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Abstract:
We created a Physics-Informed Neural Network (PINN) to model the propagation of fatigue cracks. The analyzed object is a high-pressure Nozzle of an industrial gas turbine. The models are based on a Recurrent Neural Network with an embedded Feedforward Neural Network to estimate the stress intensity factor. The thermal stresses are calculated based on engine operational data, leveraging a Finite Element Analysis. However, the time series are available just for 54% of the start-stop cycles, and only 13 crack measures were recorded. Three separate models were trained based on ten, two, and one observation, respectively. The importance of the empirical data was regulated during the training to avoid solutions inconsistent with the underlying physics. The models generalize well and predict accurately also outside the training domain. Additionally, we propose a novel method of scaling models based on PINNs and transferring knowledge between domains. It enables predicting in the target domain, even if damage measures are unavailable. The obtained results confirm the effectiveness of this approach.

Keywords:
Physics-informed neural networks , Predictive maintenance , Fatigue cracks , Regression analysis , Small data , Turbomachinery

Abstract:
In this paper several statistical learning algorithms are used to predict the maximal length of fatigue cracks based on a sample composed of 31 observations. The small-data regime is still a problem for many professionals, especially in the areas where failures occur rarely. The analyzed object is a high-pressure Nozzle of a heavy-duty gas turbine. Operating parameters of the engines are used for the regression analysis. The following algorithms are used in this work: multiple linear and polynomial regression, random forest, kernel-based methods, AdaBoost and extreme gradient boosting and artificial neural networks. A substantial part of the paper provides advice on the effective selection of features. The paper explains how to process the dataset in order to reduce uncertainty; thus, simplifying the analysis of the results. The proposed loss and cost functions are custom and promote solutions accurately predicting the longest cracks. The obtained results confirm that some of the algorithms can accurately predict maximal lengths of the fatigue cracks, even if the sample is small.

Keywords:
empirical models, fatigue cracks, predictive maintenance, regression analysis, small data, statistical learning, turbomachinery