结构健康监测是近年来工程领域的一个研究热点。本文主要基于虚拟变形法(Virtual Distortion Method, VDM)对结构健康监测中动态荷载识别、荷载损伤共同识别及其在车-桥耦合系统的应用进行了系统研究,主要内容如下:1.提出基于形函数和移动时间窗的荷载识别方法,改善了荷载识别中反卷积方法在时域里计算效率低、对噪声敏感等不足。荷载形函数方法借鉴有限元中单元形函数的概念,将荷载的时间历程近似为时间梁的变形,利用梁单元的形函数逼近荷载,将识别连续的荷载历程转化为识别离散的时间梁结点的位移,从而显著降低传递系数矩阵的维数,提高计算效率,并改善了逆问题的病态性。移动时间窗方法将动态荷载的时程分段,然后采用逐段识别并交错前进的方式,提高识别效率。两种方法有机结合,不但提高了计算效率,而且降低了对噪声的敏感性,可实现荷载的在线识别。通过一个连续梁的数值算例和一个悬臂梁的试验有效验证了该方法适用于不同类型荷载的离线与在线识别。2.提出虚拟变形等效损伤的荷载与损伤共同识别。虚拟变形法(VDM)是一种快速重分析方法,它引入虚拟变形来反映结构单元参数的变化,通过在初始模型上施加相关的虚拟变形可以很快求出结构模型改变后的响应,无需对结构系统进行重新建模分析。本文利用有限元理论推导和阐述了损伤结构的单元实际变形、虚拟变形和损伤因子之间的关系及其中的物理意义。利用这个关系将单元的损伤(包括非线性损伤)用虚拟变形来等效。把虚拟变形视为与荷载同样引起结构响应的激励,从而利用提出的荷载识别方法(荷载形函数和移动时间窗)结合未损伤结构的模型直接识别虚拟变形和荷载,无需优化迭代,可快速实现荷载与损伤的共同识别,包括损伤大小和损伤类型,能用于离线与在线识别。该方法与约束子结构方法相结合可以识别共存的局部子结构的荷载与损伤。通过一个五跨空间桁架的数值算例(考虑线性损伤和呼吸裂缝两种损伤形式)和悬臂梁试验验证了该方法的有效性。3.提出基于VDM快速重分析思想的荷载与损伤优化识别。虚拟变形等效损伤的共同识别方法要求传感器的数目至少等于荷载数目和损伤单元的虚拟变形数目之和。该方法以损伤因子为优化变量,所需传感器的数目只需大于未知荷载数目。在优化过程中,利用VDM思想能准确地构造给定损伤因子下的系统脉冲响应,避免了重复构造系统参数矩阵,提高了计算效率。并利用二次多项式插值逼近结构响应和损伤因子的关系,然后通过该多项式可快速估计给定损伤下的结构响应,进一步提高优化效率。此外,结合约束子结构方法可实现局部子结构的荷载与损伤共同识别。在一个三跨框架梁的数值算例和悬臂梁试验中,附加质量、单元刚度损伤和未知荷载均能得到有效识别。4.对VDM方法进行扩展,提出移动动态影响矩阵的概念,并利用其实现移动质量的识别。利用移动动态影响矩阵能快速准确地计算移动质量过桥时的结构响应,避免了时时重构移动质量-桥耦合系统的时变参数矩阵。以此为基础,提出耦合系统中移动质量的快速识别方法,避免了直接识别移动荷载中常遇到的病态问题,具有较高的识别精度和计算效率,对噪声鲁棒性强,使用少于移动质量数目的传感器就可以进行精确识别。结合一个简支梁和三跨框架梁的数值算例验证了该方法的有效性。5.移动车辆振动系统模型相比较移动质点模型更接近与实际情况,而且可以反映车的动力行为。鉴于此,本文利用双自由度质量-弹簧阻尼模型模拟移动车辆振动系统。借助VDM的快速重分析思想,以移动车体的参数修正因子为变量优化识别车体参数。每步优化中利用提出的移动动态影响矩阵,避免了时时重构车-桥耦合系统的时变系统参数矩阵,提高了优化速度。并进一步讨论了路面粗糙度对不同车辆简化模型的影响。结合一个框架梁的数值仿真算例验证不同车辆简化模型的识别效果,证实该方法的有效性。6.在前面研究的基础上,提出车-桥耦合系统中移动体参数和结构损伤的共同识别方法,实现利用较少的传感器就可以得到精确的识别结果。并推导了基于伴随变量的快速灵敏度分析方法,首先以移动质量为车辆模型阐述推导主要理论公式;然后考虑路面粗糙度影响,识别双自由度质量-弹簧阻尼模型参数和结构损伤。在一个三跨框架梁数值算例中,针对是否考虑路面粗糙度的影响两种工况,分别进行了移动体参数和桥梁结构损伤的共同识别,算例结果表明识别结果对模型误差、噪声不敏感,识别精度高。
逆变焊机
Recently Structure Health Monitoring (SHM) has become a hot research topic in civil engineering, of which structural dynamic load identification and damage identification are two important components. In this paper, dynamic load identification, coexistent load and damage identification as well as its applications in moving vehicle-bridge coupled system are studied mainly using Virtual Distortion Method (VDM). The main contents are as follows:1. The deconvolution technique is a popular method for load identification because of its simple expression. However, the solution is hard to be obtained with long measured time or high sampling frequency in time domain, and sensitive to measurement noises. Aiming at improving these drawbacks, this paper proposes an identification method based on load shape function and moving time window. In load shape function method, the concept of shape function in FEM is borrowed to approximate the load time history which is compared to the distortion of a‘time beam’. Therefore reconstruction of the discrete load time history is converted into solving the very limited node displacements of‘time beam’, and hence the dimension of the transfer matrix is obviously decreased, which makes the identification much easier. In addition, ill-conditioning of the inverse problem has been improved. Independently, load can be reconstructed repeatedly in a moving time window which increases the computational efficiency obviously. Moreover, unknown loads can be identified online by combining the two methods, which not only increases the computational efficiency but also the robustness to noise pollution. A numerical example of a continuous beam and an experiment of a cantilever beam are performed and validate that different types of loads can be identified off-line and online effectively.2. Based on VDM, identification of coexistent load and damage is proposed, in which structural damage is modeled by virtual distortions. VDM is a quick reanalysis method, which introduces virtual distortion to reflect the modification of the system parameter. In case of known original intact system, responses of the modified system can be obtained quickly by adding the relative virtual distortion on the intact system, such that reanalysis of the whole system is avoided. In this paper, the physical relation among damage extent, virtual distortions and the final response of the damaged structure are deduced and expressed using the finite element (FE) method, via which structural damage (including nonlinear damage) can be simulated by virtual distortions, such that the damage and the structural response is decoupled numerically. Then through the intact structural model, unknown loads and virtual distortions can be solved directly using the proposed load identification method (based on load shape function and moving time window). In this way, coexistent load and damage (both the extents and types) can be identified quickly without optimization, which can be used for off-line and online monitoring. Moreover, this method can be performed for local substructure identification by cooperating with Isolated Substructure Method. A five- span space truss numerical model (considering the constant damage and breathing crack damage) and a cantilever beam experiment are used to validate the effectiveness of the proposed method.3. An optimization method of coexistent load and damage identification via VDM-based reanalysis is proposed. Damage parameters are considered as the only optimization variables, and the corresponding loads are estimated by solving the deconvolution problem between the measured responses and the impulse responses of the damaged system. In this way, the number of sensors is determined mainly by the number of the unknown loads. It needs fewer sensors than the method which models the structural damage by virtual distortions. The latter requires the number of sensors equal to or bigger than the total number of the unknown loads and virtual distortions. During the optimization, usually the repeated estimation of the impulse responses is time-consuming as it requires to reassemble the numerical model of the structure according to given damage parameters. Here it is avoided by using the VDM, which computes the impulse responses of the damaged structure by combining the impulse responses of the intact structure with its responses to certain virtual distortions. Moreover, the computational efficiency is improved by a local interpolation of perturbations of the structural response with respect to damage parameters. In addition, local substructure damage and load can be identified by combing this method with Isolated Substructure Method. The proposed methodology is verified by a numerical example of a multi-span frame and an experiment of a cantilever beam. Both stiffness-related and mass-related damages can be accurately identified together with the unknown load.4. Moving dynamic influence matrix (MDIM) is proposed, which is an extension of dynamic influence matrix defined in VDM. It does not depend on moving masses and needs to be computed only once for a certain bridge and given velocities of the masses. Thereupon, in the analysis of the coupled moving mass–bridge system, system responses can be computed quickly to different moving masses, which avoid the repeated assembling of the system mass matrix in each time step. Taking advantage of the moving dynamic influence matrix, this paper presents a fast and accurate moving mass identification method. The measured structural response is used to identify the moving mass, while unknown mass is taken as the optimization variables instead of the usually chosen moving mass-equivalent force. In this way well-conditioning of the identification is ensured and the number of the necessary sensors is decreased. Numerical experiments of a simple supported beam and a frame with 5% measurement error demonstrate that moving masses can be identified presicely using fewer sensors than that which takes moving forces as variables.5. A mass-spring damping model with two degree of freedoms (Dofs) is used to simulate the moving vehicle, which is more close to the characteristic of the real vehicle and can reflect its vibrating behavior in comparison with the moving mass model. An effective method to identify moving vehicle parameters is proposed using the concept of VDM and the proposed dynamic moving influence matrix, which chooses unknown vehicle parameters as the optimization variables and identifies them by minimizing the square distance between the measured structural response and the estimated response. During the optimization, the numerical costs are considerably reduced by avoiding the repeated construction of the variant system matrix. Further, the influence of the road roughness on different moving vehicle model is discussed and testified. Numerical example of a three-span frame with 5% measurement error compares the effectiveness of different simplified vehicle models and demonstrates that multiple moving vehicles can be identified using fewer sensors by the proposed method.6. A method for simultaneous identification of moving vehicles and damages of the supporting structure from its measured responses is presented. This method is performed based on the previous studies like moving vehicle identification, coexistent damage and load identification. Damage extents and vehicle parameters are chosen as the optimization variables, which allow the ill-conditioning to be avoided and decrease the number of the required sensors. The adjoint variable method is used for fast sensitivity analysis. First moving mass model is used to deduce and illustrate the basic theoretical formulas. And then considering the influence of road roughness, a two Dofs mass-spring damping model is used for the simultaneous identification. In a three-span beam numerical example, identification is verified respectively with the road roughness considered or neglected. Vehicle parameters and damage extents can be identified accurately with proper vehicle model under 5% rms measurement error and 5% model error.