scholarly journals Structural reliability and its sensitivity analysis based on the saddlepoint approximation-line sampling method by dichotomy of golden section

2019 ◽  
Vol 39 (1) ◽  
pp. 11-20
Author(s):  
Ganqing Zhang ◽  
Yanghui Xiang ◽  
Huixin Guo ◽  
Yonghong Nie
Keyword(s):  
Failure Probability ◽  
Structural Reliability ◽  
Golden Section ◽  
Saddlepoint Approximation ◽  
International Study ◽  
Normal Variable ◽  
Line Sampling ◽  
Golden Section Method ◽  
Variable Space ◽  
Solution Efficiency

In order to solve the structural reliability and its sensitivity of the implicit nonlinear performance function (PF) the advantages of the saddlepoint approximation (SA) and line sampling (LS) are merged. Also, the merits of dichotomy and the solution efficiency of the golden section method are combined to propose the saddlepoint approximation-line sampling (SA-LS) method based on the dichotomy of the golden section point. This is complicated and changeable in the non normal variable space, which is a very hot issue of the present international study. For each sample, it is quick to find its zeropoint in PF along the important line sampling direction by the previously mentioned dichotomy so that the structural failure probability can be transformed into the mean of a series linear PFs failure probability, and the reliability sensitivity is just the derivative or partial one of the probability with respect to the relational variables. Examples show that the SA-LS method based on the dichotomy of the golden section point is of high precision and fast velocity in analyzing the structural reliability and sensitivity of the implicit nonlinear PF that are complicated and changeable in the non-normal variable space.

A New Numerical Method for General Failure Probability with Fuzzy Failure Region

2007 ◽  
Vol 353-358 ◽  
pp. 997-1000 ◽  
Author(s):  
Lei Chen ◽  
Zhen Zhou Lu
Keyword(s):  
Numerical Method ◽  
Failure Probability ◽  
High Efficiency ◽  
Joint Probability ◽  
Line Sampling ◽  
Failure Region ◽  
Random Failure ◽  
Total Integral ◽  
Variable Space ◽  
General Reliability

For general reliability analysis with fuzzy failure region F % , the general failure probability F P% is defined as the integral of product of μF% [g( y)] , the membership of performance function ( ) g y to F % , and joint Probability Density Function (PDF) f ( y) over , the total variable space, i.e. [ ( )] ( ) F F P μ g f d % = ∫ ∫ % y y y L . On the basis of line sampling, an efficient method for random failure probability analysis with clear failure region, a new numerical method is presented to calculate F P% . In the presented method, the total integral region is split into m clear sub-regions i F in a way that the value of g( y) in i F can be approximately viewed as i g , a constant independent of y , and the value of [ ( )] F μ % g y in i F can be viewed as a constant ( ) F i μ g % subsequently. Due to the closely invariant property of [ ( )] F μ g % x in i F and 1 2 m = F I F ILI F , F P% is transformed into the sum of ( ) F i μ g % ( ) i F ∫L∫ f y dy , where ( ) i F ∫L∫ f y dy is the random failure probability with the clear failure region i F and can be obtained by line sampling. The high efficiency of the presented method resulted from that of the line sampling is demonstrated by the illustration.

Estimating the Interval of Failure Probability Fluctuation Under Uncertain Input Variable Distributions

2016 ◽  
Author(s):  
Jorge E. Hurtado
Keyword(s):  
Monte Carlo Simulation ◽  
Monte Carlo ◽  
Failure Probability ◽  
Structural Reliability ◽  
Reliability Measures ◽  
Computational Labor ◽  
Variable Space ◽  
Uncertain Input ◽  
Uncertain Distribution ◽  
Form Approach

Structural reliability analysis often faces the problem that the input variable distributions are uncertain and thus the interval for reliability measures must be determined. A Monte Carlo simulation consists in estimating the failure probability for several sets of random realizations of the distributions, thus implying a huge computational labor, much higher than in conventional Monte Carlo. In this paper a method for drastically simplifying this task is proposed. The method exploits the ordering statistics representation property of the reliability plot, which is shown to approximately obey an orthogonal hyperbolic pattern. Accordingly a two-level FORM approach is used to derive the polar vectors for building two plots, one for the input variable space and another for the uncertain distribution parameter space. It is demonstrated that the extrema of the failure probability are contained amongst the samples located in extreme sectors of the parameter plot as pointed out by the hyperbolae.

scholarly journals Neglect Of Parameter Estimation Uncertainty Can Significantly Overestimate Structural Reliability

2015 ◽  
Vol 15 (2) ◽  
Author(s):  
Árpád Rózsás ◽  
Miroslav Sýkora
Keyword(s):  
Parameter Estimation ◽  
Bayesian Statistics ◽  
Failure Probability ◽  
Structural Reliability ◽  
Probabilistic Models ◽  
Estimation Uncertainty ◽  
Point Estimates ◽  
Distribution Parameters ◽  
Order Of Magnitude ◽  
Parameter Estimation Uncertainty

Abstract Parameter estimation uncertainty is often neglected in reliability studies, i.e. point estimates of distribution parameters are used for representative fractiles, and in probabilistic models. A numerical example examines the effect of this uncertainty on structural reliability using Bayesian statistics. The study reveals that the neglect of parameter estimation uncertainty might lead to an order of magnitude underestimation of failure probability.

ON THE ACCELERATION OF OPTIMIZATION METHODS FOR THE PROBLEM OF SYNTHESIS OF MULTILAYER OPTICAL COATINGS

2021 ◽  
Vol 6 ◽  
pp. 13-26
Author(s):  
Alexander Mitsa ◽  
◽  
Petr Stetsyuk ◽  
Alexander Levchuk ◽  
Vasily Petsko ◽  
...  
Keyword(s):  
Objective Function ◽  
Golden Section ◽  
Optical Coatings ◽  
Generalized Gradient ◽  
Arithmetic Operations ◽  
Section Method ◽  
Suffix Arrays ◽  
Multidimensional Search ◽  
Golden Section Method ◽  
Speed Up

Five ways to speed up the multidimensional search in order to solve the problem of synthesis of multilayer optical coatings by using the methods of zero and first orders have been considered. The first way is to use an analytical derivative for the target quality function of the multilayer coating. It allows us to calculate accurately (within the computer arithmetic) the value of the gradient of a smooth objective function and generalized gradient of a non-smooth objective one. The first way requires the same number of arithmetic operations as well as finite-difference methods of calculating the gradient and the generalized gradient. The second way is to use a speedy finding of the objective function gradient using the prefix- and suffix-arrays in the analytical method of calculating the gradient. This technique allows us to reduce the number of arithmetic operations thrice for large-scale problems. The third way is the use of tabulating the values of trigonometric functions to calculate the characteristic matrices. This technique reduces the execution time of multiplication operations of characteristic matrices ten times depending on the computer’s specifications. For some computer architectures, this advantage is more than 140 times. The fourth method is the use of the golden section method for the one-dimensional optimization in the problems of synthesis of optical coatings. In particular, when solving one partial problem it is shown that the ternary search method requires approximately 40% more time than the golden section method. The fifth way is to use the effective implementation of multiplication of two matrices. It lies in changing the order of the second and third cycles for the well-known method of multiplying two matrices and fixing in a common variable value of the element of the first matrix. This allows us to speed up significantly the multiplication operation of two matrices. For matrices having 1000 x 1000 dimension the acceleration is from 2 to 15 times, depending on the computer's specifications.

Focusing of Scattering Light by Improved Feedback Wavefront Shaping Technique Based on Golden Section Method

2017 ◽  
Vol 37 (6) ◽  
pp. 0626005
Author(s):  
胡显声 Hu Xiansheng ◽  
蒲继雄 Pu Jixiong ◽  
冀旋旋 Ji Xuanxuan ◽  
陈子阳 Chen Ziyang
Keyword(s):  
Golden Section ◽  
Section Method ◽  
Shaping Technique ◽  
Golden Section Method ◽  
Wavefront Shaping ◽  
Scattering Light

scholarly journals Fault Location of Active Distribution Networks Based on the Golden Section Method

2020 ◽  
Vol 2020 ◽  
pp. 1-9
Author(s):  
Haizhu Yang ◽  
Xiangyang Liu ◽  
Yiming Guo ◽  
Peng Zhang
Keyword(s):  
Fault Location ◽  
Golden Section ◽  
Flow Analysis ◽  
Energy Resource ◽  
Distribution Networks ◽  
Load Flow ◽  
Distributed Energy ◽  
Load Flow Analysis ◽  
Distributed Energy Resource ◽  
Golden Section Method

Aiming at the problem of fault location in distribution networks with distributed energy resources (DERs), a fault location method based on the concepts of minimum fault reactance and golden section is proposed in this paper. Considering the influence of distributed energy resource supply on fault point current in distribution networks, an improved trapezoidal iteration method is proposed for load flow analysis and fault current calculation. This method only needs to measure the synchronous current of the distributed energy resource and does not need to measure the voltage information. Therefore, the investment in equipment is reduced. Validation is made using the IEEE 34-node test feeder. The simulation results show that the method is suitable for fault location of distribution networks with multiple distributed generators. This method can accurately locate the faults of the active distribution network under different conditions.

Improved Line Sampling Reliability Analysis Method and its Application

2007 ◽  
Vol 353-358 ◽  
pp. 1001-1004 ◽  
Author(s):  
Shu Fang Song ◽  
Zhen Zhou Lu
Keyword(s):  
Markov Chain ◽  
Reliability Analysis ◽  
Failure Probability ◽  
Low Cycle Fatigue ◽  
Limit State ◽  
Computational Cost ◽  
State Function ◽  
Line Sampling ◽  
Failure Region ◽  
Important Direction

For reliability analysis of implicit limit state function, an improved line sampling method is presented on the basis of sample simulation in failure region. In the presented method, Markov Chain is employed to simulate the samples located at failure region, and the important direction of line sampling is obtained from these simulated samples. Simultaneously, the simulated samples can be used as the samples for line sampling to evaluate the failure probability. Since the Markov Chain samples are recycled for both determination of the important direction and calculation of the failure probability, the computational cost of the line sampling is reduced greatly. The practical application in reliability analysis for low cycle fatigue life of an aeronautical engine turbine disc structure under 0-takeoff-0 cycle load shows that the presented method is rational and feasible.

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