Self-correcting iterative learning fault estimation for discrete parabolic distributed parameter systems with variable pass lengths

• Published in: Journal of the Franklin Institute Vol. 362; no. 13; p. 107939
• Main Authors: Shi, Jiantao, Tang, Jiawen, Yue, Dongdong, Chen, Chuang
• Format: Journal Article
• Language: English
• Published: Elsevier Inc 15.08.2025
• Subjects: Distributed parameter systems; Self-correcting iterative learning; Spatiotemporal faults; Variable pass lengths; Self-correcting iterative learning; Variable pass lengths; Distributed parameter systems; Spatiotemporal faults
• ISSN: 0016-0032
• DOI: 10.1016/j.jfranklin.2025.107939

This article addresses the fault estimation (FE) problem for parabolic distributed parameter systems (PDPSs) subject to variable pass lengths, where incomplete historical data and spatiotemporal dynamics pose significant challenges to accurate estimation. To cope with these issues, a self-correcting iterative learning (SCIL) algorithm is proposed for the simultaneous estimation of time-domain and spatiotemporal faults. The algorithm incorporates a recursive interval Gaussian distribution and a Bernoulli distribution to characterize pass length variability and time-point reachability, thereby supporting fault estimation under variable pass lengths across trials. A convergence analysis under the (L2,λ)-norm framework is conducted, and sufficient conditions are derived to ensure bounded fault estimation error in expectation. Numerical simulations validate the effectiveness of the proposed method in improving estimation accuracy and robustness under varying pass lengths.