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A wavelet multiscale-homotopy method for the parameter identification problem of partial differential equations

COMPUTERS & MATHEMATICS WITH APPLICATIONS 2016年第7期71卷 1519-1523页

作者： Liu, Tao Northeast Univ Qinhuangdao Sch Math & Stat Qinhuangdao 066004 Peoples R China

By introducing the wavelet multiscale method and the homotopy method to the inversion process for the parameter identification problem of partial differential equations, a joint inversion method called the wavelet multiscale-homotopy method is proposed, which is globally convergent, computationally efficient, and has the anti-noise ability. As a practical problem, the parameter identification problem of the saturation equation in the fractional flow formulation of the two-phase porous media flow equations is solved. Numerical results validate the method's merits. (C) 2016 Elsevier Ltd. All rights reserved.

关键词： Inverse problem parameter identification problem Partial differential equation Wavelet multiscale method Homotopy method

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Solving the parameter identification problem using Shuffled Frog Leaping with Opposition-Based Initialization

Solving the Parameter Identification Problem using Shuffled ...

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1st International eConference on Computer and Knowledge Engineering (ICCKE)

作者： Ahandani, Morteza Alinia Banimahd, Reza Shrjoposht, Naser Pourqorban Islamic Azad Univ Dept Elect Engn Langaroud Branch Langaroud Iran Sahand Univ Technol Dept Elect Engn Tabriz Iran Univ Tabriz Dept Control Engn Tabriz Iran

ISBN: (纸本)9781467357135;9781467357128

The parameter identification problem can be modeled as a non-linear optimization problem. In this problem, some unknown parameters of a mathematical model presented by an ordinary differential equation using some experimental data must be estimated. This paper presents a shuffled frog leaping algorithm for solving parameter identification problem. An opposition-based initialization strategy is used to choose the fitter members as initial population. Two test cases are considered to examine the efficiency of utilized algorithm. The comparison results of shuffled frog leaping and other methods proposed in the different literature demonstrate that the shuffled frog leaping has a comparable performance than other evolutionary algorithms.

关键词： shuffled frog leaping parameter identification problem opposition-based initialization

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Derivation of accurate tensor data of materials in SAW devices by solving a parameter identification problem

Derivation of accurate tensor data of materials in SAW devic...

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IEEE International Ultrasonics Symposium

作者： Gerold Grunauer Markus Mayer Gholamreza Dadgar Javid Thomas Ebner Karl Wagner Hans Josef Pesch TDK / Epcos AG Universit?t Bayreuth

ISBN: (纸本)9781467345613

Accurate simulation of SAW devices requires accurate material tensor data. However, literature values are in most cases measured on certain engineered test devices and do often not reflect real world production processes with the necessary accuracy. In this work, a parameter identification method is outlined, which can be used to estimate material parameters from admittance measurements of resonators produced by the desired process. In order to speed up the computation, the gradients necessary for the optimization method (e.g. quasi-newton) are derived using techniques from optimal control theory. The algorithm has been tested on a set of resonators composed of a substrate, an electrode and a passivation layer.

关键词： parameter identification problem passivation layer electrode

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Coefficient identification of the regularized p-Stokes equations

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NONLINEAR ANALYSIS-REAL WORLD APPLICATIONS 2025年 81卷

作者： Schmidt, Niko Univ Kiel Christian Albrechts Pl 4 D-24118 Kiel Germany

The Antarctic and Greenland ice sheet simulation is challenging due to unknown parameters in the p-Stokes equations. In this work, we prove the existence of a solution to a parameter identification for the ice rheology and the friction coefficient. Additionally, we verify G & acirc;teaux differentiability of the coefficient-to-state operator by extending a similar result for distributed control. Moreover, we have more complicated boundary conditions. We only have to add a small diffusion term and assume the nonlinear exponent, which is given in applications, to be small enough to obtain the results. Finally, we state the adjoint equation and prove existence and uniqueness of a solution for this equation.

关键词： parameter identification problem G & acirc teaux differentiability Coefficient-to-state operator Glaciology

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A novel particle swarm algorithm for solving parameter identification problems on graphics hardware

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INTERNATIONAL JOURNAL OF COMPUTATIONAL SCIENCE AND ENGINEERING 2011年第1-2期6卷 43-51页

作者： Wang, Jing Wu, Zhijian Wang, Hui Wuhan Univ State Key Lab Software Engn Wuhan 430072 Hunan Peoples R China Jiangxi Univ Finance & Econ Sch Software & Commun Engn Nanchang 330013 Jiangxi Peoples R China

This paper presents a fine-grained novel particle swarm optimisation (PSO) algorithm on graphics hardware. It has good performance on a collection of parameter identification problems. In this algorithm, a generalised opposition-based learning (GOBL) strategy is embedded into PSO algorithm. This strategy can transform the current solution space to provide more chances of finding better solutions, and the parallel computing on graphics hardware can accelerate the convergence rate significantly. Experiment results show that the novel algorithm on graphics hardware has not only a good tolerability with the noise in the observed data but also a very high speedup.

关键词： particle swarm optimisation PSO graphics hardware opposition-based learning OBL parameter identification problem inverse problem

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A recursive identification algorithm for linear discrete periodic systems

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IET CONTROL THEORY AND APPLICATIONS 2023年第3期17卷 331-340页

作者： Lv, Lingling Zheng, Bingqian Zhang, Jinhua Zhang, Lei Inst North China Univ Water Resources & Elect Pow Zhengzhou Henan Peoples R China Henan Univ Sch Comp & Informat Engn Inst Data & Knowledge Engn Kaifeng 475004 Henan Peoples R China

The parameter identification problem of linear discrete period time-varying (LDPV) systems is studied in this paper and a two-step identification algorithm based on the recursive least squares principle is proposed. The recursive principle-based identification algorithm is mostly used to deal with the parameter identification of time-invariant systems. Combine with the cyclic reconstruction method, the LDPV system is converted to a linear time-invariant system. Then, based on this and combined with recursive least squares identification, a discrimination algorithm is proposed for the parameter estimation of the LDPV system. Finally, a numerical simulation example is given to demonstrate the effectiveness of the proposed algorithm.

关键词： periodic control Simulation, modelling and identification time-invariant systems Time-varying control systems recursive identification algorithm Linear control systems linear discrete period time-varying systems parameter estimation two-step identification algorithm cyclic reconstruction method discrete systems Discrete control systems discrimination algorithm LDPV system parameter identification problem Interpolation and function approximation (numerical analysis) recursive least squares identification linear systems least squares approximations linear time-invariant system time-varying systems recursive principle-based identification algorithm recursive least squares principle

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Sparsity and level set regularization for near-field electromagnetic imaging in 3D*

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INVERSE problemS 2020年第2期36卷 025012-025012页

作者： Hiles, A. J. Dorn, O. Univ Manchester Alan Turing BldgOxford Rd Manchester M13 9PL Lancs England

In this paper, we propose and compare two novel reconstruction strategies for near-field electromagnetic imaging of regions in 3D surrounded by walls or shields. Our focus is on the estimation of electrical conductivity profiles inside regions which are roughly equivalent in size to small rooms or medium-sized containers, from electromagnetic data obtained at one given frequency. This setup has interesting applications in the surveillance of activities behind walls, the screening of boxes or containers at ports or airports, or the monitoring of processes inside regions which might contain hazardous materials. Moreover, the techniques proposed here can easily be adjusted to imaging situations at larger or smaller scale;as often found in geophysical or non-destructive testing applications. The two novel regularization techniques proposed here are based on a sparsity promoting regularization scheme on the one hand, and a level set based shape evolution technique on the other. In our numerical simulations, we perform 3D reconstructions from noisy simulated data and compare the results with those obtained from a standard L-2-type reconstruction approach. Our results suggest, in the applications considered here, that the two proposed novel schemes are potentially able to yield significantly improved reconstructions compared to more traditional techniques.

关键词： inverse problem low frequency electromagnetics sparsity regularization level set regularization through the wall imaging shape identification parameter identification problem

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An Iterative and Adaptive Lie-Group Method for Solving the Calderon Inverse problem

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CMES-COMPUTER MODELING IN ENGINEERING & SCIENCES 2010年第3期64卷 299-326页

作者： Liu, Chein-Shan Atluri, Satya N. Natl Taiwan Univ Dept Civil Engn Taipei 10764 Taiwan Univ Calif Irvine Ctr Aerosp Res & Educ Irvine CA USA

We solve the Calderon inverse conductivity problem [Calderon (1980, 2006)], for an elliptic type equation in a rectangular plane domain, to recover an unknown conductivity function inside the domain, from the over-specified Cauchy data on the bottom of the rectangle. The Calderon inverse problem exhibits threefold simultaneous difficulties: ill-posedness of the inverse Cauchy problem, ill-posedness of the parameter identification, and no information inside the domain being available on the impedance function. In order to solve this problem, we discretize the whole domain into many sub-domains of finite strips, each with a small height. Thus the Calderon inverse problem is reduced to an inverse Cauchy problem and a parameter identification problem in each finite strip. An effective combination of the Lie-group adaptive method (LGAM), together with a finite-strip method is developed, where the Lie-group equation can adaptively solve the semi-discretized ODEs to find the unknown conductivity coefficients through iterations. The success of the present method hinges on a rationale that the local ODEs and the global Lie-group equation have to be self-adaptive during the iteration process. Thus, we have a computationally inexpensive mathematical algorithm to solve the Calderon inverse problem. The feasibility, accuracy and efficiency of present method are evaluated by comparing the estimated results for the unknown impedance function in the domain, in the Calderon inverse problem, with some postulated exact solutions. It may be concluded that the iterative and adaptive Lie-group method presented in this paper, may provide a simple and effective means of solving the Calderon inverse problem in general domains.

关键词： Calderon's inverse problem Inverse Cauchy problem parameter identification problem Lie-group adaptive method Iterative method

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parameter identification for portfolio optimization with a slow stochastic factor

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JOURNAL OF INVERSE AND ILL-POSED problemS 2022年第6期30卷 777-789页

作者： Hu, Lei Xu, Dinghua Shanghai Univ Finance & Econ Sch Math Guoding Rd 777 Shanghai 200433 Peoples R China Zhejiang Sci Tech Univ Sch Sci Hangzhou 310018 Peoples R China

In this paper, we intend to identify two significant parameters - expected return and absolute risk aversion - in the Merton portfolio optimization problem under an exponential utility function where volatility is driven by a slow mean-reverting diffusion process. First, we find the approximate solution of the fully nonlinear Hamilton-Jacobi-Bellman equation for the Merton model by the stochastic asymptotic approximation method. Second, we estimate parameters - expected return and absolute risk aversion - through the approximate solution and prove the uniqueness and stability of the parameter identification problem. Finally, we provide an illustrative example to demonstrate the capacity and efficiency of our method.

关键词： Portfolio optimization slow stochastic factor asymptotic approximation parameter identification problem inverse problems

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parameter-identification IN A SOIL WITH CONSTANT DIFFUSIVITY

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TRANSPORT IN POROUS MEDIA 1991年第5-6期6卷 759-769页

作者： ZACHMANN, D WHITE, I CSIRO DIV ENVIRONM MECHCANBERRAACT 2601AUSTRALIA

We consider infiltration into a soil that is assumed to have hydraulic conductivity of the form K = K(s)e(alpha-h) and water content of the form theta = beta-K - theta(r). Here h denotes capillary pressure head while K(s), alpha, beta and theta(r) represent soil specific parameters. These assumptions linearize the flow equation and permit a closed form solution that displays the roles of all the parameters appearing in the hydraulic function K and theta. We assume K(s) and theta(r) to be known. A measurement of diffusivity fixes the product of alpha and beta resulting in a parameter identification problem for one parameter. We show that this parameter identification problem, in some cases, has a unique solution. We also show that, in some cases, this parameter identification problem can have multiple solutions, or no solution. In addition it is shown that solutions to the parameter identification problem can be very sensitive to small changes in the problem data.

关键词： parameter identification problem CONSTANT DIFFUSIVITY DARCY LAW

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