Robust-to-noise feature extraction via generalization of correlation relationship in the frequency domain

Damage diagnosis of a high-dimensional structural signal is a complicated and time-consuming task. In the worse case, if the signal is measured under noisy ambient loads, the extracted features lead to unreliable results in damage diagnosis. In this study, a robust feature extraction method is presented by using time series analysis and correlation relationship generalized in the frequency domain. At first, a time-series model of the response signal is obtained, and the parameters of the model containing inherent and dynamic characteristics of the signal are separated from the model residual, which is influenced by the noise of ambient loads. Upon measuring the model parameters, the high-dimensional signal is transferred to a space with a lower value in size, and the issues due to high-dimensional data are addressed. By using the obtained parameters, the characteristic function of the signal is calculated in the frequency domain. By utilizing a generalized correlation coefficient relationship in the frequency domain, a 2D damage-sensitive feature being a complex value can be extracted from the characteristic function. Structural damage is detected by investigating the angle of the feature extracted. Moreover, by attending to the real part of the feature, the location of damage can be identified. To investigate the abilities of the new feature in damage diagnosis tasks, a real-world structure, S101 Bridge, is examined. To demonstrate the advantages of the new feature in structural damage diagnosis, the outcomes of this study in different levels of damage diagnosis, i.e., damage detection and damage localization, are compared to some state-of-the-art techniques in the field of Structural Health Monitoring (SHM). The achievements of this study clearly show the abilities of the proposed feature for damage diagnosis of real-world structures, especially in the case of high-dimensional data and noisy ambient excitations. Moreover, in comparison to other techniques, the proposed damage diagnosis algorithm in this paper can detect and localize structural damage with more accuracy.