Mode Shape Curvature Research Articles

Delamination monitoring in CFRP laminated plates under noisy conditions using complex-wavelet 2D curvature mode shapes

Delamination monitoring in carbon fiber reinforced polymer (CFRP) laminated plates is crucial to ensure the integrity and safety of the structures that accommodate the plates. To identify delaminations in CFRP laminated plates, the two-dimensional (2D) curvature mode shape method is a prevailing method that features instant and simultaneous determination of the presence and location of the delamination. However, this method has two noticeable deficiencies in characterizing incipient small-sized delaminations, namely lack of damage sensitivity and inadequate noise robustness. To this end, this study proposes a new dynamics feature of the complex-wavelet 2D curvature mode shape to discriminate small-sized delaminations. This feature is delicately formulated based on the integration of the 2D curvature mode shape with the complex wavelet. The complex-wavelet 2D curvature mode shape is superior to the 2D curvature mode shape by virtue of its stronger damage sensitivity and noise robustness. These merits can be attributed to the adjustable localization and the multi-scale properties of the second-order Gabor wavelet, respectively. Proof of concept of the complex-wavelet 2D curvature mode shape is numerically undertaken in a finite-element laminated CFRP plate with a small-sized delamination, with emphasis on sensitivity to damage and robustness against noise. The applicability of the feature is experimentally validated on a CFRP laminated plate with a small-sized delamination, whose mode shapes are acquired via the non-contact measurement using a scanning laser vibrometer. The numerical and experimental results show that the complex-wavelet 2D curvature mode shape can effectively designate the presence and location of the delaminations in CFRP laminated plates under noisy conditions.

Model- and Non-model-based Damage Detection Methods Using Vibration Data

Modal parameters of a structure, including natural frequencies, modal damping ratios and mode shapes, are directly related to its material properties, such as mass, damping and stiffness. Changes in material properties of astructure due to occurrence of damage can result in those in its modal properties. In this work, model- and non-modelbased structural damage detection methods by use of modal parameters are introduced. The model-based method uses changes in natural frequencies of a structure; it requires an accurate physics-based model of the structure and a minimum amount of vibration measurement. The nonmodel-based methods use measured mode shapes and curvature mode shapes, and they do not require use of structural models. Experimental damage detection on a space frame, a beam and a plate are carried out to validate the model- and non-model-based methods.

Damage detection in shear buildings using different estimated curvature

Summary This study investigates the damage localization employing the curvature of the lateral displacement envelope in shear building structures. Both the finite difference method and the proposed interpolation method are applied to evaluate the curvature of mode shapes and frequency response functions (FRFs) in a 12-story shear building. The interpolated displacement function used in the proposed method considers appropriate continuity and boundary conditions for the shear buildings. Numerical studies show that using the curvature by the proposed method could reduce the occurrences of false damage localization when the vibration responses include small simulated noise. Moreover, the existing FRF curvature method could perform worse than random guessing to find correct damage locations at the cost of the considerable number of false alarms. However, the poor detection performance of the existing method may be enhanced significantly by using the proposed method to evaluate the curvature of the FRFs if the simulated noise is under a small level. The proposed method is shown to perform better than the finite difference method to improve the effectiveness of the curvature-based methods for damage detection.

Non-model-based damage identification of plates using principal, mean and Gaussian curvature mode shapes

Mode shapes have been extensively used to identify structural damage. This paper presents a new non-model-based method that uses principal, mean and Gaussian curvature mode shapes (CMSs) to identify damage in plates; the method is applicable to mode shapes associated with low and high elastic modes on dense and coarse measurement grids and robust against measurement noise. A multi-scale discrete differential-geometry scheme is proposed to calculate principal, mean and Gaussian CMSs associated with a mode shape of a plate, which can alleviate adverse effects of measurement noise on calculating the CMSs. Principal, mean and Gaussian CMSs of a damaged plate and those of an undamaged one are used to yield four curvature damage indices (CDIs), including Maximum-CDIs, Minimum-CDIs, Mean-CDIs and Gaussian-CDIs. Damage can be identified near regions with consistently higher values of the CDIs. It is shown that a mode shape of an undamaged plate can be well approximated using a polynomial of a properly determined order that fits a mode shape of a damaged one, provided that the undamaged plate has a smooth geometry and is made of material that has no stiffness and mass discontinuities. Fitting and convergence indices are introduced to quantify the level of approximation of a mode shape from a polynomial fit to that of a damaged plate and to determine the proper order of the polynomial fit, respectively. A weight function is applied to the proposed CDIs to alleviate adverse effects of measurement noise on the CDIs and manifest existence of damage in the CDIs. A mode shape of an aluminum plate with damage in the form of a machined thickness reduction area was measured to experimentally investigate effectiveness of the proposed CDIs in damage identification; the damage on the plate was successfully identified. The experimental damage identification results were numerically verified by applying the proposed method to the mode shape associated with the same mode as that of the measured one from a finite element model of the damaged plate.

A Baseline-Free Modal Strain Energy Method for Damage Localisation

This study describes the work carried out with the intention of accomplishing the ultimate objective of effective damage detection in structures, using their vibration parameters. As compared to the other vibration parameters, i.e., mode shape curvatures, damage indices, and flexibility curvatures, modal strain energy method (MSEM) showed high stability of damage detection. However, MSEM requires the information of a baseline model or healthy structure, which is then compared with that of a tested structure, to locate any stiffness reduction. In this paper, a baseline-free approach is presented to improve the accuracy of damage detection using the MSEM. Results from numerical simulations with experimental testing on a beam are presented by considering various damage scenarios, i.e., single and multiple damage with damage severity as small as 25% and as large as 50% thickness reduction. For all cases, the proposed approach is found to generate results with comparatively fewer noisy peaks in the damage index without requiring any reference or baseline data.

Experimental structural damage localization in beam structure using spatial continuous wavelet transform and mode shape curvature methods

Abstract An experimental dynamic vibration test using a non-contact scanning laser vibrometer is performed in order to extract the deflection shapes of two aluminium beams containing a notch cut out with a mill and two carbon/epoxy composite beams containing an impact damage of different severities. All of the beams are subjected to the clamped-clamped boundary conditions. These shapes are used as an input in a continuous wavelet transform technique for damage detection. In total, 78 wavelet functions with scale factors from 1 till 128 are used for the aluminium beams, whereas deflection shapes for composite beams are obtained in two dimensions, thus a two-dimensional wavelet transform is employed using 16 wavelet functions, all at scales from1 till 16. The scale, which is most suitable for damage identification, is found by calculating standardized damage index and the parameter called damage estimate reliability for the scales under investigation. Another method, based on mode shape curvature squares, is also applied to identify the damage. A baseline data of deflection shapes at a healthy state is not required for both methods to work. Damage identification results are compared for both methods. To assess the robustness of an algorithm involving both methods, different sensor densities are simulated by reducing the input deflection shapes by integer factors.

Comparative Study of Mode Shapes Curvature and Damage Locating Vector Methods for Damage Detection of Structures

A number of damage detection techniques have been proposed to be applied for structural health monitoring systems. In this paper a comparative study of mode shape curvature and damage locating vector methods were considered for predicting damage of structures. The mode shape curvature method is based on the difference of mode shapes between damage and undamaged structures, while damage locating vector is based on difference of flexibility matrix of damage and undamaged structures. Three type of structures were considered in this paper. The first test structure is a shear building, the second is a beam-type, and the third is a plane truss system. For each type of structures a numerical model is carried out for simulations. Several damage scenarios were considered to evaluate both methods. From the numerical experiment, it can be shown that both methods in general have demonstrated a good sensitivity for damage detections. For shear building and beam structures both methods have the ability to predict the damage locations. Due to the nature of the methods, however, for plane truss structures, while the damage locating vector method can predict the damaged members, the mode shape curvature method can predict only the nodes in the vicinity of the damaged member of plane truss structures.

Modal strain identification using sub-microstrain FBG data from a pre-stressed concrete beam during progressive damage testing

Vibration-based damage identification can constitute a successful approach for Structural Health Monitoring (SHM) of civil structures. It is a non-destructive condition assessment method, dependent on the identification of changes in the modal characteristics of a structure that are related to damage. However, the damage identification from the modal characteristics of existing structures currently suffers from a low sensitivity of eigenfrequencies and mode shapes to certain types of damage. Furthermore, the sensitivity of eigenfrequencies to environmental influences may be sufficiently high to completely mask the effect even of severe damage. Modal strains and curvatures are more sensitive to local damage, but the direct monitoring of these quantities is challenging when the strain level is very low. In the present work, the identification of the modal strains of a pre-stressed concrete beam, subjected to a progressive damage test, is performed. Dynamic measurements are conducted on the beam at the beginning of each cycle and its response is recorded with multiplexed Fiber-optic Bragg Grating (FBG) strain sensors. Bending, lateral and torsional modes are accurately identified from dynamic strains with a typical measured root mean square (RMS) strain value of about 0.35 micro-strains. The evolution of the modal characteristics of the beam after each loading cycle is investigated. Changes of the eigenfrequency values, the amplitude and the curvature of the strain mode shapes are observed. The changes in the strain mode shapes appear at the locations where the damage is induced, and are already identified from an early damaged state.

Structural damage detection using MAC-Fast Multi Swarm Optimization technique (MAC-FMSO)

Damage detection of structures is important to ensure the service of civil engineering infrastructures. Many techniques have been developed for damage detection of structures in the literature. In this paper a new technique, a so called MAC-FMSO technique, is developed by using a combination of Modal Assurance Criterion (MAC) and Fast Multi Swarm Optimization (FMSO) techniques. By using this method, not only the damage location can be assured, but also the loss of strength and loss of stiffness of structures might be quantified. The first stage is to obtain the damaged member’s location by using second level of damage detection techniques, such as mode shape curvature method, damage locating vector, or strain energy method. After obtaining the damaged member, the MACFMSO technique is used to obtain the loss of stiffness from the candidate of damaged members. The results show that the MAC-FMSO algorithm has the ability to predict the loss of stiffness in the damaged members. In this case, the MAC-FMSO technique can be considered as an efficient and effective tool at the third level of damage detections. This is because this technique successfully measures the loss of strength or loss of stiffness of the damage member or part of structures. At the end of the paper, the MAC-FMSO technique is applied to predict the location of damage and loss of stiffness of three different structures. The first application is a simply supported beam with three different damage scenarios; the second application is a 13-bar plane truss structure with two different scenarios, and the third application is a shear building structure with three different scenarios. The results of simulation show that the MAC-FMSO technique can accurately predict the loss of stiffness of the damaged member as well as the location of the damage.

Identification of internal damage in ballastless tracks based on Gaussian curvature mode shapes

In order to solve existing problems of ballastless tracks, such as various kinds of internal damage and detection difficulties, this paper presents a method based on Gaussian curvature mode shapes. The proposed method has been validated according to relevant numerical simulations and laboratory tests (e.g. those performed for detecting interlayer damage of CRTS II plate-type ballastless tracks), and had led to the following conclusion: if no damage exists in ballastless tracks, the Gaussian curvature mode shapes will be smooth and continuous under different order modes of the track slabs and no obvious peaks will be found. According to the numerical simulation, in vertical and bending vibration modes of damaged track slabs (e.g. the second-, third-, fourth-, ninth- and tenth-order), the Gaussian curvature modes have obvious peaks at damaged locations; and the second-, third- and fourth-order Gaussian curvature modes of track slabs have discontinuity points at damaged locations according to the calculation made in the modal test for the scale model of damaged ballastless tracks. Moreover, the method based on Gaussian curvature mode shapes can be used for detecting and locating internal damage of ballastless tracks accurately.

Experimental validation of cost-effective vision-based structural health monitoring

Monitoring structural displacement responses can provide quantitative information for both structural safety evaluations and maintenance purposes. To overcome the limitations of conventional displacement sensors, advanced noncontact vision-based systems offer a promising alternative. This study validates the potentials of the vision displacement sensor for cost-effective structural health monitoring. The results of laboratory experiments on simply-supported beam structures demonstrate the high accuracy of the vision sensor for dense full-field displacement measurements. The identified natural frequencies and mode shapes from measurements by using one camera match well with those from an array of accelerometers. Moreover, the smoother mode shapes make possible the noncontact damage detection based on the conventional mode shape curvature index. This study also discusses the issues concerning the practical applications of the vision displacement sensors, such as the scaling factor determination, measurement with small camera tilt angles, tradeoffs between the measurement resolution and measurement points or field of view, etc. Furthermore, the remote, real-time and multi-point measurement capacities of the vision sensor are confirmed through field tests of Manhattan Bridge during train passing.

Simulation and detection of small crack-like surface flaws and slots in simply-supported beams using curvature analysis of analytical and numerical modal displacement data

Purpose The purpose of this paper is to employ analytical and numerical techniques to generate modal displacement data of damaged beams containing very small crack-like surface flaws or slots and to use the data in the development of damage detection methodology. The detection method involves the use of double differentiation of the modal data for identification of the flaw location and magnitude. Design/methodology/approach The modal displacements of damaged beams are simulated analytically using the Bernoulli-Euler theory and numerically using the finite element method. The principle used in the analytical approach is based on changes in the transverse displacement due to the localized reduction of the flexural rigidity of the beam. Curvature analysis is employed to identify and locate the structural flaws from the modal data. The curvature mode shapes are calculated using a central difference approximation. The effects of random noise on the detectability of the structural flaws are also computed. Findings The analytical approach is much more robust in simulating modal displacement data for beams with crack-like surface flaws or slots than the finite element analysis (FEA) approach especially for crack-like surface flaws or slots of very small depths. The structural flaws are detectable in the presence of random noise of up to 5 per cent. Originality/value Simulating the effects of small crack-like surface flaws is important because it is essential to develop techniques to detect cracks at an early stage of their development. The FEA approach can only simulate the effects of crack-like surface flaws or slots with depth ratio greater than 10 per cent. On the other hand, the analytical approach using the Bernoulli-Euler theory can simulate the effects of crack-like surface flaws or slots with depth ratio as small as 2 per cent.

Damage Identification Dependence on Number of Vibration Modes Using Mode Shape Curvature Squares

In this paper a damage identification algorithm for multiple damage sites based on mode shape curvature square method of vibration mode shapes in aluminium beam is reported. The required mode shape curvature of a healthy structure was obtained via interpolation of mode shape curvature of a damaged structure with Fourier series functions of different orders. Algorithm employed calculations of standardized damage index distributions over beam coordinate. Finite element simulations of proposed methodology involving various artificial noise levels and reduction of mode shape input data points were validated on the damage identification results of experimentally measured mode shapes which were measured using scanning laser vibrometer. Results show that the algorithm is capable of capturing the areas of damage. The term called damage estimate reliability was introduced in terms of likelihood of the chosen approximation function to capture the location of damage.

Determination of Damage Location in Reinforced Concrete Beams Using Mode Shape Curvature Square (MSCS) Method

This paper presents a numerical algorithm technique to detect cracks propagated in concrete beams based on the frequency response curve of the beam determined from vibration testing. Impact tests on simply supported reinforced concrete beams were conducted to measure vibration on the beam. The ICATS software was carried out to capture the Frequency Response Functions (FRFs) data at each load step. Utilizing the FRFs data, a numerical algorithm based on finite different methods was performed to compute the different FRFs between undamage and damage beams based on the mode shape curvature square (MSCS) method. The numerical damage location was defined by subtracting the MSCS undamage to damage of beams. Therefore, the accurate damage location was identified by comparing the numerical and observed experimental results.

Modal-based damage identification for the nonlinear model of modern wind turbine blade

In this paper, the modal-based indices are used in damage identification of the wind turbine blade. In contrast of many of previous researches, the geometric nonlinearity due to the large structural deformation of the modern wind turbines blade is considered. In the first step, the finite element model (FEM) of the rotating blade is solved to obtain the modal features of the deformed structure under operational aerodynamic loading. Next, the accuracy and efficiency of the various modal-based damage indices including the frequency, mode shape, curvature of mode shape, modal assurance, modal strain energy (MSE) and the difference of indices (between the intact and damaged blades) are investigated. To adapt the MSE index calculation in nonlinear modeling, a new approach is introduced to include the effects of the structural nonlinearity. Furthermore, the effect of the damage length, its location and severity and also the effect of rotational speed and amplitude of loading are studied. The generic 5-MW NREL blade is used for the simulation study. The results show enough sensitivity of the mode shape curvature and MSE indices to the local damages. Moreover, the importance of geometric nonlinearity in the damage detection of the modern wind turbines is demonstrated.

Detection of low-velocity impact-induced delaminations in composite laminates using Auto-Regressive models

In this paper, the detection of delaminations in carbon-fiber-reinforced-plastic (CFRP) laminate plates induced by low-velocity impacts (LVI) is investigated by means of Auto-Regressive (AR) models obtained from the time histories of the acquired responses of the composite specimens. A couple of piezoelectric patches for actuation and sensing purposes are employed. The proposed structural health monitoring (SHM) routine begins with the selection of the suitable locations of the piezoelectric transducers via the numerical analysis of the curvature mode shapes of the CFRP plates. The normalized data recorded for the undamaged plate configuration are then analyzed to obtain the most suitable AR model using five techniques based on the Akaike Information Criterion (AIC), the Akaike Final Prediction Error (FPE), the Partial Autocorrelation Function (PAF), the Root Mean Squared (RMS) of the AR residuals for different order p, and the Singular Value Decomposition (SVD). Linear Discriminant Analysis (LDA) is then applied on the AR model parameters to enhance the performance of the proposed delamination identification routine. Results show the effectiveness of the developed procedure when a reduced number of sensors is available.

Mode shape-based damage detection in plate structure without baseline data

In this paper, a mode shape curvature-based method for detection and localization of damage in plate-like structures is described. The proposed algorithm requires only the mode shape curvature data of the damaged structure. The damage index is defined as the absolute difference between the measured curvature of the damaged structure and the smoothed polynomial representing the curvature of the healthy structure. To examine the advantages and limitations of the proposed method, several sets of numerical simulations are carried out. Simulated test cases considering different levels of damage severity, measurement noise and sensor sparsity are studied to evaluate the robustness of the method under the noisy experimental data and limited sensor data. Applicability and effectiveness of the proposed damage detection method are further demonstrated experimentally on an aluminium plate containing mill-cut damage. The modal frequencies and the corresponding mode shapes are obtained via finite element models for numerical simulations and by using a scanning laser vibrometer for the experimental study. Copyright © 2016 John Wiley & Sons, Ltd.

Output-only damage detection using vehicle-induced displacement response and mode shape curvature index

Most of the existing bridge superstructure damage detection methods are based on acceleration or strain response due to ambient excitation. This paper proposes a bridge damage detection procedure that utilizes vehicle-induced displacement response without requiring prior knowledge about the traffic excitation and road surface roughness. This study is partially motivated by the recent advances in convenient measurement of structural displacements enabled by video-based sensors. Vehicle–bridge interaction analysis shows that when subjected to moving vehicles, the bridge displacement response is dominated by the first-order mode component. This justifies the proposed damage detection method that only requires the first-order mode shape curvature. While conventionally the mode shapes are extracted based on operational modal analysis, the first-order mode shape is extracted by directly analyzing the power spectral density functions of measured bridge displacement responses under vehicle excitations. Numerical simulations are carried out to investigate the feasibility and performance of the proposed damage detection method using three damage scenarios including damage at single, double, and multiple locations, each involving several extents of damage defined by the reduction in element stiffness. The results reveal that all the damage cases can be successfully identified. Furthermore, the damage detection performance is evaluated for cases involving different classes of road surface roughness and less measurement points. The study demonstrates the potential of the proposed model-free and time-efficient method for damage detection of bridge structures. Copyright © 2016 John Wiley & Sons, Ltd.

Damage Identification in Polymer Composite Beams Based on Spatial Continuous Wavelet Transform

In present paper, the damage identification in two polymer composite beams is shown with two methods - spatial continuous wavelet transform (CWT) and mode shape curvature squares (MSCS) using experimental data from operational deflection shapes (ODS). Damage was introduced via low velocity impact drop tower. Statistical hypothesis approach was used to calculate standardized damage index (SDI) that served as a damage indicator for both methods. In order to truncate smaller magnitude SDI peaks, a threshold of 1.28, corresponding to the confidence level of 90%, was applied. Damage estimate reliability (DER) vs wavelet scale test was performed in order to quantify the reliability of damage detection in terms of percentage at each scale parameter. Overall, 78 different wavelet functions were tested. Results indicate that both methods are capable to locate the area of damage.

Research on Calculation and Location of Defects in Derrick Tower

Having suffered from the serious environment for ages leads to a decline in the carrying capacity of the derrick as a result of different types of defects. Aiming at a certain derrick tower, finite element analysis software ANSYS was used to calculate and analyze the mode difference of curvature of derrick before and after the damage based on the theory of damage identification from changes in curvature mode shape. Then the conclusion is confirmed by experiments. It shows that local corrosion and bending will cause the change of first two order curvature mode of derrick, and the more is the local damage, the bigger is the mode difference of curvature.