AN IMPEDANCE ANALYSIS FOR CRACK DETECTION IN THE TIMOSHENKO BEAM BASED ON THE ANTI-RESONANCE TECHNIQUE

An alternative technique for crack detection in a Timoshenko beam based on the first anti-resonant frequency is presented in this paper.Unlike the natural frequency,the anti-resonant frequency is a local parameter rather than a global parameter of structures,thus the proposed technique can be used to locate the structural defects.An impedance analysis of a cracked beam stimulated by a harmonic force based on the Timoshenko beam formulation is investigated.In order to characterize the local discontinuity due to cracks,a rotational spring model based on fracture mechanics is proposed to model the crack.Subsequently,the proposed method is verified by a numerical example of a simply-supported beam with a crack.The effect of the crack size on the anti-resonant frequency is investigated.The position of the crack of the simply-supported beam is also determined by the anti-resonance technique.The proposed technique is further applied to the"contaminated"anti-resonant frequency to detect crack damage,which is obtained by adding 1-3% noise to the calculated data.It is found that the proposed technique is effective and free from the environment noise.Finally,an experimental study is performed,which further verifies the validity of the proposed crack identification technique.     

Statistical detection of structural damage based on model reduction

This paper proposes a statistical method for damage detection based on the finite element （FE） model reduction technique that utilizes measured modal data with a limited number of sensors. A deterministic damage detection process is formulated based on the model reduction technique. The probabilistie process is integrated into the deterministic damage detection process using a perturbation technique, resulting in a statistical structural damage detection method. This is achieved by deriving the first- and second-order partial derivatives of uncertain parameters, such as elasticity of the damaged member, with respect to the measurement noise, which allows expectation and covariance matrix of the uncertain parameters to be calculated. Besides the theoretical development, this paper reports numerical verification of the proposed method using a portal frame example and Monte Carlo simulation.     

DAMAGE DETECTION STRATEGY FOR RETICULATED STRUCTURES BASED ON INCOMPLETE STRAIN MODE

Damage detection based on strain responses of vibration is highly attractive for monitoring long-span reticulated structures.However,there are a lot of structure members in reticulated structures and it is impossible to install strain sensors in each member.Therefore,how to locate and quantify damages with the incomplete mode shapes obtained from few strain sensors is a challenge topic.A new strategy,named incomplete strain mode damage detection(ISMDD) strategy,is proposed in this paper.In the strategy,the distribution of the strain sensors in the reticulated structures can be optimized through sensitive analysis on strain mode perturbation matrix,which can be obtained by perturbation theory.Mode assurance criterion(MAC) value is applied in damage location,and the members with relative large MAC values are defined as damage members.In addition,damage index obtained by solving the perturbation equation is used for damage quantification.Numerical analysis on a long-span reticulated structure,including damage location and quantification for single-and multi-member damages,detection for different damage quantity,the effect analysis of sensor quantity,are performed to verify the effectiveness of the proposed ISMDD strategy.It can be shown from the analysis that the ISMDD strategy is effective in damage location and quantification for both single-and multi-member damages.And the quantity of strain sensors has effect on damage location,but has no obvious influence on damage quantification.Additionally,the anti-noise pollution ability analysis of the ISMDD strategy is carried out,which shows that the ISMDD strategy has excellent anti-noise pollution ability for both single-and multi-damaged members.     

A SINGULAR VALUE DECOMPOSITION BASED TRUNCATION ALGORITHM IN SOLVING THE STRUCTURAL DAMAGE EQUATIONS

The structural damage identification through modal data often leads to solving a set of linear equations. Special numerical treatment is sometimes required for an accurate and stable solution owing to the ill conditioning of the equations. Based on the singular value decomposition (SVD) of the coefficient matrix, an error based truncation algorithm is proposed in this paper. By rejection of selected small singular values, the influence of noise can be reduced. A simply-supported beam is used as a simulation example to compare the results to other methods.Illustrative numerical examples demonstrate the good efficiency and stability of the algorithm in the nondestructive identification of structural damage through modal data.     

DAMAGE DETECTION BASED ON OPTIMIZED INCOMPLETE MODE SHAPE AND FREQUENCY

For the purpose of structural health monitoring, a damage detection method combined with optimum sensor placement is proposed in this paper. The back sequential sensor placement(BSSP) algorithm is introduced to optimize the sensor locations with the aim of maximizing the 2-norm of information matrix, since the EI method is not suitable for optimum sensor placement based on eigenvector sensitivity analysis. Structural damage detection is carried out based on the respective advantages of mode shape and frequency. The optimized incomplete mode shapes yielded from the optimal sensor locations are used to localize structural damage. After the potential damage elements have been preliminarily identified, an iteration scheme is adopted to estimate the damage extent of the potential damage elements based on the changes in the frequency. The effectiveness of this method is demonstrated using a numerical example of a 31-bar truss structure.     

Non-probabilistic information fusion technique for structural damage identification based on measured dynamic data with uncertainty

Based on measured natural frequencies and acceleration responses,a non-probabilistic information fusion technique is proposed for the structural damage detection by adopting the set-membership identification(SMI) and twostep model updating procedure.Due to the insufficiency and uncertainty of information obtained from measurements,the uncertain problem of damage identification is addressed with interval variables in this paper.Based on the first-order Taylor series expansion,the interval bounds of the elemental stiffness parameters in undamaged and damaged models are estimated,respectively.The possibility of damage existence(PoDE) in elements is proposed as the quantitative measure of structural damage probability,which is more reasonable in the condition of insufficient measurement data.In comparison with the identification method based on a single kind of information,the SMI method will improve the accuracy in damage identification,which reflects the information fusion concept based on the non-probabilistic set.A numerical example is performed to demonstrate the feasibility and effectiveness of the proposed technique.     

Surface integral analogy approaches for predicting noise from 3D high-lift low-noise wings

Three surface integral approaches of the acoustic analogies are studied to predict the noise from three concep- tual configurations of three-dimensional high-lift low-noise wings. The approaches refer to the Kirchhoff method, the Ffowcs Williams and Hawkings （FW-H） method of the permeable integral surface and the Curle method that is known as a special case of the FW-H method. The first two approaches are used to compute the noise generated by the core flow region where the energetic structures exist. The last approach is adopted to predict the noise specially from the pressure perturbation on the wall. A new way to con- struct the integral surface that encloses the core region is proposed for the first two methods. Considering the local properties of the flow around the complex object-the actual wing with high-lift devices-the integral surface based on the vorticity is constructed to follow the flow structures. The surface location is discussed for the Kirchhoff method and the FW-H method because a common surface is used for them. The noise from the core flow region is studied on the basis of the dependent integral quantities, which are indicated by the Kirchhoff formulation and by the FW-H formulation. The role of each wall component on noise contribution is analyzed using the Curle formulation. Effects of the volume integral terms of Lighthill＇s stress tensors on the noise pre-diction are then evaluated by comparing the results of the Curle method with the other two methods.     

Test analysis of detection of damage to a complicated spatial model structure

A two-stage damage detection approach is proposed and experimentally demonstrated on a complicated spatial model structure with a limited number of measurements. In the experiment,five known damage patterns,including 3 brace damage cases and 2 joint damage cases,were simulated by removing braces and weakening beam-column connections in the structure. The limited acceleration response data generated by hammer impact were used for system identification,and modal parameters were extracted by using the eigensystem realization algorithm. In the first stage,the possible damaged locations are determined by using the damage index and the characteristics of the analytical model itself,and the extent of damage for those substructures identified at stage I is estimated in the second stage by using a second-order eigen-sensitivity approximation method. The main contribution of this paper is to test the two-stage method by using the real dynamic data of a complicated spatial model structure with limited sensors. The analysis results indicate that the two-stage approach is ableto detect the location of both damage cases,only the severity of brace damage cases can be assessed,and the reasonable analytical model is critical for successful damage detection.     

Damage Imaging in Mesoscale Concrete Modeling Based on the Ultrasonic Time-Reversal Technique

A novel method combining the time-reversal method(TRM)with wavelet analysis was proposed for damage imaging in mesoscale concrete modeling.The damage was imaged by the convergence of time-reversed wave signals after wavelet analysis.Through numerical study,three concrete models of different damage sizes were built with randomly distributed aggregate particles.The time-reversal process was simulated using the reverse damage-scattered ultrasonic wave signals as excitations recorded by the sensors.Then,the wavelet analysis was employed to extract certain frequency component,which can enhance detection precision and the signalto-noise ratio.The damage imaging showed clearly the location of the defect.The results from experimental testing also demonstrated that this detection technique is an efficient and effective method for damage imaging in mesoscale concrete.     

DEVELOPMENT OF EXPERIMENTAL METHODS FOR IMPACT TESTING BY COMBINING HOPKINSON PRESSURE BAR WITH OTHER TECHNIQUES

The split Hopkinson pressure bar（SHPB） technique and the wave propagation inverse analysis（WPIA） technique are both extensively used to experimentally investigate the impact behavior of materials, although neither of them alone provides a fully satisfactory analysis. In the present paper, attention is given to new experimental techniques by incorporating a damagemodified constitutive model into the SHPB technique and combining the Hopkinson pressure bar（HPB） technique with WPIA. First, to distinguish the response due to dynamic constitutive behavior and the response due to dynamic damage evolution, the SHPB method incorporating a damage-modified constitutive model is developed, including an explicit damage-modified Zhu–Wang–Tang model and an implicit damage-modified constitutive model. Second, when the SHPB results become invalid, a method of combining new Lagrange inverse analyses with the HPB technique is developed, including cases of the HPB arranged in front of a long specimen and behind the specimen. As examples of these new methods, typical results are given for nonlinear viscoelastic polymers and concretes considering damage evolution, a super-elastic Ti–Ni alloy with phase transformation and an aluminum foam with shock waves propagating within it.     

基于振动响应的耦合弦系统损伤检测

为解决具有相近频率和相重频率特征的多跨耦合弦系统的损伤检测问题,建立了耦合弦系统在外激励作用下的有限元运动方程.利用直接积分法计算了系统强迫振动响应,将弦的局部损伤模拟为单元面积的减少,推导了振动响应对弦单元面积的灵敏度,并利用此响应灵敏度进行弦的局部损伤识别.数值算例表明:此方法能快速准确地识别出耦合弦的局部损伤,并且对模拟的人工噪声不敏感.     

结构损伤诊断的改进灵敏度方法

提出一种改进的灵敏度方法用于工程结构损伤检测中.通过在迭代算法中引入一个“加速”公式来迅速获得足够精确的识别结果,避免了多次迭代,可以大大减少计算花费.用文献[8]和文献[10]中的两个数值算例对所提方法进行了验证,并把结果和原文中的计算结果进行比较.结果表明:采用改进的方法一般只需经过一次计算即可获得精度更高的识别结果,避免了多次迭代,显著减少了计算花费,显示了改进方法突出的优越性.     

基于模态参数灵敏度的损伤方程组求解正则化方法研究

基于模态参数的结构损伤识别方法是振动损伤识别领域中应用最为广泛的方法.利用模态参数灵敏度构建结构损伤方程组,对其进行求解可以识别结构损伤位置和程度.由于实际工程中模态参数不完备性和噪声的影响,结构损伤方程易出现病态问题,直接求解可能产生错误的结果.为了解决这一问题,可以引入正则化方法进行求解.然而,各类正则化方法的基本...     

On irregularity-based damage detection method for cracked beams

A new damage detection technique using irregularity profile of a structural mode shape is proposed in this paper. The mode-shape of a cracked beam is first obtained analytically by using a general function. Its irregularity profile is then extracted from the mode shape by a numerical filter. The location and size of the crack in the beam can be determined by the peak value appearing on the irregularity profile. Two types of numerical filters, i.e., triangular and Gaussian, are examined. It has been found that the former filter is more effective in damage detection than the latter one. Numerical simulations suggest that the irregularity-based method requires a relatively low measurement resolution. Noise stress tests are carried out to demonstrate the effectiveness and robustness of this method under the influence of noise. As a validation, the proposed method is applied to detect crack damage in an E-glass/epoxy laminated composite beam. The successful detection of the crack in the composite beam demonstrates that the irregularity-based method is capable of assessing both the location and size of the crack and can be used efficiently and effectively in damage identification and health monitoring of beam-type structures.     

A Combined Static/Dynamic Technique for Damage Detection of Laminated Composite Plates

There is a growing demand to develop viable techniques for effective damage detection of composite structures, and the dynamics-based approach has been broadly used in structural health monitoring. A new combined static/dynamic technique for improved damage detection of laminated composite plates is presented. The promise of the technique is that under the sustaining static load, the abnormality of dynamic response due to damage may become more pronounced and easy to be detected. The experimental program consists of testing an E-glass/epoxy composite plate with an embedded delamination under a pre-set static compressive force, and the dynamic response of laminated composite plates is measured using two different actuator–sensor systems: (1) PZT (lead–zirconate–titanate) actuators and scanning laser vibrometer (SLV) sensing system (PZT–SLV), and (2) PZT actuators and Polyvinylidenefluoride (PVDF) sensors (PZT–PVDF). The influence of sustaining static forces to dynamic response of delaminated composite plates is evaluated. The numerical finite element (FE) analysis is also conducted to verify the effectiveness of this technique. The experimental and numerical mode shapes are used to detect the presence, location, and size of the delamination and to study the effect of static load on dynamic response. Two relatively new damage detection algorithms (i.e., Simplified Gapped Smoothing Method (GSM) and Generalized Fractal Dimension (GFD)) are employed to analyze the Uniform Load Surface (ULS) calculated from the experimental and numerical data. From the dynamic response and analysis results using the damage detection algorithms, it is observed that as the sustaining static load increases, the delamination is much easier to be identified through the enlarged damage parameters. The present combined static/dynamic technique is capable of magnifying the effect of damage, thus improving the effectiveness of damage detection.     

Modified intelligent hybrid technique reducing experimental error over the entire target area

The intelligent hybrid technique proposed by Nishioka et al. can be used to analyze stress intensity factors from displacement data obtained by experiments with high accuracy and reliability. However, the hybrid technique suffers from inevitable error and noise involved in extracting displacement fields from the boundary experimentally the boundary obtained experimentally. In this paper, a modified intelligent hybrid technique is developed to improve the shortcomings of the current technique. The proposed hybrid technique reduces the influence of experimental errors not only on/along the boundary but also inside the target area. Taking the SaintVenant principle and the results of test simulations into account, the effectiveness of the proposed hybrid technique is discussed. Then, applying the proposed hybrid technique to the plate with a hole under tensile loading, the distribution of strain, stress, and displacement over the entire target area is calculated with high accuracy and reliability.     

Structural damage localization and evaluation based on modal data via a new evolutionary algorithm

This paper is intended to present a method for the localization and evaluation of damage in plates based on the changes in natural frequencies and mode shapes of the damaged plate using an optimization approach. The colonial competitive algorithm is employed to detect damage (or damages) in plates by optimizing a damage function. The performance of the proposed method is demonstrated by implementing the technique to two examples; a shear wall and a four-fixed supported plate with and without modal data noise including one or a large number of damages. The results confirm the applicability and efficiency of the presented method in detecting damage localization and quantification in the shear walls. Furthermore, the proposed method is implemented to the four-fixed supported plate aimed at demonstrating the high sensitivity of the proposed method in quantitative estimation of damaged plate structures. Finally, the reliability of the presented method is explored through the comparison of the obtained results and those of the other methods. It is concluded that the proposed method can be viewed as a powerful and robust method for structural damage detection in plate structures.     

A 2-D continuous wavelet transform of mode shape data for damage detection of plate structures

A two-dimensional (2-D) continuous wavelet transform (CWT)-based damage detection algorithm using “Dergauss2d” wavelet for plate-type structures is presented. The 2-D CWT considered in this study is based on the formulation by Antoine et al. (2004). A concept of isosurface of 2-D wavelet coefficients is proposed, and it is generated to indicate the location and approximate shape or area of the damage. The proposed algorithm is a response-based damage detection technique which only requires the mode shapes of the damaged plates. This algorithm is applied to the numerical vibration mode shapes of a cantilever plate with different types of damage to illustrate its effectiveness and viability. A comparative study with other two 2-D damage detection algorithms, i.e., 2-D gapped smoothing method (GSM) and 2-D strain energy method (SEM), is performed, and it demonstrates that the proposed 2-D CWT-based algorithm is superior in noise immunity and robust with limited sensor data. The algorithm is further implemented in an experimental modal test to detect impact damage in an FRP composite plate using smart piezoelectric actuators and sensors, demonstrating its applicability to the experimental mode shapes. The present 2-D CWT-based algorithm is among a few limited studies in the literature to explore the application of 2-D wavelets in damage detection, and as demonstrated in this study, it can be used as a viable and effective technique for damage identification of plate- or shell-type structures.