Multivariate global sensitivity analysis for dynamic models based on wavelet analysis

Dynamic models with time-dependent output are widely used in engineering for risk assessment and decision making. Global sensitivity analysis for these models is very useful for simplifying the model, improving the model performance, etc. The existent covariance decomposition based global sensitivity analysis method combines the variance based sensitivity analysis results of the model output at all the instants, which just utilizes the information of the time-dependent output in time domain. However, many significant features of time-dependent output may not be obtained from the time domain. Thus, performing global sensitivity analysis for dynamic models just with the information in time domain may be incomplete. In this paper, a new kind of sensitivity indices based on wavelet analysis is proposed. The energy distribution of model output over different frequency bands is extracted as a quantitative feature of the time-dependent output, and it contains the information of model output in both time and frequency domains. Then, a vector projection method is utilized to measure the effects of input variables on the energy distribution of model output. An efficient algorithm is also proposed to estimate the new sensitivity indices. The numerical examples show the difference between the new sensitivity indices and the covariance decomposition based sensitivity indices. Finally, the new sensitivity indices are applied to an environmental model to tell the relative importance of the input variables, which can be useful for improving the model performance.