Self-Supervised Learning for Data Scarcity in a Fatigue Damage Prognostic Problem

With the increasing availability of data for Prognostics and Health Management (PHM), Deep Learning (DL) techniques are now the subject of considerable attention for this application, often achieving more accurate Remaining Useful Life (RUL) predictions. However, one of the major challenges for DL techniques resides in the difficulty of obtaining large amounts of labelled data on industrial systems. To overcome this lack of labelled data, an emerging learning technique is considered in our work: Self-Supervised Learning, a sub-category of unsupervised learning approaches. This paper aims to investigate whether pre-training DL models in a self-supervised way on unlabelled sensors data can be useful for RUL estimation with only Few-Shots Learning, i.e. with scarce labelled data. In this research, a fatigue damage prognostics problem is addressed, through the estimation of the RUL of aluminum alloy panels (typical of aerospace structures) subject to fatigue cracks from strain gauge data. Synthetic datasets composed of strain data are used allowing to extensively investigate the influence of the dataset size on the predictive performance. Results show that the self-supervised pre-trained models are able to significantly outperform the non-pre-trained models in downstream RUL prediction task, and with less computational expense, showing promising results in prognostic tasks when only limited labelled data is available.

Variance based sensitivity analysis for Monte Carlo and importance sampling reliability assessment with Gaussian processes

Running a reliability analysis on engineering problems involving complex numerical models can be computationally very expensive, requiring advanced simulation methods to reduce the overall numerical cost. Gaussian process based active learning methods for reliability analysis have emerged as a promising way for reducing this computational cost. The learning phase of these methods consists in building a Gaussian process surrogate model of the performance function and using the uncertainty structure of the Gaussian process to enrich iteratively this surrogate model. For that purpose a learning criterion has to be defined. Then, the estimation of the probability of failure is typically obtained by a classification of a population evaluated on the final surrogate model. Hence, the estimator of the probability of failure holds two different uncertainty sources related to the surrogate model approximation and to the sampling based integration technique. In this paper, we propose a methodology to quantify the sensitivity of the probability of failure estimator to both uncertainty sources. This analysis also enables to control the whole error associated to the failure probability estimate and thus provides an accuracy criterion on the estimation. Thus, an active learning approach integrating this analysis to reduce the main source of error and stopping when the global variability is sufficiently low is introduced. The approach is proposed for both a Monte Carlo based method as well as an importance sampling based method, seeking to improve the estimation of rare event probabilities. Performance of the proposed strategy is then assessed on several examples.