Autoregressive Distributed Lag Model Based Cointegration Analysis for Batch Process Monitoring

Abstract

Abstract Batch processes have been widely applied in pharmaceutical and chemical industry. Variables in batch process exhibit obvious nonstationary and nonlinear characteristics, which brings challenges to process monitoring. Recently, cointegration theory gets more attention for its applications on the analysis of multivariate nonstationary time series. According to the cointegration theory, if the nonstationary random sequences in a system containing a cointegration relationship, there is at least one stable long-term dynamic equilibrium relationship among these nonstationary variables. Such dynamic equilibrium relationship can also be found in variables in industrial processes, since the nonstationary variables are controlled by physics, chemistry, and other internal mechanisms within a system. For multivariate variables system, Johansen test is a commonly used method to test cointegration relationship and estimate the cointegration vectors, which is based on the multivariate unconstrained vector autoregressive (VAR) model, in which all variables are assumed as indifferent endogenous variables. However, certain variables in real process, such as control variables, is not affected by such long- term equilibrium and is governed by external conditions, which is called a weakly exogenous variable. When there are weak exogenous variables in a system, the cointegration test based on the VAR model needs to be improved, as the impact of exogenous variable is neglected. In this work, considering the impact of weak exogenous variables, autoregressive distributed lag (ADL) model is adopted for cointegration test and parameters estimation. The penicillin fermentation process is presented to illustrate the effectiveness of the proposed method, in which many control parameters exert a significant impact on the state of fermentation. The monitoring results show that the interaction among variables can be better characterized, and abnormal behavior of the process can be correctly detected by proposed cointegration testing method based on autoregressive distributed lag model.