Generative adversarial wavelet neural operator: Application to fault detection and isolation of multivariate time series data

TL;DR

This work introduces the Generative Adversarial Wavelet Neural Operator (GAWNO), an unsupervised framework for fault detection and isolation in multivariate time series. By marrying wavelet neural operators with GANs in a U‑Net style architecture, GAWNO learns the distribution of normal operation and detects faults through reconstruction error, with variable-wise isolation achieved via per-variable uncertainty analysis. The approach is validated on the Tennessee Eastman Process and WWTP N2O datasets, where it consistently outperforms PCA, DPCA, LSTM, AE, and GAN baselines in terms of AUC-ROC, recall, and F1-score. The results demonstrate robust FDI performance in nonlinear, high-dimensional systems and highlight GAWNO's potential for industrial deployment and real-time fault management.

Abstract

Fault detection and isolation in complex systems are critical to ensure reliable and efficient operation. However, traditional fault detection methods often struggle with issues such as nonlinearity and multivariate characteristics of the time series variables. This article proposes a generative adversarial wavelet neural operator (GAWNO) as a novel unsupervised deep learning approach for fault detection and isolation of multivariate time series processes.The GAWNO combines the strengths of wavelet neural operators and generative adversarial networks (GANs) to effectively capture both the temporal distributions and the spatial dependencies among different variables of an underlying system. The approach of fault detection and isolation using GAWNO consists of two main stages. In the first stage, the GAWNO is trained on a dataset of normal operating conditions to learn the underlying data distribution. In the second stage, a reconstruction error-based threshold approach using the trained GAWNO is employed to detect and isolate faults based on the discrepancy values. We validate the proposed approach using the Tennessee Eastman Process (TEP) dataset and Avedore wastewater treatment plant (WWTP) and N2O emissions named as WWTPN2O datasets. Overall, we showcase that the idea of harnessing the power of wavelet analysis, neural operators, and generative models in a single framework to detect and isolate faults has shown promising results compared to various well-established baselines in the literature.

Figures (16)

• Figure 1: Generative Adversarial Network architecture (GAN). The GAN architecture for time series data is characterized by its two integral components: the generator and the discriminator. The input to the generator is typically a random noise vector sampled from a latent space. Through an iterative learning process, the generator learns the underlying temporal dependencies and patterns within the training data, aiming to generate time series samples that resemble the statistical characteristics of the original dataset. In contrast, the discriminator acts as an adversarial critic, distinguishing between real-time series data from the training set and synthetic data generated by the generator. As the generator aims to generate increasingly realistic samples, the discriminator concurrently strives to become more proficient at detecting fake data, creating a dynamic interplay that drives both components to improve over time.
• Figure 2: Schematic of the wavelet integral blocks. The input data is simultaneously passed through a wavelet filter and a 1-D CNN layer. In the wavelet filter, two levels of multi-resolution wavelet decomposition happen. The decomposed wavelet coefficients in the second level are used for kernel parameterization. Once the kernel convolution is done, the convolved data are transformed back to the time domain using inverse wavelet transform. In the CNN layer, a kernel size of one is used to preserve the shape of the data. Outputs of the wavelet parameterization and CNN are added to construct the output of the wavelet integral block.
• Figure 3: Generative adversarial Wavelet neural operator (GAWNO). (I) Generator: The input $\xi$ is random noise which first gets passed to a pointwise lifting operator parameterized with P. Then multiple layers of wavelet intergal blocks are applied, which are accompanied by a few skip connections. At last, the output Y is generated using a final pointwise projection layer parameterized with Q. (II) Discriminator: The input (real data and fake data) first gets passed to a pointwise lifting operator parameterized with P. Then multiple layers of wavelet intergal blocks are applied which are accompanied by a few skip connections. At last, the output Y is generated using a final pointwise projection layer parameterized with Q, followed by a linear integral functional layer H.
• Figure 4: Schematic of uplifting and downlifting Wavelet transform
• Figure 6: Training Results using GAWNO for Tennessee Eastman Process dataset. The input function sample comprises random noise, while the WNO-based generator generates the data. The generator is trained to learn the underlying data distribution. (a) Training with Tennessee Eastman Process dataset where grey represents actual data while blue represents the generated data (b) Data distribution histogram resulting from the GAWNO approach.