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Many methods have been developed for structural size and configuration optimization in which cross-sectional areas are usually assumed to be continuous. In most practical structural engineering design problems, however, the design variables are discrete. This paper proposes two efficient structural optimization methods based on the harmony search (HS) heuristic algorithm that treat both discrete sizing variables and integrated discrete sizing and continuous geometric variables. The HS algorithm uses a stochastic random search instead of a gradient search so the former has a new-paradigmed derivative. Several truss examples from the literature are also presented to demonstrate the effectiveness and robustness of the new method, as compared to current optimization methods.

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In this article, an efficient methodology is presented to optimize the topology of structural systems under transient loads. Equivalent static loads concept is used to deal with transient loads and to solve an alternate quasi-static optimization problem. The maximum strain energy of the structure under the transient load during the loading interval is used as objective function. The objective function is calculated in each iteration and then the dynamic optimization problem is replaced by a static optimization problem, which is subsequently solved by a convex linearization approach combining linear and reciprocal approximation functions. The optimal layout of a deep beam subjected to transient loads is considered as a case study to verify the effectiveness of the presented methodology. Results indicate that the optimal layout is dependant of the loading interval.

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Evolution Strategies (ES) are a class of Evolutionary Algorithms based on Gaussian mutation and deterministic selection. Gaussian mutation captures pair-wise dependencies between the variables through a covariance matrix. Covariance Matrix Adaptation (CMA) is a method to update this covariance matrix. In this paper, the CMA-ES, which has found many applications in solving continuous optimization problems, is employed for size optimization of steel space trusses. Design examples reveal competitive performance of the algorithm compared to the other advanced metaheuristics.

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Heavy economic losses and human casualties caused by destructive earthquakes around the world clearly show the need for a systematic approach for large scale damage detection of various types of existing structures. That could provide the proper means for the decision makers for any rehabilitation plans. The aim of this study is to present an innovative method for investigating the seismic vulnerability of the existing concrete structures with moment resisting frames (MRF). For this purpose, a number of 2-D structural models with varying number of bays and stories are designed based on the previous Iranian seismic design code, Standard 2800 (First Edition). The seismically–induced damages to these structural models are determined by performing extensive nonlinear dynamic analyses under a number of earthquake records. Using the IDARC program for dynamic analyses, the Park and Ang damage index is considered for damage evaluation of the structural models. A database is generated using the level of induced damages versus different parameters such as PGA, the ratio of number of stories to number of bays, the dynamic properties of the structures models such as natural frequencies and earthquakes. Finally, in order to estimate the vulnerability of any typical reinforced MRF concrete structures, a number of artificial neural networks are trained for estimation of the probable seismic damage index.

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In this paper an efficient method is developed for the analysis of non-regular graphs which contain regular submodels. A model is called regular if it can be expressed as the product of two or three subgraphs. Efficient decomposition methods are available in the literature for the analysis of some classes of regular models. In the present method, for a non-regular model, first the nodes of the non-regular part of such model are ordered followed by ordering the nodes of the regular part. With this ordering the graph matrices will be separated into two blocks. The eigensolution of the non-regular part can be performed by an iterative method, and those of the regular part can easily be calculated using decomposition approaches studied in our previous articles. Some numerical examples are included to illustrate the efficiency of the new method.

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In this paper an efficient method is developed for the analysis of non-regular graphs which contain regular submodels. A model is called regular if it can be expressed as the product of two or three subgraphs. Efficient decomposition methods are available in the literature for the analysis of some classes of regular models. In the present method, for a non-regular model, first the nodes of the non-regular part of such model are ordered followed by ordering the nodes of the regular part. With this ordering the graph matrices will be separated into two blocks. The eigensolution of the non-regular part can be performed by an iterative method, and those of the regular part can easily be calculated using decomposition approaches studied in our previous articles. Some numerical examples are included to illustrate the efficiency of the new method.

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Highway construction projects are one of the most important construction projects in the world. Therefore predicting the time of these kinds of projects is important. Basically highway projects are including few activities which are repeating along the horizontal direction. One of the best methods for scheduling these types of projects is linear scheduling method. The repetitive nature of the highway activities is a good reason for schedulers to use linear scheduling methods in order to estimate the time of the project. One of the most important factors in linear projects is considering the effect of the activities productivity on scheduling. The first part of the research has been proposed to quantify the main equation of the identified factors for predicting the daily production rates of the embankment activity. The second part is scheduling the highway construction projects by developing the LSMvpr method based on the application of the embankment activity productivity equation. The purpose of the research is to develop the LSMvpr method for scheduling the highway construction projects by considering the concept of activity productivity in the shape of an equation varying by independent variables changes. By the use of multiple regression analysis the coefficients of affecting factors have been calculated in order to gain a production rate equation for predicting the embankment activity productivity. A software package has been presented for scheduling a highway construction project by coding in MATLAB. The offered software used for validating the model for scheduling the highway construction projects.

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Weighted Uniform Simulation (WUS) is recently presented as one of the efficient simulation methods to obtain structural failure probability and most probable point (MPP). This method requires initial assumptions of failure probability to obtain results. Besides, it has the problem of variation in results when it conducted with few samples. In the present study three strategies have been presented that efficiently enhanced capabilities of WUS. To this aim, a progressively expanding intervals strategy proposed to eliminate the requirement to initial assumptions in WUS, while low-discrepancy samples simultaneously employed to reduce variations in failure probabilities. Moreover, to improve the accuracy of MPP, a new simple local search method proposed and combined with the simulation that strengthened the method to obtain more accurate MPP. The capabilities of proposed strategies investigated by solving several structural reliability problems and obtained results compared with traditional WUS and common reliability methods. Results show that proposed strategies efficiently improved the capabilities of conventional WUS.

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This paper is concerned with the determination of optimal sensor locations for structural modal identification in a strap-braced cold formed steel frame based on an improved genetic algorithm (IGA). Six different optimal sensor placement performance indices have been taken as the fitness functions two based on modal assurance criterion (MAC), two based on maximization of the determinant of a Fisher information matrix (FIM), one aim on the maximization of the modal energy and the last is a combination of two aforementioned indices. The decimal two-dimension array coding method instead of binary coding method is applied to code the solution. Forced mutation operator is applied whenever the identical genes produce via the crossover procedure. An improvement is also introduced to mutation operator of the IGA. A verified computational simulation of a strap-braced cold formed steel frame model has been implemented to demonstrate the effectiveness and application of the proposed method. The obtained optimal sensor placements using IGA are compared with those gained by the conventional methods based on several criteria such as norms of FIM and minimum in off-diagonal terms of MAC. The results showed that the proposed IGA can provide sensor locations as well as the conventional methods. More important, based on the criteria, four of the six fitness functions, can identify the vibration characteristics of the frame model accurately. It is shown through the example that in comparison with the MAC-based performance indices, the use of the FIM-based fitness functions results in more acceptable and reasonable configurations.

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In this research, optimal design and assessment of multiple tuned mass dampers (MTMDs) capability in mitigating the damage of nonlinear steel structures subjected to earthquake excitation has been studied. Optimal parameters of TMDs on nonlinear multi-degree-of-freedom (MDOF) structures have been determined based on minimizing the maximum relative displacement (drift) of structure where for solving the optimization problem the genetic algorithm (GA) has been used successfully. For numerical analysis, three and nine storey 2-D moment resisting nonlinear steel frames subjected to far-field and near-field earthquakes and optimal MTMDs has been designed for different values of mass ratio and TMDs number. According to the results of numerical simulations, it can be said that MTMDs mechanism could reduce the damage of nonlinear steel structures where the effectiveness increases by increasing TMDs mass ratio. Also the performance of MTMDs depends on earthquake characteristics, mass ratio and TMDs configuration where in this research the effective case has been locating TMDs on top floor in parallel configuration.

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In the area of semi-active control of civil structures, Magneto-Rheological (MR) damper has been an efficient mechanism for reducing the seismic response of structures. In this paper, an effective method based on defining an optimization problem for designing MR dampers has been proposed. In the proposed method, the parameters of semi-active control system are determined so that the maximum response of structure is minimized. To solve the optimization problem, the Genetic algorithm (GA) has been utilized. The modified Bouc-Wen model has been used to represent the dynamic behavior of MR damper while to determine the input voltage at any time step, the clipped optimal control algorithm with LQR controller has been applied. To evaluate the performance of the proposed method, a ten-storey shear frame subjected to the El-Centro excitation and for two different kinds of objective functions, optimal MR dampers have been designed. Then the performance of optimal MR damper has been tested under different excitations. The results of the numerical simulations have shown the effectiveness of the proposed method in designing optimal MR dampers that have the capability of reducing the response of the structures up to a significant level. In addition, the effect of selecting a proper objective function to achieve the best performance of MR dampers in decreasing different responses of structure has been shown.

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The use of fiber reinforced polymer (FRP) U-wrap to rehabilitate concrete beams has increased in popularity over the past few years. As such, many design codes and guidelines have been developed to enable designers to use of FRP for retrofitting reinforced concrete beams. FIB is the only guideline for design which presents a formula for torsional capacity of concrete beams strengthened with FRP. The Rackwitz-Fiessler method was applied to make a reliability assessment on the torsional capacity design of concrete beams retrofitted with U-wrap FRP laminate by this guideline. In this paper, the average of reliability index obtained is 2.92, reflecting reliability of the design procedures. This value is somehow low in comparison to target reliability level of 3.5 used in the guideline calibration and so, optimum resistance factor may be needed in future guideline revisions. From the study on the relation between average reliability index and optimum resistance factor, a value of 0.723 for the optimum resistance factor is suggested.

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In this paper, for topology optimization of double layer grids, an efficient optimization method is presented by combination of Imperialist Competitive Algorithm (ICA) and Gravitational Search Algorithm (GSA) which is called ICA-GSA method. The present hybrid method is based on ICA but the moving of countries toward their relevant imperialist is done using the law of gravity of GSA. In topology optimization process, the weight of the structure is minimized subjected to displacements of joints, internal stress and slenderness ratio of members constraints. Through numerical example, topology optimization of a typical large-scale double layer grid is obtained by ICA, GSA and ICA-GSA methods. The numerical results indicate that the proposed algorithm, ICA-GSA, executes better than ICA, GSA and the other methods presented in the literatures for topology optimization of largescale skeletal structures.

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Estimating mechanical properties of concrete before designing reinforced concrete structures is among the design requirements. Steel fibers have a considerable effect on the mechanical properties of reinforced concrete, particularly its tensile strength. So far, numerous studies have been done to estimate the relationship between tensile strength of steel fiber reinforced concrete (SFRC) and other SFRC characteristics using regression analyses. But, in order to determine appropriate relations according to these methods, we need to estimate the basic structure of relations. Genetic programming (GP) method has solved this problem. In this study, the results of 367 laboratory specimens collected from the literature are used to present some relations to predict the tensile strength of SFRC using GP. The proposed relations are more accurate than the relations which have been presented thus far.

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In this paper, two different data driven models, genetic programming (GP) and multivariate adoptive regression splines (MARS), have been adopted to create the models for prediction of bridge risk score. Input parameters of bridge risks consists of safe risk rating (SRR), functional risk rating (FRR), sustainability risk rating (SUR), environmental risk rating (ERR) and target output. The total dataset contains 66 bridges data in which 70% of dataset is taken as training and the remaining 30% is considered for testing dataset. The accuracy of the models are determined from the coefficient of determination (R²). If the R² the testing model is close to the R² value of the training model, that particular model is to be consider as robust model. The modeling mechanisms and performance is quite different for both the methods hence comparative study is carried out. Thus concluded robust models performance based on the R² value, is checked with mathematical statistical equations.  In this study both models were performed, examined and compared the results with mathematical methods successfully. From this work, it is found that both the proposed methods have good capability in predestining the results. Finally, the results reveals that genetic Programming is marginally outperforms over the MARS technique.

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This paper combines particle swarm optimization, grid search method and univariate method as a general optimization approach for any type of problems emphasizing on optimum design of steel frame structures. The new algorithm is denoted as the GSU-PSO. This method attempts to decrease the search space and only searches the space near the optimum point. To achieve this aim, the whole search space is divided into a series of grids by applying the grid search method. By using a method derived from the univariate method, the variables of the best particle change values. Finally, by considering an interval adjustment to the variables and generating particles randomly in new intervals, the particle swarm optimization allows us to swiftly find the optimum solution. This method causes converge to the optimum solution more rapidly and with less number of analyses involved. The proposed GSU-PSO algorithm is tested on several steel frames from the literature. The algorithm is implemented by interfacing MATLAB mathematical software and SAP2000 structural analysis code. The results indicated that this method has a higher convergence speed towards the optimal solution compared to the conventional and some well-known meta-heuristic algorithms. In comparison to the PSO algorithm, the proposed method required around 45% of the total number of analyses recorded and improved marginally the accuracy of solutions.

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Graph theory based methods are powerful means for representing structural systems so that their geometry and topology can be understood clearly. The combination of graph theory based methods and some metaheuristics can offer effective solutions for complex engineering optimization problems. This paper presents a Charged System Search (CSS) algorithm for the free shape optimizations of thin-walled steel sections, represented by some popular graph theory based methods. The objective is to find shapes of minimum mass and/or maximum strength for thin-walled steel sections that satisfy design constraints, which results in a general formulation for a bi-objective combinatorial optimization problem. A numerical example involving the shape optimization of thin-walled open and closed steel sections is presented to demonstrate the robustness of the method.

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This paper presents a Cuckoo Optimization Algorithm (COA) model for the cost optimization of the one-way and two-way reinforced concrete (RC) slabs according to ACI code. The objective function is the total cost of the slabs including the cost of the concrete and that of the reinforcing steel. In this paper, One-way and two-way slabs with various end conditions are formulated as ACI code. The two-way slabs are modelled and analyzed using direct design method. The problems are formulated as mixed-discrete variables such as: thickness of slab, steel bar diameter, and bar spacing. The presented model can be applied in design offices to reduce the cost of the projects. It is also the first application of the Cuckoo Optimization Algorithm to the optimization of RC slabs. In order to demonstrate the superiority of the presented method in convergence and leading to better solutions, the results of the proposed model are compared with the other optimization algorithms.

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The constitutive relationships presented for concrete modeling are often associated with unknown material constants. These constants are in fact the connectors of mathematical models to experimental results. Experimental determination of these constants is always associated with some difficulties. Their values are usually determined through trial and error procedure, with regard to experimental results. In this study, in order to determine the material constants of an elastic-damage-plastic model proposed for concrete, the results of 44 uniaxial compression and tension experiments collected from literature were used. These constants were determined by investigating the consistency of experimental and modeling results using a genetic algorithm optimization tool for all the samples; then, the precision of resulted constants were investigated by simulating cyclic and biaxial loading experiments. The simulation results were compared to those of the corresponding experimental data. The results observed in comparisons indicated the accuracy of obtained material constants in concrete modeling.