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Structural damage detection in beams by wavelet transform
Abstract
The use of a laser-based optical system and wavelet transforms is explored for the detection of changes in the properties of cantilevered aluminum beams as a result of damage. The beams were modeled using the ANSYS 5.3 finite-element method and the first six mode shapes for the damaged and the undamaged cases obtained. Damage was simulated by a reduction in the stiffness of one element. Gaussian white noise was added externally to simulate field conditions. The results show that a spatially-localized abnormality in the mode shape could be represented uniquely by a small set of wavelet coefficients while the white noise was uniformly spread throughout the wavelet space. It was observed that the damage clearly manifested in the sixth-order detail of certain modes only. A different finite-element model was used as a test beam to validate the proposed method. An actual aluminum beam, fabricated with dimensions similar to the test beam, was excited and the mode shapes recorded with the scanning laser vibrometer. Damage was created by machining a notch in the beam of the same dimensions as the finite-element test beam. An image of the damage location was obtained from the continuous wavelet transform coefficients. The magnitude of the wavelet coefficients at the damage location showed a close correlation to the severity of damage. It was observed to increase with increasing damage. The finite-element test beam results showed a close correlation to the corresponding experimental beam results. The method benefits from the fact that the undamaged mode shapes were not used to evaluate the condition of the beam, which in most field conditions is not feasible.
... Wavelet transform The wavelet transform theory was established to counter the drawbacks of eigen-theory because it required less computational effort and produced a reliable result at a higher order of modes [41]. In the wavelet theory, the dynamic signal of structural response is broken down into different frequency components to detect some of the special characteristics of the structure [42]. ...
... The wavelet transform theory was established to counter the drawbacks of eigen-theory because it required less computational effort and produced a reliable result at a higher order of modes [41]. In the wavelet theory, the dynamic signal of structural response is broken down into different frequency components or wavelets to detect some of the special characteristics of the structure [42]. The drawbacks of this technique were that the detailed dynamic analysis of the undamaged structure was not conducted or material properties of the structure were not known accurately [70]. ...
Damages can originate in engineering structures due to various detrimental and hostile conditions that leads to calamitous occurrences. Structural damage monitoring has been formally established in the past few decades and is critical for sustaining and upholding the integrity of structures in its designated service life. Real time condition monitoring and damage detection needs to be necessitated for the appropriate functioning of the concerned entity. Vibration intensive damage identification techniques have been reviewed for identifying the actual material properties such as stiffness and damping for assessing authentic health condition of machine elements as well as structures. Acceleration, velocity and displacement-based signals are measured and processed further using vibration monitoring hardware and software. The structural dynamic responses are studied and analyzed to be correlated to the presence of damages. This paper reviews the use of mode-shapes, modal strain energy, wavelet transform, wave-form fractal dimension and finite element model updating in damage identification. The challenges encountered with each technique are discussed and the proposed methodology for overcoming them. Propositions have also been made with respect to the current scenario and downsides of respective technique. The paper will be helpful for practicing engineers and researchers working in structural damage identification and control related field for conceiving novel, reliable, effective, robust, and practical methods.
... e surface interpolation method was also proved first on the basis of numerical simulation and then in the experiment [16,17]. Another example is the detection and location of the damage by means of wavelet analysis of the shape of the natural vibrations, which was first developed for the beams [18,19] and next for the plates [19][20][21] or frames [22]. e authors of this paper used a similar approach in their research. ...
... e authors declare that they have no conflicts of interest. 18 Shock and Vibration ...
This paper presents the use of laser vibrometer measurements to detect and locate damage in a metal plate. An algorithm based on local spatial filters was selected, and for the purpose of comparison, the fault location was also determined based on the wavelet analysis of mode shapes. The research was carried out first on the created finite element model of aluminum plate, where two kinds of damage of increasing size and temperature change were simulated. After obtaining positive results, a laboratory experiment was carried out, which consisted of measuring the vibration of the aluminum plate with the laser vibrometer in undamaged condition, at increased temperatures, and with various damage scenarios. The conclusions of the laboratory experiment confirm the damage detection capabilities of the methods but question their damage localization potential.
... The common practice is to establish a reference chart, using numerical or analytical models, which links the wavelet coefficient values and the damage severity. One direct way to build this relationship is to connect the wavelet coefficients at the damage locations of a certain scale to the damage severity (Okafor and Dutta, 2000;Umesha et al., 2009;Janeliukstis et al., 2017). Alternatively, damage indices derived from the use of wavelet coefficients across scales are proposed (Hong et al., 2002;Douka et al., 2003;Loutridis et al., 2004;Andreaus et al., 2017;Zhu et al., 2019). ...
... The major disadvantage of the proposed damage indices is that they are damage location dependent, which means the establishment of the reference chart requires the knowledge of the damage locations. For mode shape based analyses, they are also related to the mode order (Okafor and Dutta, 2000;Hong et al., 2002;Douka et al., 2003;Janeliukstis et al., 2017;Zhu et al., 2019). For static deflection based analyses, the damage indices also depend on the external load (Spanos et al., 2006;Umesha et al., 2009;Andreaus et al., 2017). ...
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.
... It is so because the lower modes are much easier to acquire than the higher ones. However, the measurements of higher order modes have recently become much simpler by applying a modern scanning laser vibrometer (Okafor and Dutta, 2000;Pai and Young, 2001;Waldron et al., 2002). This raises a question if the higher order modes can also be effectively applied in damage detection using the wavelet technique. ...
... This raises a question if the higher order modes can also be effectively applied in damage detection using the wavelet technique. Okafor and Dutta (2000) analysed three experimental and six numerical modes of a canti-lever beam by the wavelet transform. They concluded that the first and third translational modes showed the damage location clearly, but the second mode was inconclusive because the damage fell in the vicinity of zero-crossing for the second mode. ...
Technical difficulties prevented so far wider applications of higher mode shapes in damage detection. Yet these modes carry on a lot of, so much needed, information on damage inflicted to a structure. However, recent scanning laser-based vibration measurement techniques allow one to uti-lize these higher modes in damage detection effectively. This paper deals with the wavelet-based damage detection technique on a cantilever beam with damage in the form of a single notch of depth 20%, 10% and 5% of the beam height. The purpose of the study is to present the results of experimental and numerical analyses of damage detection based on higher order modes. The first eight modes are considered and the influ-ence of the mode order on the effectiveness of damage detection by the continuous wavelet transform is analysed in detail.
... For non-model-based methods, [41,42] proposed structural health monitoring based on dynamic fingerprints, which are functions of the structural physical properties and modal parameters. Other approaches are wavelet transformation [43][44][45][46][47] and Hilbert-Huang transform [48][49][50][51]. ...
There have been countless studies to investigate structural damage identification. This field of study is sometimes referred to as structural health monitoring. Model updating approach is a non-destructive testing method that uses characteristic values related to structural models such as natural frequencies and mode shapes to identify the damage. Researchers over the last decade have focused on several model updating techniques for structural damage detection and identification. However, various methods can be used for model updating, and it can sometimes be quite confusing to choose which method to use for each case. Since this can have serious consequences, it is imperative to understand model updating better. This paper gives an introduction to structural damage identification, while brief information on finite element model updating is described and reviewed in terms of available methods and types of measured data. Here, the performance of different model updating methods utilized in structural damage identification is compared. This study has found that researchers in the iterative method extensively use modal data-based methods and frequency-based methods. The insights gained from this study may assist those who want a brief idea about model updating and its application in structural damage identification.
... In a different work, Wu and Wang conducted experimental studies adopting SWT and identified crack location and depth in a beam subject to a static displacement [30]. Okafor and Dutta used a small set of wavelet coefficients with uniformly spread white noise to represent a spatially localized abnormality in mode shape [31]. Montanari et al. reported an optimal number of sampling intervals based on spatial CWT damage detection methods in beam structures [32]. ...
Damage detection is of great importance in reducing maintenance cost and preventing collapse of structures. Despite existing damage detection methods, the current literature lacks a comprehensive method, which: (i) is applicable to complex structures with large degrees of freedom, (ii) captures even low-level damages, and (iii) gives reasonable accuracy in the presence of uncertainty conditions such as noise and temperature. Hence, this study proposes a damage detection algorithm based on discrete wavelet transform and an ensemble of pattern recognition models, in which: (1) vibration data is decomposed through discrete wavelet transforms, (2) the decomposed data is compressed using principal component analysis, (3) individual damage models of the structure are trained through pattern recognition models of deep neural network and couple sparse coding, where the compressed decomposed vibration data as well as damage data are inputted, and (4) ultimately, the individual damage models are merged into one by majority voting to predict damage location and severity of the structure. The proposed algorithm is tested on a numerical model of a one-bay three-story steel frame, and experimental data of a large-scale bridge structure. It is found that the algorithm can precisely detect low-level damages at multiple locations, even in beam-column connections and complex structures, in the presence of uncertainty conditions such as noise and temperature.
... The simultaneous ability of reducing noises and detecting minor singularities in mode shapes, caused many researcher to utilize different Wavelet mothers such as Mexican hat [33]. Gabor [34], Haar [35] and Debauchies [36] in structural damage detection field. Zhu et al. [37] utilized Wavelet transform in order to identify damages in functionally graded beams. ...
In this paper, the location of single, double, and triple damage scenarios in reinforced concrete (RC) beams are assessed using the Wavelet transform coefficient. To achieve this goal, the numerical models of RC concrete beams were conducted based on the experimental specimens. The mode shapes and corresponding modal curvatures of the RC beam models in damaged and undamaged status were considered as input signals in Wavelet transform. By considering the Wavelet coefficient as damage index, Daubechies, Biorthogonal, and Reverse Biorthogonal Wavelet families were compared to select the most proper one to identify damage locations. Moreover, various sampling distances and their influence on the damage index were studied. In order to simulate the practical situations, two kinds of noises were added to modal data and then denoised by Wavelet analysis to check the proposed damage index in noisy conditions. The results revealed that among the wavelet families, rbio2.4 and rbio2.2 outperform others in detecting damage locations using mode shapes and modal curvatures, respectively. As expected, the sensitivity of modal curvatures to different damage scenarios is more the mode shapes. By increasing sampling distances from 25 mm to 100 mm, the accuracy of the proposed damage index reduces. In order to eliminate boundary effects, it is necessary to use windowing techniques. Applying Wavelet denoising methods on noise-contaminated modal curvatures leads to proper damage localization in both types of noises.
... Some earlier studies [6][7][8] explored the use of a continuous grid of piezoelectric lead-zirconatetitanate (PZT) (PZT) elements, which are recording vibrations and mechanical stresses toward the crack detection in mechanical structures. With the help of wavelet transform, Okafor and Dutta [9] recorded and analyzed the first six mode shapes of a damaged and undamaged aluminum cantilever beam using a scanning laser vibrometer. Jassim et al. [10] presented a nice mini-review on vibration analysis for a damage occurrence of a cantilever beam. ...
In the current work, to identify the bending mode harmonics, 30 microns thin magnetoelastic ribbons made of metallic glass are embedded inside 6 mm thick PLA plastic cantilever beams made by 3-D printing. This is possible because the ribbons are of magnetoelastic nature and thus change their mechanical state inducing a corresponding change in their magnetic state. The ribbons are placed at four different depths, starting with zero depth at the beam’s external surface all the way inside to the beam’s mid-plane. This technique is capable of detecting seven harmonics, and remarkably, these frequencies remain the same within a marginal error of 1% for all the depths. The amplitude of the modes drops with the increase in depth but is still strong enough, except at the midplane, to be used as a sensing signal. The harmonics spectrum is the unique signature of the structure’s state; this is a proof of concept that in a contactless fashion, the embedded ribbons provide useful information about the mechanical health of a structure.
... The transform may be applied and mapped to the space or time domain of the structure. Thus, they may be used to find an abrupt change in a mode shape (Okafor and Dutta, 2000;Zhu and Law, 2006;Douka et al., 2003) which is often indicative of damage. They may also be used to locate a sudden change in response from an acceleration time response (Hester and González, 2012) and (Hou et al., 2000), or analyse the displacement response at the midspan of a bridge (Zhang et al., 2009). ...
In many countries, a significant number of bridges are approaching or have exceeded their original design life, while at the same time, traffic loads are steadily increasing. It is now a requirement in many developed countries to inspect bridge infrastructure in order to provide adequate maintenance planning and guarantee adequate levels of transport service and safety. In bridge health monitoring, the use of the vibration response of the bridge, to operational loads, is advantageous since it does not cause disruption to traffic flow. The concept is that damage will alter the stiffness, mass, or damping of the system, and that this change will alter the measured dynamic response of the structure. In recent years, larger bridges are being instrumented and monitored on an ongoing basis. This provides a high level of protection to the public and early warning if the bridge becomes unsafe. However, the process is laborious, time-consuming and often very expensive, requiring the installation of sensors and data acquisition electronics on the bridge. The aim of this thesis is to verify the feasibility of a novel alternative; ‘drive-by’ damage detection in bridges, a relatively low cost method consisting of the use of a moving vehicle at highway speeds fitted with sensors to monitor bridge condition.
Vehicle-bridge interaction (VBI) models are used in numerical simulations to test the effectiveness of using data gathered from a moving vehicle to identify damage in a bridge. Initially, changes in damping of the bridge are successfully detected by a truck-trailer vehicle model containing accelerometers. The Power Spectral Density (PSD) of the time-shifted acceleration differences between signals from two sensors are used as the damage indicator. Results for the drive-by system are found to be of similar quality to results for an accelerometer located on the bridge. Results also indicate that bridge damage can be detected quite effectively in the presence of up to a 0.5% difference in axle properties and in the presence of 10% noise in the overall vehicle properties.
Bridge damping has been reported to be sensitive to damage in concrete bridges, however it is unlikely to be effective for steel bridges and is also influenced by environmental phenomena. A crack modelled as a loss in stiffness over a length of beam, is therefore introduced as an alternative approach. This poses challenges in the drive-by application as the data collected is short in duration and standard signal processing techniques often fail to detect bridge information from the vehicle response. A novel algorithm is proposed that uses an optimisation approach as an alternative to standard signal processing techniques for the analysis of short signal segments in the drive-by application. Simulations using a model of a beam in free vibration show that modest losses of stiffness in the bridge can be detected using the vehicle measurements, even in the presence of significant noise levels.
Much of the research to date in the area of drive-by inspection uses two-axle cars or truck-trailer vehicle models, retrospectively fitted with sensors. The recently developed prototype ‘Traffic Speed Deflectometer’ (TSD) is capable of performing pavement deflection surveys at speeds of up to 80 km h-1, avoiding traffic disruption and expensive traffic management. The TSD is investigated here for bridge damage detection using a simply supported finite element beam as the bridge model. Three sensors are used and time-shifted curvatures are proposed as the novel damage indicator. Simulations show that modest local losses of stiffness in a beam can be detected using measurements from the TSD, even in the presence of realistic levels of noise. Differences in the transverse position of the vehicle on the bridge from one measurement to the next, are also investigated and its effect is shown to be insignificant.
Finally, the optimisation approach and the subtraction concept that have been developed are combined in simulations for damage detection in bridges using the TSD vehicle model. In numerical VBI simulations, this research is the first to investigate using the TSD in a drive-by bridge damage detection. An optimisation approach is used as an alternative to standard signal processing techniques to overcome the challenges of the short signal. Five different levels of damage are considered, and the approach allows for noise in the signal and variation in the transverse position of the vehicle in its track. Damage can be detected clearly, even for low levels of damage. For the first time, damage detection in bridges can be effectively carried out at highway speeds in the drive-by context, without contamination from the road profile, using just two sensors.
... This is highly advantageous for characterizing damage by tolerating noise. Thus, WT has been widely used in mode shape-based damage detection methods and many different wavelets have been exploited, such as Mexican hat wavelets [16], Gabor wavelets [17], Haar wavelets [18], and Debauchies wavelets [19]. Zhu et al. [20] used WT mode shape to detect crack in functionally graded beams. ...
Mode shapes have been widely used for structural damage detection. The basic premise of this method is that damage occurring in a structure causes singularities in mode shapes, which in turn reveal damage. However, singularities induced by small damage are insignificant and susceptible to noise. To address these deficiencies, the Teager energy operator (TEO) together with wavelet transform (WT) is introduced to process mode shapes, producing TEO-WT mode shapes. It is noted that each TEO-WT mode shape has its specific sensitivity to damage at a certain location, which means that multiple damage may not be identified simultaneously from a single TEO-WT mode shape. Thus data fusion of multiple TEO-WT mode shapes is used to create an overall TEO-WT mode shape. A damage indicator (DI) is then obtained by integrating the overall TEO-WT mode shape in the scale domain. The DI features distinctive capability to suppress noise, intensify singularities caused by damage, and improve the reliability of damage detection. The efficacy of the method is verified numerically and then validated experimentally on cracked laminated composite beams. The numerical and experimental results demonstrate the capability of the method to detect multiple damage in laminated composite beams under noisy conditions.
... Damage sources Mardasi et al. (2018) Beams and plates Crack Su et al. (2018) 3-storey & 8-storey steel frame Earthquake load Ashory et al. (2018) Composite laminates plates Delamination Yang and Oyadiji (2017) Multi-layer structure Internal defects Su and Huang (2017) 8-storey steel frame Earthquake load Wu and Wang (2011) Aluminum beam Crack Taha et al. (2006) Bridge Traffic dynamic load Melhem and Kim (2003) Concrete road Traffic dynamic load Okafor and Dutta (2000) Beam Crack Hou et al. (2000) Simple structure model Breaking spring 1. METHODOLOGY ...
Embedded structures are widely encountered in construction, such as anti-slide piles in a slope and reinforced concrete frames in a building. The embedded structures are vulnerable subjected to seismic effects. After the seismic load, the integrity of the embedded structures is weakened but the damage is unlikely to be directly observed by engineers; as a result, damage detection of an embedded structure is critical. In this study, the identification of the structural damage is investigated with Wavelet and Fourier transforms. With these two approaches, the structural signal in different frequency domain can be analyzed. The advantages and disadvantages of these two approaches in identifying the damage locations are compared. An outstanding advantage of the Wavelet transform is that it is able to identify the damage location, which makes this approach attractive for engineering practice. This advantage is exemplified by a cantilever beam finite element model.
... Okafor et al, examined three laboratory forms of modes and six forms of numerical mode shape for a cantilever beam by wavelet analysis. They conclude that the first and third transverse sections of the damage site are clearly shown, but the second form of the mode is unsuccessful, since damage occurs in the empty space passing through zero for the second mode shape [14]. Another study showed that damage may occur in places with poor sensitivity for certain modal forms. ...
... They illustrated the technique by measuring the second mode shape of a light-weight cantilever beam through the processing of the LDV output signal in the frequency domain. Okafor and Dutta [14] recorded and analyzed with wavelet transform, the first six mode shapes of a damaged and undamaged aluminum cantilever beam using scanning laser vibrometer. A finite-element model of the beams showed a close correlation to the corresponding experimental beam results. ...
This work introduces for first time the use of the magnetoelastic sensors as vibration probes for damage detection in mechanical structures such as cantilever beams. The purpose is to show some of the advantages of these materials as vibration detectors, as well as the accuracy of them in detecting the natural frequencies of mechanical structures. The sensor used is a ribbon which is composed of an amorphous metallic alloy known as “Metglas 2826MB3”. Various long aluminum alloy beams of the same dimensions but with a single transverse crack at different positions and depths were tested, fixed at one end by using a hydraulic press so as to have consistent boundary conditions. The beams were excited by a single short and intense mechanical contact pulse and then left free to vibrate. The vibrations were forcing the magnetoelastic sensors to change their magnetic state dynamically and thus produce a voltage signal at a close-by external coil. The Fourier analysis reveals seven dominant peaks which lay very close (most of the error values are between 0.5–1.5 %) to the first seven bending mode peaks predicted by the finite-element-method (FEM) commercial software “ANSYS”. Thus the current work is a proof-of-principle that the magnetoelastic sensors can be used for damage detection of mechanical structures.
... Both DWT and CWT have been used on numerical models of a fixed-beam and a simple frame to detect cracks from deflected shapes [34]. Finally, CWT was used to detect damage experimentally from the deflected shape of a beam using laser measurements [21,35,36]. ...
This paper casts a response-based damage detection approach that combines different techniques for remote monitoring of structural health. An experimental study is carried out on a continuous steel I beam fabricated by the assembly of three portions joined together by bolt connections. Each beam portion has a 2mm width notch covering half of the beam depth. The test setup is designed in a fashion that not only it allows one to choose desired boundary conditions (simply supported, clamped-clamped), but it also allows different reversible damage scenarios by weakening/strengthening the stiffness of the beam at each joint. Data analysis is performed in two stages: Firstly, the Continuous Wavelet Transform (CWT) method is applied to identify abnormality of retrieved vibration mode shapes measured from specific damaged states at a few measuring points (16). However, it has been shown that the wavelet analysis quite often failed to identify slight perturbations in the mode shapes usually contaminated by noise at low level of damage severities. Secondly, the so-called Principal Component Analysis (PCA) is proposed as a comprehensive statistical study to improve the robustness of the structural health monitoring (SHM) by re-expressing the wavelet coefficients in terms of the most underlying variability. A high number of measurements (approximately 100) is conducted at each damage level to supply a large enough number of variables. The analysis has shown that the Principal Components (PCs) are oriented in a way that most significant features in the data are represented by the first few PCs with the largest variance, whereas random features caused by noise involve higher order PCs that contribute less to the overall variance. The results indicate that using the contribution of the CWT together with de-noising algorithm of the PCA may highly increase the applicability of SHM for damage decision making for beam-like structures in noisy conditions.
... Ihn and Chang demonstrated the ability to characterize damage location and size using a network of piezoelectric actuators (41). Additionally, work done by Fang et al. used frequency response functions coupled with neural networks to assess the location of damage (42), while Okafor and Dutta utilized wavelet transforms to locate damage in cantilevered beams (43). Here, radial basis function (RBF) interpolation is used to convert the responses of multiple sensory particles into an approximated stress field. ...
Developing novel techniques for monitoring structural integrity has become an important area of research in the aerospace community. One new technique exploits the stress-induced phase transformation behavior in shape memory alloy particles embedded in a structure. By monitoring changes in the mechanical and/or electromagnetic behavior of such particles, the formation or propagation of fatigue cracks in the vicinity of these particles can be detected. This work demonstrates sensory particle response to local structural damage using finite element modeling for the first time. Using an optimization method to minimize the difference between experimentally measured strain and simulated results, a good approximation of sensory particle properties can be determined and the strong sensory response of the transforming particle demonstrated. To illustrate an application of this method, a multi-scale finite element model of sensory particles embedded in the root rib of an aircraft wing is then considered. In particular, this unique model utilizes substructure modeling to maintain computational efficiency while relating globally applied loads to local structural response, allowing for the consideration of predicted particle response to crack propagation during wing loading. The effect of particle position relative to the crack tip on particle sensory response is assessed. Finally, this work demonstrates how sensory particles can be used to approximate the location of structural damage by interpolating a stress field based on the responses of multiple sensory particles in the vicinity of a propagating crack.
... In other cases, health monitoring is carried out as an inverse problem, where structural parameters, as stiffness and damping coefficient, are identified [10,11]. Wavelet transform has been also used [12][13][14], showing its ability for damage identification, however, it involves complicated calculations that require high computational effort and other specific conditions to achieve good performance. In [15] a method to detect local structural damage based on dereverberated transfer functions (DTFs), is presented. ...
A novel on-line system identification method for shear beam building models, based on a wave propagation approach, is developed as an alternative solution to modal analysis methods for the health assessment of multi-story buildings. A discrete shear beam model is introduced that is used to design an adaptive observer, allowing for the estimation of displacements and velocities, as well as the unknown shear wave velocities and damping coefficients in real-time. The adaptive observer design is based only on acceleration measurements, does not need a coordinate transformation, and uses the normalized recursive least squares method with forgetting factor and a parameter projection scheme to achieve stronger convergence. Moreover, the proposed identification scheme employs a novel parameterization based on linear integral filters, which eliminates constant disturbances and attenuates measurement noise. The algorithm efficiency is demonstrated through experimental results on a reduced scale five-story building.
... Both DWT and CWT have been used on numerical models of a fixed-beam and a simple frame to detect cracks from deflected shapes [34]. Finally, CWT was used to detect damage experimentally from the deflected shape of a beam using laser measurements [21,35,36]. ...
Early detection of damage has emerged as an important concern for engineers involved in structural condition assessments. This paper presents a damage detection approach that combines different techniques to improve detection and localization of small increments of damage using mode shapes derived from vibration tests on a structure. An experimental study is carried out on a beam with two joints that can simulate incremental damage with a system of plates and bolts. The initial condition is defined as the state when the plates are fully assembled. In this state, the beam comprises two weaker zones at the location of each joint assembly due to a 12% reduction in stiffness in comparison to an intact beam. The test setup is used to simulate incremental damage by modifying the mass and stiffness of the beam at each joint. The proposed method of detection is shown to outperform current alternative methods in detecting small increments of damage and to result in fewer false alarms. The detection procedure comprises four steps: (1) a continuous wavelet transform to detect local anomalies in the first mode shape; (2) a principal component analysis of wavelet coefficients to extract dominant patterns that are most highly correlated with incremental damage and to reduce noise; (3) statistical tests of hypothesis on the scores of principal components to detect statistically significant incremental damage, and (4) a likelihood ratio test to determine the most likely location of incremental damage along the beam.
... A ''wavelet coefficient" is calculated in the form of a scalar value at each point of a signal which can be used as an indicator to identify local anomalies, break-down points or discontinuities in the mode shapes [10]. To extend the applicability of CWT to real structures, several authors [19,28,29] demonstrated the results of their experimental studies by identifying small perturbations in the deflection profile of a beam obtained from high resolution laser-based measurements. However, for an actual bridge where a fixed reference point and a stationary environmental condition are required to derive precisely the real deflection shape of the structure, the efficiency of the laser-based scanning technology is limited by its high sensitivity to exposure conditions and ambient vibrations. ...
This paper presents a case study on statistical procedures for the detection and localization of damage along a beam. Tests are performed on a specially designed beam consisting of an assembly of three bolted sections under laboratory conditions to simulate various levels of incremental damage at two possible locations along the beam. Incremental damage is simulated by sequentially removing plate elements at each location. In this work, damage detection algorithms are tested to detect low levels of incremental damage which is usually challenging given the high noise to signal ratio. The beam is tested for two end restraint conditions, pinned-pinned and fixed-fixed. The detection algorithm combines various statistical techniques with a wavelet-based vibration damage detection method to improve the detection of low levels of incremental damage and further proposes a novel likelihood-based approach for the localization of damage along the beam. A Continuous Wavelet Transform (CWT) analysis is applied to the first mode of vibration of the beam obtained from a set of 16 equally spaced unidirectional accelerometers measuring dynamic acceleration response of the beam. A Principal Component Analysis (PCA) is performed on the wavelet coefficients in order to extract the main patterns of variation of the coefficients and to filter out noise. The scores of the first principal component are shown to be highly correlated with damage levels as demonstrated by statistical tests on changes on the location parameter of the scores in successive damage states. Given that statistically significant damage is detected, a Likelihood Ratio (LR) test is proposed to determine the most likely location of incremental damage along the beam. The results indicate that the algorithm is very efficient to detect damage at multiple locations and for the two end restraint conditions investigated.
... They have been successfully employed to process GW signals. [5][6][7][8][9] Recently, many researchers have begun to use matching pursuit (MP), which is a widely used sparse approximation or sparse representation method, to process GW signals. For example, Hong et al. proposed MP-based methods for damage detection in a rod using both nondispersive and dispersive pulse models. ...
Guided waves have been used for structural health monitoring to detect damage or defects in structures. However, guided wave signals often involve multiple modes and noise. Extracting meaningful damage information from the received guided wave signal becomes very challenging, especially when some of the modes overlap. The aim of this study is to develop an effective way to deal with noisy guided-wave signals for damage detection as well as for de-noising. To achieve this goal, a robust sparse Bayesian learning algorithm is adopted. One of the many merits of this technique is its good performance against noise. First, a Gabor dictionary is designed based on the information of the noisy signal. Each atom of this dictionary is a modulated Gaussian pulse. Then the robust sparse Bayesian learning technique is used to efficiently decompose the guided wave signal. After signal decomposition, a two-step matching scheme is proposed to extract meaningful waveforms for damage detection and localization. Results from numerical simulations and experiments on isotropic aluminum plate structures are presented to verify the effectiveness of the proposed approach in mode identification and signal de-noising for damage detection.
... This happens, for instance, when the defect is located on a nodal line for certain mode shapes: demodulation cannot recover the presence of the defect. Wavelet processing has also been intensively investigated in the last decade for structural health assessment [11,12,13]. Cao et al. [14] also proposed to use wavelet processing on mode shapes extracted by SLDV. ...
Continuous Scanning Laser Doppler Vibrometry (CSLDV) is a well-known technique within the structural dynamic community. However, the whole potentials of CSLDV for diagnostic purposes have not been fully exploited yet. This paper presents a time domain approach for identifying damages in structures. The method, which is based on a wavelet processing of vibration data collected by CSLDV, does not need any a-priori knowledge of the vibration behavior of the undamaged sample. Applications on real test cases are presented and discussed in the paper, demonstrating the promising performance of the approach as a non-destructive testing technique.
... A useful review on the elastic parameter estimation methods has been given by Bonnet and Constantinescu [4]. Okafor and dutta [5] used wavelet transformation technique to detect the position and magnitude of damage (stiffness degradation) of aluminium cantilevered beam. ...
A study on material parameter identification of linearly elastic structures is presented in this work by minimizing the norm of the error in constitutive equation (ECE) from partial and corrupted measurements in transient dynamics. The identification problem is formulated as an optimization problem where the objective function measures the constitutive discrepancy due to the incompatible pair of stress and strain fields. These two fields are generated by solving two different forward problems related to linear elasticity. In the inverse algorithm, we used an effective penalty based approach to weakly satisfy the measured partial strain or displacement data. This technique not only allows us to incorporate the measurement field but helps to regularize the ill-posedness of the inverse problem. Here, we have proposed explicit material parameter update formulas for linear elastic materials. Eventually numerical examples of reconstruction of Young's modulus for 1D bar and beam are given here to present application of the proposed algorithm.
... Here, we show novel results on how measured wave velocity responds to composite damage under loading, and its relationship with the characteristic damage state. Wavelet analysis has been adopted by many researchers to date, e.g., to mention a few, Paget et al. (2003), Kessler et al. (2002), Kim and Melhem (2004), Sohn et al. (2004), Okafor and Dutta (2000), Rizzo et al. (2007). However, to the best of our knowledge, the contour technique and interpretation shown in this article are new. ...
As composite materials become a mainstream engineering material for load-bearing components, the need for understanding and monitoring the component's integrity over its operational life is critical. Non-visible or barely visible damage are difficult to detect, and thorough routine inspections are expensive. Embedded sensors are a possible solution, but fabrication processes and post-processing of the sensors readings have been a challenge. In this paper, interaction of embedded sensors and the damaged host structure was studied. Specifically, barely visible impact and fatigue-damaged specimens were investigated. Custom sensors were fabricated using piezoelectric elements. Strain gauges and piezoelectric elements were embedded into fiberglass/epoxy panels fabricated via vacuum assisted resin transfer molding. The performance of the two types of sensors are compared and discussed.
... They stated that higher order mode shapes could better detect damage in rods. In another study, Okafor and Dutta (2000) worked on damage detection of aluminum cantilever beams using CWT of experimental and numerical mode shapes. Wavelet transform of experimental mode shapes indicated that, the second mode shape was not sensitive to the presence of damage because damage fell in the vicinity of zero-crossing point. ...
In recent decades, wavelet transforms as a strong signal processing tool have attracted attention of researchers for damage identification. Apart from the wide application of wavelet transforms for damage identification, influence of higher order modes on the quality of damage detection has been a challenging matter for researchers. In this study, influence of higher order modes and different mass configurations on the quality of damage detection through Discrete Wavelet Transform (DWT) was studied. Nine different damage scenarios were imposed to four cantilever structures having different mass configurations. The first four mode shapes of the cantilever structures were measured experimentally and analyzed by DWT. A damage index was defined in order to study the influence of higher order modes. Results of this study showed that change in the mass configuration had a great impact on the quality of damage detection even when the changes altered natural frequencies slightly. It was observed that for successful damage detection all available mode shapes should be taken into account and measured mode shapes had no significant priority for damage detection over each other.
... However, no investigation has been performed on the feasibility of the method in the presence of noise and no relation has been found between the characteristic values of the wavelet transform and the damage degree. A first attempt to estimate the damage degree was made by Okafor and Dutta (2000). Specifically, Daubechies wavelets were used to wavelet transform the mode shapes of a damaged cantilever beam, and a regression analysis by a least-squares method was conducted to correlate the peaks of the wavelet coefficients with the corresponding damage degree. ...
... Compared with natural frequency and modal damping, mode shape conveys more spatial information, which is conducive to localization and quantification of the damage (Parloo et al., 2003). In relatively recent studies, a series of damage features have been derived from the mode shape, such as curvature mode shape (Pandey et al., 1991; Abdel Wahab and De Roeck, 1999; Chandrashekhar and Ganguli, 2009; Milazzo and Aliabadi, 2013; Xiang et al., 2013), strain energy mode shape (Shi et al., 2000; Ren and De Roeck, 2002; Srinivas et al., 2011), wavelet coefficients of mode shape (Okafor and Dutta, 2000; Wang and Wu, 2011; Zhong and Oyadiji, 2011; Xu et al., 2013 ), etc. All these damage features, however , exhibit respective advantages and disadvantages for use in damage depiction. ...
This study concerns damage detection in plate-type structures using fractal surface singularities with noncontact laser measurement of structural dynamic responses. The fractal dimension analysis aided by linear isomorphism is used to deal with mode shapes for a plate with damage. With this method, the linear isomorphism is utilized to remove the local extrema while preserving the damage information of a mode shape, giving a retrofitted mode shape. The retrofitted mode shape is processed by Katz’s fractal dimension analysis to produce a fractal dimension surface with its singular peak indicating the presence and location of the damage. In the method, a series of high-resolution mode shapes of the plate are used, which are acquired by using a noncontact measurement system consisting of a piezoceramic transducer as the actuator and a scanning laser vibrometer as the sensor. The capability of the method to locate and quantify damage is numerically demonstrated using a two-side-clamped aluminum plate with cracks of various depths; the efficacy of the method in identifying complex cracks is experimentally validated using a suspended aluminum plate bearing a cross-like crack. The numerical and experimental results show that the proposed method can accurately identify complex damage in plates, requiring neither benchmark models for the entire structure under investigation, or any prior knowledge of the material properties and the boundary conditions of the structure.
... However, no investigation has been performed on the feasibility of the method in the presence of noise and no relation has been found between the characteristic values of the wavelet transform and the damage degree. A first attempt to estimate the damage degree was made by Okafor and Dutta (2000). Specifically, Daubechies wavelets were used to wavelet transform the mode shapes of a damaged cantilever beam, and a regression analysis by a least-squares method was conducted to correlate the peaks of the wavelet coefficients with the corresponding damage degree. ...
... The transform may be applied and mapped to the space or time domain of the structure. Thus, they may be used to find an abrupt change in a mode shape [21]- [23], often indicative of damage, locate a sudden change in response from an acceleration time response [24] and [25], or analyse the displacement response at the mid-span of a bridge [26]. In each case, the energy of the abnormal signal indicates the size of the crack. ...
This paper investigates a novel method for damage detection using a moving force identification algorithm. The method aims to detect the changes in the predicted forces applied by vehicles crossing a bridge, which are shown to be sensitive to damage. A two-dimensional vehicle–bridge interaction model is used in theoretical simulations to assess the effectiveness of the method in detecting changes in stiffness. Fleets of similar vehicles are simulated, and the force pattern of greatest frequency is used as the damage indicator. Results indicate that the method is more sensitive to damage than direct measurements of displacement and can detect a loss in stiffness due to a crack with a depth of as little as 6% of the beam depth. Copyright © 2015 John Wiley & Sons, Ltd.
... However, no investigation has been performed on the feasibility of the method in the presence of noise and no relation has been found between the characteristic values of the wavelet transform and the damage degree. A first attempt to estimate the damage degree was made by Okafor and Dutta (2000). Specifically, Daubechies wavelets were used to wavelet transform the mode shapes of a damaged cantilever beam, and a regression analysis by a least-squares method was conducted to correlate the peaks of the wavelet coefficients with the corresponding damage degree. ...
... However, no investigation has been performed on the feasibility of the method in the presence of noise and no relation has been found between the characteristic values of the wavelet transform and the damage degree. A first attempt to estimate the damage degree was made by Okafor and Dutta (2000). Specifically, Daubechies wavelets were used to wavelet transform the mode shapes of a damaged cantilever beam, and a regression analysis by a least-squares method was conducted to correlate the peaks of the wavelet coefficients with the corresponding damage degree. ...
... However, no investigation has been performed on the feasibility of the method in the presence of noise and no relation has been found between the characteristic values of the wavelet transform and the damage degree. A first attempt to estimate the damage degree was made by Okafor and Dutta (2000). Specifically, Daubechies wavelets were used to wavelet transform the mode shapes of a damaged cantilever beam, and a regression analysis by a least-squares method was conducted to correlate the peaks of the wavelet coefficients with the corresponding damage degree. ...
In this paper we provide a review of wavelet
analysis in the context of applications to vibrations problems.
First, we give an introduction to the important concepts and
mathematical properties of wavelets within the framework of
time–frequency analysis of signals. Next, wavelet analysis is
discussed as applied to relevant themes in vibrations, such as
time-varying spectra estimation, random field synthesis, system
identification, damage detection, and material characterization.
In view of the large number of related books and journal
articles published in recent decades, the list of selected references
in the paper is not meant to be exhaustive. Nevertheless,
the cited references aim to point out the salient features
of wavelet analysis, and to identify significant contributions in
each theme, with the goal of expediting additional research
and development efforts.
... In Patsias and Staszewski (2002), the authors use the WT and DWT with the successive recorded images of a vibrating cantilever to extract mode shapes which are again processed by WT to locate the the groove simulating a crack. A similar use of WT is reported in Okafor and Dutta (2000), to detect the presence, location and amplitude of the damage in a cantilever beam using displacement data obtained using a laser vibrometer. In Demetriou and Hou (2002), the damage detection capability of wavelet transform and an artificial neural network based algorithm are compared for simple spring mass systems with nonlinear system stiffness. ...
In practical applications of wavelet transform, engineers and practitioners encounter challenges that arise due to the disparity between wavelet theory, which deals with continuous functions, and the digital nature of signals in engineering contexts. In particular, wavelet transform theory does not consider the effect of changes in digital signals on the result of the wavelet transform. This paper emphasizes the influence of the type of digital signals on the accuracy of wavelet transform in engineering applications and proposes an efficient wavelet function based on the derivative of the signal for better damage detection in beam structures. For this purpose, the obtained signals from the mode shapes of the steel beam are used to examine the efficiency of the proposed derivative-based wavelet transform. The effects of changes in boundary conditions, location of damage, and level of damage on the performance of the proposed method, are evaluated. Findings show that when we use the derivate of the signal in the wavelet transform, the location of damage in all damage scenarios is detected with high accuracy. This research demonstrates the importance of the type of signal used in the wavelet transform for enhancing the precision of fault and damage detection in signals.
Several popular time-frequency techniques, including the Wigner-Ville distribution, smoothed pseudo-Wigner-Ville distribution, wavelet transform, synchrosqueezing transform, Hilbert-Huang transform, and Gabor-Wigner transform, are investigated to determine how well they can identify damage to structures. In this work, a synchroextracting transform (SET) based on the short-time Fourier transform is proposed for estimating post-earthquake structural damage. The performance of SET for artificially generated signals and actual earthquake signals is examined with existing methods. Amongst other tested techniques, SET improves frequency resolution to a great extent by lowering the influence of smearing along the time-frequency plane. Hence, interpretation and readability with the proposed method are improved, and small changes in the time-varying frequency characteristics of the damaged buildings are easily detected through the SET method.
Composite laminates are becoming increasingly popular in a large variety of applications due to their favourable mechanical properties. However, laminates production processes can lead to various defects in the final material. The most common type is related to thickness variations, e.g. delaminations between layers, which can compromise the mechanical strength of the structure. Therefore, there is a great interest in developing non-destructive and non-contact quality control techniques for composite material assessment to minimize process costs. An interesting approach is the use of laser Doppler vibrometry combined with signal analysis based on Lamb waves propagation. In this work, we used an impulsive force given by a piezoelectric disk to the specimen and a laser Doppler vibrometer acquiring the points velocity over time along a scanning grid on the surface. The specimen is a fiberglass reinforced flat panel with seven different orientated layers which presents a delamination of about 22 mm. The maximum thickness-frequency product achieved in this analysis has been 0.2 MHz∙mm. In contrast to state-of-the-art methods for identifying thickness variation based on local estimation of the principal wave number, the proposed algorithm makes use of a tracking filter of the wave front of the propagating A0 mode waves, returning a final image in polar coordinates. The final information given by the algorithm provides the position of the delamination and, hence, can be used as a pass/failure test. State-of-the-art methods are also able to identify the shape of the defect but pay the price of a higher computational cost by using at least 4D matrix processing unlike our method which only uses 3D matrices.
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.
p>Laminated composites and sandwich structures are increasingly being used in different engineering applications such as in aeronautical, marine and offshore structures where high stiffness, light weight, good corrosion resistance and temperature stability are the primary issues. During their service life, these structures experience extreme loadings and harsh environmental conditions potentially leading to structural damage. This could significantly reduce mechanical strength and result in performance degradation of the structure. Therefore, in order to maintain the performance of the structure, localisation and quantification of the damage is a promising research area. Since the determination of the severity and the location of the damage is an inverse and non-unique problem, an intelligent algorithm is needed to perform the damage detection analysis. This study presents a damage detection algorithm, which uses vibration-based analysis data obtained from beam-like structures to locate and quantify the damage by using artificial neural networks. The inputs and the corresponding outputs required to train the neural networks are obtained from the finite element analyses for different vibration modes of the beams. Multi- layer feedforward backpropogation neural networks have been designed and trained by using different damage scenarios. After validation of the neural networks, new damage cases obtained from finite element and experimental analyses have been introduced and neural networks have been tested for location and severity predictions. The results from the neural networks depict that severity and location of the damage can be predicted by using as input the global (natural frequencies) and the local (strain or curvature mode shapes) dynamic behaviour of the beam-like structures.</p
هدف اصلی این پروژه یافتن بهترین روش برای تشخیص زودهنگام ترک های خستگی در سیستم روتور - یاتاقان دیسک می باشد. برای بررسی اثر ترک تنفسی بر سیستم روتور، ابتدا سیستم موردنظر با استفاده از روش المان محدود مدلسازی شده است. در ادامه ماتریس های ضرایب معادله حرکت استخراج شده اند و پس از آن مدلسازی ترک و رفتار تنفسی آن انجام شده اند. در مرحله بعد با روش عددی "هوبولت" پاسخ های سیستم روتور در دو حالت کارکرد پایدار و شروع به کار (سیگنال گذرا)همچنین برای عمق های مختلف تَرک در شفت بدست آمده اند. برای بررسی پاسخ سیستم از نمودارهای سیگنال زمانی، تبدیل فوریه، تبدیل فوریه زمان کوتاه، انرژی ضرایب ویولت گسسته و نهایتاً نمودار انرژی ضرایب تبدیل ویولت پیوسته بهره برده شده است. با بررسی روش های فوق، نشانه های وجود ترک تنفسی و ترک کاملاً باز در سیستم روتور یاتاقان دیسک .معرفی شده اند
هدف اصلی این پروژه یافتن بهترین روش برای تشخیص زودهنگام ترکهای خستگی در سیستم روتور -
یاتاقان دیسک میباشد. برای بررسی اثر ترک تنفسی بر سیستم روتور، ابتدا سیستم موردنظر با استفاده -
از روش المان محدود مدلسازی شده است. در ادامه ماتریسهای ضرایب معادله حرکت استخراج شدهاند
و پس از آن مدلسازی ترک و رفتار تنفسی آن انجام شدهاند. در مرحله بعد با روش عددی "هوبولت"
پاسخهای سیستم روتور در دو حالت کارکرد پایدار و شروع به کار )سیگنال گذرا( همچنین برای عمق-
های مختلف تَرک در شفت بدست آمدهاند. برای بررسی پاسخ سیستم از نمودارهای سیگنال زمانی،
تبدیل فوریه، تبدیل فوریه زمان کوتاه، انرژی ضرایب ویولت گسسته و نهایتاً نمودار انرژی ضرایب تبدیل
ویولت پیوسته بهره برده شده است. با بررسی روشهای فوق، نشانههای وجود ترک تنفسی و ترک کاملاً
باز در سیستم روتور یاتاقان دیسک معرفی شدهاند.
In this paper, after stating the reasons for the appearance of wavelet transformation and its increasing use for diagnosing purposes, the mathematical relation of the continuous wavelet transform has presented. Then the two principal factors of the wavelet functions (i.e. the number of moments equal to zero, and the resolution that it can have) have investigated. Moreover, the role of these two factors in selecting the mother wavelet function according to the nature of the main signal in terms of transient or steady-state have studied. In the following, the wavelet functions that are more commonly used in the field of diagnosing mechanical machines have introduced by citing related sources and examples. According to the results of the paper, it has been determined that the Daubechies wavelet function has almost the most common application.
Structural health monitoring (SHM) is a process of implementing a damage detection strategy in existing structures to evaluate their condition to ensure safety. The changes in the material, geometric and/or structural properties affect structural responses, which can be captured and analyzed for condition assessment. Various vibration-based damage detection algorithms have been developed in the past few decades. Among them, wavelet transform (WT) gained popularity as an efficient method of signal processing to build a framework to identify modal properties and detect damage in structures. This article presents the state-of-the-art implementation of various WT tools in SHM with a focus on civil structures. The unique features and limitations of WT, and a comparison of WT and other signal processing methods, are further discussed. The comprehensive literature review in this study will help interested researchers to investigate the use of WT in SHM to meet their specific needs.
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.
The present paper proposes a novel non-destructive testing procedure based on the exploitation of the simultaneous time and spatial sampling provided by Continuous Scanning Laser Doppler Vibrometry (CSLDV) and the feature extraction capabilities of wavelet-based processing. Two criteria for selecting in an objective way the mother-wavelet to be used in the decomposition procedure, the Relative Wavelet Energy and Energy to Shannon Entropy Ratio, are compared in terms of capability of best locating the damage. The paper demonstrates the applicability of the procedure for the identification of superficial and in-depth defects in simulated and real test cases when an area scan is performed over the test sample. The method shows promising results, since defects are identified in different severity conditions.
The present paper proposes a novel damage detection approach based on the exploitation of the simultaneous time and spatial sampling provided by CSLDV and the feature extraction capabilities of wavelet-domain processing. Superficial defects are analysed in the paper. The damage detection procedure is presented and its performances studied in a simulated application on a plate with different crack scenarios (varying crack depth ratio). Both line and area scans are analysed, considering also the influence of measurement noise. The method shows promising results, since cracks are identified in all severity conditions. An example on a sub-surface defect on a carbon-fiber panel is also presented.
In this research, an advanced signal processing technique using wavelet analysis has been developed for a guided wave structural health monitoring system. The approach was applied for the detection of delamination in carbon fibre reinforced composites. A monolithic piezoceramic actuator was attached to a laminate plate for wave generation while laser vibrometry was used to facilitate the measurements of the wave response in a sensor network. This database of wave response was then processed using the continuous wavelet transform to obtain the positional frequency content. Transforms between damaged and undamaged states were compared to ascertain the presence of defects by evaluating the total energy of the time-frequency density function. Results show high damage detection indices depending on the location of the sensor and normalisation factor applied while there are positive indications that this methodology can be extended for damage characterisation.
Wireless sensor networks are being increasingly accepted as an effective tool for structural health monitoring. The ability to deploy a wireless array of sensors efficiently and effectively is a key factor in structural health monitoring. Sensor installation and management can be difficult in practice for a variety of reasons: a hostile environment, high labour costs and bandwidth limitations. We present and evaluate a proof-of-concept application of virtual visual sensors to the well-known engineering problem of the cantilever beam, as a convenient physical sensor substitute for certain problems and environments. We demonstrate the effectiveness of virtual visual sensors as a means to achieve non-destructive evaluation. Major benefits of virtual visual sensors are its non-invasive nature, ease of installation and cost-effectiveness. The novelty of virtual visual sensors lies in the combination of marker extraction with visual tracking realised by modern computer vision algorithms. We demonstrate that by deploying a collection of virtual visual sensors on an oscillating structure, its modal shapes and frequencies can be readily extracted from a sequence of video images. Subsequently, we perform damage detection and localisation by means of a wavelet-based analysis. The contributions of this article are as follows: (1) use of a sub-pixel accuracy marker extraction algorithm to construct virtual sensors in the spatial domain, (2) embedding dynamic marker linking within a tracking-by-correspondence paradigm that offers benefits in computational efficiency and registration accuracy over traditional tracking-by-searching systems and (3) validation of virtual visual sensors in the context of a structural health monitoring application.
The field of vibration-based structural health monitoring involves extracting a feature which robustly quantifies damage-induced changes of the structural dynamics. Generally, the change of structural characteristics due to damage is analyzed by observing frequencies, mode shapes, damping, etc. However, the change of those modal features due to damage is minor, so that detecting the location of damage is difficult. Recently, an attractor-based monitoring system has been proposed. The recent study using chaotic excitation has demonstrated that the change of the attractor caused by damage is more sensitive than that of the most commonly used frequency and mode shape of the structure, in which the recurrence plot was applied successfully to the damage detection. However, damage localization has not been discussed sufficiently. An attempt in this study was made to develop a damage localization method using chaotic excitation and recurrence quantification analysis. It was demonstrated through experiment results that the proposed system makes it possible to detect damage locations.
It is often of interest to detect the time of occurrence of sudden change in structural parameters, particularly the changes in structural stiffness for health monitoring purposes as a change in stiffness also implies some damage in one or more structural elements. Although well known, it is formally shown here that a sudden change in stiffness induces a sudden change in the acceleration response. Several methods have been used in the literature to detect such sudden changes. The wavelet transform, in particular the discrete wavelets transform, is one of the popular approaches. In this approach, the sudden changes have been shown to manifest themselves as spikes in the plots of the details of the discrete wavelet transform of the acceleration response. In this paper, we provide an analytical rationale to explain what constitutes these spikes and their relationship to the discontinuity being detected. In particular, it is shown that a spike corresponds to the scaled step-response of a high-pass filter and that a step discontinuity can be detected using a high-pass filter with properly chosen cut-off frequency where the discontinuity manifests as a clear spike in the filtered output. How the measurement error and sampling frequency affect the detection is discussed. An example of a multi-degree-of-freedom system subjected to the base excitation, with sudden changes in its structural elements, is presented to illustrate the approach. Copyright © 2011 John Wiley & Sons, Ltd.
The aim of this paper is to compare wavelet, kurtosis and pseudofractal based techniques for structural health monitoring in the presence of measurement noise. A detailed comparison and assessment of these techniques have been carried out in this paper through numerical experiments for the calibration of damage extent of a simply supported beam with an open crack serving as an illustrative example. The numerical experiments are deemed critical due to limited amount of experimental data available in the field of singularity based detection of damage. A continuous detectibility map has been proposed for comparing various techniques qualitatively. Efficiency surfaces have been constructed for wavelet, kurtosis and pseudofractal based calibration of damage extent as a function of damage location and measurement noise level. Levels of noise have been identified for each technique where a sudden drop of calibration efficiency is observed marking the onset of damage masking regime by measurement noise.
The wavelet transform signal processing applied to Lamb wave signals is a potential technique allowing to detect the possible presence of defects such as delamination and fiber fracture, in layered Carbon/epoxy structures. After a short recall on continuous and discrete wavelet transforms and description of the experimental set-up, this paper presents the main results obtained by this method. Time-frequency diagrams are shown and discussed, an interpretation of phenomena is given and a method of defect localization is presented. This paper shows that it is perfectly possible to detect and localize the defects included in a Carbon/epoxy structure, by using continuous and discrete wavelet transforms applied to Lamb wave signals resulting from an integrated network of piezoelectric transducers working sequentially as emitters and receivers.
Multiresolution representations are effective for analyzing the
information content of images. The properties of the operator which
approximates a signal at a given resolution were studied. It is shown
that the difference of information between the approximation of a signal
at the resolutions 2<sup>j+1</sup> and 2<sup>j</sup> (where j is an
integer) can be extracted by decomposing this signal on a wavelet
orthonormal basis of L <sup>2</sup>( R <sup>n</sup>), the
vector space of measurable, square-integrable n -dimensional
functions. In L <sup>2</sup>( R ), a wavelet orthonormal
basis is a family of functions which is built by dilating and
translating a unique function ψ( x ). This decomposition
defines an orthogonal multiresolution representation called a wavelet
representation. It is computed with a pyramidal algorithm based on
convolutions with quadrature mirror filters. Wavelet representation lies
between the spatial and Fourier domains. For images, the wavelet
representation differentiates several spatial orientations. The
application of this representation to data compression in image coding,
texture discrimination and fractal analysis is discussed
The objective of this paper is to develop appropriate nondestructive damage detection algorithms for 2D plates. Two methods, one using the coal compliance and the other using local modal strain energy, are presented and compared in this paper. The compliance method is derived simply from the governing differential equations of motion presented in the classical plate theory. The second method is developed from expressions for the elastic strain energy of a plate. A damage index, used to indicate local damage, is defined and expressed in terms of modal displacements that are obtained numerically from mode shapes of the undamaged and the damaged structures. The possible damage locations in the structure are determined by the application of damage indicators according to previously developed decision rules. The damage indices, which are obtained for each mode, are transformed to probability space and superposed as weighted general means (WGM). In the WGM, the fraction of modal energy for the element is used as the weight of each mode. Each of the two methods is demonstrated by using a numerical example of a simply supported plate with simulated damage. Finally, the relative performances of the two methods are compared.
Application of wavelet analysis for structural health monitoring Structural Health Monitoring
- Zhou
Zhou Z and Noori M 1999 Application of wavelet analysis for structural health monitoring Structural Health Monitoring 2000: Proc. 2nd Int. Workshop on Structural Health Monitoring (8–10 September 1999, Stanford University, Stanford) ed Fu-Kuo Chang (Lancaster: Technomic) pp 946–55
Damage detection using empirical mode decomposition method and a comparison with wavelet analysis Structural Health Monitoring
- H T Vincent
- S-L Hu
Vincent H T, Hu S-L J and Hou Z 1999 Damage detection using empirical mode decomposition method and a comparison with wavelet analysis Structural Health Monitoring 2000: Proc. 2nd Int. Workshop on Structural Health Monitoring (8–10 September 1999, Stanford University, Stanford) ed Fu-Kuo Chang (Lancaster: Technomic) pp 891–900
Wavelet transform to identify the location and force-time history of transient loading in a plate Structural Health Monitoring
- Gaul
Gaul L and Hurlebaus S 1999 Wavelet transform to identify the location and force-time history of transient loading in a plate Structural Health Monitoring 2000: Proc. 2nd Int. Workshop on Structural Health Monitoring (8–10 September 1999, Stanford University, Stanford) ed Fu-Kuo Chang (Lancaster: Technomic) pp 851–60