An analytical structural global sensitivity analysis method based on direct integral

In this paper, an analytical structural global sensitivity analysis (GSA) method based on direct integral is proposed to efficiently and precisely analyse the sensitivity of model variables. Sobol’ sensitivity analysis method can comprehensively analyse the influences of model variables and their interaction on model responses, but this method is usually involved in a series of high-dimensional and high-order integrals which are generally difficult to calculate directly. Therefore, a kind of optimal polynomial response surface is established to replace the original model based on the polynomial structure-selection of error reduction ratio. This optimal polynomial has the advantages of simple structure, high precision and strong anti-noise ability. So the multiple integrals can be conveniently and analytically operated to obtain the accurate first-order and interactive sensitivity indices through the established optimal polynomial model. Compared with Sobol’ sensitivity analysis method, this proposed method is more adaptable for the complex model and practical engineering problems as well as can meliorate the accuracy of GSA. Two numerical examples and two engineering applications are studied to illustrate the applicability and effectiveness of this method.