## Remaining Useful Life Estimation Using Neural Ordinary Differential Equations

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**Published**Aug 1, 2021

**Marco Star**

**Kristoffer McKee**

## Abstract

Data-driven machinery prognostics has seen increasing popularity recently, especially with the effectiveness of deep learning methods growing. However, deep learning methods lack useful properties such as the lack of uncertainty quantification of their outputs and have a black-box nature. Neural ordinary differential equations (NODEs) use neural networks to define differential equations that propagate data from the inputs to the outputs. They can be seen as a continuous generalization of a popular network architecture used for image recognition known as the Residual Network (ResNet). This paper compares the performance of each network for machinery prognostics tasks to show the validity of Neural ODEs in machinery prognostics. The comparison is done using NASA’s Commercial Modular Aero-Propulsion System Simulation (C-MAPSS) dataset, which simulates the sensor information of degrading turbofan engines. To compare both architectures, they are set up as convolutional neural networks and the sensors are transformed to the time-frequency domain through the short-time Fourier transform (STFT). The spectrograms from the STFT are the input images to the networks and the output is the estimated RUL; hence, the task is turned into an image recognition task. The results found NODEs can compete with state-of-the-art machinery prognostics methods. While it does not beat the state-of-the-art method, it is close enough that it could warrant further research into using NODEs. The potential benefits of using NODEs instead of other network architectures are also discussed in this work.

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RUL estimation, Deep Learning, machinery prognostics

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