Damage Detection in Beam Structures Using Statistical Analysis of Hilbert-Huang Transformation of Measured Response

One of the main concerns for structures and infrastructures is to evaluate their reliability and functionality as they can suffer long-term damage due to gradual deterioration over time, or they can be imposed to natural or manmade hazards and overloading during their lifetime. Thus, Structural Health Monitoring (SHM) has been a hot research topic in order to introduce efficient methods and feasible techniques for evaluating, monitoring and improving structural reliability and life cycle management. The SHM process typically includes three stages: a) data acquisition: measurement of the structural responses using an array of sensors; b) extraction of damage-sensitive features; and c) analysis of extracted features to develop statistical models and estimate structure health condition.
During the last decades, vibration-based damage detection methods have been greatly developed. The purpose of these methods is to determine the resulting changes in structural properties including stiffness, natural frequency, mode shape and damping ratio of the structure. For example, the basis of the Fourier Transform (FT) method is to determine the structural modal parameters from the random vibration data in the frequency range. Since local damages mostly impact higher frequency modes which are hard to excite and detect, most of FT based methods are unable to detect local or light damages accurately. Therefore, time-frequency analysis is introduced to overcome the limitations of the Fourier method, the most important of which is not providing a frequency-time range of a signal. The first case of frequency-time analysis was the short-time Fourier transform method based on the Fourier transform of the data divided by the time window function. According to this method, the interaction between time and frequency is difficult due to the existence of the time window function. If the windows are smaller in the time segment, its accuracy increases and in the frequency domain it becomes less accurate.
The signal processing techniques such as wavelet transform and the Hilbert-Huang transform are playing an increasingly important role in structural health monitoring. Hilbert-Huang transform (HHT) is a novel signal-processing technique for analysing nonstationary and nonlinear signals. HHT method consists of empirical mode decomposition (EMD) and Hilbert transform (HT). According to this theory, the primary signals can be decomposed into different basic time-dependent intrinsic mode functions (IMFs) through the empirical mode decomposition (EMD). Afterward, instantaneous frequency and amplitude of each IMF can be obtained as Hilbert–Huang spectrum. The application of HHT based approaches in structural health monitoring has been widely studied through the numerical and experimental researches.
This paper proposes a damage detection method based on the amplitude coefficient correlation of responses of damaged and undamaged structures using Hilbert–Huang transform (HHT). Structural responses have been decomposed to intrinsic mode functions (IMFs) through the empirical mode decomposition (EMD) method and the changes appear in the first IMF. Therefore, every change on the original signal can be revealed on IMFs, since the original signal depends on IMFs. Also, these changes have an effect on the analytical signal and the Hilbert transform. The instantaneous amplitude in measured joints on the structure is calculated using the Hilbert transform of the first IMF of response. The coefficient correlation matrix of the damaged and undamaged elements is demonstrated by graphical diagram in order to estimate the location of the damage. In this research, the accuracy of proposed damage detection method has been verified by applying the method on a finite element model of two-span continuous concrete beam structure.
The concrete beam is 80 m long with two equal 40 m span bays covered by a concrete deck with 0.5 m thickness. The dynamic responses of the beam at all sensors have been obtained by numerical analysis of finite element model under triangular pulse loading. The responses were also contaminated with 2% random noise to consider measurement uncertainties. The damage has been modelled as stiffness reduction in a 1.25 m long segment of finite element model of beam. To evaluate the efficiency of the proposed method, different damage scenarios are studied.
IMFs of all responses at sensor locations were obtained by combination of EMD and HT, and the instantaneous frequency and amplitude of Hilbert were derived. Auto correlation of instantaneous amplitude of undamaged and damaged structures were calculated and introduced as Damage Index Correlation. According to the results, this method is able to trace the location of the damage by the comparison of the correlation coefficients. Therefore, the locations of damages in different scenarios were located with a variety of coefficients correlation in sensors. The results show that the proposed method can determine the location of the damage with an acceptable accuracy for low and moderate damage intensities in all damage scenarios.