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Vulnerability assessment of structures encounter many uncertainties like seismic excitations intensity and response of structures. The most common approach adopted to deal with these uncertainties is vulnerability assessment through fragility functions. Fragility functions exhibit the probability of exceeding a state namely performance-level as a function of seismic intensity. A common approach is finding some response points of the fragility function and then fitting a typical probability distribution like lognormal through curve fitting estimation techniques. Maximum-likelihood approach is a fitting method to find the probability distribution parameters. Performing this approach for distributions like lognormal which is defined by just two parameters are straight forward while for more complicated distribution which are based on additional characterizing parameters is not feasible, since this approach is based on minimizing an error function through classic mathematical approaches like calculating partial derivations. An applicable modification is to add an efficient optimization approach to determine maximum-likelihood function. In this article, an optimization algorithm is proposed with maximum-likelihood-estimation and the results indicate the efficiency and feasibility of future developments in finding the most appropriate fragility function.

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The main objective of this study is to optimize reinforced concrete (RC) frames in the framework of performance-based design using metaheuristics. Three improved and efficient metaheuristics are employed in this work, namely, improved multi-verse (IMV), improved black hole (IBH) and modified newton metaheuristic algorithm (MNMA). These metaheuristic algorithms are applied for performance-based design optimization of 6- and 12-story planar RC frames. The seismic response of the structures is evaluated using pushover analysis during the optimization process. The obtained results show that the IBH outperforms the other algorithms.
 

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This paper proposes a method for structural damage detection through the sensitivity analysis of modal shapes in the calculation of modal strain energy (MSE). For this purpose, sensitivity equations were solved to determine the strain energy based on dynamic data (i.e., modal shapes). An objective function was then presented through the sensitivity-based MSE to detect structural damage. Due to the nonlinearity of sensitivity equations, the objective function of the proposed formulation can be minimized through the shuffled shepherd optimization algorithm (SSOA). The first few modes were employed for damage detection in solving the inverse problem. The proposed formulation was evaluated in a few numerical examples under different conditions. The numerical results indicated that the proposed formulation was efficient and effective in solving the inverse problem of damage detection. The proposed method not only minimized sensitivity to measurement errors but also effectively identified the location and severity of structural damage.
 

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The optimization process of space structures considering the nonlinear material behavior requires significant computational efforts due to the large number of design variables and the complexities of nonlinear structural analysis. Accordingly, the Force Analogy Method (FAM) serves as an efficient tool to reduce computational workload and enhance optimization speed. In this study, the weight optimization of space structures in the inelastic region under seismic loading is carried out using the Shuffled Shepherd Optimization Algorithm (SSOA), with the nonlinear structural analysis based on the FAM. To do this, the FAM formulation for axially loaded members of space structures under seismic forces is presented. Subsequently, weight optimization is performed on two double-layer space structures: a flat double-layer structure with 200 members and a barrel vault structure with 729 members under the Kobe earthquake record. Based on the results, the optimized design using the inelastic behavior showed that the FAM provided accurate results when compared to the precise nonlinear structural analysis. The optimized design based on the FAM is considered acceptable, and the computational time for the optimization process has been significantly reduced.