演化参数反演方法

An Evolutionary Parameter Inversion Approach

给出了一类基于演化计算的演化参数反演方法 ,此类方法既可以给定参数的函数类 ,用遗传算法 (Ge neticAlgorithms)来反演参数的最优估计值 ,也可以不指定函数类形式 ,用遗传程序设计 (GeneticProgramming)的方法反演出最优的函数模型 ,使参数反演实现客观化、自动化 .由此建立反演系统后 ,在使用过程中可以根据最新获得的数据对模型中的物理参数作适时校准 ,一旦发现预报误差较大 ,就利用演化算法及时修正方程中的参数以改进预报 .运用该方法于椭圆边值问题的物理参数反演的数值模拟 ,证实了此方法的有效性 ,为物理模型参数的反演提供了一种崭新的实用方法 .

An inverse problem is to determine unknown causes based on observation of their effects. Such problems often arise in scientific research and engineering practice. We presented a general methodology based on evolutionary algorithms (EAs) for the parameter estimation of inverse problems. Giving function class of unknown parameter, genetic algorithms (GA) is used to evolve the optimal coefficient of linear combination of basis function. Without giving the class of parameter function, genetic programming (GP) is used to evolve the appropriate parameter function structure and coefficient such that the identification of parameter is objective and automatically. When applying ordinary differential equations (ODEs) or partial differential equations (PDEs) including unknown parameter to prediction models, the parameter is adaptively calibrated according to the recent observation data such that the prediction is improved by evolutionary computation. We apply this method to the numerical recovery of spatially varying physical parameters in elliptic boundary values problems. The successful numerical results demonstrated that the proposed method has the potential to solve a wide range of inverse parameter identification problems in a systematic and robust way.