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Identifying modal parameters from vibration measurements is an essential step for modal analysis and modeling of structural dynamics. A critical challenge in modal parameter identification is the determination of the physical modes from spurious modes, especially with noisy measurement data. In this study, an approach is presented to enable automated identification of modal parameters by quantifying the spatial features of full-field, high-spatial-resolution response measurements. Specifically, it is derived that the local variances of the physical and spurious mode shapes are drastically distinguishing, especially when the spatial resolution of the response measurement is high (i.e., full-field with dense spatial measurement points). This allows an effective identification of the physical modes from spurious. Experimental studies are conducted on a few structural models and detailed comparisons are performed and discussed between the presented method and existing methods, including parametric and non-parametric. • A new approach for automatically distinguishing spurious and physical modes. • Full-field measurements allow spatial and statistical analysis of mode shapes. • Local variances of physical and spurious mode shapes form well-separated clusters. • Performance is compared to existing methods both numerically and experimentally. [ABSTRACT FROM AUTHOR]

Experimental or operational modal analysis traditionally requires physically-attached wired or wireless sensors for vibration measurement of structures. This instrumentation can result in mass-loading on lightweight structures, and is costly and time-consuming to install and maintain on large civil structures, especially for long-term applications (e.g., structural health monitoring) that require significant maintenance for cabling (wired sensors) or periodic replacement of the energy supply (wireless sensors). Moreover, these sensors are typically placed at a limited number of discrete locations, providing low spatial sensing resolution that is hardly sufficient for modal-based damage localization, or model correlation and updating for larger-scale structures. Non-contact measurement methods such as scanning laser vibrometers provide high-resolution sensing capacity without the mass-loading effect; however, they make sequential measurements that require considerable acquisition time. As an alternative non-contact method, digital video cameras are relatively low-cost, agile, and provide high spatial resolution, simultaneous, measurements. Combined with vision based algorithms (e.g., image correlation, optical flow), video camera based measurements have been successfully used for vibration measurements and subsequent modal analysis, based on techniques such as the digital image correlation (DIC) and the point-tracking. However, they typically require speckle pattern or high-contrast markers to be placed on the surface of structures, which poses challenges when the measurement area is large or inaccessible. This work explores advanced computer vision and video processing algorithms to develop a novel video measurement and vision-based operational (output-only) modal analysis method that alleviate the need of structural surface preparation associated with existing vision-based methods and can be implemented in a relatively efficient and autonomous manner with little user supervision and calibration. First a multi-scale image processing method is applied on the frames of the video of a vibrating structure to extract the local pixel phases that encode local structural vibration, establishing a full-field spatiotemporal motion matrix. Then a high-spatial dimensional, yet low-modal-dimensional, over-complete model is used to represent the extracted full-field motion matrix using modal superposition, which is physically connected and manipulated by a family of unsupervised learning models and techniques, respectively. Thus, the proposed method is able to blindly extract modal frequencies, damping ratios, and full-field (as many points as the pixel number of the video frame) mode shapes from line of sight video measurements of the structure. The method is validated by laboratory experiments on a bench-scale building structure and a cantilever beam. Its ability for output (video measurements)-only identification and visualization of the weakly-excited mode is demonstrated and several issues with its implementation are discussed. [ABSTRACT FROM AUTHOR]

Randomly missing data of structural vibration responses time history often occurs in structural dynamics and health monitoring. For example, structural vibration responses are often corrupted by outliers or erroneous measurements due to sensor malfunction; in wireless sensing platforms, data loss during wireless communication is a common issue. Besides, to alleviate the wireless data sampling or communication burden, certain accounts of data are often discarded during sampling or before transmission. In these and other applications, recovery of the randomly missing structural vibration responses from the available, incomplete data, is essential for system identification and structural health monitoring; it is an ill-posed inverse problem, however. This paper explicitly harnesses the data structure itself—of the structural vibration responses—to address this (inverse) problem. What is relevant is an empirical, but often practically true, observation, that is, typically there are only few modes active in the structural vibration responses; hence a sparse representation (in frequency domain) of the single-channel data vector, or, a low-rank structure (by singular value decomposition) of the multi-channel data matrix. Exploiting such prior knowledge of data structure (intra-channel sparse or inter-channel low-rank), the new theories of ℓ 1 -minimization sparse recovery and nuclear-norm-minimization low-rank matrix completion enable recovery of the randomly missing or corrupted structural vibration response data. The performance of these two alternatives, in terms of recovery accuracy and computational time under different data missing rates, is investigated on a few structural vibration response data sets—the seismic responses of the super high-rise Canton Tower and the structural health monitoring accelerations of a real large-scale cable-stayed bridge. Encouraging results are obtained and the applicability and limitation of the presented methods are discussed. [ABSTRACT FROM AUTHOR]

Modal identification or testing of structures consists of two phases, namely, data acquisition and data analysis. Some structures, such as aircrafts, high-speed machines, and plate-like civil structures, have active modes in the high-frequency range when subjected to high-speed or broadband excitation in their operational conditions. In the data acquisition stage, the Shannon–Nyquist sampling theorem indicates that capturing the high-frequency modes (signals) requires uniform high-rate sampling, resulting in sensing too many samples, which potentially impose burdens on the data transfer (especially in wireless platform) and data analysis stage. This paper explores a new-emerging, alternative, signal sampling and analysis technique, compressed sensing, and investigates the feasibility of a new method for output-only modal identification of structures in a non-uniform low-rate random sensing framework based on a combination of compressed sensing (CS) and blind source separation (BSS). Specifically, in the data acquisition stage, CS sensors sample few non-uniform low-rate random measurements of the structural responses signals, which turn out to be sufficient to capture the underlying mode information. Then in the data analysis stage, the proposed method uses the BSS technique, complexity pursuit (CP) recently explored by the authors, to directly decouple the non-uniform low-rate random samples of the structural responses, simultaneously yielding the mode shape matrix as well as the non-uniform low-rate random samples of the modal responses. Finally, CS with ℓ 1 -minimization recovers the uniform high-rate modal response from the CP-decoupled non-uniform low-rate random samples of the modal response, thereby enabling estimation of the frequency and damping ratio. Because CS sensors are currently in laboratory prototypes and not yet commercially available, their functionality—randomly sensing few non-uniform samples—is simulated in this study, which is performed on the examples of a numerical structural model, an experimental bench-scale structural model, and a real-world seismic-excited base-isolated hospital buildings. Results show that the proposed method in the CS framework can identify the modes using non-uniform low-rate random sensing, which is far below what is required by the Nyquist sampling theorem. [ABSTRACT FROM AUTHOR]

Abstract: This paper proposes a novel output-only damage identification method based on the unsupervised blind source separation (BSS) technique termed independent component analysis (ICA). It is discovered that ICA biases to extract sparse component, which typically indicates damage, from the observed mixture signals. The measured structural responses are first preprocessed by wavelet transform (WT). The wavelet-domain signals are then fed as mixtures into the BSS model, which is solved by ICA. The obtained “interesting” source with sharp spike and its associated spatial signature in the recovered mixing matrix reveal damage instant and location respectively. Following which, identification of the time-varying modes is carried out by ICA using the structural responses before and after the identified damage instant. For illustration, numerical simulations are conducted, where damage is modeled by abrupt stiffness variation in the time-varying system. Experimental and real-world seismic-excited structure examples with time-varying stiffness are also presented to illustrate the capability of the developed WT–ICA method. Results show that the WT–ICA algorithm realizes accurate and robust blind identification of damage instant and location in single or multiple damage events. [Copyright &y& Elsevier]

Abstract: This paper addresses two problems in structural damage identification: locating damage and assessing damage severity, which are incorporated into the classification framework based on the theory of sparse representation (SR) and compressed sensing (CS). The sparsity nature implied in the classification problem itself is exploited, establishing a sparse representation framework for damage identification. Specifically, the proposed method consists of two steps: feature extraction and classification. In the feature extraction step, the modal features of both the test structure and the reference structure model are first blindly extracted by the unsupervised complexity pursuit (CP) algorithm. Then in the classification step, expressing the test modal feature as a linear combination of the bases of the over-complete reference feature dictionary—constructed by concatenating all modal features of all candidate damage classes—builds a highly underdetermined linear system of equations with an underlying sparse representation, which can be correctly recovered by -minimization; the non-zero entry in the recovered sparse representation directly assigns the damage class which the test structure (feature) belongs to. The two-step CP–SR damage identification method alleviates the training process required by traditional pattern recognition based methods. In addition, the reference feature dictionary can be of small size by formulating the issues of locating damage and assessing damage extent as a two-stage procedure and by taking advantage of the robustness of the SR framework. Numerical simulations and experimental study are conducted to verify the developed CP–SR method. The problems of identifying multiple damage, using limited sensors and partial features, and the performance under heavy noise and random excitation are investigated, and promising results are obtained. [Copyright &y& Elsevier]

Full-field measurements of structural vibrations have been achieved by incoherent optical methods with video cameras such as digital image correlation and optical flow. In contrast to coherent optical methods such as scanning laser vibrometers, incoherent optical methods are low-cost and easy to set up. However, the sensitivity (minimum measurable displacement) of incoherent optical methods is generally lower than that of coherent optical methods. Typically, the sensitivity of incoherent optical methods is essentially limited by the finite bit depth of the digital camera due to the quantization with round-off errors. Quantitatively, this theoretical sensitivity limit is determined by the bit depth B as δ p = 1 / (2 B − 1) [pixel] which corresponds to a displacement causing an intensity change of one gray level. Fortunately, natural dithering may be leveraged to overcome the quantization and exceed the sensitivity limit, achieving super -sensitivity. In this work, we first study the mechanism of the sensitivity limit induced by the quantization and the critical limitation of existing super-sensitivity methods in the full-field measurement of structural vibration. Addressing such a limitation, we present a general adaptive weighted averaging method with dithering, achieving super -sensitivity incoherent optical measurement of full-field deformational vibration of flexible structures. Specifically, both spatial and temporal samplings of the pixels are leveraged simultaneously to adaptively identify the motion (deformation) shape of the structure by principal component analysis (PCA) of spatiotemporal pixel intensities. Then, the identified deformation shape is used to perform a deformation-shape-weighted averaging over spatial pixels with dithering, revealing the sub -sensitivity displacement while retaining spatial resolution at full field. Numerical simulations and laboratory experiments are performed for principle explanation and method validation. Particularly, we derive a mathematical model of the minimum measurable vibration amplitude A ∗ for the developed super-sensitivity method, which is found to be determined by the number of spatial pixels for averaging N s and the noise level σ n in the imaging system. Thus, this work provides, for the first time, a rigorous quantification of the sensitivity of incoherent optical measurement for structural vibration, and a new quantitative method to achieve super-sensitivity full-field measurement of structural vibration. • The sensitivity of incoherent optical measurement is limited by the finite bit depth. • A super-sensitivity full-field structural vibration measurement method is proposed • Numerical simulations and laboratory experiments are conducted for method validation. • The model of the minimum measurable vibration amplitude is obtained. [ABSTRACT FROM AUTHOR]

Video-based measurement has received increased attention for modal analysis and nondestructive evaluation, playing an important role in the development of the next-generation structural sensing technologies. As these techniques have evolved, more quantitative approaches based on computer vision techniques have emerged on full-field unsupervised structural identification, exploiting the benefits provided by the use of video cameras such as high spatial sensor density and low installation costs. More recent work has started to explore the use of laser point cloud data for 3D mapping of scenes and structures. Sensors such as LIDAR provide huge amounts of measurements at high spatial resolution from which it is possible to estimate accurate structural geometry for applications such as the generation of CAD models. Unfortunately to-date, the frame rate and depth resolution of LIDAR and other sensors capable of 3D geometry measurements has not been sufficient for measuring structural dynamics. In this paper, we introduce an approach for efficient and extremely high resolution 3D structural dynamic identification/modal analysis from point cloud data acquired using a commercial, low-cost, time-of-flight imager. Vibration mode shapes and modal coordinates are extracted from this data by creating virtual Lagrangian sensors based on the point clouds parameters. First, time-varying point cloud data are collected from a vibrating structure. Then, a mesh of virtual sensors is created based on the dynamic point cloud data for tracking the structure's displacement over time. Next solutions to the blind source separation problem are employed to estimate high resolution 3D mode shapes, modal coordinates, and resonant frequencies. We demonstrate the potential of our proposed approach on laboratory tests and compare the results to the data collected from conventional laser displacement sensors. This technique represents an advance towards efficiently exploring the full advantages of using dynamic point cloud data for practical monitoring applications and has the potential to be extended for a wide range of 3D motion decomposition problems. • Computer vision technique for estimating 3D vibration modes. • This is the first attempt to exploit dynamic point clouds for structural dynamics. • A time-of-flight imager is employed to obtain dynamic measurements. • Vibration modes are estimated from the dynamic data by forming virtual sensors. • Modal estimation is blindly achieved by dimension reduction and BSS algorithms. • The technique is experimentally compared to results obtained from laser data. [ABSTRACT FROM AUTHOR]

• Computer vision for modal analysis. • Architecture independent of image pre-processing. • Results superior to conventional vibration measurement techniques. The conventional modal analysis involves physically-attached wired or wireless sensors for vibration measurement of structures. However, this method has certain disadvantages, owing to the sensor's weight and its low spatial resolution, which limits the analysis precision or the high cost of optical vibration sensors. Besides, the sensor installation and calibration in itself is a time consuming and labor-intensive process. Non-contact computer vision-based vibration measurement techniques can address the shortcomings mentioned above. In this paper, we introduce CNN-LSTM (Convolutional Neural Network, Long Short-Term Memory) deep learning based approach that can serve as a backbone for computer vision-based vibration measurement techniques. The key idea is to use each pixel of an image taken from an off the shelf camera, encapsulating the Spatio-temporal information, like a sensor to capture the modal frequencies of a vibrating structure. Non-contact "pixel-sensor" does not alter the system's dynamics and is relatively low-cost, agile, and provides measurements with very high spatial resolution. Our computer vision-based deep learning model takes the video of a vibrating structure as input and outputs the fundamental modal frequencies. We demonstrate, using reliable empirical results, that "pixel-sensor" is more efficient, autonomous, and accurate. Robustness of the deep learning model has been put to the test by using specimens of a variety of materials, and varying dimensions and results have shown high levels of sensing accuracy. [ABSTRACT FROM AUTHOR]