Sonke, Jan-Jakob; van Herk, Marcel; Alderliesten, Tanja

2015-03-01

The use of gradient information is well-known to be highly useful in single-objective optimization-based image registration methods. However, its usefulness has not yet been investigated for deformable image registration from a multi-objective optimization perspective. To this end, within a previously introduced multi-objective optimization framework, we use a smooth B-spline-based dual-dynamic transformation model that allows us to derive gradient information analytically, while still being able to account for large deformations. Within the multi-objective framework, we previously employed a powerful evolutionary algorithm (EA) that computes and advances multiple outcomes at once, resulting in a set of solutions (a so-called Pareto front) that represents efficient trade-offs between the objectives. With the addition of the B-spline-based transformation model, we studied the usefulness of gradient information in multiobjective deformable image registration using three different optimization algorithms: the (gradient-less) EA, a gradientonly algorithm, and a hybridization of these two. We evaluated the algorithms to register highly deformed images: 2D MRI slices of the breast in prone and supine positions. Results demonstrate that gradient-based multi-objective optimization significantly speeds up optimization in the initial stages of optimization. However, allowing sufficient computational resources, better results could still be obtained with the EA. Ultimately, the hybrid EA found the best overall approximation of the optimal Pareto front, further indicating that adding gradient-based optimization for multiobjective optimization-based deformable image registration can indeed be beneficial

Dai-Kou type conjugate gradient methods with a line search only using gradient.

PubMed

Huang, Yuanyuan; Liu, Changhe

2017-01-01

In this paper, the Dai-Kou type conjugate gradient methods are developed to solve the optimality condition of an unconstrained optimization, they only utilize gradient information and have broader application scope. Under suitable conditions, the developed methods are globally convergent. Numerical tests and comparisons with the PRP+ conjugate gradient method only using gradient show that the methods are efficient.

Acceleration of Convergence to Equilibrium in Markov Chains by Breaking Detailed Balance

NASA Astrophysics Data System (ADS)

Kaiser, Marcus; Jack, Robert L.; Zimmer, Johannes

2017-07-01

We analyse and interpret the effects of breaking detailed balance on the convergence to equilibrium of conservative interacting particle systems and their hydrodynamic scaling limits. For finite systems of interacting particles, we review existing results showing that irreversible processes converge faster to their steady state than reversible ones. We show how this behaviour appears in the hydrodynamic limit of such processes, as described by macroscopic fluctuation theory, and we provide a quantitative expression for the acceleration of convergence in this setting. We give a geometrical interpretation of this acceleration, in terms of currents that are antisymmetric under time-reversal and orthogonal to the free energy gradient, which act to drive the system away from states where (reversible) gradient-descent dynamics result in slow convergence to equilibrium.

Smart-Divert Powered Descent Guidance to Avoid the Backshell Landing Dispersion Ellipse

NASA Technical Reports Server (NTRS)

Carson, John M.; Acikmese, Behcet

2013-01-01

A smart-divert capability has been added into the Powered Descent Guidance (PDG) software originally developed for Mars pinpoint and precision landing. The smart-divert algorithm accounts for the landing dispersions of the entry backshell, which separates from the lander vehicle at the end of the parachute descent phase and prior to powered descent. The smart-divert PDG algorithm utilizes the onboard fuel and vehicle thrust vectoring to mitigate landing error in an intelligent way: ensuring that the lander touches down with minimum- fuel usage at the minimum distance from the desired landing location that also avoids impact by the descending backshell. The smart-divert PDG software implements a computationally efficient, convex formulation of the powered-descent guidance problem to provide pinpoint or precision-landing guidance solutions that are fuel-optimal and satisfy physical thrust bound and pointing constraints, as well as position and speed constraints. The initial smart-divert implementation enforced a lateral-divert corridor parallel to the ground velocity vector; this was based on guidance requirements for MSL (Mars Science Laboratory) landings. This initial method was overly conservative since the divert corridor was infinite in the down-range direction despite the backshell landing inside a calculable dispersion ellipse. Basing the divert constraint instead on a local tangent to the backshell dispersion ellipse in the direction of the desired landing site provides a far less conservative constraint. The resulting enhanced smart-divert PDG algorithm avoids impact with the descending backshell and has reduced conservatism.

Switching neuronal state: optimal stimuli revealed using a stochastically-seeded gradient algorithm.

PubMed

Chang, Joshua; Paydarfar, David

2014-12-01

Inducing a switch in neuronal state using energy optimal stimuli is relevant to a variety of problems in neuroscience. Analytical techniques from optimal control theory can identify such stimuli; however, solutions to the optimization problem using indirect variational approaches can be elusive in models that describe neuronal behavior. Here we develop and apply a direct gradient-based optimization algorithm to find stimulus waveforms that elicit a change in neuronal state while minimizing energy usage. We analyze standard models of neuronal behavior, the Hodgkin-Huxley and FitzHugh-Nagumo models, to show that the gradient-based algorithm: (1) enables automated exploration of a wide solution space, using stochastically generated initial waveforms that converge to multiple locally optimal solutions; and (2) finds optimal stimulus waveforms that achieve a physiological outcome condition, without a priori knowledge of the optimal terminal condition of all state variables. Analysis of biological systems using stochastically-seeded gradient methods can reveal salient dynamical mechanisms underlying the optimal control of system behavior. The gradient algorithm may also have practical applications in future work, for example, finding energy optimal waveforms for therapeutic neural stimulation that minimizes power usage and diminishes off-target effects and damage to neighboring tissue.

Stationary-phase optimized selectivity liquid chromatography: development of a linear gradient prediction algorithm.

PubMed

De Beer, Maarten; Lynen, Fréderic; Chen, Kai; Ferguson, Paul; Hanna-Brown, Melissa; Sandra, Pat

2010-03-01

Stationary-phase optimized selectivity liquid chromatography (SOS-LC) is a tool in reversed-phase LC (RP-LC) to optimize the selectivity for a given separation by combining stationary phases in a multisegment column. The presently (commercially) available SOS-LC optimization procedure and algorithm are only applicable to isocratic analyses. Step gradient SOS-LC has been developed, but this is still not very elegant for the analysis of complex mixtures composed of components covering a broad hydrophobicity range. A linear gradient prediction algorithm has been developed allowing one to apply SOS-LC as a generic RP-LC optimization method. The algorithm allows operation in isocratic, stepwise, and linear gradient run modes. The features of SOS-LC in the linear gradient mode are demonstrated by means of a mixture of 13 steroids, whereby baseline separation is predicted and experimentally demonstrated.

Performance Analysis and Design Synthesis (PADS) computer program. Volume 1: Formulation

NASA Technical Reports Server (NTRS)

1972-01-01

The program formulation for PADS computer program is presented. It can size launch vehicles in conjunction with calculus-of-variations optimal trajectories and can also be used as a general-purpose branched trajectory optimization program. In the former use, it has the Space Shuttle Synthesis Program as well as a simplified stage weight module for optimally sizing manned recoverable launch vehicles. For trajectory optimization alone or with sizing, PADS has two trajectory modules. The first trajectory module uses the method of steepest descent; the second employs the method of quasilinearization, which requires a starting solution from the first trajectory module.

Titan Explorer Entry, Descent and Landing Trajectory Design

NASA Technical Reports Server (NTRS)

Fisher, Jody L.; Lindberg, Robert E.; Lockwood, Mary Kae

2006-01-01

The Titan Explorer mission concept includes an orbiter, entry probe and inflatable airship designed to take remote and in-situ measurements of Titan's atmosphere. A modified entry, descent and landing trajectory at Titan that incorporates mid-air airship inflation (under a parachute) and separation is developed and examined for Titan Explorer. The feasibility of mid-air inflation and deployment of an airship under a parachute is determined by implementing and validating an airship buoyancy and inflation model in the trajectory simulation program, Program to Optimize Simulated Trajectories II (POST2). A nominal POST2 trajectory simulation case study is generated which examines different descent scenarios by varying airship inflation duration, orientation, and separation. The buoyancy model incorporation into POST2 is new to the software and may be used in future trajectory simulations. Each case from the nominal POST2 trajectory case study simulates a successful separation between the parachute and airship systems with sufficient velocity change as to alter their paths to avoid collision throughout their descent. The airship and heatshield also separate acceptably with a minimum distance of separation from the parachute system of 1.5 km. This analysis shows the feasibility of airship inflation on a parachute for different orientations, airship separation at various inflation times, and preparation for level-flight at Titan.

Breast ultrasound computed tomography using waveform inversion with source encoding

NASA Astrophysics Data System (ADS)

Wang, Kun; Matthews, Thomas; Anis, Fatima; Li, Cuiping; Duric, Neb; Anastasio, Mark A.

2015-03-01

Ultrasound computed tomography (USCT) holds great promise for improving the detection and management of breast cancer. Because they are based on the acoustic wave equation, waveform inversion-based reconstruction methods can produce images that possess improved spatial resolution properties over those produced by ray-based methods. However, waveform inversion methods are computationally demanding and have not been applied widely in USCT breast imaging. In this work, source encoding concepts are employed to develop an accelerated USCT reconstruction method that circumvents the large computational burden of conventional waveform inversion methods. This method, referred to as the waveform inversion with source encoding (WISE) method, encodes the measurement data using a random encoding vector and determines an estimate of the speed-of-sound distribution by solving a stochastic optimization problem by use of a stochastic gradient descent algorithm. Computer-simulation studies are conducted to demonstrate the use of the WISE method. Using a single graphics processing unit card, each iteration can be completed within 25 seconds for a 128 × 128 mm2 reconstruction region. The results suggest that the WISE method maintains the high spatial resolution of waveform inversion methods while significantly reducing the computational burden.

A coronagraph based on two spatial light modulators for active amplitude apodizing and phase corrections

NASA Astrophysics Data System (ADS)

Dou, Jiangpei; Ren, Deqing; Zhang, Xi; Zhu, Yongtian; Zhao, Gang; Wu, Zhen; Chen, Rui; Liu, Chengchao; Yang, Feng; Yang, Chao

2014-08-01

Almost all high-contrast imaging coronagraphs proposed until now are based on passive coronagraph optical components. Recently, Ren and Zhu proposed for the first time a coronagraph that integrates a liquid crystal array (LCA) for the active pupil apodizing and a deformable mirror (DM) for the phase corrections. Here, for demonstration purpose, we present the initial test result of a coronagraphic system that is based on two liquid crystal spatial light modulators (SLM). In the system, one SLM is served as active pupil apodizing and amplitude correction to suppress the diffraction light; another SLM is used to correct the speckle noise that is caused by the wave-front distortions. In this way, both amplitude and phase error can be actively and efficiently compensated. In the test, we use the stochastic parallel gradient descent (SPGD) algorithm to control two SLMs, which is based on the point spread function (PSF) sensing and evaluation and optimized for a maximum contrast in the discovery area. Finally, it has demonstrated a contrast of 10-6 at an inner working angular distance of ~6.2 λ/D, which is a promising technique to be used for the direct imaging of young exoplanets on ground-based telescopes.

An Improved Variational Method for Hyperspectral Image Pansharpening with the Constraint of Spectral Difference Minimization

NASA Astrophysics Data System (ADS)

Huang, Z.; Chen, Q.; Shen, Y.; Chen, Q.; Liu, X.

2017-09-01

Variational pansharpening can enhance the spatial resolution of a hyperspectral (HS) image using a high-resolution panchromatic (PAN) image. However, this technology may lead to spectral distortion that obviously affect the accuracy of data analysis. In this article, we propose an improved variational method for HS image pansharpening with the constraint of spectral difference minimization. We extend the energy function of the classic variational pansharpening method by adding a new spectral fidelity term. This fidelity term is designed following the definition of spectral angle mapper, which means that for every pixel, the spectral difference value of any two bands in the HS image is in equal proportion to that of the two corresponding bands in the pansharpened image. Gradient descent method is adopted to find the optimal solution of the modified energy function, and the pansharpened image can be reconstructed. Experimental results demonstrate that the constraint of spectral difference minimization is able to preserve the original spectral information well in HS images, and reduce the spectral distortion effectively. Compared to original variational method, our method performs better in both visual and quantitative evaluation, and achieves a good trade-off between spatial and spectral information.

Optical neural network system for pose determination of spinning satellites

NASA Technical Reports Server (NTRS)

Lee, Andrew; Casasent, David

1990-01-01

An optical neural network architecture and algorithm based on a Hopfield optimization network are presented for multitarget tracking. This tracker utilizes a neuron for every possible target track, and a quadratic energy function of neural activities which is minimized using gradient descent neural evolution. The neural net tracker is demonstrated as part of a system for determining position and orientation (pose) of spinning satellites with respect to a robotic spacecraft. The input to the system is time sequence video from a single camera. Novelty detection and filtering are utilized to locate and segment novel regions from the input images. The neural net multitarget tracker determines the correspondences (or tracks) of the novel regions as a function of time, and hence the paths of object (satellite) parts. The path traced out by a given part or region is approximately elliptical in image space, and the position, shape and orientation of the ellipse are functions of the satellite geometry and its pose. Having a geometric model of the satellite, and the elliptical path of a part in image space, the three-dimensional pose of the satellite is determined. Digital simulation results using this algorithm are presented for various satellite poses and lighting conditions.

Dynamic fuzzy modeling of storm water infiltration in urban fractured aquifers

USGS Publications Warehouse

Hong, Y.-S.; Rosen, Michael R.; Reeves, R.R.

2002-01-01

In an urban fractured-rock aquifer in the Mt. Eden area of Auckland, New Zealand, disposal of storm water is via "soakholes" drilled directly into the top of the fractured basalt rock. The dynamic response of the groundwater level due to the storm water infiltration shows characteristics of a strongly time-varying system. A dynamic fuzzy modeling approach, which is based on multiple local models that are weighted using fuzzy membership functions, has been developed to identify and predict groundwater level fluctuations caused by storm water infiltration. The dynamic fuzzy model is initialized by the fuzzy clustering algorithm and optimized by the gradient-descent algorithm in order to effectively derive the multiple local models-each of which is associated with a locally valid model that represents the groundwater level state as a response to different intensities of rainfall events. The results have shown that even if the number of fuzzy local models derived is small, the fuzzy modeling approach developed provides good prediction results despite the highly time-varying nature of this urban fractured-rock aquifer system. Further, it allows interpretable representations of the dynamic behavior of the groundwater system due to storm water infiltration.

Wavelet-based edge correlation incorporated iterative reconstruction for undersampled MRI.

PubMed

Hu, Changwei; Qu, Xiaobo; Guo, Di; Bao, Lijun; Chen, Zhong

2011-09-01

Undersampling k-space is an effective way to decrease acquisition time for MRI. However, aliasing artifacts introduced by undersampling may blur the edges of magnetic resonance images, which often contain important information for clinical diagnosis. Moreover, k-space data is often contaminated by the noise signals of unknown intensity. To better preserve the edge features while suppressing the aliasing artifacts and noises, we present a new wavelet-based algorithm for undersampled MRI reconstruction. The algorithm solves the image reconstruction as a standard optimization problem including a ℓ(2) data fidelity term and ℓ(1) sparsity regularization term. Rather than manually setting the regularization parameter for the ℓ(1) term, which is directly related to the threshold, an automatic estimated threshold adaptive to noise intensity is introduced in our proposed algorithm. In addition, a prior matrix based on edge correlation in wavelet domain is incorporated into the regularization term. Compared with nonlinear conjugate gradient descent algorithm, iterative shrinkage/thresholding algorithm, fast iterative soft-thresholding algorithm and the iterative thresholding algorithm using exponentially decreasing threshold, the proposed algorithm yields reconstructions with better edge recovery and noise suppression. Copyright © 2011 Elsevier Inc. All rights reserved.

Evaluating and minimizing noise impact due to aircraft flyover

NASA Technical Reports Server (NTRS)

Jacobson, I. D.; Cook, G.

1979-01-01

Existing techniques were used to assess the noise impact on a community due to aircraft operation and to optimize the flight paths of an approaching aircraft with respect to the annoyance produced. Major achievements are: (1) the development of a population model suitable for determining the noise impact, (2) generation of a numerical computer code which uses this population model along with the steepest descent algorithm to optimize approach/landing trajectories, (3) implementation of this optimization code in several fictitious cases as well as for the community surrounding Patrick Henry International Airport, Virginia.

Performance Analysis and Design Synthesis (PADS) computer program. Volume 3: User manual

NASA Technical Reports Server (NTRS)

1972-01-01

The two-fold purpose of the Performance Analysis and Design Synthesis (PADS) computer program is discussed. The program can size launch vehicles in conjunction with calculus-of-variations optimal trajectories and can also be used as a general purpose branched trajectory optimization program. For trajectory optimization alone or with sizing, PADS has two trajectory modules. The first trajectory module uses the method of steepest descent. The second module uses the method of quasi-linearization, which requires a starting solution from the first trajectory module.

Parametric Mass Modeling for Mars Entry, Descent and Landing System Analysis Study

NASA Technical Reports Server (NTRS)

Samareh, Jamshid A.; Komar, D. R.

2011-01-01

This paper provides an overview of the parametric mass models used for the Entry, Descent, and Landing Systems Analysis study conducted by NASA in FY2009-2010. The study examined eight unique exploration class architectures that included elements such as a rigid mid-L/D aeroshell, a lifting hypersonic inflatable decelerator, a drag supersonic inflatable decelerator, a lifting supersonic inflatable decelerator implemented with a skirt, and subsonic/supersonic retro-propulsion. Parametric models used in this study relate the component mass to vehicle dimensions and mission key environmental parameters such as maximum deceleration and total heat load. The use of a parametric mass model allows the simultaneous optimization of trajectory and mass sizing parameters.

Crosswind Shear Gradient Affect on Wake Vortices

NASA Technical Reports Server (NTRS)

Proctor, Fred H.; Ahmad, Nashat N.

2011-01-01

Parametric simulations with a Large Eddy Simulation (LES) model are used to explore the influence of crosswind shear on aircraft wake vortices. Previous studies based on field measurements, laboratory experiments, as well as LES, have shown that the vertical gradient of crosswind shear, i.e. the second vertical derivative of the environmental crosswind, can influence wake vortex transport. The presence of nonlinear vertical shear of the crosswind velocity can reduce the descent rate, causing a wake vortex pair to tilt and change in its lateral separation. The LES parametric studies confirm that the vertical gradient of crosswind shear does influence vortex trajectories. The parametric results also show that vortex decay from the effects of shear are complex since the crosswind shear, along with the vertical gradient of crosswind shear, can affect whether the lateral separation between wake vortices is increased or decreased. If the separation is decreased, the vortex linking time is decreased, and a more rapid decay of wake vortex circulation occurs. If the separation is increased, the time to link is increased, and at least one of the vortices of the vortex pair may have a longer life time than in the case without shear. In some cases, the wake vortices may never link.

Efficient spectral computation of the stationary states of rotating Bose-Einstein condensates by preconditioned nonlinear conjugate gradient methods

NASA Astrophysics Data System (ADS)

Antoine, Xavier; Levitt, Antoine; Tang, Qinglin

2017-08-01

We propose a preconditioned nonlinear conjugate gradient method coupled with a spectral spatial discretization scheme for computing the ground states (GS) of rotating Bose-Einstein condensates (BEC), modeled by the Gross-Pitaevskii Equation (GPE). We first start by reviewing the classical gradient flow (also known as imaginary time (IMT)) method which considers the problem from the PDE standpoint, leading to numerically solve a dissipative equation. Based on this IMT equation, we analyze the forward Euler (FE), Crank-Nicolson (CN) and the classical backward Euler (BE) schemes for linear problems and recognize classical power iterations, allowing us to derive convergence rates. By considering the alternative point of view of minimization problems, we propose the preconditioned steepest descent (PSD) and conjugate gradient (PCG) methods for the GS computation of the GPE. We investigate the choice of the preconditioner, which plays a key role in the acceleration of the convergence process. The performance of the new algorithms is tested in 1D, 2D and 3D. We conclude that the PCG method outperforms all the previous methods, most particularly for 2D and 3D fast rotating BECs, while being simple to implement.

ACIR: automatic cochlea image registration

NASA Astrophysics Data System (ADS)

Al-Dhamari, Ibraheem; Bauer, Sabine; Paulus, Dietrich; Lissek, Friedrich; Jacob, Roland

2017-02-01

Efficient Cochlear Implant (CI) surgery requires prior knowledge of the cochlea's size and its characteristics. This information helps to select suitable implants for different patients. To get these measurements, a segmentation method of cochlea medical images is needed. An important pre-processing step for good cochlea segmentation involves efficient image registration. The cochlea's small size and complex structure, in addition to the different resolutions and head positions during imaging, reveals a big challenge for the automated registration of the different image modalities. In this paper, an Automatic Cochlea Image Registration (ACIR) method for multi- modal human cochlea images is proposed. This method is based on using small areas that have clear structures from both input images instead of registering the complete image. It uses the Adaptive Stochastic Gradient Descent Optimizer (ASGD) and Mattes's Mutual Information metric (MMI) to estimate 3D rigid transform parameters. The use of state of the art medical image registration optimizers published over the last two years are studied and compared quantitatively using the standard Dice Similarity Coefficient (DSC). ACIR requires only 4.86 seconds on average to align cochlea images automatically and to put all the modalities in the same spatial locations without human interference. The source code is based on the tool elastix and is provided for free as a 3D Slicer plugin. Another contribution of this work is a proposed public cochlea standard dataset which can be downloaded for free from a public XNAT server.

Numerical experience with a class of algorithms for nonlinear optimization using inexact function and gradient information

NASA Technical Reports Server (NTRS)

Carter, Richard G.

1989-01-01

For optimization problems associated with engineering design, parameter estimation, image reconstruction, and other optimization/simulation applications, low accuracy function and gradient values are frequently much less expensive to obtain than high accuracy values. Here, researchers investigate the computational performance of trust region methods for nonlinear optimization when high accuracy evaluations are unavailable or prohibitively expensive, and confirm earlier theoretical predictions when the algorithm is convergent even with relative gradient errors of 0.5 or more. The proper choice of the amount of accuracy to use in function and gradient evaluations can result in orders-of-magnitude savings in computational cost.

Efficient two-dimensional compressive sensing in MIMO radar

NASA Astrophysics Data System (ADS)

Shahbazi, Nafiseh; Abbasfar, Aliazam; Jabbarian-Jahromi, Mohammad

2017-12-01

Compressive sensing (CS) has been a way to lower sampling rate leading to data reduction for processing in multiple-input multiple-output (MIMO) radar systems. In this paper, we further reduce the computational complexity of a pulse-Doppler collocated MIMO radar by introducing a two-dimensional (2D) compressive sensing. To do so, we first introduce a new 2D formulation for the compressed received signals and then we propose a new measurement matrix design for our 2D compressive sensing model that is based on minimizing the coherence of sensing matrix using gradient descent algorithm. The simulation results show that our proposed 2D measurement matrix design using gradient decent algorithm (2D-MMDGD) has much lower computational complexity compared to one-dimensional (1D) methods while having better performance in comparison with conventional methods such as Gaussian random measurement matrix.

Statistical Mechanics of Node-perturbation Learning with Noisy Baseline

NASA Astrophysics Data System (ADS)

Hara, Kazuyuki; Katahira, Kentaro; Okada, Masato

2017-02-01

Node-perturbation learning is a type of statistical gradient descent algorithm that can be applied to problems where the objective function is not explicitly formulated, including reinforcement learning. It estimates the gradient of an objective function by using the change in the object function in response to the perturbation. The value of the objective function for an unperturbed output is called a baseline. Cho et al. proposed node-perturbation learning with a noisy baseline. In this paper, we report on building the statistical mechanics of Cho's model and on deriving coupled differential equations of order parameters that depict learning dynamics. We also show how to derive the generalization error by solving the differential equations of order parameters. On the basis of the results, we show that Cho's results are also apply in general cases and show some general performances of Cho's model.

Development and implementation of (Q)SAR modeling within the CHARMMing web-user interface.

PubMed

Weidlich, Iwona E; Pevzner, Yuri; Miller, Benjamin T; Filippov, Igor V; Woodcock, H Lee; Brooks, Bernard R

2015-01-05

Recent availability of large publicly accessible databases of chemical compounds and their biological activities (PubChem, ChEMBL) has inspired us to develop a web-based tool for structure activity relationship and quantitative structure activity relationship modeling to add to the services provided by CHARMMing (www.charmming.org). This new module implements some of the most recent advances in modern machine learning algorithms-Random Forest, Support Vector Machine, Stochastic Gradient Descent, Gradient Tree Boosting, so forth. A user can import training data from Pubchem Bioassay data collections directly from our interface or upload his or her own SD files which contain structures and activity information to create new models (either categorical or numerical). A user can then track the model generation process and run models on new data to predict activity. © 2014 Wiley Periodicals, Inc.

Statistical optimization and artificial neural network modeling for acridine orange dye degradation using in-situ synthesized polymer capped ZnO nanoparticles.

PubMed

Dhiman, Nitesh; Markandeya; Singh, Amrita; Verma, Neeraj K; Ajaria, Nidhi; Patnaik, Satyakam

2017-05-01

ZnO NPs were synthesized by a prudent green chemistry approach in presence of polyacrylamide grafted guar gum polymer (pAAm-g-GG) to ensure uniform morphology, and functionality and appraised for their ability to degrade photocatalytically Acridine Orange (AO) dye. These ZnO@pAAm-g-GG NPs were thoroughly characterized by various spectroscopic, XRD and electron microscopic techniques. The relative quantity of ZnO NPs in polymeric matrix has been estimated by spectro-analytical procedure; AAS and TGA analysis. The impact of process parameters viz. NP's dose, contact time and AO dye concentration on percentage photocatalytic degradation of AO dyes were evaluated using multivariate optimizing tools, Response Surface Methodology (RSM) involving Box-Behnken Design (BBD) and Artificial Neural Network (ANN). Congruity of the BBD statistical model was implied by R 2 value 0.9786 and F-value 35.48. At RSM predicted optimal condition viz. ZnO@pAAm-g-GG NP's dose of 0.2g/L, contact time of 210min and AO dye concentration 10mg/L, a maximum of 98% dye degradation was obtained. ANOVA indicated appropriateness of the model for dye degradation owing to "Prob.>F" less than 0.05 for variable parameters. We further, employed three layers feed forward ANN model for validating the BBD process parameters and suitability of our chosen model. The evaluation of Levenberg-Marquardt algorithm (ANN1) and Gradient Descent with adaptive learning rate (ANN2) model employed to scrutinize the best method and found experimental values of AO dye degradation were in close to those with predicated value of ANN 2 modeling with minimum error. Copyright © 2017 Elsevier Inc. All rights reserved.

Adaptive conversion of a high-order mode beam into a near-diffraction-limited beam.

PubMed

Zhao, Haichuan; Wang, Xiaolin; Ma, Haotong; Zhou, Pu; Ma, Yanxing; Xu, Xiaojun; Zhao, Yijun

2011-08-01

We present a new method for efficiently transforming a high-order mode beam into a nearly Gaussian beam with much higher beam quality. The method is based on modulation of phases of different lobes by stochastic parallel gradient descent algorithm and coherent addition after phase flattening. We demonstrate the method by transforming an LP11 mode into a nearly Gaussian beam. The experimental results reveal that the power in the diffraction-limited bucket in the far field is increased by more than a factor of 1.5.

Angle of Attack Modulation for Mars Entry Terminal State Optimization

NASA Technical Reports Server (NTRS)

Lafleur, Jarret M.; Cerimele, Christopher J.

2009-01-01

From the perspective of atmospheric entry, descent, and landing (EDL), one of the most foreboding destinations in the solar system is Mars due in part to its exceedingly thin atmosphere. To benchmark best possible scenarios for evaluation of potential Mars EDL system designs, a study is conducted to optimize the entry-to-terminal-state portion of EDL for a variety of entry velocities and vehicle masses, focusing on the identification of potential benefits of enabling angle of attack modulation. The terminal state is envisioned as one appropriate for the initiation of terminal descent via parachute or other means. A particle swarm optimizer varies entry flight path angle, ten bank profile points, and ten angle of attack profile points to find maximum-final-altitude trajectories for a 10 30 m ellipsled at 180 different combinations of values for entry mass, entry velocity, terminal Mach number, and minimum allowable altitude. Parametric plots of maximum achievable altitude are shown, as are examples of optimized trajectories. It is shown that appreciable terminal state altitude gains (2.5-4.0 km) over pure bank angle control may be possible if angle of attack modulation is enabled for Mars entry vehicles. Gains of this magnitude could prove to be enabling for missions requiring high-altitude landing sites. Conclusions are also drawn regarding trends in the bank and angle of attack profiles that produce the optimal trajectories in this study, and directions for future work are identified.

Optimization with artificial neural network systems - A mapping principle and a comparison to gradient based methods

NASA Technical Reports Server (NTRS)

Leong, Harrison Monfook

1988-01-01

General formulae for mapping optimization problems into systems of ordinary differential equations associated with artificial neural networks are presented. A comparison is made to optimization using gradient-search methods. The performance measure is the settling time from an initial state to a target state. A simple analytical example illustrates a situation where dynamical systems representing artificial neural network methods would settle faster than those representing gradient-search. Settling time was investigated for a more complicated optimization problem using computer simulations. The problem was a simplified version of a problem in medical imaging: determining loci of cerebral activity from electromagnetic measurements at the scalp. The simulations showed that gradient based systems typically settled 50 to 100 times faster than systems based on current neural network optimization methods.

Optimal disturbances in boundary layers subject to streamwise pressure gradient

NASA Technical Reports Server (NTRS)

Ashpis, David E.; Tumin, Anatoli

2003-01-01

An analysis of the optimal non-modal growth of perturbations in a boundary layer in the presence of a streamwise pressure gradient is presented. The analysis is based on PSE equations for an incompressible fluid. Examples with Falkner-Scan profiles indicate that a favorable pressure gradient decreases the non-modal growth, while an unfavorable pressure gradient leads to an increase of the amplification. It is suggested that the transient growth mechanism be utilized to choose optimal parameters of tripping elements on a low-pressure turbine (LPT) airfoil. As an example, a boundary layer flow with a streamwise pressure gradient corresponding to the pressure distribution over a LPT airfoil is considered. It is shown that there is an optimal spacing of the tripping elements and that the transient growth effect depends on the starting point.

[Fast optimization of stepwise gradient conditions for ternary mobile phase in reversed-phase high performance liquid chromatography].

PubMed

Shan, Yi-chu; Zhang, Yu-kui; Zhao, Rui-huan

2002-07-01

In high performance liquid chromatography, it is necessary to apply multi-composition gradient elution for the separation of complex samples such as environmental and biological samples. Multivariate stepwise gradient elution is one of the most efficient elution modes, because it combines the high selectivity of multi-composition mobile phase and shorter analysis time of gradient elution. In practical separations, the separation selectivity of samples can be effectively adjusted by using ternary mobile phase. For the optimization of these parameters, the retention equation of samples must be obtained at first. Traditionally, several isocratic experiments are used to get the retention equation of solute. However, it is time consuming especially for the separation of complex samples with a wide range of polarity. A new method for the fast optimization of ternary stepwise gradient elution was proposed based on the migration rule of solute in column. First, the coefficients of retention equation of solute are obtained by running several linear gradient experiments, then the optimal separation conditions are searched according to the hierarchical chromatography response function which acts as the optimization criterion. For each kind of organic modifier, two initial linear gradient experiments are used to obtain the primary coefficients of retention equation of each solute. For ternary mobile phase, only four linear gradient runs are needed to get the coefficients of retention equation. Then the retention times of solutes under arbitrary mobile phase composition can be predicted. The initial optimal mobile phase composition is obtained by resolution mapping for all of the solutes. A hierarchical chromatography response function is used to evaluate the separation efficiencies and search the optimal elution conditions. In subsequent optimization, the migrating distance of solute in the column is considered to decide the mobile phase composition and sustaining time of the latter steps until all the solutes are eluted out. Thus the first stepwise gradient elution conditions are predicted. If the resolution of samples under the predicted optimal separation conditions is satisfactory, the optimization procedure is stopped; otherwise, the coefficients of retention equation are adjusted according to the experimental results under the previously predicted elution conditions. Then the new stepwise gradient elution conditions are predicted repeatedly until satisfactory resolution is obtained. Normally, the satisfactory separation conditions can be found only after six experiments by using the proposed method. In comparison with the traditional optimization method, the time needed to finish the optimization procedure can be greatly reduced. The method has been validated by its application to the separation of several samples such as amino acid derivatives, aromatic amines, in which satisfactory separations were obtained with predicted resolution.

Explorations on High Dimensional Landscapes: Spin Glasses and Deep Learning

NASA Astrophysics Data System (ADS)

Sagun, Levent

This thesis deals with understanding the structure of high-dimensional and non-convex energy landscapes. In particular, its focus is on the optimization of two classes of functions: homogeneous polynomials and loss functions that arise in machine learning. In the first part, the notion of complexity of a smooth, real-valued function is studied through its critical points. Existing theoretical results predict that certain random functions that are defined on high dimensional domains have a narrow band of values whose pre-image contains the bulk of its critical points. This section provides empirical evidence for convergence of gradient descent to local minima whose energies are near the predicted threshold justifying the existing asymptotic theory. Moreover, it is empirically shown that a similar phenomenon may hold for deep learning loss functions. Furthermore, there is a comparative analysis of gradient descent and its stochastic version showing that in high dimensional regimes the latter is a mere speedup. The next study focuses on the halting time of an algorithm at a given stopping condition. Given an algorithm, the normalized fluctuations of the halting time follow a distribution that remains unchanged even when the input data is sampled from a new distribution. Two qualitative classes are observed: a Gumbel-like distribution that appears in Google searches, human decision times, and spin glasses and a Gaussian-like distribution that appears in conjugate gradient method, deep learning with MNIST and random input data. Following the universality phenomenon, the Hessian of the loss functions of deep learning is studied. The spectrum is seen to be composed of two parts, the bulk which is concentrated around zero, and the edges which are scattered away from zero. Empirical evidence is presented for the bulk indicating how over-parametrized the system is, and for the edges that depend on the input data. Furthermore, an algorithm is proposed such that it would explore such large dimensional, degenerate landscapes to locate a solution with decent generalization properties. Finally, a demonstration of how the new method can explain the empirical success of some of the recent methods that have been proposed for distributed deep learning. In the second part, two applied machine learning problems are studied that are complementary to the machine learning problems of part I. First, US asylum applications cases are studied using random forests on the data of past twenty years. Using only features up to when the case opens, the algorithm can predict the outcome of the case with 80% accuracy. Next, a particular question and answer system has been studied. The questions are collected from Jeopardy! show and they fed to Google, then the results are parsed into a recurrent neural network to come up with a system that would outcome the answer to the original question. Close to 50% accuracy is achieved where human level benchmark is just a little above 60%.

Intelligence system based classification approach for medical disease diagnosis

NASA Astrophysics Data System (ADS)

Sagir, Abdu Masanawa; Sathasivam, Saratha

2017-08-01

The prediction of breast cancer in women who have no signs or symptoms of the disease as well as survivability after undergone certain surgery has been a challenging problem for medical researchers. The decision about presence or absence of diseases depends on the physician's intuition, experience and skill for comparing current indicators with previous one than on knowledge rich data hidden in a database. This measure is a very crucial and challenging task. The goal is to predict patient condition by using an adaptive neuro fuzzy inference system (ANFIS) pre-processed by grid partitioning. To achieve an accurate diagnosis at this complex stage of symptom analysis, the physician may need efficient diagnosis system. A framework describes methodology for designing and evaluation of classification performances of two discrete ANFIS systems of hybrid learning algorithms least square estimates with Modified Levenberg-Marquardt and Gradient descent algorithms that can be used by physicians to accelerate diagnosis process. The proposed method's performance was evaluated based on training and test datasets with mammographic mass and Haberman's survival Datasets obtained from benchmarked datasets of University of California at Irvine's (UCI) machine learning repository. The robustness of the performance measuring total accuracy, sensitivity and specificity is examined. In comparison, the proposed method achieves superior performance when compared to conventional ANFIS based gradient descent algorithm and some related existing methods. The software used for the implementation is MATLAB R2014a (version 8.3) and executed in PC Intel Pentium IV E7400 processor with 2.80 GHz speed and 2.0 GB of RAM.

Split Bregman multicoil accelerated reconstruction technique: A new framework for rapid reconstruction of cardiac perfusion MRI

PubMed Central

Kamesh Iyer, Srikant; Tasdizen, Tolga; Likhite, Devavrat; DiBella, Edward

2016-01-01

Purpose: Rapid reconstruction of undersampled multicoil MRI data with iterative constrained reconstruction method is a challenge. The authors sought to develop a new substitution based variable splitting algorithm for faster reconstruction of multicoil cardiac perfusion MRI data. Methods: The new method, split Bregman multicoil accelerated reconstruction technique (SMART), uses a combination of split Bregman based variable splitting and iterative reweighting techniques to achieve fast convergence. Total variation constraints are used along the spatial and temporal dimensions. The method is tested on nine ECG-gated dog perfusion datasets, acquired with a 30-ray golden ratio radial sampling pattern and ten ungated human perfusion datasets, acquired with a 24-ray golden ratio radial sampling pattern. Image quality and reconstruction speed are evaluated and compared to a gradient descent (GD) implementation and to multicoil k-t SLR, a reconstruction technique that uses a combination of sparsity and low rank constraints. Results: Comparisons based on blur metric and visual inspection showed that SMART images had lower blur and better texture as compared to the GD implementation. On average, the GD based images had an ∼18% higher blur metric as compared to SMART images. Reconstruction of dynamic contrast enhanced (DCE) cardiac perfusion images using the SMART method was ∼6 times faster than standard gradient descent methods. k-t SLR and SMART produced images with comparable image quality, though SMART was ∼6.8 times faster than k-t SLR. Conclusions: The SMART method is a promising approach to reconstruct good quality multicoil images from undersampled DCE cardiac perfusion data rapidly. PMID:27036592

A comparison of two closely-related approaches to aerodynamic design optimization

NASA Technical Reports Server (NTRS)

Shubin, G. R.; Frank, P. D.

1991-01-01

Two related methods for aerodynamic design optimization are compared. The methods, called the implicit gradient approach and the variational (or optimal control) approach, both attempt to obtain gradients necessary for numerical optimization at a cost significantly less than that of the usual black-box approach that employs finite difference gradients. While the two methods are seemingly quite different, they are shown to differ (essentially) in that the order of discretizing the continuous problem, and of applying calculus, is interchanged. Under certain circumstances, the two methods turn out to be identical. We explore the relationship between these methods by applying them to a model problem for duct flow that has many features in common with transonic flow over an airfoil. We find that the gradients computed by the variational method can sometimes be sufficiently inaccurate to cause the optimization to fail.

Evaluating the accuracy performance of Lucas-Kanade algorithm in the circumstance of PIV application

NASA Astrophysics Data System (ADS)

Pan, Chong; Xue, Dong; Xu, Yang; Wang, JinJun; Wei, RunJie

2015-10-01

Lucas-Kanade (LK) algorithm, usually used in optical flow filed, has recently received increasing attention from PIV community due to its advanced calculation efficiency by GPU acceleration. Although applications of this algorithm are continuously emerging, a systematic performance evaluation is still lacking. This forms the primary aim of the present work. Three warping schemes in the family of LK algorithm: forward/inverse/symmetric warping, are evaluated in a prototype flow of a hierarchy of multiple two-dimensional vortices. Second-order Newton descent is also considered here. The accuracy & efficiency of all these LK variants are investigated under a large domain of various influential parameters. It is found that the constant displacement constraint, which is a necessary building block for GPU acceleration, is the most critical issue in affecting LK algorithm's accuracy, which can be somehow ameliorated by using second-order Newton descent. Moreover, symmetric warping outbids the other two warping schemes in accuracy level, robustness to noise, convergence speed and tolerance to displacement gradient, and might be the first choice when applying LK algorithm to PIV measurement.

Development of a Mars Airplane Entry, Descent, and Flight Trajectory

NASA Technical Reports Server (NTRS)

Murray, James E.; Tartabini, Paul V.

2001-01-01

An entry, descent, and flight (EDF) trajectory profile for a Mars airplane mission is defined as consisting of the following elements: ballistic entry of an aeroshell; supersonic deployment of a decelerator parachute; subsonic release of a heat shield; release, unfolding, and orientation of an airplane to flight attitude; and execution of a pull up maneuver to achieve trimmed, horizontal flight. Using the Program to Optimize Simulated Trajectories (POST) a trajectory optimization problem was formulated. Model data representative of a specific Mars airplane configuration, current models of the Mars surface topography and atmosphere, and current estimates of the interplanetary trajectory, were incorporated into the analysis. The goal is to develop an EDF trajectory to maximize the surface-relative altitude of the airplane at the end of a pull up maneuver, while subject to the mission design constraints. The trajectory performance was evaluated for three potential mission sites and was found to be site-sensitive. The trajectory performance, examined for sensitivity to a number of design and constraint variables, was found to be most sensitive to airplane mass, aerodynamic performance characteristics, and the pull up Mach constraint. Based on the results of this sensitivity study, an airplane-drag optimized trajectory was developed that showed a significant performance improvement.

Conditional nonlinear optimal perturbations based on the particle swarm optimization and their applications to the predictability problems

NASA Astrophysics Data System (ADS)

Zheng, Qin; Yang, Zubin; Sha, Jianxin; Yan, Jun

2017-02-01

In predictability problem research, the conditional nonlinear optimal perturbation (CNOP) describes the initial perturbation that satisfies a certain constraint condition and causes the largest prediction error at the prediction time. The CNOP has been successfully applied in estimation of the lower bound of maximum predictable time (LBMPT). Generally, CNOPs are calculated by a gradient descent algorithm based on the adjoint model, which is called ADJ-CNOP. This study, through the two-dimensional Ikeda model, investigates the impacts of the nonlinearity on ADJ-CNOP and the corresponding precision problems when using ADJ-CNOP to estimate the LBMPT. Our conclusions are that (1) when the initial perturbation is large or the prediction time is long, the strong nonlinearity of the dynamical model in the prediction variable will lead to failure of the ADJ-CNOP method, and (2) when the objective function has multiple extreme values, ADJ-CNOP has a large probability of producing local CNOPs, hence making a false estimation of the LBMPT. Furthermore, the particle swarm optimization (PSO) algorithm, one kind of intelligent algorithm, is introduced to solve this problem. The method using PSO to compute CNOP is called PSO-CNOP. The results of numerical experiments show that even with a large initial perturbation and long prediction time, or when the objective function has multiple extreme values, PSO-CNOP can always obtain the global CNOP. Since the PSO algorithm is a heuristic search algorithm based on the population, it can overcome the impact of nonlinearity and the disturbance from multiple extremes of the objective function. In addition, to check the estimation accuracy of the LBMPT presented by PSO-CNOP and ADJ-CNOP, we partition the constraint domain of initial perturbations into sufficiently fine grid meshes and take the LBMPT obtained by the filtering method as a benchmark. The result shows that the estimation presented by PSO-CNOP is closer to the true value than the one by ADJ-CNOP with the forecast time increasing.

Sequentially reweighted TV minimization for CT metal artifact reduction.

PubMed

Zhang, Xiaomeng; Xing, Lei

2013-07-01

Metal artifact reduction has long been an important topic in x-ray CT image reconstruction. In this work, the authors propose an iterative method that sequentially minimizes a reweighted total variation (TV) of the image and produces substantially artifact-reduced reconstructions. A sequentially reweighted TV minimization algorithm is proposed to fully exploit the sparseness of image gradients (IG). The authors first formulate a constrained optimization model that minimizes a weighted TV of the image, subject to the constraint that the estimated projection data are within a specified tolerance of the available projection measurements, with image non-negativity enforced. The authors then solve a sequence of weighted TV minimization problems where weights used for the next iteration are computed from the current solution. Using the complete projection data, the algorithm first reconstructs an image from which a binary metal image can be extracted. Forward projection of the binary image identifies metal traces in the projection space. The metal-free background image is then reconstructed from the metal-trace-excluded projection data by employing a different set of weights. Each minimization problem is solved using a gradient method that alternates projection-onto-convex-sets and steepest descent. A series of simulation and experimental studies are performed to evaluate the proposed approach. Our study shows that the sequentially reweighted scheme, by altering a single parameter in the weighting function, flexibly controls the sparsity of the IG and reconstructs artifacts-free images in a two-stage process. It successfully produces images with significantly reduced streak artifacts, suppressed noise and well-preserved contrast and edge properties. The sequentially reweighed TV minimization provides a systematic approach for suppressing CT metal artifacts. The technique can also be generalized to other "missing data" problems in CT image reconstruction.

Performance Analysis and Design Synthesis (PADS) computer program. Volume 2: Program description, part 1

NASA Technical Reports Server (NTRS)

1972-01-01

The Performance Analysis and Design Synthesis (PADS) computer program has a two-fold purpose. It can size launch vehicles in conjunction with calculus-of-variations optimal trajectories and can also be used as a general-purpose branched trajectory optimization program. In the former use, it has the Space Shuttle Synthesis Program as well as a simplified stage weight module for optimally sizing manned recoverable launch vehicles. For trajectory optimization alone or with sizing, PADS has two trajectory modules. The first trajectory module uses the method of steepest descent; the second employs the method of quasilinearization, which requires a starting solution from the first trajectory module. For Volume 1 see N73-13199.

New recursive-least-squares algorithms for nonlinear active control of sound and vibration using neural networks.

PubMed

Bouchard, M

2001-01-01

In recent years, a few articles describing the use of neural networks for nonlinear active control of sound and vibration were published. Using a control structure with two multilayer feedforward neural networks (one as a nonlinear controller and one as a nonlinear plant model), steepest descent algorithms based on two distinct gradient approaches were introduced for the training of the controller network. The two gradient approaches were sometimes called the filtered-x approach and the adjoint approach. Some recursive-least-squares algorithms were also introduced, using the adjoint approach. In this paper, an heuristic procedure is introduced for the development of recursive-least-squares algorithms based on the filtered-x and the adjoint gradient approaches. This leads to the development of new recursive-least-squares algorithms for the training of the controller neural network in the two networks structure. These new algorithms produce a better convergence performance than previously published algorithms. Differences in the performance of algorithms using the filtered-x and the adjoint gradient approaches are discussed in the paper. The computational load of the algorithms discussed in the paper is evaluated for multichannel systems of nonlinear active control. Simulation results are presented to compare the convergence performance of the algorithms, showing the convergence gain provided by the new algorithms.

Effect of RF Gradient upon the Performance of the Wisconsin SRF Electron Gun

DOE Office of Scientific and Technical Information (OSTI.GOV)

Bosch, Robert; Legg, Robert A.

2013-12-01

The performance of the Wisconsin 200-MHz SRF electron gun is simulated for several values of the RF gradient. Bunches with charge of 200 pC are modeled for the case where emittance compensation is completed during post-acceleration to 85 MeV in a TESLA module. We first perform simulations in which the initial bunch radius is optimal for the design gradient of 41 MV/m. We then optimize the radius as a function of RF gradient to improve the performance for low gradients.

Kurtosis Approach for Nonlinear Blind Source Separation

NASA Technical Reports Server (NTRS)

Duong, Vu A.; Stubbemd, Allen R.

2005-01-01

In this paper, we introduce a new algorithm for blind source signal separation for post-nonlinear mixtures. The mixtures are assumed to be linearly mixed from unknown sources first and then distorted by memoryless nonlinear functions. The nonlinear functions are assumed to be smooth and can be approximated by polynomials. Both the coefficients of the unknown mixing matrix and the coefficients of the approximated polynomials are estimated by the gradient descent method conditional on the higher order statistical requirements. The results of simulation experiments presented in this paper demonstrate the validity and usefulness of our approach for nonlinear blind source signal separation.

On Vehicle Placement to Intercept Moving Targets (Preprint)

DTIC Science & Technology

2010-03-09

which is feasible only if X1 −X2 = 0 and Y1 − Y2 = 0. We now present the main result for this section. Theorem 3.4 (Minimizing expected cost) From an...Vandenberghe (2004)) leads the vehicle to the unique global minimizer of Cexp. Let V ⊂ [0,W ], and choose φ(x) such that φ(x) = 0,∀x ∈ [0,W ] \\ V. Then, Theorem ...R>0, and following gradient descent with V as the region of integration, the vehicle remains inside [0,W ] × R>0 at all subsequent times. 3 Theorem

Product Distribution Theory and Semi-Coordinate Transformations

NASA Technical Reports Server (NTRS)

Airiau, Stephane; Wolpert, David H.

2004-01-01

Product Distribution (PD) theory is a new framework for doing distributed adaptive control of a multiagent system (MAS). We introduce the technique of "coordinate transformations" in PD theory gradient descent. These transformations selectively couple a few agents with each other into "meta-agents". Intuitively, this can be viewed as a generalization of forming binding contracts between those agents. Doing this sacrifices a bit of the distributed nature of the MAS, in that there must now be communication from multiple agents in determining what joint-move is finally implemented However, as we demonstrate in computer experiments, these transformations improve the performance of the MAS.

Simulation Framework for Rapid Entry, Descent, and Landing (EDL) Analysis. Volume 2; Appendices

NASA Technical Reports Server (NTRS)

Murri, Daniel G.

2010-01-01

The NASA Engineering and Safety Center (NESC) was requested to establish the Simulation Framework for Rapid Entry, Descent, and Landing (EDL) Analysis assessment, which involved development of an enhanced simulation architecture using the Program to Optimize Simulated Trajectories II (POST2) simulation tool. The assessment was requested to enhance the capability of the Agency to provide rapid evaluation of EDL characteristics in systems analysis studies, preliminary design, mission development and execution, and time-critical assessments. Many of the new simulation framework capabilities were developed to support the Agency EDL Systems Analysis (EDL-SA) team, that is conducting studies of the technologies and architectures that are required to enable higher mass robotic and human mission to Mars. The appendices to the original report are contained in this document.

Simulation Framework for Rapid Entry, Descent, and Landing (EDL) Analysis, Phase 2 Results

NASA Technical Reports Server (NTRS)

Murri, Daniel G.

2011-01-01

The NASA Engineering and Safety Center (NESC) was requested to establish the Simulation Framework for Rapid Entry, Descent, and Landing (EDL) Analysis assessment, which involved development of an enhanced simulation architecture using the Program to Optimize Simulated Trajectories II simulation tool. The assessment was requested to enhance the capability of the Agency to provide rapid evaluation of EDL characteristics in systems analysis studies, preliminary design, mission development and execution, and time-critical assessments. Many of the new simulation framework capabilities were developed to support the Agency EDL-Systems Analysis (SA) team that is conducting studies of the technologies and architectures that are required to enable human and higher mass robotic missions to Mars. The findings, observations, and recommendations from the NESC are provided in this report.

Simulation Framework for Rapid Entry, Descent, and Landing (EDL) Analysis. Volume 1

NASA Technical Reports Server (NTRS)

Murri, Daniel G.

2010-01-01

The NASA Engineering and Safety Center (NESC) was requested to establish the Simulation Framework for Rapid Entry, Descent, and Landing (EDL) Analysis assessment, which involved development of an enhanced simulation architecture using the Program to Optimize Simulated Trajectories II (POST2) simulation tool. The assessment was requested to enhance the capability of the Agency to provide rapid evaluation of EDL characteristics in systems analysis studies, preliminary design, mission development and execution, and time-critical assessments. Many of the new simulation framework capabilities were developed to support the Agency EDL Systems Analysis (EDL-SA) team, that is conducting studies of the technologies and architectures that are required to enable higher mass robotic and human mission to Mars. The findings of the assessment are contained in this report.

Linear Subspace Ranking Hashing for Cross-Modal Retrieval.

PubMed

Li, Kai; Qi, Guo-Jun; Ye, Jun; Hua, Kien A

2017-09-01

Hashing has attracted a great deal of research in recent years due to its effectiveness for the retrieval and indexing of large-scale high-dimensional multimedia data. In this paper, we propose a novel ranking-based hashing framework that maps data from different modalities into a common Hamming space where the cross-modal similarity can be measured using Hamming distance. Unlike existing cross-modal hashing algorithms where the learned hash functions are binary space partitioning functions, such as the sign and threshold function, the proposed hashing scheme takes advantage of a new class of hash functions closely related to rank correlation measures which are known to be scale-invariant, numerically stable, and highly nonlinear. Specifically, we jointly learn two groups of linear subspaces, one for each modality, so that features' ranking orders in different linear subspaces maximally preserve the cross-modal similarities. We show that the ranking-based hash function has a natural probabilistic approximation which transforms the original highly discontinuous optimization problem into one that can be efficiently solved using simple gradient descent algorithms. The proposed hashing framework is also flexible in the sense that the optimization procedures are not tied up to any specific form of loss function, which is typical for existing cross-modal hashing methods, but rather we can flexibly accommodate different loss functions with minimal changes to the learning steps. We demonstrate through extensive experiments on four widely-used real-world multimodal datasets that the proposed cross-modal hashing method can achieve competitive performance against several state-of-the-arts with only moderate training and testing time.

Energy-Efficient Transmissions for Remote Wireless Sensor Networks: An Integrated HAP/Satellite Architecture for Emergency Scenarios

PubMed Central

Dong, Feihong; Li, Hongjun; Gong, Xiangwu; Liu, Quan; Wang, Jingchao

2015-01-01

A typical application scenario of remote wireless sensor networks (WSNs) is identified as an emergency scenario. One of the greatest design challenges for communications in emergency scenarios is energy-efficient transmission, due to scarce electrical energy in large-scale natural and man-made disasters. Integrated high altitude platform (HAP)/satellite networks are expected to optimally meet emergency communication requirements. In this paper, a novel integrated HAP/satellite (IHS) architecture is proposed, and three segments of the architecture are investigated in detail. The concept of link-state advertisement (LSA) is designed in a slow flat Rician fading channel. The LSA is received and processed by the terminal to estimate the link state information, which can significantly reduce the energy consumption at the terminal end. Furthermore, the transmission power requirements of the HAPs and terminals are derived using the gradient descent and differential equation methods. The energy consumption is modeled at both the source and system level. An innovative and adaptive algorithm is given for the energy-efficient path selection. The simulation results validate the effectiveness of the proposed adaptive algorithm. It is shown that the proposed adaptive algorithm can significantly improve energy efficiency when combined with the LSA and the energy consumption estimation. PMID:26404292

Energy-Efficient Transmissions for Remote Wireless Sensor Networks: An Integrated HAP/Satellite Architecture for Emergency Scenarios.

PubMed

Dong, Feihong; Li, Hongjun; Gong, Xiangwu; Liu, Quan; Wang, Jingchao

2015-09-03

A typical application scenario of remote wireless sensor networks (WSNs) is identified as an emergency scenario. One of the greatest design challenges for communications in emergency scenarios is energy-efficient transmission, due to scarce electrical energy in large-scale natural and man-made disasters. Integrated high altitude platform (HAP)/satellite networks are expected to optimally meet emergency communication requirements. In this paper, a novel integrated HAP/satellite (IHS) architecture is proposed, and three segments of the architecture are investigated in detail. The concept of link-state advertisement (LSA) is designed in a slow flat Rician fading channel. The LSA is received and processed by the terminal to estimate the link state information, which can significantly reduce the energy consumption at the terminal end. Furthermore, the transmission power requirements of the HAPs and terminals are derived using the gradient descent and differential equation methods. The energy consumption is modeled at both the source and system level. An innovative and adaptive algorithm is given for the energy-efficient path selection. The simulation results validate the effectiveness of the proposed adaptive algorithm. It is shown that the proposed adaptive algorithm can significantly improve energy efficiency when combined with the LSA and the energy consumption estimation.

Ring-push metric learning for person reidentification

NASA Astrophysics Data System (ADS)

He, Botao; Yu, Shaohua

2017-05-01

Person reidentification (re-id) has been widely studied because of its extensive use in video surveillance and forensics applications. It aims to search a specific person among a nonoverlapping camera network, which is highly challenging due to large variations in the cluttered background, human pose, and camera viewpoint. We present a metric learning algorithm for learning a Mahalanobis distance for re-id. Generally speaking, there exist two forces in the conventional metric learning process, one pulling force that pulls points of the same class closer and the other pushing force that pushes points of different classes as far apart as possible. We argue that, when only a limited number of training data are given, forcing interclass distances to be as large as possible may drive the metric to overfit the uninformative part of the images, such as noises and backgrounds. To alleviate overfitting, we propose the ring-push metric learning algorithm. Different from other metric learning methods that only punish too small interclass distances, in the proposed method, both too small and too large inter-class distances are punished. By introducing the generalized logistic function as the loss, we formulate the ring-push metric learning as a convex optimization problem and utilize the projected gradient descent method to solve it. The experimental results on four public datasets demonstrate the effectiveness of the proposed algorithm.

Distributed multisensory integration in a recurrent network model through supervised learning

NASA Astrophysics Data System (ADS)

Wang, He; Wong, K. Y. Michael

Sensory integration between different modalities has been extensively studied. It is suggested that the brain integrates signals from different modalities in a Bayesian optimal way. However, how the Bayesian rule is implemented in a neural network remains under debate. In this work we propose a biologically plausible recurrent network model, which can perform Bayesian multisensory integration after trained by supervised learning. Our model is composed of two modules, each for one modality. We assume that each module is a recurrent network, whose activity represents the posterior distribution of each stimulus. The feedforward input on each module is the likelihood of each modality. Two modules are integrated through cross-links, which are feedforward connections from the other modality, and reciprocal connections, which are recurrent connections between different modules. By stochastic gradient descent, we successfully trained the feedforward and recurrent coupling matrices simultaneously, both of which resembles the Mexican-hat. We also find that there are more than one set of coupling matrices that can approximate the Bayesian theorem well. Specifically, reciprocal connections and cross-links will compensate each other if one of them is removed. Even though trained with two inputs, the network's performance with only one input is in good accordance with what is predicted by the Bayesian theorem.

On the use of harmony search algorithm in the training of wavelet neural networks

NASA Astrophysics Data System (ADS)

Lai, Kee Huong; Zainuddin, Zarita; Ong, Pauline

2015-10-01

Wavelet neural networks (WNNs) are a class of feedforward neural networks that have been used in a wide range of industrial and engineering applications to model the complex relationships between the given inputs and outputs. The training of WNNs involves the configuration of the weight values between neurons. The backpropagation training algorithm, which is a gradient-descent method, can be used for this training purpose. Nonetheless, the solutions found by this algorithm often get trapped at local minima. In this paper, a harmony search-based algorithm is proposed for the training of WNNs. The training of WNNs, thus can be formulated as a continuous optimization problem, where the objective is to maximize the overall classification accuracy. Each candidate solution proposed by the harmony search algorithm represents a specific WNN architecture. In order to speed up the training process, the solution space is divided into disjoint partitions during the random initialization step of harmony search algorithm. The proposed training algorithm is tested onthree benchmark problems from the UCI machine learning repository, as well as one real life application, namely, the classification of electroencephalography signals in the task of epileptic seizure detection. The results obtained show that the proposed algorithm outperforms the traditional harmony search algorithm in terms of overall classification accuracy.

EMG-Based Estimation of Limb Movement Using Deep Learning With Recurrent Convolutional Neural Networks.

PubMed

Xia, Peng; Hu, Jie; Peng, Yinghong

2017-10-25

A novel model based on deep learning is proposed to estimate kinematic information for myoelectric control from multi-channel electromyogram (EMG) signals. The neural information of limb movement is embedded in EMG signals that are influenced by all kinds of factors. In order to overcome the negative effects of variability in signals, the proposed model employs the deep architecture combining convolutional neural networks (CNNs) and recurrent neural networks (RNNs). The EMG signals are transformed to time-frequency frames as the input to the model. The limb movement is estimated by the model that is trained with the gradient descent and backpropagation procedure. We tested the model for simultaneous and proportional estimation of limb movement in eight healthy subjects and compared it with support vector regression (SVR) and CNNs on the same data set. The experimental studies show that the proposed model has higher estimation accuracy and better robustness with respect to time. The combination of CNNs and RNNs can improve the model performance compared with using CNNs alone. The model of deep architecture is promising in EMG decoding and optimization of network structures can increase the accuracy and robustness. © 2017 International Center for Artificial Organs and Transplantation and Wiley Periodicals, Inc.

Application of modified Rosenbrock's method for optimization of nutrient media used in microorganism culturing.

PubMed

Votruba, J; Pilát, P; Prokop, A

1975-12-01

The Rosenbrock's procedure has been modified for optimization of nutrient medium composition and has been found to be less tedious than the Box-Wilson method, especially for larger numbers of optimized parameters. Its merits are particularly obvious with multiparameter optimization where the gradient method, so far the only one employed in microbiology from a variety of optimization methods (e.g., refs, 9 and 10), becomes impractical because of the excessive number of experiments required. The method suggested is also more stable during optimization than the gradient methods which are very sensitive to the selection of steps in the direction of the gradient and may thus easily shoot out of the optimized region. It is also anticipated that other direct search methods, particularly simplex design, may be easily adapted for optimization of medium composition. It is obvious that direct search methods may find an application in process improvement in antibiotic and related industries.

Gradient Optimization for Analytic conTrols - GOAT

NASA Astrophysics Data System (ADS)

Assémat, Elie; Machnes, Shai; Tannor, David; Wilhelm-Mauch, Frank

Quantum optimal control becomes a necessary step in a number of studies in the quantum realm. Recent experimental advances showed that superconducting qubits can be controlled with an impressive accuracy. However, most of the standard optimal control algorithms are not designed to manage such high accuracy. To tackle this issue, a novel quantum optimal control algorithm have been introduced: the Gradient Optimization for Analytic conTrols (GOAT). It avoids the piecewise constant approximation of the control pulse used by standard algorithms. This allows an efficient implementation of very high accuracy optimization. It also includes a novel method to compute the gradient that provides many advantages, e.g. the absence of backpropagation or the natural route to optimize the robustness of the control pulses. This talk will present the GOAT algorithm and a few applications to transmons systems.

Universal field matching in craniospinal irradiation by a background-dose gradient-optimized method.

PubMed

Traneus, Erik; Bizzocchi, Nicola; Fellin, Francesco; Rombi, Barbara; Farace, Paolo

2018-01-01

The gradient-optimized methods are overcoming the traditional feathering methods to plan field junctions in craniospinal irradiation. In this note, a new gradient-optimized technique, based on the use of a background dose, is described. Treatment planning was performed by RayStation (RaySearch Laboratories, Stockholm, Sweden) on the CT scans of a pediatric patient. Both proton (by pencil beam scanning) and photon (by volumetric modulated arc therapy) treatments were planned with three isocenters. An 'in silico' ideal background dose was created first to cover the upper-spinal target and to produce a perfect dose gradient along the upper and lower junction regions. Using it as background, the cranial and the lower-spinal beams were planned by inverse optimization to obtain dose coverage of their relevant targets and of the junction volumes. Finally, the upper-spinal beam was inversely planned after removal of the background dose and with the previously optimized beams switched on. In both proton and photon plans, the optimized cranial and the lower-spinal beams produced a perfect linear gradient in the junction regions, complementary to that produced by the optimized upper-spinal beam. The final dose distributions showed a homogeneous coverage of the targets. Our simple technique allowed to obtain high-quality gradients in the junction region. Such technique universally works for photons as well as protons and could be applicable to the TPSs that allow to manage a background dose. © 2017 The Authors. Journal of Applied Clinical Medical Physics published by Wiley Periodicals, Inc. on behalf of American Association of Physicists in Medicine.

Enhanced Fuel-Optimal Trajectory-Generation Algorithm for Planetary Pinpoint Landing

NASA Technical Reports Server (NTRS)

Acikmese, Behcet; Blackmore, James C.; Scharf, Daniel P.

2011-01-01

An enhanced algorithm is developed that builds on a previous innovation of fuel-optimal powered-descent guidance (PDG) for planetary pinpoint landing. The PDG problem is to compute constrained, fuel-optimal trajectories to land a craft at a prescribed target on a planetary surface, starting from a parachute cut-off point and using a throttleable descent engine. The previous innovation showed the minimal-fuel PDG problem can be posed as a convex optimization problem, in particular, as a Second-Order Cone Program, which can be solved to global optimality with deterministic convergence properties, and hence is a candidate for onboard implementation. To increase the speed and robustness of this convex PDG algorithm for possible onboard implementation, the following enhancements are incorporated: 1) Fast detection of infeasibility (i.e., control authority is not sufficient for soft-landing) for subsequent fault response. 2) The use of a piecewise-linear control parameterization, providing smooth solution trajectories and increasing computational efficiency. 3) An enhanced line-search algorithm for optimal time-of-flight, providing quicker convergence and bounding the number of path-planning iterations needed. 4) An additional constraint that analytically guarantees inter-sample satisfaction of glide-slope and non-sub-surface flight constraints, allowing larger discretizations and, hence, faster optimization. 5) Explicit incorporation of Mars rotation rate into the trajectory computation for improved targeting accuracy. These enhancements allow faster convergence to the fuel-optimal solution and, more importantly, remove the need for a "human-in-the-loop," as constraints will be satisfied over the entire path-planning interval independent of step-size (as opposed to just at the discrete time points) and infeasible initial conditions are immediately detected. Finally, while the PDG stage is typically only a few minutes, ignoring the rotation rate of Mars can introduce 10s of meters of error. By incorporating it, the enhanced PDG algorithm becomes capable of pinpoint targeting.

Multidisciplinary design optimization using genetic algorithms

NASA Technical Reports Server (NTRS)

Unal, Resit

1994-01-01

Multidisciplinary design optimization (MDO) is an important step in the conceptual design and evaluation of launch vehicles since it can have a significant impact on performance and life cycle cost. The objective is to search the system design space to determine values of design variables that optimize the performance characteristic subject to system constraints. Gradient-based optimization routines have been used extensively for aerospace design optimization. However, one limitation of gradient based optimizers is their need for gradient information. Therefore, design problems which include discrete variables can not be studied. Such problems are common in launch vehicle design. For example, the number of engines and material choices must be integer values or assume only a few discrete values. In this study, genetic algorithms are investigated as an approach to MDO problems involving discrete variables and discontinuous domains. Optimization by genetic algorithms (GA) uses a search procedure which is fundamentally different from those gradient based methods. Genetic algorithms seek to find good solutions in an efficient and timely manner rather than finding the best solution. GA are designed to mimic evolutionary selection. A population of candidate designs is evaluated at each iteration, and each individual's probability of reproduction (existence in the next generation) depends on its fitness value (related to the value of the objective function). Progress toward the optimum is achieved by the crossover and mutation operations. GA is attractive since it uses only objective function values in the search process, so gradient calculations are avoided. Hence, GA are able to deal with discrete variables. Studies report success in the use of GA for aircraft design optimization studies, trajectory analysis, space structure design and control systems design. In these studies reliable convergence was achieved, but the number of function evaluations was large compared with efficient gradient methods. Applicaiton of GA is underway for a cost optimization study for a launch-vehicle fuel-tank and structural design of a wing. The strengths and limitations of GA for launch vehicle design optimization is studied.

High-Fidelity Aerostructural Design Optimization of Transport Aircraft with Continuous Morphing Trailing Edge Technology

NASA Astrophysics Data System (ADS)

Burdette, David A., Jr.

Adaptive morphing trailing edge technology offers the potential to decrease the fuel burn of transonic commercial transport aircraft by allowing wings to dynamically adjust to changing flight conditions. Current configurations allow flap and aileron droop; however, this approach provides limited degrees of freedom and increased drag produced by gaps in the wing's surface. Leading members in the aeronautics community including NASA, AFRL, Boeing, and a number of academic institutions have extensively researched morphing technology for its potential to improve aircraft efficiency. With modern computational tools it is possible to accurately and efficiently model aircraft configurations in order to quantify the efficiency improvements offered by mor- phing technology. Coupled high-fidelity aerodynamic and structural solvers provide the capability to model and thoroughly understand the nuanced trade-offs involved in aircraft design. This capability is important for a detailed study of the capabilities of morphing trailing edge technology. Gradient-based multidisciplinary design opti- mization provides the ability to efficiently traverse design spaces and optimize the trade-offs associated with the design. This thesis presents a number of optimization studies comparing optimized config- urations with and without morphing trailing edge devices. The baseline configuration used throughout this work is the NASA Common Research Model. The first opti- mization comparison considers the optimal fuel burn predicted by the Breguet range equation at a single cruise point. This initial singlepoint optimization comparison demonstrated a limited fuel burn savings of less than 1%. Given the effectiveness of the passive aeroelastic tailoring in the optimized non-morphing wing, the singlepoint optimization offered limited potential for morphing technology to provide any bene- fit. To provide a more appropriate comparison, a number of multipoint optimizations were performed. With a 3-point stencil, the morphing wing burned 2.53% less fuel than its optimized non-morphing counterpart. Expanding further to a 7-point stencil, the morphing wing used 5.04% less fuel. Additional studies demonstrate that the size of the morphing device can be reduced without sizable performance reductions, and that as aircraft wings' aspect ratios increase, the effectiveness of morphing trailing edge devices increases. The final set of studies in this thesis consider mission analy- sis, including climb, multi-altitude cruise, and descent. These mission analyses were performed with a number of surrogate models, trained with O(100) optimizations. These optimizations demonstrated fuel burn reductions as large as 5% at off-design conditions. The fuel burn predicted by the mission analysis was up to 2.7% lower for the morphing wing compared to the conventional configuration.

A Model for Engaging Students in a Research Experience Involving Variational Techniques, Mathematica, and Descent Methods.

ERIC Educational Resources Information Center

Mahavier, W. Ted

2002-01-01

Describes a two-semester numerical methods course that serves as a research experience for undergraduate students without requiring external funding or the modification of current curriculum. Uses an engineering problem to introduce students to constrained optimization via a variation of the traditional isoperimetric problem of finding the curve…

Efficiency Benefits Using the Terminal Area Precision Scheduling and Spacing System

NASA Technical Reports Server (NTRS)

Thipphavong, Jane; Swenson, Harry N.; Lin, Paul; Seo, Anthony Y.; Bagasol, Leonard N.

2011-01-01

NASA has developed a capability for terminal area precision scheduling and spacing (TAPSS) to increase the use of fuel-efficient arrival procedures during periods of traffic congestion at a high-density airport. Sustained use of fuel-efficient procedures throughout the entire arrival phase of flight reduces overall fuel burn, greenhouse gas emissions and noise pollution. The TAPSS system is a 4D trajectory-based strategic planning and control tool that computes schedules and sequences for arrivals to facilitate optimal profile descents. This paper focuses on quantifying the efficiency benefits associated with using the TAPSS system, measured by reduction of level segments during aircraft descent and flight distance and time savings. The TAPSS system was tested in a series of human-in-the-loop simulations and compared to current procedures. Compared to the current use of the TMA system, simulation results indicate a reduction of total level segment distance by 50% and flight distance and time savings by 7% in the arrival portion of flight (200 nm from the airport). The TAPSS system resulted in aircraft maintaining continuous descent operations longer and with more precision, both achieved under heavy traffic demand levels.

The glucokinase mutation p.T206P is common among MODY patients of Jewish Ashkenazi descent.

PubMed

Gozlan, Yael; Tenenbaum, Ariel; Shalitin, Shlomit; Lebenthal, Yael; Oron, Tal; Cohen, Ohad; Phillip, Moshe; Gat-Yablonski, Galia

2012-09-01

Maturity-onset diabetes of the young (MODY) is characterized by an autosomal dominant mode of inheritance; a primary defect in insulin secretion with non-ketotic hyperglycemia, age of onset under 25 yr; and lack of autoantibodies. Heterozygous mutations in glucokinase (GCK) are associated with mild fasting hyperglycemia and gestational diabetes mellitus while homozygous or compound heterozygous GCK mutations result in permanent neonatal diabetes mellitus. Given that both the Israeli-Arabic and the various Israeli-Jewish communities tend to maintain ethnic seclusion, we speculated that it would be possible to identify a relatively narrow spectrum of mutations in the Israeli population. To characterize the genetic basis of GCK-MODY in the different ethnic groups of the Israeli population. Patients with clinically identified GCK-MODY and their first degree family members. Molecular analysis of GCK was performed on genomic DNA using polymerase chain reaction, denaturing gradient gel electrophoresis (DGGE), and sequencing. Bioinformatic model was preformed using the NEST program. Mutations in GCK were identified in 25 families and were all family-specific, except c.616A>C. p.T206P. This mutation was identified in six unrelated families, all patients from a Jewish-Ashkenazi descent, thus indicating an ethno-genetic correlation. A simple, fast, and relatively cheap DGGE/restriction-digestion assay was developed. The high incidence of the mutant allele in GCK-MODY patients of Jewish-Ashkenazi descent suggests a founder effect. We propose that clinically identified GCK-MODY patients of Jewish-Ashkenazi origin be first tested for this mutation. © 2011 John Wiley & Sons A/S.

Four-body trajectory optimization

NASA Technical Reports Server (NTRS)

Pu, C. L.; Edelbaum, T. N.

1974-01-01

A comprehensive optimization program has been developed for computing fuel-optimal trajectories between the earth and a point in the sun-earth-moon system. It presents methods for generating fuel optimal two-impulse trajectories which may originate at the earth or a point in space and fuel optimal three-impulse trajectories between two points in space. The extrapolation of the state vector and the computation of the state transition matrix are accomplished by the Stumpff-Weiss method. The cost and constraint gradients are computed analytically in terms of the terminal state and the state transition matrix. The 4-body Lambert problem is solved by using the Newton-Raphson method. An accelerated gradient projection method is used to optimize a 2-impulse trajectory with terminal constraint. The Davidon's Variance Method is used both in the accelerated gradient projection method and the outer loop of a 3-impulse trajectory optimization problem.

Statistical efficiency of adaptive algorithms.

PubMed

Widrow, Bernard; Kamenetsky, Max

2003-01-01

The statistical efficiency of a learning algorithm applied to the adaptation of a given set of variable weights is defined as the ratio of the quality of the converged solution to the amount of data used in training the weights. Statistical efficiency is computed by averaging over an ensemble of learning experiences. A high quality solution is very close to optimal, while a low quality solution corresponds to noisy weights and less than optimal performance. In this work, two gradient descent adaptive algorithms are compared, the LMS algorithm and the LMS/Newton algorithm. LMS is simple and practical, and is used in many applications worldwide. LMS/Newton is based on Newton's method and the LMS algorithm. LMS/Newton is optimal in the least squares sense. It maximizes the quality of its adaptive solution while minimizing the use of training data. Many least squares adaptive algorithms have been devised over the years, but no other least squares algorithm can give better performance, on average, than LMS/Newton. LMS is easily implemented, but LMS/Newton, although of great mathematical interest, cannot be implemented in most practical applications. Because of its optimality, LMS/Newton serves as a benchmark for all least squares adaptive algorithms. The performances of LMS and LMS/Newton are compared, and it is found that under many circumstances, both algorithms provide equal performance. For example, when both algorithms are tested with statistically nonstationary input signals, their average performances are equal. When adapting with stationary input signals and with random initial conditions, their respective learning times are on average equal. However, under worst-case initial conditions, the learning time of LMS can be much greater than that of LMS/Newton, and this is the principal disadvantage of the LMS algorithm. But the strong points of LMS are ease of implementation and optimal performance under important practical conditions. For these reasons, the LMS algorithm has enjoyed very widespread application. It is used in almost every modem for channel equalization and echo cancelling. Furthermore, it is related to the famous backpropagation algorithm used for training neural networks.

Longitudinal gradient coil optimization in the presence of transient eddy currents.

PubMed

Trakic, A; Liu, F; Lopez, H Sanchez; Wang, H; Crozier, S

2007-06-01

The switching of magnetic field gradient coils in magnetic resonance imaging (MRI) inevitably induces transient eddy currents in conducting system components, such as the cryostat vessel. These secondary currents degrade the spatial and temporal performance of the gradient coils, and compensation methods are commonly employed to correct for these distortions. This theoretical study shows that by incorporating the eddy currents into the coil optimization process, it is possible to modify a gradient coil design so that the fields created by the coil and the eddy currents combine together to generate a spatially homogeneous gradient that follows the input pulse. Shielded and unshielded longitudinal gradient coils are used to exemplify this novel approach. To assist in the evaluation of transient eddy currents induced within a realistic cryostat vessel, a low-frequency finite-difference time-domain (FDTD) method using the total-field scattered-field (TFSF) scheme was performed. The simulations demonstrate the effectiveness of the proposed method for optimizing longitudinal gradient fields while taking into account the spatial and temporal behavior of the eddy currents.

Solar collector parameter identification from unsteady data by a discrete-gradient optimization algorithm

NASA Technical Reports Server (NTRS)

Hotchkiss, G. B.; Burmeister, L. C.; Bishop, K. A.

1980-01-01

A discrete-gradient optimization algorithm is used to identify the parameters in a one-node and a two-node capacitance model of a flat-plate collector. Collector parameters are first obtained by a linear-least-squares fit to steady state data. These parameters, together with the collector heat capacitances, are then determined from unsteady data by use of the discrete-gradient optimization algorithm with less than 10 percent deviation from the steady state determination. All data were obtained in the indoor solar simulator at the NASA Lewis Research Center.

Gradient design for liquid chromatography using multi-scale optimization.

PubMed

López-Ureña, S; Torres-Lapasió, J R; Donat, R; García-Alvarez-Coque, M C

2018-01-26

In reversed phase-liquid chromatography, the usual solution to the "general elution problem" is the application of gradient elution with programmed changes of organic solvent (or other properties). A correct quantification of chromatographic peaks in liquid chromatography requires well resolved signals in a proper analysis time. When the complexity of the sample is high, the gradient program should be accommodated to the local resolution needs of each analyte. This makes the optimization of such situations rather troublesome, since enhancing the resolution for a given analyte may imply a collateral worsening of the resolution of other analytes. The aim of this work is to design multi-linear gradients that maximize the resolution, while fulfilling some restrictions: all peaks should be eluted before a given maximal time, the gradient should be flat or increasing, and sudden changes close to eluting peaks are penalized. Consequently, an equilibrated baseline resolution for all compounds is sought. This goal is achieved by splitting the optimization problem in a multi-scale framework. In each scale κ, an optimization problem is solved with N κ  ≈ 2 κ variables that are used to build the gradients. The N κ variables define cubic splines written in terms of a B-spline basis. This allows expressing gradients as polygonals of M points approximating the splines. The cubic splines are built using subdivision schemes, a technique of fast generation of smooth curves, compatible with the multi-scale framework. Owing to the nature of the problem and the presence of multiple local maxima, the algorithm used in the optimization problem of each scale κ should be "global", such as the pattern-search algorithm. The multi-scale optimization approach is successfully applied to find the best multi-linear gradient for resolving a mixture of amino acid derivatives. Copyright © 2017 Elsevier B.V. All rights reserved.

Using High Resolution Design Spaces for Aerodynamic Shape Optimization Under Uncertainty

NASA Technical Reports Server (NTRS)

Li, Wu; Padula, Sharon

2004-01-01

This paper explains why high resolution design spaces encourage traditional airfoil optimization algorithms to generate noisy shape modifications, which lead to inaccurate linear predictions of aerodynamic coefficients and potential failure of descent methods. By using auxiliary drag constraints for a simultaneous drag reduction at all design points and the least shape distortion to achieve the targeted drag reduction, an improved algorithm generates relatively smooth optimal airfoils with no severe off-design performance degradation over a range of flight conditions, in high resolution design spaces parameterized by cubic B-spline functions. Simulation results using FUN2D in Euler flows are included to show the capability of the robust aerodynamic shape optimization method over a range of flight conditions.

Co-optimal distribution of leaf nitrogen and hydraulic conductance in plant canopies.

PubMed

Peltoniemi, Mikko S; Duursma, Remko A; Medlyn, Belinda E

2012-05-01

Leaf properties vary significantly within plant canopies, due to the strong gradient in light availability through the canopy, and the need for plants to use resources efficiently. At high light, photosynthesis is maximized when leaves have a high nitrogen content and water supply, whereas at low light leaves have a lower requirement for both nitrogen and water. Studies of the distribution of leaf nitrogen (N) within canopies have shown that, if water supply is ignored, the optimal distribution is that where N is proportional to light, but that the gradient of N in real canopies is shallower than the optimal distribution. We extend this work by considering the optimal co-allocation of nitrogen and water supply within plant canopies. We developed a simple 'toy' two-leaf canopy model and optimized the distribution of N and hydraulic conductance (K) between the two leaves. We asked whether hydraulic constraints to water supply can explain shallow N gradients in canopies. We found that the optimal N distribution within plant canopies is proportional to the light distribution only if hydraulic conductance, K, is also optimally distributed. The optimal distribution of K is that where K and N are both proportional to incident light, such that optimal K is highest to the upper canopy. If the plant is constrained in its ability to construct higher K to sun-exposed leaves, the optimal N distribution does not follow the gradient in light within canopies, but instead follows a shallower gradient. We therefore hypothesize that measured deviations from the predicted optimal distribution of N could be explained by constraints on the distribution of K within canopies. Further empirical research is required on the extent to which plants can construct optimal K distributions, and whether shallow within-canopy N distributions can be explained by sub-optimal K distributions.

Options for Robust Airfoil Optimization under Uncertainty

NASA Technical Reports Server (NTRS)

Padula, Sharon L.; Li, Wu

2002-01-01

A robust optimization method is developed to overcome point-optimization at the sampled design points. This method combines the best features from several preliminary methods proposed by the authors and their colleagues. The robust airfoil shape optimization is a direct method for drag reduction over a given range of operating conditions and has three advantages: (1) it prevents severe degradation in the off-design performance by using a smart descent direction in each optimization iteration, (2) it uses a large number of spline control points as design variables yet the resulting airfoil shape does not need to be smoothed, and (3) it allows the user to make a tradeoff between the level of optimization and the amount of computing time consumed. For illustration purposes, the robust optimization method is used to solve a lift-constrained drag minimization problem for a two-dimensional (2-D) airfoil in Euler flow with 20 geometric design variables.

Robust Airfoil Optimization to Achieve Consistent Drag Reduction Over a Mach Range

NASA Technical Reports Server (NTRS)

Li, Wu; Huyse, Luc; Padula, Sharon; Bushnell, Dennis M. (Technical Monitor)

2001-01-01

We prove mathematically that in order to avoid point-optimization at the sampled design points for multipoint airfoil optimization, the number of design points must be greater than the number of free-design variables. To overcome point-optimization at the sampled design points, a robust airfoil optimization method (called the profile optimization method) is developed and analyzed. This optimization method aims at a consistent drag reduction over a given Mach range and has three advantages: (a) it prevents severe degradation in the off-design performance by using a smart descent direction in each optimization iteration, (b) there is no random airfoil shape distortion for any iterate it generates, and (c) it allows a designer to make a trade-off between a truly optimized airfoil and the amount of computing time consumed. For illustration purposes, we use the profile optimization method to solve a lift-constrained drag minimization problem for 2-D airfoil in Euler flow with 20 free-design variables. A comparison with other airfoil optimization methods is also included.

Pixel-By Estimation of Scene Motion in Video

NASA Astrophysics Data System (ADS)

Tashlinskii, A. G.; Smirnov, P. V.; Tsaryov, M. G.

2017-05-01

The paper considers the effectiveness of motion estimation in video using pixel-by-pixel recurrent algorithms. The algorithms use stochastic gradient decent to find inter-frame shifts of all pixels of a frame. These vectors form shift vectors' field. As estimated parameters of the vectors the paper studies their projections and polar parameters. It considers two methods for estimating shift vectors' field. The first method uses stochastic gradient descent algorithm to sequentially process all nodes of the image row-by-row. It processes each row bidirectionally i.e. from the left to the right and from the right to the left. Subsequent joint processing of the results allows compensating inertia of the recursive estimation. The second method uses correlation between rows to increase processing efficiency. It processes rows one after the other with the change in direction after each row and uses obtained values to form resulting estimate. The paper studies two criteria of its formation: gradient estimation minimum and correlation coefficient maximum. The paper gives examples of experimental results of pixel-by-pixel estimation for a video with a moving object and estimation of a moving object trajectory using shift vectors' field.

High-resolution Anorectal Manometry for Identifying Defecatory Disorders and Rectal Structural Abnormalities in Women.

PubMed

Prichard, David O; Lee, Taehee; Parthasarathy, Gopanandan; Fletcher, Joel G; Zinsmeister, Alan R; Bharucha, Adil E

2017-03-01

Contrary to conventional wisdom, the rectoanal gradient during evacuation is negative in many healthy people, undermining the utility of anorectal high-resolution manometry (HRM) for diagnosing defecatory disorders. We aimed to compare HRM and magnetic resonance imaging (MRI) for assessing rectal evacuation and structural abnormalities. We performed a retrospective analysis of 118 patients (all female; 51 with constipation, 48 with fecal incontinence, and 19 with rectal prolapse; age, 53 ± 1 years) assessed by HRM, the rectal balloon expulsion test (BET), and MRI at Mayo Clinic, Rochester, Minnesota, from February 2011 through March 2013. Thirty healthy asymptomatic women (age, 37 ± 2 years) served as controls. We used principal components analysis of HRM variables to identify rectoanal pressure patterns associated with rectal prolapse and phenotypes of patients with prolapse. Compared with patients with normal findings from the rectal BET, patients with an abnormal BET had lower median rectal pressure (36 vs 22 mm Hg, P = .002), a more negative median rectoanal gradient (-6 vs -29 mm Hg, P = .006) during evacuation, and a lower proportion of evacuation on the basis of MRI analysis (median of 40% vs 80%, P < .0001). A score derived from rectal pressure and anorectal descent during evacuation and a patulous anal canal was associated (P = .005) with large rectoceles (3 cm or larger). A principal component (PC) logistic model discriminated between patients with and without prolapse with 96% accuracy. Among patients with prolapse, there were 2 phenotypes, which were characterized by high (PC1) or low (PC2) anal pressures at rest and squeeze along with higher rectal and anal pressures (PC1) or a higher rectoanal gradient during evacuation (PC2). In a retrospective analysis of patients assessed by HRM, measurements of rectal evacuation by anorectal HRM, BET, and MRI were correlated. HRM alone and together with anorectal descent during evacuation may identify rectal prolapse and large rectoceles, respectively, and also identify unique phenotypes of rectal prolapse. Copyright © 2017 AGA Institute. Published by Elsevier Inc. All rights reserved.

Panel flutter optimization by gradient projection

NASA Technical Reports Server (NTRS)

Pierson, B. L.

1975-01-01

A gradient projection optimal control algorithm incorporating conjugate gradient directions of search is described and applied to several minimum weight panel design problems subject to a flutter speed constraint. New numerical solutions are obtained for both simply-supported and clamped homogeneous panels of infinite span for various levels of inplane loading and minimum thickness. The minimum thickness inequality constraint is enforced by a simple transformation of variables.

Learning Incoherent Sparse and Low-Rank Patterns from Multiple Tasks

PubMed Central

Chen, Jianhui; Liu, Ji; Ye, Jieping

2013-01-01

We consider the problem of learning incoherent sparse and low-rank patterns from multiple tasks. Our approach is based on a linear multi-task learning formulation, in which the sparse and low-rank patterns are induced by a cardinality regularization term and a low-rank constraint, respectively. This formulation is non-convex; we convert it into its convex surrogate, which can be routinely solved via semidefinite programming for small-size problems. We propose to employ the general projected gradient scheme to efficiently solve such a convex surrogate; however, in the optimization formulation, the objective function is non-differentiable and the feasible domain is non-trivial. We present the procedures for computing the projected gradient and ensuring the global convergence of the projected gradient scheme. The computation of projected gradient involves a constrained optimization problem; we show that the optimal solution to such a problem can be obtained via solving an unconstrained optimization subproblem and an Euclidean projection subproblem. We also present two projected gradient algorithms and analyze their rates of convergence in details. In addition, we illustrate the use of the presented projected gradient algorithms for the proposed multi-task learning formulation using the least squares loss. Experimental results on a collection of real-world data sets demonstrate the effectiveness of the proposed multi-task learning formulation and the efficiency of the proposed projected gradient algorithms. PMID:24077658

Learning Incoherent Sparse and Low-Rank Patterns from Multiple Tasks.

PubMed

Chen, Jianhui; Liu, Ji; Ye, Jieping

2012-02-01

We consider the problem of learning incoherent sparse and low-rank patterns from multiple tasks. Our approach is based on a linear multi-task learning formulation, in which the sparse and low-rank patterns are induced by a cardinality regularization term and a low-rank constraint, respectively. This formulation is non-convex; we convert it into its convex surrogate, which can be routinely solved via semidefinite programming for small-size problems. We propose to employ the general projected gradient scheme to efficiently solve such a convex surrogate; however, in the optimization formulation, the objective function is non-differentiable and the feasible domain is non-trivial. We present the procedures for computing the projected gradient and ensuring the global convergence of the projected gradient scheme. The computation of projected gradient involves a constrained optimization problem; we show that the optimal solution to such a problem can be obtained via solving an unconstrained optimization subproblem and an Euclidean projection subproblem. We also present two projected gradient algorithms and analyze their rates of convergence in details. In addition, we illustrate the use of the presented projected gradient algorithms for the proposed multi-task learning formulation using the least squares loss. Experimental results on a collection of real-world data sets demonstrate the effectiveness of the proposed multi-task learning formulation and the efficiency of the proposed projected gradient algorithms.

Providing Optimal Special Education Services to Hispanic Children and Their Families

ERIC Educational Resources Information Center

Langdon, Henriette W.

2009-01-01

The U.S. Census Bureau reported that 44.3 million people living in the United States in 2006 were of Hispanic descent. This population is far from homogeneous and includes seven major subgroups based on their origin, each with its own characteristics, which are briefly discussed. Of the 5.1 million children identified as English language learners,…

Vertical Compliance Trends in KBOS OPD Arrival Redesign

NASA Technical Reports Server (NTRS)

Stewart, Michael Jeffrey; Matthews, Bryan L.; Feary, Michael S.

2016-01-01

This report is a high-level summary of vertical compliance trends and overall rates of Area Navigation Optimized Profile Descent (RNAV OPD) utilization for Boston Logan International Airport. Specifically, we investigated trends from three RNAV OPDs and the subsequent redesigned iterations of those procedures: OOSHN3 to OOSHN4, ROBUC1 to ROBUC2, and QUABN3 to JFUND1.

Optimizing Home-School Collaboration: Strategies for School Psychologists and Latino Parent Involvement for Positive Mental Health Outcomes

ERIC Educational Resources Information Center

Olvera, Pedro; Olvera, Veronica I.

2012-01-01

Public schools across the United States are experiencing an increase in Cultural and Linguistically Diverse (CLD) students, particularly those of Latino descent. Latino children are at a high-risk for mental health problems (i.e., depression, anxiety, risk of suicide, etc.) and face greater risk factors when compared to many of their ethnic…

Direct Temperature Measurements during Netlander Descent on Mars

NASA Astrophysics Data System (ADS)

Colombatti, G.; Angrilli, F.; Ferri, F.; Francesconi, A.; Fulchignoni, M.; Lion Stoppato, P. F.; Saggi, B.

1999-09-01

A new design for a platinum thermoresistance temperature sensor has been developed and tested in Earth's atmosphere and stratosphere. It will be one of the sensors equipping the scientific package ATMIS (Atmospheric and Meteorology Instrument System), which will be devoted to the measurement of the meteorological parameters during both the entry/descent phase and the surface phase, aboard the Netlanders. In particular vertical profiles of temperature, density and pressure will allow the resolution of vertical gradients to investigate the atmospheric structure and dynamics. In view of the future missions to Mars, Netlander represents a unique chance to increase significantly the climate record both in time and in space, doubling the current knowledge of the atmospheric parameters. Furthermore is the only opportunity to conduct direct measurement of temperature and pressure (outside the boundary layer of the airbags used for the landing). The temperature sensor proposed is a platinum thermoresistance, enhancement of HASI TEM (Cassini/Huygens Mission); a substantial improvement of the performances, i.e. a faster dynamic response, has been obtained. Two different prototypes of new design sensor have been built, laboratory test are proceeding and the second one has been already flown aboard a stratospheric balloon.

Northern Hemisphere Nitrous Oxide Morphology during the 1989 AASE and the 1991-1992 AASE 2 Campaigns

NASA Technical Reports Server (NTRS)

Podolske, James R.; Loewenstein, Max; Weaver, Alex; Strahan, Susan; Chan, K. Roland

1993-01-01

Nitrous oxide vertical profiles and latitudinal distributions for the 1989 AASE and 1992 AASE II northern polar winters are developed from the ATLAS N2O dataset, using both potential temperature and pressure as vertical coordinates. Morphologies show strong descent occurring poleward of the polar jet. The AASE II morphology shows a mid latitude 'surf zone,' characterized by strong horizontal mixing, and a horizontal gradient south of 30 deg N due to the sub-tropical jet. These features are similar to those produced by two-dimensional photochemical models which include coupling between transport, radiation, and chemistry.

Northern hemisphere nitrous oxide morphology during the 1989 AASE and the 1991-1992 AASE 2 campaigns

NASA Technical Reports Server (NTRS)

Podolske, James R.; Loewenstein, Max; Weaver, Alex; Strahan, Susan E.; Chan, K. Roland

1993-01-01

Nitrous oxide vertical profiles and latitudinal distributions for the 1989 Airborne Antarctic Ozone Experiment (AASE) and 1992 AASE 2 northern polar winters are developed from the ATLAS N2O dataset, using both potential temperature and pressure as vertical coordinates. Morphologies show strong descent occuring poleward of the polar jet. The AASE 2 morphology shows a mid latitude 'surf zone', characterized by strong horizontal mixing, and a horizontal gradient south of 30 deg N due to the sub-tropical jet. These features are similar to those produced by two-dimensional photochemical models which include coupling between transport, radiation, and chemistry.

Kurtosis Approach Nonlinear Blind Source Separation

NASA Technical Reports Server (NTRS)

Duong, Vu A.; Stubbemd, Allen R.

2005-01-01

In this paper, we introduce a new algorithm for blind source signal separation for post-nonlinear mixtures. The mixtures are assumed to be linearly mixed from unknown sources first and then distorted by memoryless nonlinear functions. The nonlinear functions are assumed to be smooth and can be approximated by polynomials. Both the coefficients of the unknown mixing matrix and the coefficients of the approximated polynomials are estimated by the gradient descent method conditional on the higher order statistical requirements. The results of simulation experiments presented in this paper demonstrate the validity and usefulness of our approach for nonlinear blind source signal separation Keywords: Independent Component Analysis, Kurtosis, Higher order statistics.

Atmospheric tides on Venus. III - The planetary boundary layer

NASA Technical Reports Server (NTRS)

Dobrovolskis, A. R.

1983-01-01

Diurnal solar heating of Venus' surface produces variable temperatures, winds, and pressure gradients within a shallow layer at the bottom of the atmosphere. The corresponding asymmetric mass distribution experiences a tidal torque tending to maintain Venus' slow retrograde rotation. It is shown that including viscosity in the boundary layer does not materially affect the balance of torques. On the other hand, friction between the air and ground can reduce the predicted wind speeds from about 5 to about 1 m/sec in the lower atmosphere, more consistent with the observations from Venus landers and descent probes. Implications for aeolian activity on Venus' surface and for future missions are discussed.

Enhancement of the beam quality of non-uniform output slab laser amplifier with a 39-actuator rectangular piezoelectric deformable mirror.

PubMed

Yang, Ping; Ning, Yu; Lei, Xiang; Xu, Bing; Li, Xinyang; Dong, Lizhi; Yan, Hu; Liu, Wenjing; Jiang, Wenhan; Liu, Lei; Wang, Chao; Liang, Xingbo; Tang, Xiaojun

2010-03-29

We present a slab laser amplifier beam cleanup experimental system based on a 39-actuator rectangular piezoelectric deformable mirror. Rather than use a wave-front sensor to measure distortions in the wave-front and then apply a conjugation wave-front for compensating them, the system uses a Stochastic Parallel Gradient Descent algorithm to maximize the power contained within a far-field designated bucket. Experimental results demonstrate that at the output power of 335W, more than 30% energy concentrates in the 1x diffraction-limited area while the beam quality is enhanced greatly.

Quantum generalisation of feedforward neural networks

NASA Astrophysics Data System (ADS)

Wan, Kwok Ho; Dahlsten, Oscar; Kristjánsson, Hlér; Gardner, Robert; Kim, M. S.

2017-09-01

We propose a quantum generalisation of a classical neural network. The classical neurons are firstly rendered reversible by adding ancillary bits. Then they are generalised to being quantum reversible, i.e., unitary (the classical networks we generalise are called feedforward, and have step-function activation functions). The quantum network can be trained efficiently using gradient descent on a cost function to perform quantum generalisations of classical tasks. We demonstrate numerically that it can: (i) compress quantum states onto a minimal number of qubits, creating a quantum autoencoder, and (ii) discover quantum communication protocols such as teleportation. Our general recipe is theoretical and implementation-independent. The quantum neuron module can naturally be implemented photonically.

Genetic algorithm and graph theory based matrix factorization method for online friend recommendation.

PubMed

Li, Qu; Yao, Min; Yang, Jianhua; Xu, Ning

2014-01-01

Online friend recommendation is a fast developing topic in web mining. In this paper, we used SVD matrix factorization to model user and item feature vector and used stochastic gradient descent to amend parameter and improve accuracy. To tackle cold start problem and data sparsity, we used KNN model to influence user feature vector. At the same time, we used graph theory to partition communities with fairly low time and space complexity. What is more, matrix factorization can combine online and offline recommendation. Experiments showed that the hybrid recommendation algorithm is able to recommend online friends with good accuracy.

Railway obstacle detection algorithm using neural network

NASA Astrophysics Data System (ADS)

Yu, Mingyang; Yang, Peng; Wei, Sen

2018-05-01

Aiming at the difficulty of detection of obstacle in outdoor railway scene, a data-oriented method based on neural network to obtain image objects is proposed. First, we mark objects of images(such as people, trains, animals) acquired on the Internet. and then use the residual learning units to build Fast R-CNN framework. Then, the neural network is trained to get the target image characteristics by using stochastic gradient descent algorithm. Finally, a well-trained model is used to identify an outdoor railway image. if it includes trains and other objects, it will issue an alert. Experiments show that the correct rate of warning reached 94.85%.

A hybrid Gerchberg-Saxton-like algorithm for DOE and CGH calculation

NASA Astrophysics Data System (ADS)

Wang, Haichao; Yue, Weirui; Song, Qiang; Liu, Jingdan; Situ, Guohai

2017-02-01

The Gerchberg-Saxton (GS) algorithm is widely used in various disciplines of modern sciences and technologies where phase retrieval is required. However, this legendary algorithm most likely stagnates after a few iterations. Many efforts have been taken to improve this situation. Here we propose to introduce the strategy of gradient descent and weighting technique to the GS algorithm, and demonstrate it using two examples: design of a diffractive optical element (DOE) to achieve off-axis illumination in lithographic tools, and design of a computer generated hologram (CGH) for holographic display. Both numerical simulation and optical experiments are carried out for demonstration.

Convergence of fractional adaptive systems using gradient approach.

PubMed

Gallegos, Javier A; Duarte-Mermoud, Manuel A

2017-07-01

Conditions for boundedness and convergence of the output error and the parameter error for various Caputo's fractional order adaptive schemes based on the steepest descent method are derived in this paper. To this aim, the concept of sufficiently exciting signals is introduced, characterized and related to the concept of persistently exciting signals used in the integer order case. An application is designed in adaptive indirect control of integer order systems using fractional equations to adjust parameters. This application is illustrated for a pole placement adaptive problem. Advantages of using fractional adjustment in control adaptive schemes are experimentally obtained. Copyright © 2017 ISA. Published by Elsevier Ltd. All rights reserved.

New displacement-based methods for optimal truss topology design

NASA Technical Reports Server (NTRS)

Bendsoe, Martin P.; Ben-Tal, Aharon; Haftka, Raphael T.

1991-01-01

Two alternate methods for maximum stiffness truss topology design are presented. The ground structure approach is used, and the problem is formulated in terms of displacements and bar areas. This large, nonconvex optimization problem can be solved by a simultaneous analysis and design approach. Alternatively, an equivalent, unconstrained, and convex problem in the displacements only can be formulated, and this problem can be solved by a nonsmooth, steepest descent algorithm. In both methods, the explicit solving of the equilibrium equations and the assembly of the global stiffness matrix are circumvented. A large number of examples have been studied, showing the attractive features of topology design as well as exposing interesting features of optimal topologies.

Nonlinear optimization simplified by hypersurface deformation

DOE Office of Scientific and Technical Information (OSTI.GOV)

Stillinger, F.H.; Weber, T.A.

1988-09-01

A general strategy is advanced for simplifying nonlinear optimization problems, the ant-lion method. This approach exploits shape modifications of the cost-function hypersurface which distend basins surrounding low-lying minima (including global minima). By intertwining hypersurface deformations with steepest-descent displacements, the search is concentrated on a small relevant subset of all minima. Specific calculations demonstrating the value of this method are reported for the partitioning of two classes of irregular but nonrandom graphs, the prime-factor graphs and the pi graphs. We also indicate how this approach can be applied to the traveling salesman problem and to design layout optimization, and that itmore » may be useful in combination with simulated annealing strategies.« less

Optimal Pitch Thrust-Vector Angle and Benefits for all Flight Regimes

NASA Technical Reports Server (NTRS)

Gilyard, Glenn B.; Bolonkin, Alexander

2000-01-01

The NASA Dryden Flight Research Center is exploring the optimum thrust-vector angle on aircraft. Simple aerodynamic performance models for various phases of aircraft flight are developed and optimization equations and algorithms are presented in this report. Results of optimal angles of thrust vectors and associated benefits for various flight regimes of aircraft (takeoff, climb, cruise, descent, final approach, and landing) are given. Results for a typical wide-body transport aircraft are also given. The benefits accruable for this class of aircraft are small, but the technique can be applied to other conventionally configured aircraft. The lower L/D aerodynamic characteristics of fighters generally would produce larger benefits than those produced for transport aircraft.

Pitch Guidance Optimization for the Orion Abort Flight Tests

NASA Technical Reports Server (NTRS)

Stillwater, Ryan Allanque

2010-01-01

The National Aeronautics and Space Administration created the Constellation program to develop the next generation of manned space vehicles and launch vehicles. The Orion abort system is initiated in the event of an unsafe condition during launch. The system has a controller gains schedule that can be tuned to reduce the attitude errors between the simulated Orion abort trajectories and the guidance trajectory. A program was created that uses the method of steepest descent to tune the pitch gains schedule by an automated procedure. The gains schedule optimization was applied to three potential abort scenarios; each scenario tested using the optimized gains schedule resulted in reduced attitude errors when compared to the Orion production gains schedule.

Entry, Descent, and Landing for Human Mars Missions

NASA Technical Reports Server (NTRS)

Munk, Michelle M.; DwyerCianciolo, Alicia M.

2012-01-01

One of the most challenging aspects of a human mission to Mars is landing safely on the Martian surface. Mars has such low atmospheric density that decelerating large masses (tens of metric tons) requires methods that have not yet been demonstrated, and are not yet planned in future Mars missions. To identify the most promising options for Mars entry, descent, and landing, and to plan development of the needed technologies, NASA's Human Architecture Team (HAT) has refined candidate methods for emplacing needed elements of the human Mars exploration architecture (such as ascent vehicles and habitats) on the Mars surface. This paper explains the detailed, optimized simulations that have been developed to define the mass needed at Mars arrival to accomplish the entry, descent, and landing functions. Based on previous work, technology options for hypersonic deceleration include rigid, mid-L/D (lift-to-drag ratio) aeroshells, and inflatable aerodynamic decelerators (IADs). The hypersonic IADs, or HIADs, are about 20% less massive than the rigid vehicles, but both have their technology development challenges. For the supersonic regime, supersonic retropropulsion (SRP) is an attractive option, since a propulsive stage must be carried for terminal descent and can be ignited at higher speeds. The use of SRP eliminates the need for an additional deceleration system, but SRP is at a low Technology Readiness Level (TRL) in that the interacting plumes are not well-characterized, and their effect on vehicle stability has not been studied, to date. These architecture-level assessments have been used to define the key performance parameters and a technology development strategy for achieving the challenging mission of landing large payloads on Mars.

Single image super-resolution using self-optimizing mask via fractional-order gradient interpolation and reconstruction.

PubMed

Yang, Qi; Zhang, Yanzhu; Zhao, Tiebiao; Chen, YangQuan

2017-04-04

Image super-resolution using self-optimizing mask via fractional-order gradient interpolation and reconstruction aims to recover detailed information from low-resolution images and reconstruct them into high-resolution images. Due to the limited amount of data and information retrieved from low-resolution images, it is difficult to restore clear, artifact-free images, while still preserving enough structure of the image such as the texture. This paper presents a new single image super-resolution method which is based on adaptive fractional-order gradient interpolation and reconstruction. The interpolated image gradient via optimal fractional-order gradient is first constructed according to the image similarity and afterwards the minimum energy function is employed to reconstruct the final high-resolution image. Fractional-order gradient based interpolation methods provide an additional degree of freedom which helps optimize the implementation quality due to the fact that an extra free parameter α-order is being used. The proposed method is able to produce a rich texture detail while still being able to maintain structural similarity even under large zoom conditions. Experimental results show that the proposed method performs better than current single image super-resolution techniques. Copyright © 2017 ISA. Published by Elsevier Ltd. All rights reserved.

Optimization in Quaternion Dynamic Systems: Gradient, Hessian, and Learning Algorithms.

PubMed

Xu, Dongpo; Xia, Yili; Mandic, Danilo P

2016-02-01

The optimization of real scalar functions of quaternion variables, such as the mean square error or array output power, underpins many practical applications. Solutions typically require the calculation of the gradient and Hessian. However, real functions of quaternion variables are essentially nonanalytic, which are prohibitive to the development of quaternion-valued learning systems. To address this issue, we propose new definitions of quaternion gradient and Hessian, based on the novel generalized Hamilton-real (GHR) calculus, thus making a possible efficient derivation of general optimization algorithms directly in the quaternion field, rather than using the isomorphism with the real domain, as is current practice. In addition, unlike the existing quaternion gradients, the GHR calculus allows for the product and chain rule, and for a one-to-one correspondence of the novel quaternion gradient and Hessian with their real counterparts. Properties of the quaternion gradient and Hessian relevant to numerical applications are also introduced, opening a new avenue of research in quaternion optimization and greatly simplified the derivations of learning algorithms. The proposed GHR calculus is shown to yield the same generic algorithm forms as the corresponding real- and complex-valued algorithms. Advantages of the proposed framework are illuminated over illustrative simulations in quaternion signal processing and neural networks.

Simulated annealing in orbital flight planning

NASA Technical Reports Server (NTRS)

Soller, Jeffrey

1990-01-01

Simulated annealing is used to solve a minimum fuel trajectory problem in the space station environment. The environment is unique because the space station will define the first true multivehicle environment in space. The optimization yields surfaces which are potentially complex, with multiple local minima. Because of the likelihood of these local minima, descent techniques are unable to offer robust solutions. Other deterministic optimization techniques were explored without success. The simulated annealing optimization is capable of identifying a minimum-fuel, two-burn trajectory subject to four constraints. Furthermore, the computational efforts involved in the optimization are such that missions could be planned on board the space station. Potential applications could include the on-site planning of rendezvous with a target craft of the emergency rescue of an astronaut. Future research will include multiwaypoint maneuvers, using a knowledge base to guide the optimization.

SU-E-T-295: Simultaneous Beam Sampling and Aperture Shape Optimization for Station Parameter Optimized Radiation Therapy (SPORT)

DOE Office of Scientific and Technical Information (OSTI.GOV)

Zarepisheh, M; Li, R; Xing, L

Purpose: Station Parameter Optimized Radiation Therapy (SPORT) was recently proposed to fully utilize the technical capability of emerging digital LINACs, in which the station parameters of a delivery system, (such as aperture shape and weight, couch position/angle, gantry/collimator angle) are optimized altogether. SPORT promises to deliver unprecedented radiation dose distributions efficiently, yet there does not exist any optimization algorithm to implement it. The purpose of this work is to propose an optimization algorithm to simultaneously optimize the beam sampling and aperture shapes. Methods: We build a mathematical model whose variables are beam angles (including non-coplanar and/or even nonisocentric beams) andmore » aperture shapes. To solve the resulting large scale optimization problem, we devise an exact, convergent and fast optimization algorithm by integrating three advanced optimization techniques named column generation, gradient method, and pattern search. Column generation is used to find a good set of aperture shapes as an initial solution by adding apertures sequentially. Then we apply the gradient method to iteratively improve the current solution by reshaping the aperture shapes and updating the beam angles toward the gradient. Algorithm continues by pattern search method to explore the part of the search space that cannot be reached by the gradient method. Results: The proposed technique is applied to a series of patient cases and significantly improves the plan quality. In a head-and-neck case, for example, the left parotid gland mean-dose, brainstem max-dose, spinal cord max-dose, and mandible mean-dose are reduced by 10%, 7%, 24% and 12% respectively, compared to the conventional VMAT plan while maintaining the same PTV coverage. Conclusion: Combined use of column generation, gradient search and pattern search algorithms provide an effective way to optimize simultaneously the large collection of station parameters and significantly improves quality of resultant treatment plans as compared with conventional VMAT or IMRT treatments.« less

Measurement of lung expansion with computed tomography and comparison with quantitative histology.

PubMed

Coxson, H O; Mayo, J R; Behzad, H; Moore, B J; Verburgt, L M; Staples, C A; Paré, P D; Hogg, J C

1995-11-01

The total and regional lung volumes were estimated from computed tomography (CT), and the pleural pressure gradient was determined by using the milliliters of gas per gram of tissue estimated from the X-ray attenuation values and the pressure-volume curve of the lung. The data show that CT accurately estimated the volume of the resected lobe but overestimated its weight by 24 +/- 19%. The volume of gas per gram of tissue was less in the gravity-dependent regions due to a pleural pressure gradient of 0.24 +/- 0.08 cmH2O/cm of descent in the thorax. The proportion of tissue to air obtained with CT was similar to that obtained by quantitative histology. We conclude that the CT scan can be used to estimate total and regional lung volumes and that measurements of the proportions of tissue and air within the thorax by CT can be used in conjunction with quantitative histology to evaluate lung structure.

Operations research investigations of satellite power stations

NASA Technical Reports Server (NTRS)

Cole, J. W.; Ballard, J. L.

1976-01-01

A systems model reflecting the design concepts of Satellite Power Stations (SPS) was developed. The model is of sufficient scope to include the interrelationships of the following major design parameters: the transportation to and between orbits; assembly of the SPS; and maintenance of the SPS. The systems model is composed of a set of equations that are nonlinear with respect to the system parameters and decision variables. The model determines a figure of merit from which alternative concepts concerning transportation, assembly, and maintenance of satellite power stations are studied. A hybrid optimization model was developed to optimize the system's decision variables. The optimization model consists of a random search procedure and the optimal-steepest descent method. A FORTRAN computer program was developed to enable the user to optimize nonlinear functions using the model. Specifically, the computer program was used to optimize Satellite Power Station system components.

An historical survey of computational methods in optimal control.

NASA Technical Reports Server (NTRS)

Polak, E.

1973-01-01

Review of some of the salient theoretical developments in the specific area of optimal control algorithms. The first algorithms for optimal control were aimed at unconstrained problems and were derived by using first- and second-variation methods of the calculus of variations. These methods have subsequently been recognized as gradient, Newton-Raphson, or Gauss-Newton methods in function space. A much more recent addition to the arsenal of unconstrained optimal control algorithms are several variations of conjugate-gradient methods. At first, constrained optimal control problems could only be solved by exterior penalty function methods. Later algorithms specifically designed for constrained problems have appeared. Among these are methods for solving the unconstrained linear quadratic regulator problem, as well as certain constrained minimum-time and minimum-energy problems. Differential-dynamic programming was developed from dynamic programming considerations. The conditional-gradient method, the gradient-projection method, and a couple of feasible directions methods were obtained as extensions or adaptations of related algorithms for finite-dimensional problems. Finally, the so-called epsilon-methods combine the Ritz method with penalty function techniques.

Conjugate gradient optimization programs for shuttle reentry

NASA Technical Reports Server (NTRS)

Powers, W. F.; Jacobson, R. A.; Leonard, D. A.

1972-01-01

Two computer programs for shuttle reentry trajectory optimization are listed and described. Both programs use the conjugate gradient method as the optimization procedure. The Phase 1 Program is developed in cartesian coordinates for a rotating spherical earth, and crossrange, downrange, maximum deceleration, total heating, and terminal speed, altitude, and flight path angle are included in the performance index. The programs make extensive use of subroutines so that they may be easily adapted to other atmospheric trajectory optimization problems.

Optimization of Turbine Engine Cycle Analysis with Analytic Derivatives

NASA Technical Reports Server (NTRS)

Hearn, Tristan; Hendricks, Eric; Chin, Jeffrey; Gray, Justin; Moore, Kenneth T.

2016-01-01

A new engine cycle analysis tool, called Pycycle, was built using the OpenMDAO framework. Pycycle provides analytic derivatives allowing for an efficient use of gradient-based optimization methods on engine cycle models, without requiring the use of finite difference derivative approximation methods. To demonstrate this, a gradient-based design optimization was performed on a turbofan engine model. Results demonstrate very favorable performance compared to an optimization of an identical model using finite-difference approximated derivatives.

Fast three-dimensional inner volume excitations using parallel transmission and optimized k-space trajectories.

PubMed

Davids, Mathias; Schad, Lothar R; Wald, Lawrence L; Guérin, Bastien

2016-10-01

To design short parallel transmission (pTx) pulses for excitation of arbitrary three-dimensional (3D) magnetization patterns. We propose a joint optimization of the pTx radiofrequency (RF) and gradient waveforms for excitation of arbitrary 3D magnetization patterns. Our optimization of the gradient waveforms is based on the parameterization of k-space trajectories (3D shells, stack-of-spirals, and cross) using a small number of shape parameters that are well-suited for optimization. The resulting trajectories are smooth and sample k-space efficiently with few turns while using the gradient system at maximum performance. Within each iteration of the k-space trajectory optimization, we solve a small tip angle least-squares RF pulse design problem. Our RF pulse optimization framework was evaluated both in Bloch simulations and experiments on a 7T scanner with eight transmit channels. Using an optimized 3D cross (shells) trajectory, we were able to excite a cube shape (brain shape) with 3.4% (6.2%) normalized root-mean-square error in less than 5 ms using eight pTx channels and a clinical gradient system (Gmax  = 40 mT/m, Smax  = 150 T/m/s). This compared with 4.7% (41.2%) error for the unoptimized 3D cross (shells) trajectory. Incorporation of B0 robustness in the pulse design significantly altered the k-space trajectory solutions. Our joint gradient and RF optimization approach yields excellent excitation of 3D cube and brain shapes in less than 5 ms, which can be used for reduced field of view imaging and fat suppression in spectroscopy by excitation of the brain only. Magn Reson Med 76:1170-1182, 2016. © 2015 Wiley Periodicals, Inc. © 2015 Wiley Periodicals, Inc.

A PDE Sensitivity Equation Method for Optimal Aerodynamic Design

NASA Technical Reports Server (NTRS)

Borggaard, Jeff; Burns, John

1996-01-01

The use of gradient based optimization algorithms in inverse design is well established as a practical approach to aerodynamic design. A typical procedure uses a simulation scheme to evaluate the objective function (from the approximate states) and its gradient, then passes this information to an optimization algorithm. Once the simulation scheme (CFD flow solver) has been selected and used to provide approximate function evaluations, there are several possible approaches to the problem of computing gradients. One popular method is to differentiate the simulation scheme and compute design sensitivities that are then used to obtain gradients. Although this black-box approach has many advantages in shape optimization problems, one must compute mesh sensitivities in order to compute the design sensitivity. In this paper, we present an alternative approach using the PDE sensitivity equation to develop algorithms for computing gradients. This approach has the advantage that mesh sensitivities need not be computed. Moreover, when it is possible to use the CFD scheme for both the forward problem and the sensitivity equation, then there are computational advantages. An apparent disadvantage of this approach is that it does not always produce consistent derivatives. However, for a proper combination of discretization schemes, one can show asymptotic consistency under mesh refinement, which is often sufficient to guarantee convergence of the optimal design algorithm. In particular, we show that when asymptotically consistent schemes are combined with a trust-region optimization algorithm, the resulting optimal design method converges. We denote this approach as the sensitivity equation method. The sensitivity equation method is presented, convergence results are given and the approach is illustrated on two optimal design problems involving shocks.

Speed and convergence properties of gradient algorithms for optimization of IMRT.

PubMed

Zhang, Xiaodong; Liu, Helen; Wang, Xiaochun; Dong, Lei; Wu, Qiuwen; Mohan, Radhe

2004-05-01

Gradient algorithms are the most commonly employed search methods in the routine optimization of IMRT plans. It is well known that local minima can exist for dose-volume-based and biology-based objective functions. The purpose of this paper is to compare the relative speed of different gradient algorithms, to investigate the strategies for accelerating the optimization process, to assess the validity of these strategies, and to study the convergence properties of these algorithms for dose-volume and biological objective functions. With these aims in mind, we implemented Newton's, conjugate gradient (CG), and the steepest decent (SD) algorithms for dose-volume- and EUD-based objective functions. Our implementation of Newton's algorithm approximates the second derivative matrix (Hessian) by its diagonal. The standard SD algorithm and the CG algorithm with "line minimization" were also implemented. In addition, we investigated the use of a variation of the CG algorithm, called the "scaled conjugate gradient" (SCG) algorithm. To accelerate the optimization process, we investigated the validity of the use of a "hybrid optimization" strategy, in which approximations to calculated dose distributions are used during most of the iterations. Published studies have indicated that getting trapped in local minima is not a significant problem. To investigate this issue further, we first obtained, by trial and error, and starting with uniform intensity distributions, the parameters of the dose-volume- or EUD-based objective functions which produced IMRT plans that satisfied the clinical requirements. Using the resulting optimized intensity distributions as the initial guess, we investigated the possibility of getting trapped in a local minimum. For most of the results presented, we used a lung cancer case. To illustrate the generality of our methods, the results for a prostate case are also presented. For both dose-volume and EUD based objective functions, Newton's method far outperforms other algorithms in terms of speed. The SCG algorithm, which avoids expensive "line minimization," can speed up the standard CG algorithm by at least a factor of 2. For the same initial conditions, all algorithms converge essentially to the same plan. However, we demonstrate that for any of the algorithms studied, starting with previously optimized intensity distributions as the initial guess but for different objective function parameters, the solution frequently gets trapped in local minima. We found that the initial intensity distribution obtained from IMRT optimization utilizing objective function parameters, which favor a specific anatomic structure, would lead to a local minimum corresponding to that structure. Our results indicate that from among the gradient algorithms tested, Newton's method appears to be the fastest by far. Different gradient algorithms have the same convergence properties for dose-volume- and EUD-based objective functions. The hybrid dose calculation strategy is valid and can significantly accelerate the optimization process. The degree of acceleration achieved depends on the type of optimization problem being addressed (e.g., IMRT optimization, intensity modulated beam configuration optimization, or objective function parameter optimization). Under special conditions, gradient algorithms will get trapped in local minima, and reoptimization, starting with the results of previous optimization, will lead to solutions that are generally not significantly different from the local minimum.

Performance of local optimization in single-plane fluoroscopic analysis for total knee arthroplasty.

PubMed

Prins, A H; Kaptein, B L; Stoel, B C; Lahaye, D J P; Valstar, E R

2015-11-05

Fluoroscopy-derived joint kinematics plays an important role in the evaluation of knee prostheses. Fluoroscopic analysis requires estimation of the 3D prosthesis pose from its 2D silhouette in the fluoroscopic image, by optimizing a dissimilarity measure. Currently, extensive user-interaction is needed, which makes analysis labor-intensive and operator-dependent. The aim of this study was to review five optimization methods for 3D pose estimation and to assess their performance in finding the correct solution. Two derivative-free optimizers (DHSAnn and IIPM) and three gradient-based optimizers (LevMar, DoNLP2 and IpOpt) were evaluated. For the latter three optimizers two different implementations were evaluated: one with a numerically approximated gradient and one with an analytically derived gradient for computational efficiency. On phantom data, all methods were able to find the 3D pose within 1mm and 1° in more than 85% of cases. IpOpt had the highest success-rate: 97%. On clinical data, the success rates were higher than 85% for the in-plane positions, but not for the rotations. IpOpt was the most expensive method and the application of an analytically derived gradients accelerated the gradient-based methods by a factor 3-4 without any differences in success rate. In conclusion, 85% of the frames can be analyzed automatically in clinical data and only 15% of the frames require manual supervision. The optimal success-rate on phantom data (97% with IpOpt) on phantom data indicates that even less supervision may become feasible. Copyright © 2015 Elsevier Ltd. All rights reserved.

A Block Coordinate Descent Method for Multi-Convex Optimization with Applications to Nonnegative Tensor Factorization and Completion

DTIC Science & Technology

2012-08-01

model appears in cosmic microwave background analysis [10] which solves min A,Y λ 2 trace ( (ABY − X)>C−1(ABY − X) ) + r(Y), subject to A ∈ D (1.5...and “×n” represent outer product and tensor-matrix multiplication, respectively. (The necessary background of tensor is reviewed in Sec. 3) Most

Adaptive hybrid optimal quantum control for imprecisely characterized systems.

PubMed

Egger, D J; Wilhelm, F K

2014-06-20

Optimal quantum control theory carries a huge promise for quantum technology. Its experimental application, however, is often hindered by imprecise knowledge of the input variables, the quantum system's parameters. We show how to overcome this by adaptive hybrid optimal control, using a protocol named Ad-HOC. This protocol combines open- and closed-loop optimal control by first performing a gradient search towards a near-optimal control pulse and then an experimental fidelity estimation with a gradient-free method. For typical settings in solid-state quantum information processing, adaptive hybrid optimal control enhances gate fidelities by an order of magnitude, making optimal control theory applicable and useful.

Generalized gradient algorithm for trajectory optimization

NASA Technical Reports Server (NTRS)

Zhao, Yiyuan; Bryson, A. E.; Slattery, R.

1990-01-01

The generalized gradient algorithm presented and verified as a basis for the solution of trajectory optimization problems improves the performance index while reducing path equality constraints, and terminal equality constraints. The algorithm is conveniently divided into two phases, of which the first, 'feasibility' phase yields a solution satisfying both path and terminal constraints, while the second, 'optimization' phase uses the results of the first phase as initial guesses.

Machine Learning Interface for Medical Image Analysis.

PubMed

Zhang, Yi C; Kagen, Alexander C

2017-10-01

TensorFlow is a second-generation open-source machine learning software library with a built-in framework for implementing neural networks in wide variety of perceptual tasks. Although TensorFlow usage is well established with computer vision datasets, the TensorFlow interface with DICOM formats for medical imaging remains to be established. Our goal is to extend the TensorFlow API to accept raw DICOM images as input; 1513 DaTscan DICOM images were obtained from the Parkinson's Progression Markers Initiative (PPMI) database. DICOM pixel intensities were extracted and shaped into tensors, or n-dimensional arrays, to populate the training, validation, and test input datasets for machine learning. A simple neural network was constructed in TensorFlow to classify images into normal or Parkinson's disease groups. Training was executed over 1000 iterations for each cross-validation set. The gradient descent optimization and Adagrad optimization algorithms were used to minimize cross-entropy between the predicted and ground-truth labels. Cross-validation was performed ten times to produce a mean accuracy of 0.938 ± 0.047 (95 % CI 0.908-0.967). The mean sensitivity was 0.974 ± 0.043 (95 % CI 0.947-1.00) and mean specificity was 0.822 ± 0.207 (95 % CI 0.694-0.950). We extended the TensorFlow API to enable DICOM compatibility in the context of DaTscan image analysis. We implemented a neural network classifier that produces diagnostic accuracies on par with excellent results from previous machine learning models. These results indicate the potential role of TensorFlow as a useful adjunct diagnostic tool in the clinical setting.

Simulation and Optimization of an Airfoil with Leading Edge Slat

NASA Astrophysics Data System (ADS)

Schramm, Matthias; Stoevesandt, Bernhard; Peinke, Joachim

2016-09-01

A gradient-based optimization is used in order to improve the shape of a leading edge slat upstream of a DU 91-W2-250 airfoil. The simulations are performed by solving the Reynolds-Averaged Navier-Stokes equations (RANS) using the open source CFD code OpenFOAM. Gradients are computed via the adjoint approach, which is suitable to deal with many design parameters, but keeping the computational costs low. The implementation is verified by comparing the gradients from the adjoint method with gradients obtained by finite differences for a NACA 0012 airfoil. The simulations of the leading edge slat are validated against measurements from the acoustic wind tunnel of Oldenburg University at a Reynolds number of Re = 6 • 105. The shape of the slat is optimized using the adjoint approach resulting in a drag reduction of 2%. Although the optimization is done for Re = 6 • 105, the improvements also hold for a higher Reynolds number of Re = 7.9 • 106, which is more realistic at modern wind turbines.

Near-Optimal Re-Entry Trajectories for Reusable Launch Vehicles

NASA Technical Reports Server (NTRS)

Chou, H.-C.; Ardema, M. D.; Bowles, J. V.

1997-01-01

A near-optimal guidance law for the descent trajectory for earth orbit re-entry of a fully reusable single-stage-to-orbit pure rocket launch vehicle is derived. A methodology is developed to investigate using both bank angle and altitude as control variables and selecting parameters that maximize various performance functions. The method is based on the energy-state model of the aircraft equations of motion. The major task of this paper is to obtain optimal re-entry trajectories under a variety of performance goals: minimum time, minimum surface temperature, minimum heating, and maximum heading change; four classes of trajectories were investigated: no banking, optimal left turn banking, optimal right turn banking, and optimal bank chattering. The cost function is in general a weighted sum of all performance goals. In particular, the trade-off between minimizing heat load into the vehicle and maximizing cross range distance is investigated. The results show that the optimization methodology can be used to derive a wide variety of near-optimal trajectories.

Numerical optimization in Hilbert space using inexact function and gradient evaluations

NASA Technical Reports Server (NTRS)

Carter, Richard G.

1989-01-01

Trust region algorithms provide a robust iterative technique for solving non-convex unstrained optimization problems, but in many instances it is prohibitively expensive to compute high accuracy function and gradient values for the method. Of particular interest are inverse and parameter estimation problems, since function and gradient evaluations involve numerically solving large systems of differential equations. A global convergence theory is presented for trust region algorithms in which neither function nor gradient values are known exactly. The theory is formulated in a Hilbert space setting so that it can be applied to variational problems as well as the finite dimensional problems normally seen in trust region literature. The conditions concerning allowable error are remarkably relaxed: relative errors in the gradient error condition is automatically satisfied if the error is orthogonal to the gradient approximation. A technique for estimating gradient error and improving the approximation is also presented.

A uniplanar three-axis gradient set for in vivo magnetic resonance microscopy.

PubMed

Demyanenko, Andrey V; Zhao, Lin; Kee, Yun; Nie, Shuyi; Fraser, Scott E; Tyszka, J Michael

2009-09-01

We present an optimized uniplanar magnetic resonance gradient design specifically tailored for MR imaging applications in developmental biology and histology. Uniplanar gradient designs sacrifice gradient uniformity for high gradient efficiency and slew rate, and are attractive for surface imaging applications where open access from one side of the sample is required. However, decreasing the size of the uniplanar gradient set presents several unique engineering challenges, particularly for heat dissipation and thermal insulation of the sample from gradient heating. We demonstrate a new three-axis, target-field optimized uniplanar gradient coil design that combines efficient cooling and insulation to significantly reduce sample heating at sample-gradient distances of less than 5mm. The instrument is designed for microscopy in horizontal bore magnets. Empirical gradient current efficiencies in the prototype coils lie between 3.75G/cm/A and 4.5G/cm/A with current and heating-limited maximum gradient strengths between 235G/cm and 450G/cm at a 2% duty cycle. The uniplanar gradient prototype is demonstrated with non-linearity corrections for both high-resolution structural imaging of tissue slices and for long time-course imaging of live, developing amphibian embryos in a horizontal bore 7T magnet.

Universal approximators for multi-objective direct policy search in water reservoir management problems: a comparative analysis

NASA Astrophysics Data System (ADS)

Giuliani, Matteo; Mason, Emanuele; Castelletti, Andrea; Pianosi, Francesca

2014-05-01

The optimal operation of water resources systems is a wide and challenging problem due to non-linearities in the model and the objectives, high dimensional state-control space, and strong uncertainties in the hydroclimatic regimes. The application of classical optimization techniques (e.g., SDP, Q-learning, gradient descent-based algorithms) is strongly limited by the dimensionality of the system and by the presence of multiple, conflicting objectives. This study presents a novel approach which combines Direct Policy Search (DPS) and Multi-Objective Evolutionary Algorithms (MOEAs) to solve high-dimensional state and control space problems involving multiple objectives. DPS, also known as parameterization-simulation-optimization in the water resources literature, is a simulation-based approach where the reservoir operating policy is first parameterized within a given family of functions and, then, the parameters optimized with respect to the objectives of the management problem. The selection of a suitable class of functions to which the operating policy belong to is a key step, as it might restrict the search for the optimal policy to a subspace of the decision space that does not include the optimal solution. In the water reservoir literature, a number of classes have been proposed. However, many of these rules are based largely on empirical or experimental successes and they were designed mostly via simulation and for single-purpose reservoirs. In a multi-objective context similar rules can not easily inferred from the experience and the use of universal function approximators is generally preferred. In this work, we comparatively analyze two among the most common universal approximators: artificial neural networks (ANN) and radial basis functions (RBF) under different problem settings to estimate their scalability and flexibility in dealing with more and more complex problems. The multi-purpose HoaBinh water reservoir in Vietnam, accounting for hydropower production and flood control, is used as a case study. Preliminary results show that the RBF policy parametrization is more effective than the ANN one. In particular, the approximated Pareto front obtained with RBF control policies successfully explores the full tradeoff space between the two conflicting objectives, while most of the ANN solutions results to be Pareto-dominated by the RBF ones.

Massive parallelization of serial inference algorithms for a complex generalized linear model

PubMed Central

Suchard, Marc A.; Simpson, Shawn E.; Zorych, Ivan; Ryan, Patrick; Madigan, David

2014-01-01

Following a series of high-profile drug safety disasters in recent years, many countries are redoubling their efforts to ensure the safety of licensed medical products. Large-scale observational databases such as claims databases or electronic health record systems are attracting particular attention in this regard, but present significant methodological and computational concerns. In this paper we show how high-performance statistical computation, including graphics processing units, relatively inexpensive highly parallel computing devices, can enable complex methods in large databases. We focus on optimization and massive parallelization of cyclic coordinate descent approaches to fit a conditioned generalized linear model involving tens of millions of observations and thousands of predictors in a Bayesian context. We find orders-of-magnitude improvement in overall run-time. Coordinate descent approaches are ubiquitous in high-dimensional statistics and the algorithms we propose open up exciting new methodological possibilities with the potential to significantly improve drug safety. PMID:25328363

A Concept for Airborne Precision Spacing for Dependent Parallel Approaches

NASA Technical Reports Server (NTRS)

Barmore, Bryan E.; Baxley, Brian T.; Abbott, Terence S.; Capron, William R.; Smith, Colin L.; Shay, Richard F.; Hubbs, Clay

2012-01-01

The Airborne Precision Spacing concept of operations has been previously developed to support the precise delivery of aircraft landing successively on the same runway. The high-precision and consistent delivery of inter-aircraft spacing allows for increased runway throughput and the use of energy-efficient arrivals routes such as Continuous Descent Arrivals and Optimized Profile Descents. This paper describes an extension to the Airborne Precision Spacing concept to enable dependent parallel approach operations where the spacing aircraft must manage their in-trail spacing from a leading aircraft on approach to the same runway and spacing from an aircraft on approach to a parallel runway. Functionality for supporting automation is discussed as well as procedures for pilots and controllers. An analysis is performed to identify the required information and a new ADS-B report is proposed to support these information needs. Finally, several scenarios are described in detail.

Optimal Disturbances in Boundary Layers Subject to Streamwise Pressure Gradient

NASA Technical Reports Server (NTRS)

Ashpis, David E.; Tumin, Anatoli

2003-01-01

An analysis of the non-modal growth of perturbations in a boundary layer in the presence of a streamwise pressure gradient is presented. The analysis is based on PSE equations for an incompressible fluid. Examples with Falkner- Skan profiles indicate that a favorable pressure gradient decreases the non-modal growth while an unfavorable pressure gradient leads to an increase of the amplification. It is suggested that the transient growth mechanism be utilized to choose optimal parameters of tripping elements on a low-pressure turbine (LPT) airfoil. As an example, a boundary-layer flow with a streamwise pressure gradient corresponding to the pressure distribution over a LPT airfoil is considered. It is shown that there is an optimal spacing of the tripping elements and that the transient growth effect depends on the starting point. The amplification is found to be small at the LPT s very low Reynolds numbers, but there is a possibility to enhance the transient energy growth by means of wall cooling.

The use of singular value gradients and optimization techniques to design robust controllers for multiloop systems

NASA Technical Reports Server (NTRS)

Newsom, J. R.; Mukhopadhyay, V.

1983-01-01

A method for designing robust feedback controllers for multiloop systems is presented. Robustness is characterized in terms of the minimum singular value of the system return difference matrix at the plant input. Analytical gradients of the singular values with respect to design variables in the controller are derived. A cumulative measure of the singular values and their gradients with respect to the design variables is used with a numerical optimization technique to increase the system's robustness. Both unconstrained and constrained optimization techniques are evaluated. Numerical results are presented for a two-input/two-output drone flight control system.

The use of singular value gradients and optimization techniques to design robust controllers for multiloop systems

NASA Technical Reports Server (NTRS)

Newsom, J. R.; Mukhopadhyay, V.

1983-01-01

A method for designing robust feedback controllers for multiloop systems is presented. Robustness is characterized in terms of the minimum singular value of the system return difference matrix at the plant input. Analytical gradients of the singular values with respect to design variables in the controller are derived. A cumulative measure of the singular values and their gradients with respect to the design variables is used with a numerical optimization technique to increase the system's robustness. Both unconstrained and constrained optimization techniques are evaluated. Numerical results are presented for a two output drone flight control system.

Parallelization of Program to Optimize Simulated Trajectories (POST3D)

NASA Technical Reports Server (NTRS)

Hammond, Dana P.; Korte, John J. (Technical Monitor)

2001-01-01

This paper describes the parallelization of the Program to Optimize Simulated Trajectories (POST3D). POST3D uses a gradient-based optimization algorithm that reaches an optimum design point by moving from one design point to the next. The gradient calculations required to complete the optimization process, dominate the computational time and have been parallelized using a Single Program Multiple Data (SPMD) on a distributed memory NUMA (non-uniform memory access) architecture. The Origin2000 was used for the tests presented.

Gradient stationary phase optimized selectivity liquid chromatography with conventional columns.

PubMed

Chen, Kai; Lynen, Frédéric; Szucs, Roman; Hanna-Brown, Melissa; Sandra, Pat

2013-05-21

Stationary phase optimized selectivity liquid chromatography (SOSLC) is a promising technique to optimize the selectivity of a given separation. By combination of different stationary phases, SOSLC offers excellent possibilities for method development under both isocratic and gradient conditions. The so far available commercial SOSLC protocol utilizes dedicated column cartridges and corresponding cartridge holders to build up the combined column of different stationary phases. The present work is aimed at developing and extending the gradient SOSLC approach towards coupling conventional columns. Generic tubing was used to connect short commercially available LC columns. Fast and base-line separation of a mixture of 12 compounds containing phenones, benzoic acids and hydroxybenzoates under both isocratic and linear gradient conditions was selected to demonstrate the potential of SOSLC. The influence of the connecting tubing on the deviation of predictions is also discussed.

Robust camera calibration for sport videos using court models

NASA Astrophysics Data System (ADS)

Farin, Dirk; Krabbe, Susanne; de With, Peter H. N.; Effelsberg, Wolfgang

2003-12-01

We propose an automatic camera calibration algorithm for court sports. The obtained camera calibration parameters are required for applications that need to convert positions in the video frame to real-world coordinates or vice versa. Our algorithm uses a model of the arrangement of court lines for calibration. Since the court model can be specified by the user, the algorithm can be applied to a variety of different sports. The algorithm starts with a model initialization step which locates the court in the image without any user assistance or a-priori knowledge about the most probable position. Image pixels are classified as court line pixels if they pass several tests including color and local texture constraints. A Hough transform is applied to extract line elements, forming a set of court line candidates. The subsequent combinatorial search establishes correspondences between lines in the input image and lines from the court model. For the succeeding input frames, an abbreviated calibration algorithm is used, which predicts the camera parameters for the new image and optimizes the parameters using a gradient-descent algorithm. We have conducted experiments on a variety of sport videos (tennis, volleyball, and goal area sequences of soccer games). Video scenes with considerable difficulties were selected to test the robustness of the algorithm. Results show that the algorithm is very robust to occlusions, partial court views, bad lighting conditions, or shadows.

A Fast Neural Network Approach to Predict Lung Tumor Motion during Respiration for Radiation Therapy Applications

PubMed Central

Slama, Matous; Benes, Peter M.; Bila, Jiri

2015-01-01

During radiotherapy treatment for thoracic and abdomen cancers, for example, lung cancers, respiratory motion moves the target tumor and thus badly affects the accuracy of radiation dose delivery into the target. A real-time image-guided technique can be used to monitor such lung tumor motion for accurate dose delivery, but the system latency up to several hundred milliseconds for repositioning the radiation beam also affects the accuracy. In order to compensate the latency, neural network prediction technique with real-time retraining can be used. We have investigated real-time prediction of 3D time series of lung tumor motion on a classical linear model, perceptron model, and on a class of higher-order neural network model that has more attractive attributes regarding its optimization convergence and computational efficiency. The implemented static feed-forward neural architectures are compared when using gradient descent adaptation and primarily the Levenberg-Marquardt batch algorithm as the ones of the most common and most comprehensible learning algorithms. The proposed technique resulted in fast real-time retraining, so the total computational time on a PC platform was equal to or even less than the real treatment time. For one-second prediction horizon, the proposed techniques achieved accuracy less than one millimeter of 3D mean absolute error in one hundred seconds of total treatment time. PMID:25893194

3D craniofacial registration using thin-plate spline transform and cylindrical surface projection

PubMed Central

Chen, Yucong; Deng, Qingqiong; Duan, Fuqing

2017-01-01

Craniofacial registration is used to establish the point-to-point correspondence in a unified coordinate system among human craniofacial models. It is the foundation of craniofacial reconstruction and other craniofacial statistical analysis research. In this paper, a non-rigid 3D craniofacial registration method using thin-plate spline transform and cylindrical surface projection is proposed. First, the gradient descent optimization is utilized to improve a cylindrical surface fitting (CSF) for the reference craniofacial model. Second, the thin-plate spline transform (TPST) is applied to deform a target craniofacial model to the reference model. Finally, the cylindrical surface projection (CSP) is used to derive the point correspondence between the reference and deformed target models. To accelerate the procedure, the iterative closest point ICP algorithm is used to obtain a rough correspondence, which can provide a possible intersection area of the CSP. Finally, the inverse TPST is used to map the obtained corresponding points from the deformed target craniofacial model to the original model, and it can be realized directly by the correspondence between the original target model and the deformed target model. Three types of registration, namely, reflexive, involutive and transitive registration, are carried out to verify the effectiveness of the proposed craniofacial registration algorithm. Comparison with the methods in the literature shows that the proposed method is more accurate. PMID:28982117

3D craniofacial registration using thin-plate spline transform and cylindrical surface projection.

PubMed

Chen, Yucong; Zhao, Junli; Deng, Qingqiong; Duan, Fuqing

2017-01-01

Craniofacial registration is used to establish the point-to-point correspondence in a unified coordinate system among human craniofacial models. It is the foundation of craniofacial reconstruction and other craniofacial statistical analysis research. In this paper, a non-rigid 3D craniofacial registration method using thin-plate spline transform and cylindrical surface projection is proposed. First, the gradient descent optimization is utilized to improve a cylindrical surface fitting (CSF) for the reference craniofacial model. Second, the thin-plate spline transform (TPST) is applied to deform a target craniofacial model to the reference model. Finally, the cylindrical surface projection (CSP) is used to derive the point correspondence between the reference and deformed target models. To accelerate the procedure, the iterative closest point ICP algorithm is used to obtain a rough correspondence, which can provide a possible intersection area of the CSP. Finally, the inverse TPST is used to map the obtained corresponding points from the deformed target craniofacial model to the original model, and it can be realized directly by the correspondence between the original target model and the deformed target model. Three types of registration, namely, reflexive, involutive and transitive registration, are carried out to verify the effectiveness of the proposed craniofacial registration algorithm. Comparison with the methods in the literature shows that the proposed method is more accurate.

A fuzzy neural network for intelligent data processing

NASA Astrophysics Data System (ADS)

Xie, Wei; Chu, Feng; Wang, Lipo; Lim, Eng Thiam

2005-03-01

In this paper, we describe an incrementally generated fuzzy neural network (FNN) for intelligent data processing. This FNN combines the features of initial fuzzy model self-generation, fast input selection, partition validation, parameter optimization and rule-base simplification. A small FNN is created from scratch -- there is no need to specify the initial network architecture, initial membership functions, or initial weights. Fuzzy IF-THEN rules are constantly combined and pruned to minimize the size of the network while maintaining accuracy; irrelevant inputs are detected and deleted, and membership functions and network weights are trained with a gradient descent algorithm, i.e., error backpropagation. Experimental studies on synthesized data sets demonstrate that the proposed Fuzzy Neural Network is able to achieve accuracy comparable to or higher than both a feedforward crisp neural network, i.e., NeuroRule, and a decision tree, i.e., C4.5, with more compact rule bases for most of the data sets used in our experiments. The FNN has achieved outstanding results for cancer classification based on microarray data. The excellent classification result for Small Round Blue Cell Tumors (SRBCTs) data set is shown. Compared with other published methods, we have used a much fewer number of genes for perfect classification, which will help researchers directly focus their attention on some specific genes and may lead to discovery of deep reasons of the development of cancers and discovery of drugs.

An analytical SMASH procedure (ASP) for sensitivity-encoded MRI.

PubMed

Lee, R F; Westgate, C R; Weiss, R G; Bottomley, P A

2000-05-01

The simultaneous acquisition of spatial harmonics (SMASH) method of imaging with detector arrays can reduce the number of phase-encoding steps, and MRI scan time several-fold. The original approach utilized numerical gradient-descent fitting with the coil sensitivity profiles to create a set of composite spatial harmonics to replace the phase-encoding steps. Here, an analytical approach for generating the harmonics is presented. A transform is derived to project the harmonics onto a set of sensitivity profiles. A sequence of Fourier, Hilbert, and inverse Fourier transform is then applied to analytically eliminate spatially dependent phase errors from the different coils while fully preserving the spatial-encoding. By combining the transform and phase correction, the original numerical image reconstruction method can be replaced by an analytical SMASH procedure (ASP). The approach also allows simulation of SMASH imaging, revealing a criterion for the ratio of the detector sensitivity profile width to the detector spacing that produces optimal harmonic generation. When detector geometry is suboptimal, a group of quasi-harmonics arises, which can be corrected and restored to pure harmonics. The simulation also reveals high-order harmonic modulation effects, and a demodulation procedure is presented that enables application of ASP to a large numbers of detectors. The method is demonstrated on a phantom and humans using a standard 4-channel phased-array MRI system. Copyright 2000 Wiley-Liss, Inc.

DOE Office of Scientific and Technical Information (OSTI.GOV)

Harris, Michael D.; Dater, Manasi; Whitaker, Ross

In this study, statistical shape modeling (SSM) was used to quantify three-dimensional (3D) variation and morphologic differences between femurs with and without cam femoroacetabular impingement (FAI). 3D surfaces were generated from CT scans of femurs from 41 controls and 30 cam FAI patients. SSM correspondence particles were optimally positioned on each surface using a gradient descent energy function. Mean shapes for control and patient groups were defined from the resulting particle configurations. Morphological differences between group mean shapes and between the control mean and individual patients were calculated. Principal component analysis was used to describe anatomical variation present in bothmore » groups. The first 6 modes (or principal components) captured statistically significant shape variations, which comprised 84% of cumulative variation among the femurs. Shape variation was greatest in femoral offset, greater trochanter height, and the head-neck junction. The mean cam femur shape protruded above the control mean by a maximum of 3.3 mm with sustained protrusions of 2.5-3.0 mm along the anterolateral head-neck junction and distally along the anterior neck, corresponding well with reported cam lesion locations and soft-tissue damage. This study provides initial evidence that SSM can describe variations in femoral morphology in both controls and cam FAI patients and may be useful for developing new measurements of pathological anatomy. SSM may also be applied to characterize cam FAI severity and provide templates to guide patient-specific surgical resection of bone.« less

A fast neural network approach to predict lung tumor motion during respiration for radiation therapy applications.

PubMed

Bukovsky, Ivo; Homma, Noriyasu; Ichiji, Kei; Cejnek, Matous; Slama, Matous; Benes, Peter M; Bila, Jiri

2015-01-01

During radiotherapy treatment for thoracic and abdomen cancers, for example, lung cancers, respiratory motion moves the target tumor and thus badly affects the accuracy of radiation dose delivery into the target. A real-time image-guided technique can be used to monitor such lung tumor motion for accurate dose delivery, but the system latency up to several hundred milliseconds for repositioning the radiation beam also affects the accuracy. In order to compensate the latency, neural network prediction technique with real-time retraining can be used. We have investigated real-time prediction of 3D time series of lung tumor motion on a classical linear model, perceptron model, and on a class of higher-order neural network model that has more attractive attributes regarding its optimization convergence and computational efficiency. The implemented static feed-forward neural architectures are compared when using gradient descent adaptation and primarily the Levenberg-Marquardt batch algorithm as the ones of the most common and most comprehensible learning algorithms. The proposed technique resulted in fast real-time retraining, so the total computational time on a PC platform was equal to or even less than the real treatment time. For one-second prediction horizon, the proposed techniques achieved accuracy less than one millimeter of 3D mean absolute error in one hundred seconds of total treatment time.

Shape and Spatially-Varying Reflectance Estimation from Virtual Exemplars.

PubMed

Hui, Zhuo; Sankaranarayanan, Aswin C

2017-10-01

This paper addresses the problem of estimating the shape of objects that exhibit spatially-varying reflectance. We assume that multiple images of the object are obtained under a fixed view-point and varying illumination, i.e., the setting of photometric stereo. At the core of our techniques is the assumption that the BRDF at each pixel lies in the non-negative span of a known BRDF dictionary. This assumption enables a per-pixel surface normal and BRDF estimation framework that is computationally tractable and requires no initialization in spite of the underlying problem being non-convex. Our estimation framework first solves for the surface normal at each pixel using a variant of example-based photometric stereo. We design an efficient multi-scale search strategy for estimating the surface normal and subsequently, refine this estimate using a gradient descent procedure. Given the surface normal estimate, we solve for the spatially-varying BRDF by constraining the BRDF at each pixel to be in the span of the BRDF dictionary; here, we use additional priors to further regularize the solution. A hallmark of our approach is that it does not require iterative optimization techniques nor the need for careful initialization, both of which are endemic to most state-of-the-art techniques. We showcase the performance of our technique on a wide range of simulated and real scenes where we outperform competing methods.

A Regularized Linear Dynamical System Framework for Multivariate Time Series Analysis.

PubMed

Liu, Zitao; Hauskrecht, Milos

2015-01-01

Linear Dynamical System (LDS) is an elegant mathematical framework for modeling and learning Multivariate Time Series (MTS). However, in general, it is difficult to set the dimension of an LDS's hidden state space. A small number of hidden states may not be able to model the complexities of a MTS, while a large number of hidden states can lead to overfitting. In this paper, we study learning methods that impose various regularization penalties on the transition matrix of the LDS model and propose a regularized LDS learning framework (rLDS) which aims to (1) automatically shut down LDSs' spurious and unnecessary dimensions, and consequently, address the problem of choosing the optimal number of hidden states; (2) prevent the overfitting problem given a small amount of MTS data; and (3) support accurate MTS forecasting. To learn the regularized LDS from data we incorporate a second order cone program and a generalized gradient descent method into the Maximum a Posteriori framework and use Expectation Maximization to obtain a low-rank transition matrix of the LDS model. We propose two priors for modeling the matrix which lead to two instances of our rLDS. We show that our rLDS is able to recover well the intrinsic dimensionality of the time series dynamics and it improves the predictive performance when compared to baselines on both synthetic and real-world MTS datasets.

Multi-Constraint Multi-Variable Optimization of Source-Driven Nuclear Systems

NASA Astrophysics Data System (ADS)

Watkins, Edward Francis

1995-01-01

A novel approach to the search for optimal designs of source-driven nuclear systems is investigated. Such systems include radiation shields, fusion reactor blankets and various neutron spectrum-shaping assemblies. The novel approach involves the replacement of the steepest-descents optimization algorithm incorporated in the code SWAN by a significantly more general and efficient sequential quadratic programming optimization algorithm provided by the code NPSOL. The resulting SWAN/NPSOL code system can be applied to more general, multi-variable, multi-constraint shield optimization problems. The constraints it accounts for may include simple bounds on variables, linear constraints, and smooth nonlinear constraints. It may also be applied to unconstrained, bound-constrained and linearly constrained optimization. The shield optimization capabilities of the SWAN/NPSOL code system is tested and verified in a variety of optimization problems: dose minimization at constant cost, cost minimization at constant dose, and multiple-nonlinear constraint optimization. The replacement of the optimization part of SWAN with NPSOL is found feasible and leads to a very substantial improvement in the complexity of optimization problems which can be efficiently handled.

A Gradient-Based Multistart Algorithm for Multimodal Aerodynamic Shape Optimization Problems Based on Free-Form Deformation

NASA Astrophysics Data System (ADS)

Streuber, Gregg Mitchell

Environmental and economic factors motivate the pursuit of more fuel-efficient aircraft designs. Aerodynamic shape optimization is a powerful tool in this effort, but is hampered by the presence of multimodality in many design spaces. Gradient-based multistart optimization uses a sampling algorithm and multiple parallel optimizations to reliably apply fast gradient-based optimization to moderately multimodal problems. Ensuring that the sampled geometries remain physically realizable requires manually developing specialized linear constraints for each class of problem. Utilizing free-form deformation geometry control allows these linear constraints to be written in a geometry-independent fashion, greatly easing the process of applying the algorithm to new problems. This algorithm was used to assess the presence of multimodality when optimizing a wing in subsonic and transonic flows, under inviscid and viscous conditions, and a blended wing-body under transonic, viscous conditions. Multimodality was present in every wing case, while the blended wing-body was found to be generally unimodal.

Selectivity optimization in green chromatography by gradient stationary phase optimized selectivity liquid chromatography.

PubMed

Chen, Kai; Lynen, Frédéric; De Beer, Maarten; Hitzel, Laure; Ferguson, Paul; Hanna-Brown, Melissa; Sandra, Pat

2010-11-12

Stationary phase optimized selectivity liquid chromatography (SOSLC) is a promising technique to optimize the selectivity of a given separation by using a combination of different stationary phases. Previous work has shown that SOSLC offers excellent possibilities for method development, especially after the recent modification towards linear gradient SOSLC. The present work is aimed at developing and extending the SOSLC approach towards selectivity optimization and method development for green chromatography. Contrary to current LC practices, a green mobile phase (water/ethanol/formic acid) is hereby preselected and the composition of the stationary phase is optimized under a given gradient profile to obtain baseline resolution of all target solutes in the shortest possible analysis time. With the algorithm adapted to the high viscosity property of ethanol, the principle is illustrated with a fast, full baseline resolution for a randomly selected mixture composed of sulphonamides, xanthine alkaloids and steroids. Copyright © 2010 Elsevier B.V. All rights reserved.

Optimum Strategies for Selecting Descent Flight-Path Angles

NASA Technical Reports Server (NTRS)

Wu, Minghong G. (Inventor); Green, Steven M. (Inventor)

2016-01-01

An information processing system and method for adaptively selecting an aircraft descent flight path for an aircraft, are provided. The system receives flight adaptation parameters, including aircraft flight descent time period, aircraft flight descent airspace region, and aircraft flight descent flyability constraints. The system queries a plurality of flight data sources and retrieves flight information including any of winds and temperatures aloft data, airspace/navigation constraints, airspace traffic demand, and airspace arrival delay model. The system calculates a set of candidate descent profiles, each defined by at least one of a flight path angle and a descent rate, and each including an aggregated total fuel consumption value for the aircraft following a calculated trajectory, and a flyability constraints metric for the calculated trajectory. The system selects a best candidate descent profile having the least fuel consumption value while the fly ability constraints metric remains within aircraft flight descent flyability constraints.

A new optimal seam method for seamless image stitching

NASA Astrophysics Data System (ADS)

Xue, Jiale; Chen, Shengyong; Cheng, Xu; Han, Ying; Zhao, Meng

2017-07-01

A novel optimal seam method which aims to stitch those images with overlapping area more seamlessly has been propos ed. Considering the traditional gradient domain optimal seam method and fusion algorithm result in bad color difference measurement and taking a long time respectively, the input images would be converted to HSV space and a new energy function is designed to seek optimal stitching path. To smooth the optimal stitching path, a simplified pixel correction and weighted average method are utilized individually. The proposed methods exhibit performance in eliminating the stitching seam compared with the traditional gradient optimal seam and high efficiency with multi-band blending algorithm.

Retention prediction and separation optimization under multilinear gradient elution in liquid chromatography with Microsoft Excel macros.

PubMed

Fasoula, S; Zisi, Ch; Gika, H; Pappa-Louisi, A; Nikitas, P

2015-05-22

A package of Excel VBA macros have been developed for modeling multilinear gradient retention data obtained in single or double gradient elution mode by changing organic modifier(s) content and/or eluent pH. For this purpose, ten chromatographic models were used and four methods were adopted for their application. The methods were based on (a) the analytical expression of the retention time, provided that this expression is available, (b) the retention times estimated using the Nikitas-Pappa approach, (c) the stepwise approximation, and (d) a simple numerical approximation involving the trapezoid rule for integration of the fundamental equation for gradient elution. For all these methods, Excel VBA macros have been written and implemented using two different platforms; the fitting and the optimization platform. The fitting platform calculates not only the adjustable parameters of the chromatographic models, but also the significance of these parameters and furthermore predicts the analyte elution times. The optimization platform determines the gradient conditions that lead to the optimum separation of a mixture of analytes by using the Solver evolutionary mode, provided that proper constraints are set in order to obtain the optimum gradient profile in the minimum gradient time. The performance of the two platforms was tested using experimental and artificial data. It was found that using the proposed spreadsheets, fitting, prediction, and optimization can be performed easily and effectively under all conditions. Overall, the best performance is exhibited by the analytical and Nikitas-Pappa's methods, although the former cannot be used under all circumstances. Copyright © 2015 Elsevier B.V. All rights reserved.

Optimal Design of Gradient Materials and Bi-Level Optimization of Topology Using Targets (BOTT)

NASA Astrophysics Data System (ADS)

Garland, Anthony

The objective of this research is to understand the fundamental relationships necessary to develop a method to optimize both the topology and the internal gradient material distribution of a single object while meeting constraints and conflicting objectives. Functionally gradient material (FGM) objects possess continuous varying material properties throughout the object, and they allow an engineer to tailor individual regions of an object to have specific mechanical properties by locally modifying the internal material composition. A variety of techniques exists for topology optimization, and several methods exist for FGM optimization, but combining the two together is difficult. Understanding the relationship between topology and material gradient optimization enables the selection of an appropriate model and the development of algorithms, which allow engineers to design high-performance parts that better meet design objectives than optimized homogeneous material objects. For this research effort, topology optimization means finding the optimal connected structure with an optimal shape. FGM optimization means finding the optimal macroscopic material properties within an object. Tailoring the material constitutive matrix as a function of position results in gradient properties. Once, the target macroscopic properties are known, a mesostructure or a particular material nanostructure can be found which gives the target material properties at each macroscopic point. This research demonstrates that topology and gradient materials can both be optimized together for a single part. The algorithms use a discretized model of the domain and gradient based optimization algorithms. In addition, when considering two conflicting objectives the algorithms in this research generate clear 'features' within a single part. This tailoring of material properties within different areas of a single part (automated design of 'features') using computational design tools is a novel benefit of gradient material designs. A macroscopic gradient can be achieved by varying the microstructure or the mesostructures of an object. The mesostructure interpretation allows for more design freedom since the mesostructures can be tuned to have non-isotropic material properties. A new algorithm called Bi-level Optimization of Topology using Targets (BOTT) seeks to find the best distribution of mesostructure designs throughout a single object in order to minimize an objective value. On the macro level, the BOTT algorithm optimizes the macro topology and gradient material properties within the object. The BOTT algorithm optimizes the material gradient by finding the best constitutive matrix at each location with the object. In order to enhance the likelihood that a mesostructure can be generated with the same equivalent constitutive matrix, the variability of the constitutive matrix is constrained to be an orthotropic material. The stiffness in the X and Y directions (of the base coordinate system) can change in addition to rotating the orthotropic material to align with the loading at each region. Second, the BOTT algorithm designs mesostructures with macroscopic properties equal to the target properties found in step one while at the same time the algorithm seeks to minimize material usage in each mesostructure. The mesostructure algorithm maximizes the strain energy of the mesostructures unit cell when a pseudo strain is applied to the cell. A set of experiments reveals the fundamental relationship between target cell density and the strain (or pseudo strain) applied to a unit cell and the output effective properties of the mesostructure. At low density, a few mesostructure unit cell design are possible, while at higher density the mesostructure unit cell designs have many possibilities. Therefore, at low densities the effective properties of the mesostructure are a step function of the applied pseudo strain. At high densities, the effective properties of the mesostructure are continuous function of the applied pseudo strain. Finally, the macro and mesostructure designs are coordinated so that the macro and meso levels agree on the material properties at each macro region. In addition, a coordination effort seeks to coordinate the boundaries of adjacent mesostructure designs so that the macro load path is transmitted from one mesostructure design to its neighbors. The BOTT algorithm has several advantages over existing algorithms within the literature. First, the BOTT algorithm significantly reduces the computational power required to run the algorithm. Second, the BOTT algorithm indirectly enforces a minimum mesostructure density constraint which increases the manufacturability of the final design. Third, the BOTT algorithm seeks to transfer the load from one mesostructure to its neighbors by coordinating the boundaries of adjacent mesostructure designs. However, the BOTT algorithm can still be improved since it may have difficulty converging due to the step function nature of the mesostructure design problem at low density.

Event-Driven Random Back-Propagation: Enabling Neuromorphic Deep Learning Machines

PubMed Central

Neftci, Emre O.; Augustine, Charles; Paul, Somnath; Detorakis, Georgios

2017-01-01

An ongoing challenge in neuromorphic computing is to devise general and computationally efficient models of inference and learning which are compatible with the spatial and temporal constraints of the brain. One increasingly popular and successful approach is to take inspiration from inference and learning algorithms used in deep neural networks. However, the workhorse of deep learning, the gradient descent Gradient Back Propagation (BP) rule, often relies on the immediate availability of network-wide information stored with high-precision memory during learning, and precise operations that are difficult to realize in neuromorphic hardware. Remarkably, recent work showed that exact backpropagated gradients are not essential for learning deep representations. Building on these results, we demonstrate an event-driven random BP (eRBP) rule that uses an error-modulated synaptic plasticity for learning deep representations. Using a two-compartment Leaky Integrate & Fire (I&F) neuron, the rule requires only one addition and two comparisons for each synaptic weight, making it very suitable for implementation in digital or mixed-signal neuromorphic hardware. Our results show that using eRBP, deep representations are rapidly learned, achieving classification accuracies on permutation invariant datasets comparable to those obtained in artificial neural network simulations on GPUs, while being robust to neural and synaptic state quantizations during learning. PMID:28680387

Event-Driven Random Back-Propagation: Enabling Neuromorphic Deep Learning Machines.

PubMed

Neftci, Emre O; Augustine, Charles; Paul, Somnath; Detorakis, Georgios

2017-01-01

An ongoing challenge in neuromorphic computing is to devise general and computationally efficient models of inference and learning which are compatible with the spatial and temporal constraints of the brain. One increasingly popular and successful approach is to take inspiration from inference and learning algorithms used in deep neural networks. However, the workhorse of deep learning, the gradient descent Gradient Back Propagation (BP) rule, often relies on the immediate availability of network-wide information stored with high-precision memory during learning, and precise operations that are difficult to realize in neuromorphic hardware. Remarkably, recent work showed that exact backpropagated gradients are not essential for learning deep representations. Building on these results, we demonstrate an event-driven random BP (eRBP) rule that uses an error-modulated synaptic plasticity for learning deep representations. Using a two-compartment Leaky Integrate & Fire (I&F) neuron, the rule requires only one addition and two comparisons for each synaptic weight, making it very suitable for implementation in digital or mixed-signal neuromorphic hardware. Our results show that using eRBP, deep representations are rapidly learned, achieving classification accuracies on permutation invariant datasets comparable to those obtained in artificial neural network simulations on GPUs, while being robust to neural and synaptic state quantizations during learning.

Natural learning in NLDA networks.

PubMed

González, Ana; Dorronsoro, José R

2007-07-01

Non Linear Discriminant Analysis (NLDA) networks combine a standard Multilayer Perceptron (MLP) transfer function with the minimization of a Fisher analysis criterion. In this work we will define natural-like gradients for NLDA network training. Instead of a more principled approach, that would require the definition of an appropriate Riemannian structure on the NLDA weight space, we will follow a simpler procedure, based on the observation that the gradient of the NLDA criterion function J can be written as the expectation nablaJ(W)=E[Z(X,W)] of a certain random vector Z and defining then I=E[Z(X,W)Z(X,W)(t)] as the Fisher information matrix in this case. This definition of I formally coincides with that of the information matrix for the MLP or other square error functions; the NLDA J criterion, however, does not have this structure. Although very simple, the proposed approach shows much faster convergence than that of standard gradient descent, even when its costlier complexity is taken into account. While the faster convergence of natural MLP batch training can be also explained in terms of its relationship with the Gauss-Newton minimization method, this is not the case for NLDA training, as we will see analytically and numerically that the hessian and information matrices are different.

A new version of Stochastic-parallel-gradient-descent algorithm (SPGD) for phase correction of a distorted orbital angular momentum (OAM) beam

NASA Astrophysics Data System (ADS)

Jiao Ling, LIn; Xiaoli, Yin; Huan, Chang; Xiaozhou, Cui; Yi-Lin, Guo; Huan-Yu, Liao; Chun-YU, Gao; Guohua, Wu; Guang-Yao, Liu; Jin-KUn, Jiang; Qing-Hua, Tian

2018-02-01

Atmospheric turbulence limits the performance of orbital angular momentum-based free-space optical communication (FSO-OAM) system. In order to compensate phase distortion induced by atmospheric turbulence, wavefront sensorless adaptive optics (WSAO) has been proposed and studied in recent years. In this paper a new version of SPGD called MZ-SPGD, which combines the Z-SPGD based on the deformable mirror influence function and the M-SPGD based on the Zernike polynomials, is proposed. Numerical simulations show that the hybrid method decreases convergence times markedly but can achieve the same compensated effect compared to Z-SPGD and M-SPGD.

Combinatorial techniques to efficiently investigate and optimize organic thin film processing and properties.

PubMed

Wieberger, Florian; Kolb, Tristan; Neuber, Christian; Ober, Christopher K; Schmidt, Hans-Werner

2013-04-08

In this article we present several developed and improved combinatorial techniques to optimize processing conditions and material properties of organic thin films. The combinatorial approach allows investigations of multi-variable dependencies and is the perfect tool to investigate organic thin films regarding their high performance purposes. In this context we develop and establish the reliable preparation of gradients of material composition, temperature, exposure, and immersion time. Furthermore we demonstrate the smart application of combinations of composition and processing gradients to create combinatorial libraries. First a binary combinatorial library is created by applying two gradients perpendicular to each other. A third gradient is carried out in very small areas and arranged matrix-like over the entire binary combinatorial library resulting in a ternary combinatorial library. Ternary combinatorial libraries allow identifying precise trends for the optimization of multi-variable dependent processes which is demonstrated on the lithographic patterning process. Here we verify conclusively the strong interaction and thus the interdependency of variables in the preparation and properties of complex organic thin film systems. The established gradient preparation techniques are not limited to lithographic patterning. It is possible to utilize and transfer the reported combinatorial techniques to other multi-variable dependent processes and to investigate and optimize thin film layers and devices for optical, electro-optical, and electronic applications.

Optimization of Turbine Engine Cycle Analysis with Analytic Derivatives

NASA Technical Reports Server (NTRS)

Hearn, Tristan; Hendricks, Eric; Chin, Jeffrey; Gray, Justin; Moore, Kenneth T.

2016-01-01

A new engine cycle analysis tool, called Pycycle, was recently built using the OpenMDAO framework. This tool uses equilibrium chemistry based thermodynamics, and provides analytic derivatives. This allows for stable and efficient use of gradient-based optimization and sensitivity analysis methods on engine cycle models, without requiring the use of finite difference derivative approximation methods. To demonstrate this, a gradient-based design optimization was performed on a multi-point turbofan engine model. Results demonstrate very favorable performance compared to an optimization of an identical model using finite-difference approximated derivatives.

Novel maximum-margin training algorithms for supervised neural networks.

PubMed

Ludwig, Oswaldo; Nunes, Urbano

2010-06-01

This paper proposes three novel training methods, two of them based on the backpropagation approach and a third one based on information theory for multilayer perceptron (MLP) binary classifiers. Both backpropagation methods are based on the maximal-margin (MM) principle. The first one, based on the gradient descent with adaptive learning rate algorithm (GDX) and named maximum-margin GDX (MMGDX), directly increases the margin of the MLP output-layer hyperplane. The proposed method jointly optimizes both MLP layers in a single process, backpropagating the gradient of an MM-based objective function, through the output and hidden layers, in order to create a hidden-layer space that enables a higher margin for the output-layer hyperplane, avoiding the testing of many arbitrary kernels, as occurs in case of support vector machine (SVM) training. The proposed MM-based objective function aims to stretch out the margin to its limit. An objective function based on Lp-norm is also proposed in order to take into account the idea of support vectors, however, overcoming the complexity involved in solving a constrained optimization problem, usually in SVM training. In fact, all the training methods proposed in this paper have time and space complexities O(N) while usual SVM training methods have time complexity O(N (3)) and space complexity O(N (2)) , where N is the training-data-set size. The second approach, named minimization of interclass interference (MICI), has an objective function inspired on the Fisher discriminant analysis. Such algorithm aims to create an MLP hidden output where the patterns have a desirable statistical distribution. In both training methods, the maximum area under ROC curve (AUC) is applied as stop criterion. The third approach offers a robust training framework able to take the best of each proposed training method. The main idea is to compose a neural model by using neurons extracted from three other neural networks, each one previously trained by MICI, MMGDX, and Levenberg-Marquard (LM), respectively. The resulting neural network was named assembled neural network (ASNN). Benchmark data sets of real-world problems have been used in experiments that enable a comparison with other state-of-the-art classifiers. The results provide evidence of the effectiveness of our methods regarding accuracy, AUC, and balanced error rate.

Full-waveform inversion for the Iranian plateau

NASA Astrophysics Data System (ADS)

Masouminia, N.; Fichtner, A.; Rahimi, H.

2017-12-01

We aim to obtain a detailed tomographic model for the Iranian plateau facilitated by full-waveform inversion. By using this method, we intend to better constrain the 3-D structure of the crust and the upper mantle in the region. The Iranian plateau is a complex tectonic area resulting from the collision of the Arabian and Eurasian tectonic plates. This region is subject to complex tectonic processes such as Makran subduction zone, which runs along the southeastern coast of Iran, and the convergence of the Arabian and- Eurasian plates, which itself led to another subduction under Central Iran. This continent-continent collision has also caused shortening and crustal thickening, which can be seen today as Zagros mountain range in the south and Kopeh Dagh mountain range in the northeast. As a result of such a tectonic activity, the crust and the mantle beneath the region are expected to be highly heterogeneous. To further our understanding of the region and its tectonic history, a detailed 3-D velocity model is required.To construct a 3-D model, we propose to use full-waveform inversion, which allows us to incorporate all types of waves recorded in the seismogram, including body waves as well as fundamental- and higher-mode surface waves. Exploiting more information from the observed data using this approach is likely to constrain features which have not been found by classical tomography studies so far. We address the forward problem using Salvus - a numerical wave propagation solver, based on spectral-element method and run on high-performance computers. The solver allows us to simulate wave field propagating in highly heterogeneous, attenuating and anisotropic media, respecting the surface topography. To improve the model, we solve the optimization problem. Solution of this optimization problem is based on an iterative approach which employs adjoint methods to calculate the gradient and uses steepest descent and conjugate-gradient methods to minimize the objective function. Each iteration of such an approach is expected to bring the model closer to the true model.Our model domain extends between 25°N and 40°N in latitude and 42°E and 63°E in longitude. To constrain the 3-D structure of the area we use 83 broadband seismic stations and 146 earthquakes with magnitude Mw>4.5 -that occurred in the region between 2012 and 2017.

Gradient Material Strategies for Hydrogel Optimization in Tissue Engineering Applications

PubMed Central

2018-01-01

Although a number of combinatorial/high-throughput approaches have been developed for biomaterial hydrogel optimization, a gradient sample approach is particularly well suited to identify hydrogel property thresholds that alter cellular behavior in response to interacting with the hydrogel due to reduced variation in material preparation and the ability to screen biological response over a range instead of discrete samples each containing only one condition. This review highlights recent work on cell–hydrogel interactions using a gradient material sample approach. Fabrication strategies for composition, material and mechanical property, and bioactive signaling gradient hydrogels that can be used to examine cell–hydrogel interactions will be discussed. The effects of gradients in hydrogel samples on cellular adhesion, migration, proliferation, and differentiation will then be examined, providing an assessment of the current state of the field and the potential of wider use of the gradient sample approach to accelerate our understanding of matrices on cellular behavior. PMID:29485612

Atrioventricular nonuniformity of pericardial constraint.

PubMed

Hamilton, Douglas R; Sas, Rozsa; Tyberg, John V

2004-10-01

Physiologists and clinicians commonly refer to "pressure" as a measure of the constraining effects of the pericardium; however, "pericardial pressure" is really a local measurement of epicardial radial stress. During diastole, from the bottom of the y descent to the beginning of the a wave, pericardial pressure over the right atrium (P(pRA)) is approximately equal to that over the right ventricle (P(pRV)). However, in systole, during the interval between the bottom of the x descent and the peak of the v wave, these two pericardial pressures appear to be completely decoupled in that P(pRV) decreases, whereas P(pRA) remains constant or increases. This decoupling indicates considerable mechanical independence between the RA and RV during systole. That is, RV systolic emptying lowers P(pRV), but P(pRA) continues to increase, suggesting that the relation of the pericardium to the RA must allow effective constraint, even though the pericardium over the RV is simultaneously slack. In conclusion, we measured the pericardial pressure responsible for the previously reported nonuniformity of pericardial strain. P(pRA) and P(pRV) are closely coupled during diastole, but during systole they become decoupled. Systolic nonuniformity of pericardial constraint may augment the atrioventricular valve-opening pressure gradient in early diastole and, so, affect ventricular filling.

A comparison of discrete versus continuous adjoint states to invert groundwater flow in heterogeneous dual porosity systems

NASA Astrophysics Data System (ADS)

Delay, Frederick; Badri, Hamid; Fahs, Marwan; Ackerer, Philippe

2017-12-01

Dual porosity models become increasingly used for simulating groundwater flow at the large scale in fractured porous media. In this context, model inversions with the aim of retrieving the system heterogeneity are frequently faced with huge parameterizations for which descent methods of inversion with the assistance of adjoint state calculations are well suited. We compare the performance of discrete and continuous forms of adjoint states associated with the flow equations in a dual porosity system. The discrete form inherits from previous works by some of the authors, as the continuous form is completely new and here fully differentiated for handling all types of model parameters. Adjoint states assist descent methods by calculating the gradient components of the objective function, these being a key to good convergence of inverse solutions. Our comparison on the basis of synthetic exercises show that both discrete and continuous adjoint states can provide very similar solutions close to reference. For highly heterogeneous systems, the calculation grid of the continuous form cannot be too coarse, otherwise the method may show lack of convergence. This notwithstanding, the continuous adjoint state is the most versatile form as its non-intrusive character allows for plugging an inversion toolbox quasi-independent from the code employed for solving the forward problem.

Optimization and quantization in gradient symbol systems: a framework for integrating the continuous and the discrete in cognition.

PubMed

Smolensky, Paul; Goldrick, Matthew; Mathis, Donald

2014-08-01

Mental representations have continuous as well as discrete, combinatorial properties. For example, while predominantly discrete, phonological representations also vary continuously; this is reflected by gradient effects in instrumental studies of speech production. Can an integrated theoretical framework address both aspects of structure? The framework we introduce here, Gradient Symbol Processing, characterizes the emergence of grammatical macrostructure from the Parallel Distributed Processing microstructure (McClelland, Rumelhart, & The PDP Research Group, 1986) of language processing. The mental representations that emerge, Distributed Symbol Systems, have both combinatorial and gradient structure. They are processed through Subsymbolic Optimization-Quantization, in which an optimization process favoring representations that satisfy well-formedness constraints operates in parallel with a distributed quantization process favoring discrete symbolic structures. We apply a particular instantiation of this framework, λ-Diffusion Theory, to phonological production. Simulations of the resulting model suggest that Gradient Symbol Processing offers a way to unify accounts of grammatical competence with both discrete and continuous patterns in language performance. Copyright © 2013 Cognitive Science Society, Inc.

Automated correction of improperly rotated diffusion gradient orientations in diffusion weighted MRI.

PubMed

Jeurissen, Ben; Leemans, Alexander; Sijbers, Jan

2014-10-01

Ensuring one is using the correct gradient orientations in a diffusion MRI study can be a challenging task. As different scanners, file formats and processing tools use different coordinate frame conventions, in practice, users can end up with improperly oriented gradient orientations. Using such wrongly oriented gradient orientations for subsequent diffusion parameter estimation will invalidate all rotationally variant parameters and fiber tractography results. While large misalignments can be detected by visual inspection, small rotations of the gradient table (e.g. due to angulation of the acquisition plane), are much more difficult to detect. In this work, we propose an automated method to align the coordinate frame of the gradient orientations with that of the corresponding diffusion weighted images, using a metric based on whole brain fiber tractography. By transforming the gradient table and measuring the average fiber trajectory length, we search for the transformation that results in the best global 'connectivity'. To ensure a fast calculation of the metric we included a range of algorithmic optimizations in our tractography routine. To make the optimization routine robust to spurious local maxima, we use a stochastic optimization routine that selects a random set of seed points on each evaluation. Using simulations, we show that our method can recover the correct gradient orientations with high accuracy and precision. In addition, we demonstrate that our technique can successfully recover rotated gradient tables on a wide range of clinically realistic data sets. As such, our method provides a practical and robust solution to an often overlooked pitfall in the processing of diffusion MRI. Copyright © 2014 Elsevier B.V. All rights reserved.

Optimization of wind plant layouts using an adjoint approach

DOE PAGES

King, Ryan N.; Dykes, Katherine; Graf, Peter; ...

2017-03-10

Using adjoint optimization and three-dimensional steady-state Reynolds-averaged Navier–Stokes (RANS) simulations, we present a new gradient-based approach for optimally siting wind turbines within utility-scale wind plants. By solving the adjoint equations of the flow model, the gradients needed for optimization are found at a cost that is independent of the number of control variables, thereby permitting optimization of large wind plants with many turbine locations. Moreover, compared to the common approach of superimposing prescribed wake deficits onto linearized flow models, the computational efficiency of the adjoint approach allows the use of higher-fidelity RANS flow models which can capture nonlinear turbulent flowmore » physics within a wind plant. The steady-state RANS flow model is implemented in the Python finite-element package FEniCS and the derivation and solution of the discrete adjoint equations are automated within the dolfin-adjoint framework. Gradient-based optimization of wind turbine locations is demonstrated for idealized test cases that reveal new optimization heuristics such as rotational symmetry, local speedups, and nonlinear wake curvature effects. Layout optimization is also demonstrated on more complex wind rose shapes, including a full annual energy production (AEP) layout optimization over 36 inflow directions and 5 wind speed bins.« less

Optimization of wind plant layouts using an adjoint approach

DOE Office of Scientific and Technical Information (OSTI.GOV)

King, Ryan N.; Dykes, Katherine; Graf, Peter

Using adjoint optimization and three-dimensional steady-state Reynolds-averaged Navier–Stokes (RANS) simulations, we present a new gradient-based approach for optimally siting wind turbines within utility-scale wind plants. By solving the adjoint equations of the flow model, the gradients needed for optimization are found at a cost that is independent of the number of control variables, thereby permitting optimization of large wind plants with many turbine locations. Moreover, compared to the common approach of superimposing prescribed wake deficits onto linearized flow models, the computational efficiency of the adjoint approach allows the use of higher-fidelity RANS flow models which can capture nonlinear turbulent flowmore » physics within a wind plant. The steady-state RANS flow model is implemented in the Python finite-element package FEniCS and the derivation and solution of the discrete adjoint equations are automated within the dolfin-adjoint framework. Gradient-based optimization of wind turbine locations is demonstrated for idealized test cases that reveal new optimization heuristics such as rotational symmetry, local speedups, and nonlinear wake curvature effects. Layout optimization is also demonstrated on more complex wind rose shapes, including a full annual energy production (AEP) layout optimization over 36 inflow directions and 5 wind speed bins.« less

Parameter Optimization for Turbulent Reacting Flows Using Adjoints

NASA Astrophysics Data System (ADS)

Lapointe, Caelan; Hamlington, Peter E.

2017-11-01

The formulation of a new adjoint solver for topology optimization of turbulent reacting flows is presented. This solver provides novel configurations (e.g., geometries and operating conditions) based on desired system outcomes (i.e., objective functions) for complex reacting flow problems of practical interest. For many such problems, it would be desirable to know optimal values of design parameters (e.g., physical dimensions, fuel-oxidizer ratios, and inflow-outflow conditions) prior to real-world manufacture and testing, which can be expensive, time-consuming, and dangerous. However, computational optimization of these problems is made difficult by the complexity of most reacting flows, necessitating the use of gradient-based optimization techniques in order to explore a wide design space at manageable computational cost. The adjoint method is an attractive way to obtain the required gradients, because the cost of the method is determined by the dimension of the objective function rather than the size of the design space. Here, the formulation of a novel solver is outlined that enables gradient-based parameter optimization of turbulent reacting flows using the discrete adjoint method. Initial results and an outlook for future research directions are provided.

Gradient-based adaptation of general gaussian kernels.

PubMed

Glasmachers, Tobias; Igel, Christian

2005-10-01

Gradient-based optimizing of gaussian kernel functions is considered. The gradient for the adaptation of scaling and rotation of the input space is computed to achieve invariance against linear transformations. This is done by using the exponential map as a parameterization of the kernel parameter manifold. By restricting the optimization to a constant trace subspace, the kernel size can be controlled. This is, for example, useful to prevent overfitting when minimizing radius-margin generalization performance measures. The concepts are demonstrated by training hard margin support vector machines on toy data.

Computational methods for aerodynamic design using numerical optimization

NASA Technical Reports Server (NTRS)

Peeters, M. F.

1983-01-01

Five methods to increase the computational efficiency of aerodynamic design using numerical optimization, by reducing the computer time required to perform gradient calculations, are examined. The most promising method consists of drastically reducing the size of the computational domain on which aerodynamic calculations are made during gradient calculations. Since a gradient calculation requires the solution of the flow about an airfoil whose geometry was slightly perturbed from a base airfoil, the flow about the base airfoil is used to determine boundary conditions on the reduced computational domain. This method worked well in subcritical flow.

Application of artificial neural network to predict clay sensitivity in a high landslide prone area using CPTu data- A case study in Southwest of Sweden

NASA Astrophysics Data System (ADS)

Shahri, Abbas; Mousavinaseri, Mahsasadat; Naderi, Shima; Espersson, Maria

2015-04-01

Application of Artificial Neural Networks (ANNs) in many areas of engineering, in particular to geotechnical engineering problems such as site characterization has demonstrated some degree of success. The present paper aims to evaluate the feasibility of several various types of ANN models to predict the clay sensitivity of soft clays form piezocone penetration test data (CPTu). To get the aim, a research database of CPTu data of 70 test points around the Göta River near the Lilli Edet in the southwest of Sweden which is a high prone land slide area were collected and considered as input for ANNs. For training algorithms the quick propagation, conjugate gradient descent, quasi-Newton, limited memory quasi-Newton and Levenberg-Marquardt were developed tested and trained using the CPTu data to provide a comparison between the results of field investigation and ANN models to estimate the clay sensitivity. The reason of using the clay sensitivity parameter in this study is due to its relation to landslides in Sweden.A special high sensitive clay namely quick clay is considered as the main responsible for experienced landslides in Sweden which has high sensitivity and prone to slide. The training and testing program was started with 3-2-1 ANN architecture structure. By testing and trying several various architecture structures and changing the hidden layer in order to have a higher output resolution the 3-4-4-3-1 architecture structure for ANN in this study was confirmed. The tested algorithm showed that increasing the hidden layers up to 4 layers in ANN can improve the results and the 3-4-4-3-1 architecture structure ANNs for prediction of clay sensitivity represent reliable and reasonable response. The obtained results showed that the conjugate gradient descent algorithm with R2=0.897 has the best performance among the tested algorithms. Keywords: clay sensitivity, landslide, Artificial Neural Network

Efficacy of Metarhizium anisopliae isolate MAX-2 from Shangri-la, China under desiccation stress

PubMed Central

2014-01-01

Background Metarhizium anisopliae, a soil-borne entomopathogen found worldwide, is an interesting fungus for biological control. However, its efficacy in the fields is significantly affected by environmental conditions, particularly moisture. To overcome the weakness of Metarhizium and determine its isolates with antistress capacity, the efficacies of four M. anisopliae isolates, which were collected from arid regions of Yunnan Province in China during the dry season, were determined at different moisture levels, and the efficacy of the isolate MAX-2 from Shangri-la under desiccation stress was evaluated at low moisture level. Results M. anisopliae isolates MAX-2, MAC-6, MAL-1, and MAQ-28 showed gradient descent efficacies against sterile Tenebrio molitor larvae, and gradient descent capacities against desiccation with the decrease in moisture levels. The efficacy of MAX-2 showed no significant differences at 35% moisture level than those of the other isolates. However, significant differences were found at 8% to 30% moisture levels. The efficacies of all isolates decreased with the decrease in moisture levels. MAX-2 was relatively less affected by desiccation stress. Its efficacy was almost unaffected by the decrease at moisture levels > 25%, but slowly decreased at moisture levels < 25%. By contrast, the efficacies of other isolates rapidly decreased with the decrease in moisture levels. MAX-2 caused different infection characteristics on T. molitor larvae under desiccation stress and in wet microhabitat. Local black patches were found on the cuticles of the insects, and the cadavers dried without fungal growth under desiccation stress. However, dark black internodes and fungal growth were found after death of the insects in the wet microhabitat. Conclusions MAX-2 showed significantly higher efficacy and superior antistress capacity than the other isolates under desiccation stress. The infection of sterile T. molitor larvae at low moisture level constituted a valid laboratory bioassay system in evaluating M. anisopliae efficacy under desiccation stress. PMID:24383424

Efficacy of Metarhizium anisopliae isolate MAX-2 from Shangri-la, China under desiccation stress.

PubMed

Chen, Zi-Hong; Xu, Ling; Yang, Feng-lian; Ji, Guang-Hai; Yang, Jing; Wang, Jian-Yun

2014-01-03

Metarhizium anisopliae, a soil-borne entomopathogen found worldwide, is an interesting fungus for biological control. However, its efficacy in the fields is significantly affected by environmental conditions, particularly moisture. To overcome the weakness of Metarhizium and determine its isolates with antistress capacity, the efficacies of four M. anisopliae isolates, which were collected from arid regions of Yunnan Province in China during the dry season, were determined at different moisture levels, and the efficacy of the isolate MAX-2 from Shangri-la under desiccation stress was evaluated at low moisture level. M. anisopliae isolates MAX-2, MAC-6, MAL-1, and MAQ-28 showed gradient descent efficacies against sterile Tenebrio molitor larvae, and gradient descent capacities against desiccation with the decrease in moisture levels. The efficacy of MAX-2 showed no significant differences at 35% moisture level than those of the other isolates. However, significant differences were found at 8% to 30% moisture levels. The efficacies of all isolates decreased with the decrease in moisture levels. MAX-2 was relatively less affected by desiccation stress. Its efficacy was almost unaffected by the decrease at moisture levels > 25%, but slowly decreased at moisture levels < 25%. By contrast, the efficacies of other isolates rapidly decreased with the decrease in moisture levels. MAX-2 caused different infection characteristics on T. molitor larvae under desiccation stress and in wet microhabitat. Local black patches were found on the cuticles of the insects, and the cadavers dried without fungal growth under desiccation stress. However, dark black internodes and fungal growth were found after death of the insects in the wet microhabitat. MAX-2 showed significantly higher efficacy and superior antistress capacity than the other isolates under desiccation stress. The infection of sterile T. molitor larvae at low moisture level constituted a valid laboratory bioassay system in evaluating M. anisopliae efficacy under desiccation stress.

A resolution recognizing the 63rd anniversary of India's independence, expressing appreciation to Americans of Indian descent for their contributions to society, and expressing support and optimism for the strategic partnership and friendship between the United States and India in the future.

THOMAS, 111th Congress

Sen. Cornyn, John [R-TX

2010-08-05

Senate - 08/05/2010 Submitted in the Senate, considered, and agreed to without amendment and with a preamble by Unanimous Consent. (All Actions) Tracker: This bill has the status Agreed to in SenateHere are the steps for Status of Legislation:

A Nonlinear Programming Perspective on Sensitivity Calculations for Systems Governed by State Equations

NASA Technical Reports Server (NTRS)

Lewis, Robert Michael

1997-01-01

This paper discusses the calculation of sensitivities. or derivatives, for optimization problems involving systems governed by differential equations and other state relations. The subject is examined from the point of view of nonlinear programming, beginning with the analytical structure of the first and second derivatives associated with such problems and the relation of these derivatives to implicit differentiation and equality constrained optimization. We also outline an error analysis of the analytical formulae and compare the results with similar results for finite-difference estimates of derivatives. We then attend to an investigation of the nature of the adjoint method and the adjoint equations and their relation to directions of steepest descent. We illustrate the points discussed with an optimization problem in which the variables are the coefficients in a differential operator.

Maximizing and minimizing investment concentration with constraints of budget and investment risk

NASA Astrophysics Data System (ADS)

Shinzato, Takashi

2018-01-01

In this paper, as a first step in examining the properties of a feasible portfolio subset that is characterized by budget and risk constraints, we assess the maximum and minimum of the investment concentration using replica analysis. To do this, we apply an analytical approach of statistical mechanics. We note that the optimization problem considered in this paper is the dual problem of the portfolio optimization problem discussed in the literature, and we verify that these optimal solutions are also dual. We also present numerical experiments, in which we use the method of steepest descent that is based on Lagrange's method of undetermined multipliers, and we compare the numerical results to those obtained by replica analysis in order to assess the effectiveness of our proposed approach.

Smoothing of cost function leads to faster convergence of neural network learning

NASA Astrophysics Data System (ADS)

Xu, Li-Qun; Hall, Trevor J.

1994-03-01

One of the major problems in supervised learning of neural networks is the inevitable local minima inherent in the cost function f(W,D). This often makes classic gradient-descent-based learning algorithms that calculate the weight updates for each iteration according to (Delta) W(t) equals -(eta) (DOT)$DELwf(W,D) powerless. In this paper we describe a new strategy to solve this problem, which, adaptively, changes the learning rate and manipulates the gradient estimator simultaneously. The idea is to implicitly convert the local- minima-laden cost function f((DOT)) into a sequence of its smoothed versions {f(beta t)}Ttequals1, which, subject to the parameter (beta) t, bears less details at time t equals 1 and gradually more later on, the learning is actually performed on this sequence of functionals. The corresponding smoothed global minima obtained in this way, {Wt}Ttequals1, thus progressively approximate W-the desired global minimum. Experimental results on a nonconvex function minimization problem and a typical neural network learning task are given, analyses and discussions of some important issues are provided.

Broiler weight estimation based on machine vision and artificial neural network.

PubMed

Amraei, S; Abdanan Mehdizadeh, S; Salari, S

2017-04-01

1. Machine vision and artificial neural network (ANN) procedures were used to estimate live body weight of broiler chickens in 30 1-d-old broiler chickens reared for 42 d. 2. Imaging was performed two times daily. To localise chickens within the pen, an ellipse fitting algorithm was used and the chickens' head and tail removed using the Chan-Vese method. 3. The correlations between the body weight and 6 physical extracted features indicated that there were strong correlations between body weight and the 5 features including area, perimeter, convex area, major and minor axis length. 5. According to statistical analysis there was no significant difference between morning and afternoon data over 42 d. 6. In an attempt to improve the accuracy of live weight approximation different ANN techniques, including Bayesian regulation, Levenberg-Marquardt, Scaled conjugate gradient and gradient descent were used. Bayesian regulation with R 2 value of 0.98 was the best network for prediction of broiler weight. 7. The accuracy of the machine vision technique was examined and most errors were less than 50 g.

Adaptation to Space: An Introduction

NASA Technical Reports Server (NTRS)

Hargens, Alan R.

1995-01-01

The cardiovascular and musculoskeletal systems are normally exposed to gradients of blood pressure and weight on Earth. These gradients increase blood pressure and tissue weight in dependent tissues of the body. Exposure to actual and simulated microgravity causes blood and tissue fluid to shift from the legs to the head. Studies of humans in space have documented facial edema, space motion sickness, decreased plasma volume, muscle atrophy, and loss of bone strength. Return of astronauts to Earth is accompanied by orthostatic intolerance, decreased neuromuscular coordination, and reduced exercise capacity. These factors decrease performance during descent from orbit and increase risk during emergency egress from the spacecraft. Models of simulated microgravity include 6 deg head-down tilt, immersion, and prolonged horizontal bedrest. Head-down tilt is the most accepted model and studies using this model of up to one year have been performed in Russia. Animal models which offer clear insights into the role of gravity on vertebrates include the developing giraffe and snakes from various habitats. Finally, possible countermeasures to speed readaptation of astronauts to gravity after prolonged space flight will be discussed.

One Giant Leap for Categorizers: One Small Step for Categorization Theory

PubMed Central

Smith, J. David; Ell, Shawn W.

2015-01-01

We explore humans’ rule-based category learning using analytic approaches that highlight their psychological transitions during learning. These approaches confirm that humans show qualitatively sudden psychological transitions during rule learning. These transitions contribute to the theoretical literature contrasting single vs. multiple category-learning systems, because they seem to reveal a distinctive learning process of explicit rule discovery. A complete psychology of categorization must describe this learning process, too. Yet extensive formal-modeling analyses confirm that a wide range of current (gradient-descent) models cannot reproduce these transitions, including influential rule-based models (e.g., COVIS) and exemplar models (e.g., ALCOVE). It is an important theoretical conclusion that existing models cannot explain humans’ rule-based category learning. The problem these models have is the incremental algorithm by which learning is simulated. Humans descend no gradient in rule-based tasks. Very different formal-modeling systems will be required to explain humans’ psychology in these tasks. An important next step will be to build a new generation of models that can do so. PMID:26332587

Implementing a Bayes Filter in a Neural Circuit: The Case of Unknown Stimulus Dynamics.

PubMed

Sokoloski, Sacha

2017-09-01

In order to interact intelligently with objects in the world, animals must first transform neural population responses into estimates of the dynamic, unknown stimuli that caused them. The Bayesian solution to this problem is known as a Bayes filter, which applies Bayes' rule to combine population responses with the predictions of an internal model. The internal model of the Bayes filter is based on the true stimulus dynamics, and in this note, we present a method for training a theoretical neural circuit to approximately implement a Bayes filter when the stimulus dynamics are unknown. To do this we use the inferential properties of linear probabilistic population codes to compute Bayes' rule and train a neural network to compute approximate predictions by the method of maximum likelihood. In particular, we perform stochastic gradient descent on the negative log-likelihood of the neural network parameters with a novel approximation of the gradient. We demonstrate our methods on a finite-state, a linear, and a nonlinear filtering problem and show how the hidden layer of the neural network develops tuning curves consistent with findings in experimental neuroscience.

Field evaluation of flight deck procedures for flying CTAS descents

DOT National Transportation Integrated Search

1997-01-01

Flight deck descent procedures were developed for a field evaluation of the CTAS Descent Advisor conducted in the fall of 1995. During this study, CTAS descent clearances were issued to 185 commercial flights at Denver International Airport. Data col...

Solving the optimal attention allocation problem in manual control

NASA Technical Reports Server (NTRS)

Kleinman, D. L.

1976-01-01

Within the context of the optimal control model of human response, analytic expressions for the gradients of closed-loop performance metrics with respect to human operator attention allocation are derived. These derivatives serve as the basis for a gradient algorithm that determines the optimal attention that a human should allocate among several display indicators in a steady-state manual control task. Application of the human modeling techniques are made to study the hover control task for a CH-46 VTOL flight tested by NASA.

Optimal short-range trajectories for helicopters

DOE Office of Scientific and Technical Information (OSTI.GOV)

Slater, G.L.; Erzberger, H.

1982-12-01

An optimal flight path algorithm using a simplified altitude state model and a priori climb cruise descent flight profile was developed and applied to determine minimum fuel and minimum cost trajectories for a helicopter flying a fixed range trajectory. In addition, a method was developed for obtaining a performance model in simplified form which is based on standard flight manual data and which is applicable to the computation of optimal trajectories. The entire performance optimization algorithm is simple enough that on line trajectory optimization is feasible with a relatively small computer. The helicopter model used is the Silorsky S-61N. Themore » results show that for this vehicle the optimal flight path and optimal cruise altitude can represent a 10% fuel saving on a minimum fuel trajectory. The optimal trajectories show considerable variability because of helicopter weight, ambient winds, and the relative cost trade off between time and fuel. In general, reasonable variations from the optimal velocities and cruise altitudes do not significantly degrade the optimal cost. For fuel optimal trajectories, the optimum cruise altitude varies from the maximum (12,000 ft) to the minimum (0 ft) depending on helicopter weight.« less

How to define pathologic pelvic floor descent in MR defecography during defecation?

PubMed

Schawkat, Khoschy; Heinrich, Henriette; Parker, Helen L; Barth, Borna K; Mathew, Rishi P; Weishaupt, Dominik; Fox, Mark; Reiner, Caecilia S

2018-06-01

To assess the extents of pelvic floor descent both during the maximal straining phase and the defecation phase in healthy volunteers and in patients with pelvic floor disorders, studied with MR defecography (MRD), and to define specific threshold values for pelvic floor descent during the defecation phase. Twenty-two patients (mean age 51 ± 19.4) with obstructed defecation and 20 healthy volunteers (mean age 33.4 ± 11.5) underwent 3.0T MRD in supine position using midsagittal T2-weighted images. Two radiologists performed measurements in reference to PCL-lines in straining and during defecation. In order to identify cutoff values of pelvic floor measurements for diagnosis of pathologic pelvic floor descent [anterior, middle, and posterior compartments (AC, MC, PC)], receiver-operating characteristic (ROC) curves were plotted. Pelvic floor descent of all three compartments was significantly larger during defecation than at straining in patients and healthy volunteers (p < 0.002). When grading pelvic floor descent in the straining phase, only two healthy volunteers showed moderate PC descent (10%), which is considered pathologic. However, when applying the grading system during defecation, PC descent was overestimated with 50% of the healthy volunteers (10 of 20) showing moderate PC descent. The AUC for PC measurements during defecation was 0.77 (p = 0.003) and suggests a cutoff value of 45 mm below the PCL to identify patients with pathologic PC descent. With the adapted cutoff, only 15% of healthy volunteers show pathologic PC descent during defecation. MRD measurements during straining and defecation can be used to differentiate patients with pelvic floor dysfunction from healthy volunteers. However, different cutoff values should be used during straining and during defecation to define normal or pathologic PC descent.

Evaluation of pelvic descent disorders by dynamic contrast roentgenography.

PubMed

Takano, M; Hamada, A

2000-10-01

For precise diagnosis and rational treatment of the increasing number of patients with descent of intrapelvic organ(s) and anatomic plane(s), dynamic contrast roentgenography of multiple intrapelvic organs and planes is described. Sixty-six patients, consisting of 11 males, with a mean age (+/- standard deviation) of 65.6+/-14.2 years and with chief complaints of intrapelvic organ and perineal descent or defecation problems, were examined in this study. Dynamic contrast roentgenography was obtained by opacifying the ileum, urinary bladder, vagina, rectum, and the perineum. Films were taken at both squeeze and strain phases. On the films the lowest points of each organ and plane were plotted, and the distances from the standard line drawn at the upper surface of the sacrum were measured. The values were corrected to percentages according to the height of the sacrococcygeal bone of each patient. From these corrected values, organ or plane descents at strain and squeeze were diagnosed and graphically demonstrated as a descentgram in each patient. Among 17 cases with subjective symptoms of bladder descent, 9 cases (52.9 percent) showed roentgenographic descent. By the same token, among the cases with subjective feeling of descent of the vagina, uterus, peritoneum, perineum, rectum, and anus, roentgenographic descent was confirmed in 15 of 20 (75 percent), 7 of 9 (77.8 percent), 6 of 16 (37.5 percent), 33 of 33 (100 percent), 25 of 37 (67.6 percent), and 22 of 36 (61.6 percent), respectively. The descentgrams were divided into three patterns: anorectal descent type, female genital descent type, and total organ descent type. Dynamic contrast roentgenography and successive descentgraphy of multiple intrapelvic organs and planes are useful for objective diagnosis and rational treatment of patients with descent disorders of the intrapelvic organ(s) and plane(s).

Towards an Optimal Gradient-dependent Energy Functional of the PZ-SIC Form

DOE PAGES

Jónsson, Elvar Örn; Lehtola, Susi; Jónsson, Hannes

2015-06-01

Results of Perdew–Zunger self-interaction corrected (PZ-SIC) density functional theory calculations of the atomization energy of 35 molecules are compared to those of high-level quantum chemistry calculations. While the PBE functional, which is commonly used in calculations of condensed matter, is known to predict on average too high atomization energy (overbinding of the molecules), the application of PZ-SIC gives a large overcorrection and leads to significant underestimation of the atomization energy. The exchange enhancement factor that is optimal for the generalized gradient approximation within the Kohn-Sham (KS) approach may not be optimal for the self-interaction corrected functional. The PBEsol functional, wheremore » the exchange enhancement factor was optimized for solids, gives poor results for molecules in KS but turns out to work better than PBE in PZ-SIC calculations. The exchange enhancement is weaker in PBEsol and the functional is closer to the local density approximation. Furthermore, the drop in the exchange enhancement factor for increasing reduced gradient in the PW91 functional gives more accurate results than the plateaued enhancement in the PBE functional. A step towards an optimal exchange enhancement factor for a gradient dependent functional of the PZ-SIC form is taken by constructing an exchange enhancement factor that mimics PBEsol for small values of the reduced gradient, and PW91 for large values. The average atomization energy is then in closer agreement with the high-level quantum chemistry calculations, but the variance is still large, the F 2 molecule being a notable outlier.« less

Transient Growth Theory Prediction of Optimal Placing of Passive and Active Flow Control Devices for Separation Delay in LPT Airfoils

NASA Technical Reports Server (NTRS)

Tumin, Anatoli; Ashpis, David E.

2003-01-01

An analysis of the non-modal growth of perturbations in a boundary layer in the presence of a streamwise pressure gradient is presented. The analysis is based on PSE equations for an incompressible fluid. Examples with Falkner-Skan profiles indicate that a favorable pressure gradient decreases the non-modal growth while an unfavorable pressure gradient leads to an increase of the amplification. It is suggested that the transient growth mechanism be utilized to choose optimal parameters of tripping elements on a low-pressure turbine (LPT) airfoil. As an example, a boundary layer flow with a streamwise pressure gradient corresponding to the pressure distribution over a LPT airfoil is considered. It is shown that there is an optimal spacing of the tripping elements and that the transient growth effect depends on the starting point. At very low Reynolds numbers, there is a possibility to enhance the transient energy growth by means of wall cooling.

Gradient-Based Aerodynamic Shape Optimization Using ADI Method for Large-Scale Problems

NASA Technical Reports Server (NTRS)

Pandya, Mohagna J.; Baysal, Oktay

1997-01-01

A gradient-based shape optimization methodology, that is intended for practical three-dimensional aerodynamic applications, has been developed. It is based on the quasi-analytical sensitivities. The flow analysis is rendered by a fully implicit, finite volume formulation of the Euler equations.The aerodynamic sensitivity equation is solved using the alternating-direction-implicit (ADI) algorithm for memory efficiency. A flexible wing geometry model, that is based on surface parameterization and platform schedules, is utilized. The present methodology and its components have been tested via several comparisons. Initially, the flow analysis for for a wing is compared with those obtained using an unfactored, preconditioned conjugate gradient approach (PCG), and an extensively validated CFD code. Then, the sensitivities computed with the present method have been compared with those obtained using the finite-difference and the PCG approaches. Effects of grid refinement and convergence tolerance on the analysis and shape optimization have been explored. Finally the new procedure has been demonstrated in the design of a cranked arrow wing at Mach 2.4. Despite the expected increase in the computational time, the results indicate that shape optimization, which require large numbers of grid points can be resolved with a gradient-based approach.

Contribution to the optimal shape design of two-dimensional internal flows with embedded shocks

NASA Technical Reports Server (NTRS)

Iollo, Angelo; Salas, Manuel D.

1995-01-01

We explore the practicability of optimal shape design for flows modeled by the Euler equations. We define a functional whose minimum represents the optimality condition. The gradient of the functional with respect to the geometry is calculated with the Lagrange multipliers, which are determined by solving a co-state equation. The optimization problem is then examined by comparing the performance of several gradient-based optimization algorithms. In this formulation, the flow field can be computed to an arbitrary order of accuracy. Finally, some results for internal flows with embedded shocks are presented, including a case for which the solution to the inverse problem does not belong to the design space.

Robust automatic control system of vessel descent-rise device for plant with distributed parameters “cable – towed underwater vehicle”

NASA Astrophysics Data System (ADS)

Chupina, K. V.; Kataev, E. V.; Khannanov, A. M.; Korshunov, V. N.; Sennikov, I. A.

2018-05-01

The paper is devoted to a problem of synthesis of the robust control system for a distributed parameters plant. The vessel descent-rise device has a heave compensation function for stabilization of the towed underwater vehicle on a set depth. A sea state code, parameters of the underwater vehicle and cable vary during underwater operations, the vessel heave is a stochastic process. It means that the plant and external disturbances have uncertainty. That is why it is necessary to use the robust theory for synthesis of an automatic control system, but without use of traditional methods of optimization, because this cable has distributed parameters. The offered technique has allowed one to design an effective control system for stabilization of immersion depth of the towed underwater vehicle for various degrees of sea roughness and to provide its robustness to deviations of parameters of the vehicle and cable’s length.

Parachute Models Used in the Mars Science Laboratory Entry, Descent, and Landing Simulation

NASA Technical Reports Server (NTRS)

Cruz, Juan R.; Way, David W.; Shidner, Jeremy D.; Davis, Jody L.; Powell, Richard W.; Kipp, Devin M.; Adams, Douglas S.; Witkowski, Al; Kandis, Mike

2013-01-01

An end-to-end simulation of the Mars Science Laboratory (MSL) entry, descent, and landing (EDL) sequence was created at the NASA Langley Research Center using the Program to Optimize Simulated Trajectories II (POST2). This simulation is capable of providing numerous MSL system and flight software responses, including Monte Carlo-derived statistics of these responses. The MSL POST2 simulation includes models of EDL system elements, including those related to the parachute system. Among these there are models for the parachute geometry, mass properties, deployment, inflation, opening force, area oscillations, aerodynamic coefficients, apparent mass, interaction with the main landing engines, and off-loading. These models were kept as simple as possible, considering the overall objectives of the simulation. The main purpose of this paper is to describe these parachute system models to the extent necessary to understand how they work and some of their limitations. A list of lessons learned during the development of the models and simulation is provided. Future improvements to the parachute system models are proposed.

Simulations of Flame Acceleration and DDT in Mixture Composition Gradients

NASA Astrophysics Data System (ADS)

Zheng, Weilin; Kaplan, Carolyn; Houim, Ryan; Oran, Elaine

2017-11-01

Unsteady, multidimensional, fully compressible numerical simulations of methane-air in an obstructed channel with spatial gradients in equivalence ratios have been carried to determine the effects of the gradients on flame acceleration and transition to detonation. Results for gradients perpendicular to the propagation direction were considered here. A calibrated, optimized chemical-diffusive model that reproduces correct flame and detonation properties for methane-air over a range of equivalence ratios was derived from a combination of a genetic algorithm with a Nelder-Mead optimization scheme. Inhomogeneous mixtures of methane-air resulted in slower flame acceleration and longer distance to DDT. Detonations were more likely to decouple into a flame and a shock under sharper concentration gradients. Detailed analyses of temperature and equivalence ratio illustrated that vertical gradients can greatly affect the formation of hot spots that initiate detonation by changing the strength of leading shock wave and local equivalence ratio near the base of obstacles. This work is supported by the Alpha Foundation (Grant No. AFC215-20).

Optimized operation of dielectric laser accelerators: Single bunch

NASA Astrophysics Data System (ADS)

Hanuka, Adi; Schächter, Levi

2018-05-01

We introduce a general approach to determine the optimal charge, efficiency and gradient for laser driven accelerators in a self-consistent way. We propose a way to enhance the operational gradient of dielectric laser accelerators by leverage of beam-loading effect. While the latter may be detrimental from the perspective of the effective gradient experienced by the particles, it can be beneficial as the effective field experienced by the accelerating structure, is weaker. As a result, the constraint imposed by the damage threshold fluence is accordingly weakened and our self-consistent approach predicts permissible gradients of ˜10 GV /m , one order of magnitude higher than previously reported experimental results—with unbunched pulse of electrons. Our approach leads to maximum efficiency to occur for higher gradients as compared with a scenario in which the beam-loading effect on the material is ignored. In any case, maximum gradient does not occur for the same conditions that maximum efficiency does—a trade-off set of parameters is suggested.

Microfluidic Synthesis of Composite Cross-Gradient Materials for Investigating Cell–Biomaterial Interactions

PubMed Central

He, Jiankang; Du, Yanan; Guo, Yuqi; Hancock, Matthew J.; Wang, Ben; Shin, Hyeongho; Wu, Jinhui; Li, Dichen; Khademhosseini, Ali

2010-01-01

Combinatorial material synthesis is a powerful approach for creating composite material libraries for the high-throughput screening of cell–material interactions. Although current combinatorial screening platforms have been tremendously successful in identifying target (termed “hit”) materials from composite material libraries, new material synthesis approaches are needed to further optimize the concentrations and blending ratios of the component materials. Here we employed a microfluidic platform to rapidly synthesize composite materials containing cross-gradients of gelatin and chitosan for investigating cell–biomaterial interactions. The microfluidic synthesis of the cross-gradient was optimized experimentally and theoretically to produce quantitatively controllable variations in the concentrations and blending ratios of the two components. The anisotropic chemical compositions of the gelatin/chitosan cross-gradients were characterized by Fourier transform infrared spectrometry and X-ray photoelectron spectrometry. The three-dimensional (3D) porous gelatin/chitosan cross-gradient materials were shown to regulate the cellular morphology and proliferation of smooth muscle cells (SMCs) in a gradient-dependent manner. We envision that our microfluidic cross-gradient platform may accelerate the material development processes involved in a wide range of biomedical applications. PMID:20721897

Analysis of various descent trajectories for a hypersonic-cruise, cold-wall research airplane

NASA Technical Reports Server (NTRS)

Lawing, P. L.

1975-01-01

The probable descent operating conditions for a hypersonic air-breathing research airplane were examined. Descents selected were cruise angle of attack, high dynamic pressure, high lift coefficient, turns, and descents with drag brakes. The descents were parametrically exercised and compared from the standpoint of cold-wall (367 K) aircraft heat load. The descent parameters compared were total heat load, peak heating rate, time to landing, time to end of heat pulse, and range. Trends in total heat load as a function of cruise Mach number, cruise dynamic pressure, angle-of-attack limitation, pull-up g-load, heading angle, and drag-brake size are presented.

A piloted simulator evaluation of a ground-based 4-D descent advisor algorithm

NASA Technical Reports Server (NTRS)

Davis, Thomas J.; Green, Steven M.; Erzberger, Heinz

1990-01-01

A ground-based, four dimensional (4D) descent-advisor algorithm is under development at NASA-Ames. The algorithm combines detailed aerodynamic, propulsive, and atmospheric models with an efficient numerical integration scheme to generate 4D descent advisories. The ability is investigated of the 4D descent advisor algorithm to provide adequate control of arrival time for aircraft not equipped with on-board 4D guidance systems. A piloted simulation was conducted to determine the precision with which the descent advisor could predict the 4D trajectories of typical straight-in descents flown by airline pilots under different wind conditions. The effects of errors in the estimation of wind and initial aircraft weight were also studied. A description of the descent advisor as well as the result of the simulation studies are presented.

STS-1 operational flight profile. Volume 5: Descent, cycle 3. Appendix C: Monte Carlo dispersion analysis

NASA Technical Reports Server (NTRS)

1980-01-01

The results of three nonlinear the Monte Carlo dispersion analyses for the Space Transportation System 1 Flight (STS-1) Orbiter Descent Operational Flight Profile, Cycle 3 are presented. Fifty randomly selected simulation for the end of mission (EOM) descent, the abort once around (AOA) descent targeted line are steep target line, and the AOA descent targeted to the shallow target line are analyzed. These analyses compare the flight environment with system and operational constraints on the flight environment and in some cases use simplified system models as an aid in assessing the STS-1 descent flight profile. In addition, descent flight envelops are provided as a data base for use by system specialists to determine the flight readiness for STS-1. The results of these dispersion analyses supersede results of the dispersion analysis previously documented.

Variable fidelity robust optimization of pulsed laser orbital debris removal under epistemic uncertainty

NASA Astrophysics Data System (ADS)

Hou, Liqiang; Cai, Yuanli; Liu, Jin; Hou, Chongyuan

2016-04-01

A variable fidelity robust optimization method for pulsed laser orbital debris removal (LODR) under uncertainty is proposed. Dempster-shafer theory of evidence (DST), which merges interval-based and probabilistic uncertainty modeling, is used in the robust optimization. The robust optimization method optimizes the performance while at the same time maximizing its belief value. A population based multi-objective optimization (MOO) algorithm based on a steepest descent like strategy with proper orthogonal decomposition (POD) is used to search robust Pareto solutions. Analytical and numerical lifetime predictors are used to evaluate the debris lifetime after the laser pulses. Trust region based fidelity management is designed to reduce the computational cost caused by the expensive model. When the solutions fall into the trust region, the analytical model is used to reduce the computational cost. The proposed robust optimization method is first tested on a set of standard problems and then applied to the removal of Iridium 33 with pulsed lasers. It will be shown that the proposed approach can identify the most robust solutions with minimum lifetime under uncertainty.

Power plant fault detection using artificial neural network

NASA Astrophysics Data System (ADS)

Thanakodi, Suresh; Nazar, Nazatul Shiema Moh; Joini, Nur Fazriana; Hidzir, Hidzrin Dayana Mohd; Awira, Mohammad Zulfikar Khairul

2018-02-01

The fault that commonly occurs in power plants is due to various factors that affect the system outage. There are many types of faults in power plants such as single line to ground fault, double line to ground fault, and line to line fault. The primary aim of this paper is to diagnose the fault in 14 buses power plants by using an Artificial Neural Network (ANN). The Multilayered Perceptron Network (MLP) that detection trained utilized the offline training methods such as Gradient Descent Backpropagation (GDBP), Levenberg-Marquardt (LM), and Bayesian Regularization (BR). The best method is used to build the Graphical User Interface (GUI). The modelling of 14 buses power plant, network training, and GUI used the MATLAB software.

Incoherent beam combining based on the momentum SPGD algorithm

NASA Astrophysics Data System (ADS)

Yang, Guoqing; Liu, Lisheng; Jiang, Zhenhua; Guo, Jin; Wang, Tingfeng

2018-05-01

Incoherent beam combining (ICBC) technology is one of the most promising ways to achieve high-energy, near-diffraction laser output. In this paper, the momentum method is proposed as a modification of the stochastic parallel gradient descent (SPGD) algorithm. The momentum method can improve the speed of convergence of the combining system efficiently. The analytical method is employed to interpret the principle of the momentum method. Furthermore, the proposed algorithm is testified through simulations as well as experiments. The results of the simulations and the experiments show that the proposed algorithm not only accelerates the speed of the iteration, but also keeps the stability of the combining process. Therefore the feasibility of the proposed algorithm in the beam combining system is testified.

Frequency-domain ultrasound waveform tomography breast attenuation imaging

NASA Astrophysics Data System (ADS)

Sandhu, Gursharan Yash Singh; Li, Cuiping; Roy, Olivier; West, Erik; Montgomery, Katelyn; Boone, Michael; Duric, Neb

2016-04-01

Ultrasound waveform tomography techniques have shown promising results for the visualization and characterization of breast disease. By using frequency-domain waveform tomography techniques and a gradient descent algorithm, we have previously reconstructed the sound speed distributions of breasts of varying densities with different types of breast disease including benign and malignant lesions. By allowing the sound speed to have an imaginary component, we can model the intrinsic attenuation of a medium. We can similarly recover the imaginary component of the velocity and thus the attenuation. In this paper, we will briefly review ultrasound waveform tomography techniques, discuss attenuation and its relations to the imaginary component of the sound speed, and provide both numerical and ex vivo examples of waveform tomography attenuation reconstructions.

Deep turbulence effects mitigation with coherent combining of 21 laser beams over 7 km.

PubMed

Weyrauch, Thomas; Vorontsov, Mikhail; Mangano, Joseph; Ovchinnikov, Vladimir; Bricker, David; Polnau, Ernst; Rostov, Andrey

2016-02-15

We demonstrate coherent beam combining and adaptive mitigation of atmospheric turbulence effects over 7 km under strong scintillation conditions using a coherent fiber array laser transmitter operating in a target-in-the-loop setting. The transmitter system is composed of a densely packed array of 21 fiber collimators with integrated capabilities for piston, tip, and tilt control of the outgoing beams wavefront phases. A small cat's-eye retro reflector was used for evaluation of beam combining and turbulence compensation performance at the target plane, and to provide the feedback signal for control of piston and tip/tilt phases of the transmitted beams using the stochastic parallel gradient descent maximization of the power-in-the-bucket metric.

An experimental trip to the Calculus of Variations

NASA Astrophysics Data System (ADS)

Arroyo, Josu

2008-04-01

This paper presents a collection of experiments in the Calculus of Variations. The implementation of the Gradient Descent algorithm built on cubic-splines acting as "numerically friendly" elementary functions, give us ways to solve variational problems by constructing the solution. It wins a pragmatic point of view: one gets solutions sometimes as fast as possible, sometimes as close as possible to the true solutions. The balance speed/precision is not always easy to achieve. Starting from the most well-known, classic or historical formulation of a variational problem, section 2 describes briefly the bridge between theoretical and computational formulations. The next sections show the results of several kind of experiments; from the most basics, as those about geodesics, to the most complex, as those about vesicles.

Soft learning vector quantization and clustering algorithms based on ordered weighted aggregation operators.

PubMed

Karayiannis, N B

2000-01-01

This paper presents the development and investigates the properties of ordered weighted learning vector quantization (LVQ) and clustering algorithms. These algorithms are developed by using gradient descent to minimize reformulation functions based on aggregation operators. An axiomatic approach provides conditions for selecting aggregation operators that lead to admissible reformulation functions. Minimization of admissible reformulation functions based on ordered weighted aggregation operators produces a family of soft LVQ and clustering algorithms, which includes fuzzy LVQ and clustering algorithms as special cases. The proposed LVQ and clustering algorithms are used to perform segmentation of magnetic resonance (MR) images of the brain. The diagnostic value of the segmented MR images provides the basis for evaluating a variety of ordered weighted LVQ and clustering algorithms.

Quantitative characterization of turbidity by radiative transfer based reflectance imaging

PubMed Central

Tian, Peng; Chen, Cheng; Jin, Jiahong; Hong, Heng; Lu, Jun Q.; Hu, Xin-Hua

2018-01-01

A new and noncontact approach of multispectral reflectance imaging has been developed to inversely determine the absorption coefficient of μa, the scattering coefficient of μs and the anisotropy factor g of a turbid target from one measured reflectance image. The incident beam was profiled with a diffuse reflectance standard for deriving both measured and calculated reflectance images. A GPU implemented Monte Carlo code was developed to determine the parameters with a conjugate gradient descent algorithm and the existence of unique solutions was shown. We noninvasively determined embedded region thickness in heterogeneous targets and estimated in vivo optical parameters of nevi from 4 patients between 500 and 950nm for melanoma diagnosis to demonstrate the potentials of quantitative reflectance imaging. PMID:29760971

Aircraft symmetric flight optimization. [gradient techniques for supersonic aircraft control

NASA Technical Reports Server (NTRS)

Falco, M.; Kelley, H. J.

1973-01-01

Review of the development of gradient techniques and their application to aircraft optimal performance computations in the vertical plane of flight. Results obtained using the method of gradients are presented for attitude- and throttle-control programs which extremize the fuel, range, and time performance indices subject to various trajectory and control constraints, including boundedness of engine throttle control. A penalty function treatment of state inequality constraints which generally appear in aircraft performance problems is outlined. Numerical results for maximum-range, minimum-fuel, and minimum-time climb paths for a hypothetical supersonic turbojet interceptor are presented and discussed. In addition, minimum-fuel climb paths subject to various levels of ground overpressure intensity constraint are indicated for a representative supersonic transport. A variant of the Gel'fand-Tsetlin 'method of ravines' is reviewed, and two possibilities for further development of continuous gradient processes are cited - namely, a projection version of conjugate gradients and a curvilinear search.

Demonstration of Automatically-Generated Adjoint Code for Use in Aerodynamic Shape Optimization

NASA Technical Reports Server (NTRS)

Green, Lawrence; Carle, Alan; Fagan, Mike

1999-01-01

Gradient-based optimization requires accurate derivatives of the objective function and constraints. These gradients may have previously been obtained by manual differentiation of analysis codes, symbolic manipulators, finite-difference approximations, or existing automatic differentiation (AD) tools such as ADIFOR (Automatic Differentiation in FORTRAN). Each of these methods has certain deficiencies, particularly when applied to complex, coupled analyses with many design variables. Recently, a new AD tool called ADJIFOR (Automatic Adjoint Generation in FORTRAN), based upon ADIFOR, was developed and demonstrated. Whereas ADIFOR implements forward-mode (direct) differentiation throughout an analysis program to obtain exact derivatives via the chain rule of calculus, ADJIFOR implements the reverse-mode counterpart of the chain rule to obtain exact adjoint form derivatives from FORTRAN code. Automatically-generated adjoint versions of the widely-used CFL3D computational fluid dynamics (CFD) code and an algebraic wing grid generation code were obtained with just a few hours processing time using the ADJIFOR tool. The codes were verified for accuracy and were shown to compute the exact gradient of the wing lift-to-drag ratio, with respect to any number of shape parameters, in about the time required for 7 to 20 function evaluations. The codes have now been executed on various computers with typical memory and disk space for problems with up to 129 x 65 x 33 grid points, and for hundreds to thousands of independent variables. These adjoint codes are now used in a gradient-based aerodynamic shape optimization problem for a swept, tapered wing. For each design iteration, the optimization package constructs an approximate, linear optimization problem, based upon the current objective function, constraints, and gradient values. The optimizer subroutines are called within a design loop employing the approximate linear problem until an optimum shape is found, the design loop limit is reached, or no further design improvement is possible due to active design variable bounds and/or constraints. The resulting shape parameters are then used by the grid generation code to define a new wing surface and computational grid. The lift-to-drag ratio and its gradient are computed for the new design by the automatically-generated adjoint codes. Several optimization iterations may be required to find an optimum wing shape. Results from two sample cases will be discussed. The reader should note that this work primarily represents a demonstration of use of automatically- generated adjoint code within an aerodynamic shape optimization. As such, little significance is placed upon the actual optimization results, relative to the method for obtaining the results.

Seeking Global Minima

NASA Astrophysics Data System (ADS)

Tajuddin, Wan Ahmad

1994-02-01

Ease in finding the configuration at the global energy minimum in a symmetric neural network is important for combinatorial optimization problems. We carry out a comprehensive survey of available strategies for seeking global minima by comparing their performances in the binary representation problem. We recall our previous comparison of steepest descent with analog dynamics, genetic hill-climbing, simulated diffusion, simulated annealing, threshold accepting and simulated tunneling. To this, we add comparisons to other strategies including taboo search and one with field-ordered updating.

Human Mars Ascent Vehicle Performance Sensitivities

NASA Technical Reports Server (NTRS)

Polsgrove, Tara P.; Thomas, Herbert D.

2016-01-01

Human Mars mission architecture studies have shown that the ascent vehicle mass drives performance requirements for the descent and in-space transportation elements. Understanding the sensitivity of Mars ascent vehicle (MAV) mass to various mission and vehicle design choices enables overall transportation system optimization. This paper presents the results of a variety of sensitivity trades affecting MAV performance including: landing site latitude, target orbit, initial thrust to weight ratio, staging options, specific impulse, propellant type and engine design.