# Forecasting remaining useful life: Interpretable deep learning approach via variational Bayesian inferences

arXiv: https://arxiv.org/abs/1907.05146 · HTML: https://mlsanity.com/paper/1907.05146/

## Key facts

- Cited by 12 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 11 Jul 2019.

## Built on by (most cited first, 12 of 12)

- [A Holistic Approach to Interpretability in Financial Lending: Models, Visualizations, and Summary-Explanations](https://mlsanity.com/paper/2106.02605/) (2021)
- [Explainability through uncertainty: Trustworthy decision-making with neural networks](https://mlsanity.com/paper/2403.10168/) (2024)
- [A Benchmark on Uncertainty Quantification for Deep Learning Prognostics](https://mlsanity.com/paper/2302.04730/) (2023)
- [GAM(e) changer or not? An evaluation of interpretable machine learning models based on additive model constraints](https://mlsanity.com/paper/2204.09123/) (2022)
- [Interpretable Prognostics with Concept Bottleneck Models](https://mlsanity.com/paper/2405.17575/) (2024)
- [An Uncertainty-Informed Framework for Trustworthy Fault Diagnosis in Safety-Critical Applications](https://mlsanity.com/paper/2111.00874/) (2021)
- [Physics-Informed Deep Learning: A Promising Technique for System Reliability Assessment](https://mlsanity.com/paper/2108.10828/) (2021)
- [Explainable AI (XAI) for PHM of Industrial Asset: A State-of-The-Art, PRISMA-Compliant Systematic Review](https://mlsanity.com/paper/2107.03869/) (2021)
- [Bayesian Deep Learning for Remaining Useful Life Estimation via Stein Variational Gradient Descent](https://mlsanity.com/paper/2402.01098/) (2024)
- [Are Logistic Models Really Interpretable?](https://mlsanity.com/paper/2406.13427/) (2024)
- [A Survey on Proactive Customer Care: Enabling Science and Steps to Realize it](https://mlsanity.com/paper/2110.05015/) (2021)
- [Rethinking Log Odds: Linear Probability Modelling and Expert Advice in Interpretable Machine Learning](https://mlsanity.com/paper/2211.06360/) (2022)

## Abstract (arXiv)

Predicting the remaining useful life of machinery, infrastructure, or other equipment can facilitate preemptive maintenance decisions, whereby a failure is prevented through timely repair or replacement. This allows for a better decision support by considering the anticipated time-to-failure and thus promises to reduce costs. Here a common baseline may be derived by fitting a probability density function to past lifetimes and then utilizing the (conditional) expected remaining useful life as a prognostic. This approach finds widespread use in practice because of its high explanatory power. A more accurate alternative is promised by machine learning, where forecasts incorporate deterioration processes and environmental variables through sensor data. However, machine learning largely functions as a black-box method and its forecasts thus forfeit most of the desired interpretability. As our primary contribution, we propose a structured-effect neural network for predicting the remaining useful life which combines the favorable properties of both approaches: its key innovation is that it offers both a high accountability and the flexibility of deep learning. The parameters are estimated via variational Bayesian inferences. The different approaches are compared based on the actual time-to-failure for aircraft engines. This demonstrates the performance and superior interpretability of our method, while we finally discuss implications for decision support.