Research On Parameter Estimation Based On Intelligent Algorithm And Its Application

Partial differential equations are often used to simulate complex dynamic systems,and the parameters in the equations usually have special practical significance,especially the parameters in the heat conduction equation,such as the thermal conductivity and thermal diffusion coefficient of objects.This kind of ill-posed problem is mainly manifested as unstable,non-unique or non-existent solutions and large amount of calculation,so there is no universal theory or specific calculation method at present.Therefore,the parameter estimation method of intelligent algorithm for parameter estimation of this ill-posed problem has important application value.Parameter estimation plays an important role in various fields.In actual research,there may be errors in the experimental data due to uncontrollable factors in the experiment,or due to the particularity of the research problem,the information cannot be obtained through experiments.To effectively solve these problems,parameter estimation has been widely used in various aspects.Based on intelligent algorithms,this paper provides two methods of parameter estimation of heat sources for two-dimensional heat conduction equations.The main work is as follows:1.Based on Bayesian estimation,the two-dimensional heat conduction equation is studied.Based on the observation temperature of an observation point at different times,it is optimized by the Bayesian posterior probability formula and differential evolution algorithm,and the inversion estimation of the heat source position is given.The final numerical experiments show that as the number of iterations increases,the error of the heat source position parameter becomes smaller.After the number of iterations reaches 120,the relative error of the parameter inversion is controlled within 2%;after adding2%,5% and 10% white noise to the observed data,the relative error does not change much,indicating that the algorithm has a certain stability.2.Based on particle swarm algorithm,combining it with BP neural network,the heat source inversion of the two-dimensional heat conduction equation is studied,and the BP neural network is optimized to improve the accuracy of heat source inversion.Numerical experiments show that the parameter estimation method combining particle swarm optimization and BP neural network has certain convergence;and through error analysis,the optimized algorithm's inversion results are better and more stable,and the relative errors are within 5%.Through experiments and analysis,it is showed that the parameter estimation method provided for the heat conduction equation in this paper can solve its ill-posed problems.