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1. Baseline-Free Structural Damage Identification for Beam-Like Structures Using Curvature Waveforms of Propagating Flexural Waves

   https://doi.org/10.3390/s21072453  

   Xu, Y. F. ; Kim, J. S. ( April 2021 , Sensors)

   null (Ed.)

   Curvatures in mode shapes and operating deflection shapes have been extensively studied for vibration-based structural damage identification in recent decades. Curvatures of mode shapes and operating deflection shapes have proved capable of localizing and manifesting local effects of damage on mode shapes and operating deflection shapes in forms of local anomalies. The damage can be inversely identified in the neighborhoods of the anomalies that exist in the curvatures. Meanwhile, propagating flexural waves have also been extensively studied for structural damage identification and proved to be effective, thanks to their high damage-sensitivity and long range of propagation. In this work, a baseline-free structural damage identification method is developed for beam-like structures using curvature waveforms of propagating flexural waves. A multi-resolution local-regression temporal-spatial curvature damage index (TSCDI) is defined in a pointwise manner. A two-dimensional auxiliary TSCDI and a one-dimensional auxiliary damage index are developed to further assist the identification. Two major advantages of the proposed method are: (1) curvature waveforms of propagating flexural waves have relatively high signal-to-noise ratios due to the use of a multi-resolution central finite difference scheme, so that the local effects of the damage can be manifested, and (2) the proposed method does not require quantitative knowledge of a pristine structure associated with a structure to be examined, such as its material properties, waveforms of propagating flexural waves and boundary conditions. Numerical and experimental investigations of the proposed method are conducted on damaged beam-like structures, and the effectiveness of the proposed method is verified by the results of the investigations. 

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2. Operational modal analysis using lifted continuously scanning laser Doppler vibrometer measurements and its application to baseline-free structural damage identification

   https://doi.org/10.1177/1077546318821154  

   Xu, YF ; Chen, Da-Ming ; Zhu, WD ( February 2019 , Journal of Vibration and Control)

   A continuously scanning laser Doppler vibrometer (CSLDV) system is capable of efficient and spatially dense vibration measurements by sweeping its laser spot along a scan path assigned on a structure. This paper proposes a new operational modal analysis (OMA) method based on a data processing method for CSLDV measurements of a structure, called the lifting method, under white-noise excitation and applies a baseline-free method to identify structural damage using estimated mode shapes from the OMA method. The lifting method enables transformation of raw CSLDV measurements into measurements at individual virtual measurement points, as if the latter were made by use of an ordinary scanning laser Doppler vibrometer in a step-wise manner. It is shown that a correlation function with nonnegative time delays between lifted CSLDV measurements at two virtual measurement points on a structure under white-noise excitation and its power spectrum contain modal parameters of the structure, that is, natural frequencies, modal damping ratios, and mode shapes. The modal parameters can be estimated by using a standard OMA algorithm. A major advantage of the proposed OMA method is that curvature mode shapes associated with mode shapes estimated by the method can reflect local anomaly caused by small-sized structural damage, while those estimated by other existing OMA methods that use CSLDV measurements cannot. Numerical and experimental investigations are conducted to study the OMA method and baseline-free structural damage identification method. In the experimental investigation, effects of the scan frequency of a CSLDV system on the two methods were studied. It is shown in both the numerical and experimental investigations that modal parameters can be accurately estimated by the OMA method and structural damage can be successfully identified in neighborhoods with consistently high values of curvature damage indices.

    

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3. Machine learning based novelty detection using modal analysis

   https://doi.org/10.1111/mice.12511  

   Ozdagli, Ali I. ; Koutsoukos, Xenofon ( November 2019 , Computer-Aided Civil and Infrastructure Engineering)

   Among many structural assessment methods, the change of modal characteristics is considered a well‐accepted damage detection method. However, the presence of environmental or operational variations may pollute the baseline and prevent a dependable assessment of the change. In recent years, the use of machine learning algorithms gained interest within structural health community, especially due to their ability and success in the elimination of ambient uncertainty. This paper proposes an end‐to‐end architecture to detect damage reliably by employing machine learning algorithms. The proposed approach streamlines (a) collection of structural response data, (b) modal analysis using system identification, (c) learning model, and (d) novelty detection. The proposed system aims to extract latent features of accessible modal parameters such as natural frequencies and mode shapes measured at undamaged target structure under temperature uncertainty and to reconstruct a new representation of these features that is similar to the original using well‐established machine learning methods for damage detection. The deviation between measured and reconstructed parameters, also known as novelty index, is the essential information for detecting critical changes in the system. The approach is evaluated by analyzing the structural response data obtained from finite element models and experimental structures. For the machine learning component of the approach, both principal component analysis (PCA) and autoencoder (AE) are examined. While mode shapes are known to be a well‐researched damage indicator in the literature, to our best knowledge, this research is the first time that unsupervised machine learning is applied using PCA and AE to utilize mode shapes in addition to natural frequencies for effective damage detection. The detection performance of this pipeline is compared to a similar approach where its learning model does not utilize mode shapes. The results demonstrate that the effectiveness of the damage detection under temperature variability improves significantly when mode shapes are used in the training of learning algorithm. Especially for small damages, the proposed algorithm performs better in discriminating system changes.

    

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4. Discrete Time Signal Localization Accuracy in Gaussian Noise at Low Signal to Noise Ratios

   https://doi.org/10.1109/ACCESS.2023.3322207  

   Hall, Chris ; Djordjevic, Ivan ( January 2023 , IEEE Access)

   Convolution and matched filtering are often used to detect a known signal in the presence of noise. The probability of detection and probability of missed detection are well known and widely used statistics. Oftentimes we are not only interested in the probability of detecting a signal but also accurately estimating when the signal occurred and the error statistics associated with that time measurement. Accurately representing the timing error is important for geolocation schemes, such as Time of Arrival (TOA) and Time Difference of Arrival (TDOA), as well as other applications. The Cramér Rao Lower Bound (CRLB) and other, tighter, bounds have been calculated for the error variance on Time of Arrival estimators. However, achieving these bounds requires an amount of interpolation be performed on the signal of interest that may be greater than computational constraints allow. Furthermore, at low Signal to Noise Ratios (SNRs), the probability distribution for the error is non-Gaussian and depends on the shape of the signal of interest. In this paper we introduce a method of characterizing the localization accuracy of the matched filtering operation when used to detect a discrete signal in Additive White Gaussian Noise (AWGN) without additional interpolation. The actual localization accuracy depends on the shape of the signal that is being detected. We develop a statistical method for analyzing the localization error probability mass function for arbitrary signal shapes at any SNR. Finally, we use our proposed analysis method to calculate the error probability mass functions for a few signals commonly used in detection scenarios. These illustrative results serve as examples of the kinds of statistical results that can be generated using our proposed method. The illustrative results demonstrate our method’s unique ability to calculate the non-Gaussian, and signal shape dependent, error distribution at low Signal to Noise Ratios. The error variance calculated using the proposed method is shown to closely track simulation results, deviating from the Cramér Rao Lower Bound at low Signal to Noise Ratios. 

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5. A modal‐based Kalman filtering framework for mode extraction and decomposition of damped structures

   https://doi.org/10.1111/mice.12963  

   Hwang, Jae‐Seung ; Kwon, Dae_Kun ; Kareem, Ahsan ( December 2022 , Computer-Aided Civil and Infrastructure Engineering)

   The mode shape is one of the important modal parameters that enables to visualize the intrinsic behavior of a structure as well as the quantity of interest by extracting or separating modal response from measurements. In this study, a new output‐only framework is proposed to extract modes using a modal‐based Kalman filter defined in the modal space and identify the mode shape by manipulating the correlation between the separated modes and the measured responses. It is also shown that the proposed framework can be extended to estimate the mode shapes of a non‐classically damped structure in state space when the state variable is constructed from the measured responses and applied to the modal‐based Kalman filter. The mode shape estimation framework proposed in this study was verified by numerical simulations and full‐scale measurements. From the verification examples and their results, it was noted that the proposed modal identification framework is not influenced by the presence of noise, and it can be applied to identify the state‐space mode shapes of non‐classically damped systems as well as systems with very closely distributed modes such as buildings equipped with tuned mass dampers.

    

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