Investigation On Uncertainty And Sensitivity Analysis Of Complex Systems And Its Application To Nonlinear Dynamics On Networks

Regarding the global uncertainty and sensitivity analysis,there have been extensive strategies for quantifying the output uncertainty with given input uncertainty,and for e-valuating the importance of individual parameters in the determination of model output.A general analytic method,however,is still missing.In this dissertation,what we are in?terested in is the establishment of a theoretical framework on uncertainty and sensitivity analysis of nonlinear models.Furthermore,we also consider the formation of continuous opinion dynamics on a scale-free network.Employing the Taylor series and assuming input independence,we first derive an an-alytic formula that characterizes the variance propagation from input parameters to the model output.This formula allows one to accurately determine the uncertainty in mod-el output according to the uncertainty in input parameters.By analyzing power-law and exponential functions,it is stated that the most widely used approximation that only con-tains the first order effect of input uncertainty is sufficiently good only if the model under discussion is almost linear or the input uncertainty is negligible.Nevertheless,if a model behaves non-linearly in the neighborhood of input parameters of non-negligible uncertain-ties,our analytic method is more beneficial for model analysis.With this method,we analyze the uncertainty and sensitivity of two social systems:the economic order quantity(EOQ)model and the wind power system.The above established method is then compared to Sobol’s one which is carried out with sampling-based strategy.Sobol’s method is most widely considered in global uncer-tainty and sensitivity analysis for models of absent input correlations.Results suggest that our analytic method is different from Sobol’s one only when the model under discussion involves non-linear interaction terms of input parameters.Regarding this phenomenon,we introduce a modification on the basis of Sobol’s method.It allows one to directly understand the difference of our method from Sobol’s one.We also generalize the analytic method to model analysis of input correlations.The generalized method allows one to evaluate the effects of input correlations on the model output.This helps decide whether or not we should consider the input correlations in practice.With numerical examples,we exhibit the effectiveness and validation of our method for general models.The method is also applied to the analysis of a deterministic HIV model.Finally,we consider the formation of continuous opinion dynamics on a scale-free network.The model is designed based on a virtual gambling mechanism.One-at-a-time-based theoretical analysis provides a deep comprehending of the roles of input parameters in the formation of opinion dynamics.Sampling-based analysis tells the importance of individual input parameters and of their interaction effects in determining the model output.