No full-text available
To read the full-text of this research,
you can request a copy directly from the authors.
Crack identification using wavelets on experimental static deflection profile
Abstract
In this paper a method to localize damage in a cantilever beam using static deflection is presented. The selection of the wavelet transform for the crack localization is discussed. The efficiency of the applied wavelets is verified by analytically and experimentally determined data. The measurement of the beam displacements in a large number of spatially distributed points is obtained by processing digital photographs of the beams. The proposed technique can effectively identify the crack positions without a knowledge of structure characteristics or a mathematical model.
... This conversion is a format for translation two-dimensional curvelet provided by Candes et al [22][23]. Rucka and Wilde proposed a method to estimate the location of the damage in the beam and in the plate using a continuous wavelet transform, the location of which is determined by a peak in the spatial variation of the transformed response [24]. Bayissa et al. ...
... However, in order to evaluate the efficiency of the proposed methods, the efficiency of the above methods is examined based on laboratory data. In this section in accordance with an experimental data from the work of Rucka and Wilde [24], which is a steel plate with the specifications stated below. ...
... experimental steel plate based on Rucka and Wilde[24]. ...
In this research, the application of 2D curvelet, 2D wavelet, and Contourlet transform for damage detection of shell structure are presented. For this study, the equation of discrete curvelet transforms using unequally-spaced fast Fourier and wrapping transforms are employed. Four scenario models with one and more damages with different percentages and locations were considered for investigation of proposed methods. As real data has noise, and the existence of noise in the input data may affect the accuracy of damage detection methods. To consider the natural conditions, white noise has been applied to the data extracted from the FEM. First, the coefficients of transforms related to the noisy signal are calculated, then thresholding the previous coefficients calculated, and finally, the de-noise signal is reconstructed. Based on the presented results, the curvelet transform better identifies the location of damage than the wavelet transforms. Wavelet transform based on the direction of the damage element may be specified in some subbands. But in curvelet and Contourlet, it can better identify different damages in different directions due to the multi-directional transform. The curvelet transform has been modified based on polar space and poses challenges for non-polar (normal) discrete space. Therefore, using the Contourlet is divided into multiple directions because of each of the available general directions. According to the obtained results, the proposed methods are sensitive to the location and percentage of damage and can identify the location of damage with a low percentage of damage. Also, to confirm the results of the proposed methods, the results are evaluated using laboratory results. The results show that the proposed methods can identify the location of damages and with a percentage of damage of up to 3%.
... To ensure the structure integrity and prevent the structure damages from the deterioration at an alarm rate, advanced structural health monitoring (SHM) techniques are required and have been widely studied during last few decades (Bornn et al, 2010). Moreover, as a useful tool for signal processing to extract information from different kinds of data, wavelet transform was widely employed by researchers for damage detection (Gokdag andKopmaz, 2009, Rucka andWilde, 2006). ...
... Gokdag and Kopmaz conducted the wavelet transform on the experimental mode shapes of a damaged beam to prove the feasibility of their numerical simulation (Gokdag and Kopmaz, 2009). To obtain the mode shapes of the damaged structures, researchers used numerous sensors which were mounted on the surfaces of the specimens (Rucka and Wilde, 2006). Wavelet transform was then applied to analyze the mode shapes from the experiments to identify the crack locations. ...
... To reduce the quantity of the sensors used for the experiment and to facilitate the operation, another experimental method for damage detection using spatial wavelet transform based on the dynamic response of a damaged structure subjected to a moving load applied was developed (Umesha et al, 2009). Since the noise effects in the experimental studies were still obvious, another experimental method using digital camera to get the deflection field of a cracked cantilever beam under bending was developed (Rucka and Wilde, 2006). The damage detection effects were obvious from their findings when the crack depth was larger than 50% of the thickness of the cracked beam. ...
The main advantage gained by using wavelets is the ability to perform local analysis of a signal which is capable of revealing some hidden aspects of the data that other signal analysis techniques fail to detect. This property is particularly important for damage detection applications. This paper presents a review of numerical applications of the discrete wavelet transform (DWT) for damage detection in a beam with two fixed ends subjected to static and dynamic analyses. The modeling of damage is done in finite elements using ABAQUS 6.13 program. The technical computing software MATLAB R2011a is employed for the data processing and wavelet transform. The static and dynamic responses (in displacement) of the structure with simulated damage is used in analyses to detect the location of damage using the wavelet transform. Special attention is given to the performance of the method when the crack is close to a support. The results of analyses are presented and discussed in this paper.
... However, successful detection of the presence and the location of damage through spatial analysis has gained considerable importance recently as it has become possible to reliably measure the deflected static [5] and dynamic shapes [55] of a damaged structure using modern equipment such as Laser Doppler Vibrometer (LDV). The global change of mode shape (particularly the first natural mode shape) ...
... Narkis [82] has suggested that the use of traditional descriptors like change in natural frequencies as a marker of damage extent using pre-existing benchmark is often quite difficult in the presence of measurement noise. The use of laser-based devices [55, 119] and less expensive digital camera based methods [5,9,117, 120] combined with image processing techniques and wavelet based identification of possible existence, location, and the extent of damage using spatial data have been reported [121]. Most of these studies deal with the identification of damage position quite well. ...
... Structural Health Monitoring (SHM) addresses the continuous monitoring of a structure in terms of static and dynamic response, including the diagnoses of the onset of anomalous structural behaviour [2]. Non-destructive structural damage detection is becoming an important aspect of integrity assessment for aging, extremeevent affected, or inaccessible structures [3,5,6,132] ...
Structural Health Monitoring (SHM) is an integral part of infrastructure maintenance and management systems due to socio-economic, safety and security reasons. The behaviour of a structure under vibration depends on structure characteristics. The change of structure characteristics may suggest the change in system behaviour due to the presence of damage(s) within. Therefore the consistent, output signal guided, and system dependable markers would be convenient tool for the online monitoring, the maintenance, rehabilitation strategies, and optimized decision making policies as required by the engineers, owners, managers, and the users from both safety and serviceability aspects. SHM has a very significant advantage over traditional investigations where tangible and intangible costs of a very high degree are often incurred due to the disruption of service. Additionally, SHM through bridge-vehicle interaction opens up opportunities for continuous tracking of the condition of the structure. Research in this area is still in initial stage and is extremely promising. This PhD focuses on using bridge-vehicle interaction response for SHM of damaged or deteriorating bridges to monitor or assess them under operating conditions. In the present study, a number of damage detection markers have been investigated and proposed in order to identify the existence, location, and the extent of an open crack in the structure. The theoretical and experimental investigation has been conducted on Single Degree of Freedom linear system, simply supported beams. The novel Delay Vector Variance (DVV) methodology has been employed for characterization of structural behaviour by time-domain response analysis. Also, the analysis of responses of actual bridges using DVV method has been for the first time employed for this kind of investigation.
... This static deflection profile was used as the input signal for wavelet analysis. Rucka and Wilde [27] presented a method to localize damage in a polystyrene cantilever beam using static deflection for the purpose of damage (one open crack) detection via Gaussian and Coiflet wavelet families; the measurement of the beam displacements of spatially distributed points was obtained by processing digital photographs. In Rucka and Wilde [28], a continuous WT was applied to detect experimentally vibration-based damage both for beams and plates; for the one-dimensional problem (one open crack), Gaussian wavelets were considered, whereas for two-dimensional structure, reverse biorthogonal wavelet was applied. ...
... A wavelet with n vanishing moments is orthogonal to polynomials up to degree n À 1. Following [49] and [27], it can be shown that a wavelet with n vanishing moments can be interpreted as the n-th derivative of a function ϑ: ...
... These boundary effects, relevant for any function defined on a finite interval, represent a non-negligible limitation of the approach, because no reliable diagnosis can be formulated on the damage state at the beam ends. In [27], to avoid large discrepancy at the boundaries, the signal was extended outside its original support by a cubic spline extrapolation. Spanos et al. [23] observed that boundary effects can be eliminated if the WT is applied on the difference between the displacement responses of the damaged and undamaged beam, subject to the same load. ...
In this study, a method for crack detection and quantification in beams based on wavelet analysis is presented. The static deflection is measured at particular points along the length of (i) real damaged structures, using few displacement transducers and a laser sensor, and (ii) simulated structures, using closed-form analysis, for a given location of a concentrated load along the beam. Furthermore, the measurement of the beam displacements in a large number of spatially distributed points is made by processing digital photographs of the beam. The smoothed deflection responses of the cracked beams are then analyzed using the wavelet transform. For this purpose, a Gaus2 wavelet with two vanishing moments is utilized. The wavelet transform spikes are used as indicators to locate and quantify the damage; furthermore, the multi-scale theory of wavelet is employed, in order to eliminate or at least reduce the spurious peaks and enhance the true ones. Simply supported beams with single and double cracks are used to demonstrate the devised methodology. Open and fatigue cracks of different sizes and locations have been used in the examples. In a closed-form analysis, the damage is modeled as a bilinear rotational spring with reduced stiffness in the neighborhood of the crack location. Damage calibration of simply supported steel beams with open and fatigue cracks has been carried out experimentally using this technique. A generalized curve has been proposed to quantify the damage in a simply supported beam. Based on the experimental study, the spatial wavelet transform is proven to be effective to identify the damage zone even when the crack depth is around 3% of the height of the beam.
... Initially, Liew and Wang [12] and Wang and Deng [13] analyzed static deflections of beams for damage detection. After that, there have been numerical and experimental validations and analysis of multiple load situations [14][15][16][17][18][19]. ...
... He proposed some advanced methods to avoid the edge effect based on isomorphism and self-minimization applied to an extension of the original signal. An alternative and simplified methodology has been proposed by Rucka and Wilde [16], applying an extension of four points using a cubic spline. Previous works [20,44] also proposed the use of a window function to weight the wavelet coefficients, so the coefficients near the edges were reduced, but that implies that information is not reliable for these areas. ...
... If the number of experimental measurement points is not large enough, then an interpolation may be performed between the experimental values. In this paper a cubic spline interpolation technique is applied [16,27]. Figure 4 illustrates how the interpolation works if 5 or 13 measuring points were available and 128 interpolated points were obtained. ...
Many authors have proposed wavelet analysis as an efficient and useful numerical tool for damage detection in structures. Some of these proposals consist of the application of the wavelet analysis to the mode shapes of the structure in order to detect perturbations induced by damage. Some authors have proposed the so-called hybrid methods, in which the wavelet analysis is applied to the spatial evolution of a modal damage detection parameter. With these hybrid methods, the ability of the wavelet analysis to detect singularities and variations of a signal is used to enhance the sensitivity of the damage detection parameter. This paper presents a hybrid method based on the variation of mode shapes weighted with the variation of their natural frequencies due to the presence of damage. A Continuous Wavelet Transform is applied to each of the weighted mode shape difference between the undamaged and the damaged state, and the corresponding coefficients for each mode shape are added up. The paper includes an experimental analysis of the sensitivity of the method for a steel beam.
... Rucka and Wilde performed preliminary studies on SDI in damaged Plexiglas plate using spatial CWT-based approach [36]. Further, they presented results of SDI based on static deflections of beams [37] and vibrated beams and plates [38]. They also presented a comparative study of various wavelets applicable to the investigated problem with respect to specific parameters of wavelets: number of vanishing moments, symmetry, and a width of the effective support. ...
... The analysis shows that crack is fully detectable only in the noiseless case (SNR: 90-100 dB); in the case when SNR equals 60-70 dB, only the cracks with a depth higher than 20% of a total thickness of a tested structure can be detected and when SNR equals 50-60 dB, the cracks with a depth up to 40% of a total thickness remain undetectable following the proposed procedure. The authors of [37] stated that the noise does not corrupt the measurement signals; however the damage depth was relatively large and equalled 25% of a total thickness of a tested structure. Zhong and Oyadiji [40] achieved the damage detectability with a noise of up to 5% with respect to the magnitudes of modal shapes and with a crack depth of 5% of total thickness; however their method uses a baseline obtained from the cubic curve fitting of modal shapes. ...
... Loutridis et al. [34] recommended the reflection technique as suitable one for reducing the boundary effect in 2D SDI problems. More advanced methods of the boundary effect reduction were proposed by Rucka and Wilde [37,38]. The authors of these papers proposed the application of cubic spline interpolation of neighbor measurement points, which are much more effective in practice than previously discussed techniques. ...
The application of composite structures as elements of machines and vehicles working under various operational conditions causes degradation and occurrence of damage. Considering that composites are often used for responsible elements, for example, parts of aircrafts and other vehicles, it is extremely important to maintain them properly and detect, localize, and identify the damage occurring during their operation in possible early stage of its development. From a great variety of nondestructive testing methods developed to date, the vibration-based methods seem to be ones of the least expensive and simultaneously effective with appropriate processing of measurement data. Over the last decades a great popularity of vibration-based structural testing has been gained by wavelet analysis due to its high sensitivity to a damage. This paper presents an overview of results of numerous researchers working in the area of vibration-based damage assessment supported by the wavelet analysis and the detailed description of the Wavelet-based Structural Damage Assessment (WavStructDamAs) Benchmark, which summarizes the author’s 5-year research in this area. The benchmark covers example problems of damage identification in various composite structures with various damage types using numerous wavelet transforms and supporting tools. The benchmark is openly available and allows performing the analysis on the example problems as well as on its own problems using available analysis tools.
... Although the change in natural frequencies are easy to determine with high degree of accuracy, the natural frequency of a system may change due to several other reasons, such as, environmental degradation and wear. Several researchers have used the mode shape for the detection of crack in beams [10][11][12][13][14]. Mode shapes are spatial domain signals. ...
... They also used an intensity factor by using Hoelder exponent to relate the size of the crack to the coefficients of the wavelet transform. Rucka and Wilde [13] used CWT with Gaussian and Coiflet wavelets with four vanishing moments to detect the crack position in cantilever beams. Hong et al. [26] used CWT with Mexican hat wavelet and found that the minimum number of vanishing moments to extract the crack position in a beam should be two. ...
Presence of crack in a beam causes a slope discontinuity at the crack location in the operational deflection shape (ODS). Detecting the slope discontinuity in ODS can reveal the presence of crack in a beam. Wavelet transform is a powerful technique to detect discontinuity in a signal. Efficient detection of the crack using wavelet transform depends primarily upon the wavelet family and the number of vanishing moments. In the present work, suitable mother wavelet along with optimum number of vanishing moment is obtained for the effective detection of crack in a beam. Crack detectability is defined to quantify the effectiveness of different mother wavelet and vanishing moments. Finite element analysis is used for getting the simulated ODS. Higher resolution measurement of ODS is the requisite for effective wavelet based crack detection. Photographic method is used for obtaining the high resolution measurement of ODS for the experimental verification. The present methodology works well with the experimentally obtained ODS of the cracked beam. It is capable of detecting crack near the end support also.
... [6][7][8] The changes in modal information caused by damage are often submerged in the environmental noise. Thus, many advanced intelligence algorithms are used to detect the damage under environmental interferences, [9][10][11][12] such as the principal component analysis that has already been adopted in SHM-data analysis 13,14 and damage analysis. 15 The DI algorithms based on the static responses have developed to overcome the shortcomings of the mode-based methods. ...
... By comparing the bridge deflection before and after structural damage under the same loading condition, the damage can be detected. 10,11 However, the mentioned methods require the closure of the bridge and artificial loading, which is usually difficult to achieve. 19 The key limitation of the deflection-based DI method is that measuring the deflection requires a reference point. ...
Traditional damage identification (DI) approaches are based on the structural modal information, which is unstable and affected by the environment. This study proposes a novel bridge DI algorithm for the elastically supported beams with a constant cross‐section. The expression of the equivalent damage load (EDL) is deduced from the force–displacement relationship. The EDL only exists in the damaged areas, and it is a good damage indicator. Then, a principal component analysis‐based load estimation method is adopted to estimate the external nodal force and the EDL. To reduce the influence of the measurement noise and errors, this study furtherly proposes a robust EDL‐based damage indicator, which is calculated from multitype data. The numerical simulations and in‐field experiments have discussed the influence of several factors, including damage scenarios and loading conditions, on the proposed damage indicator. All results have shown that the proposed damage indicator is applicable and useful. The proposed approach can detect the damage in a real‐time manner with high computational efficiency, and it is useful for the in‐operation bridges.
... This mode shape was further analyzed using orthogonal WT for damage identification. Crack localization in the CB using continuous wavelet transform was discussed by Rucka and Wilde [23]. Efficiency of both Coiflet and Gaussian wavelets were verified analytically and experimentally. ...
... Several EDT's, such as: Roberts, Sobel, Canny, and Prewitt are used for the edge detection in a digital image [23]. It is important to select suitable EDT for finding edges of the deflected beam image. ...
An optimistic attempt for the detection of a crack in a beam using discrete wavelet transform is proposed. Finite element model of the simply supported beam with a transverse open crack is considered. Crack in a beam causes a slope discontinuity in the elastic line. The deflection of the beam is used to locate the slope discontinuity using wavelet transform. The effect of measurement noise on the wavelet decomposition level is studied. An inexpensive digital image based technique is employed to obtain the deflection of the cracked beam for experimental investigations. White pixels due to dust particles are removed using connected component algorithm. A suitable edge detection technique is selected for finding the edged image on the basis of peak signal to noise ratio values. The deflection of the non-cracked edge of the beam is used as an input signal for wavelet transform to detect the crack location. Detection of a crack in the beam with different crack depths is investigated experimentally. The proposed method works well with numerically simulated as well as experimentally measured cracked beam deflections.
... Then, this process is implemented sequentially, and, in this way, it is possible to assess the similarity between the MW chosen and each segment of the complete signal to be examined throughout the entire time. As a consequence of this process, the discontinuities contained in the analyzed signal will generate high CWT coefficient magnitudes, which could be related to damage [62]. ...
Highway bridges are crucial civil constructions for the transport infrastructure, which require proper attention from the corresponding institutions of each country and constant financing for their adequate maintenance; this is important because different types of damage can be generated within these structures, caused by natural disasters, among other sources, and the heavy loads they transport every day. Therefore, the development of simple, efficient, and low-cost methods is of vital importance, allowing us to identify damage in a timely manner and avoid bridges collapsing. As reported in a previous work, the wavelet energy accumulation method (WEAM) and its corresponding application in the Rio Papaloapan Bridge (RPB) represented an important advance within the field. Despite identifying damage in bridges with precision and at a low cost, there are several aspects to improve in that method. Therefore, in this work, that method was improved, eliminating several steps, and meaningfully reducing the computational burden by implementing an algorithm based on the Shannon entropy, thus giving way to the new entropy wavelet-based method (EWM). This new method was applied directly with regard to the real-life RPB, in both its healthy and damaged conditions. Also, its corresponding numerical model based on the finite element method in its healthy condition and different damage scenarios were carried out. The results indicate that the new EWM retains the advantages of WEAM, and it allows for damage identification to be completed more efficiently, increasing the precision by approximately 0.11%, and significantly reducing the computing time required to obtain results by 5.67 times.
... In mathematics, almost everywhere to predict the discontinuity detection in the image, holder exponent (HE) values are used and that are changed with respect to suitable mother wavelets [28][29][30]. The values of minimum and maximum HE represent the depth of discontinuity variations in image pixels. ...
Digital clinical histopathology is one of the crucial techniques for precise cancer cell diagnosing in modern medicine. The Synovial Sarcoma (SS) cancer cell patterns seem to be a spindle shaped cell (SSC) structure and it is very difficult to identify the exact oval shaped cell structure through pathologist’s eye perception. Meanwhile, there is necessitating for monitoring and securing the successful and effective image data processing in the the huge network data which is also a complex one. A field programmable Gate Array (FPGA) was regarded as a necessary one for this. In this work, based on FPGA a Cancer Cell classification is made for the regulation and execution. Hence, mathematically the SSC regularity structures and its discontinuities are measured by the holder exponent (HE) function. In this research work, HE values have been determined by Wavelet Transform Modulus Maxima (WTMM) and Wavelet Leader (WL) methods with basis function of Haar wavelet based on FPGA Processor. The quantitative parameters such as Mean of Asymptotic Discontinuity (MAD), Mean of Removable Discontinuity (MRD) and Number of Discontinuity Points (NDPs) have been considered to determine the prediction of discontinuity detection between WTMM and WL methods. With the help of receiver operating characteristics (ROC) curve, the significant difference of discontinuity detection performance between both the methods has been analyzed. From the experimental results, it is clear that the WL method is more practically feasible and it gives satisfactory performance, in terms of sensitivity and specificity percentage values, which are 80.56% and 59.46%, respectively in the blue color components of the SNR 20 dB noise image.
... Notably, the Haar wavelets exhibited superior performance for detecting discrete cracks whose depth ratio to the length of the beam was as low as 1/150. The observation of the wavelet sensitivity to the non-linear structure changes was confirmed experimentally by Rucka and Wilde in [38,39]. ...
The inverse problem of crack identification, localisation and severity quantification is addressed in this article. The open cracks are simulated numerically in a homogeneous Euler-Bernoulli beam. The beam rests on the Pasternak foundation. Under the assumption that the size of the crack is small compared to the height of the beam, it is shown that the problem can be solved in terms of crack-induced changes in the natural frequencies or mode shapes. Predictions of the crack characteristics (location and severity) are made by artificial neural networks or random forests. The dimensionless natural frequency parameters or the first mode shape transformed into the Haar wavelet coefficients are used at the inputs of the machine learning methods. The numerical examples indicate that the combined approach of the natural frequencies, Haar wavelets, and machine learning produces accurate predictions. The results presented in the article can help in understanding the behaviour of more complex structures under similar conditions and provide apparent influence on the design of beams.
... In their work, the authors first obtain the mode shapes and natural frequencies of the structure in the undamaged and the damaged state. The next step is an extension of the mode shapes to avoid edge effects at the beginning and the end of the signal, following the proposal by [17], who applied an extension of four points at the beginning and the end of the signal using cubic splines before applying the CWT; the resulting CWT is then clipped to the original length of the input signal. Once the extended mode shapes have been obtained, their difference / diff can be calculated: ...
Modal analysis is a powerful tool for the detection of damage in structures such as cantilever beams. The Continuous Wavelet Transform (CWT) is often used to locate damage, but may lead to unsatisfactory results when methods designed and tested successfully on simulated beams are applied to experimental tests. In the present work, a novel approach is presented that allows to reliably detect the correct damage locations along a beam in an experimental setup, using only finite-element simulated data as a reference. The novel method is based on two main innovations: (1) an image similarity assessment method making an efficient use of the full wavelet scalogram, and (2) an ensemble approach accounting for uncertainties in materials properties. The image processing method is shown to dramatically outperform three reference methods constructed for comparison, two of them based on signal processing approaches proposed in literature, combined with a neural network processing step. This superiority is demonstrated through a systematic assessment both of simulated data, where the noise level was varied for sensitivity analyses, and of experimental data. When combined with the ensemble approach the new methodology is shown to have a 100% damage recognition rate on the experimental data studied.
... The selection of an appropriate type of wavelet and the choice of its number of vanishing moments is essential for the effective use of wavelet analysis. A brief summary of the use of various wavelets along with the relevant researches can be found in (Rucka and Wilde, 2006). It has been found that wavelets with symmetric or nearly symmetric shape are the most useful in detecting the singularities in the displacement field. ...
Wavelet analysis can be used in local damage detection due to its ability of revealing discontinuities induced by damage in the displacement field. This paper focuses on the application of wavelet analysis to detect and identify multiple damages using the static deflection of beams. The local damages are located by the wavelet maxima lines and their severity are evaluated from a damage index obtained from the wavelet coefficients along the corresponding maxima lines. A series of experimental tests were conducted to examine the performance of the methodology for multiple damage scenarios. The static deflections of the beam were measured by a Digital Image Correlation system. As an application, a l1 regularization based filter is adopted to diminish the measurement noise which is critical in the application of wavelet analysis. The paper shows the capability of using wavelet analysis for closely spaced notch-type damage detection. It also analyzes the limits of the method in estimating damage with relative small severity in the presence of severe ones.
... The baseline-free methods were proposed by many researchers, including gapped smoothing method, fractal dimension method, wavelet-based method etc. [20][21][22]. The wavelet-based methods were developed by using wavelet transform in which the static deflection [23], the mode shape [24], the operational deflection shapes [25] or the active thermography [26] can be treated as the input signal. By observing the sudden change in wavelet coefficients, the wavelet transform enables the singularity in the input signal to be detected [27]. ...
This paper investigates the free vibration and crack identification of functionally graded material (FGM) plates with a through-width edge crack. The material properties of the FGM plates change continuously with the power law distribution along the plate thickness direction. The crack in an FGM plate is simulated as a massless rotational spring and the plate is separated into two sub-plates at the crack location connected by the line spring. The stress intensity factor (SIF) in the FGM strip is calculated to determine the stiffness of the spring. The governing equations of cracked FGM plates are derived from the Mindlin plate theory and solved by the differential quadrature (DQ) method to obtain modal parameters. The vibrational mode of a cracked FGM plate is analyzed by utilizing continuous wavelet transform (CWT). A novel damage index (DI) is developed based on calculated wavelet coefficients to localize the crack in FGM plates. This method can localize the crack accurately and reduce the edge effect even with the measurement noise.
... Hence, the identification of different input types cannot be accomplished using only time-domain or frequency-domain analyses. It is noteworthy that a wavelet transform can effectively illustrate the time-frequency domain characteristics of vibration inputs (Daubechies, 1990), and it has been widely adopted in identification studies (He and Zhu, 2016;Katunin, 2011;Rucka and Wilde, 2006;Zhong and Oyadiji, 2011). In addition, Yang et al. (2019) indicated that the performance of a wavelet transform is better than that of a short-time Fourier transform and the Hilbert-Huang transform, when it is used for identifying vibrations. ...
An efficient vibration control can reduce negative effects induced by environmental vibrations and thereby improve the performance of precision instruments and the qualities of manufacture. The performance of the widely used linear quadratic regulator control algorithm, a classical active control methodology, depends on the parameters of the control algorithm. Consequently, a set of fixed parameters cannot satisfy the demand for controlling various types of environmental vibrations. Therefore, this study proposes a vibration identification method based on a convolutional neural network. This method helps to optimize the linear quadratic regulator algorithm by selecting corresponding optimal parameters according to the identification results, thereby achieving the objective of optimal control subjected to various types of vibration inputs. Specifically, environmental vibration signals are collected, and the preliminary features of the vibrations (i.e. wavelet coefficient matrices or images) are adopted as input samples for the convolutional neural network. A genetic algorithm is used to optimize the parameters of the linear quadratic regulator algorithm for each type of vibration; subsequently, the trained convolutional neural network model with the best performance is used to identify the vibration and select the corresponding optimal parameters of the linear quadratic regulator algorithm under different types of vibration inputs. Case studies show that the performance of the improved linear quadratic regulator control method is significantly better than that of the conventional linear quadratic regulator algorithm with fixed parameters.
... Identification of damage in cantilever beams was studied by a number of researchers [11][12][13][14][15][16] where the mode shape was the most important dynamic factor utilised for the quantification and localization of damaged cantilever beam. As well as to the mode shape, the static deflections for damage identification in beams under uniformly distributed and tipconcentrated loading were alternative factor investigated by [17][18][19][20]. ...
A maximum static deflection and natural frequency of aluminium cantilever stepped beam (two steps) were investigated experimentally and theoretically for different values of small and large diameters and for different lengths of larger diameter step. Eighty samples of aluminium beams were manufactured using turning machine. The range of the beam diameter was 12-20 mm and the length of beam was 45 cm. Classical Rayleigh method, modified Rayleigh method and finite element using ANSYS software method were adopted to calculate the maximum static deflection and the natural frequency. A good agreement was found for the static deflection at different positions of applied load between the experimental results and the theoretical results, ANSYS and modified Rayleigh method. The experimental results of the natural frequency showed that there was a consistent with the theoretical results particularly when there is a minor difference between the larger and smaller diameters of the stepped beam. ARTICLE HISTORY
... The observation of the wavelet sensibility to non-linear structure changes was supported experimentally by Rucka and Wilde in [19,20]. ...
In this paper, the Haar wavelet discrete transform, the artificial neural networks (ANNs), and the random forests (RFs) are applied to predict the location and severity of a crack in an Euler–Bernoulli cantilever subjected to the transverse free vibration. An extensive investigation into two data collection sets and machine learning methods showed that the depth of a crack is more difficult to predict than its location. The data set of eight natural frequency parameters produces more accurate predictions on the crack depth; meanwhile, the data set of eight Haar wavelet coefficients produces more precise predictions on the crack location. Furthermore, the analysis of the results showed that the ensemble of 50 ANN trained by Bayesian regularization and Levenberg–Marquardt algorithms slightly outperforms RF.
... To address all above limitations, vision-based monitoring has been exploded due to its practical deployment and cost-effectiveness (Catbas, Zaurin, Gul, & Gokce, 2012;Zaurin & Catbas, 2010b). Regarding vision-based displacement and vibration measurement, several studies proposed algorithms for determining deflection and vibration from multi-points on a small beam by means of matching detected edges or markers between consecutive image frames collected by a digital camera (Cantatore, Cigada, Sala, & Zappa, 2009;Jurjo, Magluta, Roitman, & Gonçalves, 2010;Patsias & Staszewskiy, 2002;Poudel, Fu, & Ye, 2005;Rucka & Wilde, 2005;Shi, Xu, Wang, & Li, 2010;Sładek et al., 2013). Even though most of these studies could obtain both static deflection and dynamic vibration of a beam, the algorithms were limited for laboratory implementations. ...
... The LEDs that served as targets were tracked by locating their centers on each captured digital image. Rucka and Wilde 14 attached circular points to a lateral surface of a cracked beam that underwent static deformation, which was measured by tracking the attached points on captured digital images. Wavelet transforms of the measured deformation were used to detect the crack of the beam. ...
Research works on photogrammetry have received tremendous attention in the past few decades. One advantage of photogrammetry is that it can measure displacement and deformation of a structure in a fully non-contact, full-field manner. As a non-destructive evaluation method, photogrammetry can be used to detect structural damage by identifying local anomalies in measured deformation of a structure. Numerous methods have been proposed to measure deformations by tracking exterior features of structures, assuming that the features can be consistently identified and tracked on sequences of digital images captured by cameras. Such feature-tracking methods can fail if the features do not exist on captured images. One feasible solution to the potential failure is to artificially add exterior features to structures. However, painting and mounting such features can introduce unwanted permanent surficial modifications, mass loads, and stiffness changes to structures. In this article, a photogrammetry-based structural damage detection method is developed, where a visible laser line is projected to a surface of a structure, serving as an exterior feature to be tracked; the projected laser line is massless and its existence is temporary. A laser-line-tracking technique is proposed to track the projected laser line on captured digital images. Modal parameters of a target line corresponding to the projected laser line can be estimated by conducting experimental modal analysis. By identifying anomalies in curvature mode shapes of the target line and mapping the anomalies to the projected laser line, structural damage can be detected with identified positions and sizes. An experimental investigation of the damage detection method was conducted on a damaged beam. Modal parameters of a target line corresponding to a projected laser line were estimated, which compared well with those from a finite element model of the damaged beam. Experimental damage detection results were validated by numerical ones from the finite element model.
... The interface slip between the steel plate and concrete cube was determined using a photogrammetric technique (c.f. [34]). The digital RGB photograph (Figure 5a) was transformed into the CMYK space according to the formula ...
Adhesive bonding is increasingly being incorporated into civil engineering applications. Recently, the use of structural adhesives in steel-concrete composite systems is of particular interest. The aim of the study is an experimental investigation of the damage assessment of the connection between steel and concrete during mechanical degradation. Nine specimens consisted of a concrete cube and two adhesively bonded steel plates were examined. The inspection was based on the ultrasound monitoring during push-out tests. Ultrasonic waves were excited and registered by means of piezoelectric transducers every two seconds until the specimen failure. To determine the slip between the steel and concrete a photogrammetric method was applied. The procedure of damage evaluation is based on the monitoring of the changes in the amplitude and phase shift of signals measured during subsequent phases of degradation. To quantify discrepancies between the reference signal and other registered signals, the Sprague and Gears metric was applied. The results showed the possibilities and limitations of the proposed approach in diagnostics of adhesive connections between steel and concrete depending on the failure modes.
... Noticeably, abnormal wavelet coefficients occur near the boundaries of * W , s referred to as the boundary effect of the WT on a signal with finite length. Interpolation [45] and padding [46] methods are two types of manipulation to deal with this boundary effect. For simplicity in practice, another simple type of manipulation of vanishing abnormal wavelet coefficients [35,43,47,48] is employed in this study. ...
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.
... In addition, the global trends induced by mode shape waveforms cannot be filtered sufficiently as consequence of using Harr wavelet. Based on Wang and Deng's investigation, Rucka and Wilde [12,13], Katunin [14,15], and Cao et al. [16] and Xu et al. [17] verified the applicability of various wavelets in damage detection. The results show that the performances of wavelet transform can be essentially improved when the vanishing moment is larger than 4. In the work, Rucka and Wilde [13] pointed out that the phase information of the CWT was not stable enough for damage detection in applications. ...
The continuous wavelet transform (CWT) is one of the crucial damage identification tools in the vibration-based damage assessment. Because of the vanishing moment property, the CWT method is capable of featuring damage singularity in the higher scales, and separating the global trends and noise progressively. In the classical investigations about this issue, the localization property of the CWT is usually deemed as the most critical point. The abundant information provided by the scale-domain information and the corresponding effectiveness are, however, neglected to some extent. Ultimately, this neglect restricts the sufficient application of the CWT method in damage localization, especially in noisy conditions. In order to address this problem, the wavelet correlation operator is introduced into the CWT damage detection method as a post-processing. By means of the correlations among different scales, the proposed operator suppresses noise, cancels global trends, and intensifies the damage features for various mode shapes. The proposed method is demonstrated numerically with emphasis on characterizing damage in noisy environments, where the wavelet scale Teager-Kaiser energy operator is taken as the benchmark method for comparison. Experimental validations are conducted based on the benchmark data from composite beam specimens measured by a scanning laser vibrometer. Numerical and experimental validations/comparisons present that the introduction of wavelet correlation operator is effective for damage localization in noisy conditions.
... The modal strain energy method is another method developed from mode shapes. Cracks can cause changes in modal strain energy, and in turn they can be identified by such changes [32,[35][36][37][38][39]; recently, modern signal processing methods such as wavelet transform (WT) [40][41][42][43][44][45][46][47][48][49] and fractal dimension (FD) [50][51][52][53][54] have been applied to mode shapes for crack identification by characterizing the crack-caused singularities therein. Recent attention to crack identification methods relying on mode shape has focused on the robustness of the methods to environmental noise interference [30,33]. ...
Carbon fiber reinforced polymer laminates are increasingly used in the aerospace and civil engineering fields. Identifying cracks in carbon fiber reinforced polymer laminated beam components is of considerable significance for ensuring the integrity and safety of the whole structures. With the development of high-resolution measurement technologies, mode-shape-based crack identification in such laminated beam components has become an active research focus. Despite its sensitivity to cracks, however, this method is susceptible to noise. To address this deficiency, this study proposes a new concept of multi-resolution modal Teager–Kaiser energy, which is the Teager–Kaiser energy of a mode shape represented in multi-resolution, for identifying cracks in carbon fiber reinforced polymer laminated beams. The efficacy of this concept is analytically demonstrated by identifying cracks in Timoshenko beams with general boundary conditions; and its applicability is validated by diagnosing cracks in a carbon fiber reinforced polymer laminated beam, whose mode shapes are precisely acquired via non-contact measurement using a scanning laser vibrometer. The analytical and experimental results show that multi-resolution modal Teager–Kaiser energy is capable of designating the presence and location of cracks in these beams under noisy environments. This proposed method holds promise for developing crack identification systems for carbon fiber reinforced polymer laminates.
... Noticeably, abnormal wavelet coefficients occur near the boundaries of Re* s W , referred to as the boundary effect of the WT on a signal with finite length. Interpolation [24] and padding [25] methods are two types of manipulation to deal with this boundary effect. For simplicity in practice, another simple type of manipulation of vanishing abnormal wavelet coefficients [16,26] is employed in this study. ...
... Noticeably, abnormal wavelet coefficients occur at the ends of W Ã 1;s , W Ã 3;s , and W Ã 4;s , referred to as the boundary effect of wavelet transform on a limited signal. Interpolation [64] and padding methods [65,66] are usually used to address this boundary effect. For simplicity in this study, a simple method of vanishing abnormal wavelet coefficients is employed to eliminate the boundary effect. ...
... Since the pioneering study by Sanayei and Onipede [13] who proposed a method for the crack location in frames by making use of static measurements, some authors provided considerable efforts towards the static identification of damage in frames [14], arches [15] and beam-like structures [16], also accounting for the instrumental errors [28]. Others employed wavelet transforms to enhance the effect of cracks in the static detection profiles for a more efficacious identification procedure [29]. ...
In this paper a procedure for the static identification and reconstruction of concentrated damage distribution in beam-like structures, implemented in a dedicated software, is presented. The proposed damage identification strategy relies on the solution of an optimisation problem, by means of a genetic algorithm, which exploits the closed form solution based on the distribution theory of multi-cracked beams subjected to static loads. Precisely, the adoption of the latter closed-form solution allows a straightforward evolution of an initial random population of chromosomes, representing different damage distributions along the beam axis, towards the fittest and selected as the sought solution. This method allows the identification of the position and intensity of an arbitrary number of cracks and is limited only by the amount of data experimentally measured. The proposed procedure, which has the great advantage of being robust and very fast, has been implemented in the powerful agent based software environment NetLogo, and is here presented and validated with reference to several benchmark cases of single and multi-cracked beams considering different load scenarios and boundary conditions. Sensitivity analyses to assess the influence of instrumental errors are also included in the study.
... As it was introduced in chapter 4 more complex IE signal analysis can be helpful for bond strength estimation in repair systems. A new tool for signal analysis -wavelet multiresolution time-scale method was recently implemented in NDT for concrete structures assessment [26][27][28]. It presents the next logic step in frequency analysis of signals -a STFT method of flexible size windows. ...
According to Concrete Repair Manual as well as ACI 562-16 and European EN 1504-10 standards, a bond strength as a measure of adhesion is one the main feature of repair system necessary to be assessed. The most common laboratory and engineering method for bond strength evaluation is pull-off test. This is however a semi-destructive method that needs a repair in a place of measurement. Recently, the great interest in nondestructive techniques (NDT) development is noted. Impact-echo (IE) is considered as one of the most promising methods for this purpose.
In this paper, the study on the usability the IE test based on frequency spectrum analysis for bond strength evaluation is analyzed. Both Finite Element Method (FEM) simulation and experimental tests were performed in order to obtain potential relations between IE frequency spectrum and parameters characterizing concrete substrate quality that may affect the final bond strength and the real value of pull-off bond strength measured on samples as well. It was concluded that the IE method can be a useful tool for interface quality and bond strength evaluations in concrete repair system. However, more complex signal analysis, e.g. wavelet analysis, should be considered in the future.
... To address all above limitations, vision-based monitoring has been exploded due to its practical deployment and cost-effectiveness (Catbas, Zaurin, Gul, & Gokce, 2012;Zaurin & Catbas, 2010b). Regarding vision-based displacement and vibration measurement, several studies proposed algorithms for determining deflection and vibration from multi-points on a small beam by means of matching detected edges or markers between consecutive image frames collected by a digital camera (Cantatore, Cigada, Sala, & Zappa, 2009;Jurjo, Magluta, Roitman, & Gonçalves, 2010;Patsias & Staszewskiy, 2002;Poudel, Fu, & Ye, 2005;Rucka & Wilde, 2005;Shi, Xu, Wang, & Li, 2010;Sładek et al., 2013). Even though most of these studies could obtain both static deflection and dynamic vibration of a beam, the algorithms were limited for laboratory implementations. ...
Although vision-based methods for displacement and vibration monitoring have been used in civil engineering for more than a decade, most of these techniques require physical targets attached to the structures. This requirement makes computer vision-based monitoring for real-life structures cumbersome due to need to access certain critical locations. In this study, a non-target computer vision-based method for displacement and vibration measurement is proposed by exploring a new type of virtual markers instead of physical targets. The key-points of measurement positions obtained using a robust computer vision technique named Scale Invariant Feature Transform (SIFT) show a potential ability to take the place of classical targets. To calculate the converting ratio between pixel-based displacement and engineering unit (millimeter), a practical camera calibration method is developed to convert pixel–based displacements to engineering unit since a calibration standard (a target) is not available. Methods and approaches to handle challenges such as low contrast, changing illumination and outliers in matching key-points are also presented. The proposed method is verified and demonstrated on the UCF 4-span bridge model and on a real-life structure, with excellent results for both static and dynamic behavior of the two structures. Finally, the method requires a simple, less complicated and more cost-effective hardware compared to conventional displacement and vibration monitoring measuring technologies.
... However, the lumped quantities of frequencies are less sensitive to damage location [5][6][7][8][9]. In comparison, mode shape (containing its derivatives) provides abundant damage localization information [10][11][12][13][14][15][16][17][18][19]. It points out that Xiang et al. [19] proposed a two-step method combining curvature mode shape and wavelet finite element model-based method to determine damage locations and severities. ...
Modal curvature is one of the most important damage indices utilized in the damage identification for composite structures. However, few kinds of sensors can provide the measure for modal curvature directly. The lack of direct measurement method for modal curvature necessitates the use of the central difference estimation, which reduces the stability of the algorithm. Noise is severely amplified by the central difference, and hence limits the damage identification through the use of modal curvature estimation. Instead of numerical differentiation, the two-dimensional Fourier spectral method is employed to conduct the two-dimensional modal curvature estimation in this paper. The use of Fourier spectral method over the conventional central difference operator gives the proposed methodology the following advantages: (1) Spectral calculations for spatial derivatives are implemented in global space, thus noise can be suppressed. The k-domain generated in algorithm provides the space for spatial filtering. (2) The precise estimation for modal curvatures can be obtained by aid of the trigonometric interpolation in spectral method. (3) The proposed method calculates the modal curvatures based on fast Fourier transform, thus the efficiency is ensured. By the numerical and experimental comparisons with the classical central difference method, the suitability of the present method is verified for composite structures.
... Noticeably, abnormal wavelet coefficients occur at the ends of W Ã 1;s , W Ã 3;s , and W Ã 4;s , referred to as the boundary effect of wavelet transform on a limited signal. Interpolation [64] and padding methods [65,66] are usually used to address this boundary effect. For simplicity in this study, a simple method of vanishing abnormal wavelet coefficients is employed to eliminate the boundary effect. ...
Detection of multiple damage using modal curvature in noisy environments has become a research focus of considerable challenge and great significance over the last few years. However, a noticeable deficiency of modal curvature is its susceptibility to noise, which usually results in a noisy modal curvature with obscured damage signature. To address this deficiency, this study formulates a new concept of complex-wavelet modal curvature. Complex-wavelet modal curvature features the ability to reveal and delineate damage under noisy conditions. The effectiveness of the concept is analytically verified using cracked beams with various types of boundary conditions. The applicability is further experimentally validated by an aluminum beam with a single crack and a carbon-fiber-reinforced polymer composite beam with three cracks in the laboratory with mode shapes measured by a scanning laser vibrometer. Both analytical and experimental results have demonstrated that the complex-wavelet modal curvature is capable of revealing slight damage by eliminating noise interference, with no need for prior knowledge of either material properties or boundary conditions of the beam under inspection.
... Wavelet analyses, Empirical Mode Decomposition (EMD), Genetic algorithms are some advanced methods used in damage detection. Small cracks does not make significant changes in modal parameters, wavelet transform is useful for such cases [5]. ...
Empirical mode decomposition (EMD) is a relatively new form of time series analysis which is developed to decompose a signal into Intrinsic Mode Functions (IMFs). In this work, EMD is introduced and key aspects of its application in detection of a crack in a rectangular steel plate by analyzing the natural frequencies are proposed. This method helps to analyze a non-stationary signal.Comparative study of various signal processing techniques such as Fast Fourier Transform (FFT), Short Time Fourier Transform (STFT) and Empirical Mode Decomposition (EMD) has been performed to analyze changes in modal characteristics in order to detect a crack in a rectangular steel plate. The natural frequencies of cracked and uncracked plates obtained by EMD are also compared with Finite Element Method (FEM) results. Experiments are performed where fixed plates are excited and time domain vibration data are acquired to employ signal processing techniques. [DOI: 10.13140/RG.2.1.2467.8488; National Conference on Condition Monitoring, NCCM, 2015]
The present study is concerned with detecting a crack in the beam numerically and experimentally using maximal overlapping discrete wavelet transform (MODWT). Slope discontinuity in the beam elastic line can reveal the presence of a crack in a beam. The MODWT is used for locating the cracks in a beam. MODWT coefficients are compared with discrete wavelet transform coefficients at different noise levels. For the experimental validation, high-resolution measurements of the cantilever beam deflection are obtained using photographic measurements. The algorithm is tested for the detection of cracks away and near the ends of a beam. Crack detection near the end of the beam is difficult due to border distortion. Border distortion suppresses the signal in that region. Isomorphism is utilized to shrink the border distortion zone. It helps in the better visualization of the spike due to the crack located away from the ends. Moving averaging is applied to the MODWT-based results for better localization of the spike near the crack position.
The primary objective of this chapter is to develop output-only modal identification and structural damage detection. Identification of multidegree of freedom (MDOF) linear time invariant (LTI) and linear time variant (LTV—due to damage) systems based on time–frequency (TF) techniques—such as short-time Fourier transform (STFT), empirical mode decomposition (EMD), and wavelets—and also a newly merging blind source separation (BSS) technique is discussed. STFT, EMD, and wavelet methods developed to date are reviewed in sufficient detail. In addition, a Hilbert transform (HT) approach to determine frequency and damping is also presented. In this chapter, STFT, EMD, HT, and wavelet techniques are developed for decomposition of free-vibration response of MDOF systems into their modal components. Once the modal components are obtained, each one is processed using HT to obtain the modal frequency and damping ratios. In addition, the ratio of modal components at different degrees of freedom facilitates determination of mode shape. In cases with output-only modal identification using ambient/random response the random decrement technique is used to obtain free-vibration response.
The advantage of TF techniques is that they are signal-based; hence, they can be used for output-only modal identification. A three degree of freedom 1:10 scale model test structure is used to validate the proposed output-only modal identification techniques based on STFT, EMD, HT, and wavelets. Both measured free-vibration and forced-vibration (white noise) responses are considered. The second objective of this chapter is to show the relative ease with which the TF techniques can be used for modal identification and their potential for real-world applications wherein output-only identification is essential. Recorded ambient vibration data processed using techniques such as random decrement technique can be used to obtain the free-vibration response, so that further processing using TF-based modal identification can be performed.
In order to eliminate the wavelet boundary effect caused by the limitation of data length, a univariate predictive extension method based on phase space reconstruction and least squares support vector machine (LSSVM) is proposed. Compared with the traditional extension methods, whether in large scale or small scale, the predictive extension method can effectively eliminate the boundary effect of the wavelet transform. The predictive extension method is used to extend the average annual flow of Zamashik, Qilian, Yingluoxia, and Zhengyixia hydrological stations in the Hei River. Then, wavelet transform multiscale analysis is performed on the extended time series. The wavelet variance curve of the runoff time series after extending is obviously smoother than the unprocessed wavelet variance curve, and to a certain extent, the pseudo period caused by the wavelet boundary effect is eliminated. Analysis results show there are 10-year and 36-year cycles at Zamashik station, 10-year and 25-year cycles at Qilian station, 16-year and 38-year cycles at Yingluoxia station, and 9-year, 21-year, and 30-year cycles at Zhengyixia station.
Wavelet based crack detection has certain limitations such as, border distortion near the ends of a signal and the requirement of high measurement resolution. Border distortion restricts the crack detection near the ends of a beam. Detecting crack near the fixed end is critical as it faces the highest bending stresses. High measurement resolution is required for better localization of cracks and also to shrink the border distortion zone. In the present work, the effect of measurement resolution and wavelet scale on the border distortion is studied. Suitable wavelet scale is selected based on crack localization and smoothness of wavelet coefficients. The effect of measurement resolution on signal extension using isomorphism is presented. Photographic method is used to obtain the high resolution measurement of the beam deflection. The algorithm is tested for the detection of a crack in the border distortion zone. Also, the detection of two simultaneous cracks in the beam is presented
Researches on photogrammetry have received tremendous attention in the past few decades. In this paper, a photogrammetry-based structural damage detection method is developed, where a visible laser line is projected to a surface of a structure, serving as an exterior feature to be tracked. A laser-line-tracking technique is proposed to track the projected laser line on captured digital images. Modal parameters of a target line corresponding to the projected laser line can be estimated by conducting experimental modal analysis. By identifying anomalies in curvature mode shapes of the target line and mapping the anomalies to the projected laser line, structural damage can be detected with identified positions and sizes. An experimental investigation of the damage detection method was conducted on a damaged beam. Modal parameters of a target line corresponding to a projected laser line were estimated, which compared well with those from a finite element model of the damaged beam. Experimental damage detection results were validated by numerical ones from the finite element model.
This chapter presents a fractal dimension approach to damage detection in composite structures. This approach provides an alternative to the wavelet approach in the previous chapter and is model free. This means that the fractal approach can be used directly with measured data. We also use a static deflection profile in this chapter as a response variable. The deflection profile can be sensitive to local damage, as we shall show in this chapter. Matrix cracks are considered as a local damage and spatial variation in material properties is considered. Section 8.1 presents some background from the literature to motivate the use of fractal dimension measure in structural damage detection. Section 8.2 presents the definition of fractal dimension and an outline of the composite plate model with matrix cracks. Section 8.3 presents numerical results of composite plate static deflection and the effect of curvature, fractal dimension operator and the curvature of fractal dimension on the static deflection of a plate with a seeded local damage. Uncertainty in the material properties is introduced as a random field. Section 8.4 presents a summary of this chapter. This chapter is based on material in [1].
In this paper, the vibrational power flow of a cracked beam made of functionally graded materials (FGMs) is investigated. The Young's modulus and mass density change exponentially along the thickness direction of the beam. The cracked FGM beam is divided into two sub-beams at the crack section which are connected by a massless rotational spring. Based on the Timoshenko beam theory, the governing equations of the cracked FGM beam are derived by using the neutral plane as the reference plane. The dynamic response of the FGM beam subjected to a harmonic concentrated transverse force is solved by the wave propagation approach. The input power flow and the transmitted power flow are obtained. The effect of the crack location and depth and the Young's modulus ratio on the input power flow and the transmitted power flow is studied in detail. A new damage index (DI) for the crack identification of FGM beams is proposed by applying continuous wavelet transform (CWT) to the transmitted power flow distribution along the beam longitudinal direction. The peak of DI indicates the crack location in FGM beams with small crack depth.
Breathing cracks are often encountered in engineering structures and detection of such cracks at the earliest stage is important for safety and serviceability of the structures. In this paper, a new breathing crack identification approach based on the time-domain sensitivity analysis is proposed. For the forward problem, the crack is simply treated as a nonlinear oscillator and how to model a structure with breathing cracks is specified. As regards the inverse crack identification, it is formulated as a nonlinear least-squares optimization problem and a new sensitivity-based approach is developed to get the solution. In doing so, the sensitivity analysis of the possibly non-differentiable breathing crack models is necessarily proceeded through a smoothing strategy. Moreover, to enhance the convergence, the trust-region constraint is introduced and the Tikhonov regularization is naturally called to tackle the constraint. Numerical examples are studied to verify the feasibility and efficiency of the proposed approach in breathing crack identification.
This paper addresses the identification problem of multiple open cracks in beams based on damage-induced variations in the static deflection of the beam. A two-step non-model-based damage localization and quantification methodology is proposed. First, the damage locations can be identified from the slope discontinuities in the deflection variation using a specific linear-trend filtering function. Then, the crack depths can be assessed from characteristic expressions of rotational spring models. An experimental case study of a simply supported beam with multiple cracks is used to exam the performance of the method. The deflections of the beam were measured with a digital photogrammetric system using partial measurements. The difference between the idealized lumped spring model for the crack and the actual effect of a real crack in the damage identification process and the performance of the method for statically indeterminate beams are illustrated through numerical examples. The paper shows that the proposed method can accurately locate and quantify multiple closely spaced cracks in beams in practical applications.
Structural health monitoring has increasingly been a focus within the civil engineering research community over the last few decades. With increasing application of sensor networks in large structures and infrastructure systems, effective use and development of robust algorithms to analyze large volumes of data and to extract the desired features has become a challenging problem. In this paper, we grasp some precautions and key points of the signal processing approach, wavelet, establish a relative reliable framework, and analyze three problems that require attention when applying wavelet based damage detection approach. The cases studies how to use optimal scales for extracting mode shapes and modal curvatures in a reinforced concrete beam and how to effectively identify damages using maximum curves of wavelet coefficient differences. Moreover, how to make a recognition based on the wavelet multi-resolution analysis, wavelet packet energy, and fuzzy sets is a meaningful topic that has been addressed in this work. The relative systematic work that compasses algorithms, structures and evaluation paves a way to a framework regarding effective structural health monitoring, orientation, decision and action.
In this paper, the structural mode shapes extracted from the finite element model of a simply supported reinforced concrete beam are employed for damage identification using different types of wavelets. To start with, the parity of signals, wavelets, and their convolution, that is, wavelet transform properties, are verified. In light of the mathematical modeling complexity of modal frequency, which relates to the localization and quantification of damage in the reinforced concrete beam, the maximum curves based on multiresolution wavelet transform coefficient differences and the corresponding theoretical assumptions are described and analyzed. It is concluded that the maximum curve reaches a peak value at a specific scale for a specific case, based upon which, a new mode shape based algorithm and damage index are proposed for damage identification. The accuracy of localization as well as the sensitivity of quantification is further discussed.
Vibration data from mechanical systems carry important information that is useful for characterization and diagnosis. Standard approaches rely on continually streaming data at a fixed sampling frequency. For applications involving continuous monitoring, such as Structural Health Monitoring (SHM), such approaches result in high volume data and rely on sensors being powered for prolonged durations. Furthermore, for spatial resolution, structures are instrumented with a large array of sensors. This paper shows that both volume of data and number of sensors can be reduced significantly by applying Compressive Sensing (CS) in vibration monitoring applications. The reduction is achieved by using random sampling and capitalizing on the sparsity of vibration signals in the frequency domain. Preliminary experimental results validating CS-based frequency recovery are also provided. By exploiting the sparsity of mode shapes, CS can also enable efficient spatial reconstruction using fewer spatially distributed sensors. CS can thereby reduce the cost and power requirement of sensing as well as streamline data storage and processing in monitoring applications. In well-instrumented structures, CS can enable continued monitoring in case of sensor or computational failures.
Background/Objective: Early detection of damage in structures can prevent loss of lives and extend their service life. This has drawn considerable attention of researchers to applying Structural Health Monitoring (SHM) to detect structural damage. Wavelet Transform (WT) is a tool utilized to identify damage in structures by using structural responses. In this study, a WT damage detection method using Operational Deflection Shape (ODS) difference is presented. Method: A two-dimensional Continuous Wavelet Transform (CWT) is utilized to decompose the difference between the ODS of the intact and damaged structure to detect and locate damage. To demonstrate the ability of this technique, a numerical model of a steel plate is applied. Findings: The results show that the location of damage influences damage detectability when the decomposed signal is noisy. Improvements: This method eliminates the problem of border distortion experienced when conventional ODS is applied. The methodology shows the proposed techniques' simplicity while the results show accuracy.
In damage assessment of composite structures, the modal curvature appears to be one of the most important damage indices in the past decades. However, a noticeable deficiency of the modal curvature is its susceptibility to noise, which is mainly induced by the numerical difference estimation. This study proposes the scale-wavenumber domain filtering method based on the combination of the continuous wavelets transform, the discrete Fourier transform-based modal curvature and the scale wavenumber domain filtering method. The continuous wavelet transform provides the scale domain for noisy mode shape analysis, in which the normal fluctuations and the noise-induced fluctuations are filtered from the inspected mode shapes. The discrete Fourier transform-based modal curvature supplies the wavenumber domain expressions of the scaled mode shapes. In the scale and wavenumber domains, some special filters are designed and used in noise suppression. The effectiveness of the proposed method is analytically verified by employing the cracked composite beam model, and the performance is further validated by the experimental data from the carbon-fiber-reinforced polymer beam with crack. Based on these validations, it is observed that the proposed method is capable of revealing slight damage in noisy condition, without the requirement for the prior knowledge of material properties.
A method of non-destructively assessing the integrity of structures using measurements of the structural natural frequencies is described. It is shown how measurements made at a single point in the structure can be used to detect, locate and quantify damage. The scheme presented uses finite-element analysis, since this method may be used on any structure. The principle may, however, be used in conjunction with other mathematical techniques. Only one full analysis is required for each type of structure.
Results are presented from tests on an aluminium plate and a cross-ply carbon-fibre-reinforced plastic plate. Excellent agreement is shown between the predicted and actual damage sites and a useful indication of the magnitude of the defect is obtained.
This paper presents a methodology to nondestructively locate and estimate the size of damage in structures for which a few natural frequencies or a few mode shapes are available. First, a frequency-based damage detection (FBDD) method is outlined. A damage-localization algorithm to locate damage from changes in natural frequencies and a damage-sizing algorithm to estimate crack-size from natural frequency perturbation are formulated. Next, a mode-shape-based damage detection (MBDD) method is outlined. A damage index algorithm to localize and estimate the severity of damage from monitoring changes in modal strain energy is formulated. The FBDD method and the MBDD method are evaluated for several damage scenarios by locating and sizing damage in numerically simulated prestressed concrete beams for which two natural frequencies and mode shapes are generated from finite element models. The result of the analyses indicates that the FBDD method and the MBDD method correctly localize the damage and accurately estimate the sizes of the cracks simulated in the test beam.
In this paper, a newly derived algorithm to predict locations and severities of damage in structures using changes in modal characteristics is presented. First, two existing algorithms of damage detection are reviewed and the new algorithm is formulated in order to improve the accuracy of damage localization and severity estimation by eliminating erratic assumptions and limits in the existing algorithms. Next, the damage prediction accuracy is numerically assessed for each algorithm when applied to a two-span continuous beam for which pre- and post-damage modal parameters are available for only a few modes of vibration. Compared to the existing damage detection algorithms, the new algorithm improved the accuracy of damage localization and severity estimation results in the test beam.
The WFT localizes a signal simultaneously in time and frequency by "looking" at it through a window that is translated in time, then translated in frequency (i.e., modulated in time). These two operations give rise to the "notes" gω,t(u). The signal is then reconstructed as a superposition of such notes, with the WFT ƒ(tω,t) as the coefficient function. Consequently, any features of the signal involving time intervals much shorter than the width T of the window are underlocalized in time and must be obtained as a result of constructive and destructive interference between the notes, which means that "many notes" must be used and ƒ(ω, t) must be spread out in frequency. Similarly, any features of the signal involving time intervals much longer than T are overlocalized in time, and their construction must again use "many notes," with ƒ(ω,t) spread out in time. This can make the WFT an inefficient tool for analyzing regular time behavior that is either very rapid or very slow relative to T. The wavelet transform solves both of these problems by replacing modulation with scaling to achieve frequency localization.
In this text, the author presents mathematical background and major wavelet applications, ranging from the digital telephone to galactic structure and creation of the universe. It discusses in detail the historic origins, the algorithms and the applications of wavelets.
When a structure is subjected to damage, its dynamic response changes, characterized by shifts in the eigenvalues and modifications of the eigenvectors. Considerable effort has been put into investigating the relationship between the damage location, the damage size and the corresponding changes in the eigenparameters. In most cases, emphasis has been on using the shift in eigenvalues as a means of determining the damage location, and the information derived from the change in eigenvectors has largely remained obscure. In this paper a systematic study is presented of the relationship between damage location, damage size and the changes in the eigenvalues and eigenvectors of a cantilever when subjected to damage. A finite element model of a uniform cross sectioned cantilever was chosen to provide data for analysis. The changes in the eigenvalues and eigenvectors are shown to follow a definite trend in relation to the location and extent of damage.
This paper examines the sensitivity of wavelet technique in the detection of cracks in beam structures. Specifically, the effects of different crack characteristics, boundary conditions, and wavelet functions employed are investigated. Crack characteristics studied include the length, orientation and width of slit. The two different boundary conditions considered are simply supported and fixed end support, and the two types of wavelets compared in this study are the Haar and Gabor wavelets. The results show that the wavelet transform is a useful tool in detection of cracks in beam structures. The dimension of the crack projected along the longitudinal direction can be deduced from the analysis. The method is sensitive to the curvature of the deflection profile and is a function of the support condition. For detection of discrete cracks, Haar wavelets exhibit superior performance.
This paper deals with the detection of open cracks in beam structures that undergo transverse vibrations. The investigation is aimed at detecting the location of open cracks in damaged beams by minimizing measurement data and baseline information of the structure. The study is carried out by using the continuous wavelet transform (CWT). The application of this recent, but advanced, mathematical tool is initially presented through a theoretical background, which is believed to be valuable for bridging the gap between the CWT and previous existing techniques. It is shown how the possibility to efficiently identify localized damages by CWT comes up from the intrinsic capability of the wavelets to collect several mathematical tools in only one mathematical aspect: derivatives, convolution and appropriate smoothing of data are translated into the CWT. Simulations show how the redundancy of the CWT in the functional space is able to efficiently identify locations of open cracks in the presence of noisy or clean data. Indeed, the possibility to approach the problem by using different families of wavelets, for several available scales, allows a successful application of the characteristic microscopy of the wavelets. The technique may be promisingly applied to discrete vibrational data.
In this paper a simple method for crack identification in beam structures based on wavelet analysis is presented. The fundamental vibration mode of a cracked cantilever beam is analyzed using continuous wavelet transform and both the location and size of the crack are estimated. The position of the crack is located by the sudden change in the spatial variation of the transformed response. To estimate the size of the crack, an intensity factor is defined which relates the size of the crack to the coefficients of the wavelet transform. An intensity factor law is established which allows accurate prediction of crack size. The viability of the proposed method is investigated both analytically and experimentally in case of a cantilever beam containing a transverse surface crack. In the light of the results obtained, the advantages and limitations of the proposed method as well as suggestions for future work are presented and discussed.
This work is an in-depth study of a boundary effect detection (BED) method for pinpointing locations of small damages in beams using operational deflection shapes (ODSs) measured by a scanning laser vibrometer. The BED method requires no model or historical data for locating structural damage. It works by decomposing a measured ODS into central and boundary-layer solutions using a sliding-window least-squares curve-fitting technique. For high-order ODSs of an intact beam, boundary-layer solutions are non-zero only at structural boundaries. For a damaged beam, its boundary-layer solutions are non-zero at the original boundaries and damage locations because damage introduces new boundaries. At a damage location, the boundary-layer solution of slope changes sign, and the boundary-layer solution of displacement peaks up or dimples down. The theoretical background is shown in detail. Noise and different types of damage are simulated to show how they affect damage locating curves. Experiments are performed on several different beams with different types of damage, including surface slots, edge slots, surface holes, internal holes, and fatigue cracks. Experimental results show that this damage detection method is sensitive and reliable for locating small damages in beams.
Damage detection by the wavelet transform of the fundamental vibration mode receives much attention recently. Many investigations report successful applications of the wavelet transform in damage detection, but most of them appear to lack theoretical justifications. The objective of this contribution is to show the effectiveness of the wavelet transform by means of its capability to estimate the Lipschitz exponent. It is also addressed that the magnitude of the Lipschitz exponent can be used as a useful indicator of the damage extent. As a specific example, damaged beams are investigated both numerically and experimentally. The continuous wavelet transform (CWT) by a Mexican hat wavelet having two vanishing moments is utilized for the estimation of the Lipschitz exponent. The analysis by the CWT also gives a guideline to choose appropriate discrete wavelet transforms.
This paper discusses a structural damage detection technique based on wavelet analysis of spatially distributed structural response measurements. The premise of the technique is that damage (e.g. cracks) in a structure will cause structural response perturbations at damage sites. Such local perturbations, although they may not be apparent from the measured total response data, are often discernible from component wavelets. The viability of this new technique is demonstrated with two examples: one based on numerically simulated deflection responses of a uniform beam containing a short transverse crack under both static and dynamic loading conditions, and the other based on smooth analytical crack-tip displacement fields. In each of these examples, the deflection or displacement response is analyzed with the wavelet transform, and the presence of the crack is detected by a sudden change in the spatial variation of the transformed response. This damage detection technique may serve the purpose of structural health monitoring in situations where spatially distributed measurements of structural response in regions of critical concern can be made with, for example, networks of distributed sensors, optical fibers, computer vision and area scanning techniques. It appears that this new technique does not require any analysis of the complete structure in question, nor any knowledge of the material properties and prior stress states of the structure.
A damage in a structure alters its dynamic characteristics. The change is characterized by changes in the eigenparameters, i.e., natural frequency, damping values and the mode shapes associated with each natural frequency. Considerable effort has been spent in obtaining a relationship between the changes in eigenparameters, the damage location and the damage size. Most of the emphasis has been on using the changes in the natural frequencies and the damping values to determine the location and the size of the damage. In this paper a new parameter called curvature mode shape is investigated as a possible candidate for identifying and locating damage in a structure. By using a cantilever and a simply supported analytical beam model, it is shown here that the absolute changes in the curvature mode shapes are localized in the region of damage and hence can be used to detect damage in a structure. The changes in the curvature mode shapes increase with increasing size of damage. This information can be used to obtain the amount of damage in the structure. Finite element analysis was used to obtain the displacement mode shapes of the two models. By using a central difference approximation, curvature mode shapes were then calculated from the displacement mode shapes.
In this paper, a method for crack identification in plates based on wavelet analysis is presented. The case of an all-over part-through crack parallel to one edge of the plate is considered. The vibration modes of the plate are analyzed using the continuous wavelet transform and both the location and depth of the crack are estimated. The position of the crack is determined by the sudden change in the spatial variation of the transformed displacement response. To estimate the depth of the crack, an intensity factor is defined which relates the depth of the crack to the coefficients of the wavelet transform. An intensity factor law is established which allows accurate prediction of crack depth. The viability of the proposed approach is demonstrated using simulation examples. In view of the obtained results, the advantages and limitations of the proposed approach as well as suggestions for future work are presented and discussed.
This paper presents applications of the wavelet transform to detect cracks in frame structures, such as beams and plane frames. A simplified review of the theory behind the wavelet transform is given, and the ability of wavelets to detect crack-like damage in structures is demonstrated by means of several numerical examples. The method requires the knowledge of only the response of the damaged structure, i.e. no information about the original undamaged structure is required. In addition, it is shown that the procedure can detect the localization of the crack by using a response signal from static or dynamic loads. Moreover, the response needs to be obtained only at the regions where it is suspected that the damage may be present. The results of the simulation show that if a suitable wavelet is selected, the method is capable to extract damage information from the response signal in a simple, robust and reliable way.
Several papers that have recently appeared in the literature have shown the potential offered by certain mathematical tools (wavelets) for detecting damage in systems such as transversally vibrating beams. However, although the applications shown by different authors suggest that the tools show promise, the literature lacks a clear and concise collocation of the wavelets with respect to these previous methods that show similar (if not identical in certain circumstances) performances. In this paper, the continuous wavelet transforms (cwts) are discussed and compared, from a theoretical and numerical point of view, with those methods known as differentiator operators. Such differentiator operators adopted as filters are also able (similarly to the cwts) to reduce unwanted high frequency noise. Therefore, literature concerning differentiator filters in the digital signal processing area is investigated and several digital filters, known and modified, are analyzed and compared with the cwts in the presence of Gaussian noise. The theoretical aspects are discussed in both the non-transformed and Fourier transformed domain. This study results in an attempt to provide an elucidation on the effectiveness and the need to use the considered methods (differentiator filters and/or cwts) for detecting damage in transversally vibrating beams.
Wavelet toolbox. The MathWorks Inc
- M Misiti
- Y Misiti
- G Oppenheim
- J Poggi
Misiti M, Misiti Y, Oppenheim G, Poggi J. Wavelet toolbox. The
MathWorks Inc; 2000.
Crack identification in cantilever beam using wavelets. In: Workshop on advanced mechanics of urban structures
- Rucka M Wilde
Rucka M, Wilde K. Crack identification in cantilever beam using wavelets. In: Workshop on advanced mechanics of urban structures. 2003, p. 165–8.
Crack identification in cantilever beam using wavelets
- M Rucka
- K Wilde
Rucka M, Wilde K. Crack identification in cantilever beam using
wavelets. In: Workshop on advanced mechanics of urban structures.
2003, p. 165-8.