Johansen cointegration of frequency response functions contaminated with nonstationary colored noise for structural damage detection

This study proposes an effective damage detection method for laminated composite structures under the influence of nonstationary colored noise using condensed Frequency Response Functions (CFRFs) as damage-sensitive features (DSF). For structural health monitoring (SHM), the effect of FRF contamination with stationary white noise has primarily been explored for stationary white noise pollution, with only a few studies investigating contamination with highly correlated nonstationary colored noise, e.g., Brown noise. In the investigation, CFRFs are contaminated with signal noise produced by Brownian motion of two different signal-to-noise ratios, i.e., 20 and 10. This contamination leads to nonstationary patterns, which present a challenge for vibration-based damage detection. Therefore, in this study, a robust method based on Johansen cointegration - a concept from the field of econometrics - is developed. The proposed method aims at deriving a stationary representation of nonstationary measured CFRF signals to be subsequently fed into a sensitivity-based model-updating problem. To validate the method, it is applied to numerical examples of laminated composite plates with different numbers of ply orientations. The superior capabilities of the proposed method are demonstrated by comparing it against two state-of-the-art methods from the literature and a method based on the Sum of Unwrapped Instantaneous Hilbert Phase (SUIHP) of CFRFs previously developed by the authors. A novel metric based on the notion of mutual information is proposed to decipher why exactly the proposed method is superior to its preceding alternative. The results show that the new DSF can capture significantly more information from noisy CFRFs than the previously developed DSF. As such, for half of the cases, the proposed DSF was able to capture more than 80% of information from the colored-noisy CFRFs. This is in contrast to the previously developed method that can only capture less than 40% of information for all the cases.