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After unexpected disasters such as off the Pacific coast of Tohoku earthquake (2011) and the Kumamoto earthquake (2016), structural health monitoring techniques are strongly desired to evaluate the structural state of a building immediately. In the structural health monitoring system, the system identification (SI) method plays an important role in dealing with a large amount of monitoring data. As far as the SI methods are concerned, there may exist two branches classified into a modal-parameter SI and a physical-parameter SI. The main objective of the modal parameter SI is to identify the modal quantities and damping ratios. On the other hand, in the physical-parameter SI, the story stiffnesses of the objective building are directly identified from the floor response data. In order to assess the structural state of the possibly damaged building, the physical-parameter SI method is more appropriate for the structural health monitoring compared with the modal-parameter SI method. In this paper, from the viewpoint of the development of the structural health monitoring system using the physical-parameter SI method, a new structural damage localization algorithm for frame buildings is proposed based on the additivity on story stiffness deterioration caused by structural member damages. In the additivity on story stiffness deterioration, the sensitivities of story stiffnesses to structural damages of structural members are used to identify the location of damaged structural members. The additivity on the story stiffness deterioration can be proved by the Taylor series expansion of a multi-dimensional function. Based on the additivity on the story stiffness deterioration, the story deterioration of the damaged building with multiple structural members can be estimated by the superposition of the story stiffness variation due to the structural damage in a single member. In Section 3, it is shown that the story stiffnesses of a 1-bay 2-story frame are formulated by using the moment distribution method. Since the stiffness ratio of column and beam members are included explicitly in the formulated story stiffnesses, the sensitivity of the story stiffness to the stiffness of each structural member can be derived explicitly and we can understand that the story stiffness varies even if the structural members are damaged in other stories. Therefore, in the proposed damage localization method based on the additivity assumption, the location of the damaged members can be determined by evaluating the error of estimation of the story stiffness deterioration for various combinations of story stiffness deterioration for a single damaged member. The story stiffnesses of a multi-story frame are evaluated by estimating the relationship between the story shear force and the interstory drift derived by the time-history record of floor accelerations. In order to evaluate the story stiffness reliably, it is desirable to obtain the stationary floor responses. For denoising the observed response data, the singular value decomposition using low-rank approximation is applied to the floor acceleration records. It is confirmed that the relationship between the story shear force and the interstory drift can be derived smoothly by denoising, which is important to evaluate the story stiffness. In numerical examples, both a symmetric 2-bay 5-story frame and a setback 5-story frame subjected to two different excitation scenarios such as the ground motion and the top floor forced excitation are used to investigate the validity of the proposed damage localization method in Section 4. For the practical application to possibly damaged buildings, it is assumed that the damage severities of structural members and the number of damaged members are unknown. These problems are solved by the proposed damage localization method by improving the searching algorithm based on the superposition of story stiffness variation using the additivity assumption. |
