Damage In Beam Structures Research Articles

Correlation coefficients of vibration signals and machine learning algorithm for structural damage assessment in beams under moving load

This paper presents a novel method of assessing structural damage in beams exposed to moving loads via acceleration signals through experimental studies. In this study, beams are supported on both ends, and their dynamic response to moving loads is assessed. The raw signal has been improved using a random decrement technique. Take measurements from different locations and calculate correlation coefficients between them, then use these as features to evaluate the structure. In order to create a reliable and potential framework for predicting damage efficiently, these features are used as input variables to the machine learning model. The proposed methodology exhibits promising results in accurately discerning and predicting damage in beam structure. It demonstrates a high level of precision to subtle changes in structural integrity when trained by machine learning on the statistical feature extracted from acceleration signals. As a result of this research, methods for detecting structural damage can be made more reliable and efficient by employing machine learning techniques. Additionally, structures operating in dynamic environments can benefit significantly from the proposed methodology.

Detecting damages in metallic beam structures using a novel wavelet selection criterion

Structural damage detection using wavelet transform is effective if a suitable wavelet function is selected. However, the selection of the appropriate wavelet function can be a challenging task. This paper introduces a novel and efficient criterion for selecting the proper wavelet function. It is emphasized that there is a relationship between the accuracy of damage detection using wavelet detail coefficients and the correctness of the approximation of the original function. Accordingly, we define a ratio function and then a novel wavelet selection criterion called WSC in this study. After applying the proposed WSC criterion for 128 wavelet functions, it is found that the wavelet functions selected via the proposed criterion (both in numerical and experimental scenarios) can detect the position of damages in the beam structure with high accuracy.

A hybrid multiple input multiple output (MIMO) model for simultaneous localization and quantification of structural damage in beam structures

Minor cracks are common types of damage in beam-like structures that must be detected early to prevent complete structural failure. Detecting and addressing such damage is crucial for maintaining structural integrity, extending service life, and minimizing operational costs. In recent years, various methods for quantifying and localizing damage using vibration measurements have been developed. However, many of these methods struggle to quantify and accurately localize the damage simultaneously. This paper addresses this challenge by applying novel hybrid multi-input and multi-output (MIMO) regression algorithms. The proposed approach combines modal analysis data, which includes frequencies, with machine learning algorithms to achieve simultaneous damage localization and quantification in damaged beams. Both numerical and experimental modal analyses have been conducted to determine the first six modal frequencies. Multiple hybrid MIMO models have been trained and tested using the frequencies obtained. The trained models have been used to estimate damage location and severity, and the results are compared. The models’ performance was evaluated using seven key metrics, including mean squared error (MSE), coefficient of determination (R2), mean absolute error (MAE), and others. The Random Forest (RF) model demonstrated exceptional performance by achieving a significantly higher R2 value of 0.997 for the precise prediction of both damage location and magnitude. Optimizing these models through hyperparameter tuning significantly improved their accuracy and reliability. This approach exhibits superior efficacy, surpassing existing models, and holds promise for advancing structural health monitoring in critical applications.

A modified mode shape data-based method for beams structural damage detection

Damage detection methods based on changing modal parameters have received considerable attention in engineering applications due to the satisfactory results and the low associated cost compared with other techniques. The Mode Shape Data Based Indicator (MSDBI) is a damage indicator available in the literature, being used to identify damage in beam structures from the mode shape, mode shape slope and mode shape curvature, in the undamaged and damaged configurations of the element under study. However, in some situations, the configuration of the displacement mode shape of the ith mode, of the undamaged structure compared to the damaged one, presents mirroring. The damage identification algorithm could be a better indicator when these situations occur. Them, this paper presents a proposal to modify this method, called MSDBIM. The proposed modified method (MSDBIM) and the traditional method (MSDBI) were applied in two numerical examples that were elaborated in commercial software of finite elements, namely a simply supported concrete beam and a fixed-end steel beam in different single and multiple damage scenarios with sensitivity studies. A new discretization for the fixed-end beam was performed to assess whether there is a direct influence on the damage identification method. The results show that the proposed method (MSDBIM) performs better than the traditional method (MSDBI).

Interval analysis of mode shapes to identify damage in beam structures

AbstractVarious damage detection methods have been proposed by several researchers in the past few decades. Amongst them, the efficiency of mode shapes in detecting damage has been demonstrated by many researchers when further processed. In most cases, the processing involves expansion or reduction of the mode shape data. However, vital information that are damage‐prints are often lost during processing of the mode shape data. In addition, most of these processes involve long and complex computation, thus, leading to inaccurate damage identification. In this study, a simple and fast damage identification technique is proposed to identify damage in beam structures. Interval analysis is applied to the mode shapes of a beam structure in the damaged and undamaged states. The interval situations of each of the beam's segment via mode shape are derived to obtain the upper and lower bounds and the derived bounds are compared. To establish a relationship for identify the damaged point, a possibility of damage existence is defined for each segment of the beam structure. The mode shape increment is defined as the increase in the mode shape value. Furthermore, a damage measure index that provide enhance damage information is obtained as the product of the possibility of damage existence and mode shape increment. A numerical model of a simply supported steel beam is applied to demonstrate this method by imposing damage through thickness reduction of elements in segments. In addition, a parametric analysis is carried out to evaluate noise effect by considering varying damage severities and different noise levels. The results showed that this method is simple and provides considerable accurate results.

Damage quantification of beam structures using deflection influence line changes and sparse regularization

Influence line (IL) has emerged as very promising damage indices for bridge damage detection. This study proposed a method to localize and quantify damage in beam structures by estimating section flexibility change from deflection IL (DIL) change. To this end, the relationship between second derivative of DIL change and flexibility change was established. To remove noise interference in measurement, piecewise quadratic functions were used to fit and replace noisy DIL change curves, wherein the coefficients of quadratic function were determined via a sparse regularization method, considering the sparsity nature of damage that typically takes place in only a limited number of elements. The feasibility and accuracy of the proposed method are verified through numerical examples and laboratory experiments. Through four hypothetical damage scenarios of a simply supported beam with one or two damaged locations, its ability to quantify minor damage and its anti-noise robustness were well verified. Finally, a laboratory experiment on a simply supported aluminum beam illustrated that the location and extent of damage could be successfully identified in the single-damage and double-damage cases. The numerical and experimental results indicate that the proposed method is promising for future damage localization and quantification of bridge structures.

Damage identification technique based on mode shape analysis of beam structures

This paper presents a procedure to identify damages in beam structures using a damage index defined based on the first mode shape of the structure. The proposed damage index is sensitive to the geometrical parameters and material properties of the structure. Hence, it can be used to localize and characterize damages in beam structures using modal test results. The presented procedure requires the first natural frequency, geometrical dimensions and material properties of the intact structure and also the first mode shape of the intact and damaged structure in a limited number of locations. To demonstrate the performance of the presented procedure, finite element analysis is firstly used to determine the first natural frequency of the intact structure and also the first mode shape of the intact and damaged structures. It is demonstrated that damages cause abrupt change in the damage index value. It is shown that the damage index is not only able to highlight the location of single damage and multi damages located at different regions of the beam, but also can predict the size, and severity of damages. The presented procedure is then implemented to simulate a previous experimental layout and it is observed that the evaluation of damage regions correlates well with the experimental results. Finally, by comparing the performance of the proposed technique with the mode shape curvature method, it is demonstrated that the presented procedure is more effective than the mode shape curvature method in localizing tiny and low severe damages using a limited number of data.

Nondestructive Damage Testing of Beam Structure Based on Vibration Response Signal Analysis

Nondestructive damage-testing technology based on vibration signal analysis makes full use of the response characteristics of wave and energy. With the advantages of wide bandwidths of response frequency and high sensitivity, the nondestructive testing technology based on vibration signal analysis has a superiority in the application for the detection and characterization of structural defects, and has become one of the important methods for the nondestructive testing of structural material defects and damage. This paper presents a novel method of detection localization and quantitative analysis for local damage in beam structures, based on the response analysis of vibration signals. A damage-detection and -identification algorithm based on a unscented Kalman filter (UKF) was designed, which greatly reduces the computational workload in the process of damage identification over that in conventional methods. The method presented in this paper has significances to widen the application scope of the nondestructive testing method, and increase the recognition efficiency and effectiveness of this kind of method in engineering.

An efficient hybrid TLBO-PSO-ANN for fast damage identification in steel beam structures using IGA

The existence of damages in structures causes changes in the physical properties by reducing the modal parameters. In this paper, we develop a two-stages approach based on normalized Modal Strain Energy Damage Indicator (nMSEDI) for quick applications to predict the location of damage. A two-dimensional IsoGeometric Analysis (2D-IGA), Machine Learning Algorithm (MLA) and optimization techniques are combined to create a new tool. In the first stage, we introduce a modified damage identification technique based on frequencies using nMSEDI to locate the potential of damaged elements. In the second stage, after eliminating the healthy elements, the damage index values from nMSEDI are considered as input in the damage quantification algorithm. The hybrid of Teaching-Learning-Based Optimization (TLBO) with Artificial Neural Network (ANN) and Particle Swarm Optimization (PSO) are used along with nMSEDI. The objective of TLBO is to estimate the parameters of PSO-ANN to find a good training based on actual damage and estimated damage. The IGA model is updated using experimental results based on stiffness and mass matrix using the difference between calculated and measured frequencies as objective function. The feasibility and efficiency of nMSEDI-PSO-ANN after finding the best parameters by TLBO are demonstrated through the comparison with nMSEDI-IGA for different scenarios. The result of the analyses indicates that the proposed approach can be used to determine correctly the severity of damage in beam structures.

A two-step method for damage identification in beam structures based on influence line difference and acceleration data

This article presents a two-step approach for structural damage identification in beam structure. Damages are located using the influence line difference before and after damage, the calculation of damage severity is accomplished by acceleration data and bird mating optimizer algorithm. Local damages are simulated as the reduction of both the elemental Young’s modulus and mass of the beam. The technique for damage localization based on displacement influence line difference and its derivatives for beam structure has been outlined. An objective function that comprises dynamic acceleration is utilized in bird mating optimizer. All data are originated from only a few measurement points. Two numerical examples, namely, a simply supported beam and a four-span continuous beam, are investigated in this article. Identification results from different objective functions are compared with results from objective function conventional modal assurance criterion, which shows the superiority of the proposed function. In addition, results of dynamic responses under different types of excitation are presented. The effect of measurement noise level on damage identification results is studied. Studies in the article indicate that the proposed method is efficient and robust for identifying damages in beam structures.

Experimental Investigation of Damage Detection in Beam Using Dynamic Excitation System

Most structural failures are due to break in consisting materials. These breaks begin with a crack, the extension of which is a serious threat to the behaviour of structure. Thus the methods of distinguishing and showing cracks are the most important subjects being investigated. In this article, a new smart portable mechanical system to detect damage in beam structures via using fuzzy-genetic algorithm is introduced. Acceleration-time history of the three points of beam is obtained. The signals are then decomposed into smaller components using new EMD (Empirical Mode Decomposition) method with every IMF containing a specific range of frequency. The dominant frequencies of the structure are obtained from these IMFs using Short-term Fourier transform. Subsequently, a new method of damage detection in simply supported beams is introduced based on fuzzy-genetic algorithm. The new method is capable of identifying the location and intensity of the damage. This algorithm is developed to detect the location and intensity of the damage along the beam, which can detect the damage location and intensity based on the pattern of beam frequency variations between undamaged and damaged states.

A two-step approach for damage detection in beam based on influence line and bird mating optimizer

This paper presents a two-step approach for structural damage identification in beam structure using the influence line and bird mating optimizer (BMO). Local damage is simulated as the reduction of the elemental Young’s modulus and mass of beam element. The technique for damage localization based on influence line and its derivatives before and after damage for beam structure was outlined. An objective function comprised of dynamic acceleration is utilized for BMO algorithm. The dynamic response data under external force is calculated by Newmark integration method. Numerical examples of a simply supported beam was investigated. Effect of measurement noise is studied. Studies in the paper indicate that the proposed method is efficient and robust for identifying damages in beam structures.

Damage identification of beam structures using free response shapes obtained by use of a continuously scanning laser Doppler vibrometer system

Spatially dense operating deflection shapes and mode shapes can be rapidly obtained by use of a continuously scanning laser Doppler vibrometer (CSLDV) system, which sweeps its laser spot over a vibrating structure surface. This paper introduces a new type of vibration shapes called a free response shape (FRS) that can be obtained by use of a CSLDV system, and a new damage identification methodology using FRSs is developed for beam structures. An analytical expression of FRSs of a damped beam structure is derived, and FRSs from the analytical expression compare well with those from a finite element model. In the damage identification methodology, a free-response damage index (FRDI) is proposed, and damage regions can be identified near neighborhoods with consistently high values of FRDIs associated with different modes; an auxiliary FRDI is defined to assist identification of the neighborhoods. A FRDI associated with a mode consists of differences between curvatures of FRSs associated with the mode in a number of half-scan periods of a CSLDV system and those from polynomials that fit the FRSs with properly determined orders. A convergence index is proposed to determine the proper order of a polynomial fit. One advantage of the methodology is that the FRDI does not require any baseline information of an undamaged beam structure, if it is geometrically smooth and made of materials that have no stiffness and mass discontinuities. Another advantage is that FRDIs associated with multiple modes can be obtained using free response of a beam structure measured by a CSLDV system in one scan. The number of half-scan periods for calculation of the FRDI associated with a mode can be determined by use of the short-time Fourier transform. The proposed methodology was numerically and experimentally applied to identify damage in beam structures; effects of the scan frequency of a CSLDV system on qualities of obtained FRSs were experimentally investigated.

Damage Identification in Beam Structure using Spatial Continuous Wavelet Transform

In this paper the applicability of spatial continuous wavelet transform (CWT) technique for damage identification in the beam structure is analyzed by application of different types of wavelet functions and scaling factors. The proposed method uses exclusively mode shape data from the damaged structure. To examine limitations of the method and to ascertain its sensitivity to noisy experimental data, several sets of simulated data are analyzed. Simulated test cases include numerical mode shapes corrupted by different levels of random noise as well as mode shapes with different number of measurement points used for wavelet transform. A broad comparison of ability of different wavelet functions to detect and locate damage in beam structure is given. Effectiveness and robustness of the proposed algorithms are demonstrated experimentally on two aluminum beams containing single mill-cut damage. The modal frequencies and the corresponding mode shapes are obtained via finite element models for numerical simulations and by using a scanning laser vibrometer with PZT actuator as vibration excitation source for the experimental study.

An Improved Method of Parameter Identification and Damage Detection in Beam Structures under Flexural Vibration Using Wavelet Multi-Resolution Analysis.

This paper reports on a two-step approach for optimally determining the location and severity of damage in beam structures under flexural vibration. The first step focuses on damage location detection. This is done by defining the damage index called relative wavelet packet entropy (RWPE). The damage severities of the model in terms of loss of stiffness are assessed in the second step using the inverse solution of equations of motion of a structural system in the wavelet domain. For this purpose, the connection coefficient of the scaling function to convert the equations of motion in the time domain into the wavelet domain is applied. Subsequently, the dominant components based on the relative energies of the wavelet packet transform (WPT) components of the acceleration responses are defined. To obtain the best estimation of the stiffness parameters of the model, the least squares error minimization is used iteratively over the dominant components. Then, the severity of the damage is evaluated by comparing the stiffness parameters of the identified model before and after the occurrence of damage. The numerical and experimental results demonstrate that the proposed method is robust and effective for the determination of damage location and accurate estimation of the loss in stiffness due to damage.

A new damage detection indicator for beams based on mode shape data

In this paper, a new damage indicator based on mode shape data is introduced to identify damage in beam structures. In order to construct the indicator proposed, the mode shape, mode shape slope and mode shape curvature of a beam before and after damage are utilized. Mode shape data of the beam are first obtained here using a finite element modeling and then the slope and curvature of mode shape are evaluated via the central finite difference method. In order to assess the robustness of the proposed indicator, two test examples including a simply supported beam and a two-span beam are considered. Numerical results demonstrate that using the proposed indicator, the location of single and multiple damage cases having different characteristics can be accurately determined. Moreover, the indicator shows a better performance when compared with a well-known indicator found in the literature.

A wavelet finite element-based adaptive-scale damage detection strategy

This study employs a novel beam-type wavelet finite element model (WFEM) to fulfill an adaptive-scale damage detection strategy in which structural modeling scales are not only spatially varying but also dynamically changed according to actual needs. Dynamical equations of beam structures are derived in the context of WFEM by using the second-generation cubic Hermite multiwavelets as interpolation functions. Based on the concept of modal strain energy, damage in beam structures can be detected in a progressive manner: the suspected region is first identified using a low-scale structural model and the more accurate location and severity of the damage can be estimated using a multi-scale model with local refinement in the suspected region. Although this strategy can be implemented using traditional finite element methods, the multi-scale and localization properties of the WFEM considerably facilitate the adaptive change of modeling scales in a multi-stage process. The numerical examples in this study clearly demonstrate that the proposed damage detection strategy can progressively and efficiently locate and quantify damage with minimal computation effort and a limited number of sensors.

Detection and Quantitative Assessment of Damages in Beam Structures Using Frequency and Stiffness Changes

This paper is concerned with vibration based non-destructive evaluation of structures, with a focus on quantitative assessment of damage. In previous works, a reliable method to locate open cracks in beams has been proposed and tested using both data from numerical simulations and laboratory experiments. It bases on the fact the natural frequency of a bending vibrations mode attend different changes, depending on the loss of stored energy for the slice on which the damage is located. As bigger the mode shape curvature value on that location, so bigger the loss of stored energy and consequently the natural frequency decrease in that mode. Analyzing the natural frequency changes for a larger series of vibration modes, it’s possible to precisely locate damages. The authors succeed to find a single mathematical relation describing the frequency changes for all bending vibration modes, involving one term defining damage’s location and one defining its depth. While the first term changes for different modes, being defined by the mode shape curvature, the second maintain its value for all modes, being affected just by damage depth. This finding permits decoupling the location issue with that of quantitative assessment of damage. Latest researches, presented in this paper, succeed by finding the relation between the second term of the relation and some mechanical characteristics of the beam, i.e. extending the proposed method by including evaluation of damage severity. The approach is illustrated on a cantilever beam, modeled with 3D elements.

Damage identification using combined transient power flow balance and acceleration matching technique

This paper presents a multiobjective optimization formulation to detect and quantify crack damage in beam structures at variable locations. It is implemented at the substructure level where the concept is to balance the instantaneous power flow by equating the input power to the dissipated power and the time rate of change of kinetic and strain energies and power transferred to adjacent substructures. This imbalance is reduced to zero to identify the structural parameters or damages. For improved results, the power balance method is combined with conventional acceleration matching method where the objective is to minimize the deviation between measured and estimated accelerations—no additional sensors are required to incorporate the extra power flow balance criteria. Numerical simulations are performed for a lumped mass system, a planar truss structure, and a cantilever beam of 20 elements with multiple damages to evaluate the accuracy of the proposed method. Effects of noise are also taken into account by contaminating the measured responses with 3%, 5%, and 10% Gaussian noise. The particle swarm optimization is used as the optimization algorithm, and normalized fitness functions are defined for both power flow and acceleration components with weighted aggregation multiobjective optimization technique. The effects of various weighting factors for the combined objective function are also studied. The results demonstrate that improvement in accuracy of damage detection is achieved by the combined method, when compared with previous acceleration only matching method as well as other methods. Copyright © 2013 John Wiley & Sons, Ltd.

An improved direct stiffness calculation method for damage detection of beam structures

SUMMARY An improved Direct Stiffness Calculation (DSC) technique and a new damage index, namely Stiffness Variation Index (SVI), are proposed to detect and quantify damage in beam structures. In the DSC technique, through modal displacements and frequencies extracted from a dynamic test, the modal curvature and bending moments are obtained. Therefore, the structural bending stiffness and SVI can be explicitly calculated. By comparing the calculated stiffness with that from design data of the structure, the damage location and its severity can be determined. In the improved DSC technique, the central difference method is adopted to evaluate the modal curvature, making this technique more practical. Sensitivity of measurement errors was studied through numerical simulation via comparing the SVI with other damage indices. It is observed that the diagnosis sensitivity of the SVI using the improved DSC technique is superior to most of other damage indices. For this purpose, two sets of experiments on beams with different measurement errors were analyzed to verify the improved DSC technique. Copyright © 2012 John Wiley & Sons, Ltd.