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Adjoint sensitivity analysis and optimization of hysteretic dynamic systems with nonlinear viscous dampers

STRUCTURAL AND MULTIDISCIPLINARY optimization 2018年第6期57卷 2273-2289页

作者： Pollini, Nicolo Lavan, Oren Amir, Oded Technion Israel Inst Technol Fac Civil & Environm Engn Haifa Israel

In this paper we discuss the adjoint sensitivity analysis and optimization of hysteretic systems equipped with nonlinear viscous dampers and subjected to transient excitation. The viscous dampers are modeled via the Maxwell model, considering at the same time the stiffening and the damping contribution of the dampers. The time-history analysis adopted for the evaluation of the response of the systems relies on the Newmark-beta time integration scheme. In particular, the dynamic equilibrium in each time-step is achieved by means of the Newton-Raphson and the Runge-Kutta methods. The sensitivity of the system response is calculated with the adjoint variable method. In particular, the discretize-then-differentiate approach is adopted for calculating consistently the sensitivity of the system. The importance and the generality of the sensitivity analysis discussed herein is demonstrated in two numerical applications: the retrofitting of a structure subject to seismic excitation, and the design of a quarter-car suspension system. The MATLAB code for the sensitivity analysis considered in the first application is provided as "Supplementary Material".

关键词： Adjoint sensitivity analysis Nonlinear dynamic systems Viscous dampers gradient-based optimization

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Aggregation of Order-2 Fuzzy Sets

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IEEE TRANSACTIONS ON FUZZY SYSTEMS 2021年第11期29卷 3570-3575页

作者： Pedrycz, Witold Gacek, Adam Wang, Xianmin Univ Alberta Dept Elect & Comp Engn Edmonton AB T6R 2V4 Canada Polish Acad Sci Syst Res Inst PL-01447 Warsaw Poland King Abdulaziz Univ Fac Engn Dept Elect & Comp Engn Jeddah 21589 Saudi Arabia Lukasiewicz Res Network Inst Med Technol & Equipment PL-41800 Zabrze Poland China Univ Geosci Inst Geophys & Geomat Wuhan 430074 Peoples R China

In this article, we are concerned with a problem of aggregation of order-2 information granules, and fuzzy sets, in particular. When processing order-1 fuzzy sets, the structural information about the space over which fuzzy sets are defined is not taken into account at all. In contrast, the aggregation of order-2 fuzzy sets requires a careful attention that needs to be paid both to the closeness determined in the space of membership degrees and the collection of information granules over which such fuzzy sets are defined. We formulate an original optimization problem that simultaneously involves considerations of distances in the membership space (space of membership grades) and some measure of resemblance formed in the space of relationships of reference information granules. The gradient-based learning scheme is constructed. Some illustrative examples are included.

关键词： Fuzzy sets optimization Performance analysis Indexes Cyber-physical systems Cybernetics Linear programming Aggregation aggregation in cyber-physical systems attributed graph gradient-based optimization hierarchy of concepts order-2 fuzzy sets

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A PCA-assisted hybrid algorithm combining EAs and adjoint methods for CFD-based optimization

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APPLIED SOFT COMPUTING 2018年 73卷 520-529页

作者： Kapsoulis, Dimitrios Tsiakas, Konstantinos Trompoukis, Xenofon Asouti, Varvara Giannakoglou, Kyriakos Natl Tech Univ Athens Sch Mech Engn Parallel CFD & Optimizat Unit Athens Greece

Hybrid optimization algorithms which combine Evolutionary Algorithms (EAs) and gradient-based (GB) methods o refine the most promising solutions, are valuable tools for use in engineering optimization. Several hybrid methods can be found in the literature;differences among them are associated with the criteria used to select individuals for refinement through the GB method and the feedback the EA gets from the latter. GB methods require the gradient of the objective functions with respect to the design variables. By employing the adjoint method in problems governed by partial differential equations, the cost of computing the gradient becomes independent of the number of design variables. For multiobjective optimization problems this paper is exclusively dealing with, the availability of the gradients of all objective functions is not enough. Hybrid algorithms require the computation of descent directions in the objective space capable of improving the current front of non-dominated solutions. Using the sum of weighted objectives as the new objective function is ineffective. In this paper, a method which refrains from using arbitrarily defined weights is proposed. The method is driven by data obtained from the Principal Component Analysis (PCA) of the objective function values of the elite individuals at each generation of the EA. The PCA, with computational cost that of the solution of an eigenproblem, identifies the direction in the objective space along which the current front of non-dominated solutions should be improved. This along with the gradients computed by the adjoint method are used by the GB method to refine selected individuals. The efficiency of the proposed hybrid algorithm is further improved by employing online trained surrogate models or metamodels and Kernel PCA within the EA-based search. The proposed method is demonstrated in aerodynamic shape optimization problems, using in-house Computational Fluid Dynamics software and its adjoint. (C) 2018 E

关键词： Hybrid optimization Evolutionary multi-objective optimization gradient-based optimization Principal component analysis Adjoint method

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optimization-based model calibration of marginal and joint output distributions utilizing analytical gradients

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STRUCTURAL AND MULTIDISCIPLINARY optimization 2021年第6期63卷 2853-2868页

作者： Jo, Hwisang Lee, Kyungeun Lee, Mingyu Jung, Yongsu Lee, Ikjin Korea Adv Inst Sci & Technol Dept Mech Engn Daejeon 34141 South Korea

optimization-based model calibration (OBMC) determines statistical parameters of unknown input variables by optimizing statistical similarity between simulations and observations. gradient-based optimization algorithms have been utilized for OBMC since they require less computational cost compared with non-gradient optimization algorithms. However, OBMC using numerical gradients such as finite differences has disadvantages in the aspect of computational cost and numerical instability. For these reasons, a previous study derived analytical gradients under the assumption that performance functions are a linear single response and unknown inputs follow a normal distribution. However, to apply the model calibration to general engineering problems, analytical gradients need to be derived without any assumption. Therefore, it is proposed in this study to derive analytical gradients of marginal and joint likelihood functions to calibrate both linear and nonlinear responses. In addition, the analytical gradients are derived for five distribution types of unknown input random variables to be estimated: normal, lognormal, Gumbel, extreme, and uniform distributions. For derivation of the analytical gradients, the chain rule is utilized to combine the derivatives of the inverse function of cumulative distribution function (CDF), performance function, and joint likelihood function. Numerical examples and one engineering example using finite element analysis (FEA) are employed to verify the accuracy and efficiency of the proposed analytical gradient, and it is demonstrated that accurately calibrated output responses can be obtained by the proposed method by finding a better optimum in OBMC.

关键词： optimization-based model calibration (OBMC) gradient-based optimization Kriging surrogate model Uncertainty propagation (UP) Kernel density estimation (KDE)

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Optimal mass distribution in carbon nanotubes for extreme thermal conductivity: Analytical manipulation of isotope effects

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COMPUTATIONAL MATERIALS SCIENCE 2018年 150卷 273-282页

作者： Jang, Hong-Lae Kim, Jae-Hyun Kang, Se-Hyeon Cho, Seonho Park, Youmie Seoul Natl Univ Dept Naval Architecture & Ocean Engn 1 Gwanak Ro Seoul 08826 South Korea Inje Univ Coll Pharm 197 Inje Ro Gimhae 50834 Gyeongnam South Korea

Using a gradient-based optimization method, an optimal mass distribution for a single-walled carbon nanotube (CNT) is determined for extremal thermal conductivity. The variation of atomic mass distribution or the isotope impurity in the CNT could lead to either extremely high or low thermal conductivity. The adjoint variable method is employed for the efficient and accurate design sensitivity analysis of thermal conductivity, which can be obtained from non-equilibrium molecular dynamics (NEMD) approach. The obtained analytical sensitivity can be extensively utilized to determine the optimal distribution of atomic masses, using a density-based topology optimization method. The resulting thermal conductivity is reduced by more than 90% or increased by 70% of the one of the pristine CNT. The density of states (DOS) after the optimization indicates that the optimization process yields the effective and physically meaningful result as we interpret the resulting distribution of mass.

关键词： Carbon nanotube Thermal conductivity Isotope effect Molecular dynamics Adjoint sensitivity gradient-based optimization

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Employment of artificial intelligence approach for optimizing the solubility of drug in the supercritical CO 2 system

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CASE STUDIES IN THERMAL ENGINEERING 2024年 57卷

作者： Li, Meixiuli Jiang, Wenyan Zhao, Shuang Huang, Kai Liu, Dongxiu Shaoyang Univ Pu Ai Med Sch Dept Human Anat & Embryol Shaoyang 422000 Hunan Peoples R China Shaoyang Univ Affiliated Hosp 2 Shaoyang 422000 Hunan Peoples R China Shashi Town Hlth Ctr Shaodong 422813 Hunan Peoples R China

This paper investigates the solubility behavior of digitoxin in supercritical carbon dioxide (CO 2 ) through a comprehensive analysis employing ensemble learning techniques and various regression models. The dataset consists of temperature and pressure as input variables, with solvent density and digitoxin solubility as output variables. Utilizing bagging as the ensemble method, Gaussian process regression (GPR), Bayesian Ridge Regression (BRR), Orthogonal Matching Pursuit (OMP), and Polynomial Regression (PR) were employed as regression models. Hyperparameter tuning was achieved through gradient -based optimization. Results revealed that Polynomial Regression (PR) emerges as the most effective model for predicting both solvent density and digitoxin solubility. For solubility prediction, BAG -PR yields an R 2 score of 0.98527, with MSE and MAE of 1.4290E-03 and 3.40547E-02, respectively. Concerning solvent density, BAG -PR achieves an outstanding R 2 of 0.99766, along with MSE and MAE of 7.4759E +01 and 7.33964E +00, respectively. These results show that ensemble learning, and polynomial regression can accurately predict solubility and solvent density, revealing digitoxin ' s behavior in supercritical CO 2 .

关键词： Drug solubility Bagging regression Polynomial regression gradient-based optimization

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Autofocusing-based phase correction

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MAGNETIC RESONANCE IN MEDICINE 2018年第3期80卷 958-968页

作者： Loktyushin, Alexander Ehses, Philipp Schoelkopf, Bernhard Scheffler, Klaus Max Planck Inst Intelligent Syst Tubingen Germany Max Planck Inst Biol Cybernet Max Planck Ring 11 D-72076 Tubingen Germany German Ctr Neurodegenerat Dis DZNE Helmholtz Asso Bonn Germany Univ Tubingen Geschwister Scholl Pl Tubingen Germany

PurposePhase artifacts due to B-0 inhomogeneity can severely degrade the quality of MR images. The artifacts are particularly prominent in long-TE scans and usually appear as ghosting and blur. We propose a retrospective phase correction method based on autofocusing. The proposed method uses raw data acquired with standard imaging sequences, and does not rely on navigators or external measures of field inhomogeneity. MethodsWe formulate and solve the optimization problem, where we seek the latent phase offsets that are associated with an optimal value of the image quality measure that is evaluated in the spatial domain. As a quality measure we use entropy computed on spatial image gradients. We propose two types of objective function, both compatible with parallel imaging and accelerated image acquisition. ResultsWe evaluate the method on both synthetic and real data. In real data case we evaluate the performance on a range of sequences and images acquired with different acceleration factors. The experimental results demonstrate that our method is capable of minimizing ghosting artifacts and that the quality of the output images is similar to navigator-based reconstructions. ConclusionThe presented technique can be alternative to or complement navigator-based methods, and is able to improve images with severe phase artifacts from all standard imaging sequences. Magn Reson Med 80:958-968, 2018. (c) 2018 International Society for Magnetic Resonance in Medicine.

关键词： phase artifacts B-0 inhomogeneity autofocusing gradient-based optimization

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An extended level set method for shape and topology optimization

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JOURNAL OF COMPUTATIONAL PHYSICS 2007年第1期221卷 395-421页

作者： Wang, S. Y. Lim, K. M. Khoo, B. C. Wang, M. Y. Natl Univ Singapore Ctr Singapore MIT Alliance Singapore 117576 Singapore Natl Univ Singapore Dept Mech Engn Singapore 119260 Singapore Chinese Univ Hong Kong Dept Automat & Comp Aided Engn Shatin Hong Kong Peoples R China

In this paper, the conventional level set methods are extended as an effective approach for shape and topology optimization by the introduction of the radial basis functions (RBFs). The RBF multiquadric splines are used to construct the implicit level set function with a high level of accuracy and smoothness and to discretize the original initial value problem into an interpolation problem. The motion of the dynamic interfaces is thus governed by a system of coupled ordinary differential equations (ODEs) and a relatively smooth evolution can be maintained without reinitialization. A practical implementation of this method is further developed for solving a class of energy-based optimization problems, in which approximate solution to the original Hamilton-Jacobi equation may be justified and nucleation of new holes inside the material domain is allowed for. Furthermore, the severe constraints on the temporal and spatial discretizations can be relaxed, leading to a rapid convergence to the final design insensitive to initial guesses. The normal velocities are chosen to perform steepest gradient-based optimization by using shape sensitivity analysis and a bi-sectioning algorithm. A physically meaningful and efficient extension velocity method is also presented. The proposed method is implemented in the framework of minimum compliance design and its efficiency over the existing methods is highlighted. Numerical examples show its accuracy, convergence speed and insensitivity to initial designs in shape and topology optimization of two-dimensional (2D) problems that have been extensively investigated in the literature. (c) 2006 Elsevier Inc. All rights reserved.

关键词： topology optimization shape optimization level set method radial basis functions extension velocity gradient-based optimization

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Layout optimization of the Receiver Coils for Multitransmitter Wireless Power Transfer Systems

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IEEE JOURNAL OF EMERGING AND SELECTED TOPICS IN POWER ELECTRONICS 2017年第3期5卷 1311-1321页

作者： Lee, Seung Beop Jang, In Gwun Korea Adv Inst Sci & Technol Cho Chun Shik Grad Sch Green Transportat Daejeon 305701 South Korea

This paper presents a novel method which is proposed to determine the optimal receiver coils when the transmitter coils are predetermined for multitransmitter wireless power transfer system, using the gradient-based optimization algorithm. The fixed grid-based coil representation, which is newly introduced, allows for effective changes in the coil layout during the optimization through assigning appropriate values for the reference coil turn and relative coil turns, which are set as design variables in the proposed method. The magnetic field strength, induced voltage, and coil mass are mathematically derived in order to obtain their analytical sensitivities with respect to the design variables. As an application example, a wireless portable charger with multiple transmitter coils is selected in order to minimize the mass of the receiver coils, while satisfying the induced voltage and magnetic field strength constraints. The optimized coil layouts are then experimentally validated, which demonstrates the feasibility and potential of the proposed method.

关键词： Coil design gradient-based optimization layout optimization wireless power transfer (WPT)

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Optimal determination of force field parameters for reduced molecular dynamics model

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COMPUTER PHYSICS COMMUNICATIONS 2019年 236卷 86-94页

作者： Kim, Hyun-Seok Kim, Jae-Hyun Cha, Song-Hyun Cho, Seonho Korea Res Inst Ships & Ocean Engn KRISO 1312-31 Yuseong Daero Daejeon 34103 South Korea Seoul Natl Univ Dept Naval Architecture & Ocean Engn 1 Gwanak Ro Seoul 08826 South Korea

Using a gradient-based optimization method, the time-consuming atomistic model of substrate is replaced by computationally efficient Lennard-Jones (L-J) potential walls whose parameters are determined to appropriately represent the interactions between the nanoparticles and the substrate. To obtain the required design sensitivity with respect to design variables for the constant temperature molecular dynamics (MD) simulations that use the Nose-Hoover thermostat, the finite difference method is impractical due to the huge amount of computational costs. Thus, we developed an adjoint design sensitivity analysis (DSA) method that is efficient for the system of many design variables. In numerical examples, we replace the complicated and time-consuming silicate structure to a multiple layer model of L-J potential wall, through the design optimization that includes the design variables of epsilon, sigma, and the positions of each layer. The objective is to minimize the squared difference of time averaged performance between the full and the reduced models during the whole time span. The proposed method could lead to a significant reduction of computational costs, together with comparable outcomes from MD simulations. (C) 2018 Elsevier B.V. All rights reserved.

关键词： gradient-based optimization Adjoint design sensitivity Molecular dynamics NVT ensemble Gold nanoparticle Mica substrate

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