A Novel Demodulation Method with a Reference Signal for Operational Modal Analysis and Baseline-Free Damage Detection of a Beam Structure Under Random Excitation

Abstract

A novel demodulation method with a reference signal is developed for operational modal analysis and damage detection of a beam structure under random excitation. The novel demodulation method can process measurements of the beam by a continuously scanning laser Doppler vibrometer (CSLDV) system and measurements of a reference point on the beam by a single-point laser Doppler vibrometer to estimate its modal parameters, such as damped natural frequencies and undamped mode shapes. Damped natural frequencies of the beam are estimated from fast Fourier transforms of measurements of the CSLDV system. A cross-correlation function between a measurement of the CSLDV system and a measurement of a single-point laser Doppler vibrometer is calculated, and the cross-correlation function is multiplied by a sinusoidal signal whose frequency is an estimated damped natural frequency of the beam. The processed cross-correlation function is filtered by a low-pass filter to obtain the undamped mode shape of the beam that corresponds to its estimated damped natural frequency. Smooth polynomials are used to fit estimated undamped mode shapes of the beam, which can be considered as undamped mode shapes of an undamaged beam. Curvatures of estimated undamped mode shapes and polynomials are compared by curvature damage indices to determine the location of a damage in the beam. The novel demodulation method with a reference signal is investigated for baseline-free damage detection from both finite element simulation and experiment. Modal parameters of a finite element model of the damaged beam and a damaged beam specimen that are under random excitation are successfully estimated, and locations of damages in the beam model and beam specimen are accurately determined. The novel demodulation method with a reference signal can be used for estimating modal parameters of a beam structure under random excitation and identify locations of its damages, while a traditional demodulation method can only be used for estimating operational deflection shapes of a beam structure under sinusoidal excitation and identify locations of its damages. A lifting method that was developed for the CSLDV system can also be used for modal parameter estimation and baseline-free damage detection of a beam structure under random excitation, but it requires a high scan frequency. The novel demodulation method with a reference signal can estimate modal parameters of a beam structure and detect damages in it with a low scan frequency, which can be used for a beam structure with high natural frequencies.

Keywords: Continuously scanning laser Doppler vibrometer system, demodulation method, Random excitation, cross-correlation function, baseline-free damage detection