Damage Detection in Structural Beams Using Model Strain Energy Method and Wavelet Transform Approach

A variance-based approach for the detection and localization of cracks in a beam

Damage measures, one of the important parameters in Structural Health Monitoring (SHM), and useful in detecting the presence and location of cracks in beams, are developed in this article. This development is based on the reduced Finite element models for healthy and damaged structures. Finite element reduced-order model (ROM) methods like static condensation, system equivalent reduction expansion process (SEREP) and dynamic condensation have been used to generate reduced order models. ROM generated by static condensation are used to analyze beams under static loading while SEREP and dynamic condensation methods are used for dynamic loading. The developed damage measure is the force residue obtained from the stiffness relationship of healthy and damaged beam, which we call damage force indicator (DFI). For dynamic load cases, the measure is evaluated in the frequency domain. Sensitivity of orientation of crack prediction is performed by using different orientations of crack and comparing it with a crack of standard orientation. A general method to determine the approximate region of damage for a structure with no a priori knowledge of damage is also explained. Damage measures are verified using experimentally measured responses, to prove the efficiency of the approach.

Determining the size and location of transverse cracks in beams

Experimental study on the crack detection with optimized spatial wavelet analysis and windowing

Most of the rotating machines used in process industries or in manufacturing plant need maintenance and repair. However, failure of just one of these machines can disturb an entire process with losses in terms of production, manpower, and equipment repair or replacement. Also failure of a single machine component in process industries like petrochemicals or power stations can result in the loss of millions of rupees per down time hour. These facts together with higher costs for new equipment have placed increased demand on plant maintenance to keep existing equipment operating efficiently with higher availability. A number of non-destructive crack detection techniques have been developed, such as ultrasonic testing, X-ray technique, magnetic particle method etc. Every method has some advantages and disadvantages. In recent years, ultrasonic testing has gained greater attention for monitoring the cracks in structures and machine components. Most of these methods are very laborious and time consuming, in the case of larger components like bridges, long pipe lines, railway tracks etc. These inconveniences can be avoided by the use of vibration monitoring technique such as model analysis. Therefore the development of vibration monitoring techniques has received increasing attention in recent years. Damage in structure alters its dynamic characteristics. The change is characterized by a change in model parameters i.e. model frequencies, model damping values and mode shapes associated with each model frequencies. Changes also occur in some of the structural parameters like mass, damping, stiffness and flexibility matrices of structure. Thus a vibration technique can be suitably used as a nondestructive test for crack detection of components to be tested. In this paper, theoretical and experimental analysis of a vibrating cantilever beam with a crack is carried out. This method is used to address the inverse problem of assessing the crack location and crack size in various beam structure. The method is based on measurement of natural frequencies, which are global parameter and can be easily measured from any point on the structure. In theoretical analysis the crack is simulated by an equivalent spring, connecting the two segments of the beam. Analysis of this approximate model results in algebraic equation, which relates the natural frequencies of the beam, and crack location. Also the relationship between the natural frequencies, crack location and crack size has also been developed. For identification of crack location and crack size, it was shown that data on the variation of the first two natural frequencies are sufficient. The computation of natural frequencies of uncracked and cracked beam is facilitated by a finite element method package. This database is to be utilized in an analytical method to address the inverse problem to identify the crack location and crack size.

PurposeEnsuring the early detection of structural issues in aircraft is crucial for preserving human lives. One effective approach involves identifying cracks in composite structures. This paper employs experimental modal analysis and a multi-variable Gaussian process regression method to detect and locate cracks in glass fiber composite beams.Design/methodology/approachThe present study proposes Gaussian process regression model trained by the first three natural frequencies determined experimentally using a roving impact hammer method with crystal four-channel analyzer, uniaxial accelerometer and experimental modal analysis software. The first three natural frequencies of the cracked composite beams obtained from experimental modal analysis are used to train a multi-variable Gaussian process regression model for crack localization. Radial basis function is used as a kernel function, and hyperparameters are optimized using the negative log marginal likelihood function. Bayesian conditional probability likelihood function is used to estimate the mean and variance for crack localization in composite structures.FindingsThe efficiency of Gaussian process regression is improved in the present work with the normalization of input data. The fitted Gaussian process regression model validates with experimental modal analysis for crack localization in composite structures. The discrepancy between predicted and measured values is 1.8%, indicating strong agreement between the experimental modal analysis and Gaussian process regression methods. Compared to other recent methods in the literature, this approach significantly improves efficiency and reduces error from 18.4% to 1.8%. Gaussian process regression is an efficient machine learning algorithm for crack localization in composite structures.Originality/valueThe experimental modal analysis results are first utilized for crack localization in cracked composite structures. Additionally, the input data are normalized and employed in a machine learning algorithm, such as the multi-variable Gaussian process regression method, to efficiently determine the crack location in these structures.

The output response of any intact oscillatory system subjected to a Gaussian excitation is also Gaussian in nature. On the contrary, when the system contains any type of underlying nonlinearity, the output signal is definitely non-Gaussian. In beam structures, the presence of fatigue-breathing cracks significantly influences the dynamic response characteristics under Gaussian excitation. The presence of such cracks alters the response to be nonlinear, and the non-Gaussianity of the system will arise. In order to examine the non-Gaussianity features and ability for the detection and localization of fatigue cracks, several breathing crack identification scenarios in beam-like structures are presented in this paper. The effects of single and multiple breathing cracks corresponding to different boundary conditions on the responses of beams are studied. The results are analyzed based on the higher-order time-domain transformations. Higher-order transformations, namely the skewness and kurtosis coefficients in addition to the Shannon entropy, are exploited to provide dynamic details about the response, which the conventional second-order statistics cannot show. The results exhibit that the proposed methods are robust and immune to noise and can detect and localize breathing cracks with different sensitivities.

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

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

This study is the second part of investigation into the interface mechanical performances of cracked reinforced concrete (RC) beams strengthened with prestressed hybrid fiber reinforced polymer (HFRP). Four cases of difference crack location are considered by establishing finite element analysis models to discuss the effort of crack location on the interface stresses in the strengthened beams. The analysis results indicate that the flexural crack obviously changes the distributing of the interface stresses, and an abrupt increase of the stresses arise at the crack location. Moreover, when the crack location is closer from the interface end, the change rate of the stresses is larger.

This study carried out an experimental and numerical modal analysis of the Turkish traditional instrument 'Bendir' by an acoustical excitation source. In experimental modal analysis, Bendir was excited acoustically for specified frequencies and elastic deformations of different areas of Bendir due to the excitation were observed with a laser vibrometer. Using the Fourier series handled gained data, modal analysis was done. The first six natural frequencies obtained experimentally and numerically were compared. In addition, other hits in Bendir, symbolizing three fundamental voices such as 'dum', 'te', 'ke' were used to excite the instrument. As a result, time dependent deformation & velocity data were determined and different responses of Bendir were compared.

High magnetic field strength and high-speed gradient coil current switching are becoming ever more commonplace in magnetic resonance imaging scanners. These and other factors are combining to yield high acoustic sound pressure levels (SPLs) in and around magnetic resonance imagers. Studies have already been conducted which partially characterize this sound field, and various methods have been investigated to attenuate the noise generated. In order to predict the vibration and acoustic response of a gradient coil inside a scanner, finite element analysis (FEA) was carried out. The model was based on specific internal and external structural dimensions and the material physical properties of a gradient coil. The FEA results were verified through experimental modal testing of the same gradient coil. It was found that the experimental modal analysis results were in good agreement with the FEA results. The Lorentz force distribution on the gradient coil caused by the time varying current in the coil windings was then applied to the FEA model to obtain the velocity distribution of the coil surface as a function of time. A vibro-acoustic computational model was then developed based on the verified FEA model. The surface velocity distribution was then used to predict the sound field inside the gradient coil. The vibro-acoustic model was verified using experimental noise measurements with swept sinusoidal waveform inputs to the gradient coil conductors. The numerical methods developed in this study could provide a guide and virtual testing platform for the designer of gradient coils to predict the vibration and acoustic behavior of new designs and thereby offer the opportunity to redesign and/or optimize the design to reduce SPLs.

Early detection of cracks in beams, machines, and other structural elements with applications in the maritime industry, oil and gas sector, mining sector, and other systems or facilities have become a major concern in building and construction and other engineering fields. Cracks frequently appear first on concrete surfaces and structures under load conditions and serve as an indicator of further deterioration. Fatigue can have a momentous impact on crack. It is, therefore, significant to detect cracks at an early stage in order to avoid catastrophic consequences. As a result, researchers have devised a variety of methods to achieve this goal. This study considers the use of a simple cantilever beam to detect the presence of a crack from measured vibration data. For this experiment, a beam with cracks in various locations and another beam without cracks were considered. Some of the variables considered at different crack locations include the acceleration responses, crack locations, mode shapes, and natural frequencies. The experimental framework was built around the data by using an ANN feed-forward backpropagation algorithm with a sigmoid function of layers 2–10-4–4, divided into 70% training, 15% validation, and 15% testing sets using a data portioning approach. The statistical indices showed a mean squared error (MSE) value of 0.0000312, root mean squared error (RMSE) value of 0.000111, and coefficient of determination (R <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sup> ) value of 1.0, and regression coefficient (R) value of 1.0. The result shows a very low MAE and RMSE. It was concluded from the result of the model that the presence of crack on the test sample is minimal. ANN proved to be a satisfactory technique for the analysis of stochastic datasets.

Model updating is concerned about the correction of finite element models by processing the record of dynamic response from test structures in order to have an accurate model for any simulated analysis. Finite element model updating had emerged years ago as an important subject in structural dynamics. It has been used frequently and has been successfully applied to many fields especially in detecting the dynamic stiffness of a structure. The purpose of this study is to perform model updating of a go-kart chassis structure in order to reduce the percentage of error between the experimental modal analysis (EMA) and finite element analysis (FEA). Modal properties (natural frequency, mode shapes, and damping ratio) of the go-kart chassis structure were determined using both EMA and FEA. Correlation of the modal parameters gathered in FEA and EMA was carried out before optimizing the data from finite element. By adjusting the selective parameters, incongruities between those two analyses are generally reduced. The sensitivity of selected parameters is also obtained. The significant reduction in percentage of error before and after model updating procedure was carried out in this study clearly shows that model updating technique is a reliable method in reducing the discrepancies between EMA and FEA. Therefore, in cases of high discrepancies between analytical and actual test data, model updating can be considered as an option in order to obtain better correlation between those two sets of data.

The frequency response of a cracked beam supported by a nonlinear viscoelastic foundation has been investigated in this study. The Galerkin method in conjunction with the multiple scales method (MSM) is employed to solve the nonlinear governing equations of motion. The steady-state solutions are derived for the two different resonant conditions. A parametric sensitivity analysis is carried out and the effects of different parameters, namely the geometry and location of crack, loading position and the linear and nonlinear foundation parameters, on the frequency-response solution are examined.