缺失数据下基于EM算法的非线性过程建模

摘要

A linear parameter varying (LPV) method can develop the model of the multi-stage, non-linear process through the identification of linear multiple models. In recent years it has been of great concern. This paper investigates the identification of the LPV model with incomplete measurements. First, to indicate whether the output measurement is missing at each sampling instant, a binary variable is defined through which the availability of the output measurement is denoted. The key variable(s) can be taken as the scheduling variable(s) and the main operating point is determined based on the actual production process. Then, local models are constructed around each operating point, and EM algorithm is introduced to estimate their parameters. Both the missing data and the sampling data belonging are treated as the hidden variables. Finally, local models are combined according to an exponential weighting function. A simulated numerical example as well as the continuous stirred tank reactor (CSTR) are employed to demonstrate the effectiveness of the proposed method.%线性时变参数系统（LPV）将多阶段、非线性的过程建模转化为线性多模型的辨识问题，近年来得到了极大关注。考虑缺失数据下LPV系统的离线建模问题，首先引入一个二进制变量表征输出样本缺失状态，选取过程关键变量作为调度变量，确定主要工况点；然后围绕不同工况点建立局部子模型，将输出缺失部分和采样数据的模型归属当作隐藏变量，利用EM算法进行参数估计，再采用高斯权重函数融合各子模型。最后分别针对典型二阶过程和连续搅拌反应釜（CSTR），运用提出的多模型和算法进行仿真实验，表明有效性。