A global surrogate model technique based on principal component analysis and Kriging for uncertainty propagation of dynamic systems

Dynamic systems modeled by computationally intensive numerical models with time-dependent output are common in engineering. Efficient uncertainty propagation of such dynamic models remains a challenging task, which requires accurate prediction of time-dependent output over the entire time domain. When the output is high-dimensional, the size and multivariate nature of the data will cause new computational challenges. In this case, principal component analysis (PCA) can be used to reduce the dimension of output, which retains several principle components (PCs) that account for nearly all the uncertainty of the dynamic output. Then the Kriging model can be constructed based on these PCs instead of the entire dynamic output, which is named as PCA-K method. Based on this idea, this paper, develops a global surrogate model technique called PCA-AK for efficient uncertainty propagation of dynamic systems in the considered time interval, and further improves the reliability analysis ability of PCA-K. An adaptive sampling method is used in PCA-AK, which selects more samples near the limit state function as the training samples. In order to test the applicability of PCA-K and PCA-AK for unknown problems, a more direct pre-judgment method is also proposed in the paper to determine the reconstruction error of the PCA first. Results show that both the PCA-K and PCA-AK can dramatically improve the efficiency of the uncertainty propagation of the dynamic systems with acceptable accuracy, while PCA-AK exhibits more advantages in reliability analysis.