基于变分贝叶斯算法的线性变参数系统辨识

线性变参数系统（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，是解决非线性过程建模的一个有效手段。由于实际工业过程存在各种干扰因素，导致被建模系统呈现随机性及模型参数的不确定性。针对这一问题，考虑采用变分贝叶斯（VB）算法对LPV模型进行辨识。该算法首先给定参数相应的先验分布，通过最大化目标函数的下界，从而估计得到参数的后验分布。不仅可实现对参数的点估计，同时量化了估计值的不确定性。针对典型二阶过程和连续搅拌反应釜（CSTR），运用提出的算法进行仿真实验，表明了该贝叶斯估计方法的优越性。

Identification of linear parameter varying systems with variational Bayesian algorithm

Linear parameter varying (LPV) method is an effective tool for nonlinear process modeling, which converts modeling of multi-stage nonlinear complex process into identification of multiple linear models. Various disturbance factors in industrial processes result in stochasticity of system modeling and uncertainty of model parameters. Identification of LPV models was studied under the variational Bayesian (VB) framework. After prior probability distributions were assigned to variables and parameters, posterior distributions of these variables and parameters were estimated by maximizing lower limits of objective functions. This full Bayesian system identification approach not only provided point estimates of parameters, but also quantified uncertainty of estimation. Numerical simulation on typical two-stage process and continuous stirred tank reactor (CSTR) demonstrated effectiveness and superiority of the proposed method.