Abstract: Aiming at the data characters of multi-operating and sampling delay in real industrial process modeling, the linear parameter varying model is chosen to fit the multi-operating process. And the linear ARX model is selected as the local model structure. At the same time, the sampling time delay and data identity are taken as the hidden variables of the Expectation Maximization（EM） algorithm while calculating the Maximum Likelihood Estimation（MLE） function. Finally the parameters of local models are acquired and the local ARX models are incorporated into the integral LPV model through the Gaussian weighting function. The continuous stirring tank reactor and 3-stage high purity distillation column are selected as the simulation examples of multi-operating process. The process models are established and sampling time delay of the process data is estimated accurately at the same time. Simulation results show that the proposed method can practically cope well with the modeling of the multi-operating industrial processes.

Key words: multi-operating process, sampling delay, Expectation Maximization（EM） algorithm, parameter estimation

摘要： 针对实际的工业过程建模中存在的多工况和采样延时这两大重要数据特征，首先利用LPV模型拟合多工况过程，选取线性ARX模型作为LPV的局部模型；同时将采样延时和数据的工况归属作为EM算法的隐含变量，然后对极大似然函数进行求解，辨识出各局部模型的参数；最后采用高斯权重函数将局部ARX模型融合为整体LPV模型。采用连续搅拌反应釜和三级高纯度精馏塔作为数据采样延时情形下的多工况过程建模仿真实例，在建立过程模型的同时准确地估计数据的采样延时。仿真结果表明该方法具有良好的建模效果，对于处理数据采样延时的多工况工业过程建模问题具有非常实用的价值。

关键词: 多工况过程, 采样延时, 期望最大化（EM）算法, 参数估计