Fleet Prognosis with Physics-informed Recurrent Neural Networks

Services and warranties of large fleets of engineering assets is a very profitable business. The success of companies in that area is often related to predictive maintenance driven by advanced analytics. Therefore, accurate modeling, as a way to understand how the complex interactions between operating conditions and component capability define useful life, is key for services profitability. Unfortunately, building prognosis models for large fleets is a daunting task as factors such as duty cycle variation, harsh environments, inadequate maintenance, and problems with mass production can lead to large discrepancies between designed and observed useful lives. This paper introduces a novel physics-informed neural network approach to prognosis by extending recurrent neural networks to cumulative damage models. We propose a new recurrent neural network cell designed to merge physics-informed and data-driven layers. With that, engineers and scientists have the chance to use physics-informed layers to model parts that are well understood (e.g., fatigue crack growth) and use data-driven layers to model parts that are poorly characterized (e.g., internal loads). A simple numerical experiment is used to present the main features of the proposed physics-informed recurrent neural network for damage accumulation. The test problem consist of predicting fatigue crack length for a synthetic fleet of airplanes subject to different mission mixes. The model is trained using full observation inputs (far-field loads) and very limited observation of outputs (crack length at inspection for only a portion of the fleet). The results demonstrate that our proposed hybrid physics-informed recurrent neural network is able to accurately model fatigue crack growth even when the observed distribution of crack length does not match with the (unobservable) fleet distribution.Comment: Data and codes (including our implementation for both the multi-layer perceptron, the stress intensity and Paris law layers, the cumulative damage cell, as well as python driver scripts) used in this manuscript are publicly available on GitHub at https://github.com/PML-UCF/pinn. The data and code are released under the MIT Licens

Hybrid Physics-informed Neural Networks for Dynamical Systems

Ordinary differential equations can describe many dynamic systems. When physics is well understood, the time-dependent responses are easily obtained numerically. The particular numerical method used for integration depends on the application. Unfortunately, when physics is not fully understood, the discrepancies between predictions and observed responses can be large and unacceptable. In this thesis, we show how to directly implement integration of ordinary differential equations through recurrent neural networks using Python. We leveraged modern machine learning frameworks, such as TensorFlow and Keras. Besides offering basic models capabilities (such as multilayer perceptrons and recurrent neural networks) and optimization methods, these frameworks offer powerful automatic differentiation. With that, our approach\u27s main advantage is that one can implement hybrid models combining physics-informed and data-driven kernels, where data-driven kernels are used to reduce the gap between predictions and observations. In order to illustrate our approach, we used two case studies. The first one consisted of performing fatigue crack growth integration through Euler\u27s forward method using a hybrid model combining a data-driven stress intensity range model with a physics-based crack length increment model. The second case study consisted of performing model parameter identification of a dynamic two-degree-of-freedom system through Runge-Kutta integration. Additionally, we performed a numerical experiment for fleet prognosis with hybrid models. The problem consists of predicting fatigue crack length for a fleet of aircraft. The hybrid models are trained using full input observations (far-field loads) and very limited output observations (crack length data for only a portion of the fleet). The results demonstrate that our proposed physics-informed recurrent neural network can model fatigue crack growth even when the observed distribution of crack length does not match the fleet distribution

Lithium-ion Battery Prognosis with Variational Hybrid Physics-informed Neural Networks

Lithium-ion batteries are an increasingly popular source of power for many electric applications. Applications range from electric cars, driven by thousands of people every day, to existing and future air vehicles, such as unmanned aircraft vehicles (UAVs) and urban air mobility (UAM) drones. Therefore, robust modeling approaches are essential to ensure high reliability levels by monitoring battery state-of-charge (SOC) and forecasting the remaining useful life (RUL). Building principled-based models is challenging due to the complex electrochemistry that governs battery operation, which would entail computationally expensive models not suited for prognosis and health management applications. Alternatively, reduced-order models can be used and have the advantage of capturing the overall behavior of battery discharge, although they suffer from simplifications and residual discrepancy. We propose a hybrid solution for Li-ion battery discharge and aging prediction that directly implements models based on first-principle within modern recurrent neural networks. While reduced-order models describe part of the voltage discharge under constant or variable loading conditions, data-driven kernels reduce the gap between predictions and observations. We developed and validated our approach using the NASA Prognostics Data Repository Battery dataset, which contains experimental discharge data on Li-ion batteries obtained in a controlled environment. Our hybrid model tracks aging parameters connected to the residual capacity of the battery. In addition, we use a Bayesian approach to merge fleet-wide data in the form of priors with battery-specific discharge cycles, where the battery capacity is fully available (complete data) or only partially available (censored data). The model\u27s predictive capability is monitored throughout battery usage. This way, our proposed approach indicates when significant updates to the hybrid model are needed. Our Bayesian implementation of the hybrid variational physics-informed neural network can reliably predict the battery\u27s future residual capacity, even in cases where previous battery usage history is unknown