A novel sensitivity analysis method for multi-input-multi-output structures considering non-probabilistic correlations

Abstract

In practical engineering, a multi-input-multi-output (MIMO) structure generally features a significant number of correlated input parameters and output responses. Sensitivity analysis is usually adopted to select key parameters for improving the computational efficiency of structural analysis and design processes. Traditional sensitivity analysis methods based on probabilistic models for MIMO structures may not reliably and efficiently derive the sensitivity indexes of correlated input parameters with limited samples. To solve the above problems, a novel sensitivity analysis method for MIMO structures considering non-probabilistic correlations is proposed to estimate the influence of uncertainties and correlations among the parameters on the responses in a unified framework. Firstly, a multidimensional parallelepiped (MP) model is employed to quantify the uncertainties and non-probabilistic correlations among the parameters. A new non-probabilistic variance propagation equation based on the MP model is then proposed to derive the non-probabilistic variances of output responses. The non-probabilistic independent, correlated, and total sensitivity indexes of each parameter for multi-input-single-output (MISO) structures are defined according to the non-probabilistic variance contribution rates. A dimensional normalization method and a vector projection method are then adopted to extend the non-probabilistic sensitivity indexes of each parameter for MIMO structures with correlations. Two numerical examples and an experimental example are exemplified to verify the proficiency and efficiency of the currently proposed method.