An efficient extreme value moment method combining adaptive Kriging model for time-variant imprecise reliability analysis

To improve the efficiency and accuracy of traditional least squares method–based polynomial response surface method (RSM) for reliability analysis of structure, the application of various adaptive metamodeling approaches is notable. The moving least squares method (MLSM)–based RSM is the simplest one and found to be effective in this regard. But, its performance in reliability analysis of structure largely depends on the proper choice of the parameter of weight function involved. In the present study, a generalized scheme to appropriately obtain the hyper-parameter of the MLSM-based RSM to approximate implicit responses of structure for reliability analysis is proposed. The algorithm is hinged on the fact that for reliability analysis, one is interested in the sign of the approximated limit state function (LSF) rather than its magnitude. Thereby, it is sufficient to obtain the hyper-parameter for which the first derivative of the probability of failure as obtained from the approximated LSF with respect to the hyper-parameter is zero. The effectiveness of the proposed algorithm is elucidated through three numerical examples. The improvement achieved by the proposed MLSM-based RSM has been compared with the reliability results obtained by the MLSM-based RSM considering the commonly recommended value of the hyper-parameter and also by the approach where the parameters are obtained by leave one out cross-validation procedure.

The aim of the present paper is to develop a strategy for solving reliability-based design optimization (RBDO) problems by sparse polynomial chaos expansion (PCE). Because classic sparse regression methods cannot provide the surrogate error measure that can be employed to improve the sampling performance for failure probability estimation in RBDO, Bayesian compressed sensing with state-of-the-art performance is employed to build sparse PCE in the paper. In the meanwhile, a new active learning function is proposed to adaptively select new training points. Two goals can be achieved using this criterion; that is, most of the selected training points are selected from the desired regions to approximate limit state surfaces, and these points tend to be far away from the existing points in the current design to avoid the clustering problem. Because the sparse PCEs are built in an augmented space, it is made numerically affordable to solve the RBDO problem with no extra computational cost. The computation capability of the proposed method is demonstrated by several analytical RBDO problems. Meanwhile, the design optimization of a stiffened rib of the wing edge in a certain aircraft also verifies its good engineering applicability.

Structural reliability theory stems from the nature of randomness, fuzziness, characteristic and some other uncertainties in the process of engineering structural design, construction and employment. With the rapid development of science technology and industry, many departments have realized the importance of structural reliability problem and its potential economic benefits. Solving the problem of structural reliability has quickly become an important issue in the field of academic research. Because of the complexity of the structure and the harsh working environment which lead to a complex structural reliability problem, the traditional quality analysis method can’t explain the failure problems in practical engineering. How to solve the problem of large-scale complex structural reliability, improve the accuracy and efficiency of reliability analysis method, and further obtain great economic benefits, have become one of the most important exploration areas for the enterprises and scholars at home and abroad. The response surface method, which can replace the implicit limit state function by small amount of computation arises at this time. Through a series of deterministic response surface method, it uses polynomial function to approximate implicit limit state function. By reasonably selecting sites and iteration strategy, it ensures that the polynomial function on the failure probability can converge to the failure probability of the implicit limit state function. Response surface method, with high efficiency of clarity and precision, strong operability, combined with finite element advantage, is a reliability method widely used at present. In the process of the implementation of the response surface method, it uses three key steps of selecting the response surface function forms, obtaining sample points by the experiment design and using the regression fitting model, which has direct impact on the degree of the response surface method approximating limit state function and determines the performance of the response surface method. This is a problem that the response surface method must solve. It is the paper’s original intention to conduct the research work based on the response surface method of structural reliability optimization, improving the above three steps and the efficiency of engineering structure .The paper aims at the implicit limit state function problem, studying the structural reliability analysis of the weighted response surface method, combining the advantage of obtaining better sites by vector projection method and increases weighted coefficient by weighted response surface method. The improved weighted response surface method based on vector projection sampling is proposed. It uses the vector of the gradient projection method to get new design point and sample points, giving the actual limit state function of sample points more weights to construct the quadratic response surface function, updating the iterative response surface function, and solves the problem of the structural reliability of the implicit limit state function. Example analysis shows the characteristics of the proposed method, a steady design point can be found, and the calculation of stability has been improved considerably. The classical response surface method is optimized and reduces the defects that the calculation results are seriously affected by the interpolation coefficient. To some extent, it improves the calculation accuracy and can get relatively better results. Improved weighted response surface method based on vector projection sampling combines the advantages of obtaining test sample points by vector projection and weighted regression method, which is effective, feasible and can operate directly. It extends the application field of the response surface method to some degree and gets better approximate fitting limit state function at design point. It has better stability and robustness and provides new approach and ideas to solve the implicit limit state function.

복합재료가 신재생 에너지 산업 관련 구조물 및 해양 구조물에서 좀 더 신뢰도 있는 주 하중 부재로 사용되기 위하여 복합재료평판의 확률론적 비선형 초기 파단 하중과 원공과 곡률이 있는 복합재료판의 확률론적 비선형 좌굴 하중이 평가되었다. 주어진 설계 추출점에서의 확정론적 유한요소해석 결과를 바탕으로 반응면기법을 이용하여 한계상태면을 확률변수로 이루어진 2차 다항식으로 근사하였다. 또한, MPFP 근처에서 좀 더 정확하게 한계상태면을 근사하기 위하여 반복적 선형보간법이 적용되었다. 파괴확률을 평가하기 위하여 근사된 한계상태면 상에서 향상된 일계이차모멘트법과 몬테카를로법이 수행되었다. 마지막으로 파단에 영향을 주는 주요한 확률변수를 파악하기 위하여 변환된 확률변수에 대한 신뢰도지수의 감도를 계산하였다. Probabilistic nonlinear first ply failure loads of flat composite panels and nonlinear buckling loads of curved composite panels with cutouts are estimated to provide the more reliable main load carrying structure in the renewable energy industry and offshore structures. The response surface method approximates limit state surface to a second order polynomial form of random variables with the results of deterministic finite element analyses at given sampling design points. Furthermore, the iterative linear interpolation scheme is used to obtain a more accurate approximation of the limit state surface near the most probable failure point (MPFP). The advanced first order second moment method and the Monte Carlo method are performed on an approximated limit state surface to evaluate the probability of failure. Finally, the sensitivity of the reliability index with respect to transformed random variables is investigated to figure out the main random variables that have an effect on failures.

In structural reliability analysis, the response surface method is a powerful method to evaluate the probability of failure. However, the location of experimental points used to form a response surface function must be selected in a judicious way. It is necessary for the highly nonlinear limit state functions to consider the design point and the nonlinear trend of the limit state, because both of them influence the probability of failure. In this paper, in order to approximate the actual limit state more accurately, experimental points are selected close to the design point and the actual limit state, and consider the nonlinear trend of the limit state. Linear, quadratic and cubic polynomials without mixed terms are utilized to approximate the actual limit state. The direct Monte Carlo simulation on the approximated limit state is carried out to determine the probability of failure. Four examples are given to demonstrate the efficiency and the accuracy of the proposed method for both numerical and implicit limit states.

Abstract In this paper, uncertainties and failure criteria of structure are mathematically expressed by random variables and a limit state equation. A limit state equation is approximated by Fleishman's 3rd order polynomials and the theoretical moments of an approximated limit state equation are calculated. Fleishman introduced a 3rd order polynomial in terms of only standard normal distiribution random variables. But, in this paper, Fleishman's polynomial is extended to various random variables including beta, gamma, uniform distributions. Cumulants and a normalized limit state equation are used to calculate a theoretical moments of a limit state equation. A cumulative distribution function of a normalized limit state equation is approximated by a Pearson system. Keywords :reliability analysis, pearson system, moments, cumulants † Corresponding author: Tel: +82-42-860-2282; E-mail: lsg@kari.re.krReceived January 21 2013; Revised June 11 2013;Accepted June 12 2013Ⓒ2013 by Computational Structural Engineering Institute of KoreaThis is an Open-Access article distributed under the terms of the Creative Commons Attribution Non-Commercial License(http://creativecommons. org/licenses/by-nc/3.0) which permits unrestricted non-commercial use, distribution, and reproduction in any medium, provided the original work is properly cited.

Serviceability reliability analysis of prestressed concrete bridges

A response surface method based on support vector machines trained with an adaptive experimental design

Structural Reliability Assessment by Local Approximation of Limit State Functions Using Adaptive Markov Chain Simulation and Support Vector Regression

In this paper, a reliability-based topology optimization (RBTO) for 3-D structures was performed using bi-directional evolutionary structural optimization (BESO) and the standard response surface method (SRSM). In order to get a stable optimal topology, the most recently-developed filter scheme was implemented with BESO, and SRSM was used to generate an approximate limit state function. These results were compared with the recently announced results of RBTO for 2-D structures, and the differences between the results for the 3-D and 2-D structures were examined. A cantilever beam and an MBB beam were selected as the numerical examples. The comparison showed that the optimal topologies of deterministic topology optimization (DTO) and RBTO for the 2-D and 3-D MBB beams, respectively, are very different. Specifically, the two-support member on the left hand side comes into being along the width for the 3-D case, but not for the 2-D case. This shows that RBTO for 3-D structures should be performed as part of the design process.

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.

An artificial neural network based genetic algorithm for estimating the reliability of long span suspension bridges

Hybrid genetic algorithms for structural reliability analysis

High-order limit state functions in the response surface method for structural reliability analysis