A Variational Bayesian Approach to Modelling with Random Time-varying Time Delays

Estimating random time delays has been a critical problem in regression analysis, system identification and other modelling exercises. Especially in modelling for on-line prediction of quality variable(s), the off-line output/reference samples usually contain uncertain and time-varying time delays. In order to improve the accuracy of predictive modelling with delayed references, a probabilistic framework is considered in this study to address random reference output delays. By using Variational Bayesian inference, the proposed method is capable of providing robust parameter estimation against the reference output delays. Numerical simulations and two industrial examples are used to validate the proposed approach.