Modal Parameter Estimation in Transmissibility Functions from Digital Image Correlation Measurements

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.

Digital image correlation (DIC) measurements are affected by several sources of uncertainty. Motion blur is one of the most relevant problems in dynamic DIC applications. This work deals with the problem of compensating motion blur effects on DIC. Firstly, a robust motion blur estimation technique based on cepstral analysis is presented and validated. Secondly, the problem of image restoration has been tackled. Two image deconvolution techniques are presented: one based on cepstrum deconvolution and the other based on Wiener filter. The latter has shown better robustness in presence of noise. Each presented technique has been tested with synthetic DIC experiments. Results demonstrate that both the compensation algorithms are able to improve the accuracy of DIC measurement in presence of motion blur.

The use of 2D ultrasound elastography for measuring tendon motion and strain

Performing forced vibration tests on full-scale structures is the most reliable way of determining the relevant modal parameters in structural dynamics, such as modal frequencies, mode shapes, modal damping, and modal masses. This study describes the modal identification of a double-level curved cable-stayed bridge with separate deck systems for pedestrians and vehicles via forced vibration tests. The steady-state structural responses to sinusoidal excitations produced by an electrodynamic shaker are recorded under varying excitation frequencies, and the frequency response functions are established. The measured frequency response functions are curve fitted to estimate the modal parameters. The numerical simulation of frequency response function–based modal parameter identification of an elastically multi-supported continuous beam structure is carried out, and the emphasis has been placed on the evaluation of the effect of an additional shaker mass, excitation frequency step and range, multi-mode vibration, and noise on identification results. Finally, the modal parameters for the first lateral mode of a double-level curved cable-stayed bridge are identified by forced vibration experiments, and the results are compared with those from ambient vibration tests and free vibration tests. The effect of the unmeasured wind excitation on identification is discussed. It is shown that the effect of ambient vibration is minor for wind velocity of 3–5 m/s. The damping ratios identified by forced and free vibration tests are comparable, while those from ambient vibration are subject to large variations. The modal mass obtained from forced vibration tests is in good agreement with finite element prediction, which provides design basis for mass-type dampers.

Welding is one of the most widely used joining techniques for manufacturing complex engineering components. However, due to transient temperature cycles in the adjacent materials being joined, the local microstructure is altered and plastic strain in the surrounding materials is introduced resulting in a variation of mechanical properties across the weldment. When an extracted cross-weld test specimen is subjected to an external uniaxial load, there is interaction between the various constituents of the weld (such as the weld fused zone, heat affected zone and parent metal) resulting in development of constraint in the weaker material due to the adjacent stronger material. This affects the distribution of stress along and within the test specimen. The level of constraint developed is dependent on the strength mismatch between adjacent materials which may be graded across the heat affected zone and the specimen cross-sectional geometry. With development of digital image correlation (DIC) and its application to measuring deformation of solids, it has become feasible to measure local stress-strain properties of cross-weld samples and also specimens of variable geometry at both room and high temperature. Local deformation measured by DIC is correlated with nominal stress based on an iso-stress assumption, where it is assumed that the various regions of the weld are arranged in series and that the stress is uniform over the cross-section area at any given location in the specimen. Thus, local mechanical properties are inferred by mapping the measured local strain against the global stress. In this context the effect of constraint is important because it introduces a local stress distribution that will differ from the global net section stress and can therefore introduce errors in determination of local stress-strain properties. The influence of these factors raises questions concerning the interpretation of apparent local mechanical properties of cross-welds measured using DIC. Specifically, there is uncertainty as to whether the measured variation in local strain versus average cross-sectional stress (average global stress) represents the local mechanical properties of the material with negligible error. The severity of potential constraint errors will be influenced by the specimen geometry (particularly the tensile specimen thickness to width ratio for 2D DIC strain measurements) and the gradient of material property inhomogeneity along the specimen gauge length. In the current study, measurement of deformation in varying stress fields using DIC was carried out. Two distinct methods of introducing varying stress fields were employed: in the first case, the stress field was varied by designing an hour-glass shaped specimen with the specimen width varying as a function of the gauge length. In the second case, stress fields were varied due to a change in the specimen thickness in mismatched dissimilar metal joints. To reduce the complexity in the developed stress fields in the region near the interface, two materials were joined using solid state diffusion bonding giving a step change in the material properties across a planar interface. Test specimens spanning the interface were studied by finite element modelling and experimental tests with DIC deformation monitoring. Using DIC and a single hour-glass shaped specimen, multiple creep curves at different stress levels along the specimen gauge length have been successfully extracted for a test temperature of 525oC. The creep data obtained at 525oC from the hour-glass specimen test have been fitted to RCC-MR, Garofalo and Graham-Walles creep deformation models. A better correlation is achieved between the experimental data and the RCC-MR model predicted values when the local deformations from the single specimen are plotted as a function of time and true stress at the end of the specimen’s initial loading. From both elastic-plastic FE models and experimental local stress-strain curves extracted from DIC measurements, it can be concluded that a thin (1mm thick or less) 6mm wide test specimen should be used to extract the local mechanical properties from tensile specimens that have varying material properties along the gauge length, such as found in cross-weld test specimens. This is because the thinner specimen reduces the size of the strain concentration region adjacent to the interface where errors in measured local mechanical properties can occur. As a ‘rule of thumb’, the intrinsic stress-strain properties of the material should not be inferred from regions within 1mm of the interface for these 1mm thick samples because of concentration errors. The results obtained demonstrate the capability of DIC as a measurement technique for characterising the local deformation of specimens with varying stress fields. The findings also highlight some aspects of the technique which need to be considered when interpreting data from DIC measurements of local deformation from specimens with varying stress fields.

Modal Identification from response data only is studied for structural systems under nonstationary ambient vibration. The topic of this paper is the estimation of modal parameters from nonstationary ambient vibration data by applying the random decrement algorithm with time-varying threshold level. In the conventional random decrement algorithm, the threshold level for evaluating randomdec signatures is defined as the standard deviation value of response data of the reference channel. The distortion of randomdec signatures may be, however, induced by the error involved in noise from the original response data in practice. To improve the accuracy of identification, a modification of the sampling procedure in random decrement algorithm is proposed for modal-parameter identification from the nonstationary ambient response data. The time-varying threshold level is presented for the acquisition of available sample time history to perform averaging analysis, and defined as the temporal root-mean-square function of structural response, which can appropriately describe a wide variety of nonstationary behaviors in reality, such as the time-varying amplitude (variance) of a nonstationary process in a seismic record. Numerical simulations confirm the validity and robustness of the proposed modal-identification method from nonstationary ambient response data under noisy conditions.

As a representative method of optical non-interference measurement, digital image correlation (DIC) technology is a non-contact optical mechanics method that can measure the displacement and deformation of the whole field. However, when the measurement range of the field is too large, the existing DIC method cannot measure the full-field strain accurately, which limits the application of the DIC measurement in the case of a large size and wide-field view. To address this issue, a DIC measurement method for large-scale structures based on adaptive warping image stitching is proposed in this paper. First, multiple adjacent high-resolution images are collected at different locations of large-scale structures. Secondly, the collected images are stitched by applying the adaptive warping image stitching algorithm to obtain a panoramic image. Finally, the DIC algorithm is applied to solve the whole deformation field. In the experiments, we first verify the feasibility of the proposed method for image matching and fusion through the numerical simulation of a rigid body translation experiment. Then the accuracy and robustness of the proposed method in practical application are verified by rigid body translation and a three-point bending experiment. The experimental results demonstrate that the measurement range of DIC is improved significantly with the adaptive warping image stitching algorithm.

Analysis of mechanical behaviour and fracture interaction of multi-hole rock mass with DIC measurement

Zinc alloys are used in a wide range of application such as electronics, automotive and building construction. Their various shapes are generally obtained by metal forming operation such as stamping. Therefore, it is important to characterize the material with adequate characterization tests. Sheet Bulging Test (SBT) is well recognized in the metal forming community. Different theoretical models of the literature for the evaluation of thickness and radius of the deformed sheet in SBT have been studied in order to get the hardening curve of different materials. These theoretical models present the advantage that the experimental procedure is very simple. But Koç et al. showed their limitation, since the combination of thickness and radius evaluations depend on the material. As Zinc alloys are strongly anisotropic with a special crystalline structure, a procedure is adopted for characterizing the hardening curve of a Zinc alloy. The anisotropy is first studied with tensile test, and SBT with elliptical dies is also investigated. Parallel to this, Digital Image Correlation (DIC) measures are carried out. The results obtained from theoretical models and DIC measures are compared. Measures done on post-mortem specimens complete the comparisons. Finally, DIC measures give better results and the resulting hardening curve of the studied zinc alloy is provided.

Robotic structures are typically fabricated using discrete components that serve only a single function, such as carbon fibers or polymer composites for structural reinforcement. The ability to integrate these discrete components into a single structure provide enormous opportunities to enhance the performance of robots by reducing weight and increasing the energy storage/harvesting. We have recently been pursuing the integration of sensors and solar cells into multifunctional “skin” structures. One issue that limits the integration of these components is the effect that that the interaction between them will have on the mechanical behavior, and its subsequent impact on multifunctional performance. To minimize these effects and better understand the mechanics of multifunctional skin structures, we first pursued compliant strain sensors integrated onto the compliant wings of a flapping wing MAV to sense deformations at the wing in real time. These measurements were correlated to the thrust force of the wing. The effects of these compliant strain sensors were also determined by comparing the new thrust measurements with the original wings and with 3D Digital Image Correlation (DIC) measurements. It was determined by SRS analysis that strain sensors tended to be more sensitive to lower integral modes of the flapping frequency than the thrust measurement data, while the DIC measurements correlated more directly with thrust measurements in the time domain. Thus, it would appear that the strain sensor and DIC measurements are sensitive to different aspects of the mechanics of the multifunctional skin structures that can be taken into account when using the strain sensors for real-time sensing and control. In addition to compliant strain sensor integration, flexible Solar Cells (SCs) were also integrated onto the compliant wings. Their ability to harvest energy during flight has the potential to prolong the time of flight for more autonomous operation. The effects of the integrated SCs on the 3D shapes of the compliant wings were also characterized during flapping. The solar cells had a significant effect on the wing shape, increasing the stiffness of the wings and reducing the volume of air that the wings need to capture to generate thrust, particularly at the apex and nadir of the flapping cycle where thrust is generated by blowback. Thus, a multifunctional analysis was developed to account for the tradeoff between the extra power require to generate the necessary thrust for the MAV to stay airborne versus what is gained from integrating the SCs in order to determine how to design the multifunctional skin structures to optimize performance.

Experimental modal analysis (EMA) with oblique excitation (i.e. oblique impact testing) is useful in improving the long test time problem of conventional EMA with normal excitation (i.e. triaxial normal impact testing), in order to extract all the important dynamic characteristics of a 3D complex structure. In this study, a new methodology involving a vector projection method is introduced to find the driving point frequency response function (FRF) in the oblique direction, without the need for a special fixture with an obliquely oriented impedance head. Hence, this presents a low cost and practical solution for scaling the mode shape, as compared to the traditional approach. Moreover, the concurrent forces characteristic of oblique excitation are used in the development of the theoretical relationship between FRFs with oblique excitation and those with normal excitation. This is important for the validation of the oblique impact testing result, such as the FRF and modal parameter estimations. The experimental results show that oblique impact testing has reliable and effective results, as compared with the triaxial normal impact testing, in terms of the FRF correlation, natural frequency discrepancy, modal damping ratio error and modal assurance criterion of the unit modal mass mode shape.

A DUAL FITTING ALGORITHM FOR MODAL PARAMETERS IDENTIFICATION

An experimental investigation was conducted to evaluate the permanent strain characteristics of a granular pavement foundation layer using Repeated Load Triaxial (RLT) tests, assisted by a non-contact strain measurement system based on a Digital Image Correlation (DIC) technique. Permanent strains are generally determined from laboratory triaxial tests using global measurement of axial strains. Under cyclic loading there may be formations of localized strains and instabilities, which may not be captured by conventional measuring methods, but can have significant influence on the performance of the constructed granular layer. Results are reported from a series of 40 consolidated drained triaxial tests, to develop a better understanding of the permanent strain response of a granular material under simulated traffic loadings. The DIC technology was employed to record deformation measurements, which included acquiring high-resolution images of the specimen at every 100 cycles of repeated deviatoric stresses, using a Q-Imaging / QICAM 1394 camera, and VIC-2D image correlation software. Results indicate that there is a reasonable match between the LVDT and DIC measurements when the entire specimen length was used as the gage length. However, localized strains at the top, middle, and bottom of the specimens computed from DIC measurements deviated from the LVDT measurements. This factor should be taken into account during the pavement design phase, or for the development of pavement rutting performance models.

ABSTRACTVibration-based structural damage detection has been the focus of attention by many researchers over the last few decades. However, most methods proposed for this purpose utilize extracted modal parameters or some indices constructed based on these parameters. A literature review revealed that few papers have employed Frequency Response Functions (FRFs) for detecting structural damage. In this paper, a technique is presented for damage detection which is based on measured FRFs. Proper Orthogonal Decomposition (POD) has been implemented on spatiotemporal responses in each frequency in order to reduce the dimension of the data. This is based on the concept that the forced harmonic response of a linear vibrating system can be fully captured utilizing a single basis vector. A different approach is also presented in this paper in which POD is applied to the frequency domain data. Operational Deflection Shapes (ODSs) have been decomposed using POD to localize the damage. The efficiency of the method is demonstrated through some numerical and experimental case studies.

Identification of modal parameters of unmeasured modes using multiple FRF modal analysis method