Random Beam Structure Damage Identification Method Based Static Measurement Data And L1 Regularization

At present,many large structures are getting closer to the life span of the structure.How to understand the health status of the structure in order to carry out structural life prediction and modification and reinforcement has become a difficult problem to be solved.Among them,it is especially important to select the appropriate method to grasp the damage information of the structure without destroying the structure.Based on the results of many researchers and the L1 regularization method,the measured static displacement data is used to identify the damage of the structure.The main research contents are as follows:1.The regularization methods for several ill-posed problems are introduced.Among them,it mainly introduces Landweber iterative regularization,Tikhonov regularization(L2 regularization)and L1 regularization.Landweber iterative regularization has the characteristics of high stability and easy solution.When applied to large structures,it has the characteristics of slow convergence and large calculation,so it is not suitable for damage identification;Tikhonov regularization results are too smooth,compared with L1 regularization,and the method itself is not sparse which cannot eliminate the misjudgment of minor damage.After comparison,it is found that the sparse characteristics of L1 regularization are consistent with the target of damage recognition,and the damage recognition effect is improved.2.A static damage identification method considering model error and measurement error is introduced.The method uses the static cohesion method and the first-order Taylor expansion to establish a stochastic control equation for the damage index,and then solves the damage index based on the perturbation method and optimizes it with L1 regularization to obtain the optimized damage index and its statistical properties.The damage angle is evaluated by the probability angle.3.The simple supported beam and the continuous beam are selected as the simulation examples for analysis.The structural elastic modulus degradation is taken as the structural damage index.The calculation results show that the method can effectively identify the location and size of single damage and multiple damages.Compared with the traditional least square method,the research method of this paper eliminates the misjudgment of small damage,and the calculated damage index is about 1% larger than the exact value,but this does not affect the damage recognition effect.The method is superior to the traditional least squares method in terms of damage mean value and damage probability.4.The effectiveness of the proposed damage identification method is verified by the test of concrete beams.The static displacement measurement data with statistical characteristics is obtained by damage identification of several concrete beams.The method is compared with the traditional least squares method and found to be the beam.When in the elastic working state,both the method and the least squares method can effectively identify the location and size of the damage,and the damage index is small.When the beam is in the elastoplastic working state,there are obvious cracks on the beam surface.The damage index identified by the method corresponds to the crack on the beam surface,which shows the correctness of the recognition result.The results of the least squares method are obviously distorted,indicating the superiority of the method.