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Civil infrastructures such as bridges and buildings are prone to damage as a result of natural disasters. To understand damages induced by these events, the structure needs to be monitored. The field of engineering focusing on the process of evaluating the location and the intensity of the damage to the structure is called Structural Health Monitoring (SHM). Early damage prognosis in structures is the fundamental part of SHM. In fact, the main purpose of SHM is obtaining information about the existence, location, and the extent of damage in the structure. Since numerous structural damage detection problems can be solved as an inverse problem based on the proposed objective functions by using optimization algorithm, in this paper, related studies are investigated which discussing objective functions based on Modal Strain Energy (MSE) and flexibility methods including Modal Flexibility (MF), and Generalized Flexibility Matrix (GFM). To illustrate the extent of effectiveness of these objective functions based on the above-mentioned modal parameters, an efficiency index called Impact Factor (IF) is defined. Finally, the best objective function is introduced for each numerical case study based on IF by means of evaluating the obtained result.

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Most structures are asymmetric due to functionality requirements and limitations. This study investigates the effect of asymmetry on damage detection. For this purpose, the asymmetry has been applied to models by considering different spans’ length and also different geometry properties for the section of members. Two types of structures comprising symmetric and asymmetric truss and frame have been modeled considering multiple damage scenarios and noise-contaminated data. Three objective functions based on flexibility matrix, natural frequency and modal frequency are proposed. These objective functions are optimized utilizing multiverse optimizer (MVO). For the symmetric models using limited modal data, flexibility-based objective function has the most accurate results, while by increasing the number of mode shapes, its accuracy reduced. Among asymmetric models of truss, damage detection results of the model is more accurate than those of its symmetric pair. Between asymmetric models of frame, the results obtained from frames which have only different spans’ length are more precise than those of the symmetric model. This is while frequency-based objective functions have their least accurate results for the frame model having asymmetry only in the section properties of its elements.
 

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The main part of finite element analysis via the force method involves the formation of a suitable null basis for the equilibrium matrix. For an optimal analysis, the chosen null basis matrices should exhibit sparsity and banding, aligning with the characteristics of sparse, banded, and well-conditioned flexibility matrices. In this paper, an effective method is developed for the formation of null bases of finite element models (FEMs) consisting of shell elements. This leads to highly sparse and banded flexibility matrices. This is achieved by associating specific graphs to the FEM and choosing suitable subgraphs to generate the self-equilibrating systems (SESs) on these subgraphs. The effectiveness of the present method is showcased through two examples.