Cumulative Damage Modeling with Recurrent Neural Networks Renato Giorgiani Nascimento * and Felipe A. C. Viana † University of Central Florida, Orlando, Florida 32816 https://doi.org/10.2514/1.J059250 Maintenance of engineering assets (for example, aircraft, jet engines, and wind turbines) is a profitable business. Unfortunately, building models that estimate remaining useful life for large fleets is daunting due to factors such as duty cycle variation, harsh environments, inadequate maintenance, and mass production problems that cause discrepancies between designed and observed lives. We model cumulative damage through recurrent neural networks. Besides architectures such as long short-term memory and gated recurrent unit, we introduced a novel physics-informed approach. Essentially, we merge physics-informed and data-driven layers. With that, engineers and scientists can use physics-informed layers to model well understood phenomena (for example, fatigue crack growth) and use data-driven layers to model poorly characterized parts (for example, internal loads). A numerical experiment is used to present the main features of the proposed physics-informed recurrent neural network. The problem consists of predicting fatigue crack length for a fleet of aircraft. The 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. Nomenclature a = fatigue crack length a = state representing damage C, m = Paris law coefficients h = states representing the sequence t = time step x = input (observable) variables Δa = damage increment ΔK = stress intensity range ΔS = far-field stress I. Introduction P REDICTIVE models [1–4] are often used to model cumulative distress in critical components (diagnosis and prognosis) of engineering assets (e.g., aircraft, jet engines, and wind turbines). These models usually leverage data coming from design, manufac- turing, configuration, online sensors, historical records, inspection, maintenance, location, and satellite data. In terms of modeling, we believe most practitioners would agree that 1) machine learning models offer flexibility but tend to require large amounts of data, and b) physics-based models are grounded on first principles and require good understanding of physics of failure and degradation mechanisms. In practice, the decision between machine learning and physics-based models depends on factors such as existing knowledge (maybe even legacy models), amount and nature of data, accuracy and computational requirements, timelines for implementation, etc. The interested reader can find a discussion on how these concepts apply to defense systems in Refs. [5,6] and examples of industrial and commercial applications. ‡,§,¶,** The literature on the use of traditional and modern machine learning methods for diagnosis and prognosis is rich. For example, Si et al. [7] reviewed statistical data-driven approaches for prognoses that rely only on available past observed data and statistical models (regression, Brownian motion with drift, gamma processes, Markovian-based models, stochastic filtering-based models, hazard models, and hidden Markov models). Tamilselvan and Wang [8] discussed a multisensor health diagnosis and prognosis method using deep belief networks. They demonstrate how deep belief networks can model the probabi- listic transition between the health state and the damaged state in aircraft engines and power transformers. Interestingly, Son et al. [9] reported how they solved the same aircraft engine problem using the Wiener process combined with principal component analysis. Susto et al. [10] discussed how to approach the remaining useful life estima- tion using ensembles of classifiers. They based their work on tradi- tional support vector machines and k-nearest neighbors, and they tested it on estimating the remaining useful life of tungsten filaments used in ion implantation (important in semiconductor fabrication). Khan and Yairi [11] reviewed the application of deep learning in structural health management (simple autoencoders; denoising autoencoder; variational autoencoders; deep belief networks; restricted and deep Boltzmann machines; convolutional neural networks; and purely data-driven versions of recurrent neural networks, including the long short-term memory and gated recurrent units). They found that most approaches are still application specific (unfortunately, they did not find a clear way to select, design, or implement a deep learning architecture for structural health management). They also advise that a tradeoff study Received 19 November 2019; revision received 24 June 2020; accepted for publication 24 June 2020; published online 31 August 2020. Copyright © 2020 by Felipe A. C. Viana. Published by the American Institute of Aero- nautics and Astronautics, Inc., with permission. All requests for copying and permission to reprint should be submitted to CCC at www.copyright.com; employ the eISSN 1533-385X to initiate your request. See also AIAA Rights and Permissions www.aiaa.org/randp. *Graduate Research Assistant, Department of Mechanical and Aerospace Engineering; renato.gn@knights.ucf.edu. † Assistant Professor, Department of Mechanical and Aerospace Engineer- ing; viana@ucf.edu. Senior Member AIAA. ‡ “TrueChoice™ Commercial Services, ” GE Aviation Collaborators, 2019, https://www.geaviation.com/commercial/truechoice-commercial-services [retrieved 14 February 2019]. § “Siemens Service Programs and Agreements, ” Siemens Collaborators, 2019, http://www.industry.usa.siemens.com/services/us/en/industry-services/services- glance/service-programs-agreements/pages/service-programs-agreements.aspx [retrieved 14 February 2019]. ¶ “Engine Services–Lufthansa Technik AG, ” Lufthansa Technik AG Collaborators, 2019, https://www.lufthansa-technik.com/engine [retrieved 14 February 2019]. **“Gemini Energy Services: Wind Turbine Services, ” Gemini Energy Ser- vices Collaborators, 2019, http://www.geminienergyservices.com [retrieved 14 February 2019]. 5459 AIAA JOURNAL Vol. 58, No. 12, December 2020 Downloaded by Felipe Viana on December 15, 2020 | http://arc.aiaa.org | DOI: 10.2514/1.J059250