Transfer learning of degradation modeling and prognosis based on multivariate functional analysis with heterogeneous sampling rates

Multivariate functional principal component analysis (MFPCA) is a widely used tool for modeling and prognosis of degradation signals. However, MFPCA usually assumes samples from each process share the same sampling rate. To relax this assumption and facilitate the information sharing among multiple degradation processes, we propose a transfer learning framework to conduct modeling and prognosis of degradation data with heterogeneous sampling rates. This framework features the flexible modeling capability and focuses on transferring degradation information from correlated processes to the prognosis of an interested (target) process. More specifically, we use kernel smoothing to handle the heterogeneous sampling rates so that the mean and covariance in each sample can be successfully estimated. Then, the conditional expectation is developed to estimate the MFPC scores, which contain correlation information among processes. These MFPC scores are then updated in a Bayesian way by incorporating the observed data from the in-service unit in the target process. The updated MFPC scores deliver a superior performance of prognosis. The proposed method is validated and compared with various benchmarks in extensive numerical studies and one case study. The results show the proposed method can successfully handle the issue of heterogeneous sampling rates and provide an improved prognosis result.