Dynamic Load And Structural Damage Identification Using Virtual Distortion Method

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.