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adjoint variable method for transient nonlinear electroquasistatic problems

ELECTRICAL ENGINEERING 2023年第4期105卷 2319-2325页

作者： Ruppert, M. Greta Spaeck-Leigsnering, Yvonne Buschbaum, Julian De Gersem, Herbert Tech Univ Darmstadt Inst Accelerator Sci & Electromagnet Fields TEMF Schlossgartenstr 8 D-64289 Darmstadt Germany Tech Univ Darmstadt Grad Sch Computat Engn Dolivostr 15 D-64293 Darmstadt Germany

Many optimization problems in electrical engineering consider a large number of design parameters. A sensitivity analysis identifies the design parameters with the strongest influence on the problem of interest. This paper introduces the adjoint variable method as an efficient approach to study sensitivities of nonlinear electroquasistatic problems in time domain. In contrast to the more common direct sensitivity method, the adjoint variable method has a computational cost nearly independent of the number of parameters. The method is applied to study the sensitivity of the field grading material parameters on the performance of a 320 kV cable joint specimen, which is modeled as a finite element nonlinear transient electroquasistatic problem. Special attention is paid to the treatment of quantities of interest, which are evaluated at specific points in time or space. It is shown that the method is a valuable tool to study this strongly nonlinear and highly transient technical example.

关键词： adjoint variable method Nonlinear electroquasistatic problem Sensitivity analysis Time domain

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Input optimization for flexible multibody systems using the adjoint variable method and the flexible natural coordinates formulation

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MULTIBODY SYSTEM DYNAMICS 2023年第3-4期57卷 259-277页

作者： Vanpaemel, Simon Vermaut, Martijn Desmet, Wim Naets, Frank Katholieke Univ Leuven Dept Mech Engn Div LMSD Box 2420Celestijnenlaan 300 B-3001 Leuven Belgium Flanders MakeKU Leuven Leuven Belgium

This work discusses a sensitivity information methodology for input optimization of flexible multibody systems. Mechanisms often need to perform desired motions, and especially in the case of underactuated flexible systems, the required drive motion or torque are nontrivial to determine. In this work we present an optimization approach which exploits the adjoint variable method (AVM) in combination with the Flexible Natural Coordinates Formulation (FNCF) for obtaining the sensitivity information. The adjoint variable method has the advantage of obtaining accurate sensitivity information at a computational cost that is relatively independent of the number of model parameters. FNCF combines the advantageous properties of the Floating Frame of Reference Formulation (FFRF) and the Generalized Component Mode Synthesis (GCMS) methods for which the equations of motion are characterized by a constant mass and stiffness matrix, and quadratic constraint equations. This work shows how the specific structure of the motion equations obtained through FNCF reduces the complexity of the adjoint variable method as the required simulation derivatives for input optimization can be readily obtained and are of limited order. The approach is illustrated for an input optimization case on a flexible slider-crank multibody model, where the objective is to construct an input torque signal such that the crank's angular velocity matches a predefined reference signal.

关键词： adjoint variable method Sensitivity analysis Optimization Flexible multibody systems Flexible natural coordinates formulation Input optimization

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Sensitivity analysis of coupled acoustic-structural systems under non-stationary random excitations based on adjoint variable method

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STRUCTURAL AND MULTIDISCIPLINARY OPTIMIZATION 2021年第6期64卷 3331-3343页

作者： Shang, Linyuan Zhai, Jingjuan Zhao, Guozhong Shenyang Aerosp Univ Coll Aerosp Engn Shenyang 110136 Peoples R China Dalian Univ Technol Dept Engn Mech State Key Lab Struct Anal Ind Equipments Dalian 116024 Peoples R China

Sensitivity analysis of coupled acoustic-structural systems under non-stationary random excitations is investigated in this paper. The combined method of direct differentiation method (DDM) and pseudo excitation method (PEM) in previous work is computationally expensive for problems with large-scale design variables. To circumvent this difficulty, a fast sensitivity analysis method integrating the adjoint variable method (AVM) and PEM for coupled acoustic-structural systems under non-stationary random excitations is proposed. In this framework, the sensitivity analysis of coupled systems subject to non-stationary random excitations is transformed into a sensitivity analysis under pseudo-transient excitations with the help of PEM. On this basis, the computing efficiency of random response sensitivity is improved directly by solving the adjoint equations involved in the AVM. Numerical examples fully demonstrate the accuracy and efficiency of the proposed method.

关键词： Sensitivity analysis Coupled acoustic-structural system Non-stationary random excitation adjoint variable method

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A Shape Optimisation with the Isogeometric Boundary Element method and adjoint variable method for the Three-Dimensional Helmholtz Equation

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COMPUTER-AIDED DESIGN 2022年 142卷 103126-103126页

作者： Takahashi, Toru Sato, Daisuke Isakari, Hiroshi Matsumoto, Toshiro Nagoya Univ Grad Sch Engn Dept Mech Syst Engn Furo Cho Nagoya Aichi 4648603 Japan

This paper presents a shape optimisation system to design the shape of an acoustically-hard object in the three-dimensional open space. The boundary element method (BEM) is suitable to analyse such an exterior field. However, the conventional BEM, which is based on piecewise polynomial shape and approximate (interpolation) functions, can require many design variables because they are usually chosen as a part of the nodes of the underlying boundary element mesh. In addition, it is not easy for the conventional method to compute the gradient of the sound pressure on the surface, which is necessary to compute the shape derivative of our interest, of a given object. To overcome these issues, we employ the isogeometric boundary element method (IGBEM), which was developed in our previous work. With using the IGBEM, we can design the shape of surfaces through control points of the NURBS surfaces of the target object. We integrate the IGBEM with the nonlinear programming software through the adjoint variable method (AVM), where the resulting adjoint boundary value problem can be also solved by the IGBEM with a slight modification. The numerical verification and demonstration validate our shape optimisation framework. (C) 2021 Elsevier Ltd. All rights reserved.

关键词： Boundary element method Isogeometric analysis Shape optimisation adjoint variable method Nonlinear programming problem

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Acoustic Shape Optimization Based on Isogeometric Wideband Fast Multipole Boundary Element method with adjoint variable method

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JOURNAL OF THEORETICAL AND COMPUTATIONAL ACOUSTICS 2020年第2期28卷

作者： Wang, Jie Zheng, Changjun Chen, Leilei Chen, Haibo Univ Sci & Technol China Dept Modern Mech CAS Key Lab Mech Behav & Design Mat Hefei 230027 Anhui Peoples R China Hefei Univ Technol Inst Sound & Vibrat Res Hefei 230009 Anhui Peoples R China Xinyang Normal Univ Coll Architecture & Civil Engn Xinyang 464000 Henan Peoples R China

A shape optimization approach based on isogeometric wideband fast multipole boundary element method (IGA WFMBEM) in 2D acoustics is developed in this study. The key treatment is shape sensitivity analysis by using the adjoint variable method under isogeometric analysis (IGA) conditions. A set of efficient parameters of the wideband fast multipole method has been identified for IGA boundary element method. Shape optimization is performed by applying the method of moving asymptotes. IGA WFMBEM is validated through an acoustic scattering example. The proposed optimization approach is tested on a sound barrier and two multiple structures to demonstrate its potential for engineering problems.

关键词： Isogeometric analysis boundary element method wideband fast multipole method adjoint variable method shape optimization

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Design optimization of dynamic flexible multibody systems using the discrete adjoint variable method

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COMPUTERS & STRUCTURES 2019年 213卷 82-99页

作者： Ebrahimi, Mehran Butscher, Adrian Cheong, Hyunmin Iorio, Francesco Autodesk Res 661 Univ Ave Toronto ON MSG 1M1 Canada

The design space of dynamic multibody systems (MBSs), particularly those with flexible components, is considerably large. Consequently, having a means to efficiently explore this space and find the optimum solution within a feasible time-frame is crucial. It is well-known that for problems with several design variables, sensitivity analysis using the adjoint variable method extensively reduces the computational costs. This paper presents the novel extension of the discrete adjoint variable method to the design optimization of dynamic flexible MBSs. The extension involves deriving the adjoint equations directly from the discrete, rather than the continuous, equations of motion. This results in a system of algebraic equations that is computationally less demanding to solve compared to the system of differential algebraic equations produced by the continuous adjoint variable method. To describe the proposed method, it is integrated with a numerical time-stepping algorithm based on geometric variational integrators. The developed technique is then applied to the optimization of MBSs composed of springs, dampers, beams and rigid bodies, considering both geometrical (e.g., positions of joints) and non-geometrical (e.g., mechanical properties of components) design variables. To validate the developed methods and show their applicability, three numerical examples are provided. (C) 2018 Elsevier Ltd. All rights reserved.

关键词： Flexible multibody systems Design optimization Sensitivity analysis adjoint variable method Discrete adjoint variable method Geometrical design variables

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Simultaneous identification of damage in bridge under moving mass by adjoint variable method

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SMART STRUCTURES AND SYSTEMS 2018年第4期21卷 449-467页

作者： Mirzaee, Akbar Abbasnia, Reza Shayanfar, Mohsenali Iran Univ Sci & Technol Dept Civil Engn Tehran Iran

In this paper, a theoretical and numerical study on bridge simultaneous damage detection procedure for identifying both the system parameters and input excitation mass, are presented. This method is called 'adjoint variable method' which is an iterative gradient-based model updating method based on the dynamic response sensitivity. The main advantage of proposed method is inclusion of an analytical method to augment the accuracy and speed of the solution. Moving mass is a model which takes into account the inertia effects of the vehicle. This interaction model is a time varying system and proposed method is capable of detecting damage in this variable system. Robustness of proposed method is illustrated by correctly detection of the location and extension of predetermined single, multiple and random damages in all ranges of speed and mass ratio of moving vehicle. A comparison study of common sensitivity and proposed method confirms its efficiency and performance improvement in sensitivity-based damage detection methods. Various sources of errors including the effects of measurement noise and initial assumption error in stability of method are also discussed.

关键词： damage detection finite element model updating sensitivity Ill posed problem simultaneous identification adjoint variable method

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A comparative study of design sensitivity analysis based on adjoint variable method for transient response of non-viscously damped systems

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MECHANICAL SYSTEMS AND SIGNAL PROCESSING 2018年 110卷 390-411页

作者： Ding, Zhe Li, Li Li, Xiaobai Kong, Jianyi Wuhan Univ Sci & Technol Sch Machinery & Automat Minist Educ Key Lab Met Equipment & Control Technol Wuhan 430081 Hubei Peoples R China Huazhong Univ Sci & Technol Sch Mech Sci & Engn State Key Lab Digital Mfg Equipment & Technol Wuhan 430074 Hubei Peoples R China Wuhan Univ Sci & Technol Sch Machinery & Automat Hubei Key Lab Mech Transmiss & Mfg Engn Wuhan 430081 Hubei Peoples R China

In this paper, design sensitivity analysis methods for the transient response of non viscously damped systems are considered. The damping forces of the non-viscously damped systems depend on the past history of motion via convolution integrals over some suitable kernel functions. The adjoint variable method (AVM) is adopted to develop the design sensitivity analysis. Two numerical solution schemes, namely the discretize-then-differentiate method and the differentiate-then-discretize method, are introduced to complete the AVM for the sensitivity analysis of non-viscously damped systems. The discretize-then-differentiate AVM discretizes the equations of motion based on the Newmark-beta implicit integration method first and then differentiates the discrete equations. On the contrary, the differentiate-then-discretize AVM firstly differentiates the equations of motion after transforming it into a state-space form, and then discretizes the equations based on a modified precise integration method (PIM). The numerical accuracy, efficiency, consistency and implementation effort are discussed and compared. Two numerical examples are presented to show the effectiveness of both methods. The results indicate that, by considering both computational accuracy and efficiency, the PIM based differentiate-then-discretize method is more suitable than the Newmark-beta based discretize-then-differentiate method for the sensitivity analysis of transient responses for non-viscously damped systems. (C) 2018 Elsevier Ltd. All rights reserved.

关键词： Non-viscous damping Sensitivity analysis adjoint variable method Transient response Discretize-then-differentiate method

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Structural sensitivity analysis of flexible multibody systems modeled with the floating frame of reference approach using the adjoint variable method

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MULTIBODY SYSTEM DYNAMICS 2017年第3期40卷 287-302页

作者： Held, Alexander Knuefer, Sven Seifried, Robert Hamburg Univ Technol Inst Mech & Ocean Engn Eiendorfer Str 42 D-21073 Hamburg Germany

For the efficient analysis and optimization of flexible multibody systems, gradient information is often required. Next to simple and easy-to-implement finite difference approaches, analytical methods, such as the adjoint variable method, have been developed and are now well established for the sensitivity analysis in multibody dynamics. They allow the computation of exact gradients and require normally less computational effort for large-scale problems. In the current work, we apply the adjoint variable method to flexible multibody systems with kinematic loops, which are modeled using the floating frame of reference formulation. Thereby, in order to solve ordinary differential equations only, the equations of motion are brought into minimal form using coordinate partitioning, and the constraint equations at position and velocity level are incorporated in the adjoint dynamics. For testing and illustrative purposes, the procedure is applied to compute the structural gradient for a flexible piston rod of a slider-crank mechanism.

关键词： Sensitivity analysis Flexible multibody system Floating frame of reference formulation adjoint variable method

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2D Acoustic Design Sensitivity Analysis Based on adjoint variable method Using Different Types of Boundary Elements

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ACOUSTICS AUSTRALIA 2016年第2期44卷 343-357页

作者： Chen, Leilei Liu, Linchao Zhao, Wenchang Chen, Haibo Xinyang Normal Univ Coll Civil Engn Xinyang 464000 Henan Peoples R China Univ Sci & Technol China Dept Modern Mech CAS Key Lab Mech Behav & Design Mat Hefei 230026 Anhui Peoples R China

Continuous linear and quadratic boundary elements are often applied to numerical solution. Discontinuous higher-order boundary elements are developed for 2D acoustic problems to achieve higher accuracy in this paper. The Burton-Miller formulation is used to overcome the fictitious frequency problem when using a single Helmholtz boundary integral equation for exterior boundary-value problem. The strong singular integrals in Burton-Miller formulation using different types of element discretization are evaluated explicitly and directly, respectively. An example of scattering by an infinite rigid cylinder is presented to compare the performance of different types of elements. The effect of the position of nodes on the performance of discontinuous elements is studied, and an empirical value for optimal nodal position is concluded in this paper. adjoint variable method is applied to evaluate the sensitivity value of the objective function, and the method of moving asymptotes is used for structural optimization analysis of noise barrier.

关键词： Discontinuous boundary element Shape sensitivity analysis adjoint variable method Structural optimization analysis

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