Uncertainty quantification for structural response field with ultra-high dimensions

Abstract

The structural response field is crucial for understanding mechanical behavior, especially under uncertain conditions. However, current uncertainty quantification predominantly address one-dimensional output under multi-dimensional input. For the structural full field response with ultra-high dimension, quantifying corresponding uncertainties becomes a formidable task. This paper introduces an efficient uncertainty quantification method for structural response field. Initially, the manifold learning is introduced to transform uncertainty quantification of ultra-high-dimensional responses into the quantification of low-dimensional manifold projections. Subsequently, polynomial chaos expansions facilitate uncertainty propagation, allowing for the effective evaluation of statistical moments for each projection. Leveraging the established manifold structure enables obtaining analytical solutions for statistical moments of full field responses without additional computational costs. In the absence of prior information, the derivative λ-PDF is utilized to model uncertainty of response at any position, so as to realize the visualization of uncertainty. The proposed uncertainty quantification for structural response field provides a non-intrusive analysis framework, which can conveniently deal with structural multi-field coupling problems. Finally, three engineering examples involving multi field coupling are presented to demonstrate the effectiveness and practicability of proposed uncertainty quantification of structural response field.