شناسایی آسیب ساختاری برای پل های راه آهن بر مبنای رفتار ناشی از پل قطار و تجزیه و تحلیل حساسیت

A damage identification approach using train-induced responses and sensitivity analysis is proposed for the nondestructive evaluation of railway bridges. The dynamic responses of railway bridges under moving trains composed of multiple vehicles are calculated by a train–bridge dynamic interaction analysis. Using the stiffness variation of the bridge element as an index for damage identification, the sensitivities of train-induced bridge responses to structural damage are analyzed and the sensitivity matrices are formed. By comparing the theoretical measurement responses of one measurement point in two different states, the damage indices of all elements are updated iteratively, and finally the absolute or relative damage is located and quantified. A three-span continuous bridge numerical example proves that the proposed dynamic response sensitivity-based FE model updating damage identification method is not only effective to detect local damage of railway bridges, but also insensitive to the track irregularity and the measurement noise.

Damage in bridges can result in changes of their mechanical properties such as mass, stiffness, damping and boundary conditions, which can be reflected by changes in their global dynamic characteristics. The damage identification based on the global dynamic characteristics of structures has become currently a topic of very active research in civil and mechanical engineering. Various damage identification methods have been proposed by utilizing such parameters as natural frequencies [1] and [2], mode shapes [3] and [4], curvature mode shapes [5], modal damping [6], modal strain energies [7], frequency response functions [8] and stiffness or flexibility sensitivities [9] and [10]. Doebling et al. [11] comprehensively reviewed the literature, focusing on frequency-domain damage detection algorithms for linear structures. Zou et al. [12] summarized the methods on vibration-based damage detection and health monitoring for composite structures. Housner et al. [13] gave a good summary on state-of-the-art methods in control and health monitoring of civil engineering structures. The fundamental principle of these methods is to compare the structural behavior in the damaged state with that in the undamaged state. In order to detect the damage locations and to determine the damage extents, it is necessary to model the undamaged state of the structure. A reliable method can be obtained by comparing the experimentally measured data of a structure in its initial state with those predicted by an initial mathematical model [14] and [15]. However, for an accurate model based damage assessment, often a lot of sensors and manual processing are needed, jeopardizing the online damage detection of structures in service. From the view of structural online health monitoring, it is desirable to locate and quantify the damage directly from the time-domain dynamic responses of bridges under operating loads such as running vehicles. For this purpose, much research has been conducted. Liu and Chen [16] presented an inverse technique for identifying stiffness distribution in structures using the structural dynamic responses, where the sensitivity matrices of structural displacements with respect to the stiffness factors were calculated by Newton’s method. Cattarius and Inman [17] detected the damage in smart structures from the time histories of structural responses. Chen and Li [18] and Shi et al. [19] proposed methods to identify both structural parameters and input loads from output-only measurements. Ling et al. [20] proposed an element level system identification method with unknown input with Rayleigh damping. Lu and Law [21, and Lu et al. [22] studied the features of dynamic response sensitivities under sinusoidal, impulsive and random excitations, and then used them in the structural damage identification. For large civil structures such as long-span bridges, it is usually difficult to excite them by impulsive or sinusoidal loads, so the passing vehicles are more suitable as excitation sources. Majumder and Manohar [23] proposed a time-domain approach for damage detection in bridges using both the vehicle response and the bridge response, in which the vehicle was considered as a single degree-of-freedom system with sprung and unsprung masses. Zhu and Law [24] studied the damage detection of simply supported concrete bridges, in which the moving forces and the damage indices are identified at the same time from the measured responses of multiple points. In the above references, none is considering the damage detection of railway bridges from the dynamic responses due to passing trains composed of multiple vehicles. All papers also presume prior knowledge of the FE model in the undamaged state. In this paper, a detailed train–bridge dynamic interaction model is established, in which the train is composed of multiple 4-axle vehicles with 10 degrees-of-freedom and the bridge is discretized by beam elements. The train-induced responses of the bridge in the damaged state are used as input data for damage identification and the response sensitivities with respect to the damage indices of the elements are calculated to establish the sensitivity matrix. Using the error between the measured response and the computed one as a minimization criterion, the sensitivity equation is solved by the least-squares method, and then the damage is located and quantified with the finite element model updating technique. In the proposed method, the influences of measurement noise and track irregularities on the analysis results are discussed. An example of a three-span continuous bridge numerical example proves that the local damage of railway bridges can be effectively identified using the train-induced response of a single measurement point.

The following conclusions can be extracted from this paper: (1) The dynamic responses of the train–bridge system and the sensitivity matrices of the dynamic responses with respect to the damage indices can be calculated by the train–bridge dynamic interaction model. An iterative updating procedure using the train-induced responses and the response sensitivity matrices is proposed to locate and quantify the damages of railway bridges. (2) Only one measurement point is needed to detect the relative or absolute damage of the bridge. The location of the measurement point does not influence the identified results much. (3) The proposed damage identification method has a rather good stability against measurement noise. The identified results are acceptable even for a noise level up to 10%. (4) The proposed damage identification method is insensitive to the track irregularity. Although the efficacy of the proposed damage identification method is good in theory, when it is used in practice, the following aspects should be considered: (1) The considered train should be the same and run at the same speed before and after the bridge is damaged to ensure that the loads acting on the bridge are the same. (2) Disturbing environmental influences, such as wind and temperature, must be minimized. For example, the experiment should be conducted under similar wind speed and temperature conditions before and after the bridge is damaged.