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Methods for sensitivity analysis and backward propagation of uncertainty applied on mathematical models in engineering applications

Abstract : Approaches for studying uncertainty are of great necessity in all disciplines. While the forward propagation of uncertainty has been investigated extensively, the backward propagation is still under studied. In this thesis, a new method for backward propagation of uncertainty is presented. The aim of this method is to determine the input uncertainty starting from the given data of the uncertain output. In parallel, sensitivity analysis methods are also of great necessity in revealing the influence of the inputs on the output in any modeling process. This helps in revealing the most significant inputs to be carried in an uncertainty study. In this work, the Sobol sensitivity analysis method, which is one of the most efficient global sensitivity analysis methods, is considered and its application framework is developed. This method relies on the computation of sensitivity indexes, called Sobol indexes. These indexes give the effect of the inputs on the output. Usually inputs in Sobol method are considered to vary as continuous random variables in order to compute the corresponding indexes. In this work, the Sobol method is demonstrated to give reliable results even when applied in the discrete case. In addition, another advancement for the application of the Sobol method is done by studying the variation of these indexes with respect to some factors of the model or some experimental conditions. The consequences and conclusions derived from the study of this variation help in determining different characteristics and information about the inputs. Moreover, these inferences allow the indication of the best experimental conditions at which estimation of the inputs can be done.
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Submitted on : Wednesday, December 5, 2018 - 11:05:10 AM
Last modification on : Saturday, August 15, 2020 - 4:39:37 AM
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  • HAL Id : tel-01945221, version 1


Iman Alhossen. Methods for sensitivity analysis and backward propagation of uncertainty applied on mathematical models in engineering applications. Mechanical engineering [physics.class-ph]. Université Paul Sabatier - Toulouse III, 2017. English. ⟨NNT : 2017TOU30314⟩. ⟨tel-01945221⟩



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