Physics-informed Gaussian process probabilistic modeling with multi-source data for prognostics of degradation processes

The integration of physics-based and data-driven methods in prognostics has become increasingly important in understanding the underlying degradation process using available knowledge. In this paper, we propose a physics-informed Gaussian process modeling method with multi-source data (PIGP-MD) that improves the predictive power of standard Gaussian process model by incorporating the prior knowledge from both physical models and historical data, and the current knowledge from limited observation data. We first propose a PIGP modeling method that incorporates the prior knowledge solely from physical models. In PIGP, a standard GP directly trained with current observation data is used to truncate the random realizations generated from physical models within the confidence bounds of the GP prediction. The truncated random realizations are used to derive the PIGP's nonstationary priors including the mean and autocovariance functions, as the unknown stochastic degradation process is considered as a nonstationary Gaussian process. Built upon PIGP, we propose PIGP-MD to filter credible knowledge from historical data. Some random realizations are generated from the credible knowledge from historical data and combined with the truncated random realizations generated from physical models. The combined random realizations are used to derive the nonstationary priors of PIGP-MD in the same way. With the physics model-informed and historical data-driven nonstationary priors as well as the current observation data, we can efficiently obtain the posterior future prediction without any parameter optimization. We demonstrate the applicability and efficacy of our proposed method for fatigue damage prognostics.