Accurate and efficient calculation of discrete correlation functions and power spectra

作者：Xu Y F; Liu J M; Zhu W D^*

来源：Journal of Sound and Vibration, 2015, 347: 246-265.

DOI：10.1016/j.jsv.2015.02.076

Operational modal analysis (OMA), or output only modal analysis, has been widely conducted especially when excitation applied on a structure is unknown or difficult to measure. Discrete cross correlation functions and cross power spectra between a reference data series and measured response data series are bases for OMA to identify modal properties of a structure. Such functions and spectra can be efficiently transformed from each other using the discrete Fourier transform (DFT) and inverse DFT (IDFT) based on the cross correlation theorem. However, a direct application of the theorem and transforms, including the DFT and IDFT, can yield physically erroneous results due to periodic extension of the OFT on a function of a finite length to be transformed, which is false most of the Lime. Padding zero series to ends of data series before applying the theorem and transforms can reduce the errors, but the results are still physically erroneous. A new methodology is developed in this work to calculate discrete cross correlation functions of non negative time delays and associated cross power spectra, referred to as half spectra, for OMA. The methodology can be extended to cross correlation functions of any time delays and associated cross power spectra, referred to as full spectra. The new methodology is computationally efficient due to use of the transforms. Data series are properly processed to avoid the errors caused by the periodic extension, and the resulting cross-correlation functions and associated cross-power spectra perfectly comply with their definitions. A coherence function, a convergence function, and a convergence index are introduced to evaluate qualities of measured cross-correlation functions and associated cross-power spectra. The new methodology was numerically and experimentally applied to an ideal two-degree-of-freedom (2-DOF) mass-spring-damper system and a damaged aluminum beam, respectively, and OMA was conducted using half spectra to estimate their natural frequencies, damping ratios, and mode shapes. Natural frequencies, damping ratios, and mode shapes of the 2-DOF system obtained from OMA agree well with theoretical ones from complex modal analysis; natural frequencies, damping ratios, and mode shapes of the beam from OMA agreed well with those from experimental modal analysis.

• 出版日期2015-7-7
• 单位哈尔滨工业大学