A comparative analysis of intrusive and non-intrusive PCE methods for random mode computation

Random eigenmodes present a significant challenge in the analysis of uncertain dynamical systems, particularly when traditional Monte Carlo methods become computationally prohibitive for high-dimensional problems. While Polynomial Chaos Expansion (PCE) offers a promising alternative, the choice between intrusive (physics-based) and non-intrusive (data-driven) implementations remains a critical yet understudied decision. This paper presents the first comprehensive comparison of these PCE approaches for random eigenmode computation, examining their theoretical foundations, implementation complexities, and computational efficiency. Through systematic analysis of a three-degree-of-freedom system with varying uncertainty parameters, we demonstrate that intrusive PCE achieves superior accuracy for low-dimensional problems, while non-intrusive PCE shows better scalability for higher-dimensional systems. Our findings reveal a previously undocumented trade-off between implementation complexity and computational efficiency, establishing clear criteria for approach selection based on problem dimensionality and accuracy requirements. These insights extend beyond modal analysis to the broader field of uncertainty quantification in computational mechanics, providing practical guidelines for selecting optimal PCE strategies in various engineering applications. The methodological framework presented here opens new possibilities for efficient uncertainty analysis in large-scale dynamical systems.