Bayesian Statistic Based Multivariate Gaussian Process Approach for Offline/Online Fatigue Crack Growth Prediction

Offline and online fatigue crack growth prediction of Aluminum 2024 compact-tension (CT) specimens under variable loading has been modeled, using multivariate Gaussian Process (GP) technique. The GP model is a Bayesian statistic stochastic model that projects the input space to an output space by probabilistically inferring the underlying nonlinear function. For the offline prediction, the input space of the model is trained with parameters that affect fatigue crack growth, such as the number of fatigue cycles, minimum load, maximum load, and load ratio. For the online prediction, the model input space is trained using piezoelectric sensor signal features rather than training the input space with loading parameters, which are difficult to measure in a real time scenario. Principal Component Analysis (PCA) is used to extract the principal features from sensor signals. In both the offline and online case, the output space is trained with known associated crack lengths or crack growth rates. Once the GP model is trained, a new output space for which the corresponding crack length or crack growth rate is not known, is predicted using the trained GP model. The models are validated through several numerical examples.