An Adaptive Observer-Based Algorithm for Solving Inverse Source Problem for the Wave Equation-Reference-Cited by-同舟云学术

An Adaptive Observer-Based Algorithm for Solving Inverse Source Problem for the Wave Equation

Published:2015 Issue: Volume:2015 Page:1-8
ISSN:1024-123X
Container-title:Mathematical Problems in Engineering
language:en
Short-container-title:Mathematical Problems in Engineering

Author:

Asiri Sharefa¹^ORCID,Zayane-Aissa Chadia¹,Laleg-Kirati Taous-Meriem¹

Affiliation:

1. Computer, Electrical and Mathematical Sciences and Engineering, King Abdullah University of Science & Technology, P.O. Box 4700, Thuwal 23955-6900, Saudi Arabia

Abstract

Observers are well known in control theory. Originally designed to estimate the hidden states of dynamical systems given some measurements, the observers scope has been recently extended to the estimation of some unknowns, for systems governed by partial differential equations. In this paper, observers are used to solve inverse source problem for a one-dimensional wave equation. An adaptive observer is designed to estimate the state and source components for a fully discretized system. The effectiveness of the algorithm is emphasized in noise-free and noisy cases and an insight on the impact of measurements’ size and location is provided.

Publisher

Hindawi Limited

Subject

General Engineering,General Mathematics

Link

http://downloads.hindawi.com/journals/mpe/2015/796539.pdf

Reference16 articles.

1. Adjoint centroid-moment tensor inversions

2. Source Estimation by Full Wave Form Inversion

3. A numerical algorithm for solving inverse problems of two-dimensional wave equations

4. A Regularization Homotopy Method for the Inverse Problem of 2-D Wave Equation and Well Log Constraint Inversion

Cited by 6 articles. 订阅此论文施引文献订阅此论文施引文献，注册后可以免费订阅5篇论文的施引文献，订阅后可以查看论文全部施引文献

1. Source Inversion Based on Distributed Acoustic Sensing-Type Data;Mathematics;2024-06-14

2. Solutions for non-homogeneous wave equations subject to unusual and Neumann boundary conditions;Applied Mathematics and Computation;2022-10

3. Iterative Learning Based Modulating Functions Method for Distributed Solar Source Estimation;IEEE Control Systems Letters;2021-12

4. Moving-Horizon Modulating Functions-Based Algorithm for Online Source Estimation in a First-Order Hyperbolic Partial Differential Equation;Journal of Solar Energy Engineering;2017-09-28

5. Source Estimation for the Damped Wave Equation Using Modulating Functions Method: Application to the Estimation of the Cerebral Blood Flow;IFAC-PapersOnLine;2017-07