Non-probabilistic sensitivity analysis method for multi-input-multi-output structures considering correlations

Sensitivity analysis is an important step to investigate the influence level of input parameters on output responses. However, many traditional sensitivity analysis methods based on probability models are difficult to apply to multi-input-multi-output (MIMO) structures with limited samples. To solve the above issues, a sensitivity analysis method for MIMO structures based on non-probabilistic (NP) variance considering correlations is proposed. Firstly, the sensitivity analysis problems can be categorized into two groups based on multiple-input multiple-output (MIMO) structures and multiple-input single-output (MISO) structures. Secondly, the multidimensional ellipsoidal model is adopted to quantify the NP uncertainties and correlations of input parameters with limited samples. Subsequently, the NP variance propagation equation is newly derived to evaluate the NP variance of the output responses. More importantly, the NP variance of output responses is decomposed as the NP variance and NP covariance items of each parameter and the total contribution, independent contribution, and correlated contribution are defined to quantify the influence level of each input parameter on the NP variances of output responses for MISO and MIMO structures. Finally, two numerical examples and two experimental examples are investigated to verify the accuracy and effectiveness of the proposed method.