Propagation of Modeling Uncertainty by Polynomial Chaos Expansion in Multidisciplinary Analysis

Multidisciplinary analysis (MDA) is nowadays a powerful tool for analysis and optimization of complex systems. The present study is interested in the case where MDA involves feedback loops between disciplines (i.e. the output of a discipline is the input of another and vice-versa). When the models for each discipline involve non-negligible modeling uncertainties, it is important to be able to efficiently propagate these uncertainties to the outputs of the MDA. The present study introduces a polynomial chaos expansion (PCE) based approach to propagate modeling uncertainties in MDA. It is assumed that the response of each disciplinary solver is affected by an uncertainty modeled by a random field over the design and coupling variables space. A semi intrusive PCE formulation of the problem is proposed to solve the corresponding nonlinear stochastic system. Application of the proposed method S.Dubreuil, MD-16-1194 1 emphasizes an important particular case in which each disciplinary solver is replaced by a surrogate model (e.g. kriging). Three application problems are treated, which show that the proposed approach can approximate arbitrary (non Gaussian) distributions very well at significantly reduced computational cost. Nomenclature x Lower case letter denoted deterministic variables (scalar or vector). X Upper case letter denoted random variables (scalar or vector). x (k 0) An exponent in parenthesis is used to set the value of the variable, i.e. x (k 0) is a given value of the deterministic variable x.

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