Uncertainty Quantification in Remaining Useful Life of Aerospace Components using State Space Models and Inverse FORM

This paper investigates the use of the inverse first-order reliability method (inverse- FORM) to quantify the uncertainty in the remaining useful life (RUL) of aerospace components. The prediction of remaining useful life is an integral part of system health prognosis, and directly helps in online health monitoring and decision-making. However, the prediction of remaining useful life is affected by several sources of uncertainty, and therefore it is necessary to quantify the uncertainty in the remaining useful life prediction. While system parameter uncertainty and physical variability can be easily included in inverse-FORM, this paper extends the methodology to include: (1) future loading uncertainty, (2) process noise; and (3) uncertainty in the state estimate. The inverse-FORM method has been used in this paper to (1) quickly obtain probability bounds on the remaining useful life prediction; and (2) calculate the entire probability distribution of remaining useful life prediction, and the results are verified against Monte Carlo sampling. The proposed methodology is illustrated using a numerical example

Uncertainty Quantification in Machine Learning for Engineering Design and Health Prognostics: A Tutorial

On top of machine learning models, uncertainty quantification (UQ) functions as an essential layer of safety assurance that could lead to more principled decision making by enabling sound risk assessment and management. The safety and reliability improvement of ML models empowered by UQ has the potential to significantly facilitate the broad adoption of ML solutions in high-stakes decision settings, such as healthcare, manufacturing, and aviation, to name a few. In this tutorial, we aim to provide a holistic lens on emerging UQ methods for ML models with a particular focus on neural networks and the applications of these UQ methods in tackling engineering design as well as prognostics and health management problems. Toward this goal, we start with a comprehensive classification of uncertainty types, sources, and causes pertaining to UQ of ML models. Next, we provide a tutorial-style description of several state-of-the-art UQ methods: Gaussian process regression, Bayesian neural network, neural network ensemble, and deterministic UQ methods focusing on spectral-normalized neural Gaussian process. Established upon the mathematical formulations, we subsequently examine the soundness of these UQ methods quantitatively and qualitatively (by a toy regression example) to examine their strengths and shortcomings from different dimensions. Then, we review quantitative metrics commonly used to assess the quality of predictive uncertainty in classification and regression problems. Afterward, we discuss the increasingly important role of UQ of ML models in solving challenging problems in engineering design and health prognostics. Two case studies with source codes available on GitHub are used to demonstrate these UQ methods and compare their performance in the life prediction of lithium-ion batteries at the early stage and the remaining useful life prediction of turbofan engines

A belief function theory based approach to combining different representation of uncertainty in prognostics

International audienceIn this work, we consider two prognostic approaches for the prediction of the remaining useful life (RUL) of degrading equipment. The first approach is based on Gaussian Process Regression (GPR) and provides the probability distribution of the equipment RUL; the second approach adopts a Similarity-Based Regression (SBR) method for the RUL prediction and belief function theory for modeling the uncertainty on the prediction. The performance of the two approaches is comparable and we propose a method for combining their outcomes in an ensemble. The least commitment principle is adopted to transform the RUL probability density function supplied by the GPR method into a belief density function. Then, the Dempster's rule is used to aggregate the belief assignments provided by the GPR and the SBR approaches. The ensemble method is applied to the problem of predicting the RUL of filters used to clean the sea water entering the condenser of the boiling water reactor (BWR) in a Swedish nuclear power plant. The results by the ensemble method are shown to be more satisfactory than that provided by the individual GPR and SBR approaches from the point of view of the representation of the uncertainty in the RUL prediction