Damage In Beam-like Structures Research Articles

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.

Non-Destructive Damage Evaluation Based on Static Response for Beam-like Structures Considering Shear Deformation

Shear deformation plays an important role in certain structures, and neglecting shear deformation can affect the accuracy of structural response. This paper proposes a non-destructive damage evaluation method that considers shear deformation, based on static response, for identifying corrosion in beam-like structures. The influence of shear deformation on nodal displacement for simply supported beams with different cross-sections was analyzed. The results indicate that even small errors yield inaccurate identification results when neglecting shear deformation. To solve this problem, analytical displacements of the structure were determined based on the Timoshenko beam theory, and the objective function was established. Additionally, the damage identification results were obtained by minimizing the objective function using the interior point method. Several progressively complex examples were used to demonstrate the effectiveness of the proposed method in identifying damage in beam-like structures.

An enhanced single damage identification in beams using natural frequency shifts and analytic modal curvatures

This article presents an improved procedure for detecting single damage in beam-like structures. Many damage detection methods are based on the analysis of beam natural frequency shifts in damaged and intact states and its analytical modal curvatures. They identify the damage by constructing curves of damage coefficients along the beam and visually determining the point of their mutual intersection. However, for some cases, the absence of an unambiguous point of intersection of these curves or the low accuracy of its localization makes it difficultto use these methods. To accurately determine the mutual intersection of damage coefficient curves, this work proposes to use a subset of modes without one having its curvature close to zero at the site of the alleged damage. This approach greatly simplifies the determination of the point of intersection of the curves of damagecoefficients. An enhanced procedure for the numerical determination of this intersection point is also proposed,rather than the visual one used in existing methods. The effectiveness of the proposed technique was confirmedby numerical simulation followed by experimental verification.

Damage identification for beam-like structures based on proper orthogonal modes of guided wavefields

Damage in structures can cause local anomalies in a guided wavefield due to reflection of guided waves in neighborhoods of damage. These local anomalies can be used for baseline-free damage identification if the structures are geometrically smooth and made of materials that have no stiffness and mass discontinuities. Recently, guided wavefield-based methods have been studied for damage identification by extracting and localizing local anomalies in guided wavefields in the time- and frequency–wavenumber domains. Meanwhile, proper orthogonal modes (POMs) obtained by the proper orthogonal decomposition have been studied for vibration-based damage identification. In this paper, the effectiveness of POMs of guided wavefields for damage identification in beam-like structures is studied. Since local anomalies in the POMs can be covered by global trends of the POMs, the continuous wavelet transform is used to suppress the global trends and intensify the local anomalies. The fundamental mechanism of how the continuous wavelet transform with Gaussian wavelet functions of a proper order can suppress the global trends of POMs and intensify local anomalies of POMs is explained. Significant POMs used for damage identification are determined by an adaptive truncation technique. The proper orders of the Gaussian wavelet functions, i.e., their number of vanishing moments, are determined based on the modal assurance criterion and a statistical criterion. The continuous wavelet transform of the significant POMs with Gaussian wavelet functions of the proper orders is used to yield an accumulative damage index. Numerical and experimental investigations of the proposed method are conducted on damaged beam-like structures. Their results verified that the proposed method is accurate and noise-robust for identifying the location and extent of damage in beam-like structures.

Vision-Based Damage Detection for One-Fixed-End Structures Based on Aligned Marker Space and Decision Fusion

It is possible to detect damage in structures based only on vision-system-based assessment of their deformation shape under load. There is, however, a gap between available methods designed to detect damage in beam-like structures and engineering needs for monitoring structures of many different shapes. In this article, a new Aligned Marker Space method of morphing vision data is introduced. The method allows damage detection of any engineering object with one fixed support as if it were a cantilever beam. The paper also presents a new fusion technique to combine the results of several damage-detection methods for an increase in accuracy and sensitivity. The methods are tested based on numerical simulation of various structures, a blender-based simulation, and a set of practical experiments in which crane structures are subjected to damage of different sizes and locations. The optimization of damage detection methods' metaparemeters is performed using an evolutionary algorithm designed to find the Pareto front of the solutions. The assessment of the influence of different factors, like camera position, damage position, or repetition of the experiment, is provided.

Data-driven identification of structural damage under unknown seismic excitations using the energy integrals of strain signals transformed from transmissibility functions

In recent years, the methodology based on the energy variations of structural dynamic strain responses has been developed. Although it is an efficient data-driven structural damage identification approach, it can only be used for structures under impulse or known excitations. To overcome this limitation, an improved method is proposed in this paper for the rapid damage identification of beam-like structures using structural dynamic strain responses under unknown seismic excitations. The influence of different excitations to an intact and damaged structure, in which the intact structure is under ambient excitations and structural damage is caused by unknown seismic excitations, is eliminated via the transmissibility functions (TFs) of measured structural strain responses. Contrary to the previous TFs of structural acceleration or displacement responses, TFs of structural strains is more sensitive to local damage in beam-like structures. Moreover, power spectral density transmissibility functions (PSDTFs) are used instead of the traditional Fourier transform TFs. Then, through the inverse Fourier transformation in the frequency domain, the PSDTFs are returned to the time-domain signals to avoid the problem of selecting the proper frequency band in previous studies on identifying structural damage based on TFs in the frequency domain. Finally, structural damage can be identified based on the energy variations of the time-domain strain signals from the intact and damaged structures. Numerical examples of structural damage identification of a seven-storey planar frame and a cable-stayed bridge girder under unknown seismic excitations are provided to demonstrate the effectiveness and robustness of the improved method. Moreover, structural damage identification of a laboratory cable-stayed bridge tower model subjected to shaking table tests is performed to validate the good performance of the proposed method.

Locating and Quantifying Damage in Beam-like Structures Using Modal Flexibility-based Deflection Changes

This paper presents an enhanced method to locate and quantify damage in beam-like structures using changes in deflections estimated from modal flexibility (MF) matrices. The method is developed from explicit relationship between a series of MF-based deflection change vectors and the damage characteristics. Based on this, three damage locating criteria are defined and used to detect and locate damage. Once the damage is located, its severity is estimated conveniently from a closed-form function. The capability of the proposed method is examined through numerical and experimental verifications on a steel beam model. The result shows that the method accurately locates and quantifies damage under various scenarios using a few modes of vibration, with satisfactory or even better results compared to those obtained from traditional static deflection-based method. The performance of the proposed method is also compared with three well-known vibration-based damage detection methods using changes in MF and modal strain energy. It is found that the proposed method outperformed the other three methods, especially for multiple damage cases. As beams can represent various structural components, the proposed method provides a promising damage identification tool targeting the application to real-life structures.

Explicit dynamic response of damaged beams with application to uncertain and identification problems

The influence of damage in beam-like structures is a problem widely analysed in the literature in view of its importance towards the assessment of the residual carrying capacity and the evaluation of the inevitable changes of the dynamic properties. Usually, the dynamic properties and the forced vibrations of structures, cannot be explicitly inferred, particularly in the presence of damage, since the computation of the roots of a highly nonlinear determinantal equation is preliminarily required. Rather, explicit formulations are usually preferred for their ease to use and the possibility to perform parametric analyses, very useful in the case of uncertain parameters, and also to address inverse problems. In this paper, aiming at proposing an explicit formulation of the dynamic response of cracked beams, a model which makes use of the distribution theory and does not require the enforcement of continuity conditions at the cracked sections is employed. Approximated explicit expressions of the main modal parameters related to crack severities are here provided and the reliability of the proposed formulas are verified with reference solutions. The approximated modal parameters can then be used to obtain explicitly the forced vibrations of cracked beams. The proposed methodology is here adopted to address both direct and inverse problems. First, the variability of the dynamic response of cracked beams due to the presence of cracks with uncertain, but bounded, depths is investigated; then, upper and lower bounds of the response are evaluated by making use of both time and frequency domain analyses. In addition, the possibility to adopt the same explicit approach for the identification of damage intensities considering frequency measurements is explored.

A Hybrid Wavelet Based–Approach and Genetic Algorithm to Detect Damage in Beam-Like Structures without Baseline Data

This paper proposes an optimized damage identification method in beam-like structures using genetic algorithm (GA) without baseline data. For this purpose, a vibration-based damage identification algorithm using a damage indicator called ‘Relative Wavelet Packet Entropy’ (RWPE) was implemented to determine the location and extent of damage. The procedure does not require vibration signals from an undamaged structure because the method of comparing signals from different locations in the existing state was found to be effective. To ameliorate the algorithm, GA was utilized to identify the best choice for “mother wavelet function” and “decomposition level” of the signals by means of the fundamental fitness function to optimize the algorithm. This resulted in the high accuracy of the damage identification algorithm. In addition, this method has eliminated the difficulties in selecting the type of mother wavelet function for damage identification purposes. To investigate the robustness and accuracy of the proposed method, numerical examples and experimental cases with different damage depths were considered and conducted. The results demonstrated that the proposed method has great potential in the identification of damage location and depth of cut in beam-like structures since it does not require the recorded data from an undamaged beam as a baseline for damage detection. Moreover, the relationship between damage location and depth of damage has been evaluated and results showed that the algorithm can be applied to actual structures.

Comparative study between the R-ODS and DND methods for damage detection in structures

Measured vibration responses can be processed either in their original time domain or after converting to the frequency domain for the purpose of damage detection. Recently, two new vibration-based methods have been presented separately which successfully identified the location of damage in beam-like structures. One of the methods utilises the vibration responses of cracked structures in time domain and is called deviation from normal distribution (DND). The DND method calculates the difference between actual and normal distribution of vibration responses in time domain to locate cracks. The other method is called residual operational deflection shape (R-ODS) which uses the amplitude and phase of the exciting frequency and its higher harmonics in the frequency domain as a method of crack detection. Previously, these methods were applied only to single cracked beams with sinusoidal excitation and their results were encouraging. Here, the application of the two methods has been extended to multiple cracked beams as well as rotors. Also, the effect of different types of excitations on the detection process using the two methods has been investigated through numerical and experimental examples.

Detecting minute damage in beam-like structures using the neutral axis location

The neutral axis is the curve within a cross-section of a beam under loading at which the normal stress and strain vanish. The neutral axis is correlated with the centroid of stiffness which depends on material and geometric properties of the beam cross-section. The centroid is sensitive to changes in area and stiffness of the cross-section, i.e. damage. The neutral axis is a universal parameter in beam-like structures, and since the majority of structural systems is based on beams, the neutral axis location can be used as a damage sensitive feature in a variety of structures. In this paper the sensitivity of the neutral axis location to minute damage is studied through a test structure with induced artificial damage. The structure was equipped with long-gauge fiber-optic strain sensors in three cross-sections, one with partial delamination in the concrete, one with a small crack, and one with no damage (healthy). The structure was monitored during lifting and transport, and dynamic tests were performed in close-to-real conditions. A detailed uncertainty analysis was performed both on the evaluations of the centroid location and the neutral axis measurements. A Z-score hypothesis test was used to set thresholds and determine whether the damage was detected or not. The results show that the neutral axis location is sensitive to minute damage, and that the latter can be detected within the uncertainty limits in on-site conditions.

Damage detection in beam-like structure based on wavelet packet

Modern and efficient methods of structural damage detection focus on signal processing and have drawn researchers’ attention in recent years. These methods mainly are based on Wavelet Packet Transforms (WPT). The WPT is an extension of the Wavelet Transform, which provides a complete level-by-level decomposition of signal. The wavelet packets are alternative bases formed by the linear combinations of the usual wavelet functions. Therefore, the WPT enables the extraction of features from the signals that combine the stationary and non-stationary characteristics with an arbitrary timefrequency resolution. In this study, a damage detection index called Wavelet Packet Energy Rate Index (WPERI) is proposed for the diagnosing of damage in beam-like structures with two different damage scenarios. For this purpose, the measured vibration signals of an experimental model of the beam were decomposed into the wavelet packet components and the wavelet energy rate index which were computed to indicate the structural damages. It will be shown that, the advantage of this method is applying minimum number of sensors which therefore makes this method practical and economical in comparison with other methods, for example Continues Wavelet Transform and Discrete Wavelet Transform. Also, in spite of low signal to noise ratio, the damage location and intensity will be identified correctly.

Vibration-Based Damage Localization in Flexural Structures Using Normalized Modal Macrostrain Techniques from Limited Measurements

Abstract: This article presents damage locating indices based on normalized modal macrostrain (MMS) as improvement on the typical curvature-dependent methods. Vulnerability to noise and the use of numerical differentiation procedures are the key factors for the poor performance of many curvature-dependent methods using displacement mode shapes. Whereas dynamic distributed strain measurement data from long-gauge FBG sensors have significantly improved the performance of many damage identification methods, the sensitivity to local damage diminishes as the gauge length increases. The proposed model-free damage identification techniques based on normalized MMS vectors are successfully implemented to locate damage in beam-like structures through numerical simulations and experimental verifications. The unique advantages of the techniques are their simplicity, robustness to noise, ability to precisely identify small damage extents, and localize single and multiple damage states using limited measurable modes from few sensors.

Localization and quantification of damage in beam-like structures using sensitivities of principal component analysis results

Principal component analysis (PCA) is known as an efficient method for dynamic system identification and diagnosis. This paper addresses a damage diagnosis method based on sensitivities of PCA in the frequency domain for linear-form structures. The aim is not only to detect the presence of damage, but also to localize and to evaluate it. The Frequency response functions measured at different locations on the beam are considered as data for the PCA process. Sensitivities of principal components obtained from PCA to beam parameters are computed and inspected according to the location of sensors; their variation from the healthy state to the damaged state indicates damage locations. The damage can be evaluated next providing that a structural model is available; this evaluation is based on a model updating procedure. It is worth noting that the diagnosis process does not require a modal identification achievement. Both numerical and experimental examples are used for better illustration.

Quantification and localisation of damage in beam-like structures by using artificial neural networks with experimental validation

This paper presents a damage detection algorithm using a combination of global (changes in natural frequencies) and local (curvature mode shapes) vibration-based analysis data as input in artificial neural networks (ANNs) for location and severity prediction of damage in beam-like structures. A finite element analysis tool has been used to obtain the dynamic characteristics of intact and damaged cantilever steel beams for the first three natural modes. Different damage scenarios have been introduced by reducing the local thickness of the selected elements at different locations along finite element model (FEM) of the beam structure. The necessary features for damage detection have been selected by performing sensitivity analyses and different input–output sets have been introduced to various ANNs. In order to check the robustness of the input used in the analysis and to simulate the experimental uncertainties, artificial random noise has been generated numerically and added to noise-free data during the training of the ANNs. In the experimental analysis, two steel beams with eight distributed surface-bonded electrical strain gauges and an accelerometer mounted at the tip have been used to obtain modal parameters such as resonant frequencies and strain mode shapes. Finally, trained feed-forward backpropagation ANNs have been tested using the data obtained from the experimental damage case for quantification and localisation of the damage.