Physics-Infused Fuzzy Generative Adversarial Network for Robust Failure Prognosis

Prognostics aid in the longevity of fielded systems or products. Quantifying the system's current health enable prognosis to enhance the operator's decision-making to preserve the system's health. Creating a prognosis for a system can be difficult due to (a) unknown physical relationships and/or (b) irregularities in data appearing well beyond the initiation of a problem. Traditionally, three different modeling paradigms have been used to develop a prognostics model: physics-based (PbM), data-driven (DDM), and hybrid modeling. Recently, the hybrid modeling approach that combines the strength of both PbM and DDM based approaches and alleviates their limitations is gaining traction in the prognostics domain. In this paper, a novel hybrid modeling approach for prognostics applications based on combining concepts from fuzzy logic and generative adversarial networks (GANs) is outlined. The FuzzyGAN based method embeds a physics-based model in the aggregation of the fuzzy implications. This technique constrains the output of the learning method to a realistic solution. Results on a bearing problem showcases the efficacy of adding a physics-based aggregation in a fuzzy logic model to improve GAN's ability to model health and give a more accurate system prognosis.

Fuzzy Generative Adversarial Networks

Generative Adversarial Networks (GANs) are well-known tools for data generation and semi-supervised classification. GANs, with less labeled data, outperform Deep Neural Networks (DNNs) and Convolutional Neural Networks (CNNs) in classification across various tasks, this shows promise for developing GANs capable of trespassing into the domain of semi-supervised regression. However, developing GANs for regression introduce two major challenges: (1) inherent instability in the GAN formulation and (2) performing regression and achieving stability simultaneously. This paper introduces techniques that show improvement in the GANs' regression capability through mean absolute error (MAE) and mean squared error (MSE). We bake a differentiable fuzzy logic system at multiple locations in a GAN because fuzzy logic systems have demonstrated high efficacy in classification and regression settings. The fuzzy logic takes the output of either or both the generator and the discriminator to either or both predict the output, $y$, and evaluate the generator's performance. We outline the results of applying the fuzzy logic system to CGAN and summarize each approach's efficacy. This paper shows that adding a fuzzy logic layer can enhance GAN's ability to perform regression; the most desirable injection location is problem-specific, and we show this through experiments over various datasets. Besides, we demonstrate empirically that the fuzzy-infused GAN is competitive with DNNs.