Dynamic identification of a reinforced concrete damaged bridge

The results of a series of harmonically forced tests carried out on a reinforced concrete single-span bridge subjected to increasing levels of damage are interpreted in this paper. The deck structure of the bridge consists of a slab and three simply supported beams. The damage is represented by a series of notches made on a lateral beam to simulate the effect of incremental concentrated damage. The variation of lower natural frequencies shows an anomalous increase in the transition from one intermediate damage configuration to the next ones. Vibration mode shapes show an appreciable asymmetry in the reference configuration, despite the nominal symmetry of the bridge. A justification of this unexpected dynamic behavior is presented in this paper. The analysis is based on progressive identification of an accurate finite element model of the reference configuration and on reconstruction of damage evolution from natural frequency and vibration mode measurements. Changes in modal curvature of the first two vibration modes evaluated along the main beams are successfully used to identify the location of the damage.     

SINGULARITY DETECTION FOR STRUCTURAL HEALTH MONITORING USING HOLDER EXPONENTS

The majority of structural health monitoring studies reported in the technical literature focus on identifying damage-sensitive features that can be extracted from dynamic response data. However, many of these studies assume the structure can be modelled as a linear system before and after damage and use parameters of these models as the damage-sensitive features. The study summarised in this paper proposes a damage-sensitive feature that takes advantage of the non-linearities associated with discontinuities introduced into the dynamic response data as a result of certain types of damage. Specifically, the Holder exponent, a measure of the degree to which a signal is differentiable, is the feature that is used to detect the presence of damage and determine when that damage occurred. A procedure for capturing the time-varying nature of the Holder exponent based on wavelet transforms is demonstrated through applications to non-stationary random signals with underlying discontinuities and then to a harmonically excited mechanical system that contains a loose part. Also, a classification procedure is developed to quantify when changes in the Holder exponent are significant. The results presented herein show the Holder exponent to be an effective feature for identifying damage that introduces discontinuities into the measured dynamic response data.     

基于曲率模态与柔度曲率的损伤识别

以含两条裂纹的两端固定梁为例,采用曲率模态差和模态柔度曲率差来检测结构的损伤。首先将梁的裂纹模拟为无质量的等效扭转弹簧,推导了裂纹梁的特征微分方程,利用边界条件和裂纹位置的连续性条件推导得到该裂纹梁的振形函数解析表达式。然后用中心差分法分别求解裂纹梁损伤前后的曲率模态值和模态柔度曲率值,利用其差值确定梁的损伤位置,进而确定损伤程度。最后讨论了曲率模态和柔度曲率对结构损伤识别的敏感性。     

Environmental effects on the identified natural frequencies of the Dowling Hall Footbridge

Continuous monitoring of structural vibrations is becoming increasingly common as sensors and data acquisition systems become more affordable, and as system and damage identification methods develop. In vibration-based structural health monitoring, the dynamic modal parameters of a structure are usually used as damage-sensitive features. The modal parameters are often sensitive to changing environmental conditions such as temperature, humidity, or excitation amplitude. Environmental conditions can have as large an effect on the modal parameters as significant structural damage, so these effects should be accounted for before applying damage identification methods. This paper presents results from a continuous monitoring system installed on the Dowling Hall Footbridge on the campus of Tufts University. Significant variability in the identified natural frequencies is observed; these changes in natural frequency are strongly correlated with temperature. Several nonlinear models are proposed to represent the relationship between the identified natural frequencies and measured temperatures. The final model is then validated using independent sets of measured data. Finally, confidence intervals are estimated for the identified natural frequencies as a function of temperature. The ratio of observed outliers to the expected rate of outliers based on the confidence level can be used as a damage detection index.     

基于模态应变能比与神经网络的复合材料结构损伤辨识

从结构动力学特性入手，以模态应变能比作为表征结构损伤的标识量，对含损伤的复合材料机翼结构进行损伤辨识仿真，通过神经网络建立起损伤标识量和损伤状态之间的映射模型。仿真结果表明，模态应变能比对结构损伤位置和损伤程度都比较敏感，是一种有效的损伤标识量。神经网络可准确地识别出结构的损伤位置和损伤程度，应用于损伤识别是有效的。     

几种常用损伤动力指纹的适用性研究

通过讨论几种常用动力指纹的模态灵敏度,研究了它们的适用性。采用特征灵敏度分析技术,导出了频率、振型和模态柔度对结构参数的灵敏度计算表达式,在此基础上定义了模态加权指针来定量描述各阶模态的损伤动力指纹对结构损伤的灵敏度。通过典型模态稀疏和模态密集结构模型的数值模拟研究发现：对于模态稀疏的简单结构。低阶模态柔度对结构损伤较为敏感;对于模态密集的复杂结构。低阶频率、振型和模态柔度的损伤灵敏度均较差,而且模态柔度在低阶模态条件下远没有在高阶模态条件下对结构损伤敏感。     

一种结构损伤评估的两阶段法研究

结构损伤会引起结构动力特性的改变,这种改变可以用模态参数和结构参数表示。文中将柔度投影法和遗传算法相结合,提出一种基于不完整模态数据的结构损伤定位和定量评估的两阶段法。第一阶段,用柔度投影法进行损伤定位,并进行深入分析。第二阶段,用遗传算法确定损伤程度。文中提出一种用于遗传搜索的新的目标函数形式。最后,用一六跨平面桁架桥模型进行数值模拟,验证文中所提方法的有效性。     

Finite element model updating of concrete-filled steel tubular arch bridge under operational condition using modal flexibility

This paper presents finite element (FE) model updating method for real bridge structure under operational condition using modal flexibility. The theoretical background of the updating procedure is presented. The case study of a simulated simply supported beam demonstrates an effectiveness of modal flexibility in objective function. This objective function is then implemented in case study of a real concrete-filled tubular arch bridge. The bridge was tested under operational condition. Followed by the three-dimensional FE modeling of the bridge, an eigenvalue sensitivity study is carried out to select the most sensitive parameters to the concerned modes. Guyan technique is used to the mass normalization of the mode shapes extracted from ambient modal test to calculate the modal flexibility. The updated FE model of the bridge is able to produce a sufficient improvement on modal parameters of the concerned modes, which is in close agreement with the experiment results and updated parameters still preserve the physical meaning in practice.     

EFFECTS OF TESTING,ANALYSIS, DAMAGE,AND ENVIRONMENT ON MODAL PARAMETERS

Experimental and analytical modal analysis techniques have been widely used in civil engineering for a number of years, mostly in seismic applications. Since the beginning of this decade, these techniques have received considerable attention in non-seismic applications such as structural damage detection, analytical model calibration and remote-monitoring systems. In these applications, most studies have concentrated on correlating modal parameters to changes in structural condition. However, for reliable performance of modal techniques in field situations, it is essential to understand and establish the variability of modal parameters due to test procedures and in-service environments of structures. New York has been researching this subject extensively for the past few years, and has tested several structures including (1) a 1/6-scale model highway bridge, (2) an abandoned fracture-critical highway bridge and (3) an in-service highway bridge. Both the abandoned highway bridge and model bridge were tested under intact and simulated-damage conditions. This paper briefly describes these studies. Results indicate that modal frequencies in conjunction with mode shapes may be used to identify the existence of bridge damage or deterioration of interest, but it is difficult to isolate damage locations using these modal parameters. Operating conditions affect the modal properties and are critical in establishing a baseline for structural monitoring.     

MODELLING AND IDENTIFICATION OF THE DYNAMIC RESPONSE OF A SUPPORTED BRIDGE

This paper describes the dynamic tests performed on a simply supported bridge in Northern Italy under traffic excitation. The acceleration data have been used for the identification of the natural frequencies, viscous damping ratios and mode shapes of the bridge. Modal parameters have been extracted using the wavelet estimation technique, previously implemented by the authors of this paper. This work represents the first attempt in using the wavelet estimation technique directly on transient data and not on the impulse response estimates obtained via the random decrement technique. The capability of the wavelet estimation technique for extracting modal parameters from transient time responses has first been inspected by analysing a simulated set of data. The data have been obtained from the analytical continuous model of a three-span supported bridge. The bridge, excited by moving vehicles, has been modelled as a supported orthotropic plate and its response has been evaluated using the convolution technique. The vehicles have been modelled as multi-body systems, with linear suspensions and tyres flexibility, having globally seven degrees of freedom. An iterative procedure to include the dynamic interaction between the bridge and the vehicles has been implemented. The real bridge, 20 m long approximately, has been monitored using six capacitive accelerometers, measuring the accelerations in seven points of its north edge in two points of its south edge. In particular, the accelerometers on the south edge have been kept in fixed positions, acting as reference points. On the north edge, one accelerometer has been kept fixed at the mid-span location, while the remaining three have been positioned in two different set-ups. Each test has been repeated four times. The estimation of the modal parameters has been performed three times, using as reference point each of the fixed accelerometers. The results obtained from each estimation have been evaluated by means of a modal estimation ‘quality index’ introduced within the wavelet estimation technique.     

Frequency response function shape-based methods for structural damage localisation

The ultilisation of structural shape signals for damage localisation has shown some promise, especially in the applications where an accurate finite element model of the structure is not available. For this purpose, traditional shape signals, like mode shapes, flexibility matrices, uniform load surface (ULS) and operational deflection shapes (ODS) have been widely used. Using frequency response function (FRF) shapes for structural damage localisation is however, a relatively new but promising technique. Unlike mode shapes, ULS and ODS, FRF shapes are defined on broadband data and so have potential to reveal damage location more clearly. Another advantage of using FRF shapes is that the test data can be directly used without the necessity of conducting modal identification. Nevertheless, some problems associated with this approach still remain to be solved. No solid foundation or deduction about the use of FRF shapes for damage localisation has been given in any literature so far. In addition, it has been observed that this method only works for a low-frequency range. This limitation of FRF shapes has not been explained or well treated so far. In this study, a scheme of using FRF shapes for structural damage localisation is proposed. Methods within this scheme include some important modifications like using the imaginary parts of FRF shapes and normalising FRF shapes before comparison. The theoretical explanation of using FRF shapes for damage localisation is presented and the limitations of the previous FRF shape methods have been overcome. The proposed methods have shown great potential in structural damage localisation.     

An experimental study on damage detection of structures using a timber beam

Using vibration methods for the damage detection and structural health monitoring in bridge structures is rapidly developing. However, very little work has so far been reported on timber bridges. This paper intends to address such shortcomings by experimental investigation on a timber beam using a vibration based method to detect damage. A promising damage detection algorithm based on modal strain energy was adopted and modified to locate/evaluate damage. A laboratory investigation was conducted on a timber beam inflicted with various damage scenarios using modal tests. The modal parameters obtained from the undamaged and damaged state of the test beam were used in the computation of damage index, were then applied using a damage detection algorithm utilising modal strain energy and a statistical approach to detect location of damage. A mode shape reconstruction technique was used to enhance the capability of the damage detection algorithm with limited number of sensors. The test results and analysis show that location of damage can be accurately identified with limited sensors. The modified method is less dependent on the number of modes selected and can detect damage with a higher degree of confidence.     

基于摄动方法的受损薄板模态分析

将结构的损伤用δ函数进行表达，建立损伤条件下薄板的自由振动方程。利用一阶摄动方法给出摄动项的一般表达式，并结合δ函数的性质，求出受损薄板模态参数的解析表达式。以一个四边简支的受损薄板为数值算例，计算损伤条件下其模态参数的变化。最后分析损伤情况对模态参数的影响，为利用动力学特性对板的损伤监控和检测提供理论依据。     

Novel Laplacian scheme and multiresolution modal curvatures for structural damage identification

Modal curvature is more sensitive to structural damage than directly measured mode shape, and the standard Laplace operator is commonly used to acquire the modal curvatures from the mode shapes. However, the standard Laplace operator is very prone to noise, which often leads to the degraded modal curvatures incapable of identifying damage. To overcome this problem, a novel Laplacian scheme is proposed, from which an improved damage identification algorithm is developed. The proposed step-by-step procedures in the algorithm include: (1) By progressively upsampling the standard Laplace operator, a new Laplace operator is constructed, from which a Laplace operator array is formed; (2) by applying the Laplace operator array to the retrieved mode shape of a damaged structure, the multiresolution curvature mode shapes are produced, on which the damage trait, previously shadowed under the standard Laplace operator, can be revealed by a ridge of multiresolution modal curvatures; (3) a Gaussian filter is then incorporated into the new Laplace operator to produce a more versatile Laplace operator with properties of both the smoothness and differential capabilities, in which the damage feature is effectively strengthened; and (4) a smoothened nonlinear energy operator is introduced to further enhance the damage feature by eliminating the trend interference of the multiresolution modal curvatures, and it results in a significantly improved damage trait. The proposed algorithm is tested using the data generated by an analytical crack beam model, and its applicability is validated with an experimental program of a delaminated composite beam using scanning laser vibrometer (SLV) to acquire mode shapes. The results are compared in each step, showing increasing degree of improvement for damage effect. Numerical and experimental results demonstrate that the proposed novel Laplacian scheme provides a promising damage identification algorithm, which exhibits apparent advantages (e.g., high-noise insusceptibility, insightful in damage revealment, and visualized damage presentation) over the standard Laplace operator.     

Structural crack detection without updated baseline model by single and multiobjective optimization

Identification, localization and quantification of structural damage can be performed through a model-updating procedure. Model-updating methods require a baseline finite element (FE) model of the undamaged structure, which imposes a restriction on their applicability and can become very problematic especially for large and complex civil structures. Modeling errors in the baseline model whose effects exceed the modal sensitivity to damage are critical and make an accurate estimation of damage impossible. This paper presents an identification algorithm using modal data for assessing structural damage that is based on FE-updating procedures and takes modeling error into account. To overcome its influence, differences of mode shapes and frequencies before and after damage for both numerical model and experimental measurements are used instead of the mode shapes and frequencies themselves. To formulate the objective function, two different approaches have been considered taking into account how these differences are grouped: a single-objective approach and a multiobjective approach. The effectiveness of both approaches is verified against numerical and experimental results.     

Dynamic testing of a damaged bridge

In this paper the results of a campaign of dynamic tests carried out on an existing reinforced concrete single-span bridge subjected to increasing levels of damage are presented. The deck structure consists of a slab and three simply supported beams. The damage is represented by a series of notches made on a lateral beam to simulate the effect of incremental concentrated damage. The modal parameters of the lower vibration modes were estimated from frequency response measurements obtained under harmonic excitation. The variation of natural frequencies shows an anomalous increase in the transition from one intermediate configuration to the next damage configurations. Changes in vibration modes are appreciable from the earliest level of damage. In particular, changes in modal curvature of lower modes do provide indication on the damage location.     

振型曲率在板类结构动力检测中的应用

以四边简支方形弹性薄板为研究对象，通过数值计算得到板损伤前后的多阶模态参数，进而得到板面内两个方向的位移振型曲率并用于板的损伤检测研究。结果表明：当布置有足够数量的振型测点时，振型曲率及板损伤前后的振型曲率差均可用于板损伤的探测与定位，并能大致判断损伤的程度；当振型测点间距过大，或测点偏离损伤区域时，均可能导致检测的失败。     

Development of scanning damage index for the damage detection of plate structures using modal strain energy method

This work presents a novel approach of nondestructive detection of damage in plate structures by using experimental modal analysis (EMA) and modal strain energy method (MSEM). An aluminum alloy 6061 thin plate with a surface crack is investigated in this study. EMA is conducted on the plate to obtain the mode shapes before and after damage. The modal displacements of each mode shape are then used to compute the modal strain energy. For all measured mode shapes, a damage index is defined by using the ratio of modal strain energies of the plate before and after damage. In fact, small damage causes very little change in system response, but it is an essential early warning of structure damage. As the second-order derivatives, modal strain energy is much more sensitive to the small change of structural response than frequencies and mode shapes. It is therefore feasible to approach the small damage by using a damage index defined by fractional MSE of the structure before and after damage. In this study, a scanning damage index (SDI) is developed by moving damage indices obtained from the local area throughout the structure as if a scanning sensor is used to inspect the structure. The damage indices in overlap areas are added up and the summation may intensify the signals of damage in the plate. Limited by the numbers of measured point, a differential quadrature method is employed to calculate the partial differential terms in strain energy formula. Experimental results show that SDI well identifies a surface crack location by using only few measured mode shapes of the aluminum plate. This novel approach provides a flexible, cost-effective, and nondestructive damage evaluation in either local or global structure. Its applicability to different types of structures and different sizes of damage is to be experimentally validated in the future work.     

大型复杂结构损伤识别两步法研究

基于模型修正技术及模态柔度曲率差方法提出了一种解决大型复杂结构损伤识别问题的两步法。首先运用基于模型修正的损伤识别方法进行模糊识别,通过建立带约束边界非线性最小二乘目标函数,极小化结构实测模态与解析模态之间的误差,将损伤识别问题转化为优化问题,并采用信赖域方法求解该优化问题,识别出损伤所属单元组。然后运用模态柔度曲率差方法,对损伤进行精确定位。对某导弹发射台骨架的数值仿真及试验研究结果表明,该损伤识别两步法识别效果较为理想,为解决大型复杂结构的损伤识别问题提供了新思路。     

COMPARATIVE STUDY OF MODAL ANALYSIS TECHNIQUES FOR BRIDGE DYNAMIC CHARACTERISTICS

The purpose of this paper is to present the results of a comparative study of various techniques for evaluating bridge dynamic properties from experimental data. The paper presents a review and synthesis of the work presented in a developed session of the International Modal Analysis Conference of February 2001. Research teams all over the world were invited to participate on a study to compare modal analysis techniques for evaluating the dynamic characteristics of bridges from forced, free and ambient vibration data. The Z24-Bridge, a three-span reinforced concrete bridge in Switzerland, was selected as a case study. The two objectives of the exercise were to compare the modal analysis techniques that are usually employed in the laboratories of the participants and to compare results from typical excitation techniques for large civil engineering structures. A total of six research teams accepted the challenge. The system identification methods that they used ranged from the basic peak-picking method to the advanced subspace identification method. All teams compared at least two excitation types.