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    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.