Fault detection and isolation using probabilistic wavelet neural operator auto-encoder with application to dynamic processes

Fault detection and isolation are crucial aspects that need to be considered for the safe and reliable operation of process systems. The modern industrial process frequently employs various sensors to measure multiple process variables. However, complex temporal dependencies and intra-channel, as well as inter-channel correlations in the observed multivariate data pause major challenges during fault detection. In this paper, we present the probabilistic wavelet neural operator auto-encoder (PWNOAE), an operator learning model that aims to learn the distribution of these multivariate process data and apply them for fault detection and isolation. Neural operators are networks that can efficiently learn operator dynamics in addition to function dynamics and therefore have better generalizability compared to other models. The proposed PWNOAE utilizes healthy data for learning the distribution, which is then used as a reference for detecting and isolating faults online. For learning the distribution of multivariate time series, the proposed PWNOAE combines the integral kernel with wavelet transformation in a probabilistic fashion. As wavelets help in the time-frequency localization of time series, PWNOAE exploits them to learn complex time-frequency characteristics underlying the multivariate datasets. The fidelity of the proposed PWNOAE is demonstrated using the Tennessee Eastman benchmark data and industrial data recorded from a pressurized heavy-water nuclear reactor operated by the Nuclear Power Corporation of India. The obtained results demonstrate the proposed method's notable efficacy and success in detecting and isolating faults in the time series data compared to various well-established baselines in the literature.