Approach for Uncertainty Propagation and Robust Design in CFD Using Sensitivity Derivatives

NASA Technical Reports Server (NTRS)

Putko, Michele M.; Newman, Perry A.; Taylor, Arthur C., III; Green, Lawrence L.

2001-01-01

This paper presents an implementation of the approximate statistical moment method for uncertainty propagation and robust optimization for a quasi 1-D Euler CFD (computational fluid dynamics) code. Given uncertainties in statistically independent, random, normally distributed input variables, a first- and second-order statistical moment matching procedure is performed to approximate the uncertainty in the CFD output. Efficient calculation of both first- and second-order sensitivity derivatives is required. In order to assess the validity of the approximations, the moments are compared with statistical moments generated through Monte Carlo simulations. The uncertainties in the CFD input variables are also incorporated into a robust optimization procedure. For this optimization, statistical moments involving first-order sensitivity derivatives appear in the objective function and system constraints. Second-order sensitivity derivatives are used in a gradient-based search to successfully execute a robust optimization. The approximate methods used throughout the analyses are found to be valid when considering robustness about input parameter mean values.

Optimal fractional order PID design via Tabu Search based algorithm.

PubMed

Ateş, Abdullah; Yeroglu, Celaleddin

2016-01-01

This paper presents an optimization method based on the Tabu Search Algorithm (TSA) to design a Fractional-Order Proportional-Integral-Derivative (FOPID) controller. All parameter computations of the FOPID employ random initial conditions, using the proposed optimization method. Illustrative examples demonstrate the performance of the proposed FOPID controller design method. Copyright © 2015 ISA. Published by Elsevier Ltd. All rights reserved.

Development of a fast and feasible spectrum modeling technique for flattening filter free beams

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

Cho, Woong; Bush, Karl; Mok, Ed

Purpose: To develop a fast and robust technique for the determination of optimized photon spectra for flattening filter free (FFF) beams to be applied in convolution/superposition dose calculations. Methods: A two-step optimization method was developed to derive optimal photon spectra for FFF beams. In the first step, a simple functional form of the photon spectra proposed by Ali ['Functional forms for photon spectra of clinical linacs,' Phys. Med. Biol. 57, 31-50 (2011)] is used to determine generalized shapes of the photon spectra. In this method, the photon spectra were defined for the ranges of field sizes to consider the variationsmore » of the contributions of scattered photons with field size. Percent depth doses (PDDs) for each field size were measured and calculated to define a cost function, and a collapsed cone convolution (CCC) algorithm was used to calculate the PDDs. In the second step, the generalized functional form of the photon spectra was fine-tuned in a process whereby the weights of photon fluence became the optimizing free parameters. A line search method was used for the optimization and first order derivatives with respect to the optimizing parameters were derived from the CCC algorithm to enhance the speed of the optimization. The derived photon spectra were evaluated, and the dose distributions using the optimized spectra were validated. Results: The optimal spectra demonstrate small variations with field size for the 6 MV FFF beam and relatively large variations for the 10 MV FFF beam. The mean energies of the optimized 6 MV FFF spectra were decreased from 1.31 MeV for a 3 Multiplication-Sign 3 cm{sup 2} field to 1.21 MeV for a 40 Multiplication-Sign 40 cm{sup 2} field, and from 2.33 MeV at 3 Multiplication-Sign 3 cm{sup 2} to 2.18 MeV at 40 Multiplication-Sign 40 cm{sup 2} for the 10 MV FFF beam. The developed method could significantly improve the agreement between the calculated and measured PDDs. Root mean square differences on the optimized PDDs were observed to be 0.41% (3 Multiplication-Sign 3 cm{sup 2}) down to 0.21% (40 Multiplication-Sign 40 cm{sup 2}) for the 6 MV FFF beam, and 0.35% (3 Multiplication-Sign 3 cm{sup 2}) down to 0.29% (40 Multiplication-Sign 40 cm{sup 2}) for the 10 MV FFF beam. The first order derivatives from the functional form were found to improve the speed of computational time up to 20 times compared to the other techniques. Conclusions: The derived photon spectra resulted in good agreements with measured PDDs over the range of field sizes investigated. The suggested method is easily applicable to commercial radiation treatment planning systems since it only requires measured PDDs as input.« less

Optimal control of LQR for discrete time-varying systems with input delays

NASA Astrophysics Data System (ADS)

Yin, Yue-Zhu; Yang, Zhong-Lian; Yin, Zhi-Xiang; Xu, Feng

2018-04-01

In this work, we consider the optimal control problem of linear quadratic regulation for discrete time-variant systems with single input and multiple input delays. An innovative and simple method to derive the optimal controller is given. The studied problem is first equivalently converted into a problem subject to a constraint condition. Last, with the established duality, the problem is transformed into a static mathematical optimisation problem without input delays. The optimal control input solution to minimise performance index function is derived by solving this optimisation problem with two methods. A numerical simulation example is carried out and its results show that our two approaches are both feasible and very effective.

Topology optimization in acoustics and elasto-acoustics via a level-set method

NASA Astrophysics Data System (ADS)

Desai, J.; Faure, A.; Michailidis, G.; Parry, G.; Estevez, R.

2018-04-01

Optimizing the shape and topology (S&T) of structures to improve their acoustic performance is quite challenging. The exact position of the structural boundary is usually of critical importance, which dictates the use of geometric methods for topology optimization instead of standard density approaches. The goal of the present work is to investigate different possibilities for handling topology optimization problems in acoustics and elasto-acoustics via a level-set method. From a theoretical point of view, we detail two equivalent ways to perform the derivation of surface-dependent terms and propose a smoothing technique for treating problems of boundary conditions optimization. In the numerical part, we examine the importance of the surface-dependent term in the shape derivative, neglected in previous studies found in the literature, on the optimal designs. Moreover, we test different mesh adaptation choices, as well as technical details related to the implicit surface definition in the level-set approach. We present results in two and three-space dimensions.

Aerodynamic design using numerical optimization

NASA Technical Reports Server (NTRS)

Murman, E. M.; Chapman, G. T.

1983-01-01

The procedure of using numerical optimization methods coupled with computational fluid dynamic (CFD) codes for the development of an aerodynamic design is examined. Several approaches that replace wind tunnel tests, develop pressure distributions and derive designs, or fulfill preset design criteria are presented. The method of Aerodynamic Design by Numerical Optimization (ADNO) is described and illustrated with examples.

Adjoint-Based Methodology for Time-Dependent Optimization

NASA Technical Reports Server (NTRS)

Yamaleev, N. K.; Diskin, B.; Nielsen, E. J.

2008-01-01

This paper presents a discrete adjoint method for a broad class of time-dependent optimization problems. The time-dependent adjoint equations are derived in terms of the discrete residual of an arbitrary finite volume scheme which approximates unsteady conservation law equations. Although only the 2-D unsteady Euler equations are considered in the present analysis, this time-dependent adjoint method is applicable to the 3-D unsteady Reynolds-averaged Navier-Stokes equations with minor modifications. The discrete adjoint operators involving the derivatives of the discrete residual and the cost functional with respect to the flow variables are computed using a complex-variable approach, which provides discrete consistency and drastically reduces the implementation and debugging cycle. The implementation of the time-dependent adjoint method is validated by comparing the sensitivity derivative with that obtained by forward mode differentiation. Our numerical results show that O(10) optimization iterations of the steepest descent method are needed to reduce the objective functional by 3-6 orders of magnitude for test problems considered.

Hedged Monte-Carlo: low variance derivative pricing with objective probabilities

NASA Astrophysics Data System (ADS)

Potters, Marc; Bouchaud, Jean-Philippe; Sestovic, Dragan

2001-01-01

We propose a new ‘hedged’ Monte-Carlo ( HMC) method to price financial derivatives, which allows to determine simultaneously the optimal hedge. The inclusion of the optimal hedging strategy allows one to reduce the financial risk associated with option trading, and for the very same reason reduces considerably the variance of our HMC scheme as compared to previous methods. The explicit accounting of the hedging cost naturally converts the objective probability into the ‘risk-neutral’ one. This allows a consistent use of purely historical time series to price derivatives and obtain their residual risk. The method can be used to price a large class of exotic options, including those with path dependent and early exercise features.

Designing stellarator coils by a modified Newton method using FOCUS

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

Zhu, Caoxiang; Hudson, Stuart R.; Song, Yuntao

To find the optimal coils for stellarators, nonlinear optimization algorithms are applied in existing coil design codes. However, none of these codes have used the information from the second-order derivatives. In this paper, we present a modified Newton method in the recently developed code FOCUS. The Hessian matrix is calculated with analytically derived equations. Its inverse is approximated by a modified Cholesky factorization and applied in the iterative scheme of a classical Newton method. Using this method, FOCUS is able to recover the W7-X modular coils starting from a simple initial guess. Results demonstrate significant advantages.

Designing stellarator coils by a modified Newton method using FOCUS

NASA Astrophysics Data System (ADS)

Zhu, Caoxiang; Hudson, Stuart R.; Song, Yuntao; Wan, Yuanxi

2018-06-01

To find the optimal coils for stellarators, nonlinear optimization algorithms are applied in existing coil design codes. However, none of these codes have used the information from the second-order derivatives. In this paper, we present a modified Newton method in the recently developed code FOCUS. The Hessian matrix is calculated with analytically derived equations. Its inverse is approximated by a modified Cholesky factorization and applied in the iterative scheme of a classical Newton method. Using this method, FOCUS is able to recover the W7-X modular coils starting from a simple initial guess. Results demonstrate significant advantages.

Designing stellarator coils by a modified Newton method using FOCUS

DOE PAGES

Zhu, Caoxiang; Hudson, Stuart R.; Song, Yuntao; ...

2018-03-22

To find the optimal coils for stellarators, nonlinear optimization algorithms are applied in existing coil design codes. However, none of these codes have used the information from the second-order derivatives. In this paper, we present a modified Newton method in the recently developed code FOCUS. The Hessian matrix is calculated with analytically derived equations. Its inverse is approximated by a modified Cholesky factorization and applied in the iterative scheme of a classical Newton method. Using this method, FOCUS is able to recover the W7-X modular coils starting from a simple initial guess. Results demonstrate significant advantages.

Parallel Aircraft Trajectory Optimization with Analytic Derivatives

NASA Technical Reports Server (NTRS)

Falck, Robert D.; Gray, Justin S.; Naylor, Bret

2016-01-01

Trajectory optimization is an integral component for the design of aerospace vehicles, but emerging aircraft technologies have introduced new demands on trajectory analysis that current tools are not well suited to address. Designing aircraft with technologies such as hybrid electric propulsion and morphing wings requires consideration of the operational behavior as well as the physical design characteristics of the aircraft. The addition of operational variables can dramatically increase the number of design variables which motivates the use of gradient based optimization with analytic derivatives to solve the larger optimization problems. In this work we develop an aircraft trajectory analysis tool using a Legendre-Gauss-Lobatto based collocation scheme, providing analytic derivatives via the OpenMDAO multidisciplinary optimization framework. This collocation method uses an implicit time integration scheme that provides a high degree of sparsity and thus several potential options for parallelization. The performance of the new implementation was investigated via a series of single and multi-trajectory optimizations using a combination of parallel computing and constraint aggregation. The computational performance results show that in order to take full advantage of the sparsity in the problem it is vital to parallelize both the non-linear analysis evaluations and the derivative computations themselves. The constraint aggregation results showed a significant numerical challenge due to difficulty in achieving tight convergence tolerances. Overall, the results demonstrate the value of applying analytic derivatives to trajectory optimization problems and lay the foundation for future application of this collocation based method to the design of aircraft with where operational scheduling of technologies is key to achieving good performance.

Aerodynamic design applying automatic differentiation and using robust variable fidelity optimization

NASA Astrophysics Data System (ADS)

Takemiya, Tetsushi

In modern aerospace engineering, the physics-based computational design method is becoming more important, as it is more efficient than experiments and because it is more suitable in designing new types of aircraft (e.g., unmanned aerial vehicles or supersonic business jets) than the conventional design method, which heavily relies on historical data. To enhance the reliability of the physics-based computational design method, researchers have made tremendous efforts to improve the fidelity of models. However, high-fidelity models require longer computational time, so the advantage of efficiency is partially lost. This problem has been overcome with the development of variable fidelity optimization (VFO). In VFO, different fidelity models are simultaneously employed in order to improve the speed and the accuracy of convergence in an optimization process. Among the various types of VFO methods, one of the most promising methods is the approximation management framework (AMF). In the AMF, objective and constraint functions of a low-fidelity model are scaled at a design point so that the scaled functions, which are referred to as "surrogate functions," match those of a high-fidelity model. Since scaling functions and the low-fidelity model constitutes surrogate functions, evaluating the surrogate functions is faster than evaluating the high-fidelity model. Therefore, in the optimization process, in which gradient-based optimization is implemented and thus many function calls are required, the surrogate functions are used instead of the high-fidelity model to obtain a new design point. The best feature of the AMF is that it may converge to a local optimum of the high-fidelity model in much less computational time than the high-fidelity model. However, through literature surveys and implementations of the AMF, the author xx found that (1) the AMF is very vulnerable when the computational analysis models have numerical noise, which is very common in high-fidelity models, and that (2) the AMF terminates optimization erroneously when the optimization problems have constraints. The first problem is due to inaccuracy in computing derivatives in the AMF, and the second problem is due to erroneous treatment of the trust region ratio, which sets the size of the domain for an optimization in the AMF. In order to solve the first problem of the AMF, automatic differentiation (AD) technique, which reads the codes of analysis models and automatically generates new derivative codes based on some mathematical rules, is applied. If derivatives are computed with the generated derivative code, they are analytical, and the required computational time is independent of the number of design variables, which is very advantageous for realistic aerospace engineering problems. However, if analysis models implement iterative computations such as computational fluid dynamics (CFD), which solves system partial differential equations iteratively, computing derivatives through the AD requires a massive memory size. The author solved this deficiency by modifying the AD approach and developing a more efficient implementation with CFD, and successfully applied the AD to general CFD software. In order to solve the second problem of the AMF, the governing equation of the trust region ratio, which is very strict against the violation of constraints, is modified so that it can accept the violation of constraints within some tolerance. By accepting violations of constraints during the optimization process, the AMF can continue optimization without terminating immaturely and eventually find the true optimum design point. With these modifications, the AMF is referred to as "Robust AMF," and it is applied to airfoil and wing aerodynamic design problems using Euler CFD software. The former problem has 21 design variables, and the latter 64. In both problems, derivatives computed with the proposed AD method are first compared with those computed with the finite differentiation (FD) method, and then, the Robust AMF is implemented along with the sequential quadratic programming (SQP) optimization method with only high-fidelity models. The proposed AD method computes derivatives more accurately and faster than the FD method, and the Robust AMF successfully optimizes shapes of the airfoil and the wing in a much shorter time than SQP with only high-fidelity models. These results clearly show the effectiveness of the Robust AMF. Finally, the feasibility of reducing computational time for calculating derivatives and the necessity of AMF with an optimum design point always in the feasible region are discussed as future work.

Optimal remediation of unconfined aquifers: Numerical applications and derivative calculations

NASA Astrophysics Data System (ADS)

Mansfield, Christopher M.; Shoemaker, Christine A.

1999-05-01

This paper extends earlier work on derivative-based optimization for cost-effective remediation to unconfined aquifers, which have more complex, nonlinear flow dynamics than confined aquifers. Most previous derivative-based optimization of contaminant removal has been limited to consideration of confined aquifers; however, contamination is more common in unconfined aquifers. Exact derivative equations are presented, and two computationally efficient approximations, the quasi-confined (QC) and head independent from previous (HIP) unconfined-aquifer finite element equation derivative approximations, are presented and demonstrated to be highly accurate. The derivative approximations can be used with any nonlinear optimization method requiring derivatives for computation of either time-invariant or time-varying pumping rates. The QC and HIP approximations are combined with the nonlinear optimal control algorithm SALQR into the unconfined-aquifer algorithm, which is shown to compute solutions for unconfined aquifers in CPU times that were not significantly longer than those required by the confined-aquifer optimization model. Two of the three example unconfined-aquifer cases considered obtained pumping policies with substantially lower objective function values with the unconfined model than were obtained with the confined-aquifer optimization, even though the mean differences in hydraulic heads predicted by the unconfined- and confined-aquifer models were small (less than 0.1%). We suggest a possible geophysical index based on differences in drawdown predictions between unconfined- and confined-aquifer models to estimate which aquifers require unconfined-aquifer optimization and which can be adequately approximated by the simpler confined-aquifer analysis.

New adaptive method to optimize the secondary reflector of linear Fresnel collectors

DOE PAGES

Zhu, Guangdong

2017-01-16

Performance of linear Fresnel collectors may largely depend on the secondary-reflector profile design when small-aperture absorbers are used. Optimization of the secondary-reflector profile is an extremely challenging task because there is no established theory to ensure superior performance of derived profiles. In this work, an innovative optimization method is proposed to optimize the secondary-reflector profile of a generic linear Fresnel configuration. The method correctly and accurately captures impacts of both geometric and optical aspects of a linear Fresnel collector to secondary-reflector design. The proposed method is an adaptive approach that does not assume a secondary shape of any particular form,more » but rather, starts at a single edge point and adaptively constructs the next surface point to maximize the reflected power to be reflected to absorber(s). As a test case, the proposed optimization method is applied to an industrial linear Fresnel configuration, and the results show that the derived optimal secondary reflector is able to redirect more than 90% of the power to the absorber in a wide range of incidence angles. Here, the proposed method can be naturally extended to other types of solar collectors as well, and it will be a valuable tool for solar-collector designs with a secondary reflector.« less

New adaptive method to optimize the secondary reflector of linear Fresnel collectors

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

Zhu, Guangdong

Performance of linear Fresnel collectors may largely depend on the secondary-reflector profile design when small-aperture absorbers are used. Optimization of the secondary-reflector profile is an extremely challenging task because there is no established theory to ensure superior performance of derived profiles. In this work, an innovative optimization method is proposed to optimize the secondary-reflector profile of a generic linear Fresnel configuration. The method correctly and accurately captures impacts of both geometric and optical aspects of a linear Fresnel collector to secondary-reflector design. The proposed method is an adaptive approach that does not assume a secondary shape of any particular form,more » but rather, starts at a single edge point and adaptively constructs the next surface point to maximize the reflected power to be reflected to absorber(s). As a test case, the proposed optimization method is applied to an industrial linear Fresnel configuration, and the results show that the derived optimal secondary reflector is able to redirect more than 90% of the power to the absorber in a wide range of incidence angles. Here, the proposed method can be naturally extended to other types of solar collectors as well, and it will be a valuable tool for solar-collector designs with a secondary reflector.« less

Estimating of aquifer parameters from the single-well water-level measurements in response to advancing longwall mine by using particle swarm optimization

NASA Astrophysics Data System (ADS)

Buyuk, Ersin; Karaman, Abdullah

2017-04-01

We estimated transmissivity and storage coefficient values from the single well water-level measurements positioned ahead of the mining face by using particle swarm optimization (PSO) technique. The water-level response to the advancing mining face contains an semi-analytical function that is not suitable for conventional inversion shemes because the partial derivative is difficult to calculate . Morever, the logaritmic behaviour of the model create difficulty for obtaining an initial model that may lead to a stable convergence. The PSO appears to obtain a reliable solution that produce a reasonable fit between water-level data and model function response. Optimization methods have been used to find optimum conditions consisting either minimum or maximum of a given objective function with regard to some criteria. Unlike PSO, traditional non-linear optimization methods have been used for many hydrogeologic and geophysical engineering problems. These methods indicate some difficulties such as dependencies to initial model, evolution of the partial derivatives that is required while linearizing the model and trapping at local optimum. Recently, Particle swarm optimization (PSO) became the focus of modern global optimization method that is inspired from the social behaviour of birds of swarms, and appears to be a reliable and powerful algorithms for complex engineering applications. PSO that is not dependent on an initial model, and non-derivative stochastic process appears to be capable of searching all possible solutions in the model space either around local or global optimum points.

Optimal control problem for linear fractional-order systems, described by equations with Hadamard-type derivative

NASA Astrophysics Data System (ADS)

Postnov, Sergey

2017-11-01

Two kinds of optimal control problem are investigated for linear time-invariant fractional-order systems with lumped parameters which dynamics described by equations with Hadamard-type derivative: the problem of control with minimal norm and the problem of control with minimal time at given restriction on control norm. The problem setting with nonlocal initial conditions studied. Admissible controls allowed to be the p-integrable functions (p > 1) at half-interval. The optimal control problem studied by moment method. The correctness and solvability conditions for the corresponding moment problem are derived. For several special cases the optimal control problems stated are solved analytically. Some analogies pointed for results obtained with the results which are known for integer-order systems and fractional-order systems describing by equations with Caputo- and Riemann-Liouville-type derivatives.

CONORBIT: constrained optimization by radial basis function interpolation in trust regions

DOE PAGES

Regis, Rommel G.; Wild, Stefan M.

2016-09-26

Here, this paper presents CONORBIT (CONstrained Optimization by Radial Basis function Interpolation in Trust regions), a derivative-free algorithm for constrained black-box optimization where the objective and constraint functions are computationally expensive. CONORBIT employs a trust-region framework that uses interpolating radial basis function (RBF) models for the objective and constraint functions, and is an extension of the ORBIT algorithm. It uses a small margin for the RBF constraint models to facilitate the generation of feasible iterates, and extensive numerical tests confirm that such a margin is helpful in improving performance. CONORBIT is compared with other algorithms on 27 test problems, amore » chemical process optimization problem, and an automotive application. Numerical results show that CONORBIT performs better than COBYLA, a sequential penalty derivative-free method, an augmented Lagrangian method, a direct search method, and another RBF-based algorithm on the test problems and on the automotive application.« less

New scale-down methodology from commercial to lab scale to optimize plant-derived soft gel capsule formulations on a commercial scale.

PubMed

Oishi, Sana; Kimura, Shin-Ichiro; Noguchi, Shuji; Kondo, Mio; Kondo, Yosuke; Shimokawa, Yoshiyuki; Iwao, Yasunori; Itai, Shigeru

2018-01-15

A new scale-down methodology from commercial rotary die scale to laboratory scale was developed to optimize a plant-derived soft gel capsule formulation and eventually manufacture superior soft gel capsules on a commercial scale, in order to reduce the time and cost for formulation development. Animal-derived and plant-derived soft gel film sheets were prepared using an applicator on a laboratory scale and their physicochemical properties, such as tensile strength, Young's modulus, and adhesive strength, were evaluated. The tensile strength of the animal-derived and plant-derived soft gel film sheets was 11.7 MPa and 4.41 MPa, respectively. The Young's modulus of the animal-derived and plant-derived soft gel film sheets was 169 MPa and 17.8 MPa, respectively, and both sheets showed a similar adhesion strength of approximately 4.5-10 MPa. Using a D-optimal mixture design, plant-derived soft gel film sheets were prepared and optimized by varying their composition, including variations in the mass of κ-carrageenan, ι-carrageenan, oxidized starch and heat-treated starch. The physicochemical properties of the sheets were evaluated to determine the optimal formulation. Finally, plant-derived soft gel capsules were manufactured using the rotary die method and the prepared soft gel capsules showed equivalent or superior physical properties compared with pre-existing soft gel capsules. Therefore, we successfully developed a new scale-down methodology to optimize the formulation of plant-derived soft gel capsules on a commercial scale. Copyright © 2017 Elsevier B.V. All rights reserved.

A dynamic multi-level optimal design method with embedded finite-element modeling for power transformers

NASA Astrophysics Data System (ADS)

Zhang, Yunpeng; Ho, Siu-lau; Fu, Weinong

2018-05-01

This paper proposes a dynamic multi-level optimal design method for power transformer design optimization (TDO) problems. A response surface generated by second-order polynomial regression analysis is updated dynamically by adding more design points, which are selected by Shifted Hammersley Method (SHM) and calculated by finite-element method (FEM). The updating stops when the accuracy requirement is satisfied, and optimized solutions of the preliminary design are derived simultaneously. The optimal design level is modulated through changing the level of error tolerance. Based on the response surface of the preliminary design, a refined optimal design is added using multi-objective genetic algorithm (MOGA). The effectiveness of the proposed optimal design method is validated through a classic three-phase power TDO problem.

Optimal preconditioning of lattice Boltzmann methods

NASA Astrophysics Data System (ADS)

Izquierdo, Salvador; Fueyo, Norberto

2009-09-01

A preconditioning technique to accelerate the simulation of steady-state problems using the single-relaxation-time (SRT) lattice Boltzmann (LB) method was first proposed by Guo et al. [Z. Guo, T. Zhao, Y. Shi, Preconditioned lattice-Boltzmann method for steady flows, Phys. Rev. E 70 (2004) 066706-1]. The key idea in this preconditioner is to modify the equilibrium distribution function in such a way that, by means of a Chapman-Enskog expansion, a time-derivative preconditioner of the Navier-Stokes (NS) equations is obtained. In the present contribution, the optimal values for the free parameter γ of this preconditioner are searched both numerically and theoretically; the later with the aid of linear-stability analysis and with the condition number of the system of NS equations. The influence of the collision operator, single- versus multiple-relaxation-times (MRT), is also studied. Three steady-state laminar test cases are used for validation, namely: the two-dimensional lid-driven cavity, a two-dimensional microchannel and the three-dimensional backward-facing step. Finally, guidelines are suggested for an a priori definition of optimal preconditioning parameters as a function of the Reynolds and Mach numbers. The new optimally preconditioned MRT method derived is shown to improve, simultaneously, the rate of convergence, the stability and the accuracy of the lattice Boltzmann simulations, when compared to the non-preconditioned methods and to the optimally preconditioned SRT one. Additionally, direct time-derivative preconditioning of the LB equation is also studied.

Finite dimensional approximation of a class of constrained nonlinear optimal control problems

NASA Technical Reports Server (NTRS)

Gunzburger, Max D.; Hou, L. S.

1994-01-01

An abstract framework for the analysis and approximation of a class of nonlinear optimal control and optimization problems is constructed. Nonlinearities occur in both the objective functional and in the constraints. The framework includes an abstract nonlinear optimization problem posed on infinite dimensional spaces, and approximate problem posed on finite dimensional spaces, together with a number of hypotheses concerning the two problems. The framework is used to show that optimal solutions exist, to show that Lagrange multipliers may be used to enforce the constraints, to derive an optimality system from which optimal states and controls may be deduced, and to derive existence results and error estimates for solutions of the approximate problem. The abstract framework and the results derived from that framework are then applied to three concrete control or optimization problems and their approximation by finite element methods. The first involves the von Karman plate equations of nonlinear elasticity, the second, the Ginzburg-Landau equations of superconductivity, and the third, the Navier-Stokes equations for incompressible, viscous flows.

Maximum likelihood identification and optimal input design for identifying aircraft stability and control derivatives

NASA Technical Reports Server (NTRS)

Stepner, D. E.; Mehra, R. K.

1973-01-01

A new method of extracting aircraft stability and control derivatives from flight test data is developed based on the maximum likelihood cirterion. It is shown that this new method is capable of processing data from both linear and nonlinear models, both with and without process noise and includes output error and equation error methods as special cases. The first application of this method to flight test data is reported for lateral maneuvers of the HL-10 and M2/F3 lifting bodies, including the extraction of stability and control derivatives in the presence of wind gusts. All the problems encountered in this identification study are discussed. Several different methods (including a priori weighting, parameter fixing and constrained parameter values) for dealing with identifiability and uniqueness problems are introduced and the results given. The method for the design of optimal inputs for identifying the parameters of linear dynamic systems is also given. The criterion used for the optimization is the sensitivity of the system output to the unknown parameters. Several simple examples are first given and then the results of an extensive stability and control dervative identification simulation for a C-8 aircraft are detailed.

Second-order variational equations for N-body simulations

NASA Astrophysics Data System (ADS)

Rein, Hanno; Tamayo, Daniel

2016-07-01

First-order variational equations are widely used in N-body simulations to study how nearby trajectories diverge from one another. These allow for efficient and reliable determinations of chaos indicators such as the Maximal Lyapunov characteristic Exponent (MLE) and the Mean Exponential Growth factor of Nearby Orbits (MEGNO). In this paper we lay out the theoretical framework to extend the idea of variational equations to higher order. We explicitly derive the differential equations that govern the evolution of second-order variations in the N-body problem. Going to second order opens the door to new applications, including optimization algorithms that require the first and second derivatives of the solution, like the classical Newton's method. Typically, these methods have faster convergence rates than derivative-free methods. Derivatives are also required for Riemann manifold Langevin and Hamiltonian Monte Carlo methods which provide significantly shorter correlation times than standard methods. Such improved optimization methods can be applied to anything from radial-velocity/transit-timing-variation fitting to spacecraft trajectory optimization to asteroid deflection. We provide an implementation of first- and second-order variational equations for the publicly available REBOUND integrator package. Our implementation allows the simultaneous integration of any number of first- and second-order variational equations with the high-accuracy IAS15 integrator. We also provide routines to generate consistent and accurate initial conditions without the need for finite differencing.

Analysis of neighborhood behavior in lead optimization and array design.

PubMed

Papadatos, George; Cooper, Anthony W J; Kadirkamanathan, Visakan; Macdonald, Simon J F; McLay, Iain M; Pickett, Stephen D; Pritchard, John M; Willett, Peter; Gillet, Valerie J

2009-02-01

Neighborhood behavior describes the extent to which small structural changes defined by a molecular descriptor are likely to lead to small property changes. This study evaluates two methods for the quantification of neighborhood behavior: the optimal diagonal method of Patterson et al. and the optimality criterion method of Horvath and Jeandenans. The methods are evaluated using twelve different types of fingerprint (both 2D and 3D) with screening data derived from several lead optimization projects at GlaxoSmithKline. The principal focus of the work is the design of chemical arrays during lead optimization, and the study hence considers not only biological activity but also important drug properties such as metabolic stability, permeability, and lipophilicity. Evidence is provided to suggest that the optimality criterion method may provide a better quantitative description of neighborhood behavior than the optimal diagonal method.

Adjoint-based optimization of PDEs in moving domains

NASA Astrophysics Data System (ADS)

Protas, Bartosz; Liao, Wenyuan

2008-02-01

In this investigation we address the problem of adjoint-based optimization of PDE systems in moving domains. As an example we consider the one-dimensional heat equation with prescribed boundary temperatures and heat fluxes. We discuss two methods of deriving an adjoint system necessary to obtain a gradient of a cost functional. In the first approach we derive the adjoint system after mapping the problem to a fixed domain, whereas in the second approach we derive the adjoint directly in the moving domain by employing methods of the noncylindrical calculus. We show that the operations of transforming the system from a variable to a fixed domain and deriving the adjoint do not commute and that, while the gradient information contained in both systems is the same, the second approach results in an adjoint problem with a simpler structure which is therefore easier to implement numerically. This approach is then used to solve a moving boundary optimization problem for our model system.

Fuel management optimization using genetic algorithms and code independence

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

DeChaine, M.D.; Feltus, M.A.

1994-12-31

Fuel management optimization is a hard problem for traditional optimization techniques. Loading pattern optimization is a large combinatorial problem without analytical derivative information. Therefore, methods designed for continuous functions, such as linear programming, do not always work well. Genetic algorithms (GAs) address these problems and, therefore, appear ideal for fuel management optimization. They do not require derivative information and work well with combinatorial. functions. The GAs are a stochastic method based on concepts from biological genetics. They take a group of candidate solutions, called the population, and use selection, crossover, and mutation operators to create the next generation of bettermore » solutions. The selection operator is a {open_quotes}survival-of-the-fittest{close_quotes} operation and chooses the solutions for the next generation. The crossover operator is analogous to biological mating, where children inherit a mixture of traits from their parents, and the mutation operator makes small random changes to the solutions.« less

Design of two-channel filter bank using nature inspired optimization based fractional derivative constraints.

PubMed

Kuldeep, B; Singh, V K; Kumar, A; Singh, G K

2015-01-01

In this article, a novel approach for 2-channel linear phase quadrature mirror filter (QMF) bank design based on a hybrid of gradient based optimization and optimization of fractional derivative constraints is introduced. For the purpose of this work, recently proposed nature inspired optimization techniques such as cuckoo search (CS), modified cuckoo search (MCS) and wind driven optimization (WDO) are explored for the design of QMF bank. 2-Channel QMF is also designed with particle swarm optimization (PSO) and artificial bee colony (ABC) nature inspired optimization techniques. The design problem is formulated in frequency domain as sum of L2 norm of error in passband, stopband and transition band at quadrature frequency. The contribution of this work is the novel hybrid combination of gradient based optimization (Lagrange multiplier method) and nature inspired optimization (CS, MCS, WDO, PSO and ABC) and its usage for optimizing the design problem. Performance of the proposed method is evaluated by passband error (ϕp), stopband error (ϕs), transition band error (ϕt), peak reconstruction error (PRE), stopband attenuation (As) and computational time. The design examples illustrate the ingenuity of the proposed method. Results are also compared with the other existing algorithms, and it was found that the proposed method gives best result in terms of peak reconstruction error and transition band error while it is comparable in terms of passband and stopband error. Results show that the proposed method is successful for both lower and higher order 2-channel QMF bank design. A comparative study of various nature inspired optimization techniques is also presented, and the study singles out CS as a best QMF optimization technique. Copyright © 2014 ISA. Published by 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

Laplace-Fourier-domain dispersion analysis of an average derivative optimal scheme for scalar-wave equation

NASA Astrophysics Data System (ADS)

Chen, Jing-Bo

2014-06-01

By using low-frequency components of the damped wavefield, Laplace-Fourier-domain full waveform inversion (FWI) can recover a long-wavelength velocity model from the original undamped seismic data lacking low-frequency information. Laplace-Fourier-domain modelling is an important foundation of Laplace-Fourier-domain FWI. Based on the numerical phase velocity and the numerical attenuation propagation velocity, a method for performing Laplace-Fourier-domain numerical dispersion analysis is developed in this paper. This method is applied to an average-derivative optimal scheme. The results show that within the relative error of 1 per cent, the Laplace-Fourier-domain average-derivative optimal scheme requires seven gridpoints per smallest wavelength and smallest pseudo-wavelength for both equal and unequal directional sampling intervals. In contrast, the classical five-point scheme requires 23 gridpoints per smallest wavelength and smallest pseudo-wavelength to achieve the same accuracy. Numerical experiments demonstrate the theoretical analysis.

Optimization of magnetization transfer measurements: statistical analysis by stochastic simulation. Application to creatine kinase kinetics.

PubMed

Rydzy, M; Deslauriers, R; Smith, I C; Saunders, J K

1990-08-01

A systematic study was performed to optimize the accuracy of kinetic parameters derived from magnetization transfer measurements. Three techniques were investigated: time-dependent saturation transfer (TDST), saturation recovery (SRS), and inversion recovery (IRS). In the last two methods, one of the resonances undergoing exchange is saturated throughout the experiment. The three techniques were compared with respect to the accuracy of the kinetic parameters derived from experiments performed in a given, fixed, amount of time. Stochastic simulation of magnetization transfer experiments was performed to optimize experimental design. General formulas for the relative accuracies of the unidirectional rate constant (k) were derived for each of the three experimental methods. It was calculated that for k values between 0.1 and 1.0 s-1, T1 values between 1 and 10 s, and relaxation delays appropriate for the creatine kinase reaction, the SRS method yields more accurate values of k than does the IRS method. The TDST method is more accurate than the SRS method for reactions where T1 is long and k is large, within the range of k and T1 values examined. Experimental verification of the method was carried out on a solution in which the forward (PCr----ATP) rate constant (kf) of the creatine kinase reaction was measured.

The q-G method : A q-version of the Steepest Descent method for global optimization.

PubMed

Soterroni, Aline C; Galski, Roberto L; Scarabello, Marluce C; Ramos, Fernando M

2015-01-01

In this work, the q-Gradient (q-G) method, a q-version of the Steepest Descent method, is presented. The main idea behind the q-G method is the use of the negative of the q-gradient vector of the objective function as the search direction. The q-gradient vector, or simply the q-gradient, is a generalization of the classical gradient vector based on the concept of Jackson's derivative from the q-calculus. Its use provides the algorithm an effective mechanism for escaping from local minima. The q-G method reduces to the Steepest Descent method when the parameter q tends to 1. The algorithm has three free parameters and it is implemented so that the search process gradually shifts from global exploration in the beginning to local exploitation in the end. We evaluated the q-G method on 34 test functions, and compared its performance with 34 optimization algorithms, including derivative-free algorithms and the Steepest Descent method. Our results show that the q-G method is competitive and has a great potential for solving multimodal optimization problems.

A Scalable, Parallel Approach for Multi-Point, High-Fidelity Aerostructural Optimization of Aircraft Configurations

NASA Astrophysics Data System (ADS)

Kenway, Gaetan K. W.

This thesis presents new tools and techniques developed to address the challenging problem of high-fidelity aerostructural optimization with respect to large numbers of design variables. A new mesh-movement scheme is developed that is both computationally efficient and sufficiently robust to accommodate large geometric design changes and aerostructural deformations. A fully coupled Newton-Krylov method is presented that accelerates the convergence of aerostructural systems and provides a 20% performance improvement over the traditional nonlinear block Gauss-Seidel approach and can handle more exible structures. A coupled adjoint method is used that efficiently computes derivatives for a gradient-based optimization algorithm. The implementation uses only machine accurate derivative techniques and is verified to yield fully consistent derivatives by comparing against the complex step method. The fully-coupled large-scale coupled adjoint solution method is shown to have 30% better performance than the segregated approach. The parallel scalability of the coupled adjoint technique is demonstrated on an Euler Computational Fluid Dynamics (CFD) model with more than 80 million state variables coupled to a detailed structural finite-element model of the wing with more than 1 million degrees of freedom. Multi-point high-fidelity aerostructural optimizations of a long-range wide-body, transonic transport aircraft configuration are performed using the developed techniques. The aerostructural analysis employs Euler CFD with a 2 million cell mesh and a structural finite element model with 300 000 DOF. Two design optimization problems are solved: one where takeoff gross weight is minimized, and another where fuel burn is minimized. Each optimization uses a multi-point formulation with 5 cruise conditions and 2 maneuver conditions. The optimization problems have 476 design variables are optimal results are obtained within 36 hours of wall time using 435 processors. The TOGW minimization results in a 4.2% reduction in TOGW with a 6.6% fuel burn reduction, while the fuel burn optimization resulted in a 11.2% fuel burn reduction with no change to the takeoff gross weight.

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.

On optimal soft-decision demodulation. [in digital communication system

NASA Technical Reports Server (NTRS)

Lee, L.-N.

1976-01-01

A necessary condition is derived for optimal J-ary coherent demodulation of M-ary (M greater than 2) signals. Optimality is defined as maximality of the symmetric cutoff rate of the resulting discrete memoryless channel. Using a counterexample, it is shown that the condition derived is generally not sufficient for optimality. This condition is employed as the basis for an iterative optimization method to find the optimal demodulator decision regions from an initial 'good guess'. In general, these regions are found to be bounded by hyperplanes in likelihood space; the corresponding regions in signal space are found to have hyperplane asymptotes for the important case of additive white Gaussian noise. Some examples are presented, showing that the regions in signal space bounded by these asymptotic hyperplanes define demodulator decision regions that are virtually optimal.

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

Kwon, Deukwoo; Little, Mark P.; Miller, Donald L.

Purpose: To determine more accurate regression formulas for estimating peak skin dose (PSD) from reference air kerma (RAK) or kerma-area product (KAP). Methods: After grouping of the data from 21 procedures into 13 clinically similar groups, assessments were made of optimal clustering using the Bayesian information criterion to obtain the optimal linear regressions of (log-transformed) PSD vs RAK, PSD vs KAP, and PSD vs RAK and KAP. Results: Three clusters of clinical groups were optimal in regression of PSD vs RAK, seven clusters of clinical groups were optimal in regression of PSD vs KAP, and six clusters of clinical groupsmore » were optimal in regression of PSD vs RAK and KAP. Prediction of PSD using both RAK and KAP is significantly better than prediction of PSD with either RAK or KAP alone. The regression of PSD vs RAK provided better predictions of PSD than the regression of PSD vs KAP. The partial-pooling (clustered) method yields smaller mean squared errors compared with the complete-pooling method.Conclusion: PSD distributions for interventional radiology procedures are log-normal. Estimates of PSD derived from RAK and KAP jointly are most accurate, followed closely by estimates derived from RAK alone. Estimates of PSD derived from KAP alone are the least accurate. Using a stochastic search approach, it is possible to cluster together certain dissimilar types of procedures to minimize the total error sum of squares.« less

Tunning PID controller using particle swarm optimization algorithm on automatic voltage regulator system

NASA Astrophysics Data System (ADS)

Aranza, M. F.; Kustija, J.; Trisno, B.; Hakim, D. L.

2016-04-01

PID Controller (Proportional Integral Derivative) was invented since 1910, but till today still is used in industries, even though there are many kind of modern controllers like fuzz controller and neural network controller are being developed. Performance of PID controller is depend on on Proportional Gain (Kp), Integral Gain (Ki) and Derivative Gain (Kd). These gains can be got by using method Ziegler-Nichols (ZN), gain-phase margin, Root Locus, Minimum Variance dan Gain Scheduling however these methods are not optimal to control systems that nonlinear and have high-orde, in addition, some methods relative hard. To solve those obstacles, particle swarm optimization (PSO) algorithm is proposed to get optimal Kp, Ki and Kd. PSO is proposed because PSO has convergent result and not require many iterations. On this research, PID controller is applied on AVR (Automatic Voltage Regulator). Based on result of analyzing transient, stability Root Locus and frequency response, performance of PID controller is better than Ziegler-Nichols.

Designing optimal universal pulses using second-order, large-scale, non-linear optimization

NASA Astrophysics Data System (ADS)

Anand, Christopher Kumar; Bain, Alex D.; Curtis, Andrew Thomas; Nie, Zhenghua

2012-06-01

Recently, RF pulse design using first-order and quasi-second-order pulses has been actively investigated. We present a full second-order design method capable of incorporating relaxation, inhomogeneity in B0 and B1. Our model is formulated as a generic optimization problem making it easy to incorporate diverse pulse sequence features. To tame the computational cost, we present a method of calculating second derivatives in at most a constant multiple of the first derivative calculation time, this is further accelerated by using symbolic solutions of the Bloch equations. We illustrate the relative merits and performance of quasi-Newton and full second-order optimization with a series of examples, showing that even a pulse already optimized using other methods can be visibly improved. To be useful in CPMG experiments, a universal refocusing pulse should be independent of the delay time and insensitive of the relaxation time and RF inhomogeneity. We design such a pulse and show that, using it, we can obtain reliable R2 measurements for offsets within ±γB1. Finally, we compare our optimal refocusing pulse with other published refocusing pulses by doing CPMG experiments.

Mathematical modeling of synthetic unit hydrograph case study: Citarum watershed

NASA Astrophysics Data System (ADS)

Islahuddin, Muhammad; Sukrainingtyas, Adiska L. A.; Kusuma, M. Syahril B.; Soewono, Edy

2015-09-01

Deriving unit hydrograph is very important in analyzing watershed's hydrologic response of a rainfall event. In most cases, hourly measures of stream flow data needed in deriving unit hydrograph are not always available. Hence, one needs to develop methods for deriving unit hydrograph for ungagged watershed. Methods that have evolved are based on theoretical or empirical formulas relating hydrograph peak discharge and timing to watershed characteristics. These are usually referred to Synthetic Unit Hydrograph. In this paper, a gamma probability density function and its variant are used as mathematical approximations of a unit hydrograph for Citarum Watershed. The model is adjusted with real field condition by translation and scaling. Optimal parameters are determined by using Particle Swarm Optimization method with weighted objective function. With these models, a synthetic unit hydrograph can be developed and hydrologic parameters can be well predicted.

Multi-disciplinary optimization of aeroservoelastic systems

NASA Technical Reports Server (NTRS)

Karpel, Mordechay

1990-01-01

Efficient analytical and computational tools for simultaneous optimal design of the structural and control components of aeroservoelastic systems are presented. The optimization objective is to achieve aircraft performance requirements and sufficient flutter and control stability margins with a minimal weight penalty and without violating the design constraints. Analytical sensitivity derivatives facilitate an efficient optimization process which allows a relatively large number of design variables. Standard finite element and unsteady aerodynamic routines are used to construct a modal data base. Minimum State aerodynamic approximations and dynamic residualization methods are used to construct a high accuracy, low order aeroservoelastic model. Sensitivity derivatives of flutter dynamic pressure, control stability margins and control effectiveness with respect to structural and control design variables are presented. The performance requirements are utilized by equality constraints which affect the sensitivity derivatives. A gradient-based optimization algorithm is used to minimize an overall cost function. A realistic numerical example of a composite wing with four controls is used to demonstrate the modeling technique, the optimization process, and their accuracy and efficiency.

Multidisciplinary optimization of aeroservoelastic systems using reduced-size models

NASA Technical Reports Server (NTRS)

Karpel, Mordechay

1992-01-01

Efficient analytical and computational tools for simultaneous optimal design of the structural and control components of aeroservoelastic systems are presented. The optimization objective is to achieve aircraft performance requirements and sufficient flutter and control stability margins with a minimal weight penalty and without violating the design constraints. Analytical sensitivity derivatives facilitate an efficient optimization process which allows a relatively large number of design variables. Standard finite element and unsteady aerodynamic routines are used to construct a modal data base. Minimum State aerodynamic approximations and dynamic residualization methods are used to construct a high accuracy, low order aeroservoelastic model. Sensitivity derivatives of flutter dynamic pressure, control stability margins and control effectiveness with respect to structural and control design variables are presented. The performance requirements are utilized by equality constraints which affect the sensitivity derivatives. A gradient-based optimization algorithm is used to minimize an overall cost function. A realistic numerical example of a composite wing with four controls is used to demonstrate the modeling technique, the optimization process, and their accuracy and efficiency.

A level set-based topology optimization method for simultaneous design of elastic structure and coupled acoustic cavity using a two-phase material model

NASA Astrophysics Data System (ADS)

Noguchi, Yuki; Yamamoto, Takashi; Yamada, Takayuki; Izui, Kazuhiro; Nishiwaki, Shinji

2017-09-01

This papers proposes a level set-based topology optimization method for the simultaneous design of acoustic and structural material distributions. In this study, we develop a two-phase material model that is a mixture of an elastic material and acoustic medium, to represent an elastic structure and an acoustic cavity by controlling a volume fraction parameter. In the proposed model, boundary conditions at the two-phase material boundaries are satisfied naturally, avoiding the need to express these boundaries explicitly. We formulate a topology optimization problem to minimize the sound pressure level using this two-phase material model and a level set-based method that obtains topologies free from grayscales. The topological derivative of the objective functional is approximately derived using a variational approach and the adjoint variable method and is utilized to update the level set function via a time evolutionary reaction-diffusion equation. Several numerical examples present optimal acoustic and structural topologies that minimize the sound pressure generated from a vibrating elastic structure.

An Efficient Power Regeneration and Drive Method of an Induction Motor by Means of an Optimal Torque Derived by Variational Method

NASA Astrophysics Data System (ADS)

Inoue, Kaoru; Ogata, Kenji; Kato, Toshiji

When the motor speed is reduced by using a regenerative brake, the mechanical energy of rotation is converted to the electrical energy. When the regenerative torque is large, the corresponding current increases so that the copper loss also becomes large. On the other hand, the damping effect of rotation increases according to the time elapse when the regenerative torque is small. In order to use the limited energy effectively, an optimal regenerative torque should be discussed in order to regenerate electrical energy as much as possible. This paper proposes a design methodology of a regenerative torque for an induction motor to maximize the regenerative electric energy by means of the variational method. Similarly, an optimal torque for acceleration is derived in order to minimize the energy to drive. Finally, an efficient motor drive system with the proposed optimal torque and the power storage system stabilizing the DC link voltage will be proposed. The effectiveness of the proposed methods are illustrated by both simulations and experiments.

Optimization for minimum sensitivity to uncertain parameters

NASA Technical Reports Server (NTRS)

Pritchard, Jocelyn I.; Adelman, Howard M.; Sobieszczanski-Sobieski, Jaroslaw

1994-01-01

A procedure to design a structure for minimum sensitivity to uncertainties in problem parameters is described. The approach is to minimize directly the sensitivity derivatives of the optimum design with respect to fixed design parameters using a nested optimization procedure. The procedure is demonstrated for the design of a bimetallic beam for minimum weight with insensitivity to uncertainties in structural properties. The beam is modeled with finite elements based on two dimensional beam analysis. A sequential quadratic programming procedure used as the optimizer supplies the Lagrange multipliers that are used to calculate the optimum sensitivity derivatives. The method was perceived to be successful from comparisons of the optimization results with parametric studies.

Separation of 20 coumarin derivatives using the capillary electrophoresis method optimized by a series of Doehlert experimental designs.

PubMed

Woźniakiewicz, Michał; Gładysz, Marta; Nowak, Paweł M; Kędzior, Justyna; Kościelniak, Paweł

2017-05-15

The aim of this study was to develop the first CE-based method enabling separation of 20 structurally similar coumarin derivatives. To facilitate method optimization a series of three consequent Doehlert experimental designs with the response surface methodology was employed, using number of peaks and the adjusted time of analysis as the selected responses. Initially, three variables were examined: buffer pH, ionic strength and temperature (No. 1 Doehlert design). The optimal conditions provided only partial separation, on that account, several buffer additives were examined at the next step: organic cosolvents and cyclodextrin (No. 2 Doehlert design). The optimal cyclodextrin type was also selected experimentally. The most promising results were obtained for the buffers fortified with methanol, acetonitrile and heptakis(2,3,6-tri-O-methyl)-β-cyclodextrin. Since these additives may potentially affect acid-base equilibrium and ionization state of analytes, the third Doehlert design (No. 3) was used to reconcile concentration of these additives with optimal pH. Ultimately, the total separation of all 20 compounds was achieved using the borate buffer at basic pH 9.5 in the presence of 10mM cyclodextrin, 9% (v/v) acetonitrile and 36% (v/v) methanol. Identity of all compounds was confirmed using the in-lab build UV-VIS spectra library. The developed method succeeded in identification of coumarin derivatives in three real samples. It demonstrates a huge resolving power of CE assisted by addition of cyclodextrins and organic cosolvents. Our unique optimization approach, based on the three Doehlert designs, seems to be prospective for future applications of this technique. Copyright © 2017 Elsevier B.V. All rights reserved.

On the validity of the arithmetic-geometric mean method to locate the optimal solution in a supply chain system

NASA Astrophysics Data System (ADS)

Chung, Kun-Jen

2012-08-01

Cardenas-Barron [Cardenas-Barron, L.E. (2010) 'A Simple Method to Compute Economic order Quantities: Some Observations', Applied Mathematical Modelling, 34, 1684-1688] indicates that there are several functions in which the arithmetic-geometric mean method (AGM) does not give the minimum. This article presents another situation to reveal that the AGM inequality to locate the optimal solution may be invalid for Teng, Chen, and Goyal [Teng, J.T., Chen, J., and Goyal S.K. (2009), 'A Comprehensive Note on: An Inventory Model under Two Levels of Trade Credit and Limited Storage Space Derived without Derivatives', Applied Mathematical Modelling, 33, 4388-4396], Teng and Goyal [Teng, J.T., and Goyal S.K. (2009), 'Comment on 'Optimal Inventory Replenishment Policy for the EPQ Model under Trade Credit Derived without Derivatives', International Journal of Systems Science, 40, 1095-1098] and Hsieh, Chang, Weng, and Dye [Hsieh, T.P., Chang, H.J., Weng, M.W., and Dye, C.Y. (2008), 'A Simple Approach to an Integrated Single-vendor Single-buyer Inventory System with Shortage', Production Planning and Control, 19, 601-604]. So, the main purpose of this article is to adopt the calculus approach not only to overcome shortcomings of the arithmetic-geometric mean method of Teng et al. (2009), Teng and Goyal (2009) and Hsieh et al. (2008), but also to develop the complete solution procedures for them.

Neural Network and Regression Approximations in High Speed Civil Transport Aircraft Design Optimization

NASA Technical Reports Server (NTRS)

Patniak, Surya N.; Guptill, James D.; Hopkins, Dale A.; Lavelle, Thomas M.

1998-01-01

Nonlinear mathematical-programming-based design optimization can be an elegant method. However, the calculations required to generate the merit function, constraints, and their gradients, which are frequently required, can make the process computational intensive. The computational burden can be greatly reduced by using approximating analyzers derived from an original analyzer utilizing neural networks and linear regression methods. The experience gained from using both of these approximation methods in the design optimization of a high speed civil transport aircraft is the subject of this paper. The Langley Research Center's Flight Optimization System was selected for the aircraft analysis. This software was exercised to generate a set of training data with which a neural network and a regression method were trained, thereby producing the two approximating analyzers. The derived analyzers were coupled to the Lewis Research Center's CometBoards test bed to provide the optimization capability. With the combined software, both approximation methods were examined for use in aircraft design optimization, and both performed satisfactorily. The CPU time for solution of the problem, which had been measured in hours, was reduced to minutes with the neural network approximation and to seconds with the regression method. Instability encountered in the aircraft analysis software at certain design points was also eliminated. On the other hand, there were costs and difficulties associated with training the approximating analyzers. The CPU time required to generate the input-output pairs and to train the approximating analyzers was seven times that required for solution of the problem.

Photovoltaic design optimization for terrestrial applications

NASA Technical Reports Server (NTRS)

Ross, R. G., Jr.

1978-01-01

As part of the Jet Propulsion Laboratory's Low-Cost Solar Array Project, a comprehensive program of module cost-optimization has been carried out. The objective of these studies has been to define means of reducing the cost and improving the utility and reliability of photovoltaic modules for the broad spectrum of terrestrial applications. This paper describes one of the methods being used for module optimization, including the derivation of specific equations which allow the optimization of various module design features. The method is based on minimizing the life-cycle cost of energy for the complete system. Comparison of the life-cycle energy cost with the marginal cost of energy each year allows the logical plant lifetime to be determined. The equations derived allow the explicit inclusion of design parameters such as tracking, site variability, and module degradation with time. An example problem involving the selection of an optimum module glass substrate is presented.

Two neural network algorithms for designing optimal terminal controllers with open final time

NASA Technical Reports Server (NTRS)

Plumer, Edward S.

1992-01-01

Multilayer neural networks, trained by the backpropagation through time algorithm (BPTT), have been used successfully as state-feedback controllers for nonlinear terminal control problems. Current BPTT techniques, however, are not able to deal systematically with open final-time situations such as minimum-time problems. Two approaches which extend BPTT to open final-time problems are presented. In the first, a neural network learns a mapping from initial-state to time-to-go. In the second, the optimal number of steps for each trial run is found using a line-search. Both methods are derived using Lagrange multiplier techniques. This theoretical framework is used to demonstrate that the derived algorithms are direct extensions of forward/backward sweep methods used in N-stage optimal control. The two algorithms are tested on a Zermelo problem and the resulting trajectories compare favorably to optimal control results.

Employing Sensitivity Derivatives for Robust Optimization under Uncertainty in CFD

NASA Technical Reports Server (NTRS)

Newman, Perry A.; Putko, Michele M.; Taylor, Arthur C., III

2004-01-01

A robust optimization is demonstrated on a two-dimensional inviscid airfoil problem in subsonic flow. Given uncertainties in statistically independent, random, normally distributed flow parameters (input variables), an approximate first-order statistical moment method is employed to represent the Computational Fluid Dynamics (CFD) code outputs as expected values with variances. These output quantities are used to form the objective function and constraints. The constraints are cast in probabilistic terms; that is, the probability that a constraint is satisfied is greater than or equal to some desired target probability. Gradient-based robust optimization of this stochastic problem is accomplished through use of both first and second-order sensitivity derivatives. For each robust optimization, the effect of increasing both input standard deviations and target probability of constraint satisfaction are demonstrated. This method provides a means for incorporating uncertainty when considering small deviations from input mean values.

Shape optimization using a NURBS-based interface-enriched generalized FEM

DOE PAGES

Najafi, Ahmad R.; Safdari, Masoud; Tortorelli, Daniel A.; ...

2016-11-26

This study presents a gradient-based shape optimization over a fixed mesh using a non-uniform rational B-splines-based interface-enriched generalized finite element method, applicable to multi-material structures. In the proposed method, non-uniform rational B-splines are used to parameterize the design geometry precisely and compactly by a small number of design variables. An analytical shape sensitivity analysis is developed to compute derivatives of the objective and constraint functions with respect to the design variables. Subtle but important new terms involve the sensitivity of shape functions and their spatial derivatives. As a result, verification and illustrative problems are solved to demonstrate the precision andmore » capability of the method.« less

Macroscopic relationship in primal-dual portfolio optimization problem

NASA Astrophysics Data System (ADS)

Shinzato, Takashi

2018-02-01

In the present paper, using a replica analysis, we examine the portfolio optimization problem handled in previous work and discuss the minimization of investment risk under constraints of budget and expected return for the case that the distribution of the hyperparameters of the mean and variance of the return rate of each asset are not limited to a specific probability family. Findings derived using our proposed method are compared with those in previous work to verify the effectiveness of our proposed method. Further, we derive a Pythagorean theorem of the Sharpe ratio and macroscopic relations of opportunity loss. Using numerical experiments, the effectiveness of our proposed method is demonstrated for a specific situation.

Using a derivative-free optimization method for multiple solutions of inverse transport problems

DOE PAGES

Armstrong, Jerawan C.; Favorite, Jeffrey A.

2016-01-14

Identifying unknown components of an object that emits radiation is an important problem for national and global security. Radiation signatures measured from an object of interest can be used to infer object parameter values that are not known. This problem is called an inverse transport problem. An inverse transport problem may have multiple solutions and the most widely used approach for its solution is an iterative optimization method. This paper proposes a stochastic derivative-free global optimization algorithm to find multiple solutions of inverse transport problems. The algorithm is an extension of a multilevel single linkage (MLSL) method where a meshmore » adaptive direct search (MADS) algorithm is incorporated into the local phase. Furthermore, numerical test cases using uncollided fluxes of discrete gamma-ray lines are presented to show the performance of this new algorithm.« less

Estimation of Gravity Parameters Related to Simple Geometrical Structures by Developing an Approach Based on Deconvolution and Linear Optimization Techniques

NASA Astrophysics Data System (ADS)

Asfahani, J.; Tlas, M.

2015-10-01

An easy and practical method for interpreting residual gravity anomalies due to simple geometrically shaped models such as cylinders and spheres has been proposed in this paper. This proposed method is based on both the deconvolution technique and the simplex algorithm for linear optimization to most effectively estimate the model parameters, e.g., the depth from the surface to the center of a buried structure (sphere or horizontal cylinder) or the depth from the surface to the top of a buried object (vertical cylinder), and the amplitude coefficient from the residual gravity anomaly profile. The method was tested on synthetic data sets corrupted by different white Gaussian random noise levels to demonstrate the capability and reliability of the method. The results acquired show that the estimated parameter values derived by this proposed method are close to the assumed true parameter values. The validity of this method is also demonstrated using real field residual gravity anomalies from Cuba and Sweden. Comparable and acceptable agreement is shown between the results derived by this method and those derived from real field data.

Optimization of GPS water vapor tomography technique with radiosonde and COSMIC historical data

NASA Astrophysics Data System (ADS)

Ye, Shirong; Xia, Pengfei; Cai, Changsheng

2016-09-01

The near-real-time high spatial resolution of atmospheric water vapor distribution is vital in numerical weather prediction. GPS tomography technique has been proved effectively for three-dimensional water vapor reconstruction. In this study, the tomography processing is optimized in a few aspects by the aid of radiosonde and COSMIC historical data. Firstly, regional tropospheric zenith hydrostatic delay (ZHD) models are improved and thus the zenith wet delay (ZWD) can be obtained at a higher accuracy. Secondly, the regional conversion factor of converting the ZWD to the precipitable water vapor (PWV) is refined. Next, we develop a new method for dividing the tomography grid with an uneven voxel height and a varied water vapor layer top. Finally, we propose a Gaussian exponential vertical interpolation method which can better reflect the vertical variation characteristic of water vapor. GPS datasets collected in Hong Kong in February 2014 are employed to evaluate the optimized tomographic method by contrast with the conventional method. The radiosonde-derived and COSMIC-derived water vapor densities are utilized as references to evaluate the tomographic results. Using radiosonde products as references, the test results obtained from our optimized method indicate that the water vapor density accuracy is improved by 15 and 12 % compared to those derived from the conventional method below the height of 3.75 km and above the height of 3.75 km, respectively. Using the COSMIC products as references, the results indicate that the water vapor density accuracy is improved by 15 and 19 % below 3.75 km and above 3.75 km, respectively.

Derivative-free generation and interpolation of convex Pareto optimal IMRT plans

NASA Astrophysics Data System (ADS)

Hoffmann, Aswin L.; Siem, Alex Y. D.; den Hertog, Dick; Kaanders, Johannes H. A. M.; Huizenga, Henk

2006-12-01

In inverse treatment planning for intensity-modulated radiation therapy (IMRT), beamlet intensity levels in fluence maps of high-energy photon beams are optimized. Treatment plan evaluation criteria are used as objective functions to steer the optimization process. Fluence map optimization can be considered a multi-objective optimization problem, for which a set of Pareto optimal solutions exists: the Pareto efficient frontier (PEF). In this paper, a constrained optimization method is pursued to iteratively estimate the PEF up to some predefined error. We use the property that the PEF is convex for a convex optimization problem to construct piecewise-linear upper and lower bounds to approximate the PEF from a small initial set of Pareto optimal plans. A derivative-free Sandwich algorithm is presented in which these bounds are used with three strategies to determine the location of the next Pareto optimal solution such that the uncertainty in the estimated PEF is maximally reduced. We show that an intelligent initial solution for a new Pareto optimal plan can be obtained by interpolation of fluence maps from neighbouring Pareto optimal plans. The method has been applied to a simplified clinical test case using two convex objective functions to map the trade-off between tumour dose heterogeneity and critical organ sparing. All three strategies produce representative estimates of the PEF. The new algorithm is particularly suitable for dynamic generation of Pareto optimal plans in interactive treatment planning.

Performance of a cavity-method-based algorithm for the prize-collecting Steiner tree problem on graphs

NASA Astrophysics Data System (ADS)

Biazzo, Indaco; Braunstein, Alfredo; Zecchina, Riccardo

2012-08-01

We study the behavior of an algorithm derived from the cavity method for the prize-collecting steiner tree (PCST) problem on graphs. The algorithm is based on the zero temperature limit of the cavity equations and as such is formally simple (a fixed point equation resolved by iteration) and distributed (parallelizable). We provide a detailed comparison with state-of-the-art algorithms on a wide range of existing benchmarks, networks, and random graphs. Specifically, we consider an enhanced derivative of the Goemans-Williamson heuristics and the dhea solver, a branch and cut integer linear programming based approach. The comparison shows that the cavity algorithm outperforms the two algorithms in most large instances both in running time and quality of the solution. Finally we prove a few optimality properties of the solutions provided by our algorithm, including optimality under the two postprocessing procedures defined in the Goemans-Williamson derivative and global optimality in some limit cases.

Portfolio Optimization with Stochastic Dividends and Stochastic Volatility

ERIC Educational Resources Information Center

Varga, Katherine Yvonne

2015-01-01

We consider an optimal investment-consumption portfolio optimization model in which an investor receives stochastic dividends. As a first problem, we allow the drift of stock price to be a bounded function. Next, we consider a stochastic volatility model. In each problem, we use the dynamic programming method to derive the Hamilton-Jacobi-Bellman…

Overcoming Communication Restrictions in Collectives

NASA Technical Reports Server (NTRS)

Tumer, Kagan; Agogino, Adrian K.

2004-01-01

Many large distributed system are characterized by having a large number of components (eg., agents, neurons) whose actions and interactions determine a %orld utility which rates the performance of the overall system. Such collectives are often subject to communication restrictions, making it difficult for components which try to optimize their own private utilities, to take actions that also help optimize the world utility. In this article we address that coordination problem and derive four utility functions which present different compromises between how aligned a component s private utility is with the world utility and how readily that component can determine the actions that optimize its utility. The results show that the utility functions specifically derived to operate under communication restrictions outperform both traditional methods and previous collective-based methods by up to 75%.

Numerical Optimization Using Computer Experiments

NASA Technical Reports Server (NTRS)

Trosset, Michael W.; Torczon, Virginia

1997-01-01

Engineering design optimization often gives rise to problems in which expensive objective functions are minimized by derivative-free methods. We propose a method for solving such problems that synthesizes ideas from the numerical optimization and computer experiment literatures. Our approach relies on kriging known function values to construct a sequence of surrogate models of the objective function that are used to guide a grid search for a minimizer. Results from numerical experiments on a standard test problem are presented.

Nanomaterials derived from metal-organic frameworks

NASA Astrophysics Data System (ADS)

Dang, Song; Zhu, Qi-Long; Xu, Qiang

2018-01-01

The thermal transformation of metal-organic frameworks (MOFs) generates a variety of nanostructured materials, including carbon-based materials, metal oxides, metal chalcogenides, metal phosphides and metal carbides. These derivatives of MOFs have characteristics such as high surface areas, permanent porosities and controllable functionalities that enable their good performance in sensing, gas storage, catalysis and energy-related applications. Although progress has been made to tune the morphologies of MOF-derived structures at the nanometre scale, it remains crucial to further our knowledge of the relationship between morphology and performance. In this Review, we summarize the synthetic strategies and optimized methods that enable control over the size, morphology, composition and structure of the derived nanomaterials. In addition, we compare the performance of materials prepared by the MOF-templated strategy and other synthetic methods. Our aim is to reveal the relationship between the morphology and the physico-chemical properties of MOF-derived nanostructures to optimize their performance for applications such as sensing, catalysis, and energy storage and conversion.

Communication: Time-dependent optimized coupled-cluster method for multielectron dynamics

NASA Astrophysics Data System (ADS)

Sato, Takeshi; Pathak, Himadri; Orimo, Yuki; Ishikawa, Kenichi L.

2018-02-01

Time-dependent coupled-cluster method with time-varying orbital functions, called time-dependent optimized coupled-cluster (TD-OCC) method, is formulated for multielectron dynamics in an intense laser field. We have successfully derived the equations of motion for CC amplitudes and orthonormal orbital functions based on the real action functional, and implemented the method including double excitations (TD-OCCD) and double and triple excitations (TD-OCCDT) within the optimized active orbitals. The present method is size extensive and gauge invariant, a polynomial cost-scaling alternative to the time-dependent multiconfiguration self-consistent-field method. The first application of the TD-OCC method of intense-laser driven correlated electron dynamics in Ar atom is reported.

Communication: Time-dependent optimized coupled-cluster method for multielectron dynamics.

PubMed

Sato, Takeshi; Pathak, Himadri; Orimo, Yuki; Ishikawa, Kenichi L

2018-02-07

Time-dependent coupled-cluster method with time-varying orbital functions, called time-dependent optimized coupled-cluster (TD-OCC) method, is formulated for multielectron dynamics in an intense laser field. We have successfully derived the equations of motion for CC amplitudes and orthonormal orbital functions based on the real action functional, and implemented the method including double excitations (TD-OCCD) and double and triple excitations (TD-OCCDT) within the optimized active orbitals. The present method is size extensive and gauge invariant, a polynomial cost-scaling alternative to the time-dependent multiconfiguration self-consistent-field method. The first application of the TD-OCC method of intense-laser driven correlated electron dynamics in Ar atom is reported.

Extremal Optimization: Methods Derived from Co-Evolution

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

Boettcher, S.; Percus, A.G.

1999-07-13

We describe a general-purpose method for finding high-quality solutions to hard optimization problems, inspired by self-organized critical models of co-evolution such as the Bak-Sneppen model. The method, called Extremal Optimization, successively eliminates extremely undesirable components of sub-optimal solutions, rather than ''breeding'' better components. In contrast to Genetic Algorithms which operate on an entire ''gene-pool'' of possible solutions, Extremal Optimization improves on a single candidate solution by treating each of its components as species co-evolving according to Darwinian principles. Unlike Simulated Annealing, its non-equilibrium approach effects an algorithm requiring few parameters to tune. With only one adjustable parameter, its performance provesmore » competitive with, and often superior to, more elaborate stochastic optimization procedures. We demonstrate it here on two classic hard optimization problems: graph partitioning and the traveling salesman problem.« less

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.

Automatic differentiation evaluated as a tool for rotorcraft design and optimization

NASA Technical Reports Server (NTRS)

Walsh, Joanne L.; Young, Katherine C.

1995-01-01

This paper investigates the use of automatic differentiation (AD) as a means for generating sensitivity analyses in rotorcraft design and optimization. This technique transforms an existing computer program into a new program that performs sensitivity analysis in addition to the original analysis. The original FORTRAN program calculates a set of dependent (output) variables from a set of independent (input) variables, the new FORTRAN program calculates the partial derivatives of the dependent variables with respect to the independent variables. The AD technique is a systematic implementation of the chain rule of differentiation, this method produces derivatives to machine accuracy at a cost that is comparable with that of finite-differencing methods. For this study, an analysis code that consists of the Langley-developed hover analysis HOVT, the comprehensive rotor analysis CAMRAD/JA, and associated preprocessors is processed through the AD preprocessor ADIFOR 2.0. The resulting derivatives are compared with derivatives obtained from finite-differencing techniques. The derivatives obtained with ADIFOR 2.0 are exact within machine accuracy and do not depend on the selection of step-size, as are the derivatives obtained with finite-differencing techniques.

Optimization Algorithm for Kalman Filter Exploiting the Numerical Characteristics of SINS/GPS Integrated Navigation Systems.

PubMed

Hu, Shaoxing; Xu, Shike; Wang, Duhu; Zhang, Aiwu

2015-11-11

Aiming at addressing the problem of high computational cost of the traditional Kalman filter in SINS/GPS, a practical optimization algorithm with offline-derivation and parallel processing methods based on the numerical characteristics of the system is presented in this paper. The algorithm exploits the sparseness and/or symmetry of matrices to simplify the computational procedure. Thus plenty of invalid operations can be avoided by offline derivation using a block matrix technique. For enhanced efficiency, a new parallel computational mechanism is established by subdividing and restructuring calculation processes after analyzing the extracted "useful" data. As a result, the algorithm saves about 90% of the CPU processing time and 66% of the memory usage needed in a classical Kalman filter. Meanwhile, the method as a numerical approach needs no precise-loss transformation/approximation of system modules and the accuracy suffers little in comparison with the filter before computational optimization. Furthermore, since no complicated matrix theories are needed, the algorithm can be easily transplanted into other modified filters as a secondary optimization method to achieve further efficiency.

Optimizing some 3-stage W-methods for the time integration of PDEs

NASA Astrophysics Data System (ADS)

Gonzalez-Pinto, S.; Hernandez-Abreu, D.; Perez-Rodriguez, S.

2017-07-01

The optimization of some W-methods for the time integration of time-dependent PDEs in several spatial variables is considered. In [2, Theorem 1] several three-parametric families of three-stage W-methods for the integration of IVPs in ODEs were studied. Besides, the optimization of several specific methods for PDEs when the Approximate Matrix Factorization Splitting (AMF) is used to define the approximate Jacobian matrix (W ≈ fy(yn)) was carried out. Also, some convergence and stability properties were presented [2]. The derived methods were optimized on the base that the underlying explicit Runge-Kutta method is the one having the largest Monotonicity interval among the thee-stage order three Runge-Kutta methods [1]. Here, we propose an optimization of the methods by imposing some additional order condition [7] to keep order three for parabolic PDE problems [6] but at the price of reducing substantially the length of the nonlinear Monotonicity interval of the underlying explicit Runge-Kutta method.

A new rational-based optimal design strategy of ship structure based on multi-level analysis and super-element modeling method

NASA Astrophysics Data System (ADS)

Sun, Li; Wang, Deyu

2011-09-01

A new multi-level analysis method of introducing the super-element modeling method, derived from the multi-level analysis method first proposed by O. F. Hughes, has been proposed in this paper to solve the problem of high time cost in adopting a rational-based optimal design method for ship structural design. Furthermore, the method was verified by its effective application in optimization of the mid-ship section of a container ship. A full 3-D FEM model of a ship, suffering static and quasi-static loads, was used as the analyzing object for evaluating the structural performance of the mid-ship module, including static strength and buckling performance. Research results reveal that this new method could substantially reduce the computational cost of the rational-based optimization problem without decreasing its accuracy, which increases the feasibility and economic efficiency of using a rational-based optimal design method in ship structural design.

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.

Procedures for shape optimization of gas turbine disks

NASA Technical Reports Server (NTRS)

Cheu, Tsu-Chien

1989-01-01

Two procedures, the feasible direction method and sequential linear programming, for shape optimization of gas turbine disks are presented. The objective of these procedures is to obtain optimal designs of turbine disks with geometric and stress constraints. The coordinates of the selected points on the disk contours are used as the design variables. Structural weight, stress and their derivatives with respect to the design variables are calculated by an efficient finite element method for design senitivity analysis. Numerical examples of the optimal designs of a disk subjected to thermo-mechanical loadings are presented to illustrate and compare the effectiveness of these two procedures.

A weak Hamiltonian finite element method for optimal guidance of an advanced launch vehicle

NASA Technical Reports Server (NTRS)

Hodges, Dewey H.; Calise, Anthony J.; Bless, Robert R.; Leung, Martin

1989-01-01

A temporal finite-element method based on a mixed form of the Hamiltonian weak principle is presented for optimal control problems. The mixed form of this principle contains both states and costates as primary variables, which are expanded in terms of nodal values and simple shape functions. Time derivatives of the states and costates do not appear in the governing variational equation; the only quantities whose time derivatives appear therein are virtual states and virtual costates. Numerical results are presented for an elementary trajectory optimization problem; they show very good agreement with the exact solution along with excellent computational efficiency and self-starting capability. The feasibility of this approach for real-time guidance applications is evaluated. A simplified model for an advanced launch vehicle application that is suitable for finite-element solution is presented.

Inversion of Robin coefficient by a spectral stochastic finite element approach

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

Jin Bangti; Zou Jun

2008-03-01

This paper investigates a variational approach to the nonlinear stochastic inverse problem of probabilistically calibrating the Robin coefficient from boundary measurements for the steady-state heat conduction. The problem is formulated into an optimization problem, and mathematical properties relevant to its numerical computations are investigated. The spectral stochastic finite element method using polynomial chaos is utilized for the discretization of the optimization problem, and its convergence is analyzed. The nonlinear conjugate gradient method is derived for the optimization system. Numerical results for several two-dimensional problems are presented to illustrate the accuracy and efficiency of the stochastic finite element method.

An Optimal Estimation Method to Obtain Surface Layer Turbulent Fluxes from Profile Measurements

NASA Astrophysics Data System (ADS)

Kang, D.

2015-12-01

In the absence of direct turbulence measurements, the turbulence characteristics of the atmospheric surface layer are often derived from measurements of the surface layer mean properties based on Monin-Obukhov Similarity Theory (MOST). This approach requires two levels of the ensemble mean wind, temperature, and water vapor, from which the fluxes of momentum, sensible heat, and water vapor can be obtained. When only one measurement level is available, the roughness heights and the assumed properties of the corresponding variables at the respective roughness heights are used. In practice, the temporal mean with large number of samples are used in place of the ensemble mean. However, in many situations the samples of data are taken from multiple levels. It is thus desirable to derive the boundary layer flux properties using all measurements. In this study, we used an optimal estimation approach to derive surface layer properties based on all available measurements. This approach assumes that the samples are taken from a population whose ensemble mean profile follows the MOST. An optimized estimate is obtained when the results yield a minimum cost function defined as a weighted summation of all error variance at each sample altitude. The weights are based one sample data variance and the altitude of the measurements. This method was applied to measurements in the marine atmospheric surface layer from a small boat using radiosonde on a tethered balloon where temperature and relative humidity profiles in the lowest 50 m were made repeatedly in about 30 minutes. We will present the resultant fluxes and the derived MOST mean profiles using different sets of measurements. The advantage of this method over the 'traditional' methods will be illustrated. Some limitations of this optimization method will also be discussed. Its application to quantify the effects of marine surface layer environment on radar and communication signal propagation will be shown as well.

Optimal thresholds for the estimation of area rain-rate moments by the threshold method

NASA Technical Reports Server (NTRS)

Short, David A.; Shimizu, Kunio; Kedem, Benjamin

1993-01-01

Optimization of the threshold method, achieved by determination of the threshold that maximizes the correlation between an area-average rain-rate moment and the area coverage of rain rates exceeding the threshold, is demonstrated empirically and theoretically. Empirical results for a sequence of GATE radar snapshots show optimal thresholds of 5 and 27 mm/h for the first and second moments, respectively. Theoretical optimization of the threshold method by the maximum-likelihood approach of Kedem and Pavlopoulos (1991) predicts optimal thresholds near 5 and 26 mm/h for lognormally distributed rain rates with GATE-like parameters. The agreement between theory and observations suggests that the optimal threshold can be understood as arising due to sampling variations, from snapshot to snapshot, of a parent rain-rate distribution. Optimal thresholds for gamma and inverse Gaussian distributions are also derived and compared.

Efficient Convex Optimization for Energy-Based Acoustic Sensor Self-Localization and Source Localization in Sensor Networks.

PubMed

Yan, Yongsheng; Wang, Haiyan; Shen, Xiaohong; Leng, Bing; Li, Shuangquan

2018-05-21

The energy reading has been an efficient and attractive measure for collaborative acoustic source localization in practical application due to its cost saving in both energy and computation capability. The maximum likelihood problems by fusing received acoustic energy readings transmitted from local sensors are derived. Aiming to efficiently solve the nonconvex objective of the optimization problem, we present an approximate estimator of the original problem. Then, a direct norm relaxation and semidefinite relaxation, respectively, are utilized to derive the second-order cone programming, semidefinite programming or mixture of them for both cases of sensor self-location and source localization. Furthermore, by taking the colored energy reading noise into account, several minimax optimization problems are formulated, which are also relaxed via the direct norm relaxation and semidefinite relaxation respectively into convex optimization problems. Performance comparison with the existing acoustic energy-based source localization methods is given, where the results show the validity of our proposed methods.

Efficient Convex Optimization for Energy-Based Acoustic Sensor Self-Localization and Source Localization in Sensor Networks

PubMed Central

Yan, Yongsheng; Wang, Haiyan; Shen, Xiaohong; Leng, Bing; Li, Shuangquan

2018-01-01

The energy reading has been an efficient and attractive measure for collaborative acoustic source localization in practical application due to its cost saving in both energy and computation capability. The maximum likelihood problems by fusing received acoustic energy readings transmitted from local sensors are derived. Aiming to efficiently solve the nonconvex objective of the optimization problem, we present an approximate estimator of the original problem. Then, a direct norm relaxation and semidefinite relaxation, respectively, are utilized to derive the second-order cone programming, semidefinite programming or mixture of them for both cases of sensor self-location and source localization. Furthermore, by taking the colored energy reading noise into account, several minimax optimization problems are formulated, which are also relaxed via the direct norm relaxation and semidefinite relaxation respectively into convex optimization problems. Performance comparison with the existing acoustic energy-based source localization methods is given, where the results show the validity of our proposed methods. PMID:29883410

Taboo Search: An Approach to the Multiple Minima Problem

NASA Astrophysics Data System (ADS)

Cvijovic, Djurdje; Klinowski, Jacek

1995-02-01

Described here is a method, based on Glover's taboo search for discrete functions, of solving the multiple minima problem for continuous functions. As demonstrated by model calculations, the algorithm avoids entrapment in local minima and continues the search to give a near-optimal final solution. Unlike other methods of global optimization, this procedure is generally applicable, easy to implement, derivative-free, and conceptually simple.

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.

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.

Aerodynamic Design Optimization on Unstructured Meshes Using the Navier-Stokes Equations

NASA Technical Reports Server (NTRS)

Nielsen, Eric J.; Anderson, W. Kyle

1998-01-01

A discrete adjoint method is developed and demonstrated for aerodynamic design optimization on unstructured grids. The governing equations are the three-dimensional Reynolds-averaged Navier-Stokes equations coupled with a one-equation turbulence model. A discussion of the numerical implementation of the flow and adjoint equations is presented. Both compressible and incompressible solvers are differentiated and the accuracy of the sensitivity derivatives is verified by comparing with gradients obtained using finite differences. Several simplifying approximations to the complete linearization of the residual are also presented, and the resulting accuracy of the derivatives is examined. Demonstration optimizations for both compressible and incompressible flows are given.

Quad-rotor flight path energy optimization

NASA Astrophysics Data System (ADS)

Kemper, Edward

Quad-Rotor unmanned areal vehicles (UAVs) have been a popular area of research and development in the last decade, especially with the advent of affordable microcontrollers like the MSP 430 and the Raspberry Pi. Path-Energy Optimization is an area that is well developed for linear systems. In this thesis, this idea of path-energy optimization is extended to the nonlinear model of the Quad-rotor UAV. The classical optimization technique is adapted to the nonlinear model that is derived for the problem at hand, coming up with a set of partial differential equations and boundary value conditions to solve these equations. Then, different techniques to implement energy optimization algorithms are tested using simulations in Python. First, a purely nonlinear approach is used. This method is shown to be computationally intensive, with no practical solution available in a reasonable amount of time. Second, heuristic techniques to minimize the energy of the flight path are tested, using Ziegler-Nichols' proportional integral derivative (PID) controller tuning technique. Finally, a brute force look-up table based PID controller is used. Simulation results of the heuristic method show that both reliable control of the system and path-energy optimization are achieved in a reasonable amount of time.

A modular approach to large-scale design optimization of aerospace systems

NASA Astrophysics Data System (ADS)

Hwang, John T.

Gradient-based optimization and the adjoint method form a synergistic combination that enables the efficient solution of large-scale optimization problems. Though the gradient-based approach struggles with non-smooth or multi-modal problems, the capability to efficiently optimize up to tens of thousands of design variables provides a valuable design tool for exploring complex tradeoffs and finding unintuitive designs. However, the widespread adoption of gradient-based optimization is limited by the implementation challenges for computing derivatives efficiently and accurately, particularly in multidisciplinary and shape design problems. This thesis addresses these difficulties in two ways. First, to deal with the heterogeneity and integration challenges of multidisciplinary problems, this thesis presents a computational modeling framework that solves multidisciplinary systems and computes their derivatives in a semi-automated fashion. This framework is built upon a new mathematical formulation developed in this thesis that expresses any computational model as a system of algebraic equations and unifies all methods for computing derivatives using a single equation. The framework is applied to two engineering problems: the optimization of a nanosatellite with 7 disciplines and over 25,000 design variables; and simultaneous allocation and mission optimization for commercial aircraft involving 330 design variables, 12 of which are integer variables handled using the branch-and-bound method. In both cases, the framework makes large-scale optimization possible by reducing the implementation effort and code complexity. The second half of this thesis presents a differentiable parametrization of aircraft geometries and structures for high-fidelity shape optimization. Existing geometry parametrizations are not differentiable, or they are limited in the types of shape changes they allow. This is addressed by a novel parametrization that smoothly interpolates aircraft components, providing differentiability. An unstructured quadrilateral mesh generation algorithm is also developed to automate the creation of detailed meshes for aircraft structures, and a mesh convergence study is performed to verify that the quality of the mesh is maintained as it is refined. As a demonstration, high-fidelity aerostructural analysis is performed for two unconventional configurations with detailed structures included, and aerodynamic shape optimization is applied to the truss-braced wing, which finds and eliminates a shock in the region bounded by the struts and the wing.

Relaxation-optimized transfer of spin order in Ising spin chains

NASA Astrophysics Data System (ADS)

Stefanatos, Dionisis; Glaser, Steffen J.; Khaneja, Navin

2005-12-01

In this paper, we present relaxation optimized methods for the transfer of bilinear spin correlations along Ising spin chains. These relaxation optimized methods can be used as a building block for the transfer of polarization between distant spins on a spin chain, a problem that is ubiquitous in multidimensional nuclear magnetic resonance spectroscopy of proteins. Compared to standard techniques, significant reduction in relaxation losses is achieved by these optimized methods when transverse relaxation rates are much larger than the longitudinal relaxation rates and comparable to couplings between spins. We derive an upper bound on the efficiency of the transfer of the spin order along a chain of spins in the presence of relaxation and show that this bound can be approached by the relaxation optimized pulse sequences presented in the paper.

Application of Multi-Objective Human Learning Optimization Method to Solve AC/DC Multi-Objective Optimal Power Flow Problem

NASA Astrophysics Data System (ADS)

Cao, Jia; Yan, Zheng; He, Guangyu

2016-06-01

This paper introduces an efficient algorithm, multi-objective human learning optimization method (MOHLO), to solve AC/DC multi-objective optimal power flow problem (MOPF). Firstly, the model of AC/DC MOPF including wind farms is constructed, where includes three objective functions, operating cost, power loss, and pollutant emission. Combining the non-dominated sorting technique and the crowding distance index, the MOHLO method can be derived, which involves individual learning operator, social learning operator, random exploration learning operator and adaptive strategies. Both the proposed MOHLO method and non-dominated sorting genetic algorithm II (NSGAII) are tested on an improved IEEE 30-bus AC/DC hybrid system. Simulation results show that MOHLO method has excellent search efficiency and the powerful ability of searching optimal. Above all, MOHLO method can obtain more complete pareto front than that by NSGAII method. However, how to choose the optimal solution from pareto front depends mainly on the decision makers who stand from the economic point of view or from the energy saving and emission reduction point of view.

An n -material thresholding method for improving integerness of solutions in topology optimization

DOE PAGES

Watts, Seth; Tortorelli, Daniel A.

2016-04-10

It is common in solving topology optimization problems to replace an integer-valued characteristic function design field with the material volume fraction field, a real-valued approximation of the design field that permits "fictitious" mixtures of materials during intermediate iterations in the optimization process. This is reasonable so long as one can interpolate properties for such materials and so long as the final design is integer valued. For this purpose, we present a method for smoothly thresholding the volume fractions of an arbitrary number of material phases which specify the design. This method is trivial for two-material design problems, for example, themore » canonical topology design problem of specifying the presence or absence of a single material within a domain, but it becomes more complex when three or more materials are used, as often occurs in material design problems. We take advantage of the similarity in properties between the volume fractions and the barycentric coordinates on a simplex to derive a thresholding, method which is applicable to an arbitrary number of materials. As we show in a sensitivity analysis, this method has smooth derivatives, allowing it to be used in gradient-based optimization algorithms. Finally, we present results, which show synergistic effects when used with Solid Isotropic Material with Penalty and Rational Approximation of Material Properties material interpolation functions, popular methods of ensuring integerness of solutions.« less

Research in navigation and optimization for space trajectories

NASA Technical Reports Server (NTRS)

Pines, S.; Kelley, H. J.

1979-01-01

Topics covered include: (1) initial Cartesian coordinates for rapid precision orbit prediction; (2) accelerating convergence in optimization methods using search routines by applying curvilinear projection ideas; (3) perturbation-magnitude control for difference-quotient estimation of derivatives; and (4) determining the accelerometer bias for in-orbit shuttle trajectories.

MRF energy minimization and beyond via dual decomposition.

PubMed

Komodakis, Nikos; Paragios, Nikos; Tziritas, Georgios

2011-03-01

This paper introduces a new rigorous theoretical framework to address discrete MRF-based optimization in computer vision. Such a framework exploits the powerful technique of Dual Decomposition. It is based on a projected subgradient scheme that attempts to solve an MRF optimization problem by first decomposing it into a set of appropriately chosen subproblems, and then combining their solutions in a principled way. In order to determine the limits of this method, we analyze the conditions that these subproblems have to satisfy and demonstrate the extreme generality and flexibility of such an approach. We thus show that by appropriately choosing what subproblems to use, one can design novel and very powerful MRF optimization algorithms. For instance, in this manner we are able to derive algorithms that: 1) generalize and extend state-of-the-art message-passing methods, 2) optimize very tight LP-relaxations to MRF optimization, and 3) take full advantage of the special structure that may exist in particular MRFs, allowing the use of efficient inference techniques such as, e.g., graph-cut-based methods. Theoretical analysis on the bounds related with the different algorithms derived from our framework and experimental results/comparisons using synthetic and real data for a variety of tasks in computer vision demonstrate the extreme potentials of our approach.

a Novel Discrete Optimal Transport Method for Bayesian Inverse Problems

NASA Astrophysics Data System (ADS)

Bui-Thanh, T.; Myers, A.; Wang, K.; Thiery, A.

2017-12-01

We present the Augmented Ensemble Transform (AET) method for generating approximate samples from a high-dimensional posterior distribution as a solution to Bayesian inverse problems. Solving large-scale inverse problems is critical for some of the most relevant and impactful scientific endeavors of our time. Therefore, constructing novel methods for solving the Bayesian inverse problem in more computationally efficient ways can have a profound impact on the science community. This research derives the novel AET method for exploring a posterior by solving a sequence of linear programming problems, resulting in a series of transport maps which map prior samples to posterior samples, allowing for the computation of moments of the posterior. We show both theoretical and numerical results, indicating this method can offer superior computational efficiency when compared to other SMC methods. Most of this efficiency is derived from matrix scaling methods to solve the linear programming problem and derivative-free optimization for particle movement. We use this method to determine inter-well connectivity in a reservoir and the associated uncertainty related to certain parameters. The attached file shows the difference between the true parameter and the AET parameter in an example 3D reservoir problem. The error is within the Morozov discrepancy allowance with lower computational cost than other particle methods.

Configuration optimization of space structures

NASA Technical Reports Server (NTRS)

Felippa, Carlos; Crivelli, Luis A.; Vandenbelt, David

1991-01-01

The objective is to develop a computer aid for the conceptual/initial design of aerospace structures, allowing configurations and shape to be apriori design variables. The topics are presented in viewgraph form and include the following: Kikuchi's homogenization method; a classical shape design problem; homogenization method steps; a 3D mechanical component design example; forming a homogenized finite element; a 2D optimization problem; treatment of volume inequality constraint; algorithms for the volume inequality constraint; object function derivatives--taking advantage of design locality; stiffness variations; variations of potential; and schematics of the optimization problem.

An optimization method for the problems of thermal cloaking of material bodies

NASA Astrophysics Data System (ADS)

Alekseev, G. V.; Levin, V. A.

2016-11-01

Inverse heat-transfer problems related to constructing special thermal devices such as cloaking shells, thermal-illusion or thermal-camouflage devices, and heat-flux concentrators are studied. The heatdiffusion equation with a variable heat-conductivity coefficient is used as the initial heat-transfer model. An optimization method is used to reduce the above inverse problems to the respective control problem. The solvability of the above control problem is proved, an optimality system that describes necessary extremum conditions is derived, and a numerical algorithm for solving the control problem is proposed.

Numerical Analysis of an H 1-Galerkin Mixed Finite Element Method for Time Fractional Telegraph Equation

PubMed Central

Wang, Jinfeng; Zhao, Meng; Zhang, Min; Liu, Yang; Li, Hong

2014-01-01

We discuss and analyze an H 1-Galerkin mixed finite element (H 1-GMFE) method to look for the numerical solution of time fractional telegraph equation. We introduce an auxiliary variable to reduce the original equation into lower-order coupled equations and then formulate an H 1-GMFE scheme with two important variables. We discretize the Caputo time fractional derivatives using the finite difference methods and approximate the spatial direction by applying the H 1-GMFE method. Based on the discussion on the theoretical error analysis in L 2-norm for the scalar unknown and its gradient in one dimensional case, we obtain the optimal order of convergence in space-time direction. Further, we also derive the optimal error results for the scalar unknown in H 1-norm. Moreover, we derive and analyze the stability of H 1-GMFE scheme and give the results of a priori error estimates in two- or three-dimensional cases. In order to verify our theoretical analysis, we give some results of numerical calculation by using the Matlab procedure. PMID:25184148

Solid oxide fuel cell simulation and design optimization with numerical adjoint techniques

NASA Astrophysics Data System (ADS)

Elliott, Louie C.

This dissertation reports on the application of numerical optimization techniques as applied to fuel cell simulation and design. Due to the "multi-physics" inherent in a fuel cell, which results in a highly coupled and non-linear behavior, an experimental program to analyze and improve the performance of fuel cells is extremely difficult. This program applies new optimization techniques with computational methods from the field of aerospace engineering to the fuel cell design problem. After an overview of fuel cell history, importance, and classification, a mathematical model of solid oxide fuel cells (SOFC) is presented. The governing equations are discretized and solved with computational fluid dynamics (CFD) techniques including unstructured meshes, non-linear solution methods, numerical derivatives with complex variables, and sensitivity analysis with adjoint methods. Following the validation of the fuel cell model in 2-D and 3-D, the results of the sensitivity analysis are presented. The sensitivity derivative for a cost function with respect to a design variable is found with three increasingly sophisticated techniques: finite difference, direct differentiation, and adjoint. A design cycle is performed using a simple optimization method to improve the value of the implemented cost function. The results from this program could improve fuel cell performance and lessen the world's dependence on fossil fuels.

Topology optimization of finite strain viscoplastic systems under transient loads [Dynamic topology optimization based on finite strain visco-plasticity

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

Ivarsson, Niklas; Wallin, Mathias; Tortorelli, Daniel

In this paper, a transient finite strain viscoplastic model is implemented in a gradient-based topology optimization framework to design impact mitigating structures. The model's kinematics relies on the multiplicative split of the deformation gradient, and the constitutive response is based on isotropic hardening viscoplasticity. To solve the mechanical balance laws, the implicit Newmark-beta method is used together with a total Lagrangian finite element formulation. The optimization problem is regularized using a partial differential equation filter and solved using the method of moving asymptotes. Sensitivities required to solve the optimization problem are derived using the adjoint method. To demonstrate the capabilitymore » of the algorithm, several protective systems are designed, in which the absorbed viscoplastic energy is maximized. Finally, the numerical examples demonstrate that transient finite strain viscoplastic effects can successfully be combined with topology optimization.« less

Topology optimization of finite strain viscoplastic systems under transient loads [Dynamic topology optimization based on finite strain visco-plasticity

DOE PAGES

Ivarsson, Niklas; Wallin, Mathias; Tortorelli, Daniel

2018-02-08

In this paper, a transient finite strain viscoplastic model is implemented in a gradient-based topology optimization framework to design impact mitigating structures. The model's kinematics relies on the multiplicative split of the deformation gradient, and the constitutive response is based on isotropic hardening viscoplasticity. To solve the mechanical balance laws, the implicit Newmark-beta method is used together with a total Lagrangian finite element formulation. The optimization problem is regularized using a partial differential equation filter and solved using the method of moving asymptotes. Sensitivities required to solve the optimization problem are derived using the adjoint method. To demonstrate the capabilitymore » of the algorithm, several protective systems are designed, in which the absorbed viscoplastic energy is maximized. Finally, the numerical examples demonstrate that transient finite strain viscoplastic effects can successfully be combined with topology optimization.« less

Newton's method

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

More, J. J.; Sorensen, D. C.

1982-02-01

Newton's method plays a central role in the development of numerical techniques for optimization. In fact, most of the current practical methods for optimization can be viewed as variations on Newton's method. It is therefore important to understand Newton's method as an algorithm in its own right and as a key introduction to the most recent ideas in this area. One of the aims of this expository paper is to present and analyze two main approaches to Newton's method for unconstrained minimization: the line search approach and the trust region approach. The other aim is to present some of themore » recent developments in the optimization field which are related to Newton's method. In particular, we explore several variations on Newton's method which are appropriate for large scale problems, and we also show how quasi-Newton methods can be derived quite naturally from Newton's method.« less

A survey of methods of feasible directions for the solution of optimal control problems

NASA Technical Reports Server (NTRS)

Polak, E.

1972-01-01

Three methods of feasible directions for optimal control are reviewed. These methods are an extension of the Frank-Wolfe method, a dual method devised by Pironneau and Polack, and a Zontendijk method. The categories of continuous optimal control problems are shown as: (1) fixed time problems with fixed initial state, free terminal state, and simple constraints on the control; (2) fixed time problems with inequality constraints on both the initial and the terminal state and no control constraints; (3) free time problems with inequality constraints on the initial and terminal states and simple constraints on the control; and (4) fixed time problems with inequality state space contraints and constraints on the control. The nonlinear programming algorithms are derived for each of the methods in its associated category.

Structural design using equilibrium programming formulations

NASA Technical Reports Server (NTRS)

Scotti, Stephen J.

1995-01-01

Solutions to increasingly larger structural optimization problems are desired. However, computational resources are strained to meet this need. New methods will be required to solve increasingly larger problems. The present approaches to solving large-scale problems involve approximations for the constraints of structural optimization problems and/or decomposition of the problem into multiple subproblems that can be solved in parallel. An area of game theory, equilibrium programming (also known as noncooperative game theory), can be used to unify these existing approaches from a theoretical point of view (considering the existence and optimality of solutions), and be used as a framework for the development of new methods for solving large-scale optimization problems. Equilibrium programming theory is described, and existing design techniques such as fully stressed design and constraint approximations are shown to fit within its framework. Two new structural design formulations are also derived. The first new formulation is another approximation technique which is a general updating scheme for the sensitivity derivatives of design constraints. The second new formulation uses a substructure-based decomposition of the structure for analysis and sensitivity calculations. Significant computational benefits of the new formulations compared with a conventional method are demonstrated.

An error analysis of least-squares finite element method of velocity-pressure-vorticity formulation for Stokes problem

NASA Technical Reports Server (NTRS)

Chang, Ching L.; Jiang, Bo-Nan

1990-01-01

A theoretical proof of the optimal rate of convergence for the least-squares method is developed for the Stokes problem based on the velocity-pressure-vorticity formula. The 2D Stokes problem is analyzed to define the product space and its inner product, and the a priori estimates are derived to give the finite-element approximation. The least-squares method is found to converge at the optimal rate for equal-order interpolation.

Legendre spectral-collocation method for solving some types of fractional optimal control problems

PubMed Central

Sweilam, Nasser H.; Al-Ajami, Tamer M.

2014-01-01

In this paper, the Legendre spectral-collocation method was applied to obtain approximate solutions for some types of fractional optimal control problems (FOCPs). The fractional derivative was described in the Caputo sense. Two different approaches were presented, in the first approach, necessary optimality conditions in terms of the associated Hamiltonian were approximated. In the second approach, the state equation was discretized first using the trapezoidal rule for the numerical integration followed by the Rayleigh–Ritz method to evaluate both the state and control variables. Illustrative examples were included to demonstrate the validity and applicability of the proposed techniques. PMID:26257937

Topology optimization of finite strain viscoplastic systems under transient loads

DOE PAGES

Ivarsson, Niklas; Wallin, Mathias; Tortorelli, Daniel

2018-02-08

In this paper, a transient finite strain viscoplastic model is implemented in a gradient-based topology optimization framework to design impact mitigating structures. The model's kinematics relies on the multiplicative split of the deformation gradient, and the constitutive response is based on isotropic hardening viscoplasticity. To solve the mechanical balance laws, the implicit Newmark-beta method is used together with a total Lagrangian finite element formulation. The optimization problem is regularized using a partial differential equation filter and solved using the method of moving asymptotes. Sensitivities required to solve the optimization problem are derived using the adjoint method. To demonstrate the capabilitymore » of the algorithm, several protective systems are designed, in which the absorbed viscoplastic energy is maximized. Finally, the numerical examples demonstrate that transient finite strain viscoplastic effects can successfully be combined with topology optimization.« less

A Direct Method for Fuel Optimal Maneuvers of Distributed Spacecraft in Multiple Flight Regimes

NASA Technical Reports Server (NTRS)

Hughes, Steven P.; Cooley, D. S.; Guzman, Jose J.

2005-01-01

We present a method to solve the impulsive minimum fuel maneuver problem for a distributed set of spacecraft. We develop the method assuming a non-linear dynamics model and parameterize the problem to allow the method to be applicable to multiple flight regimes including low-Earth orbits, highly-elliptic orbits (HEO), Lagrange point orbits, and interplanetary trajectories. Furthermore, the approach is not limited by the inter-spacecraft separation distances and is applicable to both small formations as well as large constellations. Semianalytical derivatives are derived for the changes in the total AV with respect to changes in the independent variables. We also apply a set of constraints to ensure that the fuel expenditure is equalized over the spacecraft in formation. We conclude with several examples and present optimal maneuver sequences for both a HE0 and libration point formation.

An Optimization Principle for Deriving Nonequilibrium Statistical Models of Hamiltonian Dynamics

NASA Astrophysics Data System (ADS)

Turkington, Bruce

2013-08-01

A general method for deriving closed reduced models of Hamiltonian dynamical systems is developed using techniques from optimization and statistical estimation. Given a vector of resolved variables, selected to describe the macroscopic state of the system, a family of quasi-equilibrium probability densities on phase space corresponding to the resolved variables is employed as a statistical model, and the evolution of the mean resolved vector is estimated by optimizing over paths of these densities. Specifically, a cost function is constructed to quantify the lack-of-fit to the microscopic dynamics of any feasible path of densities from the statistical model; it is an ensemble-averaged, weighted, squared-norm of the residual that results from submitting the path of densities to the Liouville equation. The path that minimizes the time integral of the cost function determines the best-fit evolution of the mean resolved vector. The closed reduced equations satisfied by the optimal path are derived by Hamilton-Jacobi theory. When expressed in terms of the macroscopic variables, these equations have the generic structure of governing equations for nonequilibrium thermodynamics. In particular, the value function for the optimization principle coincides with the dissipation potential that defines the relation between thermodynamic forces and fluxes. The adjustable closure parameters in the best-fit reduced equations depend explicitly on the arbitrary weights that enter into the lack-of-fit cost function. Two particular model reductions are outlined to illustrate the general method. In each example the set of weights in the optimization principle contracts into a single effective closure parameter.

Near-Optimal Operation of Dual-Fuel Launch Vehicles

NASA Technical Reports Server (NTRS)

Ardema, M. D.; Chou, H. C.; Bowles, J. V.

1996-01-01

A near-optimal guidance law for the ascent trajectory from earth surface to earth orbit of a fully reusable single-stage-to-orbit pure rocket launch vehicle is derived. Of interest are both the optimal operation of the propulsion system and the optimal flight path. A methodology is developed to investigate the optimal throttle switching of dual-fuel engines. The method is based on selecting propulsion system modes and parameters that maximize a certain performance function. This function is derived from consideration of the energy-state model of the aircraft equations of motion. Because the density of liquid hydrogen is relatively low, the sensitivity of perturbations in volume need to be taken into consideration as well as weight sensitivity. The cost functional is a weighted sum of fuel mass and volume; the weighting factor is chosen to minimize vehicle empty weight for a given payload mass and volume in orbit.

Accurate, rapid identification of dislocation lines in coherent diffractive imaging via a min-max optimization formulation

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

Ulvestad, A.; Menickelly, M.; Wild, S. M.

Defects such as dislocations impact materials properties and their response during external stimuli. Imaging these defects in their native operating conditions to establish the structure-function relationship and, ultimately, to improve performance via defect engineering has remained a considerable challenge for both electron-based and x-ray-based imaging techniques. While Bragg coherent x-ray diffractive imaging (BCDI) is successful in many cases, nuances in identifying the dislocations has left manual identification as the preferred method. Derivative-based methods are also used, but they can be inaccurate and are computationally inefficient. Here we demonstrate a derivative-free method that is both more accurate and more computationally efficientmore » than either derivative-or human-based methods for identifying 3D dislocation lines in nanocrystal images produced by BCDI. We formulate the problem as a min-max optimization problem and show exceptional accuracy for experimental images. We demonstrate a 227x speedup for a typical experimental dataset with higher accuracy over current methods. We discuss the possibility of using this algorithm as part of a sparsity-based phase retrieval process. We also provide MATLAB code for use by other researchers.« less

Accurate, rapid identification of dislocation lines in coherent diffractive imaging via a min-max optimization formulation

NASA Astrophysics Data System (ADS)

Ulvestad, A.; Menickelly, M.; Wild, S. M.

2018-01-01

Defects such as dislocations impact materials properties and their response during external stimuli. Imaging these defects in their native operating conditions to establish the structure-function relationship and, ultimately, to improve performance via defect engineering has remained a considerable challenge for both electron-based and x-ray-based imaging techniques. While Bragg coherent x-ray diffractive imaging (BCDI) is successful in many cases, nuances in identifying the dislocations has left manual identification as the preferred method. Derivative-based methods are also used, but they can be inaccurate and are computationally inefficient. Here we demonstrate a derivative-free method that is both more accurate and more computationally efficient than either derivative- or human-based methods for identifying 3D dislocation lines in nanocrystal images produced by BCDI. We formulate the problem as a min-max optimization problem and show exceptional accuracy for experimental images. We demonstrate a 227x speedup for a typical experimental dataset with higher accuracy over current methods. We discuss the possibility of using this algorithm as part of a sparsity-based phase retrieval process. We also provide MATLAB code for use by other researchers.

Corpus-Based Optimization of Language Models Derived from Unification Grammars

NASA Technical Reports Server (NTRS)

Rayner, Manny; Hockey, Beth Ann; James, Frankie; Bratt, Harry; Bratt, Elizabeth O.; Gawron, Mark; Goldwater, Sharon; Dowding, John; Bhagat, Amrita

2000-01-01

We describe a technique which makes it feasible to improve the performance of a language model derived from a manually constructed unification grammar, using low-quality untranscribed speech data and a minimum of human annotation. The method is on a medium-vocabulary spoken language command and control task.

An opinion formation based binary optimization approach for feature selection

NASA Astrophysics Data System (ADS)

Hamedmoghadam, Homayoun; Jalili, Mahdi; Yu, Xinghuo

2018-02-01

This paper proposed a novel optimization method based on opinion formation in complex network systems. The proposed optimization technique mimics human-human interaction mechanism based on a mathematical model derived from social sciences. Our method encodes a subset of selected features to the opinion of an artificial agent and simulates the opinion formation process among a population of agents to solve the feature selection problem. The agents interact using an underlying interaction network structure and get into consensus in their opinions, while finding better solutions to the problem. A number of mechanisms are employed to avoid getting trapped in local minima. We compare the performance of the proposed method with a number of classical population-based optimization methods and a state-of-the-art opinion formation based method. Our experiments on a number of high dimensional datasets reveal outperformance of the proposed algorithm over others.

Time-optimal control of the spacecraft trajectories in the Earth-Moon system

NASA Astrophysics Data System (ADS)

Starinova, O. L.; Fain, M. K.; Materova, I. L.

2017-01-01

This paper outlines the multiparametric optimization of the L1-L2 and L2-L1 missions in the Earth-Moon system using electric propulsion. The optimal control laws are obtained using the Fedorenko successful linearization method to estimate the derivatives and the gradient method to optimize the control laws. The study of the transfers is based on the restricted circular three-body problem. The mathematical model of the missions is described within the barycentric system of coordinates. The optimization criterion is the total flight time. The perturbation from the Earth, the Moon and the Sun are taking into account. The impact of the shaded areas, induced by the Earth and the Moon, is also accounted. As the results of the optimization we obtained optimal control laws, corresponding trajectories and minimal total flight times.

GlobiPack v. 1.0

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

Bartlett, Roscoe

2010-03-31

GlobiPack contains a small collection of optimization globalization algorithms. These algorithms are used by optimization and various nonlinear equation solver algorithms.Used as the line-search procedure with Newton and Quasi-Newton optimization and nonlinear equation solver methods. These are standard published 1-D line search algorithms such as are described in the book Nocedal and Wright Numerical Optimization: 2nd edition, 2006. One set of algorithms were copied and refactored from the existing open-source Trilinos package MOOCHO where the linear search code is used to globalize SQP methods. This software is generic to any mathematical optimization problem where smooth derivatives exist. There is nomore » specific connection or mention whatsoever to any specific application, period. You cannot find more general mathematical software.« less

Optimal cure cycle design of a resin-fiber composite laminate

NASA Technical Reports Server (NTRS)

Hou, Jean W.; Sheen, Jeenson

1987-01-01

A unified computed aided design method was studied for the cure cycle design that incorporates an optimal design technique with the analytical model of a composite cure process. The preliminary results of using this proposed method for optimal cure cycle design are reported and discussed. The cure process of interest is the compression molding of a polyester which is described by a diffusion reaction system. The finite element method is employed to convert the initial boundary value problem into a set of first order differential equations which are solved simultaneously by the DE program. The equations for thermal design sensitivities are derived by using the direct differentiation method and are solved by the DE program. A recursive quadratic programming algorithm with an active set strategy called a linearization method is used to optimally design the cure cycle, subjected to the given design performance requirements. The difficulty of casting the cure cycle design process into a proper mathematical form is recognized. Various optimal design problems are formulated to address theses aspects. The optimal solutions of these formulations are compared and discussed.

A Pilot Study Assessing ECG versus ECHO Ventriculoventricular Optimization in Pediatric Resynchronization Patients.

PubMed

Punn, Rajesh; Hanisch, Debra; Motonaga, Kara S; Rosenthal, David N; Ceresnak, Scott R; Dubin, Anne M

2016-02-01

Cardiac resynchronization therapy indications and management are well described in adults. Echocardiography (ECHO) has been used to optimize mechanical synchrony in these patients; however, there are issues with reproducibility and time intensity. Pediatric patients add challenges, with diverse substrates and limited capacity for cooperation. Electrocardiographic (ECG) methods to assess electrical synchrony are expeditious but have not been extensively studied in children. We sought to compare ECHO and ECG CRT optimization in children. Prospective, pediatric, single-center cross-over trial comparing ECHO and ECG optimization with CRT. Patients were assigned to undergo either ECHO or ECG optimization, followed for 6 months, and crossed-over to the other assignment for another 6 months. ECHO pulsed-wave tissue Doppler and 12-lead ECG were obtained for 5 VV delays. ECG optimization was defined as the shortest QRSD and ECHO optimization as the lowest dyssynchrony index. ECHOs/ECGs were interpreted by readers blinded to optimization technique. After each 6 month period, these data were collected: ejection fraction, velocimetry-derived cardiac index, quality of life, ECHO-derived stroke distance, M-mode dyssynchrony, study cost, and time. Outcomes for each optimization method were compared. From June 2012 to December 2013, 19 patients enrolled. Mean age was 9.1 ± 4.3 years; 14 (74%) had structural heart disease. The mean time for optimization was shorter using ECG than ECHO (9 ± 1 min vs. 68 ± 13 min, P < 0.01). Mean cost for charges was $4,400 ± 700 less for ECG. No other outcome differed between groups. ECHO optimization of synchrony was not superior to ECG optimization in this pilot study. ECG optimization required less time and cost than ECHO optimization. © 2015 Wiley Periodicals, Inc.

Topology optimization based design of unilateral NMR for generating a remote homogeneous field.

PubMed

Wang, Qi; Gao, Renjing; Liu, Shutian

2017-06-01

This paper presents a topology optimization based design method for the design of unilateral nuclear magnetic resonance (NMR), with which a remote homogeneous field can be obtained. The topology optimization is actualized by seeking out the optimal layout of ferromagnetic materials within a given design domain. The design objective is defined as generating a sensitive magnetic field with optimal homogeneity and maximal field strength within a required region of interest (ROI). The sensitivity of the objective function with respect to the design variables is derived and the method for solving the optimization problem is presented. A design example is provided to illustrate the utility of the design method, specifically the ability to improve the quality of the magnetic field over the required ROI by determining the optimal structural topology for the ferromagnetic poles. Both in simulations and experiments, the sensitive region of the magnetic field achieves about 2 times larger than that of the reference design, validating validates the feasibility of the design method. Copyright © 2017. Published by Elsevier Inc.

Calculation of Sensitivity Derivatives in an MDAO Framework

NASA Technical Reports Server (NTRS)

Moore, Kenneth T.

2012-01-01

During gradient-based optimization of a system, it is necessary to generate the derivatives of each objective and constraint with respect to each design parameter. If the system is multidisciplinary, it may consist of a set of smaller "components" with some arbitrary data interconnection and process work ow. Analytical derivatives in these components can be used to improve the speed and accuracy of the derivative calculation over a purely numerical calculation; however, a multidisciplinary system may include both components for which derivatives are available and components for which they are not. Three methods to calculate the sensitivity of a mixed multidisciplinary system are presented: the finite difference method, where the derivatives are calculated numerically; the chain rule method, where the derivatives are successively cascaded along the system's network graph; and the analytic method, where the derivatives come from the solution of a linear system of equations. Some improvements to these methods, to accommodate mixed multidisciplinary systems, are also presented; in particular, a new method is introduced to allow existing derivatives to be used inside of finite difference. All three methods are implemented and demonstrated in the open-source MDAO framework OpenMDAO. It was found that there are advantages to each of them depending on the system being solved.

A computerized traffic control algorithm to determine optimal traffic signal settings. Ph.D. Thesis - Toledo Univ.

NASA Technical Reports Server (NTRS)

Seldner, K.

1977-01-01

An algorithm was developed to optimally control the traffic signals at each intersection using a discrete time traffic model applicable to heavy or peak traffic. Off line optimization procedures were applied to compute the cycle splits required to minimize the lengths of the vehicle queues and delay at each intersection. The method was applied to an extensive traffic network in Toledo, Ohio. Results obtained with the derived optimal settings are compared with the control settings presently in use.

Optimal sixteenth order convergent method based on quasi-Hermite interpolation for computing roots.

PubMed

Zafar, Fiza; Hussain, Nawab; Fatimah, Zirwah; Kharal, Athar

2014-01-01

We have given a four-step, multipoint iterative method without memory for solving nonlinear equations. The method is constructed by using quasi-Hermite interpolation and has order of convergence sixteen. As this method requires four function evaluations and one derivative evaluation at each step, it is optimal in the sense of the Kung and Traub conjecture. The comparisons are given with some other newly developed sixteenth-order methods. Interval Newton's method is also used for finding the enough accurate initial approximations. Some figures show the enclosure of finitely many zeroes of nonlinear equations in an interval. Basins of attractions show the effectiveness of the method.

Comparative dynamics in a health investment model.

PubMed

Eisenring, C

1999-10-01

The method of comparative dynamics fully exploits the inter-temporal structure of optimal control models. I derive comparative dynamic results in a simplified demand for health model. The effect of a change in the depreciation rate on the optimal paths for health capital and investment in health is studied by use of a phase diagram.

A computational method for optimizing fuel treatment locations

Treesearch

Mark A. Finney

2006-01-01

Modeling and experiments have suggested that spatial fuel treatment patterns can influence the movement of large fires. On simple theoretical landscapes consisting of two fuel types (treated and untreated) optimal patterns can be analytically derived that disrupt fire growth efficiently (i.e. with less area treated than random patterns). Although conceptually simple,...

Determination of stresses in RC eccentrically compressed members using optimization methods

NASA Astrophysics Data System (ADS)

Lechman, Marek; Stachurski, Andrzej

2018-01-01

The paper presents an optimization method for determining the strains and stresses in reinforced concrete (RC) members subjected to the eccentric compression. The governing equations for strains in the rectangular cross-sections are derived by integrating the equilibrium equations of cross-sections, taking account of the effect of concrete softening in plastic range and the mean compressive strength of concrete. The stress-strain relationship for concrete in compression for short term uniaxial loading is assumed according to Eurocode 2 for nonlinear analysis. For reinforcing steel linear-elastic model with hardening in plastic range is applied. The task consists in the solving the set of the derived equations s.t. box constraints. The resulting problem was solved by means of fmincon function implemented from the Matlab's Optimization Toolbox. Numerical experiments have shown the existence of many points verifying the equations with a very good accuracy. Therefore, some operations from the global optimization were included: start of fmincon from many points and clusterization. The model is verified on the set of data encountered in the engineering practice.

Uncertainty in the analysis of the overall equipment effectiveness on the shop floor

NASA Astrophysics Data System (ADS)

Rößler, M. P.; Abele, E.

2013-06-01

In this article an approach will be presented which supports transparency regarding the effectiveness of manufacturing equipment by combining the fuzzy set theory with the method of the overall equipment effectiveness analysis. One of the key principles of lean production and also a fundamental task in production optimization projects is the prior analysis of the current state of a production system by the use of key performance indicators to derive possible future states. The current state of the art in overall equipment effectiveness analysis is usually performed by cumulating different machine states by means of decentralized data collection without the consideration of uncertainty. In manual data collection or semi-automated plant data collection systems the quality of derived data often diverges and leads optimization teams to distorted conclusions about the real optimization potential of manufacturing equipment. The method discussed in this paper is to help practitioners to get more reliable results in the analysis phase and so better results of optimization projects. Under consideration of a case study obtained results are discussed.

A Carrier Estimation Method Based on MLE and KF for Weak GNSS Signals.

PubMed

Zhang, Hongyang; Xu, Luping; Yan, Bo; Zhang, Hua; Luo, Liyan

2017-06-22

Maximum likelihood estimation (MLE) has been researched for some acquisition and tracking applications of global navigation satellite system (GNSS) receivers and shows high performance. However, all current methods are derived and operated based on the sampling data, which results in a large computation burden. This paper proposes a low-complexity MLE carrier tracking loop for weak GNSS signals which processes the coherent integration results instead of the sampling data. First, the cost function of the MLE of signal parameters such as signal amplitude, carrier phase, and Doppler frequency are used to derive a MLE discriminator function. The optimal value of the cost function is searched by an efficient Levenberg-Marquardt (LM) method iteratively. Its performance including Cramér-Rao bound (CRB), dynamic characteristics and computation burden are analyzed by numerical techniques. Second, an adaptive Kalman filter is designed for the MLE discriminator to obtain smooth estimates of carrier phase and frequency. The performance of the proposed loop, in terms of sensitivity, accuracy and bit error rate, is compared with conventional methods by Monte Carlo (MC) simulations both in pedestrian-level and vehicle-level dynamic circumstances. Finally, an optimal loop which combines the proposed method and conventional method is designed to achieve the optimal performance both in weak and strong signal circumstances.

Analysis and optimization of population annealing

NASA Astrophysics Data System (ADS)

Amey, Christopher; Machta, Jonathan

2018-03-01

Population annealing is an easily parallelizable sequential Monte Carlo algorithm that is well suited for simulating the equilibrium properties of systems with rough free-energy landscapes. In this work we seek to understand and improve the performance of population annealing. We derive several useful relations between quantities that describe the performance of population annealing and use these relations to suggest methods to optimize the algorithm. These optimization methods were tested by performing large-scale simulations of the three-dimensional (3D) Edwards-Anderson (Ising) spin glass and measuring several observables. The optimization methods were found to substantially decrease the amount of computational work necessary as compared to previously used, unoptimized versions of population annealing. We also obtain more accurate values of several important observables for the 3D Edwards-Anderson model.

The optimal inventory policy for EPQ model under trade credit

NASA Astrophysics Data System (ADS)

Chung, Kun-Jen

2010-09-01

Huang and Huang [(2008), 'Optimal Inventory Replenishment Policy for the EPQ Model Under Trade Credit without Derivatives International Journal of Systems Science, 39, 539-546] use the algebraic method to determine the optimal inventory replenishment policy for the retailer in the extended model under trade credit. However, the algebraic method has its limit of application such that validities of proofs of Theorems 1-4 in Huang and Huang (2008) are questionable. The main purpose of this article is not only to indicate shortcomings but also to present the accurate proofs for Huang and Huang (2008).

What is the optimal way to prepare a Bell state using measurement and feedback?

NASA Astrophysics Data System (ADS)

Martin, Leigh; Sayrafi, Mahrud; Whaley, K. Birgitta

2017-12-01

Recent work has shown that the use of quantum feedback can significantly enhance both the speed and success rate of measurement-based remote entanglement generation, but it is generally unknown what feedback protocols are optimal for these tasks. Here we consider two common measurements that are capable of projecting into pairwise entangled states, namely half- and full-parity measurements of two qubits, and determine in each case a globally optimal protocol for generation of entanglement. For the half-parity measurement, we rederive a previously described protocol using more general methods and prove that it is globally optimal for several figures of merit, including maximal concurrence or fidelity and minimal time to reach a specified concurrence or fidelity. For the full-parity measurement, we derive a protocol for rapid entanglement generation related to that of (Hill, Ralph, Phys. Rev. A 77, 014305), and then map the dynamics of the concurrence of the state to the Bloch vector length of an effective qubit. This mapping allows us to prove several optimality results for feedback protocols with full-parity measurements. We further show that our full-parity protocol transfers entanglement optimally from one qubit to the other amongst all measurement-based schemes. The methods developed here will be useful for deriving feedback protocols and determining their optimality properties in many other quantum systems subject to measurement and unitary operations.

Generalized Differential Calculus and Applications to Optimization

NASA Astrophysics Data System (ADS)

Rector, Robert Blake Hayden

This thesis contains contributions in three areas: the theory of generalized calculus, numerical algorithms for operations research, and applications of optimization to problems in modern electric power systems. A geometric approach is used to advance the theory and tools used for studying generalized notions of derivatives for nonsmooth functions. These advances specifically pertain to methods for calculating subdifferentials and to expanding our understanding of a certain notion of derivative of set-valued maps, called the coderivative, in infinite dimensions. A strong understanding of the subdifferential is essential for numerical optimization algorithms, which are developed and applied to nonsmooth problems in operations research, including non-convex problems. Finally, an optimization framework is applied to solve a problem in electric power systems involving a smart solar inverter and battery storage system providing energy and ancillary services to the grid.

An adjoint method for gradient-based optimization of stellarator coil shapes

NASA Astrophysics Data System (ADS)

Paul, E. J.; Landreman, M.; Bader, A.; Dorland, W.

2018-07-01

We present a method for stellarator coil design via gradient-based optimization of the coil-winding surface. The REGCOIL (Landreman 2017 Nucl. Fusion 57 046003) approach is used to obtain the coil shapes on the winding surface using a continuous current potential. We apply the adjoint method to calculate derivatives of the objective function, allowing for efficient computation of analytic gradients while eliminating the numerical noise of approximate derivatives. We are able to improve engineering properties of the coils by targeting the root-mean-squared current density in the objective function. We obtain winding surfaces for W7-X and HSX which simultaneously decrease the normal magnetic field on the plasma surface and increase the surface-averaged distance between the coils and the plasma in comparison with the actual winding surfaces. The coils computed on the optimized surfaces feature a smaller toroidal extent and curvature and increased inter-coil spacing. A technique for computation of the local sensitivity of figures of merit to normal displacements of the winding surface is presented, with potential applications for understanding engineering tolerances.

Variational Methods in Sensitivity Analysis and Optimization for Aerodynamic Applications

NASA Technical Reports Server (NTRS)

Ibrahim, A. H.; Hou, G. J.-W.; Tiwari, S. N. (Principal Investigator)

1996-01-01

Variational methods (VM) sensitivity analysis, which is the continuous alternative to the discrete sensitivity analysis, is employed to derive the costate (adjoint) equations, the transversality conditions, and the functional sensitivity derivatives. In the derivation of the sensitivity equations, the variational methods use the generalized calculus of variations, in which the variable boundary is considered as the design function. The converged solution of the state equations together with the converged solution of the costate equations are integrated along the domain boundary to uniquely determine the functional sensitivity derivatives with respect to the design function. The determination of the sensitivity derivatives of the performance index or functional entails the coupled solutions of the state and costate equations. As the stable and converged numerical solution of the costate equations with their boundary conditions are a priori unknown, numerical stability analysis is performed on both the state and costate equations. Thereafter, based on the amplification factors obtained by solving the generalized eigenvalue equations, the stability behavior of the costate equations is discussed and compared with the state (Euler) equations. The stability analysis of the costate equations suggests that the converged and stable solution of the costate equation is possible only if the computational domain of the costate equations is transformed to take into account the reverse flow nature of the costate equations. The application of the variational methods to aerodynamic shape optimization problems is demonstrated for internal flow problems at supersonic Mach number range. The study shows, that while maintaining the accuracy of the functional sensitivity derivatives within the reasonable range for engineering prediction purposes, the variational methods show a substantial gain in computational efficiency, i.e., computer time and memory, when compared with the finite difference sensitivity analysis.

Optimal control for a tuberculosis model with undetected cases in Cameroon

NASA Astrophysics Data System (ADS)

Moualeu, D. P.; Weiser, M.; Ehrig, R.; Deuflhard, P.

2015-03-01

This paper considers the optimal control of tuberculosis through education, diagnosis campaign and chemoprophylaxis of latently infected. A mathematical model which includes important components such as undiagnosed infectious, diagnosed infectious, latently infected and lost-sight infectious is formulated. The model combines a frequency dependent and a density dependent force of infection for TB transmission. Through optimal control theory and numerical simulations, a cost-effective balance of two different intervention methods is obtained. Seeking to minimize the amount of money the government spends when tuberculosis remain endemic in the Cameroonian population, Pontryagin's maximum principle is used to characterize the optimal control. The optimality system is derived and solved numerically using the forward-backward sweep method (FBSM). Results provide a framework for designing cost-effective strategies for diseases with multiple intervention methods. It comes out that combining chemoprophylaxis and education, the burden of TB can be reduced by 80% in 10 years.

Optimizing an Actuator Array for the Control of Multi-Frequency Noise in Aircraft Interiors

NASA Technical Reports Server (NTRS)

Palumbo, D. L.; Padula, S. L.

1997-01-01

Techniques developed for selecting an optimized actuator array for interior noise reduction at a single frequency are extended to the multi-frequency case. Transfer functions for 64 actuators were obtained at 5 frequencies from ground testing the rear section of a fully trimmed DC-9 fuselage. A single loudspeaker facing the left side of the aircraft was the primary source. A combinatorial search procedure (tabu search) was employed to find optimum actuator subsets of from 2 to 16 actuators. Noise reduction predictions derived from the transfer functions were used as a basis for evaluating actuator subsets during optimization. Results indicate that it is necessary to constrain actuator forces during optimization. Unconstrained optimizations selected actuators which require unrealistically large forces. Two methods of constraint are evaluated. It is shown that a fast, but approximate, method yields results equivalent to an accurate, but computationally expensive, method.

Rat Bone Marrow-Derived Schwann-Like Cells Differentiated by the Optimal Inducers Combination on Microfluidic Chip and Their Functional Performance

PubMed Central

Lv, Decheng

2012-01-01

Numerous researches demonstrated the possibility of derivation of Schwann-like (SC-like) cells in vitro from bone marrow stromal cells (BMSCs). However, the concentration of the induce factors were different in those studies, especially for the critical factors forskolin (FSK) and β-heregulin (HRG). Here, we used a new and useful method to build an integrated microfluidic chip for rapid analyses of the optimal combination between the induce factors FSK and HRG. The microfluidic device was mainly composed of an upstream concentration gradient generator (CGG) and a downstream cell culture module. Rat BMSCs were cultured in the cell chambers for 11 days at the different concentrations of induce factors generated by CGG. The result of immunofluorescence staining on-chip showed that the group of 4.00 µM FSK and 250.00 ng/ml HRG presented an optimal effect to promote the derivation of SC-like cells. Moreover, the optimal SC-like cells obtained on-chip were further tested using DRG co-culture and ELISA to detect their functional performance. Our findings demonstrate that SC-like cells could be obtained with high efficiency and functional performance in the optimal inducers combination. PMID:22880114

Rat bone marrow-derived Schwann-like cells differentiated by the optimal inducers combination on microfluidic chip and their functional performance.

PubMed

Tian, Xiliang; Wang, Shouyu; Zhang, Zhen; Lv, Decheng

2012-01-01

Numerous researches demonstrated the possibility of derivation of Schwann-like (SC-like) cells in vitro from bone marrow stromal cells (BMSCs). However, the concentration of the induce factors were different in those studies, especially for the critical factors forskolin (FSK) and β-heregulin (HRG). Here, we used a new and useful method to build an integrated microfluidic chip for rapid analyses of the optimal combination between the induce factors FSK and HRG. The microfluidic device was mainly composed of an upstream concentration gradient generator (CGG) and a downstream cell culture module. Rat BMSCs were cultured in the cell chambers for 11 days at the different concentrations of induce factors generated by CGG. The result of immunofluorescence staining on-chip showed that the group of 4.00 µM FSK and 250.00 ng/ml HRG presented an optimal effect to promote the derivation of SC-like cells. Moreover, the optimal SC-like cells obtained on-chip were further tested using DRG co-culture and ELISA to detect their functional performance. Our findings demonstrate that SC-like cells could be obtained with high efficiency and functional performance in the optimal inducers combination.

Automated Surgical Approach Planning for Complex Skull Base Targets: Development and Validation of a Cost Function and Semantic At-las.

PubMed

Aghdasi, Nava; Whipple, Mark; Humphreys, Ian M; Moe, Kris S; Hannaford, Blake; Bly, Randall A

2018-06-01

Successful multidisciplinary treatment of skull base pathology requires precise preoperative planning. Current surgical approach (pathway) selection for these complex procedures depends on an individual surgeon's experiences and background training. Because of anatomical variation in both normal tissue and pathology (eg, tumor), a successful surgical pathway used on one patient is not necessarily the best approach on another patient. The question is how to define and obtain optimized patient-specific surgical approach pathways? In this article, we demonstrate that the surgeon's knowledge and decision making in preoperative planning can be modeled by a multiobjective cost function in a retrospective analysis of actual complex skull base cases. Two different approaches- weighted-sum approach and Pareto optimality-were used with a defined cost function to derive optimized surgical pathways based on preoperative computed tomography (CT) scans and manually designated pathology. With the first method, surgeon's preferences were input as a set of weights for each objective before the search. In the second approach, the surgeon's preferences were used to select a surgical pathway from the computed Pareto optimal set. Using preoperative CT and magnetic resonance imaging, the patient-specific surgical pathways derived by these methods were similar (85% agreement) to the actual approaches performed on patients. In one case where the actual surgical approach was different, revision surgery was required and was performed utilizing the computationally derived approach pathway.

Singularity in structural optimization

NASA Technical Reports Server (NTRS)

Patnaik, S. N.; Guptill, J. D.; Berke, L.

1993-01-01

The conditions under which global and local singularities may arise in structural optimization are examined. Examples of these singularities are presented, and a framework is given within which the singularities can be recognized. It is shown, in particular, that singularities can be identified through the analysis of stress-displacement relations together with compatibility conditions or the displacement-stress relations derived by the integrated force method of structural analysis. Methods of eliminating the effects of singularities are suggested and illustrated numerically.

Optimal Collision Avoidance Trajectories for Unmanned/Remotely Piloted Aircraft

DTIC Science & Technology

2014-12-26

projected operational tempos (OPTEMPOs)” [15]. The Oce of the Secretary of Defense (OSD) Unmanned Systems Roadmap [15] goes on to say that the airspace...methods [63]. In an indirect method, the researcher derives the first- order necessary conditions for optimality “via the calculus of variations and...region around the ownship using a variation of a superquadric. From [116], the standard equation for a superellipsoid appears as: ✓ x a1 ◆ 2 ✏ 2

Development and optimization of an energy-regenerative suspension system under stochastic road excitation

NASA Astrophysics Data System (ADS)

Huang, Bo; Hsieh, Chen-Yu; Golnaraghi, Farid; Moallem, Mehrdad

2015-11-01

In this paper a vehicle suspension system with energy harvesting capability is developed, and an analytical methodology for the optimal design of the system is proposed. The optimization technique provides design guidelines for determining the stiffness and damping coefficients aimed at the optimal performance in terms of ride comfort and energy regeneration. The corresponding performance metrics are selected as root-mean-square (RMS) of sprung mass acceleration and expectation of generated power. The actual road roughness is considered as the stochastic excitation defined by ISO 8608:1995 standard road profiles and used in deriving the optimization method. An electronic circuit is proposed to provide variable damping in the real-time based on the optimization rule. A test-bed is utilized and the experiments under different driving conditions are conducted to verify the effectiveness of the proposed method. The test results suggest that the analytical approach is credible in determining the optimality of system performance.

Derived heuristics-based consistent optimization of material flow in a gold processing plant

NASA Astrophysics Data System (ADS)

Myburgh, Christie; Deb, Kalyanmoy

2018-01-01

Material flow in a chemical processing plant often follows complicated control laws and involves plant capacity constraints. Importantly, the process involves discrete scenarios which when modelled in a programming format involves if-then-else statements. Therefore, a formulation of an optimization problem of such processes becomes complicated with nonlinear and non-differentiable objective and constraint functions. In handling such problems using classical point-based approaches, users often have to resort to modifications and indirect ways of representing the problem to suit the restrictions associated with classical methods. In a particular gold processing plant optimization problem, these facts are demonstrated by showing results from MATLAB®'s well-known fmincon routine. Thereafter, a customized evolutionary optimization procedure which is capable of handling all complexities offered by the problem is developed. Although the evolutionary approach produced results with comparatively less variance over multiple runs, the performance has been enhanced by introducing derived heuristics associated with the problem. In this article, the development and usage of derived heuristics in a practical problem are presented and their importance in a quick convergence of the overall algorithm is demonstrated.

Fuel-optimal low-thrust formation reconfiguration via Radau pseudospectral method

NASA Astrophysics Data System (ADS)

Li, Jing

2016-07-01

This paper investigates fuel-optimal low-thrust formation reconfiguration near circular orbit. Based on the Clohessy-Wiltshire equations, first-order necessary optimality conditions are derived from the Pontryagin's maximum principle. The fuel-optimal impulsive solution is utilized to divide the low-thrust trajectory into thrust and coast arcs. By introducing the switching times as optimization variables, the fuel-optimal low-thrust formation reconfiguration is posed as a nonlinear programming problem (NLP) via direct transcription using multiple-phase Radau pseudospectral method (RPM), which is then solved by a sparse nonlinear optimization software SNOPT. To facilitate optimality verification and, if necessary, further refinement of the optimized solution of the NLP, formulas for mass costate estimation and initial costates scaling are presented. Numerical examples are given to show the application of the proposed optimization method. To fix the problem, generic fuel-optimal low-thrust formation reconfiguration can be simplified as reconfiguration without any initial and terminal coast arcs, whose optimal solutions can be efficiently obtained from the multiple-phase RPM at the cost of a slight fuel increment. Finally, influence of the specific impulse and maximum thrust magnitude on the fuel-optimal low-thrust formation reconfiguration is analyzed. Numerical results shown the links and differences between the fuel-optimal impulsive and low-thrust solutions.

Grading of Chinese Cantonese Sausage Using Hyperspectral Imaging Combined with Chemometric Methods

PubMed Central

Gong, Aiping; Zhu, Susu; He, Yong; Zhang, Chu

2017-01-01

Fast and accurate grading of Chinese Cantonese sausage is an important concern for customers, organizations, and the industry. Hyperspectral imaging in the spectral range of 874–1734 nm, combined with chemometric methods, was applied to grade Chinese Cantonese sausage. Three grades of intact and sliced Cantonese sausages were studied, including the top, first, and second grades. Support vector machine (SVM) and random forests (RF) techniques were used to build two different models. Second derivative spectra and RF were applied to select optimal wavelengths. The optimal wavelengths were the same for intact and sliced sausages when selected from second derivative spectra, while the optimal wavelengths for intact and sliced sausages selected using RF were quite similar. The SVM and RF models, using full spectra and the optimal wavelengths, obtained acceptable results for intact and sliced sausages. Both models for intact sausages performed better than those for sliced sausages, with a classification accuracy of the calibration and prediction set of over 90%. The overall results indicated that hyperspectral imaging combined with chemometric methods could be used to grade Chinese Cantonese sausages, with intact sausages being better suited for grading. This study will help to develop fast and accurate online grading of Cantonese sausages, as well as other sausages. PMID:28757578

Texture mapping via optimal mass transport.

PubMed

Dominitz, Ayelet; Tannenbaum, Allen

2010-01-01

In this paper, we present a novel method for texture mapping of closed surfaces. Our method is based on the technique of optimal mass transport (also known as the "earth-mover's metric"). This is a classical problem that concerns determining the optimal way, in the sense of minimal transportation cost, of moving a pile of soil from one site to another. In our context, the resulting mapping is area preserving and minimizes angle distortion in the optimal mass sense. Indeed, we first begin with an angle-preserving mapping (which may greatly distort area) and then correct it using the mass transport procedure derived via a certain gradient flow. In order to obtain fast convergence to the optimal mapping, we incorporate a multiresolution scheme into our flow. We also use ideas from discrete exterior calculus in our computations.

A Biogeography-Based Optimization Algorithm Hybridized with Tabu Search for the Quadratic Assignment Problem

PubMed Central

Lim, Wee Loon; Wibowo, Antoni; Desa, Mohammad Ishak; Haron, Habibollah

2016-01-01

The quadratic assignment problem (QAP) is an NP-hard combinatorial optimization problem with a wide variety of applications. Biogeography-based optimization (BBO), a relatively new optimization technique based on the biogeography concept, uses the idea of migration strategy of species to derive algorithm for solving optimization problems. It has been shown that BBO provides performance on a par with other optimization methods. A classical BBO algorithm employs the mutation operator as its diversification strategy. However, this process will often ruin the quality of solutions in QAP. In this paper, we propose a hybrid technique to overcome the weakness of classical BBO algorithm to solve QAP, by replacing the mutation operator with a tabu search procedure. Our experiments using the benchmark instances from QAPLIB show that the proposed hybrid method is able to find good solutions for them within reasonable computational times. Out of 61 benchmark instances tested, the proposed method is able to obtain the best known solutions for 57 of them. PMID:26819585

A Biogeography-Based Optimization Algorithm Hybridized with Tabu Search for the Quadratic Assignment Problem.

PubMed

Lim, Wee Loon; Wibowo, Antoni; Desa, Mohammad Ishak; Haron, Habibollah

2016-01-01

The quadratic assignment problem (QAP) is an NP-hard combinatorial optimization problem with a wide variety of applications. Biogeography-based optimization (BBO), a relatively new optimization technique based on the biogeography concept, uses the idea of migration strategy of species to derive algorithm for solving optimization problems. It has been shown that BBO provides performance on a par with other optimization methods. A classical BBO algorithm employs the mutation operator as its diversification strategy. However, this process will often ruin the quality of solutions in QAP. In this paper, we propose a hybrid technique to overcome the weakness of classical BBO algorithm to solve QAP, by replacing the mutation operator with a tabu search procedure. Our experiments using the benchmark instances from QAPLIB show that the proposed hybrid method is able to find good solutions for them within reasonable computational times. Out of 61 benchmark instances tested, the proposed method is able to obtain the best known solutions for 57 of them.

Mission and system optimization of nuclear electric propulsion vehicles for lunar and Mars missions

NASA Technical Reports Server (NTRS)

Gilland, James H.

1991-01-01

The detailed mission and system optimization of low thrust electric propulsion missions is a complex, iterative process involving interaction between orbital mechanics and system performance. Through the use of appropriate approximations, initial system optimization and analysis can be performed for a range of missions. The intent of these calculations is to provide system and mission designers with simple methods to assess system design without requiring access or detailed knowledge of numerical calculus of variations optimizations codes and methods. Approximations for the mission/system optimization of Earth orbital transfer and Mars mission have been derived. Analyses include the variation of thruster efficiency with specific impulse. Optimum specific impulse, payload fraction, and power/payload ratios are calculated. The accuracy of these methods is tested and found to be reasonable for initial scoping studies. Results of optimization for Space Exploration Initiative lunar cargo and Mars missions are presented for a range of power system and thruster options.

Applying Mathematical Optimization Methods to an ACT-R Instance-Based Learning Model.

PubMed

Said, Nadia; Engelhart, Michael; Kirches, Christian; Körkel, Stefan; Holt, Daniel V

2016-01-01

Computational models of cognition provide an interface to connect advanced mathematical tools and methods to empirically supported theories of behavior in psychology, cognitive science, and neuroscience. In this article, we consider a computational model of instance-based learning, implemented in the ACT-R cognitive architecture. We propose an approach for obtaining mathematical reformulations of such cognitive models that improve their computational tractability. For the well-established Sugar Factory dynamic decision making task, we conduct a simulation study to analyze central model parameters. We show how mathematical optimization techniques can be applied to efficiently identify optimal parameter values with respect to different optimization goals. Beyond these methodological contributions, our analysis reveals the sensitivity of this particular task with respect to initial settings and yields new insights into how average human performance deviates from potential optimal performance. We conclude by discussing possible extensions of our approach as well as future steps towards applying more powerful derivative-based optimization methods.

First and second order derivatives for optimizing parallel RF excitation waveforms.

PubMed

Majewski, Kurt; Ritter, Dieter

2015-09-01

For piecewise constant magnetic fields, the Bloch equations (without relaxation terms) can be solved explicitly. This way the magnetization created by an excitation pulse can be written as a concatenation of rotations applied to the initial magnetization. For fixed gradient trajectories, the problem of finding parallel RF waveforms, which minimize the difference between achieved and desired magnetization on a number of voxels, can thus be represented as a finite-dimensional minimization problem. We use quaternion calculus to formulate this optimization problem in the magnitude least squares variant and specify first and second order derivatives of the objective function. We obtain a small tip angle approximation as first order Taylor development from the first order derivatives and also develop algorithms for first and second order derivatives for this small tip angle approximation. All algorithms are accompanied by precise floating point operation counts to assess and compare the computational efforts. We have implemented these algorithms as callback functions of an interior-point solver. We have applied this numerical optimization method to example problems from the literature and report key observations. Copyright © 2015 Elsevier Inc. All rights reserved.

First and second order derivatives for optimizing parallel RF excitation waveforms

NASA Astrophysics Data System (ADS)

Majewski, Kurt; Ritter, Dieter

2015-09-01

For piecewise constant magnetic fields, the Bloch equations (without relaxation terms) can be solved explicitly. This way the magnetization created by an excitation pulse can be written as a concatenation of rotations applied to the initial magnetization. For fixed gradient trajectories, the problem of finding parallel RF waveforms, which minimize the difference between achieved and desired magnetization on a number of voxels, can thus be represented as a finite-dimensional minimization problem. We use quaternion calculus to formulate this optimization problem in the magnitude least squares variant and specify first and second order derivatives of the objective function. We obtain a small tip angle approximation as first order Taylor development from the first order derivatives and also develop algorithms for first and second order derivatives for this small tip angle approximation. All algorithms are accompanied by precise floating point operation counts to assess and compare the computational efforts. We have implemented these algorithms as callback functions of an interior-point solver. We have applied this numerical optimization method to example problems from the literature and report key observations.

A globally convergent LCL method for nonlinear optimization.

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

Friedlander, M. P.; Saunders, M. A.; Mathematics and Computer Science

2005-01-01

For optimization problems with nonlinear constraints, linearly constrained Lagrangian (LCL) methods solve a sequence of subproblems of the form 'minimize an augmented Lagrangian function subject to linearized constraints.' Such methods converge rapidly near a solution but may not be reliable from arbitrary starting points. Nevertheless, the well-known software package MINOS has proved effective on many large problems. Its success motivates us to derive a related LCL algorithm that possesses three important properties: it is globally convergent, the subproblem constraints are always feasible, and the subproblems may be solved inexactly. The new algorithm has been implemented in Matlab, with an optionmore » to use either MINOS or SNOPT (Fortran codes) to solve the linearly constrained subproblems. Only first derivatives are required. We present numerical results on a subset of the COPS, HS, and CUTE test problems, which include many large examples. The results demonstrate the robustness and efficiency of the stabilized LCL procedure.« less

Solving ill-posed control problems by stabilized finite element methods: an alternative to Tikhonov regularization

NASA Astrophysics Data System (ADS)

Burman, Erik; Hansbo, Peter; Larson, Mats G.

2018-03-01

Tikhonov regularization is one of the most commonly used methods for the regularization of ill-posed problems. In the setting of finite element solutions of elliptic partial differential control problems, Tikhonov regularization amounts to adding suitably weighted least squares terms of the control variable, or derivatives thereof, to the Lagrangian determining the optimality system. In this note we show that the stabilization methods for discretely ill-posed problems developed in the setting of convection-dominated convection-diffusion problems, can be highly suitable for stabilizing optimal control problems, and that Tikhonov regularization will lead to less accurate discrete solutions. We consider some inverse problems for Poisson’s equation as an illustration and derive new error estimates both for the reconstruction of the solution from the measured data and reconstruction of the source term from the measured data. These estimates include both the effect of the discretization error and error in the measurements.

Optimal variable-grid finite-difference modeling for porous media

NASA Astrophysics Data System (ADS)

Liu, Xinxin; Yin, Xingyao; Li, Haishan

2014-12-01

Numerical modeling of poroelastic waves by the finite-difference (FD) method is more expensive than that of acoustic or elastic waves. To improve the accuracy and computational efficiency of seismic modeling, variable-grid FD methods have been developed. In this paper, we derived optimal staggered-grid finite difference schemes with variable grid-spacing and time-step for seismic modeling in porous media. FD operators with small grid-spacing and time-step are adopted for low-velocity or small-scale geological bodies, while FD operators with big grid-spacing and time-step are adopted for high-velocity or large-scale regions. The dispersion relations of FD schemes were derived based on the plane wave theory, then the FD coefficients were obtained using the Taylor expansion. Dispersion analysis and modeling results demonstrated that the proposed method has higher accuracy with lower computational cost for poroelastic wave simulation in heterogeneous reservoirs.

A method for determining optimum phasing of a multiphase propulsion system for a single-stage vehicle with linearized inert weight

NASA Technical Reports Server (NTRS)

Martin, J. A.

1974-01-01

A general analytical treatment is presented of a single-stage vehicle with multiple propulsion phases. A closed-form solution for the cost and for the performance and a derivation of the optimal phasing of the propulsion are included. Linearized variations in the inert weight elements are included, and the function to be minimized can be selected. The derivation of optimal phasing results in a set of nonlinear algebraic equations for optimal fuel volumes, for which a solution method is outlined. Three specific example cases are analyzed: minimum gross lift-off weight, minimum inert weight, and a minimized general function for a two-phase vehicle. The results for the two-phase vehicle are applied to the dual-fuel rocket. Comparisons with single-fuel vehicles indicate that dual-fuel vehicles can have lower inert weight either by development of a dual-fuel engine or by parallel burning of separate engines from lift-off.

Exact and explicit optimal solutions for trajectory planning and control of single-link flexible-joint manipulators

NASA Technical Reports Server (NTRS)

Chen, Guanrong

1991-01-01

An optimal trajectory planning problem for a single-link, flexible joint manipulator is studied. A global feedback-linearization is first applied to formulate the nonlinear inequality-constrained optimization problem in a suitable way. Then, an exact and explicit structural formula for the optimal solution of the problem is derived and the solution is shown to be unique. It turns out that the optimal trajectory planning and control can be done off-line, so that the proposed method is applicable to both theoretical analysis and real time tele-robotics control engineering.

A unified convergence theory of a numerical method, and applications to the replenishment policies.

PubMed

Mi, Xiang-jiang; Wang, Xing-hua

2004-01-01

In determining the replenishment policy for an inventory system, some researchers advocated that the iterative method of Newton could be applied to the derivative of the total cost function in order to get the optimal solution. But this approach requires calculation of the second derivative of the function. Avoiding this complex computation we use another iterative method presented by the second author. One of the goals of this paper is to present a unified convergence theory of this method. Then we give a numerical example to show the application of our theory.

Optimal control penalty finite elements - Applications to integrodifferential equations

NASA Astrophysics Data System (ADS)

Chung, T. J.

The application of the optimal-control/penalty finite-element method to the solution of integrodifferential equations in radiative-heat-transfer problems (Chung et al.; Chung and Kim, 1982) is discussed and illustrated. The nonself-adjointness of the convective terms in the governing equations is treated by utilizing optimal-control cost functions and employing penalty functions to constrain auxiliary equations which permit the reduction of second-order derivatives to first order. The OCPFE method is applied to combined-mode heat transfer by conduction, convection, and radiation, both without and with scattering and viscous dissipation; the results are presented graphically and compared to those obtained by other methods. The OCPFE method is shown to give good results in cases where standard Galerkin FE fail, and to facilitate the investigation of scattering and dissipation effects.

Concerning the Development of the Wide-Field Optics for WFXT Including Methods of Optimizing X-Ray Optical Prescriptions for Wide-Field Applications

NASA Technical Reports Server (NTRS)

Weisskopf, M. C.; Elsner, R. F.; O'Dell, S. L.; Ramsey, B. D.

2010-01-01

We present a progress report on the various endeavors we are undertaking at MSFC in support of the Wide Field X-Ray Telescope development. In particular we discuss assembly and alignment techniques, in-situ polishing corrections, and the results of our efforts to optimize mirror prescriptions including polynomial coefficients, relative shell displacements, detector placements and tilts. This optimization does not require a blind search through the multi-dimensional parameter space. Under the assumption that the parameters are small enough so that second order expansions are valid, we show that the performance at the detector can be expressed as a quadratic function with numerical coefficients derived from a ray trace through the underlying Wolter I optic. The optimal values for the parameters are found by solving the linear system of equations creating by setting derivatives of this function with respect to each parameter to zero.

Analysis of the Hessian for Aerodynamic Optimization: Inviscid Flow

NASA Technical Reports Server (NTRS)

Arian, Eyal; Ta'asan, Shlomo

1996-01-01

In this paper we analyze inviscid aerodynamic shape optimization problems governed by the full potential and the Euler equations in two and three dimensions. The analysis indicates that minimization of pressure dependent cost functions results in Hessians whose eigenvalue distributions are identical for the full potential and the Euler equations. However the optimization problems in two and three dimensions are inherently different. While the two dimensional optimization problems are well-posed the three dimensional ones are ill-posed. Oscillations in the shape up to the smallest scale allowed by the design space can develop in the direction perpendicular to the flow, implying that a regularization is required. A natural choice of such a regularization is derived. The analysis also gives an estimate of the Hessian's condition number which implies that the problems at hand are ill-conditioned. Infinite dimensional approximations for the Hessians are constructed and preconditioners for gradient based methods are derived from these approximate Hessians.

Derivative Trade Optimizing Model Utilizing GP Based on Behavioral Finance Theory

NASA Astrophysics Data System (ADS)

Matsumura, Koki; Kawamoto, Masaru

This paper proposed a new technique which makes the strategy trees for the derivative (option) trading investment decision based on the behavioral finance theory and optimizes it using evolutionary computation, in order to achieve high profitability. The strategy tree uses a technical analysis based on a statistical, experienced technique for the investment decision. The trading model is represented by various technical indexes, and the strategy tree is optimized by the genetic programming(GP) which is one of the evolutionary computations. Moreover, this paper proposed a method using the prospect theory based on the behavioral finance theory to set psychological bias for profit and deficit and attempted to select the appropriate strike price of option for the higher investment efficiency. As a result, this technique produced a good result and found the effectiveness of this trading model by the optimized dealings strategy.

Optimization of complex slater-type functions with analytic derivative methods for describing photoionization differential cross sections.

PubMed

Matsuzaki, Rei; Yabushita, Satoshi

2017-05-05

The complex basis function (CBF) method applied to various atomic and molecular photoionization problems can be interpreted as an L2 method to solve the driven-type (inhomogeneous) Schrödinger equation, whose driven term being dipole operator times the initial state wave function. However, efficient basis functions for representing the solution have not fully been studied. Moreover, the relation between their solution and that of the ordinary Schrödinger equation has been unclear. For these reasons, most previous applications have been limited to total cross sections. To examine the applicability of the CBF method to differential cross sections and asymmetry parameters, we show that the complex valued solution to the driven-type Schrödinger equation can be variationally obtained by optimizing the complex trial functions for the frequency dependent polarizability. In the test calculations made for the hydrogen photoionization problem with five or six complex Slater-type orbitals (cSTOs), their complex valued expansion coefficients and the orbital exponents have been optimized with the analytic derivative method. Both the real and imaginary parts of the solution have been obtained accurately in a wide region covering typical molecular regions. Their phase shifts and asymmetry parameters are successfully obtained by extrapolating the CBF solution from the inner matching region to the asymptotic region using WKB method. The distribution of the optimized orbital exponents in the complex plane is explained based on the close connection between the CBF method and the driven-type equation method. The obtained information is essential to constructing the appropriate basis sets in future molecular applications. © 2017 Wiley Periodicals, Inc. © 2017 Wiley Periodicals, Inc.

The method of A-harmonic approximation and optimal interior partial regularity for nonlinear elliptic systems under the controllable growth condition

NASA Astrophysics Data System (ADS)

Chen, Shuhong; Tan, Zhong

2007-11-01

In this paper, we consider the nonlinear elliptic systems under controllable growth condition. We use a new method introduced by Duzaar and Grotowski, for proving partial regularity for weak solutions, based on a generalization of the technique of harmonic approximation. We extend previous partial regularity results under the natural growth condition to the case of the controllable growth condition, and directly establishing the optimal Hölder exponent for the derivative of a weak solution.

A knowledge-based approach to improving optimization techniques in system planning

NASA Technical Reports Server (NTRS)

Momoh, J. A.; Zhang, Z. Z.

1990-01-01

A knowledge-based (KB) approach to improve mathematical programming techniques used in the system planning environment is presented. The KB system assists in selecting appropriate optimization algorithms, objective functions, constraints and parameters. The scheme is implemented by integrating symbolic computation of rules derived from operator and planner's experience and is used for generalized optimization packages. The KB optimization software package is capable of improving the overall planning process which includes correction of given violations. The method was demonstrated on a large scale power system discussed in the paper.

Manual of phosphoric acid fuel cell power plant optimization model and computer program

NASA Technical Reports Server (NTRS)

Lu, C. Y.; Alkasab, K. A.

1984-01-01

An optimized cost and performance model for a phosphoric acid fuel cell power plant system was derived and developed into a modular FORTRAN computer code. Cost, energy, mass, and electrochemical analyses were combined to develop a mathematical model for optimizing the steam to methane ratio in the reformer, hydrogen utilization in the PAFC plates per stack. The nonlinear programming code, COMPUTE, was used to solve this model, in which the method of mixed penalty function combined with Hooke and Jeeves pattern search was chosen to evaluate this specific optimization problem.

Flight instrument and telemetry response and its inversion

NASA Technical Reports Server (NTRS)

Weinberger, M. R.

1971-01-01

Mathematical models of rate gyros, servo accelerometers, pressure transducers, and telemetry systems were derived and their parameters were obtained from laboratory tests. Analog computer simulations were used extensively for verification of the validity for fast and large input signals. An optimal inversion method was derived to reconstruct input signals from noisy output signals and a computer program was prepared.

Fisher classifier and its probability of error estimation

NASA Technical Reports Server (NTRS)

Chittineni, C. B.

1979-01-01

Computationally efficient expressions are derived for estimating the probability of error using the leave-one-out method. The optimal threshold for the classification of patterns projected onto Fisher's direction is derived. A simple generalization of the Fisher classifier to multiple classes is presented. Computational expressions are developed for estimating the probability of error of the multiclass Fisher classifier.

Optimal design and uncertainty quantification in blood flow simulations for congenital heart disease

NASA Astrophysics Data System (ADS)

Marsden, Alison

2009-11-01

Recent work has demonstrated substantial progress in capabilities for patient-specific cardiovascular flow simulations. Recent advances include increasingly complex geometries, physiological flow conditions, and fluid structure interaction. However inputs to these simulations, including medical image data, catheter-derived pressures and material properties, can have significant uncertainties associated with them. For simulations to predict clinically useful and reliable output information, it is necessary to quantify the effects of input uncertainties on outputs of interest. In addition, blood flow simulation tools can now be efficiently coupled to shape optimization algorithms for surgery design applications, and these tools should incorporate uncertainty information. We present a unified framework to systematically and efficient account for uncertainties in simulations using adaptive stochastic collocation. In addition, we present a framework for derivative-free optimization of cardiovascular geometries, and layer these tools to perform optimization under uncertainty. These methods are demonstrated using simulations and surgery optimization to improve hemodynamics in pediatric cardiology applications.

Photoinjector optimization using a derivative-free, model-based trust-region algorithm for the Argonne Wakefield Accelerator

NASA Astrophysics Data System (ADS)

Neveu, N.; Larson, J.; Power, J. G.; Spentzouris, L.

2017-07-01

Model-based, derivative-free, trust-region algorithms are increasingly popular for optimizing computationally expensive numerical simulations. A strength of such methods is their efficient use of function evaluations. In this paper, we use one such algorithm to optimize the beam dynamics in two cases of interest at the Argonne Wakefield Accelerator (AWA) facility. First, we minimize the emittance of a 1 nC electron bunch produced by the AWA rf photocathode gun by adjusting three parameters: rf gun phase, solenoid strength, and laser radius. The algorithm converges to a set of parameters that yield an emittance of 1.08 μm. Second, we expand the number of optimization parameters to model the complete AWA rf photoinjector (the gun and six accelerating cavities) at 40 nC. The optimization algorithm is used in a Pareto study that compares the trade-off between emittance and bunch length for the AWA 70MeV photoinjector.

Optimum Installation of Sorptive Building Materials Using Contribution Ratio of Pollution Source for Improvement of Indoor Air Quality.

PubMed

Park, Seonghyun; Seo, Janghoo

2016-04-01

Reinforcing the insulation and airtightness of buildings and the use of building materials containing new chemical substances have caused indoor air quality problems. Use of sorptive building materials along with removal of pollutants, constant ventilation, bake-out, etc. are gaining attention in Korea and Japan as methods for improving such indoor air quality problems. On the other hand, sorptive building materials are considered a passive method of reducing the concentration of pollutants, and their application should be reviewed in the early stages. Thus, in this research, activated carbon was prepared as a sorptive building material. Then, computational fluid dynamics (CFD) was conducted, and a method for optimal installation of sorptive building materials was derived according to the indoor environment using the contribution ratio of pollution source (CRP) index. The results show that a method for optimal installation of sorptive building materials can be derived by predicting the contribution ratio of pollutant sources according to the CRP index.

A parallel Jacobson-Oksman optimization algorithm. [parallel processing (computers)

NASA Technical Reports Server (NTRS)

Straeter, T. A.; Markos, A. T.

1975-01-01

A gradient-dependent optimization technique which exploits the vector-streaming or parallel-computing capabilities of some modern computers is presented. The algorithm, derived by assuming that the function to be minimized is homogeneous, is a modification of the Jacobson-Oksman serial minimization method. In addition to describing the algorithm, conditions insuring the convergence of the iterates of the algorithm and the results of numerical experiments on a group of sample test functions are presented. The results of these experiments indicate that this algorithm will solve optimization problems in less computing time than conventional serial methods on machines having vector-streaming or parallel-computing capabilities.

Optimal control strategy for an impulsive stochastic competition system with time delays and jumps

NASA Astrophysics Data System (ADS)

Liu, Lidan; Meng, Xinzhu; Zhang, Tonghua

2017-07-01

Driven by both white and jump noises, a stochastic delayed model with two competitive species in a polluted environment is proposed and investigated. By using the comparison theorem of stochastic differential equations and limit superior theory, sufficient conditions for persistence in mean and extinction of two species are established. In addition, we obtain that the system is asymptotically stable in distribution by using ergodic method. Furthermore, the optimal harvesting effort and the maximum of expectation of sustainable yield (ESY) are derived from Hessian matrix method and optimal harvesting theory of differential equations. Finally, some numerical simulations are provided to illustrate the theoretical results.

Design of optimally normal minimum gain controllers by continuation method

NASA Technical Reports Server (NTRS)

Lim, K. B.; Juang, J.-N.; Kim, Z. C.

1989-01-01

A measure of the departure from normality is investigated for system robustness. An attractive feature of the normality index is its simplicity for pole placement designs. To allow a tradeoff between system robustness and control effort, a cost function consisting of the sum of a norm of weighted gain matrix and a normality index is minimized. First- and second-order necessary conditions for the constrained optimization problem are derived and solved by a Newton-Raphson algorithm imbedded into a one-parameter family of neighboring zero problems. The method presented allows the direct computation of optimal gains in terms of robustness and control effort for pole placement problems.

The Mimetic Finite Element Method and the Virtual Element Method for elliptic problems with arbitrary regularity.

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

Manzini, Gianmarco

2012-07-13

We develop and analyze a new family of virtual element methods on unstructured polygonal meshes for the diffusion problem in primal form, that use arbitrarily regular discrete spaces V{sub h} {contained_in} C{sup {alpha}} {element_of} N. The degrees of freedom are (a) solution and derivative values of various degree at suitable nodes and (b) solution moments inside polygons. The convergence of the method is proven theoretically and an optimal error estimate is derived. The connection with the Mimetic Finite Difference method is also discussed. Numerical experiments confirm the convergence rate that is expected from the theory.

A weak Hamiltonian finite element method for optimal control problems

NASA Technical Reports Server (NTRS)

Hodges, Dewey H.; Bless, Robert R.

1989-01-01

A temporal finite element method based on a mixed form of the Hamiltonian weak principle is developed for dynamics and optimal control problems. The mixed form of Hamilton's weak principle contains both displacements and momenta as primary variables that are expanded in terms of nodal values and simple polynomial shape functions. Unlike other forms of Hamilton's principle, however, time derivatives of the momenta and displacements do not appear therein; instead, only the virtual momenta and virtual displacements are differentiated with respect to time. Based on the duality that is observed to exist between the mixed form of Hamilton's weak principle and variational principles governing classical optimal control problems, a temporal finite element formulation of the latter can be developed in a rather straightforward manner. Several well-known problems in dynamics and optimal control are illustrated. The example dynamics problem involves a time-marching problem. As optimal control examples, elementary trajectory optimization problems are treated.

A weak Hamiltonian finite element method for optimal control problems

NASA Technical Reports Server (NTRS)

Hodges, Dewey H.; Bless, Robert R.

1990-01-01

A temporal finite element method based on a mixed form of the Hamiltonian weak principle is developed for dynamics and optimal control problems. The mixed form of Hamilton's weak principle contains both displacements and momenta as primary variables that are expanded in terms of nodal values and simple polynomial shape functions. Unlike other forms of Hamilton's principle, however, time derivatives of the momenta and displacements do not appear therein; instead, only the virtual momenta and virtual displacements are differentiated with respect to time. Based on the duality that is observed to exist between the mixed form of Hamilton's weak principle and variational principles governing classical optimal control problems, a temporal finite element formulation of the latter can be developed in a rather straightforward manner. Several well-known problems in dynamics and optimal control are illustrated. The example dynamics problem involves a time-marching problem. As optimal control examples, elementary trajectory optimization problems are treated.

Weak Hamiltonian finite element method for optimal control problems

NASA Technical Reports Server (NTRS)

Hodges, Dewey H.; Bless, Robert R.

1991-01-01

A temporal finite element method based on a mixed form of the Hamiltonian weak principle is developed for dynamics and optimal control problems. The mixed form of Hamilton's weak principle contains both displacements and momenta as primary variables that are expanded in terms of nodal values and simple polynomial shape functions. Unlike other forms of Hamilton's principle, however, time derivatives of the momenta and displacements do not appear therein; instead, only the virtual momenta and virtual displacements are differentiated with respect to time. Based on the duality that is observed to exist between the mixed form of Hamilton's weak principle and variational principles governing classical optimal control problems, a temporal finite element formulation of the latter can be developed in a rather straightforward manner. Several well-known problems in dynamics and optimal control are illustrated. The example dynamics problem involves a time-marching problem. As optimal control examples, elementary trajectory optimization problems are treated.

A trust region approach with multivariate Padé model for optimal circuit design

NASA Astrophysics Data System (ADS)

Abdel-Malek, Hany L.; Ebid, Shaimaa E. K.; Mohamed, Ahmed S. A.

2017-11-01

Since the optimization process requires a significant number of consecutive function evaluations, it is recommended to replace the function by an easily evaluated approximation model during the optimization process. The model suggested in this article is based on a multivariate Padé approximation. This model is constructed using data points of ?, where ? is the number of parameters. The model is updated over a sequence of trust regions. This model avoids the slow convergence of linear models of ? and has features of quadratic models that need interpolation data points of ?. The proposed approach is tested by applying it to several benchmark problems. Yield optimization using such a direct method is applied to some practical circuit examples. Minimax solution leads to a suitable initial point to carry out the yield optimization process. The yield is optimized by the proposed derivative-free method for active and passive filter examples.

The art of spacecraft design: A multidisciplinary challenge

NASA Technical Reports Server (NTRS)

Abdi, F.; Ide, H.; Levine, M.; Austel, L.

1989-01-01

Actual design turn-around time has become shorter due to the use of optimization techniques which have been introduced into the design process. It seems that what, how and when to use these optimization techniques may be the key factor for future aircraft engineering operations. Another important aspect of this technique is that complex physical phenomena can be modeled by a simple mathematical equation. The new powerful multilevel methodology reduces time-consuming analysis significantly while maintaining the coupling effects. This simultaneous analysis method stems from the implicit function theorem and system sensitivity derivatives of input variables. Use of the Taylor's series expansion and finite differencing technique for sensitivity derivatives in each discipline makes this approach unique for screening dominant variables from nondominant variables. In this study, the current Computational Fluid Dynamics (CFD) aerodynamic and sensitivity derivative/optimization techniques are applied for a simple cone-type forebody of a high-speed vehicle configuration to understand basic aerodynamic/structure interaction in a hypersonic flight condition.

Automated Calibration For Numerical Models Of Riverflow

NASA Astrophysics Data System (ADS)

Fernandez, Betsaida; Kopmann, Rebekka; Oladyshkin, Sergey

2017-04-01

Calibration of numerical models is fundamental since the beginning of all types of hydro system modeling, to approximate the parameters that can mimic the overall system behavior. Thus, an assessment of different deterministic and stochastic optimization methods is undertaken to compare their robustness, computational feasibility, and global search capacity. Also, the uncertainty of the most suitable methods is analyzed. These optimization methods minimize the objective function that comprises synthetic measurements and simulated data. Synthetic measurement data replace the observed data set to guarantee an existing parameter solution. The input data for the objective function derivate from a hydro-morphological dynamics numerical model which represents an 180-degree bend channel. The hydro- morphological numerical model shows a high level of ill-posedness in the mathematical problem. The minimization of the objective function by different candidate methods for optimization indicates a failure in some of the gradient-based methods as Newton Conjugated and BFGS. Others reveal partial convergence, such as Nelder-Mead, Polak und Ribieri, L-BFGS-B, Truncated Newton Conjugated, and Trust-Region Newton Conjugated Gradient. Further ones indicate parameter solutions that range outside the physical limits, such as Levenberg-Marquardt and LeastSquareRoot. Moreover, there is a significant computational demand for genetic optimization methods, such as Differential Evolution and Basin-Hopping, as well as for Brute Force methods. The Deterministic Sequential Least Square Programming and the scholastic Bayes Inference theory methods present the optimal optimization results. keywords: Automated calibration of hydro-morphological dynamic numerical model, Bayesian inference theory, deterministic optimization methods.

Maximally Informative Stimuli and Tuning Curves for Sigmoidal Rate-Coding Neurons and Populations

NASA Astrophysics Data System (ADS)

McDonnell, Mark D.; Stocks, Nigel G.

2008-08-01

A general method for deriving maximally informative sigmoidal tuning curves for neural systems with small normalized variability is presented. The optimal tuning curve is a nonlinear function of the cumulative distribution function of the stimulus and depends on the mean-variance relationship of the neural system. The derivation is based on a known relationship between Shannon’s mutual information and Fisher information, and the optimality of Jeffrey’s prior. It relies on the existence of closed-form solutions to the converse problem of optimizing the stimulus distribution for a given tuning curve. It is shown that maximum mutual information corresponds to constant Fisher information only if the stimulus is uniformly distributed. As an example, the case of sub-Poisson binomial firing statistics is analyzed in detail.

Time optimal control of a jet engine using a quasi-Hermite interpolation model. M.S. Thesis

NASA Technical Reports Server (NTRS)

Comiskey, J. G.

1979-01-01

This work made preliminary efforts to generate nonlinear numerical models of a two-spooled turbofan jet engine, and subject these models to a known method of generating global, nonlinear, time optimal control laws. The models were derived numerically, directly from empirical data, as a first step in developing an automatic modelling procedure.

Optimized Hypernetted-Chain Solutions for Helium -4 Surfaces and Metal Surfaces

NASA Astrophysics Data System (ADS)

Qian, Guo-Xin

This thesis is a study of inhomogeneous Bose systems such as liquid ('4)He slabs and inhomogeneous Fermi systems such as the electron gas in metal films, at zero temperature. Using a Jastrow-type many-body wavefunction, the ground state energy is expressed by means of Bogoliubov-Born-Green-Kirkwood -Yvon and Hypernetted-Chain techniques. For Bose systems, Euler-Lagrange equations are derived for the one- and two -body functions and systematic approximation methods are physically motivated. It is shown that the optimized variational method includes a self-consistent summation of ladder- and ring-diagrams of conventional many-body theory. For Fermi systems, a linear potential model is adopted to generate the optimized Hartree-Fock basis. Euler-Lagrange equations are derived for the two-body correlations which serve to screen the strong bare Coulomb interaction. The optimization of the pair correlation leads to an expression of correlation energy in which the state averaged RPA part is separated. Numerical applications are presented for the density profile and pair distribution function for both ('4)He surfaces and metal surfaces. Both the bulk and surface energies are calculated in good agreement with experiments.

Fusion of Optimized Indicators from Advanced Driver Assistance Systems (ADAS) for Driver Drowsiness Detection

PubMed Central

Daza, Iván G.; Bergasa, Luis M.; Bronte, Sebastián; Yebes, J. Javier; Almazán, Javier; Arroyo, Roberto

2014-01-01

This paper presents a non-intrusive approach for monitoring driver drowsiness using the fusion of several optimized indicators based on driver physical and driving performance measures, obtained from ADAS (Advanced Driver Assistant Systems) in simulated conditions. The paper is focused on real-time drowsiness detection technology rather than on long-term sleep/awake regulation prediction technology. We have developed our own vision system in order to obtain robust and optimized driver indicators able to be used in simulators and future real environments. These indicators are principally based on driver physical and driving performance skills. The fusion of several indicators, proposed in the literature, is evaluated using a neural network and a stochastic optimization method to obtain the best combination. We propose a new method for ground-truth generation based on a supervised Karolinska Sleepiness Scale (KSS). An extensive evaluation of indicators, derived from trials over a third generation simulator with several test subjects during different driving sessions, was performed. The main conclusions about the performance of single indicators and the best combinations of them are included, as well as the future works derived from this study. PMID:24412904

Reinforcement-Learning-Based Robust Controller Design for Continuous-Time Uncertain Nonlinear Systems Subject to Input Constraints.

PubMed

Liu, Derong; Yang, Xiong; Wang, Ding; Wei, Qinglai

2015-07-01

The design of stabilizing controller for uncertain nonlinear systems with control constraints is a challenging problem. The constrained-input coupled with the inability to identify accurately the uncertainties motivates the design of stabilizing controller based on reinforcement-learning (RL) methods. In this paper, a novel RL-based robust adaptive control algorithm is developed for a class of continuous-time uncertain nonlinear systems subject to input constraints. The robust control problem is converted to the constrained optimal control problem with appropriately selecting value functions for the nominal system. Distinct from typical action-critic dual networks employed in RL, only one critic neural network (NN) is constructed to derive the approximate optimal control. Meanwhile, unlike initial stabilizing control often indispensable in RL, there is no special requirement imposed on the initial control. By utilizing Lyapunov's direct method, the closed-loop optimal control system and the estimated weights of the critic NN are proved to be uniformly ultimately bounded. In addition, the derived approximate optimal control is verified to guarantee the uncertain nonlinear system to be stable in the sense of uniform ultimate boundedness. Two simulation examples are provided to illustrate the effectiveness and applicability of the present approach.

Progress in navigation filter estimate fusion and its application to spacecraft rendezvous

NASA Technical Reports Server (NTRS)

Carpenter, J. Russell

1994-01-01

A new derivation of an algorithm which fuses the outputs of two Kalman filters is presented within the context of previous research in this field. Unlike other works, this derivation clearly shows the combination of estimates to be optimal, minimizing the trace of the fused covariance matrix. The algorithm assumes that the filters use identical models, and are stable and operating optimally with respect to their own local measurements. Evidence is presented which indicates that the error ellipsoid derived from the covariance of the optimally fused estimate is contained within the intersections of the error ellipsoids of the two filters being fused. Modifications which reduce the algorithm's data transmission requirements are also presented, including a scalar gain approximation, a cross-covariance update formula which employs only the two contributing filters' autocovariances, and a form of the algorithm which can be used to reinitialize the two Kalman filters. A sufficient condition for using the optimally fused estimates to periodically reinitialize the Kalman filters in this fashion is presented and proved as a theorem. When these results are applied to an optimal spacecraft rendezvous problem, simulated performance results indicate that the use of optimally fused data leads to significantly improved robustness to initial target vehicle state errors. The following applications of estimate fusion methods to spacecraft rendezvous are also described: state vector differencing, and redundancy management.

A Test of Genetic Algorithms in Relevance Feedback.

ERIC Educational Resources Information Center

Lopez-Pujalte, Cristina; Guerrero Bote, Vicente P.; Moya Anegon, Felix de

2002-01-01

Discussion of information retrieval, query optimization techniques, and relevance feedback focuses on genetic algorithms, which are derived from artificial intelligence techniques. Describes an evaluation of different genetic algorithms using a residual collection method and compares results with the Ide dec-hi method (Salton and Buckley, 1990…

Estimating irrigation water demand using an improved method and optimizing reservoir operation for water supply and hydropower generation: a case study of the Xinfengjiang reservoir in southern China

USGS Publications Warehouse

Wu, Yiping; Chen, Ji

2013-01-01

The ever-increasing demand for water due to growth of population and socioeconomic development in the past several decades has posed a worldwide threat to water supply security and to the environmental health of rivers. This study aims to derive reservoir operating rules through establishing a multi-objective optimization model for the Xinfengjiang (XFJ) reservoir in the East River Basin in southern China to minimize water supply deficit and maximize hydropower generation. Additionally, to enhance the estimation of irrigation water demand from the downstream agricultural area of the XFJ reservoir, a conventional method for calculating crop water demand is improved using hydrological model simulation results. Although the optimal reservoir operating rules are derived for the XFJ reservoir with three priority scenarios (water supply only, hydropower generation only, and equal priority), the river environmental health is set as the basic demand no matter which scenario is adopted. The results show that the new rules derived under the three scenarios can improve the reservoir operation for both water supply and hydropower generation when comparing to the historical performance. Moreover, these alternative reservoir operating policies provide the flexibility for the reservoir authority to choose the most appropriate one. Although changing the current operating rules may influence its hydropower-oriented functions, the new rules can be significant to cope with the increasingly prominent water shortage and degradation in the aquatic environment. Overall, our results and methods (improved estimation of irrigation water demand and formulation of the reservoir optimization model) can be useful for local watershed managers and valuable for other researchers worldwide.

Shape design sensitivity analysis and optimal design of structural systems

NASA Technical Reports Server (NTRS)

Choi, Kyung K.

1987-01-01

The material derivative concept of continuum mechanics and an adjoint variable method of design sensitivity analysis are used to relate variations in structural shape to measures of structural performance. A domain method of shape design sensitivity analysis is used to best utilize the basic character of the finite element method that gives accurate information not on the boundary but in the domain. Implementation of shape design sensitivty analysis using finite element computer codes is discussed. Recent numerical results are used to demonstrate the accuracy obtainable using the method. Result of design sensitivity analysis is used to carry out design optimization of a built-up structure.

General method for extracting the quantum efficiency of dispersive qubit readout in circuit QED

NASA Astrophysics Data System (ADS)

Bultink, C. C.; Tarasinski, B.; Haandbæk, N.; Poletto, S.; Haider, N.; Michalak, D. J.; Bruno, A.; DiCarlo, L.

2018-02-01

We present and demonstrate a general three-step method for extracting the quantum efficiency of dispersive qubit readout in circuit QED. We use active depletion of post-measurement photons and optimal integration weight functions on two quadratures to maximize the signal-to-noise ratio of the non-steady-state homodyne measurement. We derive analytically and demonstrate experimentally that the method robustly extracts the quantum efficiency for arbitrary readout conditions in the linear regime. We use the proven method to optimally bias a Josephson traveling-wave parametric amplifier and to quantify different noise contributions in the readout amplification chain.

A comparison of different methods to implement higher order derivatives of density functionals

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

van Dam, Hubertus J.J.

Density functional theory is the dominant approach in electronic structure methods today. To calculate properties higher order derivatives of the density functionals are required. These derivatives might be implemented manually,by automatic differentiation, or by symbolic algebra programs. Different authors have cited different reasons for using the particular method of their choice. This paper presents work where all three approaches were used and the strengths and weaknesses of each approach are considered. It is found that all three methods produce code that is suffficiently performanted for practical applications, despite the fact that our symbolic algebra generated code and our automatic differentiationmore » code still have scope for significant optimization. The automatic differentiation approach is the best option for producing readable and maintainable code.« less

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.

The Transcorrelated Method Combined with the Variational Monte Carlo Calculation: Application to Atoms

NASA Astrophysics Data System (ADS)

Umezawa, Naoto; Tsuneyuki, Shinji; Ohno, Takahisa; Shiraishi, Kenji; Chikyow, Toyohiro

2005-03-01

The transcorrelated (TC) method is a useful approach to optimize the Jastrow-Slater-type many-body wave function FD. The basic idea of the TC method [1] is based on the similarity transformation of a many-body Hamiltonian H with respect to the Jastrow factor F: HTC=frac1F H F in order to incorporate the correlation effect into HTC. Both the F and D are optimized by minimizing the variance ^2=|Hrm TCD - E D |^2 d^3N x. The optimization for F is implemented by the variational Monte Carlo calculation, and D is determined by the TC self-consistent-field equation for the one-body wave functions φμ(x), which is derived from the functional derivative of ^2 with respect to φmu(x). In this talk, we will present the results given by the transcorrelated variational Monte Carlo (TC-VMC) method for the ground state [2] and the excited states of atoms [3]. [1]S. F. Boys and N. C. Handy, Proc. Roy. Soc. A, 309, 209; 310, 43; 310, 63; 311, 309 (1969). [2]N. Umezawa and S. Tsuneyuki, J. Chem. Phys. 119, 10015 (2003). [3]N. Umezawa and S. Tsuneyuki, J. Chem. Phys. 121, 7070 (2004).

Optimization of acidic extraction of astaxanthin from Phaffia rhodozyma *

PubMed Central

Ni, Hui; Chen, Qi-he; He, Guo-qing; Wu, Guang-bin; Yang, Yuan-fan

2008-01-01

Optimization of a process for extracting astaxanthin from Phaffia rhodozyma by acidic method was investigated, regarding several extraction factors such as acids, organic solvents, temperature and time. Fractional factorial design, central composite design and response surface methodology were used to derive a statistically optimal model, which corresponded to the following optimal condition: concentration of lactic acid at 5.55 mol/L, ratio of ethanol to yeast dry weight at 20.25 ml/g, temperature for cell-disruption at 30 °C, and extraction time for 3 min. Under this condition, astaxanthin and the total carotenoids could be extracted in amounts of 1294.7 μg/g and 1516.0 μg/g, respectively. This acidic method has advantages such as high extraction efficiency, low chemical toxicity and no special requirement of instruments. Therefore, it might be a more feasible and practical method for industrial practice. PMID:18196613

Multilevel algorithms for nonlinear optimization

NASA Technical Reports Server (NTRS)

Alexandrov, Natalia; Dennis, J. E., Jr.

1994-01-01

Multidisciplinary design optimization (MDO) gives rise to nonlinear optimization problems characterized by a large number of constraints that naturally occur in blocks. We propose a class of multilevel optimization methods motivated by the structure and number of constraints and by the expense of the derivative computations for MDO. The algorithms are an extension to the nonlinear programming problem of the successful class of local Brown-Brent algorithms for nonlinear equations. Our extensions allow the user to partition constraints into arbitrary blocks to fit the application, and they separately process each block and the objective function, restricted to certain subspaces. The methods use trust regions as a globalization strategy, and they have been shown to be globally convergent under reasonable assumptions. The multilevel algorithms can be applied to all classes of MDO formulations. Multilevel algorithms for solving nonlinear systems of equations are a special case of the multilevel optimization methods. In this case, they can be viewed as a trust-region globalization of the Brown-Brent class.

Graphene-sensitized microporous membrane/solvent microextraction for the preconcentration of cinnamic acid derivatives in Rhizoma Typhonii.

PubMed

Xing, Rongrong; Hu, Shuang; Chen, Xuan; Bai, Xiaohong

2014-09-01

A novel graphene-sensitized microporous membrane/solvent microextraction method named microporous membrane/graphene/solvent synergistic microextraction, coupled with high-performance liquid chromatography and UV detection, was developed and introduced for the extraction and determination of three cinnamic acid derivatives in Rhizoma Typhonii. Several factors affecting performance were investigated and optimized, including the types of graphene and extraction solvent, concentration of graphene dispersed in octanol, sample phase pH, ionic strength, stirring rate, extraction time, extraction temperature, and sample volume. Under optimized conditions, the enrichment factors of cinnamic acid derivatives ranged from 75 to 269. Good linearities were obtained from 0.01 to 10 μg/mL for all analytes with regression coefficients between 0.9927 and 0.9994. The limits of quantification were <1 ng/mL, and satisfactory recoveries (99-104%) and precision (1.1-10.8%) were also achieved. The synergistic microextraction mechanism based on graphene sensitization was analyzed and described. The experimental results showed that the method was simple, sensitive, practical, and effective for the preconcentration and determination of cinnamic acid derivatives in Rhizoma Typhonii. © 2014 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim.

A new family of high-order compact upwind difference schemes with good spectral resolution

NASA Astrophysics Data System (ADS)

Zhou, Qiang; Yao, Zhaohui; He, Feng; Shen, M. Y.

2007-12-01

This paper presents a new family of high-order compact upwind difference schemes. Unknowns included in the proposed schemes are not only the values of the function but also those of its first and higher derivatives. Derivative terms in the schemes appear only on the upwind side of the stencil. One can calculate all the first derivatives exactly as one solves explicit schemes when the boundary conditions of the problem are non-periodic. When the proposed schemes are applied to periodic problems, only periodic bi-diagonal matrix inversions or periodic block-bi-diagonal matrix inversions are required. Resolution optimization is used to enhance the spectral representation of the first derivative, and this produces a scheme with the highest spectral accuracy among all known compact schemes. For non-periodic boundary conditions, boundary schemes constructed in virtue of the assistant scheme make the schemes not only possess stability for any selective length scale on every point in the computational domain but also satisfy the principle of optimal resolution. Also, an improved shock-capturing method is developed. Finally, both the effectiveness of the new hybrid method and the accuracy of the proposed schemes are verified by executing four benchmark test cases.

Methods of Optimizing X-Ray Optical Prescriptions for Wide-Field Applications

NASA Technical Reports Server (NTRS)

Elsner, R. F.; O'Dell, S. L.; Ramsey, B. D.; Weisskopf, M. C.

2010-01-01

We are working on the development of a method for optimizing wide-field x-ray telescope mirror prescriptions, including polynomial coefficients, mirror shell relative displacements, and (assuming 4 focal plane detectors) detector placement and tilt that does not require a search through the multi-dimensional parameter space. Under the assumption that the parameters are small enough that second order expansions are valid, we show that the performance at the detector surface can be expressed as a quadratic function of the parameters with numerical coefficients derived from a ray trace through the underlying Wolter I optic. The best values for the parameters are found by solving the linear system of equations creating by setting derivatives of this function with respect to each parameter to zero. We describe the present status of this development effort.

Strain and culture medium optimization for production enhancement of prodiginines from marine-derived Streptomyces sp. GQQ-10

NASA Astrophysics Data System (ADS)

Li, Xueping; Zhang, Guojian; Zhu, Tianjiao; Li, Dehai; Gu, Qianqun

2012-09-01

A mutant (GQQ-M6) of a Sponge-Derived streptomyces sp. GQQ-10 obtained by UV-induced mutation was used for producing prodiginines (PGs). Single factor experiments and orthogonal array design (OAD) methods were employed for medium optimization. In the single factor method, the effects of soluble starch, glucose, soybean flour, yeast extract and sodium acetate on PGs production were investigated individually. In the subsequent OAD experiments, the concentrations of these 5 key nutritional components combined with salinity were further adjusted. The mutant strain GQQ-M6 gave a 2.2-fold higher PGs production than that of the parent strain; OAD experiments offered a PGs yield of 61mg L-1, which was 10 times higher than that of the initial GQQ-10 strain under the original cultivation mode.

Control design based on a linear state function observer

NASA Technical Reports Server (NTRS)

Su, Tzu-Jeng; Craig, Roy R., Jr.

1992-01-01

An approach to the design of low-order controllers for large scale systems is proposed. The method is derived from the theory of linear state function observers. First, the realization of a state feedback control law is interpreted as the observation of a linear function of the state vector. The linear state function to be reconstructed is the given control law. Then, based on the derivation for linear state function observers, the observer design is formulated as a parameter optimization problem. The optimization objective is to generate a matrix that is close to the given feedback gain matrix. Based on that matrix, the form of the observer and a new control law can be determined. A four-disk system and a lightly damped beam are presented as examples to demonstrate the applicability and efficacy of the proposed method.

Optimization of parameter values for complex pulse sequences by simulated annealing: application to 3D MP-RAGE imaging of the brain.

PubMed

Epstein, F H; Mugler, J P; Brookeman, J R

1994-02-01

A number of pulse sequence techniques, including magnetization-prepared gradient echo (MP-GRE), segmented GRE, and hybrid RARE, employ a relatively large number of variable pulse sequence parameters and acquire the image data during a transient signal evolution. These sequences have recently been proposed and/or used for clinical applications in the brain, spine, liver, and coronary arteries. Thus, the need for a method of deriving optimal pulse sequence parameter values for this class of sequences now exists. Due to the complexity of these sequences, conventional optimization approaches, such as applying differential calculus to signal difference equations, are inadequate. We have developed a general framework for adapting the simulated annealing algorithm to pulse sequence parameter value optimization, and applied this framework to the specific case of optimizing the white matter-gray matter signal difference for a T1-weighted variable flip angle 3D MP-RAGE sequence. Using our algorithm, the values of 35 sequence parameters, including the magnetization-preparation RF pulse flip angle and delay time, 32 flip angles in the variable flip angle gradient-echo acquisition sequence, and the magnetization recovery time, were derived. Optimized 3D MP-RAGE achieved up to a 130% increase in white matter-gray matter signal difference compared with optimized 3D RF-spoiled FLASH with the same total acquisition time. The simulated annealing approach was effective at deriving optimal parameter values for a specific 3D MP-RAGE imaging objective, and may be useful for other imaging objectives and sequences in this general class.

CLFs-based optimization control for a class of constrained visual servoing systems.

PubMed

Song, Xiulan; Miaomiao, Fu

2017-03-01

In this paper, we use the control Lyapunov function (CLF) technique to present an optimized visual servo control method for constrained eye-in-hand robot visual servoing systems. With the knowledge of camera intrinsic parameters and depth of target changes, visual servo control laws (i.e. translation speed) with adjustable parameters are derived by image point features and some known CLF of the visual servoing system. The Fibonacci method is employed to online compute the optimal value of those adjustable parameters, which yields an optimized control law to satisfy constraints of the visual servoing system. The Lyapunov's theorem and the properties of CLF are used to establish stability of the constrained visual servoing system in the closed-loop with the optimized control law. One merit of the presented method is that there is no requirement of online calculating the pseudo-inverse of the image Jacobian's matrix and the homography matrix. Simulation and experimental results illustrated the effectiveness of the method proposed here. Copyright © 2016 ISA. Published by Elsevier Ltd. All rights reserved.

Optimal Mortgage Refinancing: A Closed Form Solution.

PubMed

Agarwal, Sumit; Driscoll, John C; Laibson, David I

2013-06-01

We derive the first closed-form optimal refinancing rule: Refinance when the current mortgage interest rate falls below the original rate by at least [Formula: see text] In this formula W (.) is the Lambert W -function, [Formula: see text] ρ is the real discount rate, λ is the expected real rate of exogenous mortgage repayment, σ is the standard deviation of the mortgage rate, κ/M is the ratio of the tax-adjusted refinancing cost and the remaining mortgage value, and τ is the marginal tax rate. This expression is derived by solving a tractable class of refinancing problems. Our quantitative results closely match those reported by researchers using numerical methods.

Modified harmony search

NASA Astrophysics Data System (ADS)

Mohamed, Najihah; Lutfi Amri Ramli, Ahmad; Majid, Ahmad Abd; Piah, Abd Rahni Mt

2017-09-01

A metaheuristic algorithm, called Harmony Search is quite highly applied in optimizing parameters in many areas. HS is a derivative-free real parameter optimization algorithm, and draws an inspiration from the musical improvisation process of searching for a perfect state of harmony. Propose in this paper Modified Harmony Search for solving optimization problems, which employs a concept from genetic algorithm method and particle swarm optimization for generating new solution vectors that enhances the performance of HS algorithm. The performances of MHS and HS are investigated on ten benchmark optimization problems in order to make a comparison to reflect the efficiency of the MHS in terms of final accuracy, convergence speed and robustness.

Local-in-Time Adjoint-Based Method for Optimal Control/Design Optimization of Unsteady Compressible Flows

NASA Technical Reports Server (NTRS)

Yamaleev, N. K.; Diskin, B.; Nielsen, E. J.

2009-01-01

.We study local-in-time adjoint-based methods for minimization of ow matching functionals subject to the 2-D unsteady compressible Euler equations. The key idea of the local-in-time method is to construct a very accurate approximation of the global-in-time adjoint equations and the corresponding sensitivity derivative by using only local information available on each time subinterval. In contrast to conventional time-dependent adjoint-based optimization methods which require backward-in-time integration of the adjoint equations over the entire time interval, the local-in-time method solves local adjoint equations sequentially over each time subinterval. Since each subinterval contains relatively few time steps, the storage cost of the local-in-time method is much lower than that of the global adjoint formulation, thus making the time-dependent optimization feasible for practical applications. The paper presents a detailed comparison of the local- and global-in-time adjoint-based methods for minimization of a tracking functional governed by the Euler equations describing the ow around a circular bump. Our numerical results show that the local-in-time method converges to the same optimal solution obtained with the global counterpart, while drastically reducing the memory cost as compared to the global-in-time adjoint formulation.

An investigation of using an RQP based method to calculate parameter sensitivity derivatives

NASA Technical Reports Server (NTRS)

Beltracchi, Todd J.; Gabriele, Gary A.

1989-01-01

Estimation of the sensitivity of problem functions with respect to problem variables forms the basis for many of our modern day algorithms for engineering optimization. The most common application of problem sensitivities has been in the calculation of objective function and constraint partial derivatives for determining search directions and optimality conditions. A second form of sensitivity analysis, parameter sensitivity, has also become an important topic in recent years. By parameter sensitivity, researchers refer to the estimation of changes in the modeling functions and current design point due to small changes in the fixed parameters of the formulation. Methods for calculating these derivatives have been proposed by several authors (Armacost and Fiacco 1974, Sobieski et al 1981, Schmit and Chang 1984, and Vanderplaats and Yoshida 1985). Two drawbacks to estimating parameter sensitivities by current methods have been: (1) the need for second order information about the Lagrangian at the current point, and (2) the estimates assume no change in the active set of constraints. The first of these two problems is addressed here and a new algorithm is proposed that does not require explicit calculation of second order information.

Hyperspectral wide gap second derivative analysis for in vivo detection of cervical intraepithelial neoplasia

NASA Astrophysics Data System (ADS)

Zheng, Wenli; Wang, Chaojian; Chang, Shufang; Zhang, Shiwu; Xu, Ronald X.

2015-12-01

Hyperspectral reflectance imaging technique has been used for in vivo detection of cervical intraepithelial neoplasia. However, the clinical outcome of this technique is suboptimal owing to multiple limitations such as nonuniform illumination, high-cost and bulky setup, and time-consuming data acquisition and processing. To overcome these limitations, we acquired the hyperspectral data cube in a wavelength ranging from 600 to 800 nm and processed it by a wide gap second derivative analysis method. This method effectively reduced the image artifacts caused by nonuniform illumination and background absorption. Furthermore, with second derivative analysis, only three specific wavelengths (620, 696, and 772 nm) are needed for tissue classification with optimal separability. Clinical feasibility of the proposed image analysis and classification method was tested in a clinical trial where cervical hyperspectral images from three patients were used for classification analysis. Our proposed method successfully classified the cervix tissue into three categories of normal, inflammation and high-grade lesion. These classification results were coincident with those by an experienced gynecology oncologist after applying acetic acid. Our preliminary clinical study has demonstrated the technical feasibility for in vivo and noninvasive detection of cervical neoplasia without acetic acid. Further clinical research is needed in order to establish a large-scale diagnostic database and optimize the tissue classification technique.

Hyperspectral wide gap second derivative analysis for in vivo detection of cervical intraepithelial neoplasia.

PubMed

Zheng, Wenli; Wang, Chaojian; Chang, Shufang; Zhang, Shiwu; Xu, Ronald X

2015-12-01

Hyperspectral reflectance imaging technique has been used for in vivo detection of cervical intraepithelial neoplasia. However, the clinical outcome of this technique is suboptimal owing to multiple limitations such as nonuniform illumination, high-cost and bulky setup, and time-consuming data acquisition and processing. To overcome these limitations, we acquired the hyperspectral data cube in a wavelength ranging from 600 to 800 nm and processed it by a wide gap second derivative analysis method. This method effectively reduced the image artifacts caused by nonuniform illumination and background absorption. Furthermore, with second derivative analysis, only three specific wavelengths (620, 696, and 772 nm) are needed for tissue classification with optimal separability. Clinical feasibility of the proposed image analysis and classification method was tested in a clinical trial where cervical hyperspectral images from three patients were used for classification analysis. Our proposed method successfully classified the cervix tissue into three categories of normal, inflammation and high-grade lesion. These classification results were coincident with those by an experienced gynecology oncologist after applying acetic acid. Our preliminary clinical study has demonstrated the technical feasibility for in vivo and noninvasive detection of cervical neoplasia without acetic acid. Further clinical research is needed in order to establish a large-scale diagnostic database and optimize the tissue classification technique.

Multi-Objective Programming for Lot-Sizing with Quantity Discount

NASA Astrophysics Data System (ADS)

Kang, He-Yau; Lee, Amy H. I.; Lai, Chun-Mei; Kang, Mei-Sung

2011-11-01

Multi-objective programming (MOP) is one of the popular methods for decision making in a complex environment. In a MOP, decision makers try to optimize two or more objectives simultaneously under various constraints. A complete optimal solution seldom exists, and a Pareto-optimal solution is usually used. Some methods, such as the weighting method which assigns priorities to the objectives and sets aspiration levels for the objectives, are used to derive a compromise solution. The ɛ-constraint method is a modified weight method. One of the objective functions is optimized while the other objective functions are treated as constraints and are incorporated in the constraint part of the model. This research considers a stochastic lot-sizing problem with multi-suppliers and quantity discounts. The model is transformed into a mixed integer programming (MIP) model next based on the ɛ-constraint method. An illustrative example is used to illustrate the practicality of the proposed model. The results demonstrate that the model is an effective and accurate tool for determining the replenishment of a manufacturer from multiple suppliers for multi-periods.

System Sensitivity Analysis Applied to the Conceptual Design of a Dual-Fuel Rocket SSTO

NASA Technical Reports Server (NTRS)

Olds, John R.

1994-01-01

This paper reports the results of initial efforts to apply the System Sensitivity Analysis (SSA) optimization method to the conceptual design of a single-stage-to-orbit (SSTO) launch vehicle. SSA is an efficient, calculus-based MDO technique for generating sensitivity derivatives in a highly multidisciplinary design environment. The method has been successfully applied to conceptual aircraft design and has been proven to have advantages over traditional direct optimization methods. The method is applied to the optimization of an advanced, piloted SSTO design similar to vehicles currently being analyzed by NASA as possible replacements for the Space Shuttle. Powered by a derivative of the Russian RD-701 rocket engine, the vehicle employs a combination of hydrocarbon, hydrogen, and oxygen propellants. Three primary disciplines are included in the design - propulsion, performance, and weights & sizing. A complete, converged vehicle analysis depends on the use of three standalone conceptual analysis computer codes. Efforts to minimize vehicle dry (empty) weight are reported in this paper. The problem consists of six system-level design variables and one system-level constraint. Using SSA in a 'manual' fashion to generate gradient information, six system-level iterations were performed from each of two different starting points. The results showed a good pattern of convergence for both starting points. A discussion of the advantages and disadvantages of the method, possible areas of improvement, and future work is included.

Reconfigurable Model Execution in the OpenMDAO Framework

NASA Technical Reports Server (NTRS)

Hwang, John T.

2017-01-01

NASA's OpenMDAO framework facilitates constructing complex models and computing their derivatives for multidisciplinary design optimization. Decomposing a model into components that follow a prescribed interface enables OpenMDAO to assemble multidisciplinary derivatives from the component derivatives using what amounts to the adjoint method, direct method, chain rule, global sensitivity equations, or any combination thereof, using the MAUD architecture. OpenMDAO also handles the distribution of processors among the disciplines by hierarchically grouping the components, and it automates the data transfer between components that are on different processors. These features have made OpenMDAO useful for applications in aircraft design, satellite design, wind turbine design, and aircraft engine design, among others. This paper presents new algorithms for OpenMDAO that enable reconfigurable model execution. This concept refers to dynamically changing, during execution, one or more of: the variable sizes, solution algorithm, parallel load balancing, or set of variables-i.e., adding and removing components, perhaps to switch to a higher-fidelity sub-model. Any component can reconfigure at any point, even when running in parallel with other components, and the reconfiguration algorithm presented here performs the synchronized updates to all other components that are affected. A reconfigurable software framework for multidisciplinary design optimization enables new adaptive solvers, adaptive parallelization, and new applications such as gradient-based optimization with overset flow solvers and adaptive mesh refinement. Benchmarking results demonstrate the time savings for reconfiguration compared to setting up the model again from scratch, which can be significant in large-scale problems. Additionally, the new reconfigurability feature is applied to a mission profile optimization problem for commercial aircraft where both the parametrization of the mission profile and the time discretization are adaptively refined, resulting in computational savings of roughly 10% and the elimination of oscillations in the optimized altitude profile.

Wet cooling towers: rule-of-thumb design and simulation

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

Leeper, Stephen A.

1981-07-01

A survey of wet cooling tower literature was performed to develop a simplified method of cooling tower design and simulation for use in power plant cycle optimization. The theory of heat exchange in wet cooling towers is briefly summarized. The Merkel equation (the fundamental equation of heat transfer in wet cooling towers) is presented and discussed. The cooling tower fill constant (Ka) is defined and values derived. A rule-of-thumb method for the optimized design of cooling towers is presented. The rule-of-thumb design method provides information useful in power plant cycle optimization, including tower dimensions, water consumption rate, exit air temperature,more » power requirements and construction cost. In addition, a method for simulation of cooling tower performance at various operating conditions is presented. This information is also useful in power plant cycle evaluation. Using the information presented, it will be possible to incorporate wet cooling tower design and simulation into a procedure to evaluate and optimize power plant cycles.« less

WE-FG-207B-05: Iterative Reconstruction Via Prior Image Constrained Total Generalized Variation for Spectral CT

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

Niu, S; Zhang, Y; Ma, J

Purpose: To investigate iterative reconstruction via prior image constrained total generalized variation (PICTGV) for spectral computed tomography (CT) using fewer projections while achieving greater image quality. Methods: The proposed PICTGV method is formulated as an optimization problem, which balances the data fidelity and prior image constrained total generalized variation of reconstructed images in one framework. The PICTGV method is based on structure correlations among images in the energy domain and high-quality images to guide the reconstruction of energy-specific images. In PICTGV method, the high-quality image is reconstructed from all detector-collected X-ray signals and is referred as the broad-spectrum image. Distinctmore » from the existing reconstruction methods applied on the images with first order derivative, the higher order derivative of the images is incorporated into the PICTGV method. An alternating optimization algorithm is used to minimize the PICTGV objective function. We evaluate the performance of PICTGV on noise and artifacts suppressing using phantom studies and compare the method with the conventional filtered back-projection method as well as TGV based method without prior image. Results: On the digital phantom, the proposed method outperforms the existing TGV method in terms of the noise reduction, artifacts suppression, and edge detail preservation. Compared to that obtained by the TGV based method without prior image, the relative root mean square error in the images reconstructed by the proposed method is reduced by over 20%. Conclusion: The authors propose an iterative reconstruction via prior image constrained total generalize variation for spectral CT. Also, we have developed an alternating optimization algorithm and numerically demonstrated the merits of our approach. Results show that the proposed PICTGV method outperforms the TGV method for spectral CT.« less

Extracting TSK-type Neuro-Fuzzy model using the Hunting search algorithm

NASA Astrophysics Data System (ADS)

Bouzaida, Sana; Sakly, Anis; M'Sahli, Faouzi

2014-01-01

This paper proposes a Takagi-Sugeno-Kang (TSK) type Neuro-Fuzzy model tuned by a novel metaheuristic optimization algorithm called Hunting Search (HuS). The HuS algorithm is derived based on a model of group hunting of animals such as lions, wolves, and dolphins when looking for a prey. In this study, the structure and parameters of the fuzzy model are encoded into a particle. Thus, the optimal structure and parameters are achieved simultaneously. The proposed method was demonstrated through modeling and control problems, and the results have been compared with other optimization techniques. The comparisons indicate that the proposed method represents a powerful search approach and an effective optimization technique as it can extract the accurate TSK fuzzy model with an appropriate number of rules.

Parameter estimation of a pulp digester model with derivative-free optimization strategies

NASA Astrophysics Data System (ADS)

Seiça, João C.; Romanenko, Andrey; Fernandes, Florbela P.; Santos, Lino O.; Fernandes, Natércia C. P.

2017-07-01

The work concerns the parameter estimation in the context of the mechanistic modelling of a pulp digester. The problem is cast as a box bounded nonlinear global optimization problem in order to minimize the mismatch between the model outputs with the experimental data observed at a real pulp and paper plant. MCSFilter and Simulated Annealing global optimization methods were used to solve the optimization problem. While the former took longer to converge to the global minimum, the latter terminated faster at a significantly higher value of the objective function and, thus, failed to find the global solution.

A hierarchical transition state search algorithm

NASA Astrophysics Data System (ADS)

del Campo, Jorge M.; Köster, Andreas M.

2008-07-01

A hierarchical transition state search algorithm is developed and its implementation in the density functional theory program deMon2k is described. This search algorithm combines the double ended saddle interpolation method with local uphill trust region optimization. A new formalism for the incorporation of the distance constrain in the saddle interpolation method is derived. The similarities between the constrained optimizations in the local trust region method and the saddle interpolation are highlighted. The saddle interpolation and local uphill trust region optimizations are validated on a test set of 28 representative reactions. The hierarchical transition state search algorithm is applied to an intramolecular Diels-Alder reaction with several internal rotors, which makes automatic transition state search rather challenging. The obtained reaction mechanism is discussed in the context of the experimentally observed product distribution.

Separated-pair independent particle model and the generalized Brillouin theorem: ab initio calculations on the dissociation of polyatomic molecules

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

Sundberg, Kenneth Randall

1976-01-01

A method is developed to optimize the separated-pair independent particle (SPIP) wave function; it is a special case of the separated-pair theory obtained by using two-term natural expansions of the geminals. The orbitals are optimized by a theory based on the generalized Brillouin theorem and iterative configuration interaction (CI) calculations in the space of the SPIP function and its single excitations. The geminal expansion coefficients are optimized by serial 2 x 2 CI calculations. Formulas are derived for the matrix elements. An algorithm to implement the method is presented, and the work needed to evaluate the molecular integrals is discussed.

Attitude determination and parameter estimation using vector observations - Theory

NASA Technical Reports Server (NTRS)

Markley, F. Landis

1989-01-01

Procedures for attitude determination based on Wahba's loss function are generalized to include the estimation of parameters other than the attitude, such as sensor biases. Optimization with respect to the attitude is carried out using the q-method, which does not require an a priori estimate of the attitude. Optimization with respect to the other parameters employs an iterative approach, which does require an a priori estimate of these parameters. Conventional state estimation methods require a priori estimates of both the parameters and the attitude, while the algorithm presented in this paper always computes the exact optimal attitude for given values of the parameters. Expressions for the covariance of the attitude and parameter estimates are derived.

A New Coarsening Operator for the Optimal Preconditioning of the Dual and Primal Domain Decomposition Methods: Application to Problems with Severe Coefficient Jumps

NASA Technical Reports Server (NTRS)

Farhat, Charbel; Rixen, Daniel

1996-01-01

We present an optimal preconditioning algorithm that is equally applicable to the dual (FETI) and primal (Balancing) Schur complement domain decomposition methods, and which successfully addresses the problems of subdomain heterogeneities including the effects of large jumps of coefficients. The proposed preconditioner is derived from energy principles and embeds a new coarsening operator that propagates the error globally and accelerates convergence. The resulting iterative solver is illustrated with the solution of highly heterogeneous elasticity problems.

[Research on spectra recognition method for cabbages and weeds based on PCA and SIMCA].

PubMed

Zu, Qin; Deng, Wei; Wang, Xiu; Zhao, Chun-Jiang

2013-10-01

In order to improve the accuracy and efficiency of weed identification, the difference of spectral reflectance was employed to distinguish between crops and weeds. Firstly, the different combinations of Savitzky-Golay (SG) convolutional derivation and multiplicative scattering correction (MSC) method were applied to preprocess the raw spectral data. Then the clustering analysis of various types of plants was completed by using principal component analysis (PCA) method, and the feature wavelengths which were sensitive for classifying various types of plants were extracted according to the corresponding loading plots of the optimal principal components in PCA results. Finally, setting the feature wavelengths as the input variables, the soft independent modeling of class analogy (SIMCA) classification method was used to identify the various types of plants. The experimental results of classifying cabbages and weeds showed that on the basis of the optimal pretreatment by a synthetic application of MSC and SG convolutional derivation with SG's parameters set as 1rd order derivation, 3th degree polynomial and 51 smoothing points, 23 feature wavelengths were extracted in accordance with the top three principal components in PCA results. When SIMCA method was used for classification while the previously selected 23 feature wavelengths were set as the input variables, the classification rates of the modeling set and the prediction set were respectively up to 98.6% and 100%.

3D CSEM data inversion using Newton and Halley class methods

NASA Astrophysics Data System (ADS)

Amaya, M.; Hansen, K. R.; Morten, J. P.

2016-05-01

For the first time in 3D controlled source electromagnetic data inversion, we explore the use of the Newton and the Halley optimization methods, which may show their potential when the cost function has a complex topology. The inversion is formulated as a constrained nonlinear least-squares problem which is solved by iterative optimization. These methods require the derivatives up to second order of the residuals with respect to model parameters. We show how Green's functions determine the high-order derivatives, and develop a diagrammatical representation of the residual derivatives. The Green's functions are efficiently calculated on-the-fly, making use of a finite-difference frequency-domain forward modelling code based on a multi-frontal sparse direct solver. This allow us to build the second-order derivatives of the residuals keeping the memory cost in the same order as in a Gauss-Newton (GN) scheme. Model updates are computed with a trust-region based conjugate-gradient solver which does not require the computation of a stabilizer. We present inversion results for a synthetic survey and compare the GN, Newton, and super-Halley optimization schemes, and consider two different approaches to set the initial trust-region radius. Our analysis shows that the Newton and super-Halley schemes, using the same regularization configuration, add significant information to the inversion so that the convergence is reached by different paths. In our simple resistivity model examples, the convergence speed of the Newton and the super-Halley schemes are either similar or slightly superior with respect to the convergence speed of the GN scheme, close to the minimum of the cost function. Due to the current noise levels and other measurement inaccuracies in geophysical investigations, this advantageous behaviour is at present of low consequence, but may, with the further improvement of geophysical data acquisition, be an argument for more accurate higher-order methods like those applied in this paper.

Optimal subhourly electricity resource dispatch under multiple price signals with high renewable generation availability

DOE PAGES

Chassin, David P.; Behboodi, Sahand; Djilali, Ned

2018-01-28

This article proposes a system-wide optimal resource dispatch strategy that enables a shift from a primarily energy cost-based approach, to a strategy using simultaneous price signals for energy, power and ramping behavior. A formal method to compute the optimal sub-hourly power trajectory is derived for a system when the price of energy and ramping are both significant. Optimal control functions are obtained in both time and frequency domains, and a discrete-time solution suitable for periodic feedback control systems is presented. The method is applied to North America Western Interconnection for the planning year 2024, and it is shown that anmore » optimal dispatch strategy that simultaneously considers both the cost of energy and the cost of ramping leads to significant cost savings in systems with high levels of renewable generation: the savings exceed 25% of the total system operating cost for a 50% renewables scenario.« less

Optimal subhourly electricity resource dispatch under multiple price signals with high renewable generation availability

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

Chassin, David P.; Behboodi, Sahand; Djilali, Ned

This article proposes a system-wide optimal resource dispatch strategy that enables a shift from a primarily energy cost-based approach, to a strategy using simultaneous price signals for energy, power and ramping behavior. A formal method to compute the optimal sub-hourly power trajectory is derived for a system when the price of energy and ramping are both significant. Optimal control functions are obtained in both time and frequency domains, and a discrete-time solution suitable for periodic feedback control systems is presented. The method is applied to North America Western Interconnection for the planning year 2024, and it is shown that anmore » optimal dispatch strategy that simultaneously considers both the cost of energy and the cost of ramping leads to significant cost savings in systems with high levels of renewable generation: the savings exceed 25% of the total system operating cost for a 50% renewables scenario.« less

Deterministic methods for multi-control fuel loading optimization

NASA Astrophysics Data System (ADS)

Rahman, Fariz B. Abdul

We have developed a multi-control fuel loading optimization code for pressurized water reactors based on deterministic methods. The objective is to flatten the fuel burnup profile, which maximizes overall energy production. The optimal control problem is formulated using the method of Lagrange multipliers and the direct adjoining approach for treatment of the inequality power peaking constraint. The optimality conditions are derived for a multi-dimensional multi-group optimal control problem via calculus of variations. Due to the Hamiltonian having a linear control, our optimal control problem is solved using the gradient method to minimize the Hamiltonian and a Newton step formulation to obtain the optimal control. We are able to satisfy the power peaking constraint during depletion with the control at beginning of cycle (BOC) by building the proper burnup path forward in time and utilizing the adjoint burnup to propagate the information back to the BOC. Our test results show that we are able to achieve our objective and satisfy the power peaking constraint during depletion using either the fissile enrichment or burnable poison as the control. Our fuel loading designs show an increase of 7.8 equivalent full power days (EFPDs) in cycle length compared with 517.4 EFPDs for the AP600 first cycle.

The Linear Quadratic Gaussian Multistage Game with Nonclassical Information Pattern Using a Direct Solution Method

NASA Astrophysics Data System (ADS)

Clemens, Joshua William

Game theory has application across multiple fields, spanning from economic strategy to optimal control of an aircraft and missile on an intercept trajectory. The idea of game theory is fascinating in that we can actually mathematically model real-world scenarios and determine optimal decision making. It may not always be easy to mathematically model certain real-world scenarios, nonetheless, game theory gives us an appreciation for the complexity involved in decision making. This complexity is especially apparent when the players involved have access to different information upon which to base their decision making (a nonclassical information pattern). Here we will focus on the class of adversarial two-player games (sometimes referred to as pursuit-evasion games) with nonclassical information pattern. We present a two-sided (simultaneous) optimization solution method for the two-player linear quadratic Gaussian (LQG) multistage game. This direct solution method allows for further interpretation of each player's decision making (strategy) as compared to previously used formal solution methods. In addition to the optimal control strategies, we present a saddle point proof and we derive an expression for the optimal performance index value. We provide some numerical results in order to further interpret the optimal control strategies and to highlight real-world application of this game-theoretic optimal solution.

Efficiency Improvements to the Displacement Based Multilevel Structural Optimization Algorithm

NASA Technical Reports Server (NTRS)

Plunkett, C. L.; Striz, A. G.; Sobieszczanski-Sobieski, J.

2001-01-01

Multilevel Structural Optimization (MSO) continues to be an area of research interest in engineering optimization. In the present project, the weight optimization of beams and trusses using Displacement based Multilevel Structural Optimization (DMSO), a member of the MSO set of methodologies, is investigated. In the DMSO approach, the optimization task is subdivided into a single system and multiple subsystems level optimizations. The system level optimization minimizes the load unbalance resulting from the use of displacement functions to approximate the structural displacements. The function coefficients are then the design variables. Alternately, the system level optimization can be solved using the displacements themselves as design variables, as was shown in previous research. Both approaches ensure that the calculated loads match the applied loads. In the subsystems level, the weight of the structure is minimized using the element dimensions as design variables. The approach is expected to be very efficient for large structures, since parallel computing can be utilized in the different levels of the problem. In this paper, the method is applied to a one-dimensional beam and a large three-dimensional truss. The beam was tested to study possible simplifications to the system level optimization. In previous research, polynomials were used to approximate the global nodal displacements. The number of coefficients of the polynomials equally matched the number of degrees of freedom of the problem. Here it was desired to see if it is possible to only match a subset of the degrees of freedom in the system level. This would lead to a simplification of the system level, with a resulting increase in overall efficiency. However, the methods tested for this type of system level simplification did not yield positive results. The large truss was utilized to test further improvements in the efficiency of DMSO. In previous work, parallel processing was applied to the subsystems level, where the derivative verification feature of the optimizer NPSOL had been utilized in the optimizations. This resulted in large runtimes. In this paper, the optimizations were repeated without using the derivative verification, and the results are compared to those from the previous work. Also, the optimizations were run on both, a network of SUN workstations using the MPICH implementation of the Message Passing Interface (MPI) and on the faster Beowulf cluster at ICASE, NASA Langley Research Center, using the LAM implementation of UP]. The results on both systems were consistent and showed that it is not necessary to verify the derivatives and that this gives a large increase in efficiency of the DMSO algorithm.

Optimality and stability of symmetric evolutionary games with applications in genetic selection.

PubMed

Huang, Yuanyuan; Hao, Yiping; Wang, Min; Zhou, Wen; Wu, Zhijun

2015-06-01

Symmetric evolutionary games, i.e., evolutionary games with symmetric fitness matrices, have important applications in population genetics, where they can be used to model for example the selection and evolution of the genotypes of a given population. In this paper, we review the theory for obtaining optimal and stable strategies for symmetric evolutionary games, and provide some new proofs and computational methods. In particular, we review the relationship between the symmetric evolutionary game and the generalized knapsack problem, and discuss the first and second order necessary and sufficient conditions that can be derived from this relationship for testing the optimality and stability of the strategies. Some of the conditions are given in different forms from those in previous work and can be verified more efficiently. We also derive more efficient computational methods for the evaluation of the conditions than conventional approaches. We demonstrate how these conditions can be applied to justifying the strategies and their stabilities for a special class of genetic selection games including some in the study of genetic disorders.

An optimal control method for fluid structure interaction systems via adjoint boundary pressure

NASA Astrophysics Data System (ADS)

Chirco, L.; Da Vià, R.; Manservisi, S.

2017-11-01

In recent year, in spite of the computational complexity, Fluid-structure interaction (FSI) problems have been widely studied due to their applicability in science and engineering. Fluid-structure interaction systems consist of one or more solid structures that deform by interacting with a surrounding fluid flow. FSI simulations evaluate the tensional state of the mechanical component and take into account the effects of the solid deformations on the motion of the interior fluids. The inverse FSI problem can be described as the achievement of a certain objective by changing some design parameters such as forces, boundary conditions and geometrical domain shapes. In this paper we would like to study the inverse FSI problem by using an optimal control approach. In particular we propose a pressure boundary optimal control method based on Lagrangian multipliers and adjoint variables. The objective is the minimization of a solid domain displacement matching functional obtained by finding the optimal pressure on the inlet boundary. The optimality system is derived from the first order necessary conditions by taking the Fréchet derivatives of the Lagrangian with respect to all the variables involved. The optimal solution is then obtained through a standard steepest descent algorithm applied to the optimality system. The approach presented in this work is general and could be used to assess other objective functionals and controls. In order to support the proposed approach we perform a few numerical tests where the fluid pressure on the domain inlet controls the displacement that occurs in a well defined region of the solid domain.

Introduction to Adjoint Models

NASA Technical Reports Server (NTRS)

Errico, Ronald M.

2015-01-01

In this lecture, some fundamentals of adjoint models will be described. This includes a basic derivation of tangent linear and corresponding adjoint models from a parent nonlinear model, the interpretation of adjoint-derived sensitivity fields, a description of methods of automatic differentiation, and the use of adjoint models to solve various optimization problems, including singular vectors. Concluding remarks will attempt to correct common misconceptions about adjoint models and their utilization.

Trajectories for High Specific Impulse High Specific Power Deep Space Exploration

NASA Technical Reports Server (NTRS)

Polsgrove, T.; Adams, R. B.; Brady, Hugh J. (Technical Monitor)

2002-01-01

Preliminary results are presented for two methods to approximate the mission performance of high specific impulse high specific power vehicles. The first method is based on an analytical approximation derived by Williams and Shepherd and can be used to approximate mission performance to outer planets and interstellar space. The second method is based on a parametric analysis of trajectories created using the well known trajectory optimization code, VARITOP. This parametric analysis allows the reader to approximate payload ratios and optimal power requirements for both one-way and round-trip missions. While this second method only addresses missions to and from Jupiter, future work will encompass all of the outer planet destinations and some interstellar precursor missions.

A fast method to emulate an iterative POCS image reconstruction algorithm.

PubMed

Zeng, Gengsheng L

2017-10-01

Iterative image reconstruction algorithms are commonly used to optimize an objective function, especially when the objective function is nonquadratic. Generally speaking, the iterative algorithms are computationally inefficient. This paper presents a fast algorithm that has one backprojection and no forward projection. This paper derives a new method to solve an optimization problem. The nonquadratic constraint, for example, an edge-preserving denoising constraint is implemented as a nonlinear filter. The algorithm is derived based on the POCS (projections onto projections onto convex sets) approach. A windowed FBP (filtered backprojection) algorithm enforces the data fidelity. An iterative procedure, divided into segments, enforces edge-enhancement denoising. Each segment performs nonlinear filtering. The derived iterative algorithm is computationally efficient. It contains only one backprojection and no forward projection. Low-dose CT data are used for algorithm feasibility studies. The nonlinearity is implemented as an edge-enhancing noise-smoothing filter. The patient studies results demonstrate its effectiveness in processing low-dose x ray CT data. This fast algorithm can be used to replace many iterative algorithms. © 2017 American Association of Physicists in Medicine.

Optimal quantum control of Bose-Einstein condensates in magnetic microtraps: Comparison of gradient-ascent-pulse-engineering and Krotov optimization schemes

NASA Astrophysics Data System (ADS)

Jäger, Georg; Reich, Daniel M.; Goerz, Michael H.; Koch, Christiane P.; Hohenester, Ulrich

2014-09-01

We study optimal quantum control of the dynamics of trapped Bose-Einstein condensates: The targets are to split a condensate, residing initially in a single well, into a double well, without inducing excitation, and to excite a condensate from the ground state to the first-excited state of a single well. The condensate is described in the mean-field approximation of the Gross-Pitaevskii equation. We compare two optimization approaches in terms of their performance and ease of use; namely, gradient-ascent pulse engineering (GRAPE) and Krotov's method. Both approaches are derived from the variational principle but differ in the way the control is updated, additional costs are accounted for, and second-order-derivative information can be included. We find that GRAPE produces smoother control fields and works in a black-box manner, whereas Krotov with a suitably chosen step-size parameter converges faster but can produce sharp features in the control fields.

Optimization of constrained density functional theory

NASA Astrophysics Data System (ADS)

O'Regan, David D.; Teobaldi, Gilberto

2016-07-01

Constrained density functional theory (cDFT) is a versatile electronic structure method that enables ground-state calculations to be performed subject to physical constraints. It thereby broadens their applicability and utility. Automated Lagrange multiplier optimization is necessary for multiple constraints to be applied efficiently in cDFT, for it to be used in tandem with geometry optimization, or with molecular dynamics. In order to facilitate this, we comprehensively develop the connection between cDFT energy derivatives and response functions, providing a rigorous assessment of the uniqueness and character of cDFT stationary points while accounting for electronic interactions and screening. In particular, we provide a nonperturbative proof that stable stationary points of linear density constraints occur only at energy maxima with respect to their Lagrange multipliers. We show that multiple solutions, hysteresis, and energy discontinuities may occur in cDFT. Expressions are derived, in terms of convenient by-products of cDFT optimization, for quantities such as the dielectric function and a condition number quantifying ill definition in multiple constraint cDFT.

The continuous adjoint approach to the k-ε turbulence model for shape optimization and optimal active control of turbulent flows

NASA Astrophysics Data System (ADS)

Papoutsis-Kiachagias, E. M.; Zymaris, A. S.; Kavvadias, I. S.; Papadimitriou, D. I.; Giannakoglou, K. C.

2015-03-01

The continuous adjoint to the incompressible Reynolds-averaged Navier-Stokes equations coupled with the low Reynolds number Launder-Sharma k-ε turbulence model is presented. Both shape and active flow control optimization problems in fluid mechanics are considered, aiming at minimum viscous losses. In contrast to the frequently used assumption of frozen turbulence, the adjoint to the turbulence model equations together with appropriate boundary conditions are derived, discretized and solved. This is the first time that the adjoint equations to the Launder-Sharma k-ε model have been derived. Compared to the formulation that neglects turbulence variations, the impact of additional terms and equations is evaluated. Sensitivities computed using direct differentiation and/or finite differences are used for comparative purposes. To demonstrate the need for formulating and solving the adjoint to the turbulence model equations, instead of merely relying upon the 'frozen turbulence assumption', the gain in the optimization turnaround time offered by the proposed method is quantified.

Adaptive bi-level programming for optimal gene knockouts for targeted overproduction under phenotypic constraints

PubMed Central

2013-01-01

Background Optimization procedures to identify gene knockouts for targeted biochemical overproduction have been widely in use in modern metabolic engineering. Flux balance analysis (FBA) framework has provided conceptual simplifications for genome-scale dynamic analysis at steady states. Based on FBA, many current optimization methods for targeted bio-productions have been developed under the maximum cell growth assumption. The optimization problem to derive gene knockout strategies recently has been formulated as a bi-level programming problem in OptKnock for maximum targeted bio-productions with maximum growth rates. However, it has been shown that knockout mutants in fact reach the steady states with the minimization of metabolic adjustment (MOMA) from the corresponding wild-type strains instead of having maximal growth rates after genetic or metabolic intervention. In this work, we propose a new bi-level computational framework--MOMAKnock--which can derive robust knockout strategies under the MOMA flux distribution approximation. Methods In this new bi-level optimization framework, we aim to maximize the production of targeted chemicals by identifying candidate knockout genes or reactions under phenotypic constraints approximated by the MOMA assumption. Hence, the targeted chemical production is the primary objective of MOMAKnock while the MOMA assumption is formulated as the inner problem of constraining the knockout metabolic flux to be as close as possible to the steady-state phenotypes of wide-type strains. As this new inner problem becomes a quadratic programming problem, a novel adaptive piecewise linearization algorithm is developed in this paper to obtain the exact optimal solution to this new bi-level integer quadratic programming problem for MOMAKnock. Results Our new MOMAKnock model and the adaptive piecewise linearization solution algorithm are tested with a small E. coli core metabolic network and a large-scale iAF1260 E. coli metabolic network. The derived knockout strategies are compared with those from OptKnock. Our preliminary experimental results show that MOMAKnock can provide improved targeted productions with more robust knockout strategies. PMID:23368729

Self-optimizing Pitch Control for Large Scale Wind Turbine Based on ADRC

NASA Astrophysics Data System (ADS)

Xia, Anjun; Hu, Guoqing; Li, Zheng; Huang, Dongxiao; Wang, Fengxiang

2018-01-01

Since wind turbine is a complex nonlinear and strong coupling system, traditional PI control method can hardly achieve good control performance. A self-optimizing pitch control method based on the active-disturbance-rejection control theory is proposed in this paper. A linear model of the wind turbine is derived by linearizing the aerodynamic torque equation and the dynamic response of wind turbine is transformed into a first-order linear system. An expert system is designed to optimize the amplification coefficient according to the pitch rate and the speed deviation. The purpose of the proposed control method is to regulate the amplification coefficient automatically and keep the variations of pitch rate and rotor speed in proper ranges. Simulation results show that the proposed pitch control method has the ability to modify the amplification coefficient effectively, when it is not suitable, and keep the variations of pitch rate and rotor speed in proper ranges

Combined genetic algorithm and multiple linear regression (GA-MLR) optimizer: Application to multi-exponential fluorescence decay surface.

PubMed

Fisz, Jacek J

2006-12-07

The optimization approach based on the genetic algorithm (GA) combined with multiple linear regression (MLR) method, is discussed. The GA-MLR optimizer is designed for the nonlinear least-squares problems in which the model functions are linear combinations of nonlinear functions. GA optimizes the nonlinear parameters, and the linear parameters are calculated from MLR. GA-MLR is an intuitive optimization approach and it exploits all advantages of the genetic algorithm technique. This optimization method results from an appropriate combination of two well-known optimization methods. The MLR method is embedded in the GA optimizer and linear and nonlinear model parameters are optimized in parallel. The MLR method is the only one strictly mathematical "tool" involved in GA-MLR. The GA-MLR approach simplifies and accelerates considerably the optimization process because the linear parameters are not the fitted ones. Its properties are exemplified by the analysis of the kinetic biexponential fluorescence decay surface corresponding to a two-excited-state interconversion process. A short discussion of the variable projection (VP) algorithm, designed for the same class of the optimization problems, is presented. VP is a very advanced mathematical formalism that involves the methods of nonlinear functionals, algebra of linear projectors, and the formalism of Fréchet derivatives and pseudo-inverses. Additional explanatory comments are added on the application of recently introduced the GA-NR optimizer to simultaneous recovery of linear and weakly nonlinear parameters occurring in the same optimization problem together with nonlinear parameters. The GA-NR optimizer combines the GA method with the NR method, in which the minimum-value condition for the quadratic approximation to chi(2), obtained from the Taylor series expansion of chi(2), is recovered by means of the Newton-Raphson algorithm. The application of the GA-NR optimizer to model functions which are multi-linear combinations of nonlinear functions, is indicated. The VP algorithm does not distinguish the weakly nonlinear parameters from the nonlinear ones and it does not apply to the model functions which are multi-linear combinations of nonlinear functions.

Genetic algorithm to optimize the design of main combustor and gas generator in liquid rocket engines

NASA Astrophysics Data System (ADS)

Son, Min; Ko, Sangho; Koo, Jaye

2014-06-01

A genetic algorithm was used to develop optimal design methods for the regenerative cooled combustor and fuel-rich gas generator of a liquid rocket engine. For the combustor design, a chemical equilibrium analysis was applied, and the profile was calculated using Rao's method. One-dimensional heat transfer was assumed along the profile, and cooling channels were designed. For the gas-generator design, non-equilibrium properties were derived from a counterflow analysis, and a vaporization model for the fuel droplet was adopted to calculate residence time. Finally, a genetic algorithm was adopted to optimize the designs. The combustor and gas generator were optimally designed for 30-tonf, 75-tonf, and 150-tonf engines. The optimized combustors demonstrated superior design characteristics when compared with previous non-optimized results. Wall temperatures at the nozzle throat were optimized to satisfy the requirement of 800 K, and specific impulses were maximized. In addition, the target turbine power and a burned-gas temperature of 1000 K were obtained from the optimized gas-generator design.

Automated Deep Learning-Based System to Identify Endothelial Cells Derived from Induced Pluripotent Stem Cells.

PubMed

Kusumoto, Dai; Lachmann, Mark; Kunihiro, Takeshi; Yuasa, Shinsuke; Kishino, Yoshikazu; Kimura, Mai; Katsuki, Toshiomi; Itoh, Shogo; Seki, Tomohisa; Fukuda, Keiichi

2018-06-05

Deep learning technology is rapidly advancing and is now used to solve complex problems. Here, we used deep learning in convolutional neural networks to establish an automated method to identify endothelial cells derived from induced pluripotent stem cells (iPSCs), without the need for immunostaining or lineage tracing. Networks were trained to predict whether phase-contrast images contain endothelial cells based on morphology only. Predictions were validated by comparison to immunofluorescence staining for CD31, a marker of endothelial cells. Method parameters were then automatically and iteratively optimized to increase prediction accuracy. We found that prediction accuracy was correlated with network depth and pixel size of images to be analyzed. Finally, K-fold cross-validation confirmed that optimized convolutional neural networks can identify endothelial cells with high performance, based only on morphology. Copyright © 2018 The Author(s). Published by Elsevier Inc. All rights reserved.

Evolution of Geometric Sensitivity Derivatives from Computer Aided Design Models

NASA Technical Reports Server (NTRS)

Jones, William T.; Lazzara, David; Haimes, Robert

2010-01-01

The generation of design parameter sensitivity derivatives is required for gradient-based optimization. Such sensitivity derivatives are elusive at best when working with geometry defined within the solid modeling context of Computer-Aided Design (CAD) systems. Solid modeling CAD systems are often proprietary and always complex, thereby necessitating ad hoc procedures to infer parameter sensitivity. A new perspective is presented that makes direct use of the hierarchical associativity of CAD features to trace their evolution and thereby track design parameter sensitivity. In contrast to ad hoc methods, this method provides a more concise procedure following the model design intent and determining the sensitivity of CAD geometry directly to its respective defining parameters.

Methodology for sensitivity analysis, approximate analysis, and design optimization in CFD for multidisciplinary applications. [computational fluid dynamics

NASA Technical Reports Server (NTRS)

Taylor, Arthur C., III; Hou, Gene W.

1992-01-01

Fundamental equations of aerodynamic sensitivity analysis and approximate analysis for the two dimensional thin layer Navier-Stokes equations are reviewed, and special boundary condition considerations necessary to apply these equations to isolated lifting airfoils on 'C' and 'O' meshes are discussed in detail. An efficient strategy which is based on the finite element method and an elastic membrane representation of the computational domain is successfully tested, which circumvents the costly 'brute force' method of obtaining grid sensitivity derivatives, and is also useful in mesh regeneration. The issue of turbulence modeling is addressed in a preliminary study. Aerodynamic shape sensitivity derivatives are efficiently calculated, and their accuracy is validated on two viscous test problems, including: (1) internal flow through a double throat nozzle, and (2) external flow over a NACA 4-digit airfoil. An automated aerodynamic design optimization strategy is outlined which includes the use of a design optimization program, an aerodynamic flow analysis code, an aerodynamic sensitivity and approximate analysis code, and a mesh regeneration and grid sensitivity analysis code. Application of the optimization methodology to the two test problems in each case resulted in a new design having a significantly improved performance in the aerodynamic response of interest.

Optimization of a Circular Microchannel With Entropy Generation Minimization Method

NASA Astrophysics Data System (ADS)

Jafari, Arash; Ghazali, Normah Mohd

2010-06-01

New advances in micro and nano scales are being realized and the contributions of micro and nano heat dissipation devices are of high importance in this novel technology development. Past studies showed that microchannel design depends on its thermal resistance and pressure drop. However, entropy generation minimization (EGM) as a new optimization theory stated that the rate of entropy generation should be also optimized. Application of EGM in microchannel heat sink design is reviewed and discussed in this paper. Latest principles for deriving the entropy generation relations are discussed to present how this approach can be achieved. An optimization procedure using EGM method with the entropy generation rate is derived for a circular microchannel heat sink based upon thermal resistance and pressure drop. The equations are solved using MATLAB and the obtained results are compared to similar past studies. The effects of channel diameter, number of channels, heat flux, and pumping power on the entropy generation rate and Reynolds number are investigated. Analytical correlations are utilized for heat transfer and friction coefficients. A minimum entropy generation has been observed for N = 40 and channel diameter of 90μm. It is concluded that for N = 40 and channel hydraulic diameter of 90μm, the circular microchannel heat sink is on its optimum operating point based on second law of thermodynamics.

Optimizing Associative Experimental Design for Protein Crystallization Screening

PubMed Central

Dinç, Imren; Pusey, Marc L.; Aygün, Ramazan S.

2016-01-01

The goal of protein crystallization screening is the determination of the main factors of importance to crystallizing the protein under investigation. One of the major issues about determining these factors is that screening is often expanded to many hundreds or thousands of conditions to maximize combinatorial chemical space coverage for maximizing the chances of a successful (crystalline) outcome. In this paper, we propose an experimental design method called “Associative Experimental Design (AED)” and an optimization method includes eliminating prohibited combinations and prioritizing reagents based on AED analysis of results from protein crystallization experiments. AED generates candidate cocktails based on these initial screening results. These results are analyzed to determine those screening factors in chemical space that are most likely to lead to higher scoring outcomes, crystals. We have tested AED on three proteins derived from the hyperthermophile Thermococcus thioreducens, and we applied an optimization method to these proteins. Our AED method generated novel cocktails (count provided in parentheses) leading to crystals for three proteins as follows: Nucleoside diphosphate kinase (4), HAD superfamily hydrolase (2), Nucleoside kinase (1). After getting promising results, we have tested our optimization method on four different proteins. The AED method with optimization yielded 4, 3, and 20 crystalline conditions for holo Human Transferrin, archaeal exosome protein, and Nucleoside diphosphate kinase, respectively. PMID:26955046

Optimized extreme learning machine for urban land cover classification using hyperspectral imagery

NASA Astrophysics Data System (ADS)

Su, Hongjun; Tian, Shufang; Cai, Yue; Sheng, Yehua; Chen, Chen; Najafian, Maryam

2017-12-01

This work presents a new urban land cover classification framework using the firefly algorithm (FA) optimized extreme learning machine (ELM). FA is adopted to optimize the regularization coefficient C and Gaussian kernel σ for kernel ELM. Additionally, effectiveness of spectral features derived from an FA-based band selection algorithm is studied for the proposed classification task. Three sets of hyperspectral databases were recorded using different sensors, namely HYDICE, HyMap, and AVIRIS. Our study shows that the proposed method outperforms traditional classification algorithms such as SVM and reduces computational cost significantly.

A Simple, Powerful Method for Optimal Guidance of Spacecraft Formations

NASA Technical Reports Server (NTRS)

Hughes, Steven P.

2005-01-01

One of the most interesting and challenging aspects of formation guidance law design is the coupling of the orbit design and the science return. The analyst s role is more complicated than simply to design the formation geometry and evolution. He or she is also involved in designing a significant portion of the science instrument itself. The effectiveness of the formation as a science instrument is intimately coupled with the relative geoniet,ry and evolution of the collection of spacecraft. Therefore, the science return can be maximized by optimizing the orbit design according to a performance metric relevant to the science mission goals. In this work, we present a simple method for optimal formation guidance that is applicable to missions whose performance metric, requirements, and constraints can be cast as functions that are explicitly dependent upon the orbit states and spacecraft relative positions and velocities. We present a general form for the cost and constraint functions, and derive their semi-analytic gradients with respect to the formation initial conditions. The gradients are broken down into two types. The first type are gradients of the mission specific performance metric with respect to formation geometry. The second type are derivatives of the formation geometry with respect to the orbit initial conditions. The fact that these two types of derivatives appear separately allows us to derive and implement a general framework that requires minimal modification to be applied to different missions or mission phases. To illustrate the applicability of the approach, we conclude with applications to twc missims: the Magnetospheric Mu!tiscale mission (MMS), a,nd the TJaser Interferometer Space Antenna (LISA).

A Simple, Powerful Method for Optimal Guidance of Spacecraft Formations

NASA Technical Reports Server (NTRS)

Hughes, Steven P.

2006-01-01

One of the most interesting and challenging aspects of formation guidance law design is the coupling of the orbit design and the science return. The analyst's role is more complicated than simply to design the formation geometry and evolution. He or she is also involved in designing a significant portion of the science instrument itself. The effectiveness of the formation as a science instrument is intimately coupled with the relative geometry and evolution of the collection of spacecraft. Therefore, the science return can be maximized by optimizing the orbit design according to a performance metric relevant to the science mission goals. In this work, we present a simple method for optimal formation guidance that is applicable to missions whose performance metric, requirements, and constraints can be cast as functions that are explicitly dependent upon the orbit states and spacecraft relative positions and velocities. We present a general form for the cost and constraint functions, and derive their semi-analytic gradients with respect to the formation initial conditions. The gradients are broken down into two types. The first type are gradients of the mission specific performance metric with respect to formation geometry. The second type are derivatives of the formation geometry with respect to the orbit initial conditions. The fact that these two types of derivatives appear separately allows us to derive and implement a general framework that requires minimal modification to be applied to different missions or mission phases. To illustrate the applicability of the approach, we conclude with applications to two missions: the Magnetospheric Multiscale mission (MMS) , and the Laser Interferometer Space Antenna (LISA).

Theory and design of interferometric synthetic aperture radars

NASA Technical Reports Server (NTRS)

Rodriguez, E.; Martin, J. M.

1992-01-01

A derivation of the signal statistics, an optimal estimator of the interferometric phase, and the expression necessary to calculate the height-error budget are presented. These expressions are used to derive methods of optimizing the parameters of the interferometric synthetic aperture radar system (InSAR), and are then employed in a specific design example for a system to perform high-resolution global topographic mapping with a one-year mission lifetime, subject to current technological constraints. A Monte Carlo simulation of this InSAR system is performed to evaluate its performance for realistic topography. The results indicate that this system has the potential to satisfy the stringent accuracy and resolution requirements for geophysical use of global topographic data.

Sensitivity of Lumped Constraints Using the Adjoint Method

NASA Technical Reports Server (NTRS)

Akgun, Mehmet A.; Haftka, Raphael T.; Wu, K. Chauncey; Walsh, Joanne L.

1999-01-01

Adjoint sensitivity calculation of stress, buckling and displacement constraints may be much less expensive than direct sensitivity calculation when the number of load cases is large. Adjoint stress and displacement sensitivities are available in the literature. Expressions for local buckling sensitivity of isotropic plate elements are derived in this study. Computational efficiency of the adjoint method is sensitive to the number of constraints and, therefore, the method benefits from constraint lumping. A continuum version of the Kreisselmeier-Steinhauser (KS) function is chosen to lump constraints. The adjoint and direct methods are compared for three examples: a truss structure, a simple HSCT wing model, and a large HSCT model. These sensitivity derivatives are then used in optimization.

Numerical Solutions of the Mean-Value Theorem: New Methods for Downward Continuation of Potential Fields

NASA Astrophysics Data System (ADS)

Zhang, Chong; Lü, Qingtian; Yan, Jiayong; Qi, Guang

2018-04-01

Downward continuation can enhance small-scale sources and improve resolution. Nevertheless, the common methods have disadvantages in obtaining optimal results because of divergence and instability. We derive the mean-value theorem for potential fields, which could be the theoretical basis of some data processing and interpretation. Based on numerical solutions of the mean-value theorem, we present the convergent and stable downward continuation methods by using the first-order vertical derivatives and their upward continuation. By applying one of our methods to both the synthetic and real cases, we show that our method is stable, convergent and accurate. Meanwhile, compared with the fast Fourier transform Taylor series method and the integrated second vertical derivative Taylor series method, our process has very little boundary effect and is still stable in noise. We find that the characters of the fading anomalies emerge properly in our downward continuation with respect to the original fields at the lower heights.

Selecting a restoration technique to minimize OCR error.

PubMed

Cannon, M; Fugate, M; Hush, D R; Scovel, C

2003-01-01

This paper introduces a learning problem related to the task of converting printed documents to ASCII text files. The goal of the learning procedure is to produce a function that maps documents to restoration techniques in such a way that on average the restored documents have minimum optical character recognition error. We derive a general form for the optimal function and use it to motivate the development of a nonparametric method based on nearest neighbors. We also develop a direct method of solution based on empirical error minimization for which we prove a finite sample bound on estimation error that is independent of distribution. We show that this empirical error minimization problem is an extension of the empirical optimization problem for traditional M-class classification with general loss function and prove computational hardness for this problem. We then derive a simple iterative algorithm called generalized multiclass ratchet (GMR) and prove that it produces an optimal function asymptotically (with probability 1). To obtain the GMR algorithm we introduce a new data map that extends Kesler's construction for the multiclass problem and then apply an algorithm called Ratchet to this mapped data, where Ratchet is a modification of the Pocket algorithm . Finally, we apply these methods to a collection of documents and report on the experimental results.

Robust Maneuvering Envelope Estimation Based on Reachability Analysis in an Optimal Control Formulation

NASA Technical Reports Server (NTRS)

Lombaerts, Thomas; Schuet, Stefan R.; Wheeler, Kevin; Acosta, Diana; Kaneshige, John

2013-01-01

This paper discusses an algorithm for estimating the safe maneuvering envelope of damaged aircraft. The algorithm performs a robust reachability analysis through an optimal control formulation while making use of time scale separation and taking into account uncertainties in the aerodynamic derivatives. Starting with an optimal control formulation, the optimization problem can be rewritten as a Hamilton- Jacobi-Bellman equation. This equation can be solved by level set methods. This approach has been applied on an aircraft example involving structural airframe damage. Monte Carlo validation tests have confirmed that this approach is successful in estimating the safe maneuvering envelope for damaged aircraft.

Utility indifference pricing of insurance catastrophe derivatives.

PubMed

Eichler, Andreas; Leobacher, Gunther; Szölgyenyi, Michaela

2017-01-01

We propose a model for an insurance loss index and the claims process of a single insurance company holding a fraction of the total number of contracts that captures both ordinary losses and losses due to catastrophes. In this model we price a catastrophe derivative by the method of utility indifference pricing. The associated stochastic optimization problem is treated by techniques for piecewise deterministic Markov processes. A numerical study illustrates our results.

Tunable wavefront coded imaging system based on detachable phase mask: Mathematical analysis, optimization and underlying applications

NASA Astrophysics Data System (ADS)

Zhao, Hui; Wei, Jingxuan

2014-09-01

The key to the concept of tunable wavefront coding lies in detachable phase masks. Ojeda-Castaneda et al. (Progress in Electronics Research Symposium Proceedings, Cambridge, USA, July 5-8, 2010) described a typical design in which two components with cosinusoidal phase variation operate together to make defocus sensitivity tunable. The present study proposes an improved design and makes three contributions: (1) A mathematical derivation based on the stationary phase method explains why the detachable phase mask of Ojeda-Castaneda et al. tunes the defocus sensitivity. (2) The mathematical derivations show that the effective bandwidth wavefront coded imaging system is also tunable by making each component of the detachable phase mask move asymmetrically. An improved Fisher information-based optimization procedure was also designed to ascertain the optimal mask parameters corresponding to specific bandwidth. (3) Possible applications of the tunable bandwidth are demonstrated by simulated imaging.

Automatic Parametrization of Somatosensory Evoked Potentials With Chirp Modeling.

PubMed

Vayrynen, Eero; Noponen, Kai; Vipin, Ashwati; Thow, X Y; Al-Nashash, Hasan; Kortelainen, Jukka; All, Angelo

2016-09-01

In this paper, an approach using polynomial phase chirp signals to model somatosensory evoked potentials (SEPs) is proposed. SEP waveforms are assumed as impulses undergoing group velocity dispersion while propagating along a multipath neural connection. Mathematical analysis of pulse dispersion resulting in chirp signals is performed. An automatic parameterization of SEPs is proposed using chirp models. A Particle Swarm Optimization algorithm is used to optimize the model parameters. Features describing the latencies and amplitudes of SEPs are automatically derived. A rat model is then used to evaluate the automatic parameterization of SEPs in two experimental cases, i.e., anesthesia level and spinal cord injury (SCI). Experimental results show that chirp-based model parameters and the derived SEP features are significant in describing both anesthesia level and SCI changes. The proposed automatic optimization based approach for extracting chirp parameters offers potential for detailed SEP analysis in future studies. The method implementation in Matlab technical computing language is provided online.

Microgravity vibration isolation: An optimal control law for the one-dimensional case

NASA Technical Reports Server (NTRS)

Hampton, Richard D.; Grodsinsky, Carlos M.; Allaire, Paul E.; Lewis, David W.; Knospe, Carl R.

1991-01-01

Certain experiments contemplated for space platforms must be isolated from the accelerations of the platform. An optimal active control is developed for microgravity vibration isolation, using constant state feedback gains (identical to those obtained from the Linear Quadratic Regulator (LQR) approach) along with constant feedforward gains. The quadratic cost function for this control algorithm effectively weights external accelerations of the platform disturbances by a factor proportional to (1/omega) exp 4. Low frequency accelerations are attenuated by greater than two orders of magnitude. The control relies on the absolute position and velocity feedback of the experiment and the absolute position and velocity feedforward of the platform, and generally derives the stability robustness characteristics guaranteed by the LQR approach to optimality. The method as derived is extendable to the case in which only the relative positions and velocities and the absolute accelerations of the experiment and space platform are available.

Microgravity vibration isolation: An optimal control law for the one-dimensional case

NASA Technical Reports Server (NTRS)

Hampton, R. D.; Grodsinsky, C. M.; Allaire, P. E.; Lewis, D. W.; Knospe, C. R.

1991-01-01

Certain experiments contemplated for space platforms must be isolated from the accelerations of the platforms. An optimal active control is developed for microgravity vibration isolation, using constant state feedback gains (identical to those obtained from the Linear Quadratic Regulator (LQR) approach) along with constant feedforward (preview) gains. The quadratic cost function for this control algorithm effectively weights external accelerations of the platform disturbances by a factor proportional to (1/omega)(exp 4). Low frequency accelerations (less than 50 Hz) are attenuated by greater than two orders of magnitude. The control relies on the absolute position and velocity feedback of the experiment and the absolute position and velocity feedforward of the platform, and generally derives the stability robustness characteristics guaranteed by the LQR approach to optimality. The method as derived is extendable to the case in which only the relative positions and velocities and the absolute accelerations of the experiment and space platform are available.

Derivation of an optimal directivity pattern for sweet spot widening in stereo sound reproduction

NASA Astrophysics Data System (ADS)

Ródenas, Josep A.; Aarts, Ronald M.; Janssen, A. J. E. M.

2003-01-01

In this paper the correction of the degradation of the stereophonic illusion during sound reproduction due to off-center listening is investigated. The main idea is that the directivity pattern of a loudspeaker array should have a well-defined shape such that a good stereo reproduction is achieved in a large listening area. Therefore, a mathematical description to derive an optimal directivity pattern opt that achieves sweet spot widening in a large listening area for stereophonic sound applications is described. This optimal directivity pattern is based on parametrized time/intensity trading data coming from psycho-acoustic experiments within a wide listening area. After the study, the required digital FIR filters are determined by means of a least-squares optimization method for a given stereo base setup (two pair of drivers for the loudspeaker arrays and 2.5-m distance between loudspeakers), which radiate sound in a broad range of listening positions in accordance with the derived opt. Informal listening tests have shown that the opt worked as predicted by the theoretical simulations. They also demonstrated the correct central sound localization for speech and music for a number of listening positions. This application is referred to as ``Position-Independent (PI) stereo.''

Derivation of an optimal directivity pattern for sweet spot widening in stereo sound reproduction.

PubMed

Ródenas, Josep A; Aarts, Ronald M; Janssen, A J E M

2003-01-01

In this paper the correction of the degradation of the stereophonic illusion during sound reproduction due to off-center listening is investigated. The main idea is that the directivity pattern of a loudspeaker array should have a well-defined shape such that a good stereo reproduction is achieved in a large listening area. Therefore, a mathematical description to derive an optimal directivity pattern l(opt) that achieves sweet spot widening in a large listening area for stereophonic sound applications is described. This optimal directivity pattern is based on parametrized time/intensity trading data coming from psycho-acoustic experiments within a wide listening area. After the study, the required digital FIR filters are determined by means of a least-squares optimization method for a given stereo base setup (two pair of drivers for the loudspeaker arrays and 2.5-m distance between loudspeakers), which radiate sound in a broad range of listening positions in accordance with the derived l(opt). Informal listening tests have shown that the l(opt) worked as predicted by the theoretical simulations. They also demonstrated the correct central sound localization for speech and music for a number of listening positions. This application is referred to as "Position-Independent (PI) stereo."

Fast Bayesian experimental design: Laplace-based importance sampling for the expected information gain

NASA Astrophysics Data System (ADS)

Beck, Joakim; Dia, Ben Mansour; Espath, Luis F. R.; Long, Quan; Tempone, Raúl

2018-06-01

In calculating expected information gain in optimal Bayesian experimental design, the computation of the inner loop in the classical double-loop Monte Carlo requires a large number of samples and suffers from underflow if the number of samples is small. These drawbacks can be avoided by using an importance sampling approach. We present a computationally efficient method for optimal Bayesian experimental design that introduces importance sampling based on the Laplace method to the inner loop. We derive the optimal values for the method parameters in which the average computational cost is minimized according to the desired error tolerance. We use three numerical examples to demonstrate the computational efficiency of our method compared with the classical double-loop Monte Carlo, and a more recent single-loop Monte Carlo method that uses the Laplace method as an approximation of the return value of the inner loop. The first example is a scalar problem that is linear in the uncertain parameter. The second example is a nonlinear scalar problem. The third example deals with the optimal sensor placement for an electrical impedance tomography experiment to recover the fiber orientation in laminate composites.

Multi-input multioutput orthogonal frequency division multiplexing radar waveform design for improving the detection performance of space-time adaptive processing

NASA Astrophysics Data System (ADS)

Wang, Hongyan

2017-04-01

This paper addresses the waveform optimization problem for improving the detection performance of multi-input multioutput (MIMO) orthogonal frequency division multiplexing (OFDM) radar-based space-time adaptive processing (STAP) in the complex environment. By maximizing the output signal-to-interference-and-noise-ratio (SINR) criterion, the waveform optimization problem for improving the detection performance of STAP, which is subjected to the constant modulus constraint, is derived. To tackle the resultant nonlinear and complicated optimization issue, a diagonal loading-based method is proposed to reformulate the issue as a semidefinite programming one; thereby, this problem can be solved very efficiently. In what follows, the optimized waveform can be obtained to maximize the output SINR of MIMO-OFDM such that the detection performance of STAP can be improved. The simulation results show that the proposed method can improve the output SINR detection performance considerably as compared with that of uncorrelated waveforms and the existing MIMO-based STAP method.

Flow analysis and design optimization methods for nozzle afterbody of a hypersonic vehicle

NASA Technical Reports Server (NTRS)

Baysal, Oktay

1991-01-01

This report summarizes the methods developed for the aerodynamic analysis and the shape optimization of the nozzle-afterbody section of a hypersonic vehicle. Initially, exhaust gases were assumed to be air. Internal-external flows around a single scramjet module were analyzed by solving the three dimensional Navier-Stokes equations. Then, exhaust gases were simulated by a cold mixture of Freon and Argon. Two different models were used to compute these multispecies flows as they mixed with the hypersonic airflow. Surface and off-surface properties were successfully compared with the experimental data. In the second phase of this project, the Aerodynamic Design Optimization with Sensitivity analysis (ADOS) was developed. Pre and post optimization sensitivity coefficients were derived and used in this quasi-analytical method. These coefficients were also used to predict inexpensively the flow field around a changed shape when the flow field of an unchanged shape was given. Starting with totally arbitrary initial afterbody shapes, independent computations were converged to the same optimum shape, which rendered the maximum axial thrust.

Signal processing using sparse derivatives with applications to chromatograms and ECG

NASA Astrophysics Data System (ADS)

Ning, Xiaoran

In this thesis, we investigate the sparsity exist in the derivative domain. Particularly, we focus on the type of signals which posses up to Mth (M > 0) order sparse derivatives. Efforts are put on formulating proper penalty functions and optimization problems to capture properties related to sparse derivatives, searching for fast, computationally efficient solvers. Also the effectiveness of these algorithms are applied to two real world applications. In the first application, we provide an algorithm which jointly addresses the problems of chromatogram baseline correction and noise reduction. The series of chromatogram peaks are modeled as sparse with sparse derivatives, and the baseline is modeled as a low-pass signal. A convex optimization problem is formulated so as to encapsulate these non-parametric models. To account for the positivity of chromatogram peaks, an asymmetric penalty function is also utilized with symmetric penalty functions. A robust, computationally efficient, iterative algorithm is developed that is guaranteed to converge to the unique optimal solution. The approach, termed Baseline Estimation And Denoising with Sparsity (BEADS), is evaluated and compared with two state-of-the-art methods using both simulated and real chromatogram data. Promising result is obtained. In the second application, a novel Electrocardiography (ECG) enhancement algorithm is designed also based on sparse derivatives. In the real medical environment, ECG signals are often contaminated by various kinds of noise or artifacts, for example, morphological changes due to motion artifact, non-stationary noise due to muscular contraction (EMG), etc. Some of these contaminations severely affect the usefulness of ECG signals, especially when computer aided algorithms are utilized. By solving the proposed convex l1 optimization problem, artifacts are reduced by modeling the clean ECG signal as a sum of two signals whose second and third-order derivatives (differences) are sparse respectively. At the end, the algorithm is applied to a QRS detection system and validated using the MIT-BIH Arrhythmia database (109452 anotations), resulting a sensitivity of Se = 99.87%$ and a positive prediction of +P = 99.88%.

Mechanical modeling for magnetorheological elastomer isolators based on constitutive equations and electromagnetic analysis

NASA Astrophysics Data System (ADS)

Wang, Qi; Dong, Xufeng; Li, Luyu; Ou, Jinping

2018-06-01

As constitutive models are too complicated and existing mechanical models lack universality, these models are beyond satisfaction for magnetorheological elastomer (MRE) devices. In this article, a novel universal method is proposed to build concise mechanical models. Constitutive model and electromagnetic analysis were applied in this method to ensure universality, while a series of derivations and simplifications were carried out to obtain a concise formulation. To illustrate the proposed modeling method, a conical MRE isolator was introduced. Its basic mechanical equations were built based on equilibrium, deformation compatibility, constitutive equations and electromagnetic analysis. An iteration model and a highly efficient differential equation editor based model were then derived to solve the basic mechanical equations. The final simplified mechanical equations were obtained by re-fitting the simulations with a novel optimal algorithm. In the end, verification test of the isolator has proved the accuracy of the derived mechanical model and the modeling method.

Collagen gel droplet-embedded culture drug sensitivity testing in squamous cell carcinoma cell lines derived from human oral cancers: Optimal contact concentrations of cisplatin and fluorouracil.

PubMed

Sakuma, Kaname; Tanaka, Akira; Mataga, Izumi

2016-12-01

The collagen gel droplet-embedded culture drug sensitivity test (CD-DST) is an anticancer drug sensitivity test that uses a method of three-dimensional culture of extremely small samples, and it is suited to primary cultures of human cancer cells. It is a useful method for oral squamous cell carcinoma (OSCC), in which the cancer tissues available for testing are limited. However, since the optimal contact concentrations of anticancer drugs have yet to be established in OSCC, CD-DST for detecting drug sensitivities of OSCC is currently performed by applying the optimal contact concentrations for stomach cancer. In the present study, squamous carcinoma cell lines from human oral cancer were used to investigate the optimal contact concentrations of cisplatin (CDDP) and fluorouracil (5-FU) during CD-DST for OSCC. CD-DST was performed in 7 squamous cell carcinoma cell lines derived from human oral cancers (Ca9-22, HSC-3, HSC-4, HO-1-N-1, KON, OSC-19 and SAS) using CDDP (0.15, 0.3, 1.25, 2.5, 5.0 and 10.0 µg/ml) and 5-FU (0.4, 0.9, 1.8, 3.8, 7.5, 15.0 and 30.0 µg/ml), and the optimal contact concentrations were calculated from the clinical response rate of OSCC to single-drug treatment and the in vitro efficacy rate curve. The optimal concentrations were 0.5 µg/ml for CDDP and 0.7 µg/ml for 5-FU. The antitumor efficacy of CDDP at this optimal contact concentration in CD-DST was compared to the antitumor efficacy in the nude mouse method. The T/C values, which were calculated as the ratio of the colony volume of the treatment group and the colony volume of the control group, at the optimal contact concentration of CDDP and of the nude mouse method were almost in agreement (P<0.05) and predicted clinical efficacy, indicating that the calculated optimal contact concentration is valid. Therefore, chemotherapy for OSCC based on anticancer drug sensitivity tests offers patients a greater freedom of choice and is likely to assume a greater importance in the selection of treatment from the perspectives of function preservation and quality of life, as well as representing a treatment option for unresectable, intractable or recurrent cases.

An Optimal Control Modification to Model-Reference Adaptive Control for Fast Adaptation

NASA Technical Reports Server (NTRS)

Nguyen, Nhan T.; Krishnakumar, Kalmanje; Boskovic, Jovan

2008-01-01

This paper presents a method that can achieve fast adaptation for a class of model-reference adaptive control. It is well-known that standard model-reference adaptive control exhibits high-gain control behaviors when a large adaptive gain is used to achieve fast adaptation in order to reduce tracking error rapidly. High gain control creates high-frequency oscillations that can excite unmodeled dynamics and can lead to instability. The fast adaptation approach is based on the minimization of the squares of the tracking error, which is formulated as an optimal control problem. The necessary condition of optimality is used to derive an adaptive law using the gradient method. This adaptive law is shown to result in uniform boundedness of the tracking error by means of the Lyapunov s direct method. Furthermore, this adaptive law allows a large adaptive gain to be used without causing undesired high-gain control effects. The method is shown to be more robust than standard model-reference adaptive control. Simulations demonstrate the effectiveness of the proposed method.

New subspace methods for ATR

NASA Astrophysics Data System (ADS)

Zhang, Peng; Peng, Jing; Sims, S. Richard F.

2005-05-01

In ATR applications, each feature is a convolution of an image with a filter. It is important to use most discriminant features to produce compact representations. We propose two novel subspace methods for dimension reduction to address limitations associated with Fukunaga-Koontz Transform (FKT). The first method, Scatter-FKT, assumes that target is more homogeneous, while clutter can be anything other than target and anywhere. Thus, instead of estimating a clutter covariance matrix, Scatter-FKT computes a clutter scatter matrix that measures the spread of clutter from the target mean. We choose dimensions along which the difference in variation between target and clutter is most pronounced. When the target follows a Gaussian distribution, Scatter-FKT can be viewed as a generalization of FKT. The second method, Optimal Bayesian Subspace, is derived from the optimal Bayesian classifier. It selects dimensions such that the minimum Bayes error rate can be achieved. When both target and clutter follow Gaussian distributions, OBS computes optimal subspace representations. We compare our methods against FKT using character image as well as IR data.

Parallel computing and first-principles calculations: Applications to complex ceramics and Vitamin B12

NASA Astrophysics Data System (ADS)

Ouyang, Lizhi

A systematic improvement and extension of the orthogonalized linear combinations of atomic orbitals method was carried out using a combined computational and theoretical approach. For high performance parallel computing, a Beowulf class personal computer cluster was constructed. It also served as a parallel program development platform that helped us to port the programs of the method to the national supercomputer facilities. The program, received a language upgrade from Fortran 77 to Fortran 90, and a dynamic memory allocation feature. A preliminary parallel High Performance Fortran version of the program has been developed as well. To be of more benefit though, scalability improvements are needed. In order to circumvent the difficulties of the analytical force calculation in the method, we developed a geometry optimization scheme using the finite difference approximation based on the total energy calculation. The implementation of this scheme was facilitated by the powerful general utility lattice program, which offers many desired features such as multiple optimization schemes and usage of space group symmetry. So far, many ceramic oxides have been tested with the geometry optimization program. Their optimized geometries were in excellent agreement with the experimental data. For nine ceramic oxide crystals, the optimized cell parameters differ from the experimental ones within 0.5%. Moreover, the geometry optimization was recently used to predict a new phase of TiNx. The method has also been used to investigate a complex Vitamin B12-derivative, the OHCbl crystals. In order to overcome the prohibitive disk I/O demand, an on-demand version of the method was developed. Based on the electronic structure calculation of the OHCbl crystal, a partial density of states analysis and a bond order analysis were carried out. The calculated bonding of the corrin ring of OHCbl model was coincident with the big open-ring pi bond. One interesting find of the calculation was that the Co-OH bond was weak. This, together with the ongoing projects studying different Vitamin B12 derivatives, might help us to answer questions about the Co-C cleavage of the B12 coenzyme, which is involved in many important B12 enzymatic reactions.

Rapid computation of directional wellbore drawdown in a confined aquifer via Poisson resummation

NASA Astrophysics Data System (ADS)

Blumenthal, Benjamin J.; Zhan, Hongbin

2016-08-01

We have derived a rapidly computed analytical solution for drawdown caused by a partially or fully penetrating directional wellbore (vertical, horizontal, or slant) via Green's function method. The mathematical model assumes an anisotropic, homogeneous, confined, box-shaped aquifer. Any dimension of the box can have one of six possible boundary conditions: 1) both sides no-flux; 2) one side no-flux - one side constant-head; 3) both sides constant-head; 4) one side no-flux; 5) one side constant-head; 6) free boundary conditions. The solution has been optimized for rapid computation via Poisson Resummation, derivation of convergence rates, and numerical optimization of integration techniques. Upon application of the Poisson Resummation method, we were able to derive two sets of solutions with inverse convergence rates, namely an early-time rapidly convergent series (solution-A) and a late-time rapidly convergent series (solution-B). From this work we were able to link Green's function method (solution-B) back to image well theory (solution-A). We then derived an equation defining when the convergence rate between solution-A and solution-B is the same, which we termed the switch time. Utilizing the more rapidly convergent solution at the appropriate time, we obtained rapid convergence at all times. We have also shown that one may simplify each of the three infinite series for the three-dimensional solution to 11 terms and still maintain a maximum relative error of less than 10-14.

Theory and Computation of Optimal Low- and Medium- Thrust Orbit Transfers

NASA Technical Reports Server (NTRS)

Goodson, Troy D.; Chuang, Jason C. H.; Ledsinger, Laura A.

1996-01-01

This report presents new theoretical results which lead to new algorithms for the computation of fuel-optimal multiple-burn orbit transfers of low and medium thrust. Theoretical results introduced herein show how to add burns to an optimal trajectory and show that the traditional set of necessary conditions may be replaced with a much simpler set of equations. Numerical results are presented to demonstrate the utility of the theoretical results and the new algorithms. Two indirect methods from the literature are shown to be effective for the optimal orbit transfer problem with relatively small numbers of burns. These methods are the Minimizing Boundary Condition Method (MBCM) and BOUNDSCO. Both of these methods make use of the first-order necessary conditions exactly as derived by optimal control theory. Perturbations due to Earth's oblateness and atmospheric drag are considered. These perturbations are of greatest interest for transfers that take place between low Earth orbit altitudes and geosynchronous orbit altitudes. Example extremal solutions including these effects and computed by the aforementioned methods are presented. An investigation is also made into a suboptimal multiple-burn guidance scheme. The FORTRAN code developed for this study has been collected together in a package named ORBPACK. ORBPACK's user manual is provided as an appendix to this report.

Comparison of spike-sorting algorithms for future hardware implementation.

PubMed

Gibson, Sarah; Judy, Jack W; Markovic, Dejan

2008-01-01

Applications such as brain-machine interfaces require hardware spike sorting in order to (1) obtain single-unit activity and (2) perform data reduction for wireless transmission of data. Such systems must be low-power, low-area, high-accuracy, automatic, and able to operate in real time. Several detection and feature extraction algorithms for spike sorting are described briefly and evaluated in terms of accuracy versus computational complexity. The nonlinear energy operator method is chosen as the optimal spike detection algorithm, being most robust over noise and relatively simple. The discrete derivatives method [1] is chosen as the optimal feature extraction method, maintaining high accuracy across SNRs with a complexity orders of magnitude less than that of traditional methods such as PCA.

A "Reverse-Schur" Approach to Optimization With Linear PDE Constraints: Application to Biomolecule Analysis and Design.

PubMed

Bardhan, Jaydeep P; Altman, Michael D; Tidor, B; White, Jacob K

2009-01-01

We present a partial-differential-equation (PDE)-constrained approach for optimizing a molecule's electrostatic interactions with a target molecule. The approach, which we call reverse-Schur co-optimization, can be more than two orders of magnitude faster than the traditional approach to electrostatic optimization. The efficiency of the co-optimization approach may enhance the value of electrostatic optimization for ligand-design efforts-in such projects, it is often desirable to screen many candidate ligands for their viability, and the optimization of electrostatic interactions can improve ligand binding affinity and specificity. The theoretical basis for electrostatic optimization derives from linear-response theory, most commonly continuum models, and simple assumptions about molecular binding processes. Although the theory has been used successfully to study a wide variety of molecular binding events, its implications have not yet been fully explored, in part due to the computational expense associated with the optimization. The co-optimization algorithm achieves improved performance by solving the optimization and electrostatic simulation problems simultaneously, and is applicable to both unconstrained and constrained optimization problems. Reverse-Schur co-optimization resembles other well-known techniques for solving optimization problems with PDE constraints. Model problems as well as realistic examples validate the reverse-Schur method, and demonstrate that our technique and alternative PDE-constrained methods scale very favorably compared to the standard approach. Regularization, which ordinarily requires an explicit representation of the objective function, can be included using an approximate Hessian calculated using the new BIBEE/P (boundary-integral-based electrostatics estimation by preconditioning) method.

A “Reverse-Schur” Approach to Optimization With Linear PDE Constraints: Application to Biomolecule Analysis and Design

PubMed Central

Bardhan, Jaydeep P.; Altman, Michael D.

2009-01-01

We present a partial-differential-equation (PDE)-constrained approach for optimizing a molecule’s electrostatic interactions with a target molecule. The approach, which we call reverse-Schur co-optimization, can be more than two orders of magnitude faster than the traditional approach to electrostatic optimization. The efficiency of the co-optimization approach may enhance the value of electrostatic optimization for ligand-design efforts–in such projects, it is often desirable to screen many candidate ligands for their viability, and the optimization of electrostatic interactions can improve ligand binding affinity and specificity. The theoretical basis for electrostatic optimization derives from linear-response theory, most commonly continuum models, and simple assumptions about molecular binding processes. Although the theory has been used successfully to study a wide variety of molecular binding events, its implications have not yet been fully explored, in part due to the computational expense associated with the optimization. The co-optimization algorithm achieves improved performance by solving the optimization and electrostatic simulation problems simultaneously, and is applicable to both unconstrained and constrained optimization problems. Reverse-Schur co-optimization resembles other well-known techniques for solving optimization problems with PDE constraints. Model problems as well as realistic examples validate the reverse-Schur method, and demonstrate that our technique and alternative PDE-constrained methods scale very favorably compared to the standard approach. Regularization, which ordinarily requires an explicit representation of the objective function, can be included using an approximate Hessian calculated using the new BIBEE/P (boundary-integral-based electrostatics estimation by preconditioning) method. PMID:23055839

An Optimized Method for the Measurement of Acetaldehyde by High-Performance Liquid Chromatography

PubMed Central

Guan, Xiangying; Rubin, Emanuel; Anni, Helen

2011-01-01

Background Acetaldehyde is produced during ethanol metabolism predominantly in the liver by alcohol dehydrogenase, and rapidly eliminated by oxidation to acetate via aldehyde dehydrogenase. Assessment of circulating acetaldehyde levels in biological matrices is performed by headspace gas chromatography and reverse phase high-performance liquid chromatography (RP-HPLC). Methods We have developed an optimized method for the measurement of acetaldehyde by RP-HPLC in hepatoma cell culture medium, blood and plasma. After sample deproteinization, acetaldehyde was derivatized with 2,4-dinitrophenylhydrazine (DNPH). The reaction was optimized for pH, amount of derivatization reagent,, time and temperature. Extraction methods of the acetaldehyde-hydrazone (AcH-DPN) stable derivative and product stability studies were carried out. Acetaldehyde was identified by its retention time in comparison to AcH-DPN standard, using a new chromatography gradient program, and quantitated based on external reference standards and standard addition calibration curves in the presence and absence of ethanol. Results Derivatization of acetaldehyde was performed at pH 4.0 with a 80-fold molar excess of DNPH. The reaction was completed in 40 min at ambient temperature, and the product was stable for 2 days. A clear separation of AcH-DNP from DNPH was obtained with a new 11-min chromatography program. Acetaldehyde detection was linear up to 80 μM. The recovery of acetaldehyde was >88% in culture media, and >78% in plasma. We quantitatively determined the ethanol-derived acetaldehyde in hepatoma cells, rat blood and plasma with a detection limit around 3 μM. The accuracy of the method was <9% for intraday and <15% for interday measurements, in small volume (70 μl) plasma sampling. Conclusions An optimized method for the quantitative determination of acetaldehyde in biological systems was developed using derivatization with DNPH, followed by a short RP-HPLC separation of AcH-DNP. The method has an extended linear range, is reproducible and applicable to small volume sampling of culture media and biological fluids. PMID:21895715

Ion pair-based dispersive liquid-liquid microextraction followed by high performance liquid chromatography as a new method for determining five folate derivatives in foodstuffs.

PubMed

Nojavan, Yones; Kamankesh, Marzieh; Shahraz, Farzaneh; Hashemi, Maryam; Mohammadi, Abdorreza

2015-05-01

A novel technique for simultaneous determination of five folate derivatives in various food matrices was developed by ion pair-based dispersive liquid-liquid microextraction (IP-DLLME) combined with high-performance liquid chromatography (HPLC). In the proposed method, N-methyl-N,N-dioctyloctan-1-ammonium chloride (aliquat-336) was used as an ion-pair reagent. Effective variables of microextraction process were optimized. Under optimum conditions, the method yielded a linear calibration curve ranging from 1-200 ng g(-1) with correlation coefficients (r(2)) higher than 0.98. The relative standard deviation for the seven analyses was 5.2-7.4%. Enrichment factors for the five folates ranged between 108-135. Limits of detection were 2-4.1 ng g(-1). A comparison of this method with other methods described that the new proposed method is rapid and accurate, and gives very good enrichment factors and detection limits for determining five folate derivatives. The newly developed method was successfully applied for the determination of five folate derivatives in wheat flour, egg yolk and orange juice samples. Copyright © 2015 Elsevier B.V. All rights reserved.

Parameter estimation with bio-inspired meta-heuristic optimization: modeling the dynamics of endocytosis.

PubMed

Tashkova, Katerina; Korošec, Peter; Silc, Jurij; Todorovski, Ljupčo; Džeroski, Sašo

2011-10-11

We address the task of parameter estimation in models of the dynamics of biological systems based on ordinary differential equations (ODEs) from measured data, where the models are typically non-linear and have many parameters, the measurements are imperfect due to noise, and the studied system can often be only partially observed. A representative task is to estimate the parameters in a model of the dynamics of endocytosis, i.e., endosome maturation, reflected in a cut-out switch transition between the Rab5 and Rab7 domain protein concentrations, from experimental measurements of these concentrations. The general parameter estimation task and the specific instance considered here are challenging optimization problems, calling for the use of advanced meta-heuristic optimization methods, such as evolutionary or swarm-based methods. We apply three global-search meta-heuristic algorithms for numerical optimization, i.e., differential ant-stigmergy algorithm (DASA), particle-swarm optimization (PSO), and differential evolution (DE), as well as a local-search derivative-based algorithm 717 (A717) to the task of estimating parameters in ODEs. We evaluate their performance on the considered representative task along a number of metrics, including the quality of reconstructing the system output and the complete dynamics, as well as the speed of convergence, both on real-experimental data and on artificial pseudo-experimental data with varying amounts of noise. We compare the four optimization methods under a range of observation scenarios, where data of different completeness and accuracy of interpretation are given as input. Overall, the global meta-heuristic methods (DASA, PSO, and DE) clearly and significantly outperform the local derivative-based method (A717). Among the three meta-heuristics, differential evolution (DE) performs best in terms of the objective function, i.e., reconstructing the output, and in terms of convergence. These results hold for both real and artificial data, for all observability scenarios considered, and for all amounts of noise added to the artificial data. In sum, the meta-heuristic methods considered are suitable for estimating the parameters in the ODE model of the dynamics of endocytosis under a range of conditions: With the model and conditions being representative of parameter estimation tasks in ODE models of biochemical systems, our results clearly highlight the promise of bio-inspired meta-heuristic methods for parameter estimation in dynamic system models within system biology.

Parameter estimation with bio-inspired meta-heuristic optimization: modeling the dynamics of endocytosis

PubMed Central

2011-01-01

Background We address the task of parameter estimation in models of the dynamics of biological systems based on ordinary differential equations (ODEs) from measured data, where the models are typically non-linear and have many parameters, the measurements are imperfect due to noise, and the studied system can often be only partially observed. A representative task is to estimate the parameters in a model of the dynamics of endocytosis, i.e., endosome maturation, reflected in a cut-out switch transition between the Rab5 and Rab7 domain protein concentrations, from experimental measurements of these concentrations. The general parameter estimation task and the specific instance considered here are challenging optimization problems, calling for the use of advanced meta-heuristic optimization methods, such as evolutionary or swarm-based methods. Results We apply three global-search meta-heuristic algorithms for numerical optimization, i.e., differential ant-stigmergy algorithm (DASA), particle-swarm optimization (PSO), and differential evolution (DE), as well as a local-search derivative-based algorithm 717 (A717) to the task of estimating parameters in ODEs. We evaluate their performance on the considered representative task along a number of metrics, including the quality of reconstructing the system output and the complete dynamics, as well as the speed of convergence, both on real-experimental data and on artificial pseudo-experimental data with varying amounts of noise. We compare the four optimization methods under a range of observation scenarios, where data of different completeness and accuracy of interpretation are given as input. Conclusions Overall, the global meta-heuristic methods (DASA, PSO, and DE) clearly and significantly outperform the local derivative-based method (A717). Among the three meta-heuristics, differential evolution (DE) performs best in terms of the objective function, i.e., reconstructing the output, and in terms of convergence. These results hold for both real and artificial data, for all observability scenarios considered, and for all amounts of noise added to the artificial data. In sum, the meta-heuristic methods considered are suitable for estimating the parameters in the ODE model of the dynamics of endocytosis under a range of conditions: With the model and conditions being representative of parameter estimation tasks in ODE models of biochemical systems, our results clearly highlight the promise of bio-inspired meta-heuristic methods for parameter estimation in dynamic system models within system biology. PMID:21989196

Multilevel Optimization Framework for Hierarchical Stiffened Shells Accelerated by Adaptive Equivalent Strategy

NASA Astrophysics Data System (ADS)

Wang, Bo; Tian, Kuo; Zhao, Haixin; Hao, Peng; Zhu, Tianyu; Zhang, Ke; Ma, Yunlong

2017-06-01

In order to improve the post-buckling optimization efficiency of hierarchical stiffened shells, a multilevel optimization framework accelerated by adaptive equivalent strategy is presented in this paper. Firstly, the Numerical-based Smeared Stiffener Method (NSSM) for hierarchical stiffened shells is derived by means of the numerical implementation of asymptotic homogenization (NIAH) method. Based on the NSSM, a reasonable adaptive equivalent strategy for hierarchical stiffened shells is developed from the concept of hierarchy reduction. Its core idea is to self-adaptively decide which hierarchy of the structure should be equivalent according to the critical buckling mode rapidly predicted by NSSM. Compared with the detailed model, the high prediction accuracy and efficiency of the proposed model is highlighted. On the basis of this adaptive equivalent model, a multilevel optimization framework is then established by decomposing the complex entire optimization process into major-stiffener-level and minor-stiffener-level sub-optimizations, during which Fixed Point Iteration (FPI) is employed to accelerate convergence. Finally, the illustrative examples of the multilevel framework is carried out to demonstrate its efficiency and effectiveness to search for the global optimum result by contrast with the single-level optimization method. Remarkably, the high efficiency and flexibility of the adaptive equivalent strategy is indicated by compared with the single equivalent strategy.

A New Expanded Mixed Element Method for Convection-Dominated Sobolev Equation

PubMed Central

Wang, Jinfeng; Li, Hong; Fang, Zhichao

2014-01-01

We propose and analyze a new expanded mixed element method, whose gradient belongs to the simple square integrable space instead of the classical H(div; Ω) space of Chen's expanded mixed element method. We study the new expanded mixed element method for convection-dominated Sobolev equation, prove the existence and uniqueness for finite element solution, and introduce a new expanded mixed projection. We derive the optimal a priori error estimates in L 2-norm for the scalar unknown u and a priori error estimates in (L 2)2-norm for its gradient λ and its flux σ. Moreover, we obtain the optimal a priori error estimates in H 1-norm for the scalar unknown u. Finally, we obtained some numerical results to illustrate efficiency of the new method. PMID:24701153

Applications of hybrid genetic algorithms in seismic tomography

NASA Astrophysics Data System (ADS)

Soupios, Pantelis; Akca, Irfan; Mpogiatzis, Petros; Basokur, Ahmet T.; Papazachos, Constantinos

2011-11-01

Almost all earth sciences inverse problems are nonlinear and involve a large number of unknown parameters, making the application of analytical inversion methods quite restrictive. In practice, most analytical methods are local in nature and rely on a linearized form of the problem equations, adopting an iterative procedure which typically employs partial derivatives in order to optimize the starting (initial) model by minimizing a misfit (penalty) function. Unfortunately, especially for highly non-linear cases, the final model strongly depends on the initial model, hence it is prone to solution-entrapment in local minima of the misfit function, while the derivative calculation is often computationally inefficient and creates instabilities when numerical approximations are used. An alternative is to employ global techniques which do not rely on partial derivatives, are independent of the misfit form and are computationally robust. Such methods employ pseudo-randomly generated models (sampling an appropriately selected section of the model space) which are assessed in terms of their data-fit. A typical example is the class of methods known as genetic algorithms (GA), which achieves the aforementioned approximation through model representation and manipulations, and has attracted the attention of the earth sciences community during the last decade, with several applications already presented for several geophysical problems. In this paper, we examine the efficiency of the combination of the typical regularized least-squares and genetic methods for a typical seismic tomography problem. The proposed approach combines a local (LOM) and a global (GOM) optimization method, in an attempt to overcome the limitations of each individual approach, such as local minima and slow convergence, respectively. The potential of both optimization methods is tested and compared, both independently and jointly, using the several test models and synthetic refraction travel-time date sets that employ the same experimental geometry, wavelength and geometrical characteristics of the model anomalies. Moreover, real data from a crosswell tomographic project for the subsurface mapping of an ancient wall foundation are used for testing the efficiency of the proposed algorithm. The results show that the combined use of both methods can exploit the benefits of each approach, leading to improved final models and producing realistic velocity models, without significantly increasing the required computation time.

A Collaborative Neurodynamic Approach to Multiple-Objective Distributed Optimization.

PubMed

Yang, Shaofu; Liu, Qingshan; Wang, Jun

2018-04-01

This paper is concerned with multiple-objective distributed optimization. Based on objective weighting and decision space decomposition, a collaborative neurodynamic approach to multiobjective distributed optimization is presented. In the approach, a system of collaborative neural networks is developed to search for Pareto optimal solutions, where each neural network is associated with one objective function and given constraints. Sufficient conditions are derived for ascertaining the convergence to a Pareto optimal solution of the collaborative neurodynamic system. In addition, it is proved that each connected subsystem can generate a Pareto optimal solution when the communication topology is disconnected. Then, a switching-topology-based method is proposed to compute multiple Pareto optimal solutions for discretized approximation of Pareto front. Finally, simulation results are discussed to substantiate the performance of the collaborative neurodynamic approach. A portfolio selection application is also given.

$L^1$ penalization of volumetric dose objectives in optimal control of PDEs

DOE PAGES

Barnard, Richard C.; Clason, Christian

2017-02-11

This work is concerned with a class of PDE-constrained optimization problems that are motivated by an application in radiotherapy treatment planning. Here the primary design objective is to minimize the volume where a functional of the state violates a prescribed level, but prescribing these levels in the form of pointwise state constraints leads to infeasible problems. We therefore propose an alternative approach based on L 1 penalization of the violation that is also applicable when state constraints are infeasible. We establish well-posedness of the corresponding optimal control problem, derive first-order optimality conditions, discuss convergence of minimizers as the penalty parametermore » tends to infinity, and present a semismooth Newton method for their efficient numerical solution. Finally, the performance of this method for a model problem is illustrated and contrasted with an alternative approach based on (regularized) state constraints.« less

Globally optimal superconducting magnets part II: symmetric MSE coil arrangement.

PubMed

Tieng, Quang M; Vegh, Viktor; Brereton, Ian M

2009-01-01

A globally optimal superconducting magnet coil design procedure based on the Minimum Stored Energy (MSE) current density map is outlined. The method has the ability to arrange coils in a manner that generates a strong and homogeneous axial magnetic field over a predefined region, and ensures the stray field external to the assembly and peak magnetic field at the wires are in acceptable ranges. The outlined strategy of allocating coils within a given domain suggests that coils should be placed around the perimeter of the domain with adjacent coils possessing alternating winding directions for optimum performance. The underlying current density maps from which the coils themselves are derived are unique, and optimized to possess minimal stored energy. Therefore, the method produces magnet designs with the lowest possible overall stored energy. Optimal coil layouts are provided for unshielded and shielded short bore symmetric superconducting magnets.

Overview of Sensitivity Analysis and Shape Optimization for Complex Aerodynamic Configurations

NASA Technical Reports Server (NTRS)

Newman, Perry A.; Newman, James C., III; Barnwell, Richard W.; Taylor, Arthur C., III; Hou, Gene J.-W.

1998-01-01

This paper presents a brief overview of some of the more recent advances in steady aerodynamic shape-design sensitivity analysis and optimization, based on advanced computational fluid dynamics. The focus here is on those methods particularly well- suited to the study of geometrically complex configurations and their potentially complex associated flow physics. When nonlinear state equations are considered in the optimization process, difficulties are found in the application of sensitivity analysis. Some techniques for circumventing such difficulties are currently being explored and are included here. Attention is directed to methods that utilize automatic differentiation to obtain aerodynamic sensitivity derivatives for both complex configurations and complex flow physics. Various examples of shape-design sensitivity analysis for unstructured-grid computational fluid dynamics algorithms are demonstrated for different formulations of the sensitivity equations. Finally, the use of advanced, unstructured-grid computational fluid dynamics in multidisciplinary analyses and multidisciplinary sensitivity analyses within future optimization processes is recommended and encouraged.

Aerodynamic shape optimization using control theory

NASA Technical Reports Server (NTRS)

Reuther, James

1996-01-01

Aerodynamic shape design has long persisted as a difficult scientific challenge due its highly nonlinear flow physics and daunting geometric complexity. However, with the emergence of Computational Fluid Dynamics (CFD) it has become possible to make accurate predictions of flows which are not dominated by viscous effects. It is thus worthwhile to explore the extension of CFD methods for flow analysis to the treatment of aerodynamic shape design. Two new aerodynamic shape design methods are developed which combine existing CFD technology, optimal control theory, and numerical optimization techniques. Flow analysis methods for the potential flow equation and the Euler equations form the basis of the two respective design methods. In each case, optimal control theory is used to derive the adjoint differential equations, the solution of which provides the necessary gradient information to a numerical optimization method much more efficiently then by conventional finite differencing. Each technique uses a quasi-Newton numerical optimization algorithm to drive an aerodynamic objective function toward a minimum. An analytic grid perturbation method is developed to modify body fitted meshes to accommodate shape changes during the design process. Both Hicks-Henne perturbation functions and B-spline control points are explored as suitable design variables. The new methods prove to be computationally efficient and robust, and can be used for practical airfoil design including geometric and aerodynamic constraints. Objective functions are chosen to allow both inverse design to a target pressure distribution and wave drag minimization. Several design cases are presented for each method illustrating its practicality and efficiency. These include non-lifting and lifting airfoils operating at both subsonic and transonic conditions.

A rapid and rational approach to generating isomorphous heavy-atom phasing derivatives

PubMed Central

Lu, Jinghua; Sun, Peter D.

2014-01-01

In attempts to replace the conventional trial-and-error heavy-atom derivative search method with a rational approach, we previously defined heavy metal compound reactivity against peptide ligands. Here, we assembled a composite pH and buffer-dependent peptide reactivity profile for each heavy metal compound to guide rational heavy-atom derivative search. When knowledge of the best-reacting heavy-atom compound is combined with mass spectrometry-assisted derivatization, and with a quick-soak method to optimize phasing, it is likely that the traditional heavy-atom compounds could meet the demand of modern high-throughput X-ray crystallography. As an example, we applied this rational heavy-atom phasing approach to determine a previously unknown mouse serum amyloid A2 crystal structure. PMID:25040395

Local Approximation and Hierarchical Methods for Stochastic Optimization

NASA Astrophysics Data System (ADS)

Cheng, Bolong

In this thesis, we present local and hierarchical approximation methods for two classes of stochastic optimization problems: optimal learning and Markov decision processes. For the optimal learning problem class, we introduce a locally linear model with radial basis function for estimating the posterior mean of the unknown objective function. The method uses a compact representation of the function which avoids storing the entire history, as is typically required by nonparametric methods. We derive a knowledge gradient policy with the locally parametric model, which maximizes the expected value of information. We show the policy is asymptotically optimal in theory, and experimental works suggests that the method can reliably find the optimal solution on a range of test functions. For the Markov decision processes problem class, we are motivated by an application where we want to co-optimize a battery for multiple revenue, in particular energy arbitrage and frequency regulation. The nature of this problem requires the battery to make charging and discharging decisions at different time scales while accounting for the stochastic information such as load demand, electricity prices, and regulation signals. Computing the exact optimal policy becomes intractable due to the large state space and the number of time steps. We propose two methods to circumvent the computation bottleneck. First, we propose a nested MDP model that structure the co-optimization problem into smaller sub-problems with reduced state space. This new model allows us to understand how the battery behaves down to the two-second dynamics (that of the frequency regulation market). Second, we introduce a low-rank value function approximation for backward dynamic programming. This new method only requires computing the exact value function for a small subset of the state space and approximate the entire value function via low-rank matrix completion. We test these methods on historical price data from the PJM Interconnect and show that it outperforms the baseline approach used in the industry.

Approximation of optimal filter for Ornstein-Uhlenbeck process with quantised discrete-time observation

NASA Astrophysics Data System (ADS)

Bania, Piotr; Baranowski, Jerzy

2018-02-01

Quantisation of signals is a ubiquitous property of digital processing. In many cases, it introduces significant difficulties in state estimation and in consequence control. Popular approaches either do not address properly the problem of system disturbances or lead to biased estimates. Our intention was to find a method for state estimation for stochastic systems with quantised and discrete observation, that is free of the mentioned drawbacks. We have formulated a general form of the optimal filter derived by a solution of Fokker-Planck equation. We then propose the approximation method based on Galerkin projections. We illustrate the approach for the Ornstein-Uhlenbeck process, and derive analytic formulae for the approximated optimal filter, also extending the results for the variant with control. Operation is illustrated with numerical experiments and compared with classical discrete-continuous Kalman filter. Results of comparison are substantially in favour of our approach, with over 20 times lower mean squared error. The proposed filter is especially effective for signal amplitudes comparable to the quantisation thresholds. Additionally, it was observed that for high order of approximation, state estimate is very close to the true process value. The results open the possibilities of further analysis, especially for more complex processes.

Singularities in Optimal Structural Design

NASA Technical Reports Server (NTRS)

Patnaik, S. N.; Guptill, J. D.; Berke, L.

1992-01-01

Singularity conditions that arise during structural optimization can seriously degrade the performance of the optimizer. The singularities are intrinsic to the formulation of the structural optimization problem and are not associated with the method of analysis. Certain conditions that give rise to singularities have been identified in earlier papers, encompassing the entire structure. Further examination revealed more complex sets of conditions in which singularities occur. Some of these singularities are local in nature, being associated with only a segment of the structure. Moreover, the likelihood that one of these local singularities may arise during an optimization procedure can be much greater than that of the global singularity identified earlier. Examples are provided of these additional forms of singularities. A framework is also given in which these singularities can be recognized. In particular, the singularities can be identified by examination of the stress displacement relations along with the compatibility conditions and/or the displacement stress relations derived in the integrated force method of structural analysis.

Singularities in optimal structural design

NASA Technical Reports Server (NTRS)

Patnaik, S. N.; Guptill, J. D.; Berke, L.

1992-01-01

Singularity conditions that arise during structural optimization can seriously degrade the performance of the optimizer. The singularities are intrinsic to the formulation of the structural optimization problem and are not associated with the method of analysis. Certain conditions that give rise to singularities have been identified in earlier papers, encompassing the entire structure. Further examination revealed more complex sets of conditions in which singularities occur. Some of these singularities are local in nature, being associated with only a segment of the structure. Moreover, the likelihood that one of these local singularities may arise during an optimization procedure can be much greater than that of the global singularity identified earlier. Examples are provided of these additional forms of singularities. A framework is also given in which these singularities can be recognized. In particular, the singularities can be identified by examination of the stress displacement relations along with the compatibility conditions and/or the displacement stress relations derived in the integrated force method of structural analysis.

Analytical Optimization of the Net Residual Dispersion in SPM-Limited Dispersion-Managed Systems

NASA Astrophysics Data System (ADS)

Xiao, Xiaosheng; Gao, Shiming; Tian, Yu; Yang, Changxi

2006-05-01

Dispersion management is an effective technique to suppress the nonlinear impairment in fiber transmission systems, which includes tuning the amounts of precompensation, residual dispersion per span (RDPS), and net residual dispersion (NRD) of the systems. For self-phase modulation (SPM)-limited systems, optimizing the NRD is necessary because it can greatly improve the system performance. In this paper, an analytical method is presented to optimize NRD for SPM-limited dispersion-managed systems. The method is based on the correlation between the nonlinear impairment and the output pulse broadening of SPM-limited systems; therefore, dispersion-managed systems can be optimized through minimizing the output single-pulse broadening. A set of expressions is derived to calculate the output pulse broadening of the SPM-limited dispersion-managed system, from which the analytical result of optimal NRD is obtained. Furthermore, with the expressions of pulse broadening, how the nonlinear impairment depends on the amounts of precompensation and RDPS can be revealed conveniently.

Engineering of Pulsatile Conduits from Human Pluripotent Stem Cell Derived Cardiomyocytes

DTIC Science & Technology

2017-06-01

patients with coronary heart disease . Oncotarget [Internet]. 2016 Nov 7; Available from: http://www.ncbi.nlm.nih.gov/pubmed/27835576. 4. Veronesi G...13. SUPPLEMENTARY NOTES 14. ABSTRACT We have derived cardiomyocytes ( heart cells) with high purity using an optimized approach that can coax human...induced pluripotent stem cells (hiPSCs) into heart cells in combination with a two-day lactate selection method that can remove non- cardiomyocytes from

Computing Finite-Time Lyapunov Exponents with Optimally Time Dependent Reduction

NASA Astrophysics Data System (ADS)

Babaee, Hessam; Farazmand, Mohammad; Sapsis, Themis; Haller, George

2016-11-01

We present a method to compute Finite-Time Lyapunov Exponents (FTLE) of a dynamical system using Optimally Time-Dependent (OTD) reduction recently introduced by H. Babaee and T. P. Sapsis. The OTD modes are a set of finite-dimensional, time-dependent, orthonormal basis {ui (x , t) } |i=1N that capture the directions associated with transient instabilities. The evolution equation of the OTD modes is derived from a minimization principle that optimally approximates the most unstable directions over finite times. To compute the FTLE, we evolve a single OTD mode along with the nonlinear dynamics. We approximate the FTLE from the reduced system obtained from projecting the instantaneous linearized dynamics onto the OTD mode. This results in a significant reduction in the computational cost compared to conventional methods for computing FTLE. We demonstrate the efficiency of our method for double Gyre and ABC flows. ARO project 66710-EG-YIP.

Communication: Calculation of interatomic forces and optimization of molecular geometry with auxiliary-field quantum Monte Carlo

NASA Astrophysics Data System (ADS)

Motta, Mario; Zhang, Shiwei

2018-05-01

We propose an algorithm for accurate, systematic, and scalable computation of interatomic forces within the auxiliary-field quantum Monte Carlo (AFQMC) method. The algorithm relies on the Hellmann-Feynman theorem and incorporates Pulay corrections in the presence of atomic orbital basis sets. We benchmark the method for small molecules by comparing the computed forces with the derivatives of the AFQMC potential energy surface and by direct comparison with other quantum chemistry methods. We then perform geometry optimizations using the steepest descent algorithm in larger molecules. With realistic basis sets, we obtain equilibrium geometries in agreement, within statistical error bars, with experimental values. The increase in computational cost for computing forces in this approach is only a small prefactor over that of calculating the total energy. This paves the way for a general and efficient approach for geometry optimization and molecular dynamics within AFQMC.

L1-norm kernel discriminant analysis via Bayes error bound optimization for robust feature extraction.

PubMed

Zheng, Wenming; Lin, Zhouchen; Wang, Haixian

2014-04-01

A novel discriminant analysis criterion is derived in this paper under the theoretical framework of Bayes optimality. In contrast to the conventional Fisher's discriminant criterion, the major novelty of the proposed one is the use of L1 norm rather than L2 norm, which makes it less sensitive to the outliers. With the L1-norm discriminant criterion, we propose a new linear discriminant analysis (L1-LDA) method for linear feature extraction problem. To solve the L1-LDA optimization problem, we propose an efficient iterative algorithm, in which a novel surrogate convex function is introduced such that the optimization problem in each iteration is to simply solve a convex programming problem and a close-form solution is guaranteed to this problem. Moreover, we also generalize the L1-LDA method to deal with the nonlinear robust feature extraction problems via the use of kernel trick, and hereafter proposed the L1-norm kernel discriminant analysis (L1-KDA) method. Extensive experiments on simulated and real data sets are conducted to evaluate the effectiveness of the proposed method in comparing with the state-of-the-art methods.

Lie Symmetry Analysis, Analytical Solutions, and Conservation Laws of the Generalised Whitham-Broer-Kaup-Like Equations

NASA Astrophysics Data System (ADS)

Wang, Xiu-Bin; Tian, Shou-Fu; Qin, Chun-Yan; Zhang, Tian-Tian

2017-03-01

In this article, a generalised Whitham-Broer-Kaup-Like (WBKL) equations is investigated, which can describe the bidirectional propagation of long waves in shallow water. The equations can be reduced to the dispersive long wave equations, variant Boussinesq equations, Whitham-Broer-Kaup-Like equations, etc. The Lie symmetry analysis method is used to consider the vector fields and optimal system of the equations. The similarity reductions are given on the basic of the optimal system. Furthermore, the power series solutions are derived by using the power series theory. Finally, based on a new theorem of conservation laws, the conservation laws associated with symmetries of this equations are constructed with a detailed derivation.

Subsonic Wing Optimization for Handling Qualities Using ACSYNT

NASA Technical Reports Server (NTRS)

Soban, Danielle Suzanne

1996-01-01

The capability to accurately and rapidly predict aircraft stability derivatives using one comprehensive analysis tool has been created. The PREDAVOR tool has the following capabilities: rapid estimation of stability derivatives using a vortex lattice method, calculation of a longitudinal handling qualities metric, and inherent methodology to optimize a given aircraft configuration for longitudinal handling qualities, including an intuitive graphical interface. The PREDAVOR tool may be applied to both subsonic and supersonic designs, as well as conventional and unconventional, symmetric and asymmetric configurations. The workstation-based tool uses as its model a three-dimensional model of the configuration generated using a computer aided design (CAD) package. The PREDAVOR tool was applied to a Lear Jet Model 23 and the North American XB-70 Valkyrie.

Factorization and the synthesis of optimal feedback kernels for differential-delay systems

NASA Technical Reports Server (NTRS)

Milman, Mark M.; Scheid, Robert E.

1987-01-01

A combination of ideas from the theories of operator Riccati equations and Volterra factorizations leads to the derivation of a novel, relatively simple set of hyperbolic equations which characterize the optimal feedback kernel for the finite-time regulator problem for autonomous differential-delay systems. Analysis of these equations elucidates the underlying structure of the feedback kernel and leads to the development of fast and accurate numerical methods for its computation. Unlike traditional formulations based on the operator Riccati equation, the gain is characterized by means of classical solutions of the derived set of equations. This leads to the development of approximation schemes which are analogous to what has been accomplished for systems of ordinary differential equations with given initial conditions.

Comparing Approaches to Optimize Cut-off Scores for Short Cognitive Screening Instruments in Mild Cognitive Impairment and Dementia

PubMed Central

O’Caoimh, Rónán; Gao, Yang; Svendovski, Anton; Gallagher, Paul; Eustace, Joseph; Molloy, D. William

2017-01-01

Background: Although required to improve the usability of cognitive screening instruments (CSIs), the use of cut-off scores is controversial yet poorly researched. Objective: To explore cut-off scores for two short CSIs: the Standardized Mini-Mental State Examination (SMMSE) and Quick Mild Cognitive Impairment (Qmci) screen, describing adjustments in scores for diagnosis (MCI or dementia), age (≤, >75 years), and education (<, ≥12 years), comparing two methods: the maximal accuracy approach, derived from receiver operating characteristic curves, and Youden’s Index. Methods: Pooled analysis of assessments from patients attending memory clinics in Canada between 1999–2010 : 766 with mild cognitive impairment (MCI) and 1,746 with dementia, and 875 normal controls. Results: The Qmci was more accurate than the SMMSE in differentiating controls from MCI or cognitive impairment (MCI and dementia). Employing the maximal accuracy approach, the optimal SMMSE cut-off for cognitive impairment was <28/30 (AUC 0.86, sensitivity 74%, specificity 88%) versus <63/100 for the Qmci (AUC 0.93, sensitivity 85%, specificity 85%). Using Youden’s Index, the optimal SMMSE cut-off remained <28/30 but fell slightly to <62/100 for the Qmci (sensitivity 83%, specificity 87%). The optimal cut-off for MCI was <29/30 for the SMMSE and <67/100 for the Qmci, irrespective of technique. The maximal accuracy approach generally produced higher Qmci cut-offs than Youden’s Index, both requiring adjustment for age and education. There were no clinically meaningful differences in SMMSE cut-off scores by age and education or method employed. Conclusion: Caution should be exercised selecting cut-offs as these differ by age, education, and method of derivation, with the extent of adjustment varying between CSIs. PMID:28222528

Multibody Kinematics Optimization for the Estimation of Upper and Lower Limb Human Joint Kinematics: A Systematized Methodological Review.

PubMed

Begon, Mickaël; Andersen, Michael Skipper; Dumas, Raphaël

2018-03-01

Multibody kinematics optimization (MKO) aims to reduce soft tissue artefact (STA) and is a key step in musculoskeletal modeling. The objective of this review was to identify the numerical methods, their validation and performance for the estimation of the human joint kinematics using MKO. Seventy-four papers were extracted from a systematized search in five databases and cross-referencing. Model-derived kinematics were obtained using either constrained optimization or Kalman filtering to minimize the difference between measured (i.e., by skin markers, electromagnetic or inertial sensors) and model-derived positions and/or orientations. While hinge, universal, and spherical joints prevail, advanced models (e.g., parallel and four-bar mechanisms, elastic joint) have been introduced, mainly for the knee and shoulder joints. Models and methods were evaluated using: (i) simulated data based, however, on oversimplified STA and joint models; (ii) reconstruction residual errors, ranging from 4 mm to 40 mm; (iii) sensitivity analyses which highlighted the effect (up to 36 deg and 12 mm) of model geometrical parameters, joint models, and computational methods; (iv) comparison with other approaches (i.e., single body kinematics optimization and nonoptimized kinematics); (v) repeatability studies that showed low intra- and inter-observer variability; and (vi) validation against ground-truth bone kinematics (with errors between 1 deg and 22 deg for tibiofemoral rotations and between 3 deg and 10 deg for glenohumeral rotations). Moreover, MKO was applied to various movements (e.g., walking, running, arm elevation). Additional validations, especially for the upper limb, should be undertaken and we recommend a more systematic approach for the evaluation of MKO. In addition, further model development, scaling, and personalization methods are required to better estimate the secondary degrees-of-freedom (DoF).

Optimal design of leak-proof SRAM cell using MCDM method

NASA Astrophysics Data System (ADS)

Wang, Qi; Kang, Sung-Mo

2003-04-01

As deep-submicron CMOS technology advances, on-chip cache has become a bottleneck on microprocessor's performance. Meanwhile, it also occupies a big percentage of processor area and consumes large power. Speed, power and area of SRAM are mutually contradicting, and not easy to be met simultaneously. Many existent leakage suppression techniques have been proposed, but they limit the circuit's performance. We apply a Multi-Criteria Decision Making strategy to perform a minimum delay-power-area optimization on SRAM circuit under some certain constraints. Based on an integrated device and circuit-level approach, we search for a process that yields a targeted composite performance. In consideration of the huge amount of simulation workload involved in the optimal design-seeking process, most of this process is automated to facilitate our goal-pursuant. With varying emphasis put on delay, power or area, different optimal SRAM designs are derived and a gate-oxide thickness scaling limit is projected. The result seems to indicate that a better composite performance could be achieved under a thinner oxide thickness. Under the derived optimal oxide thickness, the static leakage power consumption contributes less than 1% in the total power dissipation.

Replica Approach for Minimal Investment Risk with Cost

NASA Astrophysics Data System (ADS)

Shinzato, Takashi

2018-06-01

In the present work, the optimal portfolio minimizing the investment risk with cost is discussed analytically, where an objective function is constructed in terms of two negative aspects of investment, the risk and cost. We note the mathematical similarity between the Hamiltonian in the mean-variance model and the Hamiltonians in the Hopfield model and the Sherrington-Kirkpatrick model, show that we can analyze this portfolio optimization problem by using replica analysis, and derive the minimal investment risk with cost and the investment concentration of the optimal portfolio. Furthermore, we validate our proposed method through numerical simulations.

Quantifying rainfall-derived inflow and infiltration in sanitary sewer systems based on conductivity monitoring

NASA Astrophysics Data System (ADS)

Zhang, Mingkai; Liu, Yanchen; Cheng, Xun; Zhu, David Z.; Shi, Hanchang; Yuan, Zhiguo

2018-03-01

Quantifying rainfall-derived inflow and infiltration (RDII) in a sanitary sewer is difficult when RDII and overflow occur simultaneously. This study proposes a novel conductivity-based method for estimating RDII. The method separately decomposes rainfall-derived inflow (RDI) and rainfall-induced infiltration (RII) on the basis of conductivity data. Fast Fourier transform was adopted to analyze variations in the flow and water quality during dry weather. Nonlinear curve fitting based on the least squares algorithm was used to optimize parameters in the proposed RDII model. The method was successfully applied to real-life case studies, in which inflow and infiltration were successfully estimated for three typical rainfall events with total rainfall volumes of 6.25 mm (light), 28.15 mm (medium), and 178 mm (heavy). Uncertainties of model parameters were estimated using the generalized likelihood uncertainty estimation (GLUE) method and were found to be acceptable. Compared with traditional flow-based methods, the proposed approach exhibits distinct advantages in estimating RDII and overflow, particularly when the two processes happen simultaneously.

Human motion planning based on recursive dynamics and optimal control techniques

NASA Technical Reports Server (NTRS)

Lo, Janzen; Huang, Gang; Metaxas, Dimitris

2002-01-01

This paper presents an efficient optimal control and recursive dynamics-based computer animation system for simulating and controlling the motion of articulated figures. A quasi-Newton nonlinear programming technique (super-linear convergence) is implemented to solve minimum torque-based human motion-planning problems. The explicit analytical gradients needed in the dynamics are derived using a matrix exponential formulation and Lie algebra. Cubic spline functions are used to make the search space for an optimal solution finite. Based on our formulations, our method is well conditioned and robust, in addition to being computationally efficient. To better illustrate the efficiency of our method, we present results of natural looking and physically correct human motions for a variety of human motion tasks involving open and closed loop kinematic chains.

Comparative study of flare control laws. [optimal control of b-737 aircraft approach and landing

NASA Technical Reports Server (NTRS)

Nadkarni, A. A.; Breedlove, W. J., Jr.

1979-01-01

A digital 3-D automatic control law was developed to achieve an optimal transition of a B-737 aircraft between various initial glid slope conditions and the desired final touchdown condition. A discrete, time-invariant, optimal, closed-loop control law presented for a linear regulator problem, was extended to include a system being acted upon by a constant disturbance. Two forms of control laws were derived to solve this problem. One method utilized the feedback of integral states defined appropriately and augmented with the original system equations. The second method formulated the problem as a control variable constraint, and the control variables were augmented with the original system. The control variable constraint control law yielded a better performance compared to feedback control law for the integral states chosen.

Reconstruction of a piecewise constant conductivity on a polygonal partition via shape optimization in EIT

NASA Astrophysics Data System (ADS)

Beretta, Elena; Micheletti, Stefano; Perotto, Simona; Santacesaria, Matteo

2018-01-01

In this paper, we develop a shape optimization-based algorithm for the electrical impedance tomography (EIT) problem of determining a piecewise constant conductivity on a polygonal partition from boundary measurements. The key tool is to use a distributed shape derivative of a suitable cost functional with respect to movements of the partition. Numerical simulations showing the robustness and accuracy of the method are presented for simulated test cases in two dimensions.

Quaternion Averaging

NASA Technical Reports Server (NTRS)

Markley, F. Landis; Cheng, Yang; Crassidis, John L.; Oshman, Yaakov

2007-01-01

Many applications require an algorithm that averages quaternions in an optimal manner. For example, when combining the quaternion outputs of multiple star trackers having this output capability, it is desirable to properly average the quaternions without recomputing the attitude from the the raw star tracker data. Other applications requiring some sort of optimal quaternion averaging include particle filtering and multiple-model adaptive estimation, where weighted quaternions are used to determine the quaternion estimate. For spacecraft attitude estimation applications, derives an optimal averaging scheme to compute the average of a set of weighted attitude matrices using the singular value decomposition method. Focusing on a 4-dimensional quaternion Gaussian distribution on the unit hypersphere, provides an approach to computing the average quaternion by minimizing a quaternion cost function that is equivalent to the attitude matrix cost function Motivated by and extending its results, this Note derives an algorithm that deterniines an optimal average quaternion from a set of scalar- or matrix-weighted quaternions. Rirthermore, a sufficient condition for the uniqueness of the average quaternion, and the equivalence of the mininiization problem, stated herein, to maximum likelihood estimation, are shown.

Continuous Firefly Algorithm for Optimal Tuning of Pid Controller in Avr System

NASA Astrophysics Data System (ADS)

Bendjeghaba, Omar

2014-01-01

This paper presents a tuning approach based on Continuous firefly algorithm (CFA) to obtain the proportional-integral- derivative (PID) controller parameters in Automatic Voltage Regulator system (AVR). In the tuning processes the CFA is iterated to reach the optimal or the near optimal of PID controller parameters when the main goal is to improve the AVR step response characteristics. Conducted simulations show the effectiveness and the efficiency of the proposed approach. Furthermore the proposed approach can improve the dynamic of the AVR system. Compared with particle swarm optimization (PSO), the new CFA tuning method has better control system performance in terms of time domain specifications and set-point tracking.

An optimized method for the measurement of acetaldehyde by high-performance liquid chromatography.

PubMed

Guan, Xiangying; Rubin, Emanuel; Anni, Helen

2012-03-01

Acetaldehyde is produced during ethanol metabolism predominantly in the liver by alcohol dehydrogenase and rapidly eliminated by oxidation to acetate via aldehyde dehydrogenase. Assessment of circulating acetaldehyde levels in biological matrices is performed by headspace gas chromatography and reverse phase high-performance liquid chromatography (RP-HPLC). We have developed an optimized method for the measurement of acetaldehyde by RP-HPLC in hepatoma cell culture medium, blood, and plasma. After sample deproteinization, acetaldehyde was derivatized with 2,4-dinitrophenylhydrazine (DNPH). The reaction was optimized for pH, amount of derivatization reagent, time, and temperature. Extraction methods of the acetaldehyde-hydrazone (AcH-DNP) stable derivative and product stability studies were carried out. Acetaldehyde was identified by its retention time in comparison with AcH-DNP standard, using a new chromatography gradient program, and quantitated based on external reference standards and standard addition calibration curves in the presence and absence of ethanol. Derivatization of acetaldehyde was performed at pH 4.0 with an 80-fold molar excess of DNPH. The reaction was completed in 40 minutes at ambient temperature, and the product was stable for 2 days. A clear separation of AcH-DNP from DNPH was obtained with a new 11-minute chromatography program. Acetaldehyde detection was linear up to 80 μM. The recovery of acetaldehyde was >88% in culture media and >78% in plasma. We quantitatively determined the ethanol-derived acetaldehyde in hepatoma cells, rat blood and plasma with a detection limit around 3 μM. The accuracy of the method was <9% for intraday and <15% for interday measurements, in small volume (70 μl) plasma sampling. An optimized method for the quantitative determination of acetaldehyde in biological systems was developed using derivatization with DNPH, followed by a short RP-HPLC separation of AcH-DNP. The method has an extended linear range, is reproducible and applicable to small-volume sampling of culture media and biological fluids. Copyright © 2011 by the Research Society on Alcoholism.

Improving engineering system design by formal decomposition, sensitivity analysis, and optimization

NASA Technical Reports Server (NTRS)

Sobieski, J.; Barthelemy, J. F. M.

1985-01-01

A method for use in the design of a complex engineering system by decomposing the problem into a set of smaller subproblems is presented. Coupling of the subproblems is preserved by means of the sensitivity derivatives of the subproblem solution to the inputs received from the system. The method allows for the division of work among many people and computers.

[Object-oriented aquatic vegetation extracting approach based on visible vegetation indices.

PubMed

Jing, Ran; Deng, Lei; Zhao, Wen Ji; Gong, Zhao Ning

2016-05-01

Using the estimation of scale parameters (ESP) image segmentation tool to determine the ideal image segmentation scale, the optimal segmented image was created by the multi-scale segmentation method. Based on the visible vegetation indices derived from mini-UAV imaging data, we chose a set of optimal vegetation indices from a series of visible vegetation indices, and built up a decision tree rule. A membership function was used to automatically classify the study area and an aquatic vegetation map was generated. The results showed the overall accuracy of image classification using the supervised classification was 53.7%, and the overall accuracy of object-oriented image analysis (OBIA) was 91.7%. Compared with pixel-based supervised classification method, the OBIA method improved significantly the image classification result and further increased the accuracy of extracting the aquatic vegetation. The Kappa value of supervised classification was 0.4, and the Kappa value based OBIA was 0.9. The experimental results demonstrated that using visible vegetation indices derived from the mini-UAV data and OBIA method extracting the aquatic vegetation developed in this study was feasible and could be applied in other physically similar areas.

Systematic evaluation and optimization of modification reactions of oligonucleotides with amines and carboxylic acids for the synthesis of DNA-encoded chemical libraries.

PubMed

Franzini, Raphael M; Samain, Florent; Abd Elrahman, Maaly; Mikutis, Gediminas; Nauer, Angela; Zimmermann, Mauro; Scheuermann, Jörg; Hall, Jonathan; Neri, Dario

2014-08-20

DNA-encoded chemical libraries are collections of small molecules, attached to DNA fragments serving as identification barcodes, which can be screened against multiple protein targets, thus facilitating the drug discovery process. The preparation of large DNA-encoded chemical libraries crucially depends on the availability of robust synthetic methods, which enable the efficient conjugation to oligonucleotides of structurally diverse building blocks, sharing a common reactive group. Reactions of DNA derivatives with amines and/or carboxylic acids are particularly attractive for the synthesis of encoded libraries, in view of the very large number of building blocks that are commercially available. However, systematic studies on these reactions in the presence of DNA have not been reported so far. We first investigated conditions for the coupling of primary amines to oligonucleotides, using either a nucleophilic attack on chloroacetamide derivatives or a reductive amination on aldehyde-modified DNA. While both methods could be used for the production of secondary amines, the reductive amination approach was generally associated with higher yields and better purity. In a second endeavor, we optimized conditions for the coupling of a diverse set of 501 carboxylic acids to DNA derivatives, carrying primary and secondary amine functions. The coupling efficiency was generally higher for primary amines, compared to secondary amine substituents, but varied considerably depending on the structure of the acids and on the synthetic methods used. Optimal reaction conditions could be found for certain sets of compounds (with conversions >80%), but multiple reaction schemes are needed when assembling large libraries with highly diverse building blocks. The reactions and experimental conditions presented in this article should facilitate the synthesis of future DNA-encoded chemical libraries, while outlining the synthetic challenges that remain to be overcome.

Scope of Gradient and Genetic Algorithms in Multivariable Function Optimization

NASA Technical Reports Server (NTRS)

Shaykhian, Gholam Ali; Sen, S. K.

2007-01-01

Global optimization of a multivariable function - constrained by bounds specified on each variable and also unconstrained - is an important problem with several real world applications. Deterministic methods such as the gradient algorithms as well as the randomized methods such as the genetic algorithms may be employed to solve these problems. In fact, there are optimization problems where a genetic algorithm/an evolutionary approach is preferable at least from the quality (accuracy) of the results point of view. From cost (complexity) point of view, both gradient and genetic approaches are usually polynomial-time; there are no serious differences in this regard, i.e., the computational complexity point of view. However, for certain types of problems, such as those with unacceptably erroneous numerical partial derivatives and those with physically amplified analytical partial derivatives whose numerical evaluation involves undesirable errors and/or is messy, a genetic (stochastic) approach should be a better choice. We have presented here the pros and cons of both the approaches so that the concerned reader/user can decide which approach is most suited for the problem at hand. Also for the function which is known in a tabular form, instead of an analytical form, as is often the case in an experimental environment, we attempt to provide an insight into the approaches focusing our attention toward accuracy. Such an insight will help one to decide which method, out of several available methods, should be employed to obtain the best (least error) output. *

The Application of Auto-Disturbance Rejection Control Optimized by Least Squares Support Vector Machines Method and Time-Frequency Representation in Voltage Source Converter-High Voltage Direct Current System.

PubMed

Liu, Ying-Pei; Liang, Hai-Ping; Gao, Zhong-Ke

2015-01-01

In order to improve the performance of voltage source converter-high voltage direct current (VSC-HVDC) system, we propose an improved auto-disturbance rejection control (ADRC) method based on least squares support vector machines (LSSVM) in the rectifier side. Firstly, we deduce the high frequency transient mathematical model of VSC-HVDC system. Then we investigate the ADRC and LSSVM principles. We ignore the tracking differentiator in the ADRC controller aiming to improve the system dynamic response speed. On this basis, we derive the mathematical model of ADRC controller optimized by LSSVM for direct current voltage loop. Finally we carry out simulations to verify the feasibility and effectiveness of our proposed control method. In addition, we employ the time-frequency representation methods, i.e., Wigner-Ville distribution (WVD) and adaptive optimal kernel (AOK) time-frequency representation, to demonstrate our proposed method performs better than the traditional method from the perspective of energy distribution in time and frequency plane.

The Application of Auto-Disturbance Rejection Control Optimized by Least Squares Support Vector Machines Method and Time-Frequency Representation in Voltage Source Converter-High Voltage Direct Current System

PubMed Central

Gao, Zhong-Ke

2015-01-01

In order to improve the performance of voltage source converter-high voltage direct current (VSC-HVDC) system, we propose an improved auto-disturbance rejection control (ADRC) method based on least squares support vector machines (LSSVM) in the rectifier side. Firstly, we deduce the high frequency transient mathematical model of VSC-HVDC system. Then we investigate the ADRC and LSSVM principles. We ignore the tracking differentiator in the ADRC controller aiming to improve the system dynamic response speed. On this basis, we derive the mathematical model of ADRC controller optimized by LSSVM for direct current voltage loop. Finally we carry out simulations to verify the feasibility and effectiveness of our proposed control method. In addition, we employ the time-frequency representation methods, i.e., Wigner-Ville distribution (WVD) and adaptive optimal kernel (AOK) time-frequency representation, to demonstrate our proposed method performs better than the traditional method from the perspective of energy distribution in time and frequency plane. PMID:26098556

Invisibility problem in acoustics, electromagnetism and heat transfer. Inverse design method

NASA Astrophysics Data System (ADS)

Alekseev, G.; Tokhtina, A.; Soboleva, O.

2017-10-01

Two approaches (direct design and inverse design methods) for solving problems of designing devices providing invisibility of material bodies of detection using different physical fields - electromagnetic, acoustic and static are discussed. The second method is applied for solving problems of designing cloaking devices for the 3D stationary thermal scattering model. Based on this method the design problems under study are reduced to respective control problems. The material parameters (radial and tangential heat conductivities) of the inhomogeneous anisotropic medium filling the thermal cloak and the density of auxiliary heat sources play the role of controls. A unique solvability of direct thermal scattering problem in the Sobolev space is proved and the new estimates of solutions are established. Using these results, the solvability of control problem is proved and the optimality system is derived. Based on analysis of optimality system, the stability estimates of optimal solutions are established and numerical algorithms for solving particular thermal cloaking problem are proposed.

Sensitivity of control-augmented structure obtained by a system decomposition method

NASA Technical Reports Server (NTRS)

Sobieszczanskisobieski, Jaroslaw; Bloebaum, Christina L.; Hajela, Prabhat

1988-01-01

The verification of a method for computing sensitivity derivatives of a coupled system is presented. The method deals with a system whose analysis can be partitioned into subsets that correspond to disciplines and/or physical subsystems that exchange input-output data with each other. The method uses the partial sensitivity derivatives of the output with respect to input obtained for each subset separately to assemble a set of linear, simultaneous, algebraic equations that are solved for the derivatives of the coupled system response. This sensitivity analysis is verified using an example of a cantilever beam augmented with an active control system to limit the beam's dynamic displacements under an excitation force. The verification shows good agreement of the method with reference data obtained by a finite difference technique involving entire system analysis. The usefulness of a system sensitivity method in optimization applications by employing a piecewise-linear approach to the same numerical example is demonstrated. The method's principal merits are its intrinsically superior accuracy in comparison with the finite difference technique, and its compatibility with the traditional division of work in complex engineering tasks among specialty groups.

An optimized data fusion method and its application to improve lateral boundary conditions in winter for Pearl River Delta regional PM2.5 modeling, China

NASA Astrophysics Data System (ADS)

Huang, Zhijiong; Hu, Yongtao; Zheng, Junyu; Zhai, Xinxin; Huang, Ran

2018-05-01

Lateral boundary conditions (LBCs) are essential for chemical transport models to simulate regional transport; however they often contain large uncertainties. This study proposes an optimized data fusion approach to reduce the bias of LBCs by fusing gridded model outputs, from which the daughter domain's LBCs are derived, with ground-level measurements. The optimized data fusion approach follows the framework of a previous interpolation-based fusion method but improves it by using a bias kriging method to correct the spatial bias in gridded model outputs. Cross-validation shows that the optimized approach better estimates fused fields in areas with a large number of observations compared to the previous interpolation-based method. The optimized approach was applied to correct LBCs of PM2.5 concentrations for simulations in the Pearl River Delta (PRD) region as a case study. Evaluations show that the LBCs corrected by data fusion improve in-domain PM2.5 simulations in terms of the magnitude and temporal variance. Correlation increases by 0.13-0.18 and fractional bias (FB) decreases by approximately 3%-15%. This study demonstrates the feasibility of applying data fusion to improve regional air quality modeling.

Protein–DNA Interactions: The Story so Far and a New Method for Prediction

DOE PAGES

Jones, Susan; Thornton, Janet M.

2003-01-01

This review describes methods for the prediction of DNA binding function, and specifically summarizes a new method using 3D structural templates. The new method features the HTH motif that is found in approximately one-third of DNAbinding protein families. A library of 3D structural templates of HTH motifs was derived from proteins in the PDB. Templates were scanned against complete protein structures and the optimal superposition of a template on a structure calculated. Significance thresholds in terms of a minimum root mean squared deviation (rmsd) of an optimal superposition, and a minimum motif accessible surface area (ASA), have been calculated. Inmore » this way, it is possible to scan the template library against proteins of unknown function to make predictions about DNA-binding functionality.« less

Function Invariant and Parameter Scale-Free Transformation Methods

ERIC Educational Resources Information Center

Bentler, P. M.; Wingard, Joseph A.

1977-01-01

A scale-invariant simple structure function of previously studied function components for principal component analysis and factor analysis is defined. First and second partial derivatives are obtained, and Newton-Raphson iterations are utilized. The resulting solutions are locally optimal and subjectively pleasing. (Author/JKS)

Inverse Diffusion Curves Using Shape Optimization.

PubMed

Zhao, Shuang; Durand, Fredo; Zheng, Changxi

2018-07-01

The inverse diffusion curve problem focuses on automatic creation of diffusion curve images that resemble user provided color fields. This problem is challenging since the 1D curves have a nonlinear and global impact on resulting color fields via a partial differential equation (PDE). We introduce a new approach complementary to previous methods by optimizing curve geometry. In particular, we propose a novel iterative algorithm based on the theory of shape derivatives. The resulting diffusion curves are clean and well-shaped, and the final image closely approximates the input. Our method provides a user-controlled parameter to regularize curve complexity, and generalizes to handle input color fields represented in a variety of formats.

Transform methods for precision continuum and control models of flexible space structures

NASA Technical Reports Server (NTRS)

Lupi, Victor D.; Turner, James D.; Chun, Hon M.

1991-01-01

An open loop optimal control algorithm is developed for general flexible structures, based on Laplace transform methods. A distributed parameter model of the structure is first presented, followed by a derivation of the optimal control algorithm. The control inputs are expressed in terms of their Fourier series expansions, so that a numerical solution can be easily obtained. The algorithm deals directly with the transcendental transfer functions from control inputs to outputs of interest, and structural deformation penalties, as well as penalties on control effort, are included in the formulation. The algorithm is applied to several structures of increasing complexity to show its generality.

An automated model-based aim point distribution system for solar towers

NASA Astrophysics Data System (ADS)

Schwarzbözl, Peter; Rong, Amadeus; Macke, Ansgar; Säck, Jan-Peter; Ulmer, Steffen

2016-05-01

Distribution of heliostat aim points is a major task during central receiver operation, as the flux distribution produced by the heliostats varies continuously with time. Known methods for aim point distribution are mostly based on simple aim point patterns and focus on control strategies to meet local temperature and flux limits of the receiver. Lowering the peak flux on the receiver to avoid hot spots and maximizing thermal output are obviously competing targets that call for a comprehensive optimization process. This paper presents a model-based method for online aim point optimization that includes the current heliostat field mirror quality derived through an automated deflectometric measurement process.

Constructing analytic solutions on the Tricomi equation

NASA Astrophysics Data System (ADS)

Ghiasi, Emran Khoshrouye; Saleh, Reza

2018-04-01

In this paper, homotopy analysis method (HAM) and variational iteration method (VIM) are utilized to derive the approximate solutions of the Tricomi equation. Afterwards, the HAM is optimized to accelerate the convergence of the series solution by minimizing its square residual error at any order of the approximation. It is found that effect of the optimal values of auxiliary parameter on the convergence of the series solution is not negligible. Furthermore, the present results are found to agree well with those obtained through a closed-form equation available in the literature. To conclude, it is seen that the two are effective to achieve the solution of the partial differential equations.

Belief Propagation Algorithm for Portfolio Optimization Problems

PubMed Central

2015-01-01

The typical behavior of optimal solutions to portfolio optimization problems with absolute deviation and expected shortfall models using replica analysis was pioneeringly estimated by S. Ciliberti et al. [Eur. Phys. B. 57, 175 (2007)]; however, they have not yet developed an approximate derivation method for finding the optimal portfolio with respect to a given return set. In this study, an approximation algorithm based on belief propagation for the portfolio optimization problem is presented using the Bethe free energy formalism, and the consistency of the numerical experimental results of the proposed algorithm with those of replica analysis is confirmed. Furthermore, the conjecture of H. Konno and H. Yamazaki, that the optimal solutions with the absolute deviation model and with the mean-variance model have the same typical behavior, is verified using replica analysis and the belief propagation algorithm. PMID:26305462

Belief Propagation Algorithm for Portfolio Optimization Problems.

PubMed

Shinzato, Takashi; Yasuda, Muneki

2015-01-01

The typical behavior of optimal solutions to portfolio optimization problems with absolute deviation and expected shortfall models using replica analysis was pioneeringly estimated by S. Ciliberti et al. [Eur. Phys. B. 57, 175 (2007)]; however, they have not yet developed an approximate derivation method for finding the optimal portfolio with respect to a given return set. In this study, an approximation algorithm based on belief propagation for the portfolio optimization problem is presented using the Bethe free energy formalism, and the consistency of the numerical experimental results of the proposed algorithm with those of replica analysis is confirmed. Furthermore, the conjecture of H. Konno and H. Yamazaki, that the optimal solutions with the absolute deviation model and with the mean-variance model have the same typical behavior, is verified using replica analysis and the belief propagation algorithm.

Non-linear Multidimensional Optimization for use in Wire Scanner Fitting

NASA Astrophysics Data System (ADS)

Henderson, Alyssa; Terzic, Balsa; Hofler, Alicia; Center Advanced Studies of Accelerators Collaboration

2014-03-01

To ensure experiment efficiency and quality from the Continuous Electron Beam Accelerator at Jefferson Lab, beam energy, size, and position must be measured. Wire scanners are devices inserted into the beamline to produce measurements which are used to obtain beam properties. Extracting physical information from the wire scanner measurements begins by fitting Gaussian curves to the data. This study focuses on optimizing and automating this curve-fitting procedure. We use a hybrid approach combining the efficiency of Newton Conjugate Gradient (NCG) method with the global convergence of three nature-inspired (NI) optimization approaches: genetic algorithm, differential evolution, and particle-swarm. In this Python-implemented approach, augmenting the locally-convergent NCG with one of the globally-convergent methods ensures the quality, robustness, and automation of curve-fitting. After comparing the methods, we establish that given an initial data-derived guess, each finds a solution with the same chi-square- a measurement of the agreement of the fit to the data. NCG is the fastest method, so it is the first to attempt data-fitting. The curve-fitting procedure escalates to one of the globally-convergent NI methods only if NCG fails, thereby ensuring a successful fit. This method allows for the most optimal signal fit and can be easily applied to similar problems.

Efficiency of timing delays and electrode positions in optimization of biventricular pacing: a simulation study.

PubMed

Miri, Raz; Graf, Iulia M; Dössel, Olaf

2009-11-01

Electrode positions and timing delays influence the efficacy of biventricular pacing (BVP). Accordingly, this study focuses on BVP optimization, using a detailed 3-D electrophysiological model of the human heart, which is adapted to patient-specific anatomy and pathophysiology. The research is effectuated on ten heart models with left bundle branch block and myocardial infarction derived from magnetic resonance and computed tomography data. Cardiac electrical activity is simulated with the ten Tusscher cell model and adaptive cellular automaton at physiological and pathological conduction levels. The optimization methods are based on a comparison between the electrical response of the healthy and diseased heart models, measured in terms of root mean square error (E(RMS)) of the excitation front and the QRS duration error (E(QRS)). Intra- and intermethod associations of the pacing electrodes and timing delays variables were analyzed with statistical methods, i.e., t -test for dependent data, one-way analysis of variance for electrode pairs, and Pearson model for equivalent parameters from the two optimization methods. The results indicate that lateral the left ventricle and the upper or middle septal area are frequently (60% of cases) the optimal positions of the left and right electrodes, respectively. Statistical analysis proves that the two optimization methods are in good agreement. In conclusion, a noninvasive preoperative BVP optimization strategy based on computer simulations can be used to identify the most beneficial patient-specific electrode configuration and timing delays.

Automatic optimal filament segmentation with sub-pixel accuracy using generalized linear models and B-spline level-sets

PubMed Central

Xiao, Xun; Geyer, Veikko F.; Bowne-Anderson, Hugo; Howard, Jonathon; Sbalzarini, Ivo F.

2016-01-01

Biological filaments, such as actin filaments, microtubules, and cilia, are often imaged using different light-microscopy techniques. Reconstructing the filament curve from the acquired images constitutes the filament segmentation problem. Since filaments have lower dimensionality than the image itself, there is an inherent trade-off between tracing the filament with sub-pixel accuracy and avoiding noise artifacts. Here, we present a globally optimal filament segmentation method based on B-spline vector level-sets and a generalized linear model for the pixel intensity statistics. We show that the resulting optimization problem is convex and can hence be solved with global optimality. We introduce a simple and efficient algorithm to compute such optimal filament segmentations, and provide an open-source implementation as an ImageJ/Fiji plugin. We further derive an information-theoretic lower bound on the filament segmentation error, quantifying how well an algorithm could possibly do given the information in the image. We show that our algorithm asymptotically reaches this bound in the spline coefficients. We validate our method in comprehensive benchmarks, compare with other methods, and show applications from fluorescence, phase-contrast, and dark-field microscopy. PMID:27104582

Stereoselective synthesis, X-ray analysis, computational studies and biological evaluation of new thiazole derivatives as potential anticancer agents.

PubMed

Mabkhot, Yahia N; Alharbi, Mohammed M; Al-Showiman, Salim S; Ghabbour, Hazem A; Kheder, Nabila A; Soliman, Saied M; Frey, Wolfgang

2018-05-11

The synthesis of new thiazole derivatives is very important because of their diverse biological activities. Also , many drugs containing thiazole ring in their skeletons are available in the market such as Abafungin, Acotiamide, Alagebrium, Amiphenazole, Brecanavir, Carumonam, Cefepime, and Cefmatilen. Ethyl cyanoacetate reacted with phenylisothiocyanate, chloroacetone, in two different basic mediums to afford the thiazole derivative 6, which reacted with dimethylformamide- dimethyl acetal in the presence of DMF to afford the unexpected thiazole derivative 11. The structures of the thiazoles 6 and 11 were optimized using B3LYP/6-31G(d,p) method. The experimentally and theoretically geometric parameters agreed very well. Also, the natural charges at the different atomic sites were predicted. HOMO and LUMO demands were discussed. The anticancer activity of the prepared compounds was evaluated and showed moderate activity. Synthesis of novel thiazole derivatives was done. The structure was established using X-ray and spectral analysis. Optimized molecular structures at the B3LYP/6-31G(d,p) level were investigated. Thiazole derivative 11 has more electropositive S-atom than thiazole 6. The HOMO-LUMO energy gap is lower in the former compared to the latter. The synthesized compounds showed moderate anticancer activity.

Generation and customization of biosynthetic excitable tissues for electrophysiological studies and cell-based therapies.

PubMed

Nguyen, Hung X; Kirkton, Robert D; Bursac, Nenad

2018-05-01

We describe a two-stage protocol to generate electrically excitable and actively conducting cell networks with stable and customizable electrophysiological phenotypes. Using this method, we have engineered monoclonally derived excitable tissues as a robust and reproducible platform to investigate how specific ion channels and mutations affect action potential (AP) shape and conduction. In the first stage of the protocol, we combine computational modeling, site-directed mutagenesis, and electrophysiological techniques to derive optimal sets of mammalian and/or prokaryotic ion channels that produce specific AP shape and conduction characteristics. In the second stage of the protocol, selected ion channels are stably expressed in unexcitable human cells by means of viral or nonviral delivery, followed by flow cytometry or antibiotic selection to purify the desired phenotype. This protocol can be used with traditional heterologous expression systems or primary excitable cells, and application of this method to primary fibroblasts may enable an alternative approach to cardiac cell therapy. Compared with existing methods, this protocol generates a well-defined, relatively homogeneous electrophysiological phenotype of excitable cells that facilitates experimental and computational studies of AP conduction and can decrease arrhythmogenic risk upon cell transplantation. Although basic cell culture and molecular biology techniques are sufficient to generate excitable tissues using the described protocol, experience with patch-clamp techniques is required to characterize and optimize derived cell populations.

Optimal swimming of a sheet.

PubMed

Montenegro-Johnson, Thomas D; Lauga, Eric

2014-06-01

Propulsion at microscopic scales is often achieved through propagating traveling waves along hairlike organelles called flagella. Taylor's two-dimensional swimming sheet model is frequently used to provide insight into problems of flagellar propulsion. We derive numerically the large-amplitude wave form of the two-dimensional swimming sheet that yields optimum hydrodynamic efficiency: the ratio of the squared swimming speed to the rate-of-working of the sheet against the fluid. Using the boundary element method, we show that the optimal wave form is a front-back symmetric regularized cusp that is 25% more efficient than the optimal sine wave. This optimal two-dimensional shape is smooth, qualitatively different from the kinked form of Lighthill's optimal three-dimensional flagellum, not predicted by small-amplitude theory, and different from the smooth circular-arc-like shape of active elastic filaments.

Screening, isolation and optimization of anti–white spot syndrome virus drug derived from marine plants

PubMed Central

Chakraborty, Somnath; Ghosh, Upasana; Balasubramanian, Thangavel; Das, Punyabrata

2014-01-01

Objective To screen, isolate and optimize anti-white spot syndrome virus (WSSV) drug derived from various marine floral ecosystems and to evaluate the efficacy of the same in host–pathogen interaction model. Methods Thirty species of marine plants were subjected to Soxhlet extraction using water, ethanol, methanol and hexane as solvents. The 120 plant isolates thus obtained were screened for their in vivo anti-WSSV property in Litopenaeus vannamei. By means of chemical processes, the purified anti-WSSV plant isolate, MP07X was derived. The drug was optimized at various concentrations. Viral and immune genes were analysed using reverse transcriptase PCR to confirm the potency of the drug. Results Nine plant isolates exhibited significant survivability in host. The drug MP07X thus formulated showing 85% survivability in host. The surviving shrimps were nested PCR negative at the end of the 15 d experimentation. The lowest concentration of MP07X required intramuscularly for virucidal property was 10 mg/mL. The oral dosage of 1 000 mg/kg body weight/day survived at the rate of 85%. Neither VP28 nor ie 1 was expressed in the test samples at 42nd hour and 84th hour post viral infection. Conclusions The drug MP07X derived from Rhizophora mucronata is a potent anti-WSSV drug. PMID:25183065

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.

Well-posedness and decay for the dissipative system modeling electro-hydrodynamics in negative Besov spaces

NASA Astrophysics Data System (ADS)

Zhao, Jihong; Liu, Qiao

2017-07-01

In Guo and Wang (2012) [10], Y. Guo and Y. Wang developed a general new energy method for proving the optimal time decay rates of the solutions to dissipative equations. In this paper, we generalize this method in the framework of homogeneous Besov spaces. Moreover, we apply this method to a model arising from electro-hydrodynamics, which is a strongly coupled system of the Navier-Stokes equations and the Poisson-Nernst-Planck equations through charge transport and external forcing terms. We show that some weighted negative Besov norms of solutions are preserved along time evolution, and obtain the optimal time decay rates of the higher-order spatial derivatives of solutions by the Fourier splitting approach and the interpolation techniques.

Derivative Free Optimization of Complex Systems with the Use of Statistical Machine Learning Models

DTIC Science & Technology

2015-09-12

AFRL-AFOSR-VA-TR-2015-0278 DERIVATIVE FREE OPTIMIZATION OF COMPLEX SYSTEMS WITH THE USE OF STATISTICAL MACHINE LEARNING MODELS Katya Scheinberg...COMPLEX SYSTEMS WITH THE USE OF STATISTICAL MACHINE LEARNING MODELS 5a.  CONTRACT NUMBER 5b.  GRANT NUMBER FA9550-11-1-0239 5c.  PROGRAM ELEMENT...developed, which has been the focus of our research. 15. SUBJECT TERMS optimization, Derivative-Free Optimization, Statistical Machine Learning 16. SECURITY

Approximate analysis for repeated eigenvalue problems with applications to controls-structure integrated design

NASA Technical Reports Server (NTRS)

Kenny, Sean P.; Hou, Gene J. W.

1994-01-01

A method for eigenvalue and eigenvector approximate analysis for the case of repeated eigenvalues with distinct first derivatives is presented. The approximate analysis method developed involves a reparameterization of the multivariable structural eigenvalue problem in terms of a single positive-valued parameter. The resulting equations yield first-order approximations to changes in the eigenvalues and the eigenvectors associated with the repeated eigenvalue problem. This work also presents a numerical technique that facilitates the definition of an eigenvector derivative for the case of repeated eigenvalues with repeated eigenvalue derivatives (of all orders). Examples are given which demonstrate the application of such equations for sensitivity and approximate analysis. Emphasis is placed on the application of sensitivity analysis to large-scale structural and controls-structures optimization problems.

An optimization approach for fitting canonical tensor decompositions.

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

Dunlavy, Daniel M.; Acar, Evrim; Kolda, Tamara Gibson

Tensor decompositions are higher-order analogues of matrix decompositions and have proven to be powerful tools for data analysis. In particular, we are interested in the canonical tensor decomposition, otherwise known as the CANDECOMP/PARAFAC decomposition (CPD), which expresses a tensor as the sum of component rank-one tensors and is used in a multitude of applications such as chemometrics, signal processing, neuroscience, and web analysis. The task of computing the CPD, however, can be difficult. The typical approach is based on alternating least squares (ALS) optimization, which can be remarkably fast but is not very accurate. Previously, nonlinear least squares (NLS) methodsmore » have also been recommended; existing NLS methods are accurate but slow. In this paper, we propose the use of gradient-based optimization methods. We discuss the mathematical calculation of the derivatives and further show that they can be computed efficiently, at the same cost as one iteration of ALS. Computational experiments demonstrate that the gradient-based optimization methods are much more accurate than ALS and orders of magnitude faster than NLS.« less

Optimizing Economic Indicators in the Case of Using Two Types of State-Subsidized Chemical Fertilizers for Agricultural Production

NASA Astrophysics Data System (ADS)

Boldea, M.; Sala, F.

2010-09-01

We admit that the mathematical relation between agricultural production f(x, y) and the two types of fertilizers x and y is given by function (1). The coefficients that appear are determined by using the least squares method by comparison with the experimental data. We took into consideration the following economic indicators: absolute benefit, relative benefit, profitableness and cost price. These are maximized or minimized, thus obtaining the optimal solutions by annulling the partial derivatives.

Hybrid optimal scheduling for intermittent androgen suppression of prostate cancer

NASA Astrophysics Data System (ADS)

Hirata, Yoshito; di Bernardo, Mario; Bruchovsky, Nicholas; Aihara, Kazuyuki

2010-12-01

We propose a method for achieving an optimal protocol of intermittent androgen suppression for the treatment of prostate cancer. Since the model that reproduces the dynamical behavior of the surrogate tumor marker, prostate specific antigen, is piecewise linear, we can obtain an analytical solution for the model. Based on this, we derive conditions for either stopping or delaying recurrent disease. The solution also provides a design principle for the most favorable schedule of treatment that minimizes the rate of expansion of the malignant cell population.

Smart Phase Tuning in Microwave Photonic Integrated Circuits Toward Automated Frequency Multiplication by Design

NASA Astrophysics Data System (ADS)

Nabavi, N.

2018-07-01

The author investigates the monitoring methods for fine adjustment of the previously proposed on-chip architecture for frequency multiplication and translation of harmonics by design. Digital signal processing (DSP) algorithms are utilized to create an optimized microwave photonic integrated circuit functionality toward automated frequency multiplication. The implemented DSP algorithms are formed on discrete Fourier transform and optimization-based algorithms (Greedy and gradient-based algorithms), which are analytically derived and numerically compared based on the accuracy and speed of convergence criteria.

Petermann I and II spot size: Accurate semi analytical description involving Nelder-Mead method of nonlinear unconstrained optimization and three parameter fundamental modal field

NASA Astrophysics Data System (ADS)

Roy Choudhury, Raja; Roy Choudhury, Arundhati; Kanti Ghose, Mrinal

2013-01-01

A semi-analytical model with three optimizing parameters and a novel non-Gaussian function as the fundamental modal field solution has been proposed to arrive at an accurate solution to predict various propagation parameters of graded-index fibers with less computational burden than numerical methods. In our semi analytical formulation the optimization of core parameter U which is usually uncertain, noisy or even discontinuous, is being calculated by Nelder-Mead method of nonlinear unconstrained minimizations as it is an efficient and compact direct search method and does not need any derivative information. Three optimizing parameters are included in the formulation of fundamental modal field of an optical fiber to make it more flexible and accurate than other available approximations. Employing variational technique, Petermann I and II spot sizes have been evaluated for triangular and trapezoidal-index fibers with the proposed fundamental modal field. It has been demonstrated that, the results of the proposed solution identically match with the numerical results over a wide range of normalized frequencies. This approximation can also be used in the study of doped and nonlinear fiber amplifier.

Configuration optimization of laser guide stars and wavefront correctors for multi-conjugation adaptive optics

NASA Astrophysics Data System (ADS)

Xuan, Li; He, Bin; Hu, Li-Fa; Li, Da-Yu; Xu, Huan-Yu; Zhang, Xing-Yun; Wang, Shao-Xin; Wang, Yu-Kun; Yang, Cheng-Liang; Cao, Zhao-Liang; Mu, Quan-Quan; Lu, Xing-Hai

2016-09-01

Multi-conjugation adaptive optics (MCAOs) have been investigated and used in the large aperture optical telescopes for high-resolution imaging with large field of view (FOV). The atmospheric tomographic phase reconstruction and projection of three-dimensional turbulence volume onto wavefront correctors, such as deformable mirrors (DMs) or liquid crystal wavefront correctors (LCWCs), is a very important step in the data processing of an MCAO’s controller. In this paper, a method according to the wavefront reconstruction performance of MCAO is presented to evaluate the optimized configuration of multi laser guide stars (LGSs) and the reasonable conjugation heights of LCWCs. Analytical formulations are derived for the different configurations and are used to generate optimized parameters for MCAO. Several examples are given to demonstrate our LGSs configuration optimization method. Compared with traditional methods, our method has minimum wavefront tomographic error, which will be helpful to get higher imaging resolution at large FOV in MCAO. Project supported by the National Natural Science Foundation of China (Grant Nos. 11174274, 11174279, 61205021, 11204299, 61475152, and 61405194) and the State Key Laboratory of Applied Optics, Changchun Institute of Optics, Fine Mechanics and Physics, Chinese Academy of Sciences.

Detecting glaucomatous change in visual fields: Analysis with an optimization framework.

PubMed

Yousefi, Siamak; Goldbaum, Michael H; Varnousfaderani, Ehsan S; Belghith, Akram; Jung, Tzyy-Ping; Medeiros, Felipe A; Zangwill, Linda M; Weinreb, Robert N; Liebmann, Jeffrey M; Girkin, Christopher A; Bowd, Christopher

2015-12-01

Detecting glaucomatous progression is an important aspect of glaucoma management. The assessment of longitudinal series of visual fields, measured using Standard Automated Perimetry (SAP), is considered the reference standard for this effort. We seek efficient techniques for determining progression from longitudinal visual fields by formulating the problem as an optimization framework, learned from a population of glaucoma data. The longitudinal data from each patient's eye were used in a convex optimization framework to find a vector that is representative of the progression direction of the sample population, as a whole. Post-hoc analysis of longitudinal visual fields across the derived vector led to optimal progression (change) detection. The proposed method was compared to recently described progression detection methods and to linear regression of instrument-defined global indices, and showed slightly higher sensitivities at the highest specificities than other methods (a clinically desirable result). The proposed approach is simpler, faster, and more efficient for detecting glaucomatous changes, compared to our previously proposed machine learning-based methods, although it provides somewhat less information. This approach has potential application in glaucoma clinics for patient monitoring and in research centers for classification of study participants. Copyright © 2015 Elsevier Inc. All rights reserved.

A method of determining the refractive index of a prismatic lens.

PubMed

Buckley, John G

2010-01-01

A new method of measuring lens refractive index requiring immersion in solution and measuring lens power in air and in solution is extended. Prompted by a clinical need, the new method using lens power can be extended by applying it to prismatic power as well. This article provides a theoretical basis explaining why this can be done. The prismatic power of a prism is derived from first principles. Snell's Law and geometrical optics provide the framework for demonstrating the validity of the resulting formula. The sameness in formula derived using lens power or prism is shown, both from a paraxial and non-paraxial optics perspective. The effect of varying lens material and amount of prism is considered. The prismatic method described provides a useful alternative method of determining the refractive index of any lens. In some cases, it may be the only method available. Practitioners should consider when each method will provide optimal results.

Growth kinetics of Chlorococcum humicola - A potential feedstock for biomass with biofuel properties.

PubMed

Thomas, Jibu; Jayachithra, E V

2015-11-01

Economically viable production facilities for microalgae depend on the optimization of growth parameters with regard to nutrient requirements. Using microalgae to treat industrial effluents containing heavy metals presents an alternative to the current practice of using physical and chemical methods. Present work focuses on the statistical optimization of growth of Chlorococcum humicola to ascertain the maximum production of biomass. Plackett Burman design was carried out to screen the significant variables influencing biomass production. Further, Response Surface Methodology was employed to optimize the effect of inoculum, light intensity and pH on net biomass yield. Optimum conditions for maximum biomass yield were identified to be inoculum at 15%, light intensity to be 1500lx and pH 8.5. Theoretical and predicted values were in agreement and thus the model was found to be significant. Gas chromatography analyses of the FAME derivatives showed a high percentage of saturated fatty acids thereby confirming the biofuel properties of the oil derived from algal biomass. Copyright © 2015 Elsevier Inc. All rights reserved.

Plate equations for piezoelectrically actuated flexural mode ultrasound transducers.

PubMed

Perçin, Gökhan

2003-01-01

This paper considers variational methods to derive two-dimensional plate equations for piezoelectrically actuated flexural mode ultrasound transducers. In the absence of analytical expressions for the equivalent circuit parameters of a flexural mode transducer, it is difficult to calculate its optimal parameters and dimensions, and to choose suitable materials. The influence of coupling between flexural and extensional deformation, and coupling between the structure and the acoustic volume on the dynamic response of piezoelectrically actuated flexural mode transducer is analyzed using variational methods. Variational methods are applied to derive two-dimensional plate equations for the transducer, and to calculate the coupled electromechanical field variables. In these methods, the variations across the thickness direction vanish by using the stress resultants. Thus, two-dimensional plate equations for a stepwise laminated circular plate are obtained.

Optimal Mortgage Refinancing: A Closed Form Solution

PubMed Central

Agarwal, Sumit; Driscoll, John C.; Laibson, David I.

2013-01-01

We derive the first closed-form optimal refinancing rule: Refinance when the current mortgage interest rate falls below the original rate by at least 1ψ[ϕ+W(−exp(−ϕ))]. In this formula W(.) is the Lambert W-function, ψ=2(ρ+λ)σ,ϕ=1+ψ(ρ+λ)κ∕M(1−τ), ρ is the real discount rate, λ is the expected real rate of exogenous mortgage repayment, σ is the standard deviation of the mortgage rate, κ/M is the ratio of the tax-adjusted refinancing cost and the remaining mortgage value, and τ is the marginal tax rate. This expression is derived by solving a tractable class of refinancing problems. Our quantitative results closely match those reported by researchers using numerical methods. PMID:25843977

Approximate solution of space and time fractional higher order phase field equation

NASA Astrophysics Data System (ADS)

Shamseldeen, S.

2018-03-01

This paper is concerned with a class of space and time fractional partial differential equation (STFDE) with Riesz derivative in space and Caputo in time. The proposed STFDE is considered as a generalization of a sixth-order partial phase field equation. We describe the application of the optimal homotopy analysis method (OHAM) to obtain an approximate solution for the suggested fractional initial value problem. An averaged-squared residual error function is defined and used to determine the optimal convergence control parameter. Two numerical examples are studied, considering periodic and non-periodic initial conditions, to justify the efficiency and the accuracy of the adopted iterative approach. The dependence of the solution on the order of the fractional derivative in space and time and model parameters is investigated.

Analytic computation of energy derivatives - Relationships among partial derivatives of a variationally determined function

NASA Technical Reports Server (NTRS)

King, H. F.; Komornicki, A.

1986-01-01

Formulas are presented relating Taylor series expansion coefficients of three functions of several variables, the energy of the trial wave function (W), the energy computed using the optimized variational wave function (E), and the response function (lambda), under certain conditions. Partial derivatives of lambda are obtained through solution of a recursive system of linear equations, and solution through order n yields derivatives of E through order 2n + 1, extending Puley's application of Wigner's 2n + 1 rule to partial derivatives in couple perturbation theory. An examination of numerical accuracy shows that the usual two-term second derivative formula is less stable than an alternative four-term formula, and that previous claims that energy derivatives are stationary properties of the wave function are fallacious. The results have application to quantum theoretical methods for the computation of derivative properties such as infrared frequencies and intensities.

Application of normal fluorescence and stability-indicating derivative synchronous fluorescence spectroscopy for the determination of gliquidone in presence of its fluorescent alkaline degradation product

NASA Astrophysics Data System (ADS)

El-ghobashy, Mohamed R.; Yehia, Ali M.; Helmy, Aya H.; Youssef, Nadia F.

2018-01-01

Simple, smart and sensitive normal fluorescence and stability-indicating derivative synchronous spectrofluorimetric methods have been developed and validated for the determination of gliquidone in the drug substance and drug product. Normal spectrofluorimetric method of gliquidone was established in methanol at λ excitation 225 nm and λ emission 400 nm in concentration range 0.2-3 μg/ml with LOD equal 0.028. The fluorescence quantum yield of gliquidone was calculated using quinine sulfate as a reference and found to be 0.542. Stability-indicating first and third derivative synchronous fluorescence spectroscopy were successfully utilized to overcome the overlapped spectra in normal fluorescence of gliquidone and its alkaline degradation product. Derivative synchronous methods are based on using the synchronous fluorescence of gliquidone and its degradation product in methanol at Δ λ50 nm. Peak amplitude in the first derivative of synchronous fluorescence spectra was measured at 309 nm where degradation product showed zero-crossing without interference. The peak amplitudes in the third derivative of synchronous fluorescence spectra, peak to trough were measured at 316,329 nm where degradation product showed zero-crossing. The different experimental parameters affecting the normal and synchronous fluorescence intensity of gliquidone were studied and optimized. Moreover, the cited methods have been validated as per ICH guidelines. The peak amplitude-concentration plots of the derivative synchronous fluorescence were linear over the concentration range 0.05-2 μg/ml for gliquidone. Limits of detection were 0.020 and 0.022 in first and third derivative synchronous spectra, respectively. The adopted methods were successfully applied to commercial tablets and the results demonstrated that the derivative synchronous fluorescence spectroscopy is a powerful stability-indicating method, suitable for routine use with a short analysis time. Statistical comparison between the results obtained by normal fluorescence and derivative synchronous methods and the official one using student's t-test and F-ratio showed no significant difference regarding accuracy and precision.

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.

Møller-Plesset perturbation theory gradient in the generalized hybrid orbital quantum mechanical and molecular mechanical method

NASA Astrophysics Data System (ADS)

Jung, Jaewoon; Sugita, Yuji; Ten-no, S.

2010-02-01

An analytic gradient expression is formulated and implemented for the second-order Møller-Plesset perturbation theory (MP2) based on the generalized hybrid orbital QM/MM method. The method enables us to obtain an accurate geometry at a reasonable computational cost. The performance of the method is assessed for various isomers of alanine dipepetide. We also compare the optimized structures of fumaramide-derived [2]rotaxane and cAMP-dependent protein kinase with experiment.

Memory-optimized shift operator alternating direction implicit finite difference time domain method for plasma

NASA Astrophysics Data System (ADS)

Song, Wanjun; Zhang, Hou

2017-11-01

Through introducing the alternating direction implicit (ADI) technique and the memory-optimized algorithm to the shift operator (SO) finite difference time domain (FDTD) method, the memory-optimized SO-ADI FDTD for nonmagnetized collisional plasma is proposed and the corresponding formulae of the proposed method for programming are deduced. In order to further the computational efficiency, the iteration method rather than Gauss elimination method is employed to solve the equation set in the derivation of the formulae. Complicated transformations and convolutions are avoided in the proposed method compared with the Z transforms (ZT) ADI FDTD method and the piecewise linear JE recursive convolution (PLJERC) ADI FDTD method. The numerical dispersion of the SO-ADI FDTD method with different plasma frequencies and electron collision frequencies is analyzed and the appropriate ratio of grid size to the minimum wavelength is given. The accuracy of the proposed method is validated by the reflection coefficient test on a nonmagnetized collisional plasma sheet. The testing results show that the proposed method is advantageous for improving computational efficiency and saving computer memory. The reflection coefficient of a perfect electric conductor (PEC) sheet covered by multilayer plasma and the RCS of the objects coated by plasma are calculated by the proposed method and the simulation results are analyzed.

Eigenmode computation of cavities with perturbed geometry using matrix perturbation methods applied on generalized eigenvalue problems

NASA Astrophysics Data System (ADS)

Gorgizadeh, Shahnam; Flisgen, Thomas; van Rienen, Ursula

2018-07-01

Generalized eigenvalue problems are standard problems in computational sciences. They may arise in electromagnetic fields from the discretization of the Helmholtz equation by for example the finite element method (FEM). Geometrical perturbations of the structure under concern lead to a new generalized eigenvalue problems with different system matrices. Geometrical perturbations may arise by manufacturing tolerances, harsh operating conditions or during shape optimization. Directly solving the eigenvalue problem for each perturbation is computationally costly. The perturbed eigenpairs can be approximated using eigenpair derivatives. Two common approaches for the calculation of eigenpair derivatives, namely modal superposition method and direct algebraic methods, are discussed in this paper. Based on the direct algebraic methods an iterative algorithm is developed for efficiently calculating the eigenvalues and eigenvectors of the perturbed geometry from the eigenvalues and eigenvectors of the unperturbed geometry.

Assessment of Trading Partners for China's Rare Earth Exports Using a Decision Analytic Approach

PubMed Central

He, Chunyan; Lei, Yalin; Ge, Jianping

2014-01-01

Chinese rare earth export policies currently result in accelerating its depletion. Thus adopting an optimal export trade selection strategy is crucial to determining and ultimately identifying the ideal trading partners. This paper introduces a multi-attribute decision-making methodology which is then used to select the optimal trading partner. In the method, an evaluation criteria system is established to assess the seven top trading partners based on three dimensions: political relationships, economic benefits and industrial security. Specifically, a simple additive weighing model derived from an additive utility function is utilized to calculate, rank and select alternatives. Results show that Japan would be the optimal trading partner for Chinese rare earths. The criteria evaluation method of trading partners for China's rare earth exports provides the Chinese government with a tool to enhance rare earth industrial policies. PMID:25051534

Assessment of trading partners for China's rare earth exports using a decision analytic approach.

PubMed

He, Chunyan; Lei, Yalin; Ge, Jianping

2014-01-01

Chinese rare earth export policies currently result in accelerating its depletion. Thus adopting an optimal export trade selection strategy is crucial to determining and ultimately identifying the ideal trading partners. This paper introduces a multi-attribute decision-making methodology which is then used to select the optimal trading partner. In the method, an evaluation criteria system is established to assess the seven top trading partners based on three dimensions: political relationships, economic benefits and industrial security. Specifically, a simple additive weighing model derived from an additive utility function is utilized to calculate, rank and select alternatives. Results show that Japan would be the optimal trading partner for Chinese rare earths. The criteria evaluation method of trading partners for China's rare earth exports provides the Chinese government with a tool to enhance rare earth industrial policies.

Optimal JPWL Forward Error Correction Rate Allocation for Robust JPEG 2000 Images and Video Streaming over Mobile Ad Hoc Networks

NASA Astrophysics Data System (ADS)

Agueh, Max; Diouris, Jean-François; Diop, Magaye; Devaux, François-Olivier; De Vleeschouwer, Christophe; Macq, Benoit

2008-12-01

Based on the analysis of real mobile ad hoc network (MANET) traces, we derive in this paper an optimal wireless JPEG 2000 compliant forward error correction (FEC) rate allocation scheme for a robust streaming of images and videos over MANET. The packet-based proposed scheme has a low complexity and is compliant to JPWL, the 11th part of the JPEG 2000 standard. The effectiveness of the proposed method is evaluated using a wireless Motion JPEG 2000 client/server application; and the ability of the optimal scheme to guarantee quality of service (QoS) to wireless clients is demonstrated.

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.

Optimal Sensor Location Design for Reliable Fault Detection in Presence of False Alarms

PubMed Central

Yang, Fan; Xiao, Deyun; Shah, Sirish L.

2009-01-01

To improve fault detection reliability, sensor location should be designed according to an optimization criterion with constraints imposed by issues of detectability and identifiability. Reliability requires the minimization of undetectability and false alarm probability due to random factors on sensor readings, which is not only related with sensor readings but also affected by fault propagation. This paper introduces the reliability criteria expression based on the missed/false alarm probability of each sensor and system topology or connectivity derived from the directed graph. The algorithm for the optimization problem is presented as a heuristic procedure. Finally, a boiler system is illustrated using the proposed method. PMID:22291524

Isothermal separation processes

NASA Technical Reports Server (NTRS)

England, C.

1982-01-01

The isothermal processes of membrane separation, supercritical extraction and chromatography were examined using availability analysis. The general approach was to derive equations that identified where energy is consumed in these processes and how they compare with conventional separation methods. These separation methods are characterized by pure work inputs, chiefly in the form of a pressure drop which supplies the required energy. Equations were derived for the energy requirement in terms of regular solution theory. This approach is believed to accurately predict the work of separation in terms of the heat of solution and the entropy of mixing. It can form the basis of a convenient calculation method for optimizing membrane and solvent properties for particular applications. Calculations were made on the energy requirements for a membrane process separating air into its components.

Enhanced nonlinearity interval mapping scheme for high-performance simulation-optimization of watershed-scale BMP placement

NASA Astrophysics Data System (ADS)

Zou, Rui; Riverson, John; Liu, Yong; Murphy, Ryan; Sim, Youn

2015-03-01

Integrated continuous simulation-optimization models can be effective predictors of a process-based responses for cost-benefit optimization of best management practices (BMPs) selection and placement. However, practical application of simulation-optimization model is computationally prohibitive for large-scale systems. This study proposes an enhanced Nonlinearity Interval Mapping Scheme (NIMS) to solve large-scale watershed simulation-optimization problems several orders of magnitude faster than other commonly used algorithms. An efficient interval response coefficient (IRC) derivation method was incorporated into the NIMS framework to overcome a computational bottleneck. The proposed algorithm was evaluated using a case study watershed in the Los Angeles County Flood Control District. Using a continuous simulation watershed/stream-transport model, Loading Simulation Program in C++ (LSPC), three nested in-stream compliance points (CP)—each with multiple Total Maximum Daily Loads (TMDL) targets—were selected to derive optimal treatment levels for each of the 28 subwatersheds, so that the TMDL targets at all the CP were met with the lowest possible BMP implementation cost. Genetic Algorithm (GA) and NIMS were both applied and compared. The results showed that the NIMS took 11 iterations (about 11 min) to complete with the resulting optimal solution having a total cost of 67.2 million, while each of the multiple GA executions took 21-38 days to reach near optimal solutions. The best solution obtained among all the GA executions compared had a minimized cost of 67.7 million—marginally higher, but approximately equal to that of the NIMS solution. The results highlight the utility for decision making in large-scale watershed simulation-optimization formulations.

On simple aerodynamic sensitivity derivatives for use in interdisciplinary optimization

NASA Technical Reports Server (NTRS)

Doggett, Robert V., Jr.

1991-01-01

Low-aspect-ratio and piston aerodynamic theories are reviewed as to their use in developing aerodynamic sensitivity derivatives for use in multidisciplinary optimization applications. The basic equations relating surface pressure (or lift and moment) to normal wash are given and discussed briefly for each theory. The general means for determining selected sensitivity derivatives are pointed out. In addition, some suggestions in very general terms are included as to sample problems for use in studying the process of using aerodynamic sensitivity derivatives in optimization studies.

Automated geometric optimization for robotic HIFU treatment of liver tumors.

PubMed

Williamson, Tom; Everitt, Scott; Chauhan, Sunita

2018-05-01

High intensity focused ultrasound (HIFU) represents a non-invasive method for the destruction of cancerous tissue within the body. Heating of targeted tissue by focused ultrasound transducers results in the creation of ellipsoidal lesions at the target site, the locations of which can have a significant impact on treatment outcomes. Towards this end, this work describes a method for the optimization of lesion positions within arbitrary tumors, with specific anatomical constraints. A force-based optimization framework was extended to the case of arbitrary tumor position and constrained orientation. Analysis of the approximate reachable treatment volume for the specific case of treatment of liver tumors was performed based on four transducer configurations and constraint conditions derived. Evaluation was completed utilizing simplified spherical and ellipsoidal tumor models and randomly generated tumor volumes. The total volume treated, lesion overlap and healthy tissue ablated was evaluated. Two evaluation scenarios were defined and optimized treatment plans assessed. The optimization framework resulted in improvements of up to 10% in tumor volume treated, and reductions of up to 20% in healthy tissue ablated as compared to the standard lesion rastering approach. Generation of optimized plans proved feasible for both sub- and intercostally located tumors. This work describes an optimized method for the planning of lesion positions during HIFU treatment of liver tumors. The approach allows the determination of optimal lesion locations and orientations, and can be applied to arbitrary tumor shapes and sizes. Copyright © 2018 Elsevier Ltd. All rights reserved.

Understanding PSA and its derivatives in prediction of tumor volume: addressing health disparities in prostate cancer risk stratification

PubMed Central

Chinea, Felix M; Lyapichev, Kirill; Epstein, Jonathan I; Kwon, Deukwoo; Smith, Paul Taylor; Pollack, Alan; Cote, Richard J; Kryvenko, Oleksandr N

2017-01-01

Objectives To address health disparities in risk stratification of U.S. Hispanic/Latino men by characterizing influences of prostate weight, body mass index, and race/ethnicity on the correlation of PSA derivatives with Gleason score 6 (Grade Group 1) tumor volume in a diverse cohort. Results Using published PSA density and PSA mass density cutoff values, men with higher body mass indices and prostate weights were less likely to have a tumor volume <0.5 cm3. Variability across race/ethnicity was found in the univariable analysis for all PSA derivatives when predicting for tumor volume. In receiver operator characteristic analysis, area under the curve values for all PSA derivatives varied across race/ethnicity with lower optimal cutoff values for Hispanic/Latino (PSA=2.79, PSA density=0.06, PSA mass=0.37, PSA mass density=0.011) and Non-Hispanic Black (PSA=3.75, PSA density=0.07, PSA mass=0.46, PSA mass density=0.008) compared to Non-Hispanic White men (PSA=4.20, PSA density=0.11 PSA mass=0.53, PSA mass density=0.014). Materials and Methods We retrospectively analyzed 589 patients with low-risk prostate cancer at radical prostatectomy. Pre-operative PSA, patient height, body weight, and prostate weight were used to calculate all PSA derivatives. Receiver operating characteristic curves were constructed for each PSA derivative per racial/ethnic group to establish optimal cutoff values predicting for tumor volume ≥0.5 cm3. Conclusions Increasing prostate weight and body mass index negatively influence PSA derivatives for predicting tumor volume. PSA derivatives’ ability to predict tumor volume varies significantly across race/ethnicity. Hispanic/Latino and Non-Hispanic Black men have lower optimal cutoff values for all PSA derivatives, which may impact risk assessment for prostate cancer. PMID:28160549

A stochastic model for optimizing composite predictors based on gene expression profiles.

PubMed

Ramanathan, Murali

2003-07-01

This project was done to develop a mathematical model for optimizing composite predictors based on gene expression profiles from DNA arrays and proteomics. The problem was amenable to a formulation and solution analogous to the portfolio optimization problem in mathematical finance: it requires the optimization of a quadratic function subject to linear constraints. The performance of the approach was compared to that of neighborhood analysis using a data set containing cDNA array-derived gene expression profiles from 14 multiple sclerosis patients receiving intramuscular inteferon-beta1a. The Markowitz portfolio model predicts that the covariance between genes can be exploited to construct an efficient composite. The model predicts that a composite is not needed for maximizing the mean value of a treatment effect: only a single gene is needed, but the usefulness of the effect measure may be compromised by high variability. The model optimized the composite to yield the highest mean for a given level of variability or the least variability for a given mean level. The choices that meet this optimization criteria lie on a curve of composite mean vs. composite variability plot referred to as the "efficient frontier." When a composite is constructed using the model, it outperforms the composite constructed using the neighborhood analysis method. The Markowitz portfolio model may find potential applications in constructing composite biomarkers and in the pharmacogenomic modeling of treatment effects derived from gene expression endpoints.

Optimization of Layer Densities for Spacecraft Multilayered Insulation Systems

NASA Technical Reports Server (NTRS)

Johnson, W. L.

2009-01-01

Numerous tests of various multilayer insulation systems have indicated that there are optimal densities for these systems. However, the only method of calculating this optimal density was by a complex physics based algorithm developed by McIntosh. In the 1970's much data were collected on the performance of these insulation systems with many different variables analyzed. All formulas generated included number of layers and layer density as geometric variables in solving for the heat flux, none of them was in a differentiable form for a single geometric variable. It was recently discovered that by converting the equations from heat flux to thermal conductivity using Fourier's Law, the equations became functions of layer density, temperatures, and material properties only. The thickness and number of layers of the blanket were merged into a layer density. These equations were then differentiated with respect to layer density. By setting the first derivative equal to zero, and solving for the layer density, the critical layer density was determined. Taking a second derivative showed that the critical layer density is a minimum in the function and thus the optimum density for minimal heat leak, this is confirmed by plotting the original function. This method was checked and validated using test data from the Multipurpose Hydrogen Testbed which was designed using McIntosh's algorithm.

Finite element approximation of an optimal control problem for the von Karman equations

NASA Technical Reports Server (NTRS)

Hou, L. Steven; Turner, James C.

1994-01-01

This paper is concerned with optimal control problems for the von Karman equations with distributed controls. We first show that optimal solutions exist. We then show that Lagrange multipliers may be used to enforce the constraints and derive an optimality system from which optimal states and controls may be deduced. Finally we define finite element approximations of solutions for the optimality system and derive error estimates for the approximations.

Generalized massive optimal data compression

NASA Astrophysics Data System (ADS)

Alsing, Justin; Wandelt, Benjamin

2018-05-01

In this paper, we provide a general procedure for optimally compressing N data down to n summary statistics, where n is equal to the number of parameters of interest. We show that compression to the score function - the gradient of the log-likelihood with respect to the parameters - yields n compressed statistics that are optimal in the sense that they preserve the Fisher information content of the data. Our method generalizes earlier work on linear Karhunen-Loéve compression for Gaussian data whilst recovering both lossless linear compression and quadratic estimation as special cases when they are optimal. We give a unified treatment that also includes the general non-Gaussian case as long as mild regularity conditions are satisfied, producing optimal non-linear summary statistics when appropriate. As a worked example, we derive explicitly the n optimal compressed statistics for Gaussian data in the general case where both the mean and covariance depend on the parameters.

Optimization of block-floating-point realizations for digital controllers with finite-word-length considerations.

PubMed

Wu, Jun; Hu, Xie-he; Chen, Sheng; Chu, Jian

2003-01-01

The closed-loop stability issue of finite-precision realizations was investigated for digital controllers implemented in block-floating-point format. The controller coefficient perturbation was analyzed resulting from using finite word length (FWL) block-floating-point representation scheme. A block-floating-point FWL closed-loop stability measure was derived which considers both the dynamic range and precision. To facilitate the design of optimal finite-precision controller realizations, a computationally tractable block-floating-point FWL closed-loop stability measure was then introduced and the method of computing the value of this measure for a given controller realization was developed. The optimal controller realization is defined as the solution that maximizes the corresponding measure, and a numerical optimization approach was adopted to solve the resulting optimal realization problem. A numerical example was used to illustrate the design procedure and to compare the optimal controller realization with the initial realization.

Optimization in Cardiovascular Modeling

NASA Astrophysics Data System (ADS)

Marsden, Alison L.

2014-01-01

Fluid mechanics plays a key role in the development, progression, and treatment of cardiovascular disease. Advances in imaging methods and patient-specific modeling now reveal increasingly detailed information about blood flow patterns in health and disease. Building on these tools, there is now an opportunity to couple blood flow simulation with optimization algorithms to improve the design of surgeries and devices, incorporating more information about the flow physics in the design process to augment current medical knowledge. In doing so, a major challenge is the need for efficient optimization tools that are appropriate for unsteady fluid mechanics problems, particularly for the optimization of complex patient-specific models in the presence of uncertainty. This article reviews the state of the art in optimization tools for virtual surgery, device design, and model parameter identification in cardiovascular flow and mechanobiology applications. In particular, it reviews trade-offs between traditional gradient-based methods and derivative-free approaches, as well as the need to incorporate uncertainties. Key future challenges are outlined, which extend to the incorporation of biological response and the customization of surgeries and devices for individual patients.

Stiffness optimization of non-linear elastic structures

DOE PAGES

Wallin, Mathias; Ivarsson, Niklas; Tortorelli, Daniel

2017-11-13

Our paper revisits stiffness optimization of non-linear elastic structures. Due to the non-linearity, several possible stiffness measures can be identified and in this work conventional compliance, i.e. secant stiffness designs are compared to tangent stiffness designs. The optimization problem is solved by the method of moving asymptotes and the sensitivities are calculated using the adjoint method. And for the tangent cost function it is shown that although the objective involves the third derivative of the strain energy an efficient formulation for calculating the sensitivity can be obtained. Loss of convergence due to large deformations in void regions is addressed bymore » using a fictitious strain energy such that small strain linear elasticity is approached in the void regions. We formulate a well-posed topology optimization problem by using restriction which is achieved via a Helmholtz type filter. The numerical examples provided show that for low load levels, the designs obtained from the different stiffness measures coincide whereas for large deformations significant differences are observed.« less

Optimized theory for simple and molecular fluids.

PubMed

Marucho, M; Montgomery Pettitt, B

2007-03-28

An optimized closure approximation for both simple and molecular fluids is presented. A smooth interpolation between Perkus-Yevick and hypernetted chain closures is optimized by minimizing the free energy self-consistently with respect to the interpolation parameter(s). The molecular version is derived from a refinement of the method for simple fluids. In doing so, a method is proposed which appropriately couples an optimized closure with the variant of the diagrammatically proper integral equation recently introduced by this laboratory [K. M. Dyer et al., J. Chem. Phys. 123, 204512 (2005)]. The simplicity of the expressions involved in this proposed theory has allowed the authors to obtain an analytic expression for the approximate excess chemical potential. This is shown to be an efficient tool to estimate, from first principles, the numerical value of the interpolation parameters defining the aforementioned closure. As a preliminary test, representative models for simple fluids and homonuclear diatomic Lennard-Jones fluids were analyzed, obtaining site-site correlation functions in excellent agreement with simulation data.

A practical globalization of one-shot optimization for optimal design of tokamak divertors

NASA Astrophysics Data System (ADS)

Blommaert, Maarten; Dekeyser, Wouter; Baelmans, Martine; Gauger, Nicolas R.; Reiter, Detlev

2017-01-01

In past studies, nested optimization methods were successfully applied to design of the magnetic divertor configuration in nuclear fusion reactors. In this paper, so-called one-shot optimization methods are pursued. Due to convergence issues, a globalization strategy for the one-shot solver is sought. Whereas Griewank introduced a globalization strategy using a doubly augmented Lagrangian function that includes primal and adjoint residuals, its practical usability is limited by the necessity of second order derivatives and expensive line search iterations. In this paper, a practical alternative is offered that avoids these drawbacks by using a regular augmented Lagrangian merit function that penalizes only state residuals. Additionally, robust rank-two Hessian estimation is achieved by adaptation of Powell's damped BFGS update rule. The application of the novel one-shot approach to magnetic divertor design is considered in detail. For this purpose, the approach is adapted to be complementary with practical in parts adjoint sensitivities. Using the globalization strategy, stable convergence of the one-shot approach is achieved.

Image compression system and method having optimized quantization tables

NASA Technical Reports Server (NTRS)

Ratnakar, Viresh (Inventor); Livny, Miron (Inventor)

1998-01-01

A digital image compression preprocessor for use in a discrete cosine transform-based digital image compression device is provided. The preprocessor includes a gathering mechanism for determining discrete cosine transform statistics from input digital image data. A computing mechanism is operatively coupled to the gathering mechanism to calculate a image distortion array and a rate of image compression array based upon the discrete cosine transform statistics for each possible quantization value. A dynamic programming mechanism is operatively coupled to the computing mechanism to optimize the rate of image compression array against the image distortion array such that a rate-distortion-optimal quantization table is derived. In addition, a discrete cosine transform-based digital image compression device and a discrete cosine transform-based digital image compression and decompression system are provided. Also, a method for generating a rate-distortion-optimal quantization table, using discrete cosine transform-based digital image compression, and operating a discrete cosine transform-based digital image compression and decompression system are provided.

Stiffness optimization of non-linear elastic structures

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

Wallin, Mathias; Ivarsson, Niklas; Tortorelli, Daniel

Our paper revisits stiffness optimization of non-linear elastic structures. Due to the non-linearity, several possible stiffness measures can be identified and in this work conventional compliance, i.e. secant stiffness designs are compared to tangent stiffness designs. The optimization problem is solved by the method of moving asymptotes and the sensitivities are calculated using the adjoint method. And for the tangent cost function it is shown that although the objective involves the third derivative of the strain energy an efficient formulation for calculating the sensitivity can be obtained. Loss of convergence due to large deformations in void regions is addressed bymore » using a fictitious strain energy such that small strain linear elasticity is approached in the void regions. We formulate a well-posed topology optimization problem by using restriction which is achieved via a Helmholtz type filter. The numerical examples provided show that for low load levels, the designs obtained from the different stiffness measures coincide whereas for large deformations significant differences are observed.« less

Optimal Design of Calibration Signals in Space-Borne Gravitational Wave Detectors

NASA Technical Reports Server (NTRS)

Nofrarias, Miquel; Karnesis, Nikolaos; Gibert, Ferran; Armano, Michele; Audley, Heather; Danzmann, Karsten; Diepholz, Ingo; Dolesi, Rita; Ferraioli, Luigi; Ferroni, Valerio;

Optimal Design of Calibration Signals in Space Borne Gravitational Wave Detectors

NASA Technical Reports Server (NTRS)

Nofrarias, Miquel; Karnesis, Nikolaos; Gibert, Ferran; Armano, Michele; Audley, Heather; Danzmann, Karsten; Diepholz, Ingo; Dolesi, Rita; Ferraioli, Luigi; Thorpe, James I.

2014-01-01

Future space borne gravitational wave detectors will require a precise definition of calibration signals to ensure the achievement of their design sensitivity. The careful design of the test signals plays a key role in the correct understanding and characterization of these instruments. In that sense, methods achieving optimal experiment designs must be considered as complementary to the parameter estimation methods being used to determine the parameters describing the system. The relevance of experiment design is particularly significant for the LISA Pathfinder mission, which will spend most of its operation time performing experiments to characterize key technologies for future space borne gravitational wave observatories. Here we propose a framework to derive the optimal signals in terms of minimum parameter uncertainty to be injected to these instruments during its calibration phase. We compare our results with an alternative numerical algorithm which achieves an optimal input signal by iteratively improving an initial guess. We show agreement of both approaches when applied to the LISA Pathfinder case.

Satellite scheduling considering maximum observation coverage time and minimum orbital transfer fuel cost

NASA Astrophysics Data System (ADS)

Zhu, Kai-Jian; Li, Jun-Feng; Baoyin, He-Xi

2010-01-01

In case of an emergency like the Wenchuan earthquake, it is impossible to observe a given target on earth by immediately launching new satellites. There is an urgent need for efficient satellite scheduling within a limited time period, so we must find a way to reasonably utilize the existing satellites to rapidly image the affected area during a short time period. Generally, the main consideration in orbit design is satellite coverage with the subsatellite nadir point as a standard of reference. Two factors must be taken into consideration simultaneously in orbit design, i.e., the maximum observation coverage time and the minimum orbital transfer fuel cost. The local time of visiting the given observation sites must satisfy the solar radiation requirement. When calculating the operational orbit elements as optimal parameters to be evaluated, we obtain the minimum objective function by comparing the results derived from the primer vector theory with those derived from the Hohmann transfer because the operational orbit for observing the disaster area with impulse maneuvers is considered in this paper. The primer vector theory is utilized to optimize the transfer trajectory with three impulses and the Hohmann transfer is utilized for coplanar and small inclination of non-coplanar cases. Finally, we applied this method in a simulation of the rescue mission at Wenchuan city. The results of optimizing orbit design with a hybrid PSO and DE algorithm show that the primer vector and Hohmann transfer theory proved to be effective methods for multi-object orbit optimization.

A Complete Procedure for Predicting and Improving the Performance of HAWT's

NASA Astrophysics Data System (ADS)

Al-Abadi, Ali; Ertunç, Özgür; Sittig, Florian; Delgado, Antonio

2014-06-01

A complete procedure for predicting and improving the performance of the horizontal axis wind turbine (HAWT) has been developed. The first process is predicting the power extracted by the turbine and the derived rotor torque, which should be identical to that of the drive unit. The BEM method and a developed post-stall treatment for resolving stall-regulated HAWT is incorporated in the prediction. For that, a modified stall-regulated prediction model, which can predict the HAWT performance over the operating range of oncoming wind velocity, is derived from existing models. The model involves radius and chord, which has made it more general in applications for predicting the performance of different scales and rotor shapes of HAWTs. The second process is modifying the rotor shape by an optimization process, which can be applied to any existing HAWT, to improve its performance. A gradient- based optimization is used for adjusting the chord and twist angle distribution of the rotor blade to increase the extraction of the power while keeping the drive torque constant, thus the same drive unit can be kept. The final process is testing the modified turbine to predict its enhanced performance. The procedure is applied to NREL phase-VI 10kW as a baseline turbine. The study has proven the applicability of the developed model in predicting the performance of the baseline as well as the optimized turbine. In addition, the optimization method has shown that the power coefficient can be increased while keeping same design rotational speed.

Second derivative in the model of classical binary system

NASA Astrophysics Data System (ADS)

Abubekerov, M. K.; Gostev, N. Yu.

2016-06-01

We have obtained an analytical expression for the second derivatives of the light curve with respect to geometric parameters in the model of eclipsing classical binary systems. These expressions are essentially efficient algorithm to calculate the numerical values of these second derivatives for all physical values of geometric parameters. Knowledge of the values of second derivatives of the light curve at some point provides additional information about asymptotical behaviour of the function near this point and can significantly improve the search for the best-fitting light curve through the use of second-order optimization method. We write the expression for the second derivatives in a form which is most compact and uniform for all values of the geometric parameters and so make it easy to write a computer program to calculate the values of these derivatives.

Comparative spectral analysis of veterinary powder product by continuous wavelet and derivative transforms

NASA Astrophysics Data System (ADS)

Dinç, Erdal; Kanbur, Murat; Baleanu, Dumitru

2007-10-01

Comparative simultaneous determination of chlortetracycline and benzocaine in the commercial veterinary powder product was carried out by continuous wavelet transform (CWT) and classical derivative transform (or classical derivative spectrophotometry). In this quantitative spectral analysis, two proposed analytical methods do not require any chemical separation process. In the first step, several wavelet families were tested to find an optimal CWT for the overlapping signal processing of the analyzed compounds. Subsequently, we observed that the coiflets (COIF-CWT) method with dilation parameter, a = 400, gives suitable results for this analytical application. For a comparison, the classical derivative spectrophotometry (CDS) approach was also applied to the simultaneous quantitative resolution of the same analytical problem. Calibration functions were obtained by measuring the transform amplitudes corresponding to zero-crossing points for both CWT and CDS methods. The utility of these two analytical approaches were verified by analyzing various synthetic mixtures consisting of chlortetracycline and benzocaine and they were applied to the real samples consisting of veterinary powder formulation. The experimental results obtained from the COIF-CWT approach were statistically compared with those obtained by classical derivative spectrophotometry and successful results were reported.

A reverse engineering approach to optimize experiments for the construction of biological regulatory networks.

PubMed

Zhang, Xiaomeng; Shao, Bin; Wu, Yangle; Qi, Ouyang

2013-01-01

One of the major objectives in systems biology is to understand the relation between the topological structures and the dynamics of biological regulatory networks. In this context, various mathematical tools have been developed to deduct structures of regulatory networks from microarray expression data. In general, from a single data set, one cannot deduct the whole network structure; additional expression data are usually needed. Thus how to design a microarray expression experiment in order to get the most information is a practical problem in systems biology. Here we propose three methods, namely, maximum distance method, trajectory entropy method, and sampling method, to derive the optimal initial conditions for experiments. The performance of these methods is tested and evaluated in three well-known regulatory networks (budding yeast cell cycle, fission yeast cell cycle, and E. coli. SOS network). Based on the evaluation, we propose an efficient strategy for the design of microarray expression experiments.

PID self tuning control based on Mamdani fuzzy logic control for quadrotor stabilization

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

Priyambodo, Tri Kuntoro, E-mail: mastri@ugm.ac.id; Putra, Agfianto Eko; Department of Computer Science and Electronics, Universitas Gadjah Mada, Yogyakarta

Quadrotor as one type of UAV have the ability to perform Vertical Take Off and Landing (VTOL). It allows the Quadrotor to be stationary hovering in the air. PID (Proportional Integral Derivative) control system is one of the control methods that are commonly used. It is usually used to optimize the Quadrotor stabilization at least based on the three Eulerian angles (roll, pitch, and yaw) as input parameters for the control system. The three constants of PID can be obtained in various methods. The simplest method is tuning manually. This method has several weaknesses. For example if the three constantsmore » are not exact, the resulting response will deviate from the desired result. By combining the methods of PID with fuzzy logic systems where human expertise is implemented into the machine language is expected to further optimize the control system.« less

A New Unified Analysis of Estimate Errors by Model-Matching Phase-Estimation Methods for Sensorless Drive of Permanent-Magnet Synchronous Motors and New Trajectory-Oriented Vector Control, Part II

NASA Astrophysics Data System (ADS)

Shinnaka, Shinji

This paper presents a new unified analysis of estimate errors by model-matching extended-back-EMF estimation methods for sensorless drive of permanent-magnet synchronous motors. Analytical solutions about estimate errors, whose validity is confirmed by numerical experiments, are rich in universality and applicability. As an example of universality and applicability, a new trajectory-oriented vector control method is proposed, which can realize directly quasi-optimal strategy minimizing total losses with no additional computational loads by simply orienting one of vector-control coordinates to the associated quasi-optimal trajectory. The coordinate orientation rule, which is analytically derived, is surprisingly simple. Consequently the trajectory-oriented vector control method can be applied to a number of conventional vector control systems using model-matching extended-back-EMF estimation methods.

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

The Relationship Between Heart Rate Reserve and Oxygen Uptake Reserve in Heart Failure Patients on Optimized and Non-Optimized Beta-Blocker Therapy

PubMed Central

Carvalho, Vitor Oliveira; Guimarães, Guilherme Veiga; Bocchi, Edimar Alcides

2008-01-01

BACKGROUND The relationship between the percentage of oxygen consumption reserve and percentage of heart rate reserve in heart failure patients either on non-optimized or off beta-blocker therapy is known to be unreliable. The aim of this study was to evaluate the relationship between the percentage of oxygen consumption reserve and percentage of heart rate reserve in heart failure patients receiving optimized and non-optimized beta-blocker treatment during a treadmill cardiopulmonary exercise test. METHODS A total of 27 sedentary heart failure patients (86% male, 50±12 years) on optimized beta-blocker therapy with a left ventricle ejection fraction of 33±8% and 35 sedentary non-optimized heart failure patients (75% male, 47±10 years) with a left ventricle ejection fraction of 30±10% underwent the treadmill cardiopulmonary exercise test (Naughton protocol). Resting and peak effort values of both the percentage of oxygen consumption reserve and percentage of heart rate reserve were, by definition, 0 and 100, respectively. RESULTS The heart rate slope for the non-optimized group was derived from the points 0.949±0.088 (0 intercept) and 1.055±0.128 (1 intercept), p<0.0001. The heart rate slope for the optimized group was derived from the points 1.026±0.108 (0 intercept) and 1.012±0.108 (1 intercept), p=0.47. Regression linear plots for the heart rate slope for each patient in the non-optimized and optimized groups revealed a slope of 0.986 (almost perfect) for the optimized group, but the regression analysis for the non-optimized group was 0.030 (far from perfect, which occurs at 1). CONCLUSION The relationship between the percentage of oxygen consumption reserve and percentage of heart rate reserve in patients on optimized beta-blocker therapy was reliable, but this relationship was unreliable in non-optimized heart failure patients. PMID:19060991

An adaptive finite element method for the inequality-constrained Reynolds equation

NASA Astrophysics Data System (ADS)

Gustafsson, Tom; Rajagopal, Kumbakonam R.; Stenberg, Rolf; Videman, Juha

2018-07-01

We present a stabilized finite element method for the numerical solution of cavitation in lubrication, modeled as an inequality-constrained Reynolds equation. The cavitation model is written as a variable coefficient saddle-point problem and approximated by a residual-based stabilized method. Based on our recent results on the classical obstacle problem, we present optimal a priori estimates and derive novel a posteriori error estimators. The method is implemented as a Nitsche-type finite element technique and shown in numerical computations to be superior to the usually applied penalty methods.

Numerical Computation of a Continuous-thrust State Transition Matrix Incorporating Accurate Hardware and Ephemeris Models

NASA Technical Reports Server (NTRS)

Ellison, Donald; Conway, Bruce; Englander, Jacob

2015-01-01

A significant body of work exists showing that providing a nonlinear programming (NLP) solver with expressions for the problem constraint gradient substantially increases the speed of program execution and can also improve the robustness of convergence, especially for local optimizers. Calculation of these derivatives is often accomplished through the computation of spacecraft's state transition matrix (STM). If the two-body gravitational model is employed as is often done in the context of preliminary design, closed form expressions for these derivatives may be provided. If a high fidelity dynamics model, that might include perturbing forces such as the gravitational effect from multiple third bodies and solar radiation pressure is used then these STM's must be computed numerically. We present a method for the power hardward model and a full ephemeris model. An adaptive-step embedded eight order Dormand-Prince numerical integrator is discussed and a method for the computation of the time of flight derivatives in this framework is presented. The use of these numerically calculated derivatieves offer a substantial improvement over finite differencing in the context of a global optimizer. Specifically the inclusion of these STM's into the low thrust missiondesign tool chain in use at NASA Goddard Spaceflight Center allows for an increased preliminary mission design cadence.

Optimal control of a coupled partial and ordinary differential equations system for the assimilation of polarimetry Stokes vector measurements in tokamak free-boundary equilibrium reconstruction with application to ITER

NASA Astrophysics Data System (ADS)

Faugeras, Blaise; Blum, Jacques; Heumann, Holger; Boulbe, Cédric

2017-08-01

The modelization of polarimetry Faraday rotation measurements commonly used in tokamak plasma equilibrium reconstruction codes is an approximation to the Stokes model. This approximation is not valid for the foreseen ITER scenarios where high current and electron density plasma regimes are expected. In this work a method enabling the consistent resolution of the inverse equilibrium reconstruction problem in the framework of non-linear free-boundary equilibrium coupled to the Stokes model equation for polarimetry is provided. Using optimal control theory we derive the optimality system for this inverse problem. A sequential quadratic programming (SQP) method is proposed for its numerical resolution. Numerical experiments with noisy synthetic measurements in the ITER tokamak configuration for two test cases, the second of which is an H-mode plasma, show that the method is efficient and that the accuracy of the identification of the unknown profile functions is improved compared to the use of classical Faraday measurements.

Flow analysis and design optimization methods for nozzle-afterbody of a hypersonic vehicle

NASA Technical Reports Server (NTRS)

Baysal, O.

1992-01-01

This report summarizes the methods developed for the aerodynamic analysis and the shape optimization of the nozzle-afterbody section of a hypersonic vehicle. Initially, exhaust gases were assumed to be air. Internal-external flows around a single scramjet module were analyzed by solving the 3D Navier-Stokes equations. Then, exhaust gases were simulated by a cold mixture of Freon and Ar. Two different models were used to compute these multispecies flows as they mixed with the hypersonic airflow. Surface and off-surface properties were successfully compared with the experimental data. The Aerodynamic Design Optimization with Sensitivity analysis was then developed. Pre- and postoptimization sensitivity coefficients were derived and used in this quasi-analytical method. These coefficients were also used to predict inexpensively the flow field around a changed shape when the flow field of an unchanged shape was given. Starting with totally arbitrary initial afterbody shapes, independent computations were converged to the same optimum shape, which rendered the maximum axial thrust.

A Requirements-Driven Optimization Method for Acoustic Treatment Design

NASA Technical Reports Server (NTRS)

Berton, Jeffrey J.

2016-01-01

Acoustic treatment designers have long been able to target specific noise sources inside turbofan engines. Facesheet porosity and cavity depth are key design variables of perforate-over-honeycomb liners that determine levels of noise suppression as well as the frequencies at which suppression occurs. Layers of these structures can be combined to create a robust attenuation spectrum that covers a wide range of frequencies. Looking to the future, rapidly-emerging additive manufacturing technologies are enabling new liners with multiple degrees of freedom, and new adaptive liners with variable impedance are showing promise. More than ever, there is greater flexibility and freedom in liner design. Subject to practical considerations, liner design variables may be manipulated to achieve a target attenuation spectrum. But characteristics of the ideal attenuation spectrum can be difficult to know. Many multidisciplinary system effects govern how engine noise sources contribute to community noise. Given a hardwall fan noise source to be suppressed, and using an analytical certification noise model to compute a community noise measure of merit, the optimal attenuation spectrum can be derived using multidisciplinary systems analysis methods. The subject of this paper is an analytical method that derives the ideal target attenuation spectrum that minimizes noise perceived by observers on the ground.

Simplification of the Kalman filter for meteorological data assimilation

NASA Technical Reports Server (NTRS)

Dee, Dick P.

1991-01-01

The paper proposes a new statistical method of data assimilation that is based on a simplification of the Kalman filter equations. The forecast error covariance evolution is approximated simply by advecting the mass-error covariance field, deriving the remaining covariances geostrophically, and accounting for external model-error forcing only at the end of each forecast cycle. This greatly reduces the cost of computation of the forecast error covariance. In simulations with a linear, one-dimensional shallow-water model and data generated artificially, the performance of the simplified filter is compared with that of the Kalman filter and the optimal interpolation (OI) method. The simplified filter produces analyses that are nearly optimal, and represents a significant improvement over OI.

ANOTHER LOOK AT THE FAST ITERATIVE SHRINKAGE/THRESHOLDING ALGORITHM (FISTA)*

PubMed Central

Kim, Donghwan; Fessler, Jeffrey A.

2017-01-01

This paper provides a new way of developing the “Fast Iterative Shrinkage/Thresholding Algorithm (FISTA)” [3] that is widely used for minimizing composite convex functions with a nonsmooth term such as the ℓ1 regularizer. In particular, this paper shows that FISTA corresponds to an optimized approach to accelerating the proximal gradient method with respect to a worst-case bound of the cost function. This paper then proposes a new algorithm that is derived by instead optimizing the step coefficients of the proximal gradient method with respect to a worst-case bound of the composite gradient mapping. The proof is based on the worst-case analysis called Performance Estimation Problem in [11]. PMID:29805242

Probabilistic determination of probe locations from distance data

PubMed Central

Xu, Xiao-Ping; Slaughter, Brian D.; Volkmann, Niels

2013-01-01

Distance constraints, in principle, can be employed to determine information about the location of probes within a three-dimensional volume. Traditional methods for locating probes from distance constraints involve optimization of scoring functions that measure how well the probe location fits the distance data, exploring only a small subset of the scoring function landscape in the process. These methods are not guaranteed to find the global optimum and provide no means to relate the identified optimum to all other optima in scoring space. Here, we introduce a method for the location of probes from distance information that is based on probability calculus. This method allows exploration of the entire scoring space by directly combining probability functions representing the distance data and information about attachment sites. The approach is guaranteed to identify the global optimum and enables the derivation of confidence intervals for the probe location as well as statistical quantification of ambiguities. We apply the method to determine the location of a fluorescence probe using distances derived by FRET and show that the resulting location matches that independently derived by electron microscopy. PMID:23770585

A finite element based method for solution of optimal control problems

NASA Technical Reports Server (NTRS)

Bless, Robert R.; Hodges, Dewey H.; Calise, Anthony J.

1989-01-01

A temporal finite element based on a mixed form of the Hamiltonian weak principle is presented for optimal control problems. The mixed form of this principle contains both states and costates as primary variables that are expanded in terms of elemental values and simple shape functions. Unlike other variational approaches to optimal control problems, however, time derivatives of the states and costates do not appear in the governing variational equation. Instead, the only quantities whose time derivatives appear therein are virtual states and virtual costates. Also noteworthy among characteristics of the finite element formulation is the fact that in the algebraic equations which contain costates, they appear linearly. Thus, the remaining equations can be solved iteratively without initial guesses for the costates; this reduces the size of the problem by about a factor of two. Numerical results are presented herein for an elementary trajectory optimization problem which show very good agreement with the exact solution along with excellent computational efficiency and self-starting capability. The goal is to evaluate the feasibility of this approach for real-time guidance applications. To this end, a simplified two-stage, four-state model for an advanced launch vehicle application is presented which is suitable for finite element solution.

Application of grey-fuzzy approach in parametric optimization of EDM process in machining of MDN 300 steel

NASA Astrophysics Data System (ADS)

Protim Das, Partha; Gupta, P.; Das, S.; Pradhan, B. B.; Chakraborty, S.

2018-01-01

Maraging steel (MDN 300) find its application in many industries as it exhibits high hardness which are very difficult to machine material. Electro discharge machining (EDM) is an extensively popular machining process which can be used in machining of such materials. Optimization of response parameters are essential for effective machining of these materials. Past researchers have already used Taguchi for obtaining the optimal responses of EDM process for this material with responses such as material removal rate (MRR), tool wear rate (TWR), relative wear ratio (RWR), and surface roughness (SR) considering discharge current, pulse on time, pulse off time, arc gap, and duty cycle as process parameters. In this paper, grey relation analysis (GRA) with fuzzy logic is applied to this multi objective optimization problem to check the responses by an implementation of the derived parametric setting. It was found that the parametric setting derived by the proposed method results in better a response than those reported by the past researchers. Obtained results are also verified using the technique for order of preference by similarity to ideal solution (TOPSIS). The predicted result also shows that there is a significant improvement in comparison to the results of past researchers.

Streamflow variability and optimal capacity of run-of-river hydropower plants

NASA Astrophysics Data System (ADS)

Basso, S.; Botter, G.

2012-10-01

The identification of the capacity of a run-of-river plant which allows for the optimal utilization of the available water resources is a challenging task, mainly because of the inherent temporal variability of river flows. This paper proposes an analytical framework to describe the energy production and the economic profitability of small run-of-river power plants on the basis of the underlying streamflow regime. We provide analytical expressions for the capacity which maximize the produced energy as a function of the underlying flow duration curve and minimum environmental flow requirements downstream of the plant intake. Similar analytical expressions are derived for the capacity which maximize the economic return deriving from construction and operation of a new plant. The analytical approach is applied to a minihydro plant recently proposed in a small Alpine catchment in northeastern Italy, evidencing the potential of the method as a flexible and simple design tool for practical application. The analytical model provides useful insight on the major hydrologic and economic controls (e.g., streamflow variability, energy price, costs) on the optimal plant capacity and helps in identifying policy strategies to reduce the current gap between the economic and energy optimizations of run-of-river plants.

Investigation into the influence of laser energy input on selective laser melted thin-walled parts by response surface method

NASA Astrophysics Data System (ADS)

Liu, Yang; Zhang, Jian; Pang, Zhicong; Wu, Weihui

2018-04-01

Selective laser melting (SLM) provides a feasible way for manufacturing of complex thin-walled parts directly, however, the energy input during SLM process, namely derived from the laser power, scanning speed, layer thickness and scanning space, etc. has great influence on the thin wall's qualities. The aim of this work is to relate the thin wall's parameters (responses), namely track width, surface roughness and hardness to the process parameters considered in this research (laser power, scanning speed and layer thickness) and to find out the optimal manufacturing conditions. Design of experiment (DoE) was used by implementing composite central design to achieve better manufacturing qualities. Mathematical models derived from the statistical analysis were used to establish the relationships between the process parameters and the responses. Also, the effects of process parameters on each response were determined. Then, a numerical optimization was performed to find out the optimal process set at which the quality features are at their desired values. Based on this study, the relationship between process parameters and SLMed thin-walled structure was revealed and thus, the corresponding optimal process parameters can be used to manufactured thin-walled parts with high quality.

Accurate optimization of amino acid form factors for computing small-angle X-ray scattering intensity of atomistic protein structures

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

Tong, Dudu; Yang, Sichun; Lu, Lanyuan

2016-06-20

Structure modellingviasmall-angle X-ray scattering (SAXS) data generally requires intensive computations of scattering intensity from any given biomolecular structure, where the accurate evaluation of SAXS profiles using coarse-grained (CG) methods is vital to improve computational efficiency. To date, most CG SAXS computing methods have been based on a single-bead-per-residue approximation but have neglected structural correlations between amino acids. To improve the accuracy of scattering calculations, accurate CG form factors of amino acids are now derived using a rigorous optimization strategy, termed electron-density matching (EDM), to best fit electron-density distributions of protein structures. This EDM method is compared with and tested againstmore » other CG SAXS computing methods, and the resulting CG SAXS profiles from EDM agree better with all-atom theoretical SAXS data. By including the protein hydration shell represented by explicit CG water molecules and the correction of protein excluded volume, the developed CG form factors also reproduce the selected experimental SAXS profiles with very small deviations. Taken together, these EDM-derived CG form factors present an accurate and efficient computational approach for SAXS computing, especially when higher molecular details (represented by theqrange of the SAXS data) become necessary for effective structure modelling.« less

Optimal investment strategies and hedging of derivatives in the presence of transaction costs (Invited Paper)

NASA Astrophysics Data System (ADS)

Muratore-Ginanneschi, Paolo

2005-05-01

Investment strategies in multiplicative Markovian market models with transaction costs are defined using growth optimal criteria. The optimal strategy is shown to consist in holding the amount of capital invested in stocks within an interval around an ideal optimal investment. The size of the holding interval is determined by the intensity of the transaction costs and the time horizon. The inclusion of financial derivatives in the models is also considered. All the results presented in this contributions were previously derived in collaboration with E. Aurell.

Optimized velocity distributions for direct dark matter detection

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

Ibarra, Alejandro; Rappelt, Andreas, E-mail: ibarra@tum.de, E-mail: andreas.rappelt@tum.de

We present a method to calculate, without making assumptions about the local dark matter velocity distribution, the maximal and minimal number of signal events in a direct detection experiment given a set of constraints from other direct detection experiments and/or neutrino telescopes. The method also allows to determine the velocity distribution that optimizes the signal rates. We illustrate our method with three concrete applications: i) to derive a halo-independent upper limit on the cross section from a set of null results, ii) to confront in a halo-independent way a detection claim to a set of null results and iii) tomore » assess, in a halo-independent manner, the prospects for detection in a future experiment given a set of current null results.« less

Study of flutter related computational procedures for minimum weight structural sizing of advanced aircraft, supplemental data

NASA Technical Reports Server (NTRS)

Oconnell, R. F.; Hassig, H. J.; Radovcich, N. A.

1975-01-01

Computational aspects of (1) flutter optimization (minimization of structural mass subject to specified flutter requirements), (2) methods for solving the flutter equation, and (3) efficient methods for computing generalized aerodynamic force coefficients in the repetitive analysis environment of computer-aided structural design are discussed. Specific areas included: a two-dimensional Regula Falsi approach to solving the generalized flutter equation; method of incremented flutter analysis and its applications; the use of velocity potential influence coefficients in a five-matrix product formulation of the generalized aerodynamic force coefficients; options for computational operations required to generate generalized aerodynamic force coefficients; theoretical considerations related to optimization with one or more flutter constraints; and expressions for derivatives of flutter-related quantities with respect to design variables.

Dictionary Indexing of Electron Channeling Patterns.

PubMed

Singh, Saransh; De Graef, Marc

2017-02-01

The dictionary-based approach to the indexing of diffraction patterns is applied to electron channeling patterns (ECPs). The main ingredients of the dictionary method are introduced, including the generalized forward projector (GFP), the relevant detector model, and a scheme to uniformly sample orientation space using the "cubochoric" representation. The GFP is used to compute an ECP "master" pattern. Derivative free optimization algorithms, including the Nelder-Mead simplex and the bound optimization by quadratic approximation are used to determine the correct detector parameters and to refine the orientation obtained from the dictionary approach. The indexing method is applied to poly-silicon and shows excellent agreement with the calibrated values. Finally, it is shown that the method results in a mean disorientation error of 1.0° with 0.5° SD for a range of detector parameters.

Overtaking method based on sand-sifter mechanism: Why do optimistic value functions find optimal solutions in multi-armed bandit problems?

PubMed

Ochi, Kento; Kamiura, Moto

2015-09-01

A multi-armed bandit problem is a search problem on which a learning agent must select the optimal arm among multiple slot machines generating random rewards. UCB algorithm is one of the most popular methods to solve multi-armed bandit problems. It achieves logarithmic regret performance by coordinating balance between exploration and exploitation. Since UCB algorithms, researchers have empirically known that optimistic value functions exhibit good performance in multi-armed bandit problems. The terms optimistic or optimism might suggest that the value function is sufficiently larger than the sample mean of rewards. The first definition of UCB algorithm is focused on the optimization of regret, and it is not directly based on the optimism of a value function. We need to think the reason why the optimism derives good performance in multi-armed bandit problems. In the present article, we propose a new method, which is called Overtaking method, to solve multi-armed bandit problems. The value function of the proposed method is defined as an upper bound of a confidence interval with respect to an estimator of expected value of reward: the value function asymptotically approaches to the expected value of reward from the upper bound. If the value function is larger than the expected value under the asymptote, then the learning agent is almost sure to be able to obtain the optimal arm. This structure is called sand-sifter mechanism, which has no regrowth of value function of suboptimal arms. It means that the learning agent can play only the current best arm in each time step. Consequently the proposed method achieves high accuracy rate and low regret and some value functions of it can outperform UCB algorithms. This study suggests the advantage of optimism of agents in uncertain environment by one of the simplest frameworks. Copyright © 2015 The Authors. Published by Elsevier Ireland Ltd.. All rights reserved.

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

Sugano, Yasutaka; Mizuta, Masahiro; Takao, Seishin

Purpose: Radiotherapy of solid tumors has been performed with various fractionation regimens such as multi- and hypofractionations. However, the ability to optimize the fractionation regimen considering the physical dose distribution remains insufficient. This study aims to optimize the fractionation regimen, in which the authors propose a graphical method for selecting the optimal number of fractions (n) and dose per fraction (d) based on dose–volume histograms for tumor and normal tissues of organs around the tumor. Methods: Modified linear-quadratic models were employed to estimate the radiation effects on the tumor and an organ at risk (OAR), where the repopulation of themore » tumor cells and the linearity of the dose-response curve in the high dose range of the surviving fraction were considered. The minimization problem for the damage effect on the OAR was solved under the constraint that the radiation effect on the tumor is fixed by a graphical method. Here, the damage effect on the OAR was estimated based on the dose–volume histogram. Results: It was found that the optimization of fractionation scheme incorporating the dose–volume histogram is possible by employing appropriate cell surviving models. The graphical method considering the repopulation of tumor cells and a rectilinear response in the high dose range enables them to derive the optimal number of fractions and dose per fraction. For example, in the treatment of prostate cancer, the optimal fractionation was suggested to lie in the range of 8–32 fractions with a daily dose of 2.2–6.3 Gy. Conclusions: It is possible to optimize the number of fractions and dose per fraction based on the physical dose distribution (i.e., dose–volume histogram) by the graphical method considering the effects on tumor and OARs around the tumor. This method may stipulate a new guideline to optimize the fractionation regimen for physics-guided fractionation.« less

Systematic parameter estimation in data-rich environments for cell signalling dynamics

PubMed Central

Nim, Tri Hieu; Luo, Le; Clément, Marie-Véronique; White, Jacob K.; Tucker-Kellogg, Lisa

2013-01-01

Motivation: Computational models of biological signalling networks, based on ordinary differential equations (ODEs), have generated many insights into cellular dynamics, but the model-building process typically requires estimating rate parameters based on experimentally observed concentrations. New proteomic methods can measure concentrations for all molecular species in a pathway; this creates a new opportunity to decompose the optimization of rate parameters. Results: In contrast with conventional parameter estimation methods that minimize the disagreement between simulated and observed concentrations, the SPEDRE method fits spline curves through observed concentration points, estimates derivatives and then matches the derivatives to the production and consumption of each species. This reformulation of the problem permits an extreme decomposition of the high-dimensional optimization into a product of low-dimensional factors, each factor enforcing the equality of one ODE at one time slice. Coarsely discretized solutions to the factors can be computed systematically. Then the discrete solutions are combined using loopy belief propagation, and refined using local optimization. SPEDRE has unique asymptotic behaviour with runtime polynomial in the number of molecules and timepoints, but exponential in the degree of the biochemical network. SPEDRE performance is comparatively evaluated on a novel model of Akt activation dynamics including redox-mediated inactivation of PTEN (phosphatase and tensin homologue). Availability and implementation: Web service, software and supplementary information are available at www.LtkLab.org/SPEDRE Supplementary information: Supplementary data are available at Bioinformatics online. Contact: LisaTK@nus.edu.sg PMID:23426255

UCAV path planning in the presence of radar-guided surface-to-air missile threats

NASA Astrophysics Data System (ADS)

Zeitz, Frederick H., III

This dissertation addresses the problem of path planning for unmanned combat aerial vehicles (UCAVs) in the presence of radar-guided surface-to-air missiles (SAMs). The radars, collocated with SAM launch sites, operate within the structure of an Integrated Air Defense System (IADS) that permits communication and cooperation between individual radars. The problem is formulated in the framework of the interaction between three sub-systems: the aircraft, the IADS, and the missile. The main features of this integrated model are: The aircraft radar cross section (RCS) depends explicitly on both the aspect and bank angles; hence, the RCS and aircraft dynamics are coupled. The probabilistic nature of IADS tracking is accounted for; namely, the probability that the aircraft has been continuously tracked by the IADS depends on the aircraft RCS and range from the perspective of each radar within the IADS. Finally, the requirement to maintain tracking prior to missile launch and during missile flyout are also modeled. Based on this model, the problem of UCAV path planning is formulated as a minimax optimal control problem, with the aircraft bank angle serving as control. Necessary conditions of optimality for this minimax problem are derived. Based on these necessary conditions, properties of the optimal paths are derived. These properties are used to discretize the dynamic optimization problem into a finite-dimensional, nonlinear programming problem that can be solved numerically. Properties of the optimal paths are also used to initialize the numerical procedure. A homotopy method is proposed to solve the finite-dimensional, nonlinear programming problem, and a heuristic method is proposed to improve the discretization during the homotopy process. Based upon the properties of numerical solutions, a method is proposed for parameterizing and storing information for later recall in flight to permit rapid replanning in response to changing threats. Illustrative examples are presented that confirm the standard flying tactics of "denying range, aspect, and aim," by yielding flight paths that "weave" to avoid long exposures of aspects with large RCS.

Non-linear Multidimensional Optimization for use in Wire Scanner Fitting

NASA Astrophysics Data System (ADS)

Henderson, Alyssa; Terzic, Balsa; Hofler, Alicia; CASA and Accelerator Ops Collaboration

2013-10-01

To ensure experiment efficiency and quality from the Continuous Electron Beam Accelerator at Jefferson Lab, beam energy, size, and position must be measured. Wire scanners are devices inserted into the beamline to produce measurements which are used to obtain beam properties. Extracting physical information from the wire scanner measurements begins by fitting Gaussian curves to the data. This study focuses on optimizing and automating this curve-fitting procedure. We use a hybrid approach combining the efficiency of Newton Conjugate Gradient (NCG) method with the global convergence of three nature-inspired (NI) optimization approaches: genetic algorithm, differential evolution, and particle-swarm. In this Python-implemented approach, augmenting the locally-convergent NCG with one of the globally-convergent methods ensures the quality, robustness, and automation of curve-fitting. After comparing the methods, we establish that given an initial data-derived guess, each finds a solution with the same chi-square- a measurement of the agreement of the fit to the data. NCG is the fastest method, so it is the first to attempt data-fitting. The curve-fitting procedure escalates to one of the globally-convergent NI methods only if NCG fails, thereby ensuring a successful fit. This method allows for the most optimal signal fit and can be easily applied to similar problems. Financial support from DoE, NSF, ODU, DoD, and Jefferson Lab.

Screening, isolation and optimization of anti–white spot syndrome virus drug derived from terrestrial plants

PubMed Central

Ghosh, Upasana; Chakraborty, Somnath; Balasubramanian, Thangavel; Das, Punyabrata

2014-01-01

Objective To screen, isolate and optimize anti-white spot syndrome virus (WSSV) drug derived from various terrestrial plants and to evaluate the efficacy of the same in host–pathogen interaction model. Methods Thirty plants were subjected to Soxhlet extraction using water, ethanol, methanol and hexane as solvents. The 120 plant isolates thus obtained were screened for their in vivo anti–WSSV property in Litopenaeus vannamei. The best anti–WSSV plant isolate, TP22C was isolated and further analyzed. The drug was optimized at various concentrations. Viral and immune genes were analysed using reverse transcriptase PCR to confirm the potency of the drug. Results Seven plant isolates exhibited significant survivability in host. The drug TP22C thus formulated showed 86% survivability in host. The surviving shrimps were nested PCR negative at the end of the 15 d experimentation. The lowest concentration of TP22C required intramuscularly for virucidal property was 10 mg/mL. The oral dosage of 750 mg/kg body weight/day survived at the rate of 86%. Neither VP28 nor ie 1 was expressed in the test samples at 42nd hour and 84th hour post viral infection. Conclusions The drug TP22C derived from Momordica charantia is a potent anti-white spot syndrome virus drug. PMID:25183066

Improving flood forecasting capability of physically based distributed hydrological model by parameter optimization

NASA Astrophysics Data System (ADS)

Chen, Y.; Li, J.; Xu, H.

2015-10-01

Physically based distributed hydrological models discrete the terrain of the whole catchment into a number of grid cells at fine resolution, and assimilate different terrain data and precipitation to different cells, and are regarded to have the potential to improve the catchment hydrological processes simulation and prediction capability. In the early stage, physically based distributed hydrological models are assumed to derive model parameters from the terrain properties directly, so there is no need to calibrate model parameters, but unfortunately, the uncertanties associated with this model parameter deriving is very high, which impacted their application in flood forecasting, so parameter optimization may also be necessary. There are two main purposes for this study, the first is to propose a parameter optimization method for physically based distributed hydrological models in catchment flood forecasting by using PSO algorithm and to test its competence and to improve its performances, the second is to explore the possibility of improving physically based distributed hydrological models capability in cathcment flood forecasting by parameter optimization. In this paper, based on the scalar concept, a general framework for parameter optimization of the PBDHMs for catchment flood forecasting is first proposed that could be used for all PBDHMs. Then, with Liuxihe model as the study model, which is a physically based distributed hydrological model proposed for catchment flood forecasting, the improverd Particle Swarm Optimization (PSO) algorithm is developed for the parameter optimization of Liuxihe model in catchment flood forecasting, the improvements include to adopt the linear decreasing inertia weight strategy to change the inertia weight, and the arccosine function strategy to adjust the acceleration coefficients. This method has been tested in two catchments in southern China with different sizes, and the results show that the improved PSO algorithm could be used for Liuxihe model parameter optimization effectively, and could improve the model capability largely in catchment flood forecasting, thus proven that parameter optimization is necessary to improve the flood forecasting capability of physically based distributed hydrological model. It also has been found that the appropriate particle number and the maximum evolution number of PSO algorithm used for Liuxihe model catchment flood forcasting is 20 and 30, respectively.

Optimization of the beam shaping assembly in the D-D neutron generators-based BNCT using the response matrix method.

PubMed

Kasesaz, Y; Khalafi, H; Rahmani, F

2013-12-01

Optimization of the Beam Shaping Assembly (BSA) has been performed using the MCNP4C Monte Carlo code to shape the 2.45 MeV neutrons that are produced in the D-D neutron generator. Optimal design of the BSA has been chosen by considering in-air figures of merit (FOM) which consists of 70 cm Fluental as a moderator, 30 cm Pb as a reflector, 2mm (6)Li as a thermal neutron filter and 2mm Pb as a gamma filter. The neutron beam can be evaluated by in-phantom parameters, from which therapeutic gain can be derived. Direct evaluation of both set of FOMs (in-air and in-phantom) is very time consuming. In this paper a Response Matrix (RM) method has been suggested to reduce the computing time. This method is based on considering the neutron spectrum at the beam exit and calculating contribution of various dose components in phantom to calculate the Response Matrix. Results show good agreement between direct calculation and the RM method. Copyright © 2013 Elsevier Ltd. All rights reserved.

Nonlinear Shaping Architecture Designed with Using Evolutionary Structural Optimization Tools

NASA Astrophysics Data System (ADS)

Januszkiewicz, Krystyna; Banachowicz, Marta

2017-10-01

The paper explores the possibilities of using Structural Optimization Tools (ESO) digital tools in an integrated structural and architectural design in response to the current needs geared towards sustainability, combining ecological and economic efficiency. The first part of the paper defines the Evolutionary Structural Optimization tools, which were developed specifically for engineering purposes using finite element analysis as a framework. The development of ESO has led to several incarnations, which are all briefly discussed (Additive ESO, Bi-directional ESO, Extended ESO). The second part presents result of using these tools in structural and architectural design. Actual building projects which involve optimization as a part of the original design process will be presented (Crematorium in Kakamigahara Gifu, Japan, 2006 SANAA“s Learning Centre, EPFL in Lausanne, Switzerland 2008 among others). The conclusion emphasizes that the structural engineering and architectural design mean directing attention to the solutions which are used by Nature, designing works optimally shaped and forming their own environments. Architectural forms never constitute the optimum shape derived through a form-finding process driven only by structural optimization, but rather embody and integrate a multitude of parameters. It might be assumed that there is a similarity between these processes in nature and the presented design methods. Contemporary digital methods make the simulation of such processes possible, and thus enable us to refer back to the empirical methods of previous generations.

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

Automatic optimal filament segmentation with sub-pixel accuracy using generalized linear models and B-spline level-sets.

PubMed

Xiao, Xun; Geyer, Veikko F; Bowne-Anderson, Hugo; Howard, Jonathon; Sbalzarini, Ivo F

2016-08-01

Biological filaments, such as actin filaments, microtubules, and cilia, are often imaged using different light-microscopy techniques. Reconstructing the filament curve from the acquired images constitutes the filament segmentation problem. Since filaments have lower dimensionality than the image itself, there is an inherent trade-off between tracing the filament with sub-pixel accuracy and avoiding noise artifacts. Here, we present a globally optimal filament segmentation method based on B-spline vector level-sets and a generalized linear model for the pixel intensity statistics. We show that the resulting optimization problem is convex and can hence be solved with global optimality. We introduce a simple and efficient algorithm to compute such optimal filament segmentations, and provide an open-source implementation as an ImageJ/Fiji plugin. We further derive an information-theoretic lower bound on the filament segmentation error, quantifying how well an algorithm could possibly do given the information in the image. We show that our algorithm asymptotically reaches this bound in the spline coefficients. We validate our method in comprehensive benchmarks, compare with other methods, and show applications from fluorescence, phase-contrast, and dark-field microscopy. Copyright © 2016 The Authors. Published by Elsevier B.V. All rights reserved.

A staggered-grid convolutional differentiator for elastic wave modelling

NASA Astrophysics Data System (ADS)

Sun, Weijia; Zhou, Binzhong; Fu, Li-Yun

2015-11-01

The computation of derivatives in governing partial differential equations is one of the most investigated subjects in the numerical simulation of physical wave propagation. An analytical staggered-grid convolutional differentiator (CD) for first-order velocity-stress elastic wave equations is derived in this paper by inverse Fourier transformation of the band-limited spectrum of a first derivative operator. A taper window function is used to truncate the infinite staggered-grid CD stencil. The truncated CD operator is almost as accurate as the analytical solution, and as efficient as the finite-difference (FD) method. The selection of window functions will influence the accuracy of the CD operator in wave simulation. We search for the optimal Gaussian windows for different order CDs by minimizing the spectral error of the derivative and comparing the windows with the normal Hanning window function for tapering the CD operators. It is found that the optimal Gaussian window appears to be similar to the Hanning window function for tapering the same CD operator. We investigate the accuracy of the windowed CD operator and the staggered-grid FD method with different orders. Compared to the conventional staggered-grid FD method, a short staggered-grid CD operator achieves an accuracy equivalent to that of a long FD operator, with lower computational costs. For example, an 8th order staggered-grid CD operator can achieve the same accuracy of a 16th order staggered-grid FD algorithm but with half of the computational resources and time required. Numerical examples from a homogeneous model and a crustal waveguide model are used to illustrate the superiority of the CD operators over the conventional staggered-grid FD operators for the simulation of wave propagations.

Aerostructural Shape and Topology Optimization of Aircraft Wings

NASA Astrophysics Data System (ADS)

James, Kai

A series of novel algorithms for performing aerostructural shape and topology optimization are introduced and applied to the design of aircraft wings. An isoparametric level set method is developed for performing topology optimization of wings and other non-rectangular structures that must be modeled using a non-uniform, body-fitted mesh. The shape sensitivities are mapped to computational space using the transformation defined by the Jacobian of the isoparametric finite elements. The mapped sensitivities are then passed to the Hamilton-Jacobi equation, which is solved on a uniform Cartesian grid. The method is derived for several objective functions including mass, compliance, and global von Mises stress. The results are compared with SIMP results for several two-dimensional benchmark problems. The method is also demonstrated on a three-dimensional wingbox structure subject to fixed loading. It is shown that the isoparametric level set method is competitive with the SIMP method in terms of the final objective value as well as computation time. In a separate problem, the SIMP formulation is used to optimize the structural topology of a wingbox as part of a larger MDO framework. Here, topology optimization is combined with aerodynamic shape optimization, using a monolithic MDO architecture that includes aerostructural coupling. The aerodynamic loads are modeled using a three-dimensional panel method, and the structural analysis makes use of linear, isoparametric, hexahedral elements. The aerodynamic shape is parameterized via a set of twist variables representing the jig twist angle at equally spaced locations along the span of the wing. The sensitivities are determined analytically using a coupled adjoint method. The wing is optimized for minimum drag subject to a compliance constraint taken from a 2 g maneuver condition. The results from the MDO algorithm are compared with those of a sequential optimization procedure in order to quantify the benefits of the MDO approach. While the sequentially optimized wing exhibits a nearly-elliptical lift distribution, the MDO design seeks to push a greater portion of the load toward the root, thus reducing the structural deflection, and allowing for a lighter structure. By exploiting this trade-off, the MDO design achieves a 42% lower drag than the sequential result.

Respiratory rate estimation from the built-in cameras of smartphones and tablets.

PubMed

Nam, Yunyoung; Lee, Jinseok; Chon, Ki H

2014-04-01

This paper presents a method for respiratory rate estimation using the camera of a smartphone, an MP3 player or a tablet. The iPhone 4S, iPad 2, iPod 5, and Galaxy S3 were used to estimate respiratory rates from the pulse signal derived from a finger placed on the camera lens of these devices. Prior to estimation of respiratory rates, we systematically investigated the optimal signal quality of these 4 devices by dividing the video camera's resolution into 12 different pixel regions. We also investigated the optimal signal quality among the red, green and blue color bands for each of these 12 pixel regions for all four devices. It was found that the green color band provided the best signal quality for all 4 devices and that the left half VGA pixel region was found to be the best choice only for iPhone 4S. For the other three devices, smaller 50 × 50 pixel regions were found to provide better or equally good signal quality than the larger pixel regions. Using the green signal and the optimal pixel regions derived from the four devices, we then investigated the suitability of the smartphones, the iPod 5 and the tablet for respiratory rate estimation using three different computational methods: the autoregressive (AR) model, variable-frequency complex demodulation (VFCDM), and continuous wavelet transform (CWT) approaches. Specifically, these time-varying spectral techniques were used to identify the frequency and amplitude modulations as they contain respiratory rate information. To evaluate the performance of the three computational methods and the pixel regions for the optimal signal quality, data were collected from 10 healthy subjects. It was found that the VFCDM method provided good estimates of breathing rates that were in the normal range (12-24 breaths/min). Both CWT and VFCDM methods provided reasonably good estimates for breathing rates that were higher than 26 breaths/min but their accuracy degraded concomitantly with increased respiratory rates. Overall, the VFCDM method provided the best results for accuracy (smaller median error), consistency (smaller interquartile range of the median value), and computational efficiency (less than 0.5 s on 1 min of data using a MATLAB implementation) to extract breathing rates that varied from 12 to 36 breaths/min. The AR method provided the least accurate respiratory rate estimation among the three methods. This work illustrates that both heart rates and normal breathing rates can be accurately derived from a video signal obtained from smartphones, an MP3 player and tablets with or without a flashlight.

Tire-road friction estimation and traction control strategy for motorized electric vehicle.

PubMed

Jin, Li-Qiang; Ling, Mingze; Yue, Weiqiang

2017-01-01

In this paper, an optimal longitudinal slip ratio system for real-time identification of electric vehicle (EV) with motored wheels is proposed based on the adhesion between tire and road surface. First and foremost, the optimal longitudinal slip rate torque control can be identified in real time by calculating the derivative and slip rate of the adhesion coefficient. Secondly, the vehicle speed estimation method is also brought. Thirdly, an ideal vehicle simulation model is proposed to verify the algorithm with simulation, and we find that the slip ratio corresponds to the detection of the adhesion limit in real time. Finally, the proposed strategy is applied to traction control system (TCS). The results showed that the method can effectively identify the state of wheel and calculate the optimal slip ratio without wheel speed sensor; in the meantime, it can improve the accelerated stability of electric vehicle with traction control system (TCS).

LQR-Based Optimal Distributed Cooperative Design for Linear Discrete-Time Multiagent Systems.

PubMed

Zhang, Huaguang; Feng, Tao; Liang, Hongjing; Luo, Yanhong

2017-03-01

In this paper, a novel linear quadratic regulator (LQR)-based optimal distributed cooperative design method is developed for synchronization control of general linear discrete-time multiagent systems on a fixed, directed graph. Sufficient conditions are derived for synchronization, which restrict the graph eigenvalues into a bounded circular region in the complex plane. The synchronizing speed issue is also considered, and it turns out that the synchronizing region reduces as the synchronizing speed becomes faster. To obtain more desirable synchronizing capacity, the weighting matrices are selected by sufficiently utilizing the guaranteed gain margin of the optimal regulators. Based on the developed LQR-based cooperative design framework, an approximate dynamic programming technique is successfully introduced to overcome the (partially or completely) model-free cooperative design for linear multiagent systems. Finally, two numerical examples are given to illustrate the effectiveness of the proposed design methods.

Tire-road friction estimation and traction control strategy for motorized electric vehicle

PubMed Central

Jin, Li-Qiang; Yue, Weiqiang

2017-01-01

In this paper, an optimal longitudinal slip ratio system for real-time identification of electric vehicle (EV) with motored wheels is proposed based on the adhesion between tire and road surface. First and foremost, the optimal longitudinal slip rate torque control can be identified in real time by calculating the derivative and slip rate of the adhesion coefficient. Secondly, the vehicle speed estimation method is also brought. Thirdly, an ideal vehicle simulation model is proposed to verify the algorithm with simulation, and we find that the slip ratio corresponds to the detection of the adhesion limit in real time. Finally, the proposed strategy is applied to traction control system (TCS). The results showed that the method can effectively identify the state of wheel and calculate the optimal slip ratio without wheel speed sensor; in the meantime, it can improve the accelerated stability of electric vehicle with traction control system (TCS). PMID:28662053

Automatic Summarization as a Combinatorial Optimization Problem

NASA Astrophysics Data System (ADS)

Hirao, Tsutomu; Suzuki, Jun; Isozaki, Hideki

We derived the oracle summary with the highest ROUGE score that can be achieved by integrating sentence extraction with sentence compression from the reference abstract. The analysis results of the oracle revealed that summarization systems have to assign an appropriate compression rate for each sentence in the document. In accordance with this observation, this paper proposes a summarization method as a combinatorial optimization: selecting the set of sentences that maximize the sum of the sentence scores from the pool which consists of the sentences with various compression rates, subject to length constrains. The score of the sentence is defined by its compression rate, content words and positional information. The parameters for the compression rates and positional information are optimized by minimizing the loss between score of oracles and that of candidates. The results obtained from TSC-2 corpus showed that our method outperformed the previous systems with statistical significance.

Analytical solutions to optimal underactuated spacecraft formation reconfiguration

NASA Astrophysics Data System (ADS)

Huang, Xu; Yan, Ye; Zhou, Yang

2015-11-01

Underactuated systems can generally be defined as systems with fewer number of control inputs than that of the degrees of freedom to be controlled. In this paper, analytical solutions to optimal underactuated spacecraft formation reconfiguration without either the radial or the in-track control are derived. By using a linear dynamical model of underactuated spacecraft formation in circular orbits, controllability analysis is conducted for either underactuated case. Indirect optimization methods based on the minimum principle are then introduced to generate analytical solutions to optimal open-loop underactuated reconfiguration problems. Both fixed and free final conditions constraints are considered for either underactuated case and comparisons between these two final conditions indicate that the optimal control strategies with free final conditions require less control efforts than those with the fixed ones. Meanwhile, closed-loop adaptive sliding mode controllers for both underactuated cases are designed to guarantee optimal trajectory tracking in the presence of unmatched external perturbations, linearization errors, and system uncertainties. The adaptation laws are designed via a Lyapunov-based method to ensure the overall stability of the closed-loop system. The explicit expressions of the terminal convergent regions of each system states have also been obtained. Numerical simulations demonstrate the validity and feasibility of the proposed open-loop and closed-loop control schemes for optimal underactuated spacecraft formation reconfiguration in circular orbits.

A Subsonic Aircraft Design Optimization With Neural Network and Regression Approximators

NASA Technical Reports Server (NTRS)

Patnaik, Surya N.; Coroneos, Rula M.; Guptill, James D.; Hopkins, Dale A.; Haller, William J.

2004-01-01

The Flight-Optimization-System (FLOPS) code encountered difficulty in analyzing a subsonic aircraft. The limitation made the design optimization problematic. The deficiencies have been alleviated through use of neural network and regression approximations. The insight gained from using the approximators is discussed in this paper. The FLOPS code is reviewed. Analysis models are developed and validated for each approximator. The regression method appears to hug the data points, while the neural network approximation follows a mean path. For an analysis cycle, the approximate model required milliseconds of central processing unit (CPU) time versus seconds by the FLOPS code. Performance of the approximators was satisfactory for aircraft analysis. A design optimization capability has been created by coupling the derived analyzers to the optimization test bed CometBoards. The approximators were efficient reanalysis tools in the aircraft design optimization. Instability encountered in the FLOPS analyzer was eliminated. The convergence characteristics were improved for the design optimization. The CPU time required to calculate the optimum solution, measured in hours with the FLOPS code was reduced to minutes with the neural network approximation and to seconds with the regression method. Generation of the approximators required the manipulation of a very large quantity of data. Design sensitivity with respect to the bounds of aircraft constraints is easily generated.

Multi-disciplinary optimization of aeroservoelastic systems

NASA Technical Reports Server (NTRS)

Karpel, Mardechay

1992-01-01

The purpose of the research project was to continue the development of new methods for efficient aeroservoelastic analysis and optimization. The main targets were as follows: to complete the development of analytical tools for the investigation of flutter with large stiffness changes; to continue the work on efficient continuous gust response and sensitivity derivatives; and to advance the techniques of calculating dynamic loads with control and unsteady aerodynamic effects. An efficient and highly accurate mathematical model for time-domain analysis of flutter during which large structural changes occur was developed in cooperation with Carol D. Wieseman of NASA LaRC. The model was based on the second-year work 'Modal Coordinates for Aeroelastic Analysis with Large Local Structural Variations'. The work on continuous gust response was completed. An abstract of the paper 'Continuous Gust Response and Sensitivity Derivatives Using State-Space Models' was submitted for presentation in the 33rd Israel Annual Conference on Aviation and Astronautics, Feb. 1993. The abstract is given in Appendix A. The work extends the optimization model to deal with continuous gust objectives in a way that facilitates their inclusion in the efficient multi-disciplinary optimization scheme. Currently under development is a work designed to extend the analysis and optimization capabilities to loads and stress considerations. The work is on aircraft dynamic loads in response to impulsive and non-impulsive excitation. The work extends the formulations of the mode-displacement and summation-of-forces methods to include modes with significant local distortions, and load modes. An abstract of the paper,'Structural Dynamic Loads in Response to Impulsive Excitation' is given in appendix B. Another work performed this year under the Grant was 'Size-Reduction Techniques for the Determination of Efficient Aeroservoelastic Models' given in Appendix C.

Computational Thermochemistry: Scale Factor Databases and Scale Factors for Vibrational Frequencies Obtained from Electronic Model Chemistries.

PubMed

Alecu, I M; Zheng, Jingjing; Zhao, Yan; Truhlar, Donald G

2010-09-14

Optimized scale factors for calculating vibrational harmonic and fundamental frequencies and zero-point energies have been determined for 145 electronic model chemistries, including 119 based on approximate functionals depending on occupied orbitals, 19 based on single-level wave function theory, three based on the neglect-of-diatomic-differential-overlap, two based on doubly hybrid density functional theory, and two based on multicoefficient correlation methods. Forty of the scale factors are obtained from large databases, which are also used to derive two universal scale factor ratios that can be used to interconvert between scale factors optimized for various properties, enabling the derivation of three key scale factors at the effort of optimizing only one of them. A reduced scale factor optimization model is formulated in order to further reduce the cost of optimizing scale factors, and the reduced model is illustrated by using it to obtain 105 additional scale factors. Using root-mean-square errors from the values in the large databases, we find that scaling reduces errors in zero-point energies by a factor of 2.3 and errors in fundamental vibrational frequencies by a factor of 3.0, but it reduces errors in harmonic vibrational frequencies by only a factor of 1.3. It is shown that, upon scaling, the balanced multicoefficient correlation method based on coupled cluster theory with single and double excitations (BMC-CCSD) can lead to very accurate predictions of vibrational frequencies. With a polarized, minimally augmented basis set, the density functionals with zero-point energy scale factors closest to unity are MPWLYP1M (1.009), τHCTHhyb (0.989), BB95 (1.012), BLYP (1.013), BP86 (1.014), B3LYP (0.986), MPW3LYP (0.986), and VSXC (0.986).

Comparison of the clinical outcomes between unattended home APAP and polysomnography manual titration in obstructive sleep apnea patients.

PubMed

Wongsritrang, Krongthong; Fueangkamloon, Sumet

2013-09-01

To compare the clinical outcomes and determine the difference in therapeutic pressure between Automatic positive airway pressure (APAP) and polysomnography manual titration. Fifty patients of obstructive sleep apnea (OSA), moderate to severe cases, were randomized into two groups of intervention: 95-percentile pressure derived from APAP titration and an optimal pressure derived from manual titration. Clinical outcomes were assessed before and after four weeks. The average 95-percentile pressure derived from APAP titration was 11.7 +/- 0.3 cmH2O with median mask leak 1.3 L/min. The average optimal pressure derived from manual titration was 8.2 +/- 0.3 cmH2O. Pearson correlation analysis showed weak positive correlation (r = 0.336, p = 0.017). The Epworth Sleepiness Score (ESS), Quality of life tests: PSQI (Pittsburg Sleep Quality Index), and SF-36 (Medical Outcomes Study 36-Item Short-Form Health Survey) were improved significantly in both groups, but there were no statistical significant differences between groups. An APAP titration is an effective method of pressure determination for conventional CPAP therapy and shows no difference in clinical outcomes comparing the standard titration.

Identifying Patients with Atrioventricular Septal Defect in Down Syndrome Populations by Using Self-Normalizing Neural Networks and Feature Selection.

PubMed

Pan, Xiaoyong; Hu, Xiaohua; Zhang, Yu Hang; Feng, Kaiyan; Wang, Shao Peng; Chen, Lei; Huang, Tao; Cai, Yu Dong

2018-04-12

Atrioventricular septal defect (AVSD) is a clinically significant subtype of congenital heart disease (CHD) that severely influences the health of babies during birth and is associated with Down syndrome (DS). Thus, exploring the differences in functional genes in DS samples with and without AVSD is a critical way to investigate the complex association between AVSD and DS. In this study, we present a computational method to distinguish DS patients with AVSD from those without AVSD using the newly proposed self-normalizing neural network (SNN). First, each patient was encoded by using the copy number of probes on chromosome 21. The encoded features were ranked by the reliable Monte Carlo feature selection (MCFS) method to obtain a ranked feature list. Based on this feature list, we used a two-stage incremental feature selection to construct two series of feature subsets and applied SNNs to build classifiers to identify optimal features. Results show that 2737 optimal features were obtained, and the corresponding optimal SNN classifier constructed on optimal features yielded a Matthew's correlation coefficient (MCC) value of 0.748. For comparison, random forest was also used to build classifiers and uncover optimal features. This method received an optimal MCC value of 0.582 when top 132 features were utilized. Finally, we analyzed some key features derived from the optimal features in SNNs found in literature support to further reveal their essential roles.

Separation of porphyrin-based photosensitizer isomers by laser-induced fluorescence capillary electrophoresis.

PubMed

Peng, Xuejun; Sternberg, Ethan; Dolphin, David

2005-10-01

Methods for the separation of photosensitizer isomers, such as benzoporphyrin derivative monoacid, benzoporphyrin ethyl monoacid, 2-[1-hexyloxyethyl]-2-devinylpyropheophorbide-a, diethyleneglycol diester benzoporphyrin derivative, tin ethyl etiopurpurin, and phthalocyanine tetrasulfonate, have been systematically developed by CE. Detection was accomplished by UV absorption at 214 nm or by LIF with excitation at 442/488 nm and emission at 690 nm. The effects of three major experimental parameters of buffer types, organic solvents, and surfactant additives are described. The optimized separation conditions were determined so as to provide satisfactory separation efficiency and analysis time. The methods are shown to be suitable for the separation and determination of porphyrin and phthalocyanines regioisomers, diastereoisomers, and enantiomers.

Methodology of Numerical Optimization for Orbital Parameters of Binary Systems

NASA Astrophysics Data System (ADS)

Araya, I.; Curé, M.

2010-02-01

The use of a numerical method of maximization (or minimization) in optimization processes allows us to obtain a great amount of solutions. Therefore, we can find a global maximum or minimum of the problem, but this is only possible if we used a suitable methodology. To obtain the global optimum values, we use the genetic algorithm called PIKAIA (P. Charbonneau) and other four algorithms implemented in Mathematica. We demonstrate that derived orbital parameters of binary systems published in some papers, based on radial velocity measurements, are local minimum instead of global ones.

Investigation of evanescent coupling between tapered fiber and a multimode slab waveguide.

PubMed

Dong, Shaofei; Ding, Hui; Liu, Yiying; Qi, Xiaofeng

2012-04-01

A tapered fiber-slab waveguide coupler (TFSC) is proposed in this paper. Both the numerical analysis based on the beam propagation method and experiments are used for investigating the dependencies of TFSC transmission features on their geometric parameters. From the simulations and experimental results, the rules for fabricating a TFSC with low transmission loss and sharp resonant spectra by optimizing the configuration parameters are presented. The conclusions derived from our work may provide helpful references for optimally designing and fabricating TFSC-based devices, such as sensors, wavelength filters, and intensity modulators.

Real Time Optimal Control of Supercapacitor Operation for Frequency Response

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

Luo, Yusheng; Panwar, Mayank; Mohanpurkar, Manish

2016-07-01

Supercapacitors are gaining wider applications in power systems due to fast dynamic response. Utilizing supercapacitors by means of power electronics interfaces for power compensation is a proven effective technique. For applications such as requency restoration if the cost of supercapacitors maintenance as well as the energy loss on the power electronics interfaces are addressed. It is infeasible to use traditional optimization control methods to mitigate the impacts of frequent cycling. This paper proposes a Front End Controller (FEC) using Generalized Predictive Control featuring real time receding optimization. The optimization constraints are based on cost and thermal management to enhance tomore » the utilization efficiency of supercapacitors. A rigorous mathematical derivation is conducted and test results acquired from Digital Real Time Simulator are provided to demonstrate effectiveness.« less

Robust optimal control of material flows in demand-driven supply networks

NASA Astrophysics Data System (ADS)

Laumanns, Marco; Lefeber, Erjen

2006-04-01

We develop a model based on stochastic discrete-time controlled dynamical systems in order to derive optimal policies for controlling the material flow in supply networks. Each node in the network is described as a transducer such that the dynamics of the material and information flows within the entire network can be expressed by a system of first-order difference equations, where some inputs to the system act as external disturbances. We apply methods from constrained robust optimal control to compute the explicit control law as a function of the current state. For the numerical examples considered, these control laws correspond to certain classes of optimal ordering policies from inventory management while avoiding, however, any a priori assumptions about the general form of the policy.

Optimal thrust level for orbit insertion

NASA Astrophysics Data System (ADS)

Cerf, Max

2017-07-01

The minimum-fuel orbital transfer is analyzed in the case of a launcher upper stage using a constantly thrusting engine. The thrust level is assumed to be constant and its value is optimized together with the thrust direction. A closed-loop solution for the thrust direction is derived from the extremal analysis for a planar orbital transfer. The optimal control problem reduces to two unknowns, namely the thrust level and the final time. Guessing and propagating the costates is no longer necessary and the optimal trajectory is easily found from a rough initialization. On the other hand the initial costates are assessed analytically from the initial conditions and they can be used as initial guess for transfers at different thrust levels. The method is exemplified on a launcher upper stage targeting a geostationary transfer orbit.

A fixed full-matrix method for determining ice sheet height change from satellite altimeter: an ENVISAT case study in East Antarctica with backscatter analysis

NASA Astrophysics Data System (ADS)

Yang, Yuande; Hwang, Cheinway; E, Dongchen

2014-09-01

A new method, called the fixed full-matrix method (FFM), is used to compute height changes at crossovers of satellite altimeter ground tracks. Using the ENVISAT data in East Antarctica, FFM results in crossovers of altimeter heights that are 1.9 and 79 times more than those from the fixed half method (FHM) and the one-row method (ORM). The mean standard error of height changes is about 14 cm from ORM, which is reduced to 7 cm by FHM and to 3 cm by FFM. Unlike FHM, FFM leads to uniform errors in the first-half and second-half height-change time series. FFM has the advantage in improving the accuracy of the change of height and backscattered power over ORM and FHM. Assisted by the ICESat-derived height changes, we determine the optimal threshold correlation coefficient (TCC) for a best correction for the backscatter effect on ENVISAT height changes. The TCC value of 0.92 yields an optimal result for FFM. With this value, FFM yields ENVISAT-derived height change rates in East Antarctica mostly falling between and 3 cm/year, and matching the ICESat result to 0.94 cm/year. The ENVISAT result will provide a constraint on the current mass balance result along the Chinese expedition route CHINARE.

Evaluation of phase-diversity techniques for solar-image restoration

NASA Technical Reports Server (NTRS)

Paxman, Richard G.; Seldin, John H.; Lofdahl, Mats G.; Scharmer, Goran B.; Keller, Christoph U.

1995-01-01

Phase-diversity techniques provide a novel observational method for overcomming the effects of turbulence and instrument-induced aberrations in ground-based astronomy. Two implementations of phase-diversity techniques that differ with regard to noise model, estimator, optimization algorithm, method of regularization, and treatment of edge effects are described. Reconstructions of solar granulation derived by applying these two implementations to common data sets are shown to yield nearly identical images. For both implementations, reconstructions from phase-diverse speckle data (involving multiple realizations of turbulence) are shown to be superior to those derived from conventional phase-diversity data (involving a single realization). Phase-diverse speckle reconstructions are shown to achieve near diffraction-limited resolution and are validated by internal and external consistency tests, including a comparison with a reconstruction using a well-accepted speckle-imaging method.

Utilization of group theory in studies of molecular clusters

NASA Astrophysics Data System (ADS)

Ocak, Mahir E.

The structure of the molecular symmetry group of molecular clusters was analyzed and it is shown that the molecular symmetry group of a molecular cluster can be written as direct products and semidirect products of its subgroups. Symmetry adaptation of basis functions in direct product groups and semidirect product groups was considered in general and the sequential symmetry adaptation procedure which is already known for direct product groups was extended to the case of semidirect product groups. By using the sequential symmetry adaptation procedure a new method for calculating the VRT spectra of molecular clusters which is named as Monomer Basis Representation (MBR) method is developed. In the MBR method, calculations starts with a single monomer with the purpose of obtaining an optimized basis for that monomer as a linear combination of some primitive basis functions. Then, an optimized basis for each identical monomer is generated from the optimized basis of this monomer. By using the optimized bases of the monomers, a basis is generated generated for the solution of the full problem, and the VRT spectra of the cluster is obtained by using this basis. Since an optimized basis is used for each monomer which has a much smaller size than the primitive basis from which the optimized bases are generated, the MBR method leads to an exponential optimization in the size of the basis that is required for the calculations. Application of the MBR method has been illustrated by calculating the VRT spectra of water dimer by using the SAPT-5st potential surface of Groenenboom et al. The rest of the calculations are in good agreement with both the original calculations of Groenenboom et al. and also with the experimental results. Comparing the size of the optimized basis with the size of the primitive basis, it can be said that the method works efficiently. Because of its efficiency, the MBR method can be used for studies of clusters bigger than dimers. Thus, MBR method can be used for studying the many-body terms and for deriving accurate potential surfaces.

Inverse lithography using sparse mask representations

NASA Astrophysics Data System (ADS)

Ionescu, Radu C.; Hurley, Paul; Apostol, Stefan

2015-03-01

We present a novel optimisation algorithm for inverse lithography, based on optimization of the mask derivative, a domain inherently sparse, and for rectilinear polygons, invertible. The method is first developed assuming a point light source, and then extended to general incoherent sources. What results is a fast algorithm, producing manufacturable masks (the search space is constrained to rectilinear polygons), and flexible (specific constraints such as minimal line widths can be imposed). One inherent trick is to treat polygons as continuous entities, thus making aerial image calculation extremely fast and accurate. Requirements for mask manufacturability can be integrated in the optimization without too much added complexity. We also explain how to extend the scheme for phase-changing mask optimization.

Stochastic optimal control of ultradiffusion processes with application to dynamic portfolio management

NASA Astrophysics Data System (ADS)

Marcozzi, Michael D.

2008-12-01

We consider theoretical and approximation aspects of the stochastic optimal control of ultradiffusion processes in the context of a prototype model for the selling price of a European call option. Within a continuous-time framework, the dynamic management of a portfolio of assets is effected through continuous or point control, activation costs, and phase delay. The performance index is derived from the unique weak variational solution to the ultraparabolic Hamilton-Jacobi equation; the value function is the optimal realization of the performance index relative to all feasible portfolios. An approximation procedure based upon a temporal box scheme/finite element method is analyzed; numerical examples are presented in order to demonstrate the viability of the approach.

Optimizing microwave photodetection: input-output theory

NASA Astrophysics Data System (ADS)

Schöndorf, M.; Govia, L. C. G.; Vavilov, M. G.; McDermott, R.; Wilhelm, F. K.

2018-04-01

High fidelity microwave photon counting is an important tool for various areas from background radiation analysis in astronomy to the implementation of circuit quantum electrodynamic architectures for the realization of a scalable quantum information processor. In this work we describe a microwave photon counter coupled to a semi-infinite transmission line. We employ input-output theory to examine a continuously driven transmission line as well as traveling photon wave packets. Using analytic and numerical methods, we calculate the conditions on the system parameters necessary to optimize measurement and achieve high detection efficiency. With this we can derive a general matching condition depending on the different system rates, under which the measurement process is optimal.

A Class of Prediction-Correction Methods for Time-Varying Convex Optimization

NASA Astrophysics Data System (ADS)

Simonetto, Andrea; Mokhtari, Aryan; Koppel, Alec; Leus, Geert; Ribeiro, Alejandro

2016-09-01

This paper considers unconstrained convex optimization problems with time-varying objective functions. We propose algorithms with a discrete time-sampling scheme to find and track the solution trajectory based on prediction and correction steps, while sampling the problem data at a constant rate of $1/h$, where $h$ is the length of the sampling interval. The prediction step is derived by analyzing the iso-residual dynamics of the optimality conditions. The correction step adjusts for the distance between the current prediction and the optimizer at each time step, and consists either of one or multiple gradient steps or Newton steps, which respectively correspond to the gradient trajectory tracking (GTT) or Newton trajectory tracking (NTT) algorithms. Under suitable conditions, we establish that the asymptotic error incurred by both proposed methods behaves as $O(h^2)$, and in some cases as $O(h^4)$, which outperforms the state-of-the-art error bound of $O(h)$ for correction-only methods in the gradient-correction step. Moreover, when the characteristics of the objective function variation are not available, we propose approximate gradient and Newton tracking algorithms (AGT and ANT, respectively) that still attain these asymptotical error bounds. Numerical simulations demonstrate the practical utility of the proposed methods and that they improve upon existing techniques by several orders of magnitude.

High-throughput design and optimization of fast lithium ion conductors by the combination of bond-valence method and density functional theory

NASA Astrophysics Data System (ADS)

Xiao, Ruijuan; Li, Hong; Chen, Liquan

2015-09-01

Looking for solid state electrolytes with fast lithium ion conduction is an important prerequisite for developing all-solid-state lithium secondary batteries. By combining the simulation techniques in different levels of accuracy, e.g. the bond-valence (BV) method and the density functional theory (DFT), a high-throughput design and optimization scheme is proposed for searching fast lithium ion conductors as candidate solid state electrolytes for lithium rechargeable batteries. The screening from more than 1000 compounds is performed through BV-based method, and the ability to predict reliable tendency of the Li+ migration energy barriers is confirmed by comparing with the results from DFT calculations. β-Li3PS4 is taken as a model system to demonstrate the application of this combination method in optimizing properties of solid electrolytes. By employing the high-throughput DFT simulations to more than 200 structures of the doping derivatives of β-Li3PS4, the effects of doping on the ionic conductivities in this material are predicted by the BV calculations. The O-doping scheme is proposed as a promising way to improve the kinetic properties of this materials, and the validity of the optimization is proved by the first-principles molecular dynamics (FPMD) simulations.

School Cost Functions: A Meta-Regression Analysis

ERIC Educational Resources Information Center

Colegrave, Andrew D.; Giles, Margaret J.

2008-01-01

The education cost literature includes econometric studies attempting to determine economies of scale, or estimate an optimal school or district size. Not only do their results differ, but the studies use dissimilar data, techniques, and models. To derive value from these studies requires that the estimates be made comparable. One method to do…

Primer vector theory and applications

NASA Technical Reports Server (NTRS)

Jezewski, D. J.

1975-01-01

A method developed to compute two-body, optimal, N-impulse trajectories was presented. The necessary conditions established define the gradient structure of the primer vector and its derivative for any set of boundary conditions and any number of impulses. Inequality constraints, a conjugate gradient iterator technique, and the use of a penalty function were also discussed.

FDTD simulation of EM wave propagation in 3-D media

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

Wang, T.; Tripp, A.C.

1996-01-01

A finite-difference, time-domain solution to Maxwell`s equations has been developed for simulating electromagnetic wave propagation in 3-D media. The algorithm allows arbitrary electrical conductivity and permittivity variations within a model. The staggered grid technique of Yee is used to sample the fields. A new optimized second-order difference scheme is designed to approximate the spatial derivatives. Like the conventional fourth-order difference scheme, the optimized second-order scheme needs four discrete values to calculate a single derivative. However, the optimized scheme is accurate over a wider wavenumber range. Compared to the fourth-order scheme, the optimized scheme imposes stricter limitations on the time stepmore » sizes but allows coarser grids. The net effect is that the optimized scheme is more efficient in terms of computation time and memory requirement than the fourth-order scheme. The temporal derivatives are approximated by second-order central differences throughout. The Liao transmitting boundary conditions are used to truncate an open problem. A reflection coefficient analysis shows that this transmitting boundary condition works very well. However, it is subject to instability. A method that can be easily implemented is proposed to stabilize the boundary condition. The finite-difference solution is compared to closed-form solutions for conducting and nonconducting whole spaces and to an integral-equation solution for a 3-D body in a homogeneous half-space. In all cases, the finite-difference solutions are in good agreement with the other solutions. Finally, the use of the algorithm is demonstrated with a 3-D model. Numerical results show that both the magnetic field response and electric field response can be useful for shallow-depth and small-scale investigations.« less

Multi-Objective Memetic Search for Robust Motion and Distortion Correction in Diffusion MRI.

PubMed

Hering, Jan; Wolf, Ivo; Maier-Hein, Klaus H

2016-10-01

Effective image-based artifact correction is an essential step in the analysis of diffusion MR images. Many current approaches are based on retrospective registration, which becomes challenging in the realm of high b -values and low signal-to-noise ratio, rendering the corresponding correction schemes more and more ineffective. We propose a novel registration scheme based on memetic search optimization that allows for simultaneous exploitation of different signal intensity relationships between the images, leading to more robust registration results. We demonstrate the increased robustness and efficacy of our method on simulated as well as in vivo datasets. In contrast to the state-of-art methods, the median target registration error (TRE) stayed below the voxel size even for high b -values (3000 s ·mm -2 and higher) and low SNR conditions. We also demonstrate the increased precision in diffusion-derived quantities by evaluating Neurite Orientation Dispersion and Density Imaging (NODDI) derived measures on a in vivo dataset with severe motion artifacts. These promising results will potentially inspire further studies on metaheuristic optimization in diffusion MRI artifact correction and image registration in general.

Magnetic porous carbon derived from a bimetallic metal-organic framework for magnetic solid-phase extraction of organochlorine pesticides from drinking and environmental water samples.

PubMed

Liu, Yaxi; Gao, Zongjun; Wu, Ri; Wang, Zhenhua; Chen, Xiangfeng; Chan, T-W Dominic

2017-01-06

In this work, magnetic porous carbon material derived from a bimetallic metal-organic framework was explored as an adsorbent for magnetic solid-phase extraction of organochlorine pesticides (OCPs). The synthesized porous carbon possessed a high specific surface area and magnetization saturation. The OCPs in the samples were quantified using gas chromatography coupled with a triple quadrupole mass spectrometer. The experimental parameters, including the desorption solvent and conditions, amount of adsorbent, extraction time, extraction temperature, and ionic strength of the solution, were optimized. Under optimal conditions, the developed method displayed good linearity (r>0.99) within the concentration range of 2-500ngL -1 . Low limits of detection (0.39-0.70ngL -1 , signal-to-noise ratio=3:1) and limits of quantification (1.45-2.0ngL -1 , signal-to-noise ratio=10:1) as well as good precision (relative standard deviation<10%) were also obtained. The developed method was applied in the analysis of OCPs in drinking and environmental water samples. Copyright © 2016 Elsevier B.V. All rights reserved.

Fully Anisotropic Rotational Diffusion Tensor from Molecular Dynamics Simulations.

PubMed

Linke, Max; Köfinger, Jürgen; Hummer, Gerhard

2018-05-31

We present a method to calculate the fully anisotropic rotational diffusion tensor from molecular dynamics simulations. Our approach is based on fitting the time-dependent covariance matrix of the quaternions that describe the rigid-body rotational dynamics. Explicit analytical expressions have been derived for the covariances by Favro, which are valid irrespective of the degree of anisotropy. We use these expressions to determine an optimal rotational diffusion tensor from trajectory data. The molecular structures are aligned against a reference by optimal rigid-body superposition. The quaternion covariances can then be obtained directly from the rotation matrices used in the alignment. The rotational diffusion tensor is determined by a fit to the time-dependent quaternion covariances, or directly by Laplace transformation and matrix diagonalization. To quantify uncertainties in the fit, we derive analytical expressions and compare them with the results of Brownian dynamics simulations of anisotropic rotational diffusion. We apply the method to microsecond long trajectories of the Dickerson-Drew B-DNA dodecamer and of horse heart myoglobin. The anisotropic rotational diffusion tensors calculated from simulations agree well with predictions from hydrodynamics.

New closed-form approximation for skin chromophore mapping.

PubMed

Välisuo, Petri; Kaartinen, Ilkka; Tuchin, Valery; Alander, Jarmo

2011-04-01

The concentrations of blood and melanin in skin can be estimated based on the reflectance of light. Many models for this estimation have been built, such as Monte Carlo simulation, diffusion models, and the differential modified Beer-Lambert law. The optimization-based methods are too slow for chromophore mapping of high-resolution spectral images, and the differential modified Beer-Lambert is not often accurate enough. Optimal coefficients for the differential Beer-Lambert model are calculated by differentiating the diffusion model, optimized to the normal skin spectrum. The derivatives are then used in predicting the difference in chromophore concentrations from the difference in absorption spectra. The accuracy of the method is tested both computationally and experimentally using a Monte Carlo multilayer simulation model, and the data are measured from the palm of a hand during an Allen's test, which modulates the blood content of skin. The correlations of the given and predicted blood, melanin, and oxygen saturation levels are correspondingly r = 0.94, r = 0.99, and r = 0.73. The prediction of the concentrations for all pixels in a 1-megapixel image would take ∼ 20 min, which is orders of magnitude faster than the methods based on optimization during the prediction.

Development of a high-performance noise-reduction filter for tomographic reconstruction

NASA Astrophysics Data System (ADS)

Kao, Chien-Min; Pan, Xiaochuan

2001-07-01

We propose a new noise-reduction method for tomographic reconstruction. The method incorporates a priori information on the source image for allowing the derivation of the energy spectrum of its ideal sinogram. In combination with the energy spectrum of the Poisson noise in the measured sinogram, we are able to derive a Wiener-like filter for effective suppression of the sinogram noise. The filtered backprojection (FBP) algorithm, with a ramp filter, is then applied to the filtered sinogram to produce tomographic images. The resulting filter has a closed-form expression in the frequency space and contains a single user-adjustable regularization parameter. The proposed method is hence simple to implement and easy to use. In contrast to the ad hoc apodizing windows, such as Hanning and Butterworth filters, that are commonly used in the conventional FBP reconstruction, the proposed filter is theoretically more rigorous as it is derived by basing upon an optimization criterion, subject to a known class of source image intensity distributions.

Airfoil optimization for unsteady flows with application to high-lift noise reduction

NASA Astrophysics Data System (ADS)

Rumpfkeil, Markus Peer

The use of steady-state aerodynamic optimization methods in the computational fluid dynamic (CFD) community is fairly well established. In particular, the use of adjoint methods has proven to be very beneficial because their cost is independent of the number of design variables. The application of numerical optimization to airframe-generated noise, however, has not received as much attention, but with the significant quieting of modern engines, airframe noise now competes with engine noise. Optimal control techniques for unsteady flows are needed in order to be able to reduce airframe-generated noise. In this thesis, a general framework is formulated to calculate the gradient of a cost function in a nonlinear unsteady flow environment via the discrete adjoint method. The unsteady optimization algorithm developed in this work utilizes a Newton-Krylov approach since the gradient-based optimizer uses the quasi-Newton method BFGS, Newton's method is applied to the nonlinear flow problem, GMRES is used to solve the resulting linear problem inexactly, and last but not least the linear adjoint problem is solved using Bi-CGSTAB. The flow is governed by the unsteady two-dimensional compressible Navier-Stokes equations in conjunction with a one-equation turbulence model, which are discretized using structured grids and a finite difference approach. The effectiveness of the unsteady optimization algorithm is demonstrated by applying it to several problems of interest including shocktubes, pulses in converging-diverging nozzles, rotating cylinders, transonic buffeting, and an unsteady trailing-edge flow. In order to address radiated far-field noise, an acoustic wave propagation program based on the Ffowcs Williams and Hawkings (FW-H) formulation is implemented and validated. The general framework is then used to derive the adjoint equations for a novel hybrid URANS/FW-H optimization algorithm in order to be able to optimize the shape of airfoils based on their calculated far-field pressure fluctuations. Validation and application results for this novel hybrid URANS/FW-H optimization algorithm show that it is possible to optimize the shape of an airfoil in an unsteady flow environment to minimize its radiated far-field noise while maintaining good aerodynamic performance.

Evaluation of arterial stiffness by finger-toe pulse wave velocity: optimization of signal processing and clinical validation.

PubMed

Obeid, Hasan; Khettab, Hakim; Marais, Louise; Hallab, Magid; Laurent, Stéphane; Boutouyrie, Pierre

2017-08-01

Carotid-femoral pulse wave velocity (PWV) (cf-PWV) is the gold standard for measuring aortic stiffness. Finger-toe PWV (ft-PWV) is a simpler noninvasive method for measuring arterial stiffness. Although the validity of the method has been previously assessed, its accuracy can be improved. ft-PWV is determined on the basis of a patented height chart for the distance and the pulse transit time (PTT) between the finger and the toe pulpar arteries signals (ft-PTT). The objective of the first study, performed in 66 patients, was to compare different algorithms (intersecting tangents, maximum of the second derivative, 10% threshold and cross-correlation) for determining the foot of the arterial pulse wave, thus the ft-PTT. The objective of the second study, performed in 101 patients, was to investigate different signal processing chains to improve the concordance of ft-PWV with the gold-standard cf-PWV. Finger-toe PWV (ft-PWV) was calculated using the four algorithms. The best correlations relating ft-PWV and cf-PWV, and relating ft-PTT and carotid-femoral PTT were obtained with the maximum of the second derivative algorithm [PWV: r = 0.56, P < 0.0001, root mean square error (RMSE) = 0.9 m/s; PTT: r = 0.61, P < 0.001, RMSE = 12 ms]. The three other algorithms showed lower correlations. The correlation between ft-PTT and carotid-femoral PTT further improved (r = 0.81, P < 0.0001, RMSE = 5.4 ms) when the maximum of the second derivative algorithm was combined with an optimized signal processing chain. Selecting the maximum of the second derivative algorithm for detecting the foot of the pressure waveform, and combining it with an optimized signal processing chain, improved the accuracy of ft-PWV measurement in the current population sample. Thus, it makes ft-PWV very promising for the simple noninvasive determination of aortic stiffness in clinical practice.

Multidisciplinary design optimization of aircraft wing structures with aeroelastic and aeroservoelastic constraints

NASA Astrophysics Data System (ADS)

Jung, Sang-Young

Design procedures for aircraft wing structures with control surfaces are presented using multidisciplinary design optimization. Several disciplines such as stress analysis, structural vibration, aerodynamics, and controls are considered simultaneously and combined for design optimization. Vibration data and aerodynamic data including those in the transonic regime are calculated by existing codes. Flutter analyses are performed using those data. A flutter suppression method is studied using control laws in the closed-loop flutter equation. For the design optimization, optimization techniques such as approximation, design variable linking, temporary constraint deletion, and optimality criteria are used. Sensitivity derivatives of stresses and displacements for static loads, natural frequency, flutter characteristics, and control characteristics with respect to design variables are calculated for an approximate optimization. The objective function is the structural weight. The design variables are the section properties of the structural elements and the control gain factors. Existing multidisciplinary optimization codes (ASTROS* and MSC/NASTRAN) are used to perform single and multiple constraint optimizations of fully built up finite element wing structures. Three benchmark wing models are developed and/or modified for this purpose. The models are tested extensively.

Optimal designs based on the maximum quasi-likelihood estimator

PubMed Central

Shen, Gang; Hyun, Seung Won; Wong, Weng Kee

2016-01-01

We use optimal design theory and construct locally optimal designs based on the maximum quasi-likelihood estimator (MqLE), which is derived under less stringent conditions than those required for the MLE method. We show that the proposed locally optimal designs are asymptotically as efficient as those based on the MLE when the error distribution is from an exponential family, and they perform just as well or better than optimal designs based on any other asymptotically linear unbiased estimators such as the least square estimator (LSE). In addition, we show current algorithms for finding optimal designs can be directly used to find optimal designs based on the MqLE. As an illustrative application, we construct a variety of locally optimal designs based on the MqLE for the 4-parameter logistic (4PL) model and study their robustness properties to misspecifications in the model using asymptotic relative efficiency. The results suggest that optimal designs based on the MqLE can be easily generated and they are quite robust to mis-specification in the probability distribution of the responses. PMID:28163359

Kinematic control of redundant robots and the motion optimizability measure.

PubMed

Li, L; Gruver, W A; Zhang, Q; Yang, Z

2001-01-01

This paper treats the kinematic control of manipulators with redundant degrees of freedom. We derive an analytical solution for the inverse kinematics that provides a means for accommodating joint velocity constraints in real time. We define the motion optimizability measure and use it to develop an efficient method for the optimization of joint trajectories subject to multiple criteria. An implementation of the method for a 7-dof experimental redundant robot is present.

An Efficient Ray-Tracing Method for Determining Terrain Intercepts in EDL Simulations

NASA Technical Reports Server (NTRS)

Shidner, Jeremy D.

2016-01-01

The calculation of a ray's intercept from an arbitrary point in space to a prescribed surface is a common task in computer simulations. The arbitrary point often represents an object that is moving according to the simulation, while the prescribed surface is fixed in a defined frame. For detailed simulations, this surface becomes complex, taking the form of real-world objects such as mountains, craters or valleys which require more advanced methods to accurately calculate a ray's intercept location. Incorporation of these complex surfaces has commonly been implemented in graphics systems that utilize highly optimized graphics processing units to analyze such features. This paper proposes a simplified method that does not require computationally intensive graphics solutions, but rather an optimized ray-tracing method for an assumed terrain dataset. This approach was developed for the Mars Science Laboratory mission which landed on the complex terrain of Gale Crater. First, this paper begins with a discussion of the simulation used to implement the model and the applicability of finding surface intercepts with respect to atmosphere modeling, altitude determination, radar modeling, and contact forces influencing vehicle dynamics. Next, the derivation and assumptions of the intercept finding method are presented. Key assumptions are noted making the routines specific to only certain types of surface data sets that are equidistantly spaced in longitude and latitude. The derivation of the method relies on ray-tracing, requiring discussion on the formulation of the ray with respect to the terrain datasets. Further discussion includes techniques for ray initialization in order to optimize the intercept search. Then, the model implementation for various new applications in the simulation are demonstrated. Finally, a validation of the accuracy is presented along with the corresponding data sets used in the validation. A performance summary of the method will be shown using the analysis from the Mars Science Laboratory's terminal descent sensing model. Alternate uses will also be shown for determining horizon maps and orbiter set times.

From Geometry Optimization to Time Dependent Molecular Structure Modeling: Method Developments, ab initio Theories and Applications

NASA Astrophysics Data System (ADS)

Liang, Wenkel

This dissertation consists of two general parts: (I) developments of optimization algorithms (both nuclear and electronic degrees of freedom) for time-independent molecules and (II) novel methods, first-principle theories and applications in time dependent molecular structure modeling. In the first part, we discuss in specific two new algorithms for static geometry optimization, the eigenspace update (ESU) method in nonredundant internal coordinate that exhibits an enhanced performace with up to a factor of 3 savings in computational cost for large-sized molecular systems; the Car-Parrinello density matrix search (CP-DMS) method that enables direct minimization of the SCF energy as an effective alternative to conventional diagonalization approach. For the second part, we consider the time dependence and first presents two nonadiabatic dynamic studies that model laser controlled molecular photo-dissociation for qualitative understandings of intense laser-molecule interaction, using ab initio direct Ehrenfest dynamics scheme implemented with real-time time-dependent density functional theory (RT-TDDFT) approach developed in our group. Furthermore, we place our special interest on the nonadiabatic electronic dynamics in the ultrafast time scale, and presents (1) a novel technique that can not only obtain energies but also the electron densities of doubly excited states within a single determinant framework, by combining methods of CP-DMS with RT-TDDFT; (2) a solvated first-principles electronic dynamics method by incorporating the polarizable continuum solvation model (PCM) to RT-TDDFT, which is found to be very effective in describing the dynamical solvation effect in the charge transfer process and yields a consistent absorption spectrum in comparison to the conventional linear response results in solution. (3) applications of the PCM-RT-TDDFT method to study the intramolecular charge-transfer (CT) dynamics in a C60 derivative. Such work provides insights into the characteristics of ultrafast dynamics in photoexcited fullerene derivatives, and aids in the rational design for pre-dissociative exciton in the intramolecular CT process in organic solar cells.

Parameters-tuning of PID controller for automatic voltage regulators using the African buffalo optimization.

PubMed

Odili, Julius Beneoluchi; Mohmad Kahar, Mohd Nizam; Noraziah, A

2017-01-01

In this paper, an attempt is made to apply the African Buffalo Optimization (ABO) to tune the parameters of a PID controller for an effective Automatic Voltage Regulator (AVR). Existing metaheuristic tuning methods have been proven to be quite successful but there were observable areas that need improvements especially in terms of the system's gain overshoot and steady steady state errors. Using the ABO algorithm where each buffalo location in the herd is a candidate solution to the Proportional-Integral-Derivative parameters was very helpful in addressing these two areas of concern. The encouraging results obtained from the simulation of the PID Controller parameters-tuning using the ABO when compared with the performance of Genetic Algorithm PID (GA-PID), Particle-Swarm Optimization PID (PSO-PID), Ant Colony Optimization PID (ACO-PID), PID, Bacteria-Foraging Optimization PID (BFO-PID) etc makes ABO-PID a good addition to solving PID Controller tuning problems using metaheuristics.

Optimal Control Modification Adaptive Law for Time-Scale Separated Systems

NASA Technical Reports Server (NTRS)

Nguyen, Nhan T.

2010-01-01

Recently a new optimal control modification has been introduced that can achieve robust adaptation with a large adaptive gain without incurring high-frequency oscillations as with the standard model-reference adaptive control. This modification is based on an optimal control formulation to minimize the L2 norm of the tracking error. The optimal control modification adaptive law results in a stable adaptation in the presence of a large adaptive gain. This study examines the optimal control modification adaptive law in the context of a system with a time scale separation resulting from a fast plant with a slow actuator. A singular perturbation analysis is performed to derive a modification to the adaptive law by transforming the original system into a reduced-order system in slow time. A model matching conditions in the transformed time coordinate results in an increase in the actuator command that effectively compensate for the slow actuator dynamics. Simulations demonstrate effectiveness of the method.

Optimal Control Modification for Time-Scale Separated Systems

NASA Technical Reports Server (NTRS)

Nguyen, Nhan T.

2012-01-01

Recently a new optimal control modification has been introduced that can achieve robust adaptation with a large adaptive gain without incurring high-frequency oscillations as with the standard model-reference adaptive control. This modification is based on an optimal control formulation to minimize the L2 norm of the tracking error. The optimal control modification adaptive law results in a stable adaptation in the presence of a large adaptive gain. This study examines the optimal control modification adaptive law in the context of a system with a time scale separation resulting from a fast plant with a slow actuator. A singular perturbation analysis is performed to derive a modification to the adaptive law by transforming the original system into a reduced-order system in slow time. A model matching conditions in the transformed time coordinate results in an increase in the actuator command that effectively compensate for the slow actuator dynamics. Simulations demonstrate effectiveness of the method.

Optimal charge control strategies for stationary photovoltaic battery systems

NASA Astrophysics Data System (ADS)

Li, Jiahao; Danzer, Michael A.

2014-07-01

Battery systems coupled to photovoltaic (PV) modules for example fulfill one major function: they locally decouple PV generation and consumption of electrical power leading to two major effects. First, they reduce the grid load, especially at peak times and therewith reduce the necessity of a network expansion. And second, they increase the self-consumption in households and therewith help to reduce energy expenses. For the management of PV batteries charge control strategies need to be developed to reach the goals of both the distribution system operators and the local power producer. In this work optimal control strategies regarding various optimization goals are developed on the basis of the predicted household loads and PV generation profiles using the method of dynamic programming. The resulting charge curves are compared and essential differences discussed. Finally, a multi-objective optimization shows that charge control strategies can be derived that take all optimization goals into account.

Comparing the Caputo, Caputo-Fabrizio and Atangana-Baleanu derivative with fractional order: Fractional cubic isothermal auto-catalytic chemical system

NASA Astrophysics Data System (ADS)

Saad, K. M.

2018-03-01

In this work we extend the standard model for a cubic isothermal auto-catalytic chemical system (CIACS) to a new model of a fractional cubic isothermal auto-catalytic chemical system (FCIACS) based on Caputo (C), Caputo-Fabrizio (CF) and Atangana-Baleanu in the Liouville-Caputo sense (ABC) fractional time derivatives, respectively. We present approximate solutions for these extended models using the q -homotopy analysis transform method ( q -HATM). We solve the FCIACS with the C derivative and compare our results with those obtained using the CF and ABC derivatives. The ranges of convergence of the solutions are found and the optimal values of h , the auxiliary parameter, are derived. Finally, these solutions are compared with numerical solutions of the various models obtained using finite differences and excellent agreement is found.

Performance and robustness of optimal fractional fuzzy PID controllers for pitch control of a wind turbine using chaotic optimization algorithms.

PubMed

Asgharnia, Amirhossein; Shahnazi, Reza; Jamali, Ali

2018-05-11

The most studied controller for pitch control of wind turbines is proportional-integral-derivative (PID) controller. However, due to uncertainties in wind turbine modeling and wind speed profiles, the need for more effective controllers is inevitable. On the other hand, the parameters of PID controller usually are unknown and should be selected by the designer which is neither a straightforward task nor optimal. To cope with these drawbacks, in this paper, two advanced controllers called fuzzy PID (FPID) and fractional-order fuzzy PID (FOFPID) are proposed to improve the pitch control performance. Meanwhile, to find the parameters of the controllers the chaotic evolutionary optimization methods are used. Using evolutionary optimization methods not only gives us the unknown parameters of the controllers but also guarantees the optimality based on the chosen objective function. To improve the performance of the evolutionary algorithms chaotic maps are used. All the optimization procedures are applied to the 2-mass model of 5-MW wind turbine model. The proposed optimal controllers are validated using simulator FAST developed by NREL. Simulation results demonstrate that the FOFPID controller can reach to better performance and robustness while guaranteeing fewer fatigue damages in different wind speeds in comparison to FPID, fractional-order PID (FOPID) and gain-scheduling PID (GSPID) controllers. Copyright © 2018 ISA. Published by Elsevier Ltd. All rights reserved.

Variability in Tropospheric Ozone over China Derived from Assimilated GOME-2 Ozone Profiles

NASA Astrophysics Data System (ADS)

van Peet, J. C. A.; van der A, R. J.; Kelder, H. M.

2016-08-01

A tropospheric ozone dataset is derived from assimilated GOME-2 ozone profiles for 2008. Ozone profiles are retrieved with the OPERA algorithm, using the optimal estimation method. The retrievals are done on a spatial resolution of 160×160 km on 16 layers ranging from the surface up to 0.01 hPa. By using the averaging kernels in the data assimilation, the algorithm maintains the high resolution vertical structures of the model, while being constrained by observations with a lower vertical resolution.

Fault diagnosis of rolling element bearing using a new optimal scale morphology analysis method.

PubMed

Yan, Xiaoan; Jia, Minping; Zhang, Wan; Zhu, Lin

2018-02-01

Periodic transient impulses are key indicators of rolling element bearing defects. Efficient acquisition of impact impulses concerned with the defects is of much concern to the precise detection of bearing defects. However, transient features of rolling element bearing are generally immersed in stochastic noise and harmonic interference. Therefore, in this paper, a new optimal scale morphology analysis method, named adaptive multiscale combination morphological filter-hat transform (AMCMFH), is proposed for rolling element bearing fault diagnosis, which can both reduce stochastic noise and reserve signal details. In this method, firstly, an adaptive selection strategy based on the feature energy factor (FEF) is introduced to determine the optimal structuring element (SE) scale of multiscale combination morphological filter-hat transform (MCMFH). Subsequently, MCMFH containing the optimal SE scale is applied to obtain the impulse components from the bearing vibration signal. Finally, fault types of bearing are confirmed by extracting the defective frequency from envelope spectrum of the impulse components. The validity of the proposed method is verified through the simulated analysis and bearing vibration data derived from the laboratory bench. Results indicate that the proposed method has a good capability to recognize localized faults appeared on rolling element bearing from vibration signal. The study supplies a novel technique for the detection of faulty bearing. Copyright © 2018. Published by Elsevier Ltd.

Ultra-high-performance supercritical fluid chromatography with quadrupole-time-of-flight mass spectrometry (UHPSFC/QTOF-MS) for analysis of lignin-derived monomeric compounds in processed lignin samples.

PubMed

Prothmann, Jens; Sun, Mingzhe; Spégel, Peter; Sandahl, Margareta; Turner, Charlotta

2017-12-01

The conversion of lignin to potentially high-value low molecular weight compounds often results in complex mixtures of monomeric and oligomeric compounds. In this study, a method for the quantitative and qualitative analysis of 40 lignin-derived compounds using ultra-high-performance supercritical fluid chromatography coupled to quadrupole-time-of-flight mass spectrometry (UHPSFC/QTOF-MS) has been developed. Seven different columns were explored for maximum selectivity. Makeup solvent composition and ion source settings were optimised using a D-optimal design of experiment (DoE). Differently processed lignin samples were analysed and used for the method validation. The new UHPSFC/QTOF-MS method showed good separation of the 40 compounds within only 6-min retention time, and out of these, 36 showed high ionisation efficiency in negative electrospray ionisation mode. Graphical abstract A rapid and selective method for the quantitative and qualitative analysis of 40 lignin-derived compounds using ultra-high-performance supercritical fluid chromatography coupled to quadrupole-time-of-flight mass spectrometry (UHPSFC/QTOF-MS).

Finding the Right Candidate for the Right Position: A Fast NMR-Assisted Combinatorial Method for Optimizing Nucleic Acids Binders.

PubMed

Jiménez-Moreno, Ester; Montalvillo-Jiménez, Laura; Santana, Andrés G; Gómez, Ana M; Jiménez-Osés, Gonzalo; Corzana, Francisco; Bastida, Agatha; Jiménez-Barbero, Jesús; Cañada, Francisco Javier; Gómez-Pinto, Irene; González, Carlos; Asensio, Juan Luis

2016-05-25

Development of strong and selective binders from promiscuous lead compounds represents one of the most expensive and time-consuming tasks in drug discovery. We herein present a novel fragment-based combinatorial strategy for the optimization of multivalent polyamine scaffolds as DNA/RNA ligands. Our protocol provides a quick access to a large variety of regioisomer libraries that can be tested for selective recognition by combining microdialysis assays with simple isotope labeling and NMR experiments. To illustrate our approach, 20 small libraries comprising 100 novel kanamycin-B derivatives have been prepared and evaluated for selective binding to the ribosomal decoding A-Site sequence. Contrary to the common view of NMR as a low-throughput technique, we demonstrate that our NMR methodology represents a valuable alternative for the detection and quantification of complex mixtures, even integrated by highly similar or structurally related derivatives, a common situation in the context of a lead optimization process. Furthermore, this study provides valuable clues about the structural requirements for selective A-site recognition.

Hermite WENO limiting for multi-moment finite-volume methods using the ADER-DT time discretization for 1-D systems of conservation laws

DOE PAGES

Norman, Matthew R.

2014-11-24

New Hermite Weighted Essentially Non-Oscillatory (HWENO) interpolants are developed and investigated within the Multi-Moment Finite-Volume (MMFV) formulation using the ADER-DT time discretization. Whereas traditional WENO methods interpolate pointwise, function-based WENO methods explicitly form a non-oscillatory, high-order polynomial over the cell in question. This study chooses a function-based approach and details how fast convergence to optimal weights for smooth flow is ensured. Methods of sixth-, eighth-, and tenth-order accuracy are developed. We compare these against traditional single-moment WENO methods of fifth-, seventh-, ninth-, and eleventh-order accuracy to compare against more familiar methods from literature. The new HWENO methods improve upon existingmore » HWENO methods (1) by giving a better resolution of unreinforced contact discontinuities and (2) by only needing a single HWENO polynomial to update both the cell mean value and cell mean derivative. Test cases to validate and assess these methods include 1-D linear transport, the 1-D inviscid Burger's equation, and the 1-D inviscid Euler equations. Smooth and non-smooth flows are used for evaluation. These HWENO methods performed better than comparable literature-standard WENO methods for all regimes of discontinuity and smoothness in all tests herein. They exhibit improved optimal accuracy due to the use of derivatives, and they collapse to solutions similar to typical WENO methods when limiting is required. The study concludes that the new HWENO methods are robust and effective when used in the ADER-DT MMFV framework. Finally, these results are intended to demonstrate capability rather than exhaust all possible implementations.« less

Shape design sensitivity analysis and optimization of three dimensional elastic solids using geometric modeling and automatic regridding. Ph.D. Thesis

NASA Technical Reports Server (NTRS)

Yao, Tse-Min; Choi, Kyung K.

1987-01-01

An automatic regridding method and a three dimensional shape design parameterization technique were constructed and integrated into a unified theory of shape design sensitivity analysis. An algorithm was developed for general shape design sensitivity analysis of three dimensional eleastic solids. Numerical implementation of this shape design sensitivity analysis method was carried out using the finite element code ANSYS. The unified theory of shape design sensitivity analysis uses the material derivative of continuum mechanics with a design velocity field that represents shape change effects over the structural design. Automatic regridding methods were developed by generating a domain velocity field with boundary displacement method. Shape design parameterization for three dimensional surface design problems was illustrated using a Bezier surface with boundary perturbations that depend linearly on the perturbation of design parameters. A linearization method of optimization, LINRM, was used to obtain optimum shapes. Three examples from different engineering disciplines were investigated to demonstrate the accuracy and versatility of this shape design sensitivity analysis method.

Evaluating Imputation Algorithms for Low-Depth Genotyping-By-Sequencing (GBS) Data

PubMed Central

2016-01-01

Well-powered genomic studies require genome-wide marker coverage across many individuals. For non-model species with few genomic resources, high-throughput sequencing (HTS) methods, such as Genotyping-By-Sequencing (GBS), offer an inexpensive alternative to array-based genotyping. Although affordable, datasets derived from HTS methods suffer from sequencing error, alignment errors, and missing data, all of which introduce noise and uncertainty to variant discovery and genotype calling. Under such circumstances, meaningful analysis of the data is difficult. Our primary interest lies in the issue of how one can accurately infer or impute missing genotypes in HTS-derived datasets. Many of the existing genotype imputation algorithms and software packages were primarily developed by and optimized for the human genetics community, a field where a complete and accurate reference genome has been constructed and SNP arrays have, in large part, been the common genotyping platform. We set out to answer two questions: 1) can we use existing imputation methods developed by the human genetics community to impute missing genotypes in datasets derived from non-human species and 2) are these methods, which were developed and optimized to impute ascertained variants, amenable for imputation of missing genotypes at HTS-derived variants? We selected Beagle v.4, a widely used algorithm within the human genetics community with reportedly high accuracy, to serve as our imputation contender. We performed a series of cross-validation experiments, using GBS data collected from the species Manihot esculenta by the Next Generation (NEXTGEN) Cassava Breeding Project. NEXTGEN currently imputes missing genotypes in their datasets using a LASSO-penalized, linear regression method (denoted ‘glmnet’). We selected glmnet to serve as a benchmark imputation method for this reason. We obtained estimates of imputation accuracy by masking a subset of observed genotypes, imputing, and calculating the sample Pearson correlation between observed and imputed genotype dosages at the site and individual level; computation time served as a second metric for comparison. We then set out to examine factors affecting imputation accuracy, such as levels of missing data, read depth, minor allele frequency (MAF), and reference panel composition. PMID:27537694

Evaluating Imputation Algorithms for Low-Depth Genotyping-By-Sequencing (GBS) Data.

PubMed

Chan, Ariel W; Hamblin, Martha T; Jannink, Jean-Luc

2016-01-01

Well-powered genomic studies require genome-wide marker coverage across many individuals. For non-model species with few genomic resources, high-throughput sequencing (HTS) methods, such as Genotyping-By-Sequencing (GBS), offer an inexpensive alternative to array-based genotyping. Although affordable, datasets derived from HTS methods suffer from sequencing error, alignment errors, and missing data, all of which introduce noise and uncertainty to variant discovery and genotype calling. Under such circumstances, meaningful analysis of the data is difficult. Our primary interest lies in the issue of how one can accurately infer or impute missing genotypes in HTS-derived datasets. Many of the existing genotype imputation algorithms and software packages were primarily developed by and optimized for the human genetics community, a field where a complete and accurate reference genome has been constructed and SNP arrays have, in large part, been the common genotyping platform. We set out to answer two questions: 1) can we use existing imputation methods developed by the human genetics community to impute missing genotypes in datasets derived from non-human species and 2) are these methods, which were developed and optimized to impute ascertained variants, amenable for imputation of missing genotypes at HTS-derived variants? We selected Beagle v.4, a widely used algorithm within the human genetics community with reportedly high accuracy, to serve as our imputation contender. We performed a series of cross-validation experiments, using GBS data collected from the species Manihot esculenta by the Next Generation (NEXTGEN) Cassava Breeding Project. NEXTGEN currently imputes missing genotypes in their datasets using a LASSO-penalized, linear regression method (denoted 'glmnet'). We selected glmnet to serve as a benchmark imputation method for this reason. We obtained estimates of imputation accuracy by masking a subset of observed genotypes, imputing, and calculating the sample Pearson correlation between observed and imputed genotype dosages at the site and individual level; computation time served as a second metric for comparison. We then set out to examine factors affecting imputation accuracy, such as levels of missing data, read depth, minor allele frequency (MAF), and reference panel composition.

Multivariable optimization of an auto-thermal ammonia synthesis reactor using genetic algorithm

NASA Astrophysics Data System (ADS)

Anh-Nga, Nguyen T.; Tuan-Anh, Nguyen; Tien-Dung, Vu; Kim-Trung, Nguyen

2017-09-01

The ammonia synthesis system is an important chemical process used in the manufacture of fertilizers, chemicals, explosives, fibers, plastics, refrigeration. In the literature, many works approaching the modeling, simulation and optimization of an auto-thermal ammonia synthesis reactor can be found. However, they just focus on the optimization of the reactor length while keeping the others parameters constant. In this study, the other parameters are also considered in the optimization problem such as the temperature of feed gas enters the catalyst zone. The optimal problem requires the maximization of a multivariable objective function which subjects to a number of equality constraints involving the solution of coupled differential equations and also inequality constraints. The solution of an optimization problem can be found through, among others, deterministic or stochastic approaches. The stochastic methods, such as evolutionary algorithm (EA), which is based on natural phenomenon, can overcome the drawbacks such as the requirement of the derivatives of the objective function and/or constraints, or being not efficient in non-differentiable or discontinuous problems. Genetic algorithm (GA) which is a class of EA, exceptionally simple, robust at numerical optimization and is more likely to find a true global optimum. In this study, the genetic algorithm is employed to find the optimum profit of the process. The inequality constraints were treated using penalty method. The coupled differential equations system was solved using Runge-Kutta 4th order method. The results showed that the presented numerical method could be applied to model the ammonia synthesis reactor. The optimum economic profit obtained from this study are also compared to the results from the literature. It suggests that the process should be operated at higher temperature of feed gas in catalyst zone and the reactor length is slightly longer.

Inverse Electrocardiographic Source Localization of Ischemia: An Optimization Framework and Finite Element Solution

PubMed Central

Wang, Dafang; Kirby, Robert M.; MacLeod, Rob S.; Johnson, Chris R.

2013-01-01

With the goal of non-invasively localizing cardiac ischemic disease using body-surface potential recordings, we attempted to reconstruct the transmembrane potential (TMP) throughout the myocardium with the bidomain heart model. The task is an inverse source problem governed by partial differential equations (PDE). Our main contribution is solving the inverse problem within a PDE-constrained optimization framework that enables various physically-based constraints in both equality and inequality forms. We formulated the optimality conditions rigorously in the continuum before deriving finite element discretization, thereby making the optimization independent of discretization choice. Such a formulation was derived for the L2-norm Tikhonov regularization and the total variation minimization. The subsequent numerical optimization was fulfilled by a primal-dual interior-point method tailored to our problem’s specific structure. Our simulations used realistic, fiber-included heart models consisting of up to 18,000 nodes, much finer than any inverse models previously reported. With synthetic ischemia data we localized ischemic regions with roughly a 10% false-negative rate or a 20% false-positive rate under conditions up to 5% input noise. With ischemia data measured from animal experiments, we reconstructed TMPs with roughly 0.9 correlation with the ground truth. While precisely estimating the TMP in general cases remains an open problem, our study shows the feasibility of reconstructing TMP during the ST interval as a means of ischemia localization. PMID:23913980

A rapid and rational approach to generating isomorphous heavy-atom phasing derivatives.

PubMed

Lu, Jinghua; Sun, Peter D

2014-09-01

In attempts to replace the conventional trial-and-error heavy-atom derivative search method with a rational approach, we previously defined heavy metal compound reactivity against peptide ligands. Here, we assembled a composite pH- and buffer-dependent peptide reactivity profile for each heavy metal compound to guide rational heavy-atom derivative search. When knowledge of the best-reacting heavy-atom compound is combined with mass spectrometry assisted derivatization, and with a quick-soak method to optimize phasing, it is likely that the traditional heavy-atom compounds could meet the demand of modern high-throughput X-ray crystallography. As an example, we applied this rational heavy-atom phasing approach to determine a previously unknown mouse serum amyloid A2 crystal structure. Published 2014. This article is a U.S. Government work and is in the public domain in the USA.

Novel pyrazolyl-s-triazine derivatives, molecular structure and antimicrobial activity

NASA Astrophysics Data System (ADS)

Sharma, Anamika; Ghabbour, Hazem; Khan, Shams Tabrez; de la Torre, Beatriz G.; Albericio, Fernando; El-Faham, Ayman

2017-10-01

A new series of pyrazole-containing s-triazine derivatives were synthesized by reaction of the corresponding s-triazinyl hydrazine derivatives with acetylacetone in the presence of HClO4 or DMF/TEA. The former method allowed the preparation of the target products with higher yields. All compounds were fully characterized. X-ray single crystal diffraction for two representative compounds (4-(4,6-bis(3,5-dimethyl-1H-pyrazol-1-yl)-1,3,5-triazin-2-yl)morpholine and N-benzyl-4-(3,5-dimethyl-1H-pyrazol-1-yl)-6-(piperidin-1-yl)-1,3,5-triazin-2-amine) was studied and the molecular structures were optimized using the DFT/B3LYP method. The structures were found to be in agreement with X-ray structures. The antimicrobial and antifungal activity of the prepared compounds were tested against the growth of several microorganisms.

Beam angle optimization for intensity-modulated radiation therapy using a guided pattern search method

NASA Astrophysics Data System (ADS)

Rocha, Humberto; Dias, Joana M.; Ferreira, Brígida C.; Lopes, Maria C.

2013-05-01

Generally, the inverse planning of radiation therapy consists mainly of the fluence optimization. The beam angle optimization (BAO) in intensity-modulated radiation therapy (IMRT) consists of selecting appropriate radiation incidence directions and may influence the quality of the IMRT plans, both to enhance better organ sparing and to improve tumor coverage. However, in clinical practice, most of the time, beam directions continue to be manually selected by the treatment planner without objective and rigorous criteria. The goal of this paper is to introduce a novel approach that uses beam’s-eye-view dose ray tracing metrics within a pattern search method framework in the optimization of the highly non-convex BAO problem. Pattern search methods are derivative-free optimization methods that require a few function evaluations to progress and converge and have the ability to better avoid local entrapment. The pattern search method framework is composed of a search step and a poll step at each iteration. The poll step performs a local search in a mesh neighborhood and ensures the convergence to a local minimizer or stationary point. The search step provides the flexibility for a global search since it allows searches away from the neighborhood of the current iterate. Beam’s-eye-view dose metrics assign a score to each radiation beam direction and can be used within the pattern search framework furnishing a priori knowledge of the problem so that directions with larger dosimetric scores are tested first. A set of clinical cases of head-and-neck tumors treated at the Portuguese Institute of Oncology of Coimbra is used to discuss the potential of this approach in the optimization of the BAO problem.

Nanoarchitectures for Metal-Organic Framework-Derived Nanoporous Carbons toward Supercapacitor Applications.

PubMed

Salunkhe, Rahul R; Kaneti, Yusuf Valentino; Kim, Jeonghun; Kim, Jung Ho; Yamauchi, Yusuke

2016-12-20

The future advances of supercapacitors depend on the development of novel carbon materials with optimized porous structures, high surface area, high conductivity, and high electrochemical stability. Traditionally, nanoporous carbons (NPCs) have been prepared by a variety of methods, such as templated synthesis, carbonization of polymer precursors, physical and chemical activation, etc. Inorganic solid materials such as mesoporous silica and zeolites have been successfully utilized as templates to prepare NPCs. However, the hard-templating methods typically involve several synthetic steps, such as preparation of the original templates, formation of carbon frameworks, and removal of the original templates. Therefore, these methods are not favorable for large-scale production. Metal-organic frameworks (MOFs) with high surface areas and large pore volumes have been studied over the years, and recently, enormous efforts have been made to utilize MOFs for electrochemical applications. However, their low conductivity and poor stability still present major challenges toward their practical applications in supercapacitors. MOFs can be used as precursors for the preparation of NPCs with high porosity. Their parent MOFs can be prepared with endless combinations of organic and inorganic constituents by simple coordination chemistry, and it is possible to control their porous architectures, pore volumes, surface areas, etc. These unique properties of MOF-derived NPCs make them highly attractive for many technological applications. Compared with carbonaceous materials prepared using conventional precursors, MOF-derived carbons have significant advantages in terms of a simple synthesis with inherent diversity affording precise control over porous architectures, pore volumes, and surface areas. In this Account, we will summarize our recent research developments on the preparation of three-dimensional (3-D) MOF-derived carbons for supercapacitor applications. This Account will be divided into three main sections: (1) useful background on carbon materials for supercapacitor applications, (2) the importance of MOF-derived carbons, and (3) potential future developments of MOF-derived carbons for supercapacitors. This Account focuses mostly on carbons derived from two types of MOFs, namely, zeolite imidazolate framework-8 (ZIF-8) and ZIF-67. By using examples from our previous works, we will show the uniqueness of these carbons for achieving high performance by control of the chemical reactions/conditions as well proper utilization in asymmetric/symmetric supercapacitor configurations. This Account will promote further developments of MOF-derived multifunctional carbon materials with controlled porous architectures for optimization of their electrochemical performance toward supercapacitor applications.

Efficient Regressions via Optimally Combining Quantile Information*

PubMed Central

Zhao, Zhibiao; Xiao, Zhijie

2014-01-01

We develop a generally applicable framework for constructing efficient estimators of regression models via quantile regressions. The proposed method is based on optimally combining information over multiple quantiles and can be applied to a broad range of parametric and nonparametric settings. When combining information over a fixed number of quantiles, we derive an upper bound on the distance between the efficiency of the proposed estimator and the Fisher information. As the number of quantiles increases, this upper bound decreases and the asymptotic variance of the proposed estimator approaches the Cramér-Rao lower bound under appropriate conditions. In the case of non-regular statistical estimation, the proposed estimator leads to super-efficient estimation. We illustrate the proposed method for several widely used regression models. Both asymptotic theory and Monte Carlo experiments show the superior performance over existing methods. PMID:25484481

Optimization of droplets for UV-NIL using coarse-grain simulation of resist flow

NASA Astrophysics Data System (ADS)

Sirotkin, Vadim; Svintsov, Alexander; Zaitsev, Sergey

2009-03-01

A mathematical model and numerical method are described, which make it possible to simulate ultraviolet ("step and flash") nanoimprint lithography (UV-NIL) process adequately even using standard Personal Computers. The model is derived from 3D Navier-Stokes equations with the understanding that the resist motion is largely directed along the substrate surface and characterized by ultra-low values of the Reynolds number. By the numerical approximation of the model, a special finite difference method is applied (a coarse-grain method). A coarse-grain modeling tool for detailed analysis of resist spreading in UV-NIL at the structure-scale level is tested. The obtained results demonstrate the high ability of the tool to calculate optimal dispensing for given stamp design and process parameters. This dispensing provides uniform filled areas and a homogeneous residual layer thickness in UV-NIL.

Adaptive infinite impulse response system identification using modified-interior search algorithm with Lèvy flight.

PubMed

Kumar, Manjeet; Rawat, Tarun Kumar; Aggarwal, Apoorva

2017-03-01

In this paper, a new meta-heuristic optimization technique, called interior search algorithm (ISA) with Lèvy flight is proposed and applied to determine the optimal parameters of an unknown infinite impulse response (IIR) system for the system identification problem. ISA is based on aesthetics, which is commonly used in interior design and decoration processes. In ISA, composition phase and mirror phase are applied for addressing the nonlinear and multimodal system identification problems. System identification using modified-ISA (M-ISA) based method involves faster convergence, single parameter tuning and does not require derivative information because it uses a stochastic random search using the concepts of Lèvy flight. A proper tuning of control parameter has been performed in order to achieve a balance between intensification and diversification phases. In order to evaluate the performance of the proposed method, mean square error (MSE), computation time and percentage improvement are considered as the performance measure. To validate the performance of M-ISA based method, simulations has been carried out for three benchmarked IIR systems using same order and reduced order system. Genetic algorithm (GA), particle swarm optimization (PSO), cat swarm optimization (CSO), cuckoo search algorithm (CSA), differential evolution using wavelet mutation (DEWM), firefly algorithm (FFA), craziness based particle swarm optimization (CRPSO), harmony search (HS) algorithm, opposition based harmony search (OHS) algorithm, hybrid particle swarm optimization-gravitational search algorithm (HPSO-GSA) and ISA are also used to model the same examples and simulation results are compared. Obtained results confirm the efficiency of the proposed method. Copyright © 2017 ISA. Published by Elsevier Ltd. All rights reserved.

Quantum approach to classical statistical mechanics.

PubMed

Somma, R D; Batista, C D; Ortiz, G

2007-07-20

We present a new approach to study the thermodynamic properties of d-dimensional classical systems by reducing the problem to the computation of ground state properties of a d-dimensional quantum model. This classical-to-quantum mapping allows us to extend the scope of standard optimization methods by unifying them under a general framework. The quantum annealing method is naturally extended to simulate classical systems at finite temperatures. We derive the rates to assure convergence to the optimal thermodynamic state using the adiabatic theorem of quantum mechanics. For simulated and quantum annealing, we obtain the asymptotic rates of T(t) approximately (pN)/(k(B)logt) and gamma(t) approximately (Nt)(-c/N), for the temperature and magnetic field, respectively. Other annealing strategies are also discussed.

'Extremotaxis': computing with a bacterial-inspired algorithm.

PubMed

Nicolau, Dan V; Burrage, Kevin; Nicolau, Dan V; Maini, Philip K

2008-01-01

We present a general-purpose optimization algorithm inspired by "run-and-tumble", the biased random walk chemotactic swimming strategy used by the bacterium Escherichia coli to locate regions of high nutrient concentration The method uses particles (corresponding to bacteria) that swim through the variable space (corresponding to the attractant concentration profile). By constantly performing temporal comparisons, the particles drift towards the minimum or maximum of the function of interest. We illustrate the use of our method with four examples. We also present a discrete version of the algorithm. The new algorithm is expected to be useful in combinatorial optimization problems involving many variables, where the functional landscape is apparently stochastic and has local minima, but preserves some derivative structure at intermediate scales.

Nonlinear model predictive control of a wave energy converter based on differential flatness parameterisation

NASA Astrophysics Data System (ADS)

Li, Guang

2017-01-01

This paper presents a fast constrained optimization approach, which is tailored for nonlinear model predictive control of wave energy converters (WEC). The advantage of this approach relies on its exploitation of the differential flatness of the WEC model. This can reduce the dimension of the resulting nonlinear programming problem (NLP) derived from the continuous constrained optimal control of WEC using pseudospectral method. The alleviation of computational burden using this approach helps to promote an economic implementation of nonlinear model predictive control strategy for WEC control problems. The method is applicable to nonlinear WEC models, nonconvex objective functions and nonlinear constraints, which are commonly encountered in WEC control problems. Numerical simulations demonstrate the efficacy of this approach.

Determination of oxygen and nitrogen derivatives of polycyclic aromatic hydrocarbons in fractions of asphalt mixtures using liquid chromatography coupled to mass spectrometry with atmospheric pressure chemical ionization.

PubMed

Nascimento, Paulo Cicero; Gobo, Luciana Assis; Bohrer, Denise; Carvalho, Leandro Machado; Cravo, Margareth Coutinho; Leite, Leni Figueiredo Mathias

2015-12-01

Liquid chromatography coupled to mass spectrometry with atmospheric pressure chemical ionization was used for the determination of polycyclic aromatic hydrocarbon derivatives, the oxygenated polycyclic aromatic hydrocarbons and nitrated polycyclic aromatic hydrocarbons, formed in asphalt fractions. Two different methods have been developed for the determination of five oxygenated and seven nitrated polycyclic aromatic hydrocarbons that are characterized by having two or more condensed aromatic rings and present mutagenic and carcinogenic properties. The parameters of the atmospheric pressure chemical ionization interface were optimized to obtain the highest possible sensitivity for all compounds. The detection limits of the methods ranged from 0.1 to 57.3 μg/L for nitrated and from 0.1 to 6.6 μg/L for oxygenated derivatives. The limits of quantification were in the range of 4.6-191 μg/L for nitrated and 0.3-8.9 μg/L for oxygenated derivatives. The methods were validated against a diesel particulate extract standard reference material (National Institute of Standards and Technology SRM 1975), and the obtained concentrations (two nitrated derivatives) agreed with the certified values. The methods were applied in the analysis of asphalt samples after their fractionation into asphaltenes and maltenes, according to American Society for Testing and Material D4124, where the maltenic fraction was further separated into its basic, acidic, and neutral parts following the method of Green. Only two nitrated derivatives were found in the asphalt sample, quinoline and 2-nitrofluorene, with concentrations of 9.26 and 2146 mg/kg, respectively, whereas no oxygenated derivatives were detected. © 2015 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim.