Nonparametric model and response analysis of the complex uncertain pipeline-casing system

The external pipeline system of an aero-engine comprises numerous components with parameter uncertainties, exhibiting high-dimensional uncertainty. When coupled with the casing, it significantly affects the system's vibration response. This paper incorporates such complex pipeline system into casing vibration environment analysis. For complex systems, parametric models prove computationally expensive and limited to known uncertainties, reducing their suitability. In contrast, nonparametric models grounded in random matrix (RM) theory - typically employed for non-parameterizable uncertainties - show strong potential for high-dimensional uncertainty problems. However, conventional nonparametric RM models contain practically meaningless entries, introducing deviations from true physical systems. To address this, this paper proposes a filtered nonparametric model that improves upon the direct nonparametric approach. The filtering process, requiring only entry-wise operations, further enhances computational efficiency. The paper establishes nonparametric models to characterize high-dimensional parameter uncertainty in the pipeline system, and provides an efficient unified framework for coupled pipeline-casing system response prediction. 2D and 3D numerical examples based on real aero-engine structures are developed. The results show that the proposed filtered method effectively avoids the error divergence observed in the direct method, achieving closer alignment with full parametric benchmarks. The validated asymptotic consistency - demonstrated by converging nonparametric and parametric results with increasing uncertainty dimensionality - establishes that nonparametric models can effectively characterize high-dimensional parametric uncertainties, extending their utility beyond conventional non-parameterizable uncertainty applications.