Moving Load Identification Based On Dictionary Learning

The moving load applied on bridge during service plays a crucial role in security performance and condition assessment.As moving load can hardly be measured directly,the indirect identification method by using structural dynamic response and system characteristics has become a realistic choice.With the advantages of effectively reducing the solution quantity,improving the identification efficiency and suppressing the noise,the sparse regularization and dictionary based moving load identification method has been widely used.The accuracy of such methods is determined by the adaptability of dictionary to the moving load.However,it is difficult for the commonly used pre-determined fixed dictionary to fit the loads with unknown complex forms.To improve the identification accuracy,this paper introduces the concept of dictionary learning based on response data into the field of moving load identification,and proposes a moving load identification method accordingly.The main work and conclusions are as follows:(1)A moving load identification method based on sparse dictionary model and sparse K-SVD dictionary learning algorithm is proposed.The accuracy of dictionary based moving load identification method is limited by the adaptability of the dictionary to the moving load,while the proposed method trains the dictionary to be adaptive to the data via dictionary learning algorithm.Firstly,the moving force is discretized in the time domain and the moving load-response equation is established accordingly.Secondly,the moving load is decomposed into the product of a force dictionary and a sparse vector,which is deemed as the first sparsity.Meanwhile,the force dictionary is decomposed into the product of a core dictionary and a sparse matrix,which is deemed as the second sparsity.Then the load dictionary is learned by updating the coordinates of double sparsity alternatively using sparse K-SVD algorithm,thus the forms of atoms in load dictionary is updated.Finally,the moving load is reconstructed with the updated load dictionary and sparse vector.(2)Numerical examples of a simply supported beam subjected to simple,complex and unknown forms of moving load are simulated to investigate the effectiveness of the proposed method.The dictionary learning algorithm is started with concatenated trigonometric functions as the initial core load dictionary and the unit diagonal square matrix as the initial sparse matrix.The atoms’ style of the initial dictionary is compared with that of the dictionary trained by the sparse K-SVD dictionary learning algorithm,and the identification accuracy using the two dictionaries is compared,thus the superiority of the proposed method is verified.The robustness of the proposed method is analyzed by designing different noise levels for the measured dynamic response.(3)The moving vehicle experiment is carried out on a bridge model established in the laboratory to examine the effeteness of the proposed method.The strain response and acceleration response data of the bridge model with different vehicle speed conditions are collected.The proposed method is then employed to identify the moving load time-history of the front and rear axle according to the measured response.The results are compared with the real axle weights of the vehicle,meanwhile,the theoretical responses of the measurement points under the reconstructed moving load is calculated and compared with the measured responses to verify the effectiveness of the proposed method.