• Proceedings of the Computational Structural Engineering Institute Conference
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• 1993.10a
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• pp.248-255
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• 1993

Recently, due to the increasing attention to the structural safety under uncertain environments, many researches on the structural reliability analysis have been peformed. Some useful methods are available to evaluate performance reliability of structures with explicit limit states. However, for large structures, in which structural behaviors can be analyzed with finite element models and the limit states are only expressed implicitly, Monte-Carlo simulation method has been mainly used. However, Monte-Carlo simulation method spends too much computational time on repetitive structural analysis. Many alternative methods are suggested to reduce the computational work required in Monte-Carlo simulation. Response surface method is widely used to improve the efficiency of structural reliability analysis. Response surface method is based on the concept of approximating simple polynomial function of basic random variables for the limit state which is not easily expressed in explicit forms of design random variables. The response surface method has simple algorithm. However, the accuracy of results highly depends on how properly the stochastic characteristics of the original limit state has been represented by approximated function, In this study, an improved response surface method is proposed in which the sampling points for creating response surface are modified to represent the failure surface more adequately and the combined use of a linear response surface function and Rackwitz-Fiessler method has been employed. The method is found to be more effective and efficient than previous response surface methods. In addition more consistent convergence is achieved, Accuracy of the proposed method has been investigated through example.

• Structural Engineering and Mechanics
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• v.57 no.4
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• pp.587-602
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• 2016

In structural reliability analysis, the response surface method is widely adopted because of its numerical efficiency. It should be understood that the response function must approximate the actual limit state function accurately in the main region influencing failure probability where it is evaluated. However, the size of main region influencing failure probability was not defined clearly in current response surface methods. In this study, the concept of sub-region of interest is constructed, and an improved response surface method is proposed based on the sub-region of interest. The sub-region of interest can clearly define the size of main region influencing failure probability, so that the accuracy of the evaluation of failure probability is increased. Some examples are introduced to demonstrate the efficiency and the accuracy of the proposed method for both numerical and implicit limit state functions.

• The Journal of Asian Finance, Economics and Business
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• v.2 no.2
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• pp.13-18
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• 2015

In this paper the DRC model is presented for solving multi objective problem. The proposed model is a combination of data envelopment analysis, Cuckoo algorithm and the response surface method. Due to reasons like costs, time and irreversible damages, it is not possible to analyze each and every one of the proposed models in practice, so the simulation is used. Since the number of experiments for simulation process is high then the optimization has gone to practice and directs the simulation process. The response surface method is used as one of the approaches of simulation optimization. Furthermore, data envelopment analysis is used to consider several response surfaces as efficiency response surface. Then this efficiency response surface is solved by Cuckoo algorithms. The main advantage of DRC model is to make one efficiency response surface function instate of multi surface function for every output and also using the advantages of Cuckoo algorithms. In order to demonstrate the effectiveness of the proposed approach, the branches of Refah bank in Mashhad is analyzed and the results are presented.

• Journal of The Korean Society of Agricultural Engineers
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• v.55 no.3
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• pp.75-84
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• 2013

The seepage quantity analysis of reservoir embankment is very important for assessment of embankment safety. However, the conventional analysis does not consider uncertainty of soil properties. Permeability is known that the coefficient of variation is larger than other soil properties and seepage quantity is highly dependent on the permeability of embankment. Therefore, probabilistic analysis should be carried out for seepage analysis. To designers, however, the probabilistic analysis is not an easy task. In this paper, the method that can be performed probabilistic analysis easily and efficiently through the numerical analysis based commercial program is proposed. Stochastic response surface method is used for approximate the limit state function and when estimating the coefficients, the moving least squares method is applied in order to reduce local error. The probabilistic analysis is performed by LHC-MCS through the response surface. This method was applied to two type (homogeneous, core zone) earth dams and permeability of embankment body and core are considered as random variables. As a result, seepage quantity was predicted effectively by response surface and probabilistic analysis could be successfully implemented.

• Structural Engineering and Mechanics
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• v.42 no.2
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• pp.175-189
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• 2012

This paper presents an algorithm for structural reliability with the response surface method. For this aim, an approach with three stages is proposed named as improved response surface method. In the algorithm, firstly, a quadratic approximate function is formed and design point is determined with First Order Reliability Method. Secondly, a point close to the exact limit state function is searched using the design point. Lastly, vector projected method is used to generate the sample points and Second Order Reliability Method is performed to obtain reliability index and probability of failure. Five numerical examples are selected to illustrate the proposed algorithm. The limit state functions of three examples (cantilever beam, highly nonlinear limit state function and dynamic response of an oscillator) are defined explicitly and the others (frame and truss structures) are defined implicitly. ANSYS finite element program is utilized to obtain the response of the structures which are needed in the reliability analysis of implicit limit state functions. The results (reliability index, probability of failure and limit state function evaluations) obtained from the improved response surface are compared with those of Monte Carlo Simulation, First Order Reliability Method, Second Order Reliability Method and Classical Response Surface Method. According to the results, proposed algorithm gives better results for both reliability index and limit state function evaluations.

• Structural Engineering and Mechanics
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• v.17 no.2
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• pp.267-279
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• 2004

This paper presents an improved Monte Carlo simulation for the probabilistic determination of initial cable forces of cable-stayed bridges under dead loads using the response surfaces method. A response surface (i.e. a quadratic response surface without cross-terms) is used to approximate structural response. The use of the response surface eliminates the need to perform a deterministic analysis in each simulation loop. In addition, use of the response surface requires fewer simulation loops than conventional Monte Carlo simulation. Thereby, the computation time is saved significantly. The statistics (e.g. mean value, standard deviation) of the structural response are calculated through conventional Monte Carlo simulation method. By using Monte Carlo simulation, it is possible to use the existing deterministic finite element code without modifying it. Probabilistic analysis of a truss demonstrates the proposed method' efficiency and accuracy; probabilistic determination of initial cable forces of a cable-stayed bridge under dead loads verifies the method's applicability.

• Proceedings of the Korean Society of Precision Engineering Conference
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• 2004.10a
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• pp.700-703
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• 2004

A reliability analysis and design procedure based on the design of experiment (DOE) is combined with the response surface method (RSM) for numerical efficiency. The procedure established is based on a 3$^n$ full factorial DOE for numerical quadrature using explicit formula of optimum levels and weights derived for general distributions. The full factorial moment method (FFMM) shows good performance in terms of accuracy and ability to treat non-normally distributed random variables. But, the FFMM becomes very inefficient because the number of function evaluation required increases exponentially as the number of random variables considered increases. To enhance the efficiency, the response surface moment method (RSMM) is proposed. In RSMM, experiments only with high probability are conducted and the rest of data are complemented by a quadratic response surface approximation without mixed terms. The response surface is updated by conducting experiments one by one until the value of failure probability is converged. It is calculated using the Pearson system and the four statistical moments obtained from the experimental data. A measure for checking the relative importance of an experimental point is proposed and named as influence index. During the update of response surface, mixed terms can be added into the formulation.

• Structural Engineering and Mechanics
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• v.34 no.6
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• pp.779-799
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• 2010

In order to consider high-order effects on the actual limit state function, a new response surface method is proposed for structural reliability analysis by the use of high-order approximation concept in this study. Hermite polynomials are used to determine the highest orders of input random variables, and the sampling points for the determination of highest orders are located on Gaussian points of Gauss-Hermite integration. The cross terms between two random variables, only in case that their corresponding percent contributions to the total variation of limit state function are significant, will be added to the response surface function to improve the approximation accuracy. As a result, significant reduction in computational cost is achieved with this strategy. Due to the addition of cross terms, the additional sampling points, laid on two-dimensional Gaussian points off axis on the plane of two significant variables, are required to determine the coefficients of the approximated limit state function. All available sampling points are employed to construct the final response surface function. Then, Monte Carlo Simulation is carried out on the final approximation response surface function to estimate the failure probability. Due to the use of high order polynomial, the proposed method is more accurate than the traditional second-order or linear response surface method. It also provides much more efficient solutions than the available high-order response surface method with less loss in accuracy. The efficiency and the accuracy of the proposed method compared with those of various response surface methods available are illustrated by five numerical examples.

• Structural Engineering and Mechanics
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• v.62 no.2
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• pp.139-142
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• 2017

For the conventional computational methods for structural reliability analysis, the common limitations are long computational time, large number of iteration and low accuracy. Thus, a new novel method for structural reliability analysis has been proposed in this paper based on response surface method incorporated with an improved genetic algorithm. The genetic algorithm is first improved from the conventional genetic algorithm. Then, it is used to produce the response surface and the structural reliability is finally computed using the proposed method. The proposed method can be used to compute structural reliability easily whether the limit state function is explicit or implicit. It has been verified by two practical engineering cases that the algorithm is simple, robust, high accuracy and fast computation.

• Transactions of Materials Processing
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• v.22 no.1
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• pp.36-41
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• 2013

The present study examines the micro-pattern replication on a plastic film using ultrasonic imprinting. Ultrasonic imprinting uses ultrasonic waves to generate repetitive microscale deformation in the polymer film. The resulting deformation heat on the surface of the film causes the surface region to soften sufficiently so that a replication of the micro-pattern can be obtained. To successfully replicate the micro-pattern on a large area of polymer film, a high replication ratio is needed as well as good uniformity over the entire region. In this study, a horn design is investigated by finite element analysis and is optimized through a response surface analysis. In the ultrasonic imprinting experiments, the response surface method was also used to determine the optimal processing conditions for better replication characteristics.