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, Therefore, the residuals are IID if x and y ? ? are used as the inputs and outputs of the ANN. Then, the algorithm described above is valid when the variance-covariance C is under the form of Eq.7. However
is used in this study for the consideration of input uncertainties in ANN-based GMPEs model. It consists in introducing the first order Taylor expansion of the GMPE model with input uncertainties. Considering uncertainty on input parameters, the model reads: y ij = µ(M w,i , ln R jb,ij , ln V s 30,j ) + ? i + ? ij = µ( ? M w,i + ?M i , ln R jb,ij , ln?Vln? ln?V s 30,j + ?V s j ), ANN GMPEs models with input uncertainties The FOSM method, 1997. ,
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