A probabilistic Bayesian recurrent neural network for remaining useful life prognostics considering epistemic and aleatory uncertainties

Abstract

Deep learning-based approach has emerged as a promising solution to handle big machinery data from multi-sensor suites in complex physical assets and predict their remaining useful life (RUL). However, most recent deep learningbased approaches deliver a single-point estimate of RUL as these models represent the weights of a neural network as a deterministic value and hence cannot convey uncertainty in the RUL prediction. This practice usually provides overly confident predictions that might cause severe consequences in safetycritical industries. To address this issue, this paper proposes a probabilistic Bayesian recurrent neural network (RNN) for RUL prognostics considering epistemic and aleatory uncertainties. The epistemic uncertainty is handled by Bayesian RNN layers as extensions from the Frequentist RNN layers using the Flipout method. The aleatory uncertainty is covered by a probabilistic output that follows a Gaussian distribution parameterized by the two neurons in the output layer. The network is trained using Bayes by backprop with the Flipout method. The proposed model is demonstrated by the open-access Commercial Modular Aero-Propulsion System Simulation (C-MAPSS) dataset of turbofan engines and a comparative study of the Frequentist RNN counterparts, the Monte Carlo Dropout-based RNN, and the state-of-the-art models for C-MAPSS datasets. The results demonstrate the promising performance and robustness of the proposed model in RUL prognostics.

Conformal Prediction with Temporal Quantile Adjustments

“…Various other techniques, outside the ambit of CP, have also been extended to quantify uncertainty in time series forecasting as well. For instance, approximate Bayesian methods [8,51,34,32,23,13,26] are quite popular for uncertainty quantification, and have been extended to RNNs [12,7]. Finally, one may also use the idea of directly predicting the quantiles (as opposed to the point estimate) in regression tasks [46,25], and applying it to time series forecasting [52,14].…”

End-to-End Pipeline for Uncertainty Quantification and Remaining Useful Life Estimation: An Application on Aircraft Engines

“…The remaining useful life is not merely a target variable that can be predicted from sensor measurements, but it is a variable that needs to be inferred from a longer trend of degradation patterns and when those begin to occur. In this view, and due to the advances in the general field of artificial intelligence (AI), deep learning (DL) and DNNs have proven to be a successful candidate to the RUL estimation task (Lei et al, 2018;Benker, Furtner, Semm, & Zaeh, 2021;Kefalas, Baratchi, Apostolidis, van den Herik, & Bäck, 2021;Caceres, Gonzalez, Zhou, & Droguett, 2021;Peng, Ye, & Chen, 2020;B. Wang, Lei, Yan, Li, & Guo, 2020).…”

“…DNNs owe their success to their representational power and their capacity to learn sets of hierarchical features from simpler features due to their deep, multilayer architectures (Goodfellow, Yoshua Bengio, & Aaron Courville, 2016). However, most of the state-of-the-art DL approaches used in prognostics provide mainly point estimates to their RUL predictions (Peng et al, 2020;Caceres et al, 2021;Biggio, Wieland, Chao, Kastanis, & Fink, 2021). This is because DNNs do not inherently quantify the uncertainty associated with their predictions but instead treat their weights and biases as deterministic values.…”

Ensemble of Hybrid Neural Networks to Compensate for Epistemic Uncertainties: A Case Study in System Prognosis

“…Thus, in the task of RUL estimation for prognosis analysis the key challenge is the extrapolation of damage accumulation models under the influence of varying levels of uncertainty. There is a vast literature concerning uncertainty quantification and estimation in PHM analyzes and RUL estimation Baraldi et al (2010); Sankararaman (2015); Dewey et al (2019); Li et al (2021); Caceres et al (2021). In this contribution we focus specifically on the effects of epistemic uncertainty (i.e., incomplete or lack of knowledge) in damage extrapolation for prognosis analysis.…”