• Title, Summary, Keyword: Response Surface Method

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Improved Response Surface Method Using Modified Selection Technique of Sampling Points (개선된 평가점 선정기법을 이용한 응답면기법)

  • 김상효;나성원;황학주
    • Proceedings of the Computational Structural Engineering Institute Conference
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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.

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A new high-order response surface method for structural reliability analysis

  • Li, Hong-Shuang;Lu, Zhen-Zhou;Qiao, Hong-Wei
    • 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.

A Study on Response Surface Method Using the Vector Projection Technique (벡터투영법을 이용한 응답면기법에 관한 연구)

  • 김상효;나성원;김우곤
    • Proceedings of the Computational Structural Engineering Institute Conference
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    • pp.167-174
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    • 1994
  • In this study, an improved response surface method is proposed. By using gradient projection method, the sampling points for creating response surface are evaluated at the region close to the failure surface. This points are combined with linear response surface function and Rackwitz-Fiessler algorithm. Also, a method controlling the range of selecting sampling points considering the non-linearity of the limit states is proposed to reduce the error produced by approximating the non-linear limit state to linear response surface. With the examples the result of the proposed method is found to be more accurate and efficient than the previous response surface method.

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An improved response surface method for reliability analysis of structures

  • Basaga, Hasan Basri;Bayraktar, Alemdar;Kaymaz, Irfan
    • 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.

Design Optimization of Auto-body Members for Crashworthiness Enhancement with the Response Surface Method (반응표면법을 이용한 차체 부재의 충돌성능 향상을 위한 설계 최적화)

  • Na Sungyul;Song Junghan;Huh Hoon;Kim Hyunsub
    • Transactions of the Korean Society of Automotive Engineers
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    • v.13 no.4
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    • pp.81-89
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    • 2005
  • The response surface method is the statistical method which can be applied to the non-sensitivity based optimization. The response surface which is constructed by the least square method contains only the polynomial terms so that the global maximum and minimum points are easily obtained. In this paper, this response surface method is utilized to optimize the crashworthiness of auto-body members. As the first step, the thickness of a simple circular tube is optimized to confirm the application of the response surface method to the crashworthiness. Optimization of the thickness on the front side member is, then, performed with the constructed response surface of the absorbed energy and deformation. Optimization results demonstrate that the absorbed energy and the deformation pattern of the front side member is improved in the viewpoint of enhancement of the crashworthiness.

An efficient Reliability Analysis Method Based on The Design of Experiments Augmented by The Response Surface Method (실험계획법과 반응표면법을 이용한 효율적인 신뢰도 기법의 개발)

  • 이상훈;곽병만
    • Proceedings of the Korean Society of Precision Engineering Conference
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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.

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Probabilistic determination of initial cable forces of cable-stayed bridges under dead loads

  • Cheng, Jin;Xiao, Ru-Cheng;Jiang, Jian-Jing
    • 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.

SIZE OPTIMIATION OF AN ENGINE ROOM MEMBER FOR CRASHWORTHINESS USING RESPONSE SURFACE METHOD

  • Oh, S.;Ye, B.W.;Sin, H.C.
    • International Journal of Automotive Technology
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    • v.8 no.1
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    • pp.93-102
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    • 2007
  • The frontal crash optimization of an engine room member using the response surface method was studied. The engine room member is composed of the front side member and the sub-frame. The thicknesses of the panels on the front side member and the sub-frame were selected as the design variables. The purpose of the optimization was to reduce the weight of the structure, under the constraint that the objective quantity of crash energy is absorbed. The response surface method was used to approximate the crash behavior in mathematical form for optimization procedure. To research the effect of the regression method, two different methodologies were used in constructing the response surface model, the least square method and the moving least square method. The optimum with the two methods was verified by the simulation result. The precision of the surrogate model affected the optimal design. The moving least square method showed better approximation than the least square method. In addition to the deterministic optimization, the reliability-based design optimization using the response surface method was executed to examine the effect of uncertainties in design variables. The requirement for reliability made the optimal structure be heavier than the result of the deterministic optimization. Compared with the deterministic optimum, the optimal design using the reliability-based design optimization showed higher crash energy absorption and little probability of failure in achieving the objective.

The Optimization of Bank Branches Efficiency by Means of Response Surface Method and Data Envelopment Analysis: A Case of Iran

  • Shadkam, Elham;Bijari, Mehdi
    • 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.

Capabilities of stochastic response surface method and response surface method in reliability analysis

  • Jiang, Shui-Hua;Li, Dian-Qing;Zhou, Chuang-Bing;Zhang, Li-Min
    • Structural Engineering and Mechanics
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    • v.49 no.1
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    • pp.111-128
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    • 2014
  • The stochastic response surface method (SRSM) and the response surface method (RSM) are often used for structural reliability analysis, especially for reliability problems with implicit performance functions. This paper aims to compare these two methods in terms of fitting the performance function, accuracy and efficiency in estimating probability of failure as well as statistical moments of system output response. The computational procedures of two response surface methods are briefly introduced first. Then their capabilities are demonstrated and compared in detail through two examples. The results indicate that the probability of failure mainly reflects the accuracy of the response surface function (RSF) fitting the performance function in the vicinity of the design point, while the statistical moments of system output response reflect the accuracy of the RSF fitting the performance function in the entire space. In addition, the performance function can be well fitted by the SRSM with an optimal order polynomial chaos expansion both in the entire physical and in the independent standard normal spaces. However, it can be only well fitted by the RSM in the vicinity of the design point. For reliability problems involving random variables with approximate normal distributions, such as normal, lognormal, and Gumbel Max distributions, both the probability of failure and statistical moments of system output response can be accurately estimated by the SRSM, whereas the RSM can only produce the probability of failure with a reasonable accuracy.