Robust Estimation of ARX Models With Time Varying Time Delays Using Variational Bayesian Approach

Area of Science:

• Process control and system identification.
• Statistical modeling and machine learning.

Background:

• Accurate identification of dynamic systems is crucial for effective control.
• Time-varying time delays and data outliers pose significant challenges in real-world process identification.
• Existing methods often struggle with correlated delay variations and uncertainty quantification.

Purpose of the Study:

• To develop a robust method for identifying processes with time-varying time delays.
• To model the correlation between consecutive time delays using Markov chains.
• To address measurement noise and outliers using a t-distribution and estimate parameters with uncertainty quantification.

Main Methods:

• Modeling time-varying time delay correlation with Markov chain transition probabilities.
• Adopting a t-distribution to model measurement noise, robust to outliers.
• Applying the variational Bayesian (VB) approach for parameter and time delay estimation.
• Quantifying uncertainty in parameter and time delay estimates via full probability distributions.

Main Results:

• The proposed variational Bayesian method effectively identifies processes with time-varying time delays.
• The method demonstrates robustness against outliers in measured data.
• Uncertainty in estimated parameters and time delays is successfully captured.
• Validation through a numerical example and a pilot-scale hybrid-tank experiment confirms effectiveness.

Conclusions:

• The developed VB approach offers a robust and uncertainty-aware solution for identifying systems with correlated, time-varying delays and noisy data.
• This method provides a significant advancement over classical algorithms like expectation-maximization for complex process identification tasks.
• The findings are applicable to various engineering fields requiring accurate dynamic system modeling.