(375j) Probabilistic Distribution Reconstruction Model for Few-Shot Fault Monitoring in Chemical Processes

In recent years, with the rapid iteration of digitalization, automation, and the Internet of Things (IoT) in industrial production, Fault Detection and Diagnosis (FDD) methods have played an increasingly critical role in achieving the developmental goals of process safety [1]. In previous fault detection models, ranging from the initial Principal Component Analysis (PCA), Partial Least Squares (PLS), and other traditional multivariate statistical analysis methods to Convolutional Neural Networks (CNN), Long Short-Term Memory networks (LSTM), Graph Neural Networks (GNN), and other deep neural network methods, fault detection has been conducted by establishing thresholds through normal data. However, in industrial environments, due to the extensive time span of normal operating conditions, the obtained fault conditions are very limited [2]. If further monitoring tasks are to be completed, it becomes necessary to reconstruct the original distribution of fault data: when there is a probabilistic dependency between different variables, then from the perspective of the joint distribution, any sensor fault becomes more evident.

Variational Autoencoders (VAE) are common probabilistic distribution reconstruction models. Given that they assume the latent space to be a multivariate Gaussian distribution, they are generally not suitable for more complex probability distributions. Moreover, considering the inherent uncertain and complex nature of chemical processes, assuming that the true distribution of process data follows a specific parametric distribution (i.e. Gaussian distribution) is unrealistic. Therefore, finding a model that can effectively reconstruct the data distribution is crucial. The Denoising Diffusion Probabilistic Model (DDPM) offers a novel approach to extracting the original data distribution [3]. By adding noise and then removing it, the complex joint distribution of variables is gradually transformed into a simpler distribution. Through learning on normal and fault data, the denoising process actually encapsulates a wealth of information about the probabilistic distribution between variables. In this regard, this study proposes a new construction model. Before processing, data is first extracted for its periodical features and trends using the Gramian Angular Field (GAF), and then the processed two-dimensional image is used as input for the DDPM module for reconstruction. During the denoising process of the DDPM module, this study compares two different denoising networks: U-Net and ResNet. The study models the distribution using data from normal operations, then samples different fault modes in the latent space. After denoising, these samples are used as a pseudo fault dataset for fault detection, thereby avoiding detection biases caused by class imbalance to a certain extent.

This study employed the CSTH (Continuous Stirred Tank Heater) [4] and the Tennessee Eastman Process (TEP) [5] datasets for verification and tested it on an industrial case from a petrochemical company. The comprehensive results show that compared to other models, such as VAE and LSTM-VAE, this model can achieve similar fault detection performance, providing a new perspective for the problem of few-shot fault monitoring to a certain extent. Moreover, the incorporation of random sampling in the DDPM module endows the DDPM-GAF architecture with excellent robustness and stability. This eloquently demonstrates the model's effective performance in extracting the distribution of multi-dimensional time-series variables from few-shot samples. We will continue our research, and the complete results will be presented in a forthcoming extended paper.

[1] Bi, X. et al. (2022). One step forward for smart chemical process fault detection and diagnosis. Computers & Chemical Engineering.

[2] Wu, H., Zhao, J. (2020). Fault detection and diagnosis based on transfer learning for multimode chemical processes. Computers and Chemical Engineering, 135, 106731.

[3] Ho, J., et al. (2020). Denoising diffusion probabilistic models. Advances in Neural Information Processing Systems 33, 6840–6851.

[4] Thornhill, N.F., Patwardhan, S.C., Shah, S.L. (2008). A continuous stirred tank heater simulation model with applications. J. Process Control 18, 347–360.

[5] Bathelt, A., Ricker, N.L., Jelali, M. (2015). Revision of the Tennessee Eastman Process Model. IFAC-PapersOnLine 48, 309–314.