基于贝叶斯推理的水环境系统参数识别

Parameters identification for water environmental system based on Bayesian inference

为了克服监测数据有限而且存在误差给水环境系统参数识别带来的困难,以一维河流水质模型方程为例,构建了水环境系统参数识别的贝叶斯算法.结合模型参数的先验分布和水质监测数据,通过贝叶斯定理计算获得了表征参数分布规律的联合后验概率密度函数.通过马尔科夫链蒙特卡罗模拟对后验分布进行了采样,获得了参数的后验边缘概率密度,并在此基础上获得了参数的数学期望等统计量.计算结果表明采用贝叶斯推理获得的模型参数估计具有很高的精度.此算法构造直观、简单,成功解决了水环境系统参数的可识别性问题.

To overcome the difficulty in the identification of parameters of the water environmental system caused by the limited observation data with noise, Bayesian algorithm was constructed for the parameters identification of the water environmental system, taking one dimensional water quality model as example. Combined with the prior distribution of the model parameters and water quality observation data, joint posterior probability function which stands for the distribution characters was obtained by Bayes＇ Theorem. Markov chain monte carlo simulation（MCMC） was taken to sample the posterior distribution to get the marginal posterior probability function of the parameters, and the statistical quantities such as the mathematic expectation were calculated. The computational results indicate that parameters estimation by Bayesian method and MCMC sampling has a high precision. The algorithm＇s construction is direct and simple, which solves the identification problem of the water environmental system successfully.