Dirichlet过程混合模型在非线性过程监控中的应用

Nonparametric bayesian based on mixture of dirichlet process in application of fault detection

针对高斯混合模型在模型选择阶段易产生有噪声或过拟合的模型估计问题,提出基于Dirichlet过程混合模型的非参数贝叶斯故障诊断方法.通过重新定义高斯混合模型中的混合权重,利用stick-breaking法建立Dirichlet过程混合模型.通过具有截断作用的变分法近似推理出模型参数以及隐含变量,利用所得后验对故障模型进行估计,并提出基于后验概率的监测统计量以度量出故障状态在后验中的波动.在连续搅拌釜式反应器和Tennessee Eastman化工过程上的实验结果表明,该方法在故障检测方面优于传统的核主元分析法,并且具有较高的故障诊断率.

A nonparametric Bayesian fault detection method based on Dirichlet process mixture model was proposed to resolve the issues of Gaussian mixture model, i. e. , noisy model size estimates and overfitting proneness in the model estimation. The construction of Dirichlet process mixture model was constructed baseed on the stick-breaking method and the redefinition of the mixing weight in Gaussian mixture model. The parameters and latent variables was approximatively infered by an efficient truncated variational Bayesian inference algorithm. The resulting posterior distribution was utilized to the estimation of fault model. The monitoring statistic was proposed to measure the variation inside the posterior. The results on the non-isothermal continuous stirred-tank reactor and Tennessee Eastman chemical plant simulation show that the performances of fault diagnosis by the presented method are superior to that by kernel principal component analysis with higher accuracy.