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11 April 2007 Characterizing the auto-bispectrum as a detector of nonlinearity in structural systems
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Higher-order spectra (HOS) appear often in the analysis and identification of nonlinear systems. The auto-bispectrum is one example of a HOS and is frequently used in the analysis of stationary structural response data to detect the presence of certain types structural nonlinearities. In this work we use a closed-form expression for the auto-bispectrum, derived previously by the authors, to find the bispectral frequency most sensitive to the nonlinearity. We then explore the properties of nonlinearity detectors based on estimates of the magnitude of the auto-bispectrum at this frequency. We specifically consider the case where the bispectrum is estimated using the direct method based on the Fourier Transform. The performance of the detector is quantified using a Receiver Operator Characteristic (ROC) curve illustrating the trade-off between Type-I error and power of detection (1-Type-II error). Theoretically derived ROC curves are compared to those obtained via numerical simulation. Results are presented for different levels of nonlinearity. Possible consequences are discussed with regard to the detection of damage-induced nonlinearities in structures.
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Jonathan M. Nichols, Attilio Milanese, and Pier Marzocca "Characterizing the auto-bispectrum as a detector of nonlinearity in structural systems", Proc. SPIE 6532, Health Monitoring of Structural and Biological Systems 2007, 65320X (11 April 2007);

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