Full-field Mode Research Articles

A novel framework and validation for the dynamic characterization of civil structures via ground-based lidar

While there has been substantial research conducted on the use of Ground-Based Lidar (GBL; i.e., Terrestrial Laser Scanners) in monitoring the static deformation of civil structures, its application in monitoring dynamic vibrations of structures, which is critical for structural health monitoring (SHM), has only been studied to a limited extent. Traditional contact-based SHM frameworks are constrained by a limited number of sensors and the need for physical access for instrumentation placement. Although recent case studies demonstrate GBL's potential in quantifying dynamic displacements, there is a need for more comprehensive research to validate the accuracy of GBL-based dynamic measurements under various GBL- and structure-based parameters in an autonomous and scalable framework. Therefore, the main objective of this study is to develop and comprehensively validate a novel end-to-end framework to monitor the dynamic vibrations of structures using GBL through extensive experimentation in a controlled laboratory environment. In this study, a novel two-step spatio-temporal algorithm was developed to extract the dynamic vibrations of structures from the dynamic point clouds. The framework leverages the Density-based Spatial Clustering of Applications with Noise (DBSCAN) and change detection algorithms. The impact of several GBL-based parameters on the accuracy of the operational modal analysis results was investigated across six single-degree-of-freedom structures with unique natural frequencies. The GBL-based parameters included the resolution, quality, and point-to-point distance of the dynamic point clouds. Accelerometers and infrared-based sensors were used for the validation of GBL measurements and operational modal analysis results. To validate GBL's full-field mode shapes across the tested specimen configurations, analytical and finite element models were constructed to provide high-fidelity mode shapes as ground-truth data. The results show that the GBL can detect sub-millimeter structural vibrations, and that the resulting natural frequencies and operational deflected shapes closely match those of traditional sensing modalities, and the analytical and finite element models. This study concludes that GBL can be used reliably for remotely monitoring the dynamic response of structures at a high spatial resolution. However, further research is warranted to evaluate the full extents of the proposed framework.

Efficient Modal Identification and Optimal Sensor Placement via Dynamic DIC Measurement and Feature-Based Data Compression

Full-field non-contact vibration measurements provide a rich dataset for analysing structural dynamics. However, implementing the identification algorithm directly using high-spatial resolution data can be computationally expensive in modal identification. To address this challenge, performing identification in a shape-preserving but lower-dimensional feature space is more feasible. The full-field mode shapes can then be reconstructed from the identified feature mode shapes. This paper discusses two approaches, namely data-dependent and data-independent, for constructing the feature spaces. The applications of these approaches to modal identification on a curved plate are studied, and their performance is compared. In a case study involving a curved plate, it was found that a spatial data compression ratio as low as 1% could be achieved without compromising the integrity of the shape features essential for a full-field modal. Furthermore, the paper explores the optimal point-wise sensor placement using the feature space. It presents an alternative, data-driven method for optimal sensor placement that eliminates the need for a normal model, which is typically required in conventional approaches. Combining a small number of point-wise sensors with the constructed feature space can accurately reconstruct the full-field response. This approach demonstrates a two-step structural health monitoring (SHM) preparation process: offline full-field identification of the structure and the recommended point-wise sensor placement for online long-term monitoring.

Full-Field Mode Shape Identification Based on Subpixel Edge Detection and Tracking

Most research on computer vision (CV)-based vibration measurement is limited to the determination of discrete or coarse mode shapes of the structure. The continuous edge of the structure in images has rich optical features, and thus, by identifying and tracking the movement of the structure’s edge, it is possible to determine high-resolution full-field mode shapes of the structure without a preset target. The present study proposes a CV-based method of full-field mode shape identification using the subpixel edge detection and tracking techniques. Firstly, the Canny operator is applied on each frame of the structure vibration video to extract the pixel-level edges, and the improved Zernike orthogonal moment (ZOM) subpixel edge detection technique is adopted to relocate the precise structure edges. Then, all the detected edge points are tracked to obtain the full-field dense displacement time history that is subsequently used to determine the structure frequencies and compute full-field mode shapes by combining the covariance driven stochastic subspace identification (SSI-COV) with the hierarchical cluster analysis. Finally, the proposed method is verified on the aluminum cantilever beam in the laboratory and the Humen Bridge in the field. The results show that the proposed method is able to detect more precise structure edges and identify the full-field displacement and mode shapes of structures without the need for installing artificial targets on the structure in advance, which provides valuable information for the structural condition assessment, especially for structures with small-amplitude vibrations.

Full-field mode shape estimation of a rotating structure subject to random excitation using a tracking continuously scanning laser Doppler vibrometer via a two-dimensional scan scheme

A two-dimensional (2D) scan scheme is developed for a tracking continuously scanning laser Doppler vibrometer (CSLDV) system to scan the whole surface of a rotating structure subject to random excitation. A tracking CSLDV system is developed to track a rotating structure and sweep its laser spot on its surface. The measured response of the structure using the 2D scan scheme of the tracking CSLDV system is considered as the response of the whole surface of the structure subject to random excitation. The measured response can be processed by an operational modal analysis (OMA) method called the improved demodulation method based on a rigorous nonuniform rotating plate model to obtain modal parameters of the rotating structure, such as damped natural frequencies and undamped full-field mode shapes. Damped natural frequencies of the rotating structure are estimated from the fast Fourier transform of the measured response. Undamped full-field mode shapes are estimated by multiplying the measured response by sinusoids whose frequencies are estimated damped natural frequencies. Experimental investigation of the 2D scan scheme of the tracking CSLDV system and OMA method is conducted, and damped natural frequencies and undamped full-field mode shapes of a rotating fan blade with different constant speeds are estimated. It is theoretically and experimentally shown that damped natural frequencies of the rotating fan blade increases with its rotation speed.

Image Motion Extraction of Structures Using Computer Vision Techniques: A Comparative Study.

Vibrational measurements play an important role for structural health monitoring, e.g., modal extraction and damage diagnosis. Moreover, conditions of civil structures can be mostly assessed by displacement responses. However, installing displacement transducers between the ground and floors in real-world buildings is unrealistic due to lack of reference points and structural scales and complexity. Alternatively, structural displacements can be acquired using computer vision-based motion extraction techniques. These extracted motions not only provide vibrational responses but are also useful for identifying the modal properties. In this study, three methods, including the optical flow with the Lucas–Kanade method, the digital image correlation (DIC) with bilinear interpolation, and the in-plane phase-based motion magnification using the Riesz pyramid, are introduced and experimentally verified using a four-story steel-frame building with a commercially available camera. First, the three displacement acquiring methods are introduced in detail. Next, the displacements are experimentally obtained from these methods and compared to those sensed from linear variable displacement transducers. Moreover, these displacement responses are converted into modal properties by system identification. As seen in the experimental results, the DIC method has the lowest average root mean squared error (RMSE) of 1.2371 mm among these three methods. Although the phase-based motion magnification method has a larger RMSE of 1.4132 mm due to variations in edge detection, this method is capable of providing full-field mode shapes over the building.

Spatiotemporal compressive sensing of full-field Lagrangian continuous displacement response from optical flow of edge: Identification of full-field dynamic modes

The present state of condition monitoring of civil infrastructure involves the application of a large number of contact-based vibration sensors at different locations of the structures. The traditional vibration sensors, such as accelerometers or strain gauges, require considerable effort in laying out the connection wires. Also, their cost of maintenance is quite high considering the harsh environment they are exposed to. In recent times, there is a growing urge in developing contactless, vision-based vibration sensors that potentially alleviate the previously mentioned drawbacks. In a previous paper, the authors proposed a framework of acquiring full-field spatiotemporal Lagrangian displacement response of a continuous vibrating edge from its video by computing the optical-flow of the edge using d’Alembertian of Gaussian filter. Such spatially dense measurements are required to compute full-field mode shapes. But, from the perspective of condition monitoring of large infrastructures, such spatially dense measurements record a large amount of high dimensional data over the whole period of acquisition time. It poses a considerable challenge in the form of an increase in storage and data transmission capacity. In this paper, such drawbacks are addressed by suggesting a computational strategy of spatiotemporal compressive sensing of the full-field Lagrangian displacement response from the video of the vibrating structure with unknown geometric properties and boundary conditions. The non-uniformly sampled data, simultaneously both in the spatial and temporal dimension, still retains the low order dynamics of the system from which the full-field and high dimensional displacement responses are reconstructed. Subsequently, the modal parameters and full-field mode shapes are estimated from the reconstructed full-field Lagrangian displacement response. The experimental validation of the proposed method satisfactorily reconstructs the dense full-field displacement response along with estimating full-field dynamic modes from the low-dimensional spatiotemporal sub-sampled measurement data for a three-story steel frame and an aluminum cantilever beam for different compression ratios. The applicability of the proposed method is demonstrated on a simulated wind turbine tower model with unknown geometry or boundary conditions. The full-field displacement response and mode shapes of the non-prismatic wind turbine tower with a concentrated mass at the top are successfully reconstructed from the noise-induced sub-sampled data.

Full-Field and Quantitative Analysis of a Thin Liquid Film at the Nanoscale by Combining Digital Holography and White Light Interferometry

Visualizing and measuring thin-film thickness at the nanoscale during dynamic evolution has been an open challenge for long term. Here, a joint-imaging method and the thereof innovative procedure are presented for merging digital holography (DH) and white light colorimetric interferometry (WLCI) measurement data in a single intelligent tool. This approach allows a complete quantitative study of the dynamic evolution of freestanding thin films under high spatial resolution and full-field modality over a large area. By merging interferometric and holographic fringes, it is possible to overcome the lack of DH in thickness measurements of ultrathin layers, providing a reliable reference for full-field quantitative mapping of the whole film with interferometric accuracy. Thanks to the proposed approach, the time-related and concentration-related evolution of surfactant film thickness can be studied. The thickness distribution curves reveal the small changes in the film thickness with time and concentration. The reported tool opens a route for comprehending deeply the physics behind the behavior of freestanding thin liquid films as it provides an in situ, continuous monitoring of film formation and dynamic evolution without limits of thickness range and in full-field mode. This can be of fundamental importance to many fields of applications, such as fluids, polymers, biotechnology, bottom-up fabrication, etc.

Identification of full-field dynamic modes using continuous displacement response estimated from vibrating edge video

The video of vibrating structure provides dense quantitative continuous spatial information that is harnessed using various computer vision algorithms in the past decade. Computer vision algorithms that implement sparse optical flow, have been successful in acquiring the Lagrangian representation of motion. Such vision-based measurement already proved its potential in replacing the need for a contact based vibration measurement sensors. In order to obtain full-field, spatially dense, vibrational modes, a large number of discrete sensors would be necessary throughout the specimen’s length, making it impractical. The phase-based video processing method is found to be successful in visualizing full-field operational mode shapes of a vibrating structure. However, the phase-based optical flow provides an Eulerian representation of the motion at every pixel of the image space, which does not acquire the full-field spatiotemporal Lagrangian displacement trajectory of the structure. Hence, there is a need to design a target-free, noncontact vision-based framework that can directly extract and quantify full-field dynamic modes of a real-life vibrating structural member from its video, by acquiring the trajectory of every particle on the structure at each frame of the video using optical flow. The continuous edge of a moving object is a rich optical feature whose motion perpendicular to its orientation can be tracked in Lagrangian coordinates using optical flow. In a recent paper by authors, the method of measuring full-field displacement response of a vibrating continuous edge of a structural member has been reported. In this paper, the full-field displacement response is acquired using the recently presented method and subsequently, its spatially dense dynamic modes are extracted from its video using the acquired full-field spatiotemporal displacement response of the vibrating structure. The full-field dynamic modes and modal parameters are extracted using the Hankel dynamic mode decomposition method, which is applicable both for linear, as well as nonlinear dynamical systems. Further, experimental validation of the proposed method is presented for two kinds of structures (1) a three-story steel frame, and (2) an aluminum cantilever beam, both undergoing free vibration. The results obtained using the proposed method is validated with the displacement measured using Laser Doppler Vibrometer at a particular point of the edge. The extracted modal properties using the proposed methodology compares satisfactorily with the results of the eigensystem realization algorithm applied to the discrete point accelerometer measurements attached at all three floors of the frame. Also, the numerically obtained mode shapes from the analytical model of the cantilever beam validate the estimated modal parameters and the full-field mode shapes. To validate the efficacy of the proposed method in real-world structures, part of the vibrating cable of Tacoma Narrows bridge is tracked from its video, moments before its collapse. The proposed method does successfully extract the dominating vibrational modes of the cables of the Tacoma Narrows bridge.

Measurement of Chladni Mode Shapes with an Optical Lever Method.

Quantitatively determining the Chladni pattern of an elastic plate is of great interest in both physical science and engineering applications. In this paper, a method of measuring mode shapes of a vibrating plate based on an optical lever method is proposed. Three circular acrylic plates were employed in the measurement under different center harmonic excitations. Different from a traditional method, only an ordinary laser pen and a light screen made of ground glass are employed in this novel approach. The approach is as follows: the laser pen projects a beam to the vibrating plate perpendicularly, and then the beam is reflected to the light screen in the distance, on which a line segment made of the reflected spot is formed. Due to the principle of vision persistence, the light spot could be read as a bright straight line. The relationship between the slope of the mode shape, length of the light spot and the distance of the vibrating plate and the light screen can be obtained with algebraic operations. Then the mode shape can be determined by integrating the slope distribution with suitable boundary conditions. The full-field mode shapes of Chladni plate could also be determined further in such a simple way.

Affinity propagation clustering of full-field, high-spatial-dimensional measurements for robust output-only modal identification: A proof-of-concept study

Determination of the model order is a challenging problem in system identification, especially in output-only or operational modal identification where some modes are weakly excited. Although existing methods such as the stabilization diagram method (spectral information) are effective, they do not scale to high-dimensional data, which is usually needed for high-fidelity characterization of structural dynamics and has been made available in the emerging full-field measurement techniques using optical methods such as photogrammetry and laser vibrometers.In this proof-of-concept study we present a new non-parametric, data-driven approach for robust output-only identification of high-spatial-dimensional modal parameters of basic structures by efficiently processing and interactively exploiting the full-field measurement (i.e., very dense spatial measurement points). Specifically, we first over-estimate the system model once, producing a pool of candidate modes associated with their modal frequencies and full-field, high-spatial-dimensional mode shapes. This is accomplished by a data-driven method termed affinity propagation clustering (APC), where the active clusters, which are the active modes in our formulations, emerge from the “message-passing” procedure and does not require a pre-determination of the cluster number (mode or model order). Next, rather than using the spectral information to distinguish the physical and spurious modes in the stabilization diagram method, we exploit and visualize the spatial, full-field mode shape associated with each candidate mode to do so. We conduct extensive experiments on basic structural models with comparisons to a few existing methods. The results indicate that the new method is computationally efficient for identifying high-spatial-dimensional modal parameters, and robust to identify weak modes by exploiting the full-field measurement. We also discuss its applicability and limitations for structures with complex geometry (shapes).

High-dimensional quantum gates using full-field spatial modes of photons

Unitary transformations are the fundamental building blocks of gates and operations in quantum information processing, allowing the complete manipulation of quantum systems in a coherent manner. In the case of photons, optical elements that can perform unitary transformations are readily available only for some degrees of freedom, e.g., wave plates for polarization. However, for high-dimensional states encoded in the transverse spatial modes of light, performing arbitrary unitary transformations remains a challenging task for both theoretical proposals and actual implementations. Following the idea of multi-plane light conversion, we show that it is possible to perform a broad variety of unitary operations at high quality by using only a few phase modulation planes. More importantly, we experimentally implement several high-dimensional quantum gates for up to five-dimensional states encoded in the full-field mode structure of photons. In particular, we realize cyclic and quantum Fourier transformations, known as Pauli X ^ -gates and Hadamard H ^ -gates, respectively, with an average visibility of more than 90%. In addition, we demonstrate near-perfect “unitarity” by means of quantum process tomography, unveiling a process purity of 99%. Last, we demonstrate the benefit of the two independent spatial degrees of freedom, i.e., azimuthal and radial, and implement a two-qubit controlled-NOT quantum operation on a single photon. Thus, our demonstrations open up new paths to implement high-dimensional quantum operations, which can be applied to various tasks in quantum communication, computation, and sensing schemes.

Full-field mode sorter using two optimized phase transformations for high-dimensional quantum cryptography

High-dimensional encoding schemes have emerged as a novel way to perform quantum information tasks. For high dimensionality, temporal and transverse spatial modes of photons are the two paradigmatic degrees of freedom commonly used in such experiments. Nevertheless, general devices for multi-outcome measurements are still needed to take full advantage of the high-dimensional nature of encoding schemes. We propose a general full-field mode sorting scheme consisting of only up to two optimized phase elements based on evolutionary algorithms that allows for joint sorting of azimuthal and radial modes. We further study the performance of our scheme through simulations in the context of high-dimensional quantum cryptography, where sorting in different mutually unbiased bases and high-fidelity measurement schemes are crucial.

Damage Detection Using Modal Rotational Mode Shapes Obtained with a Uniform Rate CSLDV Measurement

With the rapid development of a continuously scanning laser Doppler vibrometer (CSLDV) technique, the full-field mode shapes of structures with high accuracy can be obtained. In this paper, a novel damage detection method using modal rotational mode shapes obtained with a uniform rate CSLDV measurement is proposed. The modal rotational damage indicators considering the changes of modal rotational mode shapes between the damaged and the undamaged states are established. Because the modal rotational mode shapes are obtained through the derivative of the detailed displacement mode shapes of transitional degree-of-freedoms (DOFs) with respect to the orthogonal directions, they are more sensitive than the normal displacement mode shapes. The uniform rate CSLDV measurement is essentially a uniform straight-line scanning technique and the measured mode shapes can be directly obtained through the demodulation of vibration signals. Besides, taking it for granted that a priori knowledge of the undamaged structure is not known, the undamaged mode shapes can be reconstructed from the measured damaged data using the fitted polynomial functions in which the minimum number of polynomial function coefficients are determined by a fit value threshold. The proposed method is firstly demonstrated by numerical simulation of the crack plate and then a plate structure with three damaged cases is taken as an example for further experimental study. The experimental results indicate the following: (1) The uniform rate CSLDV measurement can obtain the high accuracy modal rotational mode shapes with the advantage of eliminating the contaminated noise in the measurement; (2) the modal rotational damage indicators of the torsional modes are the most sensitive to the crack damage and they can clearly identify single, multiple damages and locations of the plate, and even slight crack damage, respectively. The effectiveness of the method paves the way for practical applications, such as ultra-light or composite structures.

A simple approach to determine the mode shapes of Chladni plates based on the optical lever method

This article introduces a simple approach based on the optical lever method to quantitatively determine the Chladni patterns of 2D plane standing waves on an elastic plate. Only an ordinary laser pen and a light screen made of ground glass are auxiliarily used during the measurement, which can be done quickly during classroom demonstrations in college physics courses. Three circular acrylic plates each with a thickness of 1 mm are tested under different center harmonic excitations. The beam from the laser pen is projected to the vibrating plate perpendicularly and reflected to the light screen in the distance, and the slope of the mode shape at the laser point can be determined with the length of the light spot on the light screen. Then, the observed mode shape can be obtained by integrating the slope distribution. Theoretical models and numerical simulations are also conducted to verify the accuracy of the present method, and results show that they compare very well. The present approach can be further applied to determine the full-field mode shapes of Chladni plates in a rather simple fashion.

Experimental modal analysis on full-field DSLR camera footage using spectral optical flow imaging

High-speed camera measurements are increasingly being used in modal analysis to instantaneously measure full-field structural responses by extracting the displacement information from images using digital-image-correlation and other optical-flow methods. High-speed cameras capable of filming full frame at high frame rates can be very expensive and produce image resolutions of only approximately 1 mega pixel, which is why this research aims at measuring and identifying the full-field response using cheaper, still-frame cameras with a higher image and intensity resolution, such as digital single-lens reflex (DSLR) and mirrorless cameras. Using spectral optical flow imaging (SOFI) full-field operational shapes can be acquired using still-frame cameras. This study demonstrates the hybrid modal-parameter identification of full-field mode shapes using an accelerometer and a DSLR camera for responses far above the DSLR camera's frame rate (demonstrated up to 1 kHz).

The behaviour of ferric iron during partial melting of peridotite

In order to better understand the behaviour of Fe3+ during partial melting of a mid-ocean-ridge-basalt (MORB) mantle source, we performed partial melting experiments of a spinel peridotite at 1.5 GPa, between 1320 and 1450 °C, and over a range of oxygen fugacities (fO2) varying from FMQ-3.5 to FMQ+6 (log-units relative to FMQ = Fayalite-Magnetite-Quartz oxygen buffer). Changes in fO2 were achieved using different capsule materials and by varying the oxidation state of the starting material. Fe3+ contents of spinels and glasses were examined using Fe K-edge X-ray Absorption Near Edge Structure (XANES) spectroscopy in full-field mode. Our results show that this method allows Fe3+/ƩFe measurements to be made of spinels in our experimental charges but is not suitable for quantifying Fe3+/ƩFe of glasses, particularly at relatively low fO2 where melt Fe2O3 contents are small. We therefore employed several methods (Fe3+/ƩFe ratios of spinels measured by XANES and calculated by stoichiometry, and Fe-alloy sliding redox sensors) to assess the fO2 of the samples. These were then used to calculate the Fe3+/ƩFe ratios of glasses using published models, which were further constrained by Mössbauer spectroscopy measurements on an additional set of partial melting experiments.For a particular initial redox state, the Fe3+/ΣFe ratio in melts remains approximately constant with partial melting degree. This is explained by a slight decrease of the bulk partition coefficient of Fe2O3 (DFe2O3peridotite-melt) as the degree of partial melting increases. The Fe3+/ΣFe ratios of resulting melts are thus restricted to a relatively narrow range over large degrees of melting, as observed for global MORB glass analyses. This observation is also confirmed by pMELTS calculations employing different bulk Fe3+/ΣFe ratios. We conclude that the Fe2O3 content in MORB can be accounted for through partial melting of a mantle source containing 0.1–0.5 wt% Fe2O3 and a bulk DFe2O3peridotite-melt ranging from 0.3 to 0.1.

A framework for the identification of full-field structural dynamics using sequences of images in the presence of non-ideal operating conditions

Recent developments in the ability to automatically and efficiently extract natural frequencies, damping ratios, and full-field mode shapes from video of vibrating structures has great potential for reducing the resources and time required for performing experimental and operational modal analysis at very high spatial resolution. Furthermore, these techniques have the added advantage that they can be implemented remotely and in a non-contact fashion. Emerging full-field imaging techniques therefore have potential to allow the identification of the modal properties of structures in regimes that used to be challenging. For instance, these techniques suggest that the high spatial resolution structural identification could be performed on an aircraft during flight using a ground or aircraft-based imager. They also have the potential to identify the dynamics of microscopic systems. In order to realize this capability it will be necessary to develop techniques that can extract full-field structural dynamics in the presence of non-ideal operating conditions. In this work, we develop a framework for the deployment of emerging algorithms that allow the automatic extraction of high-resolution, full-field modal parameters in the presence of non-ideal operating conditions. One of the most notable non-ideal operating conditions is the rigid body motion of both the structure being measured as well as the imager performing the measurement. We demonstrate an instantiation of the framework by showing how it can be used to address, in-plane, translational, rigid body motion. The development of a frame-to-frame keypoint–based technique for identifying full-field structural dynamics in the presence of either rigid body motion is presented and demonstrated in the context of the framework for the deployment of full-field structural identification techniques in the presence of non-ideal operating conditions. It is expected that this framework will ultimately help enable the collection of full-field structural dynamics using measurement platforms including unmanned aerial vehicles, robotic telescopes, satellites, imagers mounted in high-vibration environments (seismic, industrial, harsh weather), characterization of microscopic structures, and human-carried imagers. If imager-based structural identification techniques mature to the point that they can be used in non-ideal field conditions, it could open up the possibility that the structural health monitoring community will be able to think beyond monitoring individual structures, to full-field structural integrity monitoring at the city scale.

Full-field modal analysis during base motion excitation using high-speed 3D digital image correlation

In recent years, many efforts have been made to exploit full-field measurement optical techniques for modal identification. Three-dimensional digital image correlation using high-speed cameras has been extensively employed for this purpose. Modal identification algorithms are applied to process the frequency response functions (FRF), which relate the displacement response of the structure to the excitation force. However, one of the most common tests for modal analysis involves the base motion excitation of a structural element instead of force excitation. In this case, the relationship between response and excitation is typically based on displacements, which are known as transmissibility functions. In this study, a methodology for experimental modal analysis using high-speed 3D digital image correlation and base motion excitation tests is proposed. In particular, a cantilever beam was excited from its base with a random signal, using a clamped edge join. Full-field transmissibility functions were obtained through the beam and converted into FRF for proper identification, considering a single degree-of-freedom theoretical conversion. Subsequently, modal identification was performed using a circle-fit approach. The proposed methodology facilitates the management of the typically large amounts of data points involved in the DIC measurement during modal identification. Moreover, it was possible to determine the natural frequencies, damping ratios and full-field mode shapes without requiring any additional tests. Finally, the results were experimentally validated by comparing them with those obtained by employing traditional accelerometers, analytical models and finite element method analyses. The comparison was performed by using the quantitative indicator modal assurance criterion. The results showed a high level of correspondence, consolidating the proposed experimental methodology.

High frequency modal identification on noisy high-speed camera data

Abstract Vibration measurements using optical full-field systems based on high-speed footage are typically heavily burdened by noise, as the displacement amplitudes of the vibrating structures are often very small (in the range of micrometers, depending on the structure). The modal information is troublesome to measure as the structure’s response is close to, or below, the noise level of the camera-based measurement system. This paper demonstrates modal parameter identification for such noisy measurements. It is shown that by using the Least-Squares Complex-Frequency method combined with the Least-Squares Frequency-Domain method, identification at high-frequencies is still possible. By additionally incorporating a more precise sensor to identify the eigenvalues, a hybrid accelerometer/high-speed camera mode shape identification is possible even below the noise floor. An accelerometer measurement is used to identify the eigenvalues, while the camera measurement is used to produce the full-field mode shapes close to 10 kHz. The identified modal parameters improve the quality of the measured modal data and serve as a reduced model of the structure’s dynamics.

Reference-free detection of minute, non-visible, damage using full-field, high-resolution mode shapes output-only identified from digital videos of structures

Detecting damage in structures based on the change in their dynamics or modal parameters (modal frequencies and mode shapes) has been extensively studied for three decades. The success of such a global, passive, vibration-based method in field applications, however, has long been hindered by the bottleneck of low spatial resolution vibration sensor measurements. The primary reason is that damage typically initiates and develops in local regions that need to be captured and characterized by very high spatial resolution vibration measurements and modal parameters (mode shapes), which are extremely difficult to obtain using traditional vibration measurement techniques. For example, accelerometers and strain-gauge sensors are typically placed at a limited number of discrete locations, providing low spatial resolution vibration measurements. Laser vibrometers provide high-resolution measurements, but are expensive and make sequential measurements that are time- and labor-consuming. Recently, digital video cameras—which are relatively low cost, agile, and able to provide high spatial resolution, simultaneous, pixel measurements—have emerged as a promising tool to achieve full-field, high spatial resolution vibration measurements. Combined with advanced vision processing and unsupervised machine algorithms, a new method has recently been developed to blindly and efficiently extract the full-field, high-resolution, dynamic parameters from the video measurements of an operating, output-only structure. This work studies the feasibility of performing damage detection using the full-field, very high spatial resolution mode shape (of the fundamental mode) blindly extracted from the video of the operating (output-only) structure without any knowledge of reference (healthy) structural information. A spatial fractal dimension analysis is applied on the full-field mode shape of the damaged structure to detect damage-induced irregularity. Additionally, the equivalence between the fractal dimension and the squared curvature (modal strain energy) of the mode shape curve, when of high spatial resolution, is mathematically derived. Laboratory experiments are conducted on bench-scale structures, including a building structure and a cantilever beam, to validate the approach. The results illustrate that using the full-field, very high-resolution mode shape enables detection of minute, non-visible, damage in a global, completely passive sensing manner, which was previously not possible to achieve.