Multivariate Coupling Sensitivity Analysis Method Based on a Back-Propagation Network and Its Application

Abstract

Sensitivity analysis is a technique for quantitatively analyzing the variation in a dependent variable caused by each independent variable. In this study, a global sensitivity analysis method is proposed that is suitable and effective for multivariable and nonlinear systems. Specifically, sensitivity is defined before nonlinear multipolynomial expansion is conducted according to the Taylor midvalue theorem to intuitively determine nonlinear relationships between the rate of change in the dependent variable and each independent variable. A back-propagation network is also used to determine these relationships. The detailed computational steps and methods for evaluating the results are provided. The proposed method was tested using computer simulation and with an actual hydrological engineering problem. Computer simulations aided the design of experimental plans directed at linear and nonlinear polynomials. The experimental results showed that sensitivity analysis of dependent variables and each independent variable depends on two main characteristics: (1) the relation mapped between dependent variables and each independent variable, and (2) the value of each independent variable. The randomness of the sample, the structure of the back-propagation network, and the parameters did not significantly affect the final sensitivity calculation results. Analysis of the hydrological engineering problem showed that, given antecedent runoff and precipitation, the main factor that affected runoff in the Nenjiang River basin during flood season was antecedent precipitation whereas antecedent runoff was the main factor in the nonflood season. These results were reasonable and consistent with hydrological laws. Based on theoretical experiments and an actual engineering example, this preliminary study demonstrated the feasibility and effectiveness of this method of global sensitivity analysis in addressing complex problems.