Physics Informed Machine Learning (PIML) methods for estimating the remaining useful lifetime (RUL) of aircraft engines
Sriram Nagaraj, Truman Hickok
TL;DR
This work tackles remaining useful lifetime (RUL) prediction for aircraft engines using the NASA C-MAPSS dataset within a physics-informed machine learning framework. It advances beyond purely data-driven DL by discovering and leveraging stochastic physics: it estimates time-varying mean and variance functions $\mu(t)$ and $\rho(t)$ from sensor time series, handling both unimodal and multimodal distributions via $K$-means, and uses these quantities to augment an LSTM predictor. A key novelty is a dual discovery-solution approach and a physics-informed synthetic data generator, grounded in a stochastic differential equation view $dS(t) = a(t)dt + b(t)dW(t)$ and moment dynamics, which yields improved RUL accuracy over data-only DL across four C-MAPSS operating conditions. The framework is flexible and scalable to other sensor modalities and partially observed physics, with potential benefits for uncertainty quantification and broader predictive diagnostics.
Abstract
This paper is aimed at using the newly developing field of physics informed machine learning (PIML) to develop models for predicting the remaining useful lifetime (RUL) aircraft engines. We consider the well-known benchmark NASA Commercial Modular Aero-Propulsion System Simulation (C-MAPSS) data as the main data for this paper, which consists of sensor outputs in a variety of different operating modes. C-MAPSS is a well-studied dataset with much existing work in the literature that address RUL prediction with classical and deep learning methods. In the absence of published empirical physical laws governing the C-MAPSS data, our approach first uses stochastic methods to estimate the governing physics models from the noisy time series data. In our approach, we model the various sensor readings as being governed by stochastic differential equations, and we estimate the corresponding transition density mean and variance functions of the underlying processes. We then augment LSTM (long-short term memory) models with the learned mean and variance functions during training and inferencing. Our PIML based approach is different from previous methods, and we use the data to first learn the physics. Our results indicate that PIML discovery and solutions methods are well suited for this problem and outperform previous data-only deep learning methods for this data set and task. Moreover, the framework developed herein is flexible, and can be adapted to other situations (other sensor modalities or combined multi-physics environments), including cases where the underlying physics is only partially observed or known.