# Fleet Prognosis with Physics-informed Recurrent Neural Networks

**Authors:** Renato Giorgiani Nascimento, Felipe A. C. Viana  
**arXiv:** [1901.05512](https://arxiv.org/abs/1901.05512)  
**Date:** 2019-01-16  
**Summary page:** https://www.summarizepaper.com/en/paper/1901.05512v1/

## Key points

- Services and warranties of large fleets of engineering assets are highly profitable
- Success in this area relies on predictive maintenance driven by advanced analytics
- Accurate modeling is crucial for understanding complex interactions between operating conditions and component capability
- Building prognosis models for large fleets can be challenging due to various factors
- A novel approach using physics-informed recurrent neural networks (RNNs) extended to cumulative damage models is introduced
- The proposed RNN cell merges physics-informed and data-driven layers, allowing for modeling of well-understood and poorly characterized parts
- A numerical experiment is conducted to demonstrate the effectiveness of the approach in predicting fatigue crack length in a synthetic fleet of airplanes
- Despite differences in observed and unobservable crack length distributions, the hybrid physics-informed RNN accurately models fatigue crack growth
- The approach combines physics-informed and data-driven approaches within recurrent neural networks for fleet prognosis
- It has the potential to improve accuracy in modeling complex interactions in large fleets of engineering assets

## Summary

The services and warranties of large fleets of engineering assets are highly profitable, with the success of companies in this area often relying on predictive maintenance driven by advanced analytics. Accurate modeling plays a crucial role in understanding how complex interactions between operating conditions and component capability define useful life, ultimately impacting services profitability. However, building prognosis models for large fleets can be challenging due to factors such as duty cycle variation, harsh environments, inadequate maintenance, and problems with mass production. To address these challenges, this paper introduces a novel approach to prognosis using physics-informed recurrent neural networks (RNNs) extended to cumulative damage models. The proposed RNN cell is designed to merge physics-informed and data-driven layers, providing engineers and scientists with the opportunity to model well-understood parts (e.g., fatigue crack growth) using physics-informed layers and poorly characterized parts (e.g., internal loads) using data-driven layers. To demonstrate the effectiveness of this approach, a simple numerical experiment is conducted. The experiment involves predicting fatigue crack length for a synthetic fleet of airplanes subjected to different mission mixes. The model is trained using full observation inputs (far-field loads) but limited observation outputs (crack length at inspection for only a portion of the fleet). Despite the observed distribution of crack length not matching the unobservable fleet distribution, the results show that the proposed hybrid physics-informed RNN accurately models fatigue crack growth. In conclusion, this paper presents an innovative method for fleet prognosis by combining physics-informed and data-driven approaches within recurrent neural networks. This approach has the potential to significantly improve accuracy in modeling complex interactions between operating conditions and component capability in large fleets of engineering assets. The availability of publicly accessible data and code further enhances its practical applicability.