基于差分演化算法的双曲型方程参数识别

基于差分演化算法的双曲型方程参数识别 Parameter Identification of Hyperbolic Equation Based on Differential Evolution Algorithm 刘会超 LIU Huichao 1 2 first-author 吴志健 WU Zhijian 1 李焕哲 LI Huanzhe 1 3 王智超 WANG Zhichao 1 武汉大学计算机学院/软件工程国家重点实验室 武汉大学计算机学院/软件工程国家重点实验室 State Key Laboratory of Software Engineering/School of Computer,Wuhan University State Key Laboratory of Software Engineering/School of Computer,Wuhan University 黄淮学院信息工程学院 黄淮学院信息工程学院 School of Information Engineering,Huanghuai University School of Information Engineering,Huanghuai University 石家庄经济学院信息工程学院 石家庄经济学院信息工程学院 Department of Information Engineering,Shijiazhuang University of Economics Department of Information Engineering,Shijiazhuang University of Economics 差分演化算法在求解复杂优化问题时具有简单、高效的优点.本文将差分演化算法用于求解一类双曲型偏微分方程的参数识别问题,并根据所求问题的特点对算法进行了若干改进:包括基于帽子函数的参数表示和个体编码方法,用于增强算法性能的一般反向学习机制和平滑算子,以及将Tikhonov正则化和全变差正则化相结合的个体适应度计算方法.数值模拟显示,本文的算法可有效求解一维双曲型偏微分方程的参数识别问题.该算法不仅获得了高质量的近似解,而且还具有较快的收敛速度. Differential evolution algorithm（ DE） is a simple and efficient method when solving complex optimization problems. In this paper,DE was used to solve a class of parameter identification problems of hyperbolic partial differential equation,and according to the characteristics of the problems some improvements for DE were introduced. They included the parametric representation and individual coding method based on the hat function,the performance enhance schemes of the generalized opposition-based learning mechanism and the smoothing operator,and a new fitness value evaluation method which composed of the Tikhonov regularization and total variation regularization. Numerical simulations show that the proposed DE algorithm is very effective for the parameter identification problem of one-dimensional hyperbolic partial differential equation. The algorithm not only obtains the high precision solutions,but also achieves the faster convergence speed. 差分演化算法 反问题 参数识别 双曲型偏微分方程 反向学习 正则化 differential evolution algorithm inverse problem parameter identification hyperbolic partial differential equation opposition-based learning regularization 10.14188/j.1671-8836.2015.02.003 O175.27 国家自然科学基金（61070008,61364025）;河南省基础与前沿技术研究项目（122300410071）;河北省科技支撑计划项目（12210319）;南通市科技局应用研究项目（BK2014057） 2015-02-01 2021-03-31 2 61