Bayesian wavelet method for multivariate model assessment of dynamic systems

In this paper an energy-based Bayesian wavelet method is presented for validation assessment of multivariate predictive models under uncertainty, using time-series data collected from a dynamic system. Time history data are decomposed into multiple time–frequency resolutions using a discrete wavelet packet transform method. As a signal feature, wavelet packet component energy is computed in terms of the decomposed coefficients. The effectiveness of the selected feature is assessed using both cross-correlation and cross-coherence metrics. A generalized likelihood ratio is derived as a quantitative validation metric based on Bayes’ theorem and Gaussian distribution assumption of errors of the wavelet packet component energy between validation data and model prediction. The multivariate model is then assessed based on the Bayesian point and interval hypothesis testing approaches. The probability density function of the likelihood ratio is constructed using the statistics of multiple response quantities and Monte Carlo simulation. The proposed methodology is implemented in the validation of a structural dynamics problem, using multivariate time-series data sets. Sensitivity analysis is also performed to investigate the effect of parameter selection on the model validation decision.