A generalized sensitivity analysis method based on variance and covariance decomposition of summatory functions for multi-input multi-output systems

Abstract Sensitivity analysis is a useful means to quantify the impact of a set of input variables on an output response. However, many traditional sensitivity analysis methods are applicable only to multi-input single-output (MISO) systems and are powerless for multi-input multi-output (MIMO) systems. This paper presents a global sensitivity analysis method based on variance and covariance decomposition (VCD-GSA) of summatory functions for MIMO systems. For a MIMO system with n input variables and m output responses, a set of summatory functions can be constructed by the addition and subtraction of any two output response functions. Each output response function is represented using this set of summatory functions. The variances and covariances of all the output responses are obtained by the integral calculation of the high-dimensional model representations(HDMRs) of these summatory functions. We define the total fluctuation by the sum of the variances and covariances on multiple responses, and the partial fluctuations by the sum of partial variances of a series of summatory functions. Subsequently, we define the s-order sensitivity index of the MIMO system by the ratio of the partial fluctuation on s-order function terms in HDMRs and total fluctuation. The variable sensitivity index is the sum of all of the s-order sensitivity indices, including the contribution of the input variable. The proposed VCD-GSA method is suitable for a uniform or Gaussian distribution . It is also suitable for some complex problems involving variables with correlation. Several numerical examples and engineering applications demonstrate the advantage and practicality of the proposed VCD-GSA method.