Robust Estimation of ARX Models With Time Varying Time Delays Using Variational Bayesian Approach
针对工业过程中时变时滞和测量异常值问题，提出用马尔可夫链建模时滞相关性、用t分布处理噪声，并用变分贝叶斯方法估计模型参数和时滞，能给出参数和时滞的完整概率分布。
This paper is concerned with robust identification of processes with time-varying time delays. In reality, the delay values do not simply change randomly, but there is a correlation between consecutive delays. In this paper, the correlation of time delay is modeled by the transition probability of a Markov chain. Furthermore, the measured data are often contaminated by outliers, and therefore, -distribution is adopted to model the measurement noise. The variational Bayesian (VB) approach is applied to estimate the model parameters along with time delays. Compared with the classical expectation-maximization algorithm, VB approach has the advantage of capturing the uncertainty of the estimated parameter and time delays by providing their full probabilities. The effectiveness of the proposed method is demonstrated by both a numerical example and a pilot-scale hybrid-tank experiment.