تجزیه و تحلیل حساسیت در حضور مدل عدم اطمینان و ورودی های همبسته

The first motivation of this work is to take into account model uncertainty in sensitivity analysis (SA). We present with some examples, a methodology to treat uncertainty due to a mutation of the studied model. Development of this methodology has highlighted an important problem, frequently encountered in SA: how to interpret sensitivity indices when random inputs are non-independent? This paper suggests a strategy for the problem of SA of models with non-independent random inputs. We propose a new application of the multidimensional generalization of classical sensitivity indices, resulting from group sensitivities (sensitivity of the output of the model to a group of inputs), and describe an estimation method based on Monte-Carlo simulations. Practical and theoretical applications illustrate the interest of this method.

In many fields like structural reliability, behavior of thermohydraulic systems, or nuclear safety, mathematical models are used for simulation, when experiments are too expensive or even impracticable, and for prediction. In this context, sensitivity analysis (SA) tries to answer the following question: how does the output depend on its uncertain inputs? Application for SA are model calibration or model validation, and decision making process, where it is generally very useful to know which variables mostly contribute to output variability. We distinguish two classes in SA: local SA and global SA. Local SA studies how little variations of inputs around a given value change the value of the output. Global SA takes into account all the variation range of the inputs, and tries to apportion the output uncertainty to the uncertainty in the input factors. We review quickly in Section 2 a class of global SA methods based on decomposing the variance output. The purpose of our works is to take into account a type of model uncertainty in SA, which is often encountered in practice: consider that a model, on which SA has been made is subsequently modified. In this case, is it possible to obtain information about SA of the transformed model, without doing a new complete SA, but by using instead results obtained from the original model? In Section 3, we present some useful strategies to answer this question. For some possible mutations, sensitivity indices of the transformed model can be formally related to those of original model. We also present in Section 4, a new application of group sensitivities (sensitivity of the output of the model to a group of inputs), for models with non-independent input factors.

Two lines of investigation have been described in this paper. The first concerns the computation of sensitivity indices for transformed models for a few tractable cases. Practical applications on a radiological impact software are presented. In the second, we applied group sensitivities for models with correlated inputs. This work is illustrated by an application in nuclear engineering, on a computer code with a large number of inputs. Further developments are envisaged, concerning faster estimation of group sensitivity indices. Another application of works on model mutation is the taking into account in SA of the error due to the use of response surface. This application is introduced in [13].,