A Bayesian deep learning framework for interval estimation of remaining useful life in complex systems by incorporating general degradation characteristics

Abstract

Deep learning has emerged as a powerful tool to model complicated relationships between inputs and outputs in various fields including degradation modeling and prognostics. Existing deep learning-based prognostic approaches are often used in a black-box manner and provide only point estimations of remaining useful life. However, accurate interval estimations of the remaining useful life are crucial to understand the stochastic nature of degradation processes and perform reliable risk analysis and maintenance decision making. This study proposes a novel Bayesian deep learning framework that incorporates general characteristics of degradation processes and provides the interval estimations of remaining useful life. The proposed method enjoys several unique advantages: (i) providing a general approach by not assuming any particular type of degradation processes nor the availability of domain-specific prior knowledge such as a failure threshold; (ii) offering the interval estimations of the remaining useful life; (iii) systematically modeling two types of uncertainties embedded in prognostics; and (iv) exhibiting great prognostic performance and wide applicability to complex systems that may involve multiple sensor signals, multiple failure modes, and multiple operational conditions. Numerical studies demonstrate improved prognostic performance and practicality of the proposed method over benchmark approaches. Additional numerical results including the analysis of sensitivity and computational costs are given in the online supplemental materials.

Keywords:

• Bayesian neural network
• prognostics
• multiple sensors
• multiple failure modes
• multiple operational conditions
• variational inference

Additional information

Funding

This work was supported in part by the office of Naval Research under Grant N00014-17-1-2261, and in part by the Department of Energy under award number DE-NE0008805.

Notes on contributors

Minhee Kim

Minhee Kim received a BS degree in industrial and management engineering from Pohang University of Science and Technology (POSTECH), Pohang, Korea, in 2017. Currently, she is working towards a PhD degree at the Department of Industrial and Systems Engineering, University of Wisconsin–Madison, Madison, WI, USA. Her research interests are degradation modeling and prognostics, and Bayesian deep learning including Gaussian processes and Bayesian neural networks.

Kaibo Liu

Kaibo Liu (M’14) received a BS degree in industrial engineering from the Hong Kong University of Science, and Technology, Hong Kong, China in 2009, an MS degree in statistics and a PhD degree in industrial engineering from the Georgia Institute of Technology, Atlanta, GA, USA, in 2011 and 2013, respectively. Currently, he is an associate professor with the Department of Industrial and Systems Engineering, University of Wisconsin–Madison, Madison, WI, USA. His research interests are data fusion for process modeling, monitoring, diagnosis, prognostics and decision making. Dr. Liu is a member of ASQ, SME, INFORMS, IEEE, and IISE.