Wavelet spectrum analysis approach to model validation of dynamic systems

作者：Jiang Xiaomo^*; Mahadevan Sankaran

来源：Mechanical Systems and Signal Processing, 2011, 25(2): 575-590.

DOI：10.1016/j.ymssp.2010.05.012

• Wavelet coherence analysis
• Wavelet cross-spectra
• Model validation
• Hypothesis test
• Dynamic system

Feature-based validation techniques for dynamic system models could be unreliable for nonlinear, stochastic, and transient dynamic behavior, where the time series is usually non-stationary. This paper presents a wavelet spectral analysis approach to validate a computational model for a dynamic system. Continuous wavelet transform is performed on the time series data for both model prediction and experimental observation using a Morlet wavelet function. The wavelet cross-spectrum is calculated for the two sets of data to construct a time-frequency phase difference map. The Box-plot, an exploratory data analysis technique, is applied to interpret the phase difference for validation purposes. In addition, wavelet time-frequency coherence is calculated using the locally and globally smoothed wavelet power spectra of the two data sets. Significance tests are performed to quantitatively verify whether the wavelet time-varying coherence is significant at a specific time and frequency point, considering uncertainties in both predicted and observed time series data. The proposed wavelet spectrum analysis approach is illustrated with a dynamics validation challenge problem developed at the Sandia National Laboratories. A comparison study is conducted to demonstrate the advantages of the proposed methodologies over classical frequency-independent cross-correlation analysis and time-independent cross-coherence analysis for the validation of dynamic systems.

• 出版日期2011-2