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Koopman–PCE-based confidence-bounded fault diagnosis and recovery for hydrogen demand tracking in a membrane reactor
Publikationstyp
Journal Article
Date Issued
2026-06-01
Sprache
English
Author(s)
Journal
Volume
213
Article Number
109728
Citation
Computers & Chemical Engineering 213: 109728 (2026)
Publisher DOI
Scopus ID
Publisher
Elsevier
Actuator loss-of-effectiveness (LOE) faults and matched disturbances can severely degrade tracking performance in nonlinear control affine systems, especially when the fault severity and disturbance bounds are unknown. This paper develops a fault recovery framework that combines (i) a Koopman based predictor for data-driven fault detection and identification (FDI), (ii) polynomial chaos expansion (PCE) to quantify uncertainty and provide confidence bounds on the estimated fault parameters, and (iii) an adaptive deep neural network (DNN) augmentation that compensates residual fault and disturbance effects in closed loop. We first rewrite the plant under the standard matched disturbance assumption into an effective input form, which exposes LOE faults and disturbances as a single input channel uncertainty. Using this structure, we derive the faulted tracking error dynamics under a nominal controller and a DNN augmentation. In the offline phase, we generate expert demonstrations across fault and disturbance scenarios and train a baseline DNN fault compensator by supervised learning. To decide which part of the network should be adapted online, we evaluate the average causal effect (ACE) of each layer on the closed-loop tracking error and select a single layer for online updates. During operation, a Koopman–PCE assisted FDI module estimates the actuator effectiveness matrix and
supplies a confidence bound that is used to reconfigure the nominal controller. We then propose a single layer adaptive update law and prove uniform ultimate boundedness (UUB) of the tracking and weight errors. Finally, we show that the FDI estimates tighten the residual bound and reduce the ultimate tracking error bound, with an explicit dependence on estimation accuracy. We validate these claims numerically by evaluating FDI accuracy, confidence-band behavior, residual tightening, and closed-loop recovery under out-of-distribution fault scenarios, showing that FDI alone gives the lowest RMSE while the combined FDI with adaptive NN scheme reduces worst-case tracking excursions.
supplies a confidence bound that is used to reconfigure the nominal controller. We then propose a single layer adaptive update law and prove uniform ultimate boundedness (UUB) of the tracking and weight errors. Finally, we show that the FDI estimates tighten the residual bound and reduce the ultimate tracking error bound, with an explicit dependence on estimation accuracy. We validate these claims numerically by evaluating FDI accuracy, confidence-band behavior, residual tightening, and closed-loop recovery under out-of-distribution fault scenarios, showing that FDI alone gives the lowest RMSE while the combined FDI with adaptive NN scheme reduces worst-case tracking excursions.
Subjects
Loss-of-effectiveness actuator faults
Koopman operator
Polynomial chaos expansion
Fault detection and identification
Adaptive deep neural network
Uniform ultimate boundedness
DDC Class
540: Chemistry