Estimation of sensitivity coefficients of nonlinear model input parameters which have a multinormal distribution Original Research Article

This paper considers the estimation of sensitivity coefficients based on sequential random sampling when the input parameters of a nonlinear model are correlated and have a multinormal distribution. Due to the difficulties in generating sequential random samples for correlated model inputs and the properties of response surface models, sampling-based (simulation- and experiment-based) methods could not be used to estimate sensitivity coefficients of correlated model inputs. For this reason, an algorithm based on multi-expressions of multinormal distribution has been developed and used to generate sequential random samples for estimation of sensitivity coefficients. The multi-expression approach has very high accuracy in generating multinormal random samples. The estimated sensitivity coefficients based on sequential random samples changed when sample size changed. Most estimates converged with a sample size of 5000. Model structure mainly determined the speed of convergence. Both correlation among input parameters and model structure influenced the estimates of sensitivity coefficients. The sensitivity coefficients were compared to global partial derivatives that were computed using numerical integration.