Identification Of Multiple Cracks Research Articles

Data-driven algorithm based on the scaled boundary finite element method and deep learning for the identification of multiple cracks in massive structures

Structural defect identification is a vital aspect of structural health monitoring used to assess the safety of engineering structures. However, quantitatively determining the dimensions of structural defects is often difficult. Therefore, this study presents an innovative data-driven algorithm that combines the scaled boundary finite element method (SBFEM) and a deep learning framework based on a dilated causal convolutional neural network (CNN) to identify crack-like defects in large-scale structures. The SBFEM is used to simulate different crack-like defects. Mesh generation is significantly simplified by a simple procedure that requires only changing the scale centre at the crack tip and the positions of the nodes at the crack opening. This minimises remeshing and enables simple generation of sufficient data to train the neural network. In addition, an absorbing boundary model based on Rayleigh damping is used to avoid computing the entire model when simulating wave propagation in massive structures. To ensure that sequential data remain ordered and to obtain a large receptive field without increasing the complexity of the neural network, a dilated causal CNN is employed in the deep learning framework. Therefore, more historical information is captured, and the complex mapping relationship between the echo signal and the crack information is efficiently learnt. The proposed model can accurately identify the number, location, and depth of cracks in massive structures. Moreover, it is robust to noise, which is demonstrated via numerical examples. Therefore, the proposed algorithm provides valuable insight into the detection and diagnosis of structural defects, which can ultimately improve the safety of engineering structures.

Singular spectrum analysis based structural damage identification in beams with multiple breathing cracks

This paper presents a generalized vibration-based multiple breathing crack localization technique in beams with an unknown number of cracks based on Singular Spectrum Analysis (SSA). Localization of multiple breathing cracks is a highly challenging inverse problem, as all these breathing cracks (more than two) might be in a similar state (either opening or closing state) at any particular time instant or in contrasting states (while some breathing cracks are opening, others in closing state) during vibration. The level of nonlinearity of vibration response is strongly dependent not only on each crack size, and location but also on the application of driving force along the cracked beam. The concept of varied input frequency excitation sources is employed in the present work for multiple breathing crack identification over the tedious traditional approach of varying input force application positions. The major advantage of using singular spectrum analysis in the present work is that it can reliably isolate and extract the very low-amplitude nonlinear sensitive components (super harmonics and intermodulation) being buried in the total response based on the pairwise eigenvalue property of harmonic components. Investigations have been carried out by varying the number, spatial locations, and also intensities of the breathing cracks. Sensitivities associated with measurement noise and also with limited sensors are also investigated. The results of both numerical and experimental investigations carried out in this paper concluded that the proposed SSA can effectively localize closely spaced or sparsely spaced (i.e.,, spatially far apart) multiple cracks in the beam. The proposed SSA approach is data-driven, works with limited sensors, and does not need reference healthy state measurements.

A New Nonlinear Damage Indicator Based on Spectral Correlation for Identification of Multiple Breathing Cracks in Beam-Like Structures

A New Nonlinear Damage Indicator Based on Spectral Correlation for Identification of Multiple Breathing Cracks in Beam-Like Structures

A novel time domain-based multiple breathing crack diagnosis technique using Quadratic-Teager Kaiser Energy (Q-TKE)

This paper presents a generalized time domain-based multiple breathing crack localization technique in beams with an unknown number of cracks based on Quadratic-Teager Kaiser Energy (Q-TKE) using vibration data. Localization of multiple breathing cracks is a highly challenging inverse problem, as all these breathing cracks (more than two) might be in a similar state (either opening or closing state) at any particular time instant or in contrasting states (while some breathing cracks are opening, others are in closing state) during vibration. The level of nonlinearity of vibration response is strongly dependent not only on each crack size and location but also on the application of driving force along the cracked beam. The concept of varied input frequency excitation sources is employed in the present work for multiple breathing crack identification over the tedious traditional approach of varying input force application positions. The major advantage of using Q-TKE in the present work is that it can reliably isolate and extract the very low-amplitude nonlinear sensitive components (superharmonics and intermodulation) being buried in the total response and enhance them in the time domain signal itself. Investigations have been carried out by varying the number, spatial locations, and also intensities of the breathing cracks. Sensitivities associated with measurement noise and also with limited sensors is also investigated. The results of both numerical and experimental investigations carried out in this paper concluded that the proposed Q-TKE can effectively localize closely spaced or sparsely spaced (i.e., spatially far apart) multiple cracks in the beam. The proposed Q-TKE approach is data-driven, works with limited sensors, and does not need reference healthy state measurements.

A Method of Shear-Horizontal EMAT Based on Dual-Reception Magnetic Encoded Spatial Pulse Compression for Multiple Cracks Identification and Location

A Method of Shear-Horizontal EMAT Based on Dual-Reception Magnetic Encoded Spatial Pulse Compression for Multiple Cracks Identification and Location

Effective Identification and Localization of Single and Multiple Breathing Cracks in Beams under Gaussian Excitation Using Time-Domain Analysis

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.

Identification of Multiple Cracks in Composite Laminated Beams Using Perturbation to Dynamic Equilibrium.

Identification of cracks in beam-type components is significant to ensure the safety of structures. Among the approaches relying on mode shapes, the concept of transverse pseudo-force (TPF) has been well proved for single and multiple crack identification in beams made of isotropic materials; however, there is a noticeable gap between the concept of TPF and its applications in composite laminated beams. To fill this gap, an enhanced TPF approach that relies on perturbation to dynamic equilibrium is proposed for the identification of multiple cracks in composite laminated beams. Starting from the transverse equation of motion, this study formulates the TPF in a composite laminated beam for the identification of multiple cracks. The capability of the approach is numerically verified using the FE method. The applicability of the approach is experimentally validated on a carbon fiber-reinforced polymer laminated beam with three cracks, the mode shapes of which are acquired through non-contact vibration measurement using a scanning laser vibrometer. In particular, a statistic manner is utilized to enable the approach to be feasible to real scenarios in the absence of material and structural information; besides, an integrating scheme is utilized to enable the approach to be capable of identifying cracks even in the vicinity of nodes of mode shapes.

Numerical and experimental verification of a method of identification of localized damages in a rod by natural frequencies of longitudinal vibration

A method for identification of multiple transverse cracks and other localized defects in a rod by means of two spectra of longitudinal vibrations that correspond to free–free and fixed–free end conditions is presented. A numerical algorithm is developed that implements the method. The algorithm was tested on experimental data obtained on a cylindrical sample of aluminum alloy D16 with the created localized damages. The experiments were carried out on a rod with free ends. The created damages were ring grooves symmetrically located relative to the middle of the rod. With the help of such experiments, natural frequencies were obtained that correspond to two types of boundary conditions for a half-length rod. The experimental data were processed using the developed algorithm. The results showed that the model on which the developed algorithm is based describes well the longitudinal vibrations of the rod with localized damages in a fairly wide frequency range, and the algorithm enables to reconstruct multiple damages accurately enough.

Identification of multiple cracks in a beam by natural frequencies

A problem of reconstruction of multiple cracks in a beam by means of the natural frequencies corresponding to transverse vibration of the beam is considered. The cracks are simulated by massless rotational springs. It is proved that the cracks can be uniquely identified by three spectra corresponding to three different types of the end conditions. The problem is solved by reducing it to the inverse spectral problem for an ordinary differential equation of fourth order. A method for identifying damage caused by cracks has been developed. The method is based on minimization of the objective function, built with the knowledge of the three spectra. Numerical examples are considered.

Identification of Transverse Cracks in a Rod Using Eigenfrequencies of Transverse Vibrations

A problem on identification of multiple cracks in a rod by means of eigenfrequencies of transverse vibrations is considered. The cracks are modeled by weightless rotational springs. It has been proven that cracks can be uniquely identified using three spectra corresponding to three different types of boundary conditions. A numerical method for assessing fracture caused by cracks has been developed. The method is based on minimizing the objective function obtained by taking into account three spectra. Theoretically, fracture reconstruction is possible using several different spectra triplets. In the article, by means of various examples and using the developed numerical method, a comparative performance analysis of using various theoretically acceptable triplets of spectra is carried out.

Identification of multiple cracks in noisy conditions using scale-correlation-based multiscale product of SWPT with laser vibration measurement

Simultaneous identification of multiple cracks is an unresolved issue in the structural health monitoring field. To address this issue, a new method is proposed for identifying multiple structural cracks using the scale-correlation-based multiscale product of the stationary wavelet packet transform (SWPT) of high-order (greater than 6) mode shapes, with particular emphasis on the ability of the method to distinguish damage in noisy conditions. With the method, the SWPT is firstly utilized to decompose a noisy high order mode shape into a set of uniform-frequency sub-bands. In each sub-band the SWPT coefficients have the property of shift invariance. Secondly, a scale correlation is introduced to screen out valid SWPT sub-bands containing an informative crack feature. On these sub-bands, manipulation of scale-correlation-based multiscale products is implemented to yield a multiscale product curve by multiplying sub-band coefficients across scales at every temporal step. In the curve, abrupt peaks form damage indicators that can pinpoint the locations of multiple cracks. In the damage indicator, the function of scale correlation in distinguishing effective sub-bands endows the scale-correlation-based multiscale product with strong ability to reveal damage while suppressing noise. The method is numerically verified using high-order mode shapes of beam-type structures with multiple cracks and experimentally validated on high-order mode shapes acquired using a scanning laser vibrometer, both demonstrating high accuracy and strong robustness against noise in the identification of multiple cracks. The proposed scale-correlation-based multiscale product forms a sophisticated mechanism for identifying multiple damage in noisy conditions, with promise for developing damage identification methods for a wide spectrum of structures.

Research on geometric features of phase diagram and crack identification of cantilever beam with breathing crack

Geometric features of the phase diagram of a cantilever beam with a breathing crack are investigated. Influences of crack properties on the phase diagram geometry are studied and a method for crack identification based on phase diagram features is proposed. The pixel method is used to estimate different phase diagram areas. Multiple crack identification indexes are defined under the conditions of primary and super-harmonic resonance. The effects of crack location and depth on each index are analyzed. The contour lines for multiple identification indexes are used to estimate crack parameters. Numerical calculations indicate that the phase diagrams for super-harmonic resonance are more sensitive to crack parameters and that the proposed method is both feasible and effective.

Identification of multiple cracks in an anisotropic elastic plate by boundary data

A linear elastic, anisotropic plate, which can contain multiple, rectilinear cracks is considered. It is assumed that the loads applied to the boundary of the plate and the displacements of the boundary are measured in a single static experiment. A method for the cracks identification using the known overdetermined boundary data is developed. The developed method is based on the reciprocity gap concept, generalized functions theory and methods of cluster analysis. Numerical examples are considered.

Sub-Structural Parameter Identification Including Cracks of Beam Structure Using PZT Patch

This paper presents the numerical simulation of damage identification of beam structures using novel One Dimensional (1-D) PZT patch model with sub-structuring applied to the PZT Patch boundaries. The 1-D PZT patch model is simple and requires less computational effort than 2-D or 3-D models. A hybrid element constituted of 1-D beam element and a PZT sensor is used with reduced material properties which is very convenient for beams and is a novel application. The accuracy of 1-D hybrid element with cracked structure is first verified experimentally. The stiffness, damping and crack parameters are identified by minimizing the deviation between the predicted and measured voltage from the PZT patch using an optimization algorithm. The numerical signals are polluted with 5% Gaussian noise to simulate experimental noise. Numerical studies are performed on a beam and a nine member frame structure for sub-structural parameter and multiple crack identification. The PZT patches are attached at either ends of beam member to be identified. Sub-structuring is done to isolate the beam with patch, thus reducing the size of model to be identified. The numerical results show significant improvement in identification accuracy compared to other methods.

Fast simulations for solving fracture mechanics inverse problems using POD-RBF XIGA and Jaya algorithm

An inverse algorithm based on Proper Orthogonal Decomposition (POD) and Radial Basis Functions (RBF) for single and multiple cracks identification in plate structures is presented. The inverse analyses combine experimental fracture mechanics tests with numerical models based on the eXtended IsoGeometric Analysis (XIGA) method. The proposed technique identifies the location of cracks in a plate using static strains as input data. Simple and powerful algorithms, namely Jaya and Cuckoo search algorithms are coupled with the proposed XIGA-POD-RBF technique. The objective function is expressed as the difference between the strains of the actual cracks and those of the estimated ones. It is found that the proposed methodology is able to accurately estimate the cracks' locations with high accuracy and much faster than other techniques used in the literature. The stability of the identification algorithm based on Jaya is tested against measurement uncertainty by introducing a white Gaussian noise in the input data. The results show high stability for noise levels up to 4%.

Experimental investigation and identification of single and multiple cracks in synthetic fiber concrete beams

The tensile behavior of fiber-reinforced concrete is recognized as being superior to that of ordinary concrete, and since serviceability is a primary concern in existing design specifications, it is important to evaluate its post-cracking performance. This research experimentally identified and investigated cracks in concrete beams reinforced with synthetic fibers. Concrete beams with and without longitudinal reinforcement were studied in order to assess both single and multiple cracking scenarios. Synthetic fiber volume fractions of 0.5% and 1% were used to prepare the specimens, and the results were compared with those of concrete beams with no synthetic fibers. Six unreinforced beams and six reinforced beams with flexural behavior were tested. The digital image correlation (DIC) method was utilized to record the width, spacing, number, and locations of the cracks for all the specimens during the displacement control-type loading. The results indicated that using 1% synthetic fiber increased the failure load of the reinforced concrete beams and improved the serviceability by reducing the number of cracks and the width of the cracks. When the cracks opened significantly, the beams with 1% fiber dosage were able to carry higher loads due to the bridging action of the fibers at the crack locations.

A procedure for the identification of multiple cracks on beams and frames by static measurements

A procedure for the identification of multiple cracks on beams and frames by static measurements

On multiple crack identification by ultrasonic scanning

The present work develops an approach which reduces operator equations arising in the engineering problems to the problem of minimizing the discrepancy functional. For this minimization, an algorithm of random global search is proposed, which is allied to some genetic algorithms. The efficiency of the method is demonstrated by the solving problem of simultaneous identification of several linear cracks forming an array in an elastic medium by using the circular Ultrasonic scanning.

Identification of multiple cracks in 2D elasticity by means of the reciprocity principle and cluster analysis

An inverse 2D elastostatic problem is considered. It is assumed that an isotropic, linear elastic body can contain a finite number of rectilinear, well-separated cracks. The surfaces of the cracks are assumed to be free of the loads. A method is developed for reconstruction the cracks by means of the applied loads and displacements on the boundary of the body, obtained in a single static test. The method is based on the reciprocity principle, elements of the theory of distributions, and cluster analysis. Numerical examples are considered.

Multiple cracks identification for piezoelectric structures

We propose a novel iterative procedure to solve the inverse problem of detecting multiple cracks in two-dimensional piezoelectric structures under dynamic electric loads. The effect of dynamic electric loads and a time-harmonic excitation with a single frequency is investigated. The crack is detected through the solution of an inverse time-dependent problem. The extended finite element method (XFEM) is employed for solving the forward problem as it allows the use of a single regular mesh for a large number of iterations with different crack geometries. The Newmark-beta method is employed for the time integration. In each iteration the forward problem is solved for various crack geometries, and at each iteration, the mechanical and electrical response of the piezoelectric structure is minimized at known specific points along the boundary to match the measured data. The minimization of the objective function is performed by multilevel coordinate search (MCS) method. The algorithm is an intermediate between purely heuristic methods and methods that allow an assessment of the quality of the minimum obtained and is in spirit similar to the direct method for global optimization. In this paper, the XFEM-MCS methodology under the dynamic electric load is applied to two-dimensional electromechanical problems where different number of straight cracks are considered. The results show that this methodology can be effectively employed for detecting multiple cracks in piezoelectric materials.