Multiple Cracks In Beam Research Articles

Vibration-based damage detection of beams using Hybrid Genetic Algorithm with combined l0 and l1 regularization

Vibration-based damage detection is an effective way of identifying beam damages before they become severe and potentially catastrophic. This paper introduces a novel and robust method for detecting multiple cracks in beams using a Hybrid Genetic Algorithm (HGA). The objective function of the proposed method, based on dynamic properties, can be employed with partial modal information and is enhanced by including the initial residuals between numerical and experimental models along with combined l0 and l1 regularization. This enhancement mitigates the impact of limited modal data, experimental noise, and modeling inaccuracies. Additionally, a method of selecting an appropriate regularization parameter by analyzing residual and solution norm curves is presented. The performance of the proposed method is evaluated and verified using both numerical simulations and experimental studies on a steel cantilever beam under four damage scenarios. In the experimental study, natural frequencies and mode shapes were determined under ambient vibration conditions using Enhanced Frequency Domain Decomposition (EFDD) and the Stochastic Subspace Identification (SSI) method. Finite element models of the beam were developed in ABAQUS software for numerical analysis, and a comparative study of numerical and experimental data was conducted. The proposed approach successfully identifies, locates and quantifies single and multiple damages in the beam, demonstrating its reliability and effectiveness, particularly in scenarios with limited modal data and significant experimental noise.

Crack identification in beam-type structural elements using a piezoelectric sensor

ABSTRACT A crack or any kind of damage induces a sharp discontinuity in the rotational displacement curve in a structure under load. However, if the beam is not loaded sufficiently or crack depth is very small, the discontinuity may not be possible to identify through conventional methods. This study proposes a non-destructive approach to reveal the presence of a crack in structural components based on the measurement of very small discontinuity in rotational displacement by employing a piezoelectric sensor (PZT). An analytical model of a statically loaded cracked beam with PZT attached to the beam is developed for various boundary conditions. The solution is obtained through Ritz approximation. Rotational displacements at different points along the length of the beam are determined. Subsequently, a finite element analysis on ABAQUS platform is carried out for comparison. The results obtained from these analyses are validated with the experimental data published in open literature. Two distinct techniques are employed to monitor the damage in slender and short length beams. the efficacy of the technique in the detection of small cracks in structure is established. It is also shown that the presence of multiple cracks in beams having various boundary conditions can be monitored by a single non-destructive investigation following the method.

Assessing multiple cracks in beams by a method based on the damage location coefficients

In this paper, we analyze the case of structural integrity assessment when the beams have several cracks. The relationship between the location and the severity of one crack and the resulting frequency shift is known. That is why we can design databases containing many defects for which we can calculate precisely the frequency changes and the subsequent damage location coefficients. When the natural frequency evolution of several vibration modes is monitored, we can find alteration due to the crack. Comparing the results of the measurements with the values contained in the database, for instance by involving a bin-by-bin dissimilarity estimator, we can find the location and severity of the crack. For multiple cracks, this approach was not investigated. In this study, we design a database for two cracks affecting at the same time the beam. For these cracks, which have various severities and locations, we calculated the frequency changes by applying the superposition principle. Afterward, we find the frequency shifts for a test structure by means of the finite element method. The comparison between the damage location coefficients in the database and the signature of the damages achieved by simulation is made by the software we have developed in Visual Basic for Application in Excel. We succeed to find the severity and the location of the two cracks for all considered crack configurations.

Guided wave-based identification of multiple cracks in beams using a Bayesian approach

A guided wave damage identification method using a model-based approach is proposed to identify multiple cracks in beam-like structures. The guided wave propagation is simulated using spectral finite element method and a crack element is proposed to take into account the mode conversion effect. The Bayesian model class selection algorithm is employed to determine the crack number and then the Bayesian statistical framework is used to identify the crack parameters and the associated uncertainties. In order to improve the efficiency and ensure the reliability of identification, the Transitional Markov Chain Monte Carlo (TMCMC) method is implemented in the Bayesian approach. A series of numerical case studies are carried out to assess the performance of the proposed method, in which the sensitivity of different guided wave modes and effect of different levels of measurement noise in identifying different numbers of cracks is studied in detail. The proposed method is also experimentally verified using guided wave data obtained from laser vibrometer. The results show that the proposed method is able to accurately identify the number, locations and sizes of the cracks, and also quantify the associated uncertainties. In addition the proposed method is robust under measurement noise and different situations of the cracks.

A concept of complex-wavelet modal curvature for detecting multiple cracks in beams under noisy conditions

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.

Structural damage identification using transfer matrix with lumped crack properties

A novel damage detection scheme is developed for detecting multiple cracks in beams, based on a transfer matrix (TM) approach. Lumped Crack TM of a beam element with multiple cracks is derived based on lumped crack properties. A cracked beam element is assumed as two intact beam elements connected with a hinge or torsional spring. The crack is modelled as an element of zero length and mass, but with elastic properties. Lumped crack approach is simpler for multiple cracks than the possible alternative methods. The state vector at a node includes displacements, forces and moments at that node; when it is multiplied with TM the state vector at the adjacent node can be obtained. The crack identification strategy used here, involves measuring the initial state vector at a node, in the zone of interest. The displacements at the adjacent nodes are measured and these are predicted using TM. Using an optimization algorithm the unknown crack parameters in the TM are solved by minimizing the deviation between measured and predicted displacements. The method is verified using several numerical models as well as experiments with cracked beams. The TM is shown to be suitable for local identification and also fast and accurate compare to other methods.

A Novel Methodology Using Simplified Approaches for Identification of Cracks in Beams

In this paper, natural frequency based forward and inverse methods are proposed for identifying multiple cracks in beams. Forward methods include simplified definition of the natural frequency drops caused by the cracks. The ratios between natural frequencies obtained from multi-cracked and un-cracked beams are determined by an approach that uses the local flexibility model of cracks. This approach does not consider nonlinear crack effects that can be easily neglected when the number of cracks is not excessive. In addition, an expression, which removes the necessity of repeating natural frequency analyses, is given for identifying the connection between the crack depths and natural frequency drops. These simplified approaches play crucial role in solving inverse problem using constituted crack detection methodology. Solution needs a number of measured modal frequency knowledge two times more than the number of cracks to be detected. Efficiencies of the methods are verified using the natural frequency ratios obtained by the finite element package. The crack detection methodology is also validated using some experimental natural frequency ratios given in current literature. Results show that the locations and depths ratios of cracks are successfully predicted by using the methods presented.

A new adaptable multiple-crack detection algorithm in beam-like structures

In this article, a simple method for detecting, localizing and quantifying multiple cracks in beams using natural frequencies is presented. We model cracks as rotational springs and demonstrate a relationship among natural frequencies, crack locations and depths. The main advantage of our method is that it can detect adaptably the unknown number of cracks intervened. Concise, simple calculations and good accuracy are other advantages of this method. We present a number of numerical examples for several beams to validate our method.

On multiple crack detection in beam structures

This study presents an inverse procedure to identify multiple cracks in beams using an evolutionary algorithm. By considering the crack detection procedure as an optimization problem, an objective function can be constructed based on the change of the eigenfrequencies and some strain energy parameters. Each crack is modeled by a rotational spring. The changes in natural frequencies due to the presence of the cracks are related to a damage index vector. Then, the bees algorithm, a swarm-based evolutionary optimization technique, is used to optimize the objective function and find the damage index vector, whose positive components show the number and position of the cracks. A second objective function is also optimized to find the crack depths. Several experimental studies on cracked cantilever beams are conducted to ensure the integrity of the proposed method. The results show that the number of cracks as well as their sizes and locations can be predicted well through this method.

Identification of multiple cracks in beams under bending

The identification of a transverse crack on a beam is the subject of many investigators. Identifying the crack means to find its position and depth. In many cases there are more than one cracks on a beam. Then the solutions, or the combinations of parameters characterising the cracks are more and the problem becomes more complicated particularly when the crack must be identified using one more parameter, the relative each other angular position. In the present paper the dynamic behaviour of a cracked beam with two transverse surface cracks is studied. Each crack is characterised by its depth, position and relative angle. Both cracks are considered to lie in arbitrary angular positions with respect to the longitudinal axis of the beam and at any distance from the left end. A local compliance matrix of two degrees of freedom, bending in the horizontal and the vertical planes is used to model the rotating transverse crack in the shaft and is calculated based on the available expressions of the stress intensity factors and the associated expressions for the strain energy release rates. The compliance matrix is calculated for the first time at any angle of rotation. Thus, the compliance is given as a function of both the crack depth and the angular location. These expressions are usable, due to the stress intensity function limitations, only for limited regions around the zero angular position of the crack and not for every crack angle. For these cases, B-spline curves are used to interpolate the known points and a function in analytical form is given for every crack depth and angle. It is well known that when a crack exists in a structure, such as a beam, then the natural frequency of vibration decreases. This reduction is studied here for six independent parameters namely the depth, the location, and the rotational angle of each crack. By keeping these six parameters constant, the first three flexural eigenmodes can be computed and plotted. Due to its sensitivity in slope or displacement changes the theory of wavelets is used here to identify the locations of the cracks reducing thus the number of independent parameters. As it is well known the existence of a crack on a beam in bending, creates in the elastic line of the beam a slope discontinuity analog generally to the crack depth and additionally here to the angular position. The wavelet transformation of a vibration mode or of the vibration response of the structure under some circumstances could be used to locate the cracks. If the positions are known, then the depths and the respective angles can be determined. Here the diagrams of the first three eigenvalues versus both the crack depth and the rotational angle, are used to identify the remaining unknown parameters for both cracks.

Experimental verification of a method of detection of multiple cracks in beams based on frequency measurements

A method for prediction of location and size of multiple cracks based on measurement of natural frequencies has been verified experimentally for slender cantilever beams with two and three normal edge cracks. The analysis is based on energy method and representation of a crack by a rotational spring. For theoretical prediction the beam is divided into a number of segments and each segment is considered to be associated with a damage index. The damage index is an indicator of the extent of strain energy stored in the rotational spring. The crack size is computed using a standard relation between stiffness and crack size. Number of measured frequencies equal to twice the number of cracks is adequate for the prediction of location and size of all the cracks. The accuracy of prediction of crack details is encouraging. The maximum error in predicting location of cracks decreases with an increase in the number of cracks. It is less than 10% and 20% for two and three cracks respectively. The maximum error in predicting the crack size is less than 12% and 30% respectively for the two cases. A strategy to overcome failure in the prediction for cases with one of the cracks located near an anti-node has been suggested.