scholarly journals Spoke Model for Calculating Reliability Index and Safety Factor of Slopes

2013 ◽  
Vol 2013 ◽  
pp. 1-7 ◽  
Author(s):  
Ping Wang ◽  
Dongyan Liu ◽  
Haibin Huang ◽  
Dongsheng Liu
Keyword(s):  
Reliability Analysis ◽  
Safety Factor ◽  
Reliability Index ◽  
Slip Surface ◽  
Limit State ◽  
Iterative Solution ◽  
Practical Method ◽  
State Function ◽  
Limit State Function ◽  
Searching Method

Considering the disadvantages of the slice method commonly employed in reliability analysis of slopes, a novel method (Spoke model) was proposed for reliability analysis and safety factor calculation of slopes in this work based on geometrical relationship among slices. The safety factor and the coefficients of limit state function of slopes could be achieved with the Gaussian integral method. The minimum safety factor and the minimum reliability index, as well as their corresponding coordinates on the slip surface, can be calculated with the improved JC method and the searching method. A novel and practical method for reliability analysis of slopes has been achieved. With this method the slice process could be avoided, which helps to eliminate some calculation errors caused by oversimplified assumption. Moreover, the explicit expression of safety factor in this method requires no repeated iterative solution, which is employed in traditional slice methods, as well as can be developed into a limit state function required by calculation of the reliability index. It is demonstrated that this method works efficiently and succinctly in evaluation of reliability index and safety factor for soil slopes.

scholarly journals High Dimension Model Representation-Based Response Surface for Reliability Analysis of Tunnel

2018 ◽  
Vol 2018 ◽  
pp. 1-10
Author(s):  
Hongbo Zhao
Keyword(s):  
Reliability Analysis ◽  
Response Surface ◽  
Reliability Index ◽  
Limit State ◽  
State Function ◽  
Limit State Function ◽  
Implicit Function ◽  
Surface Method ◽  
Reliability Method ◽  
Rock Tunnel

Uncertainty is an important prosperity to rock tunnel. Reliability analysis is widely used to deal with the uncertainty. But it is difficult to be adopted in rock tunnel using the traditional reliability method because the limit state function is an implicit function. High dimension model representation (HDMR) can approximate the high dimensional, nonlinear, and implicit function using the low dimensional function. In this study, the HDMR method was adapted to approximate the limit state function through combining with response surface method (RSM). A new reliability analysis approach of HDMR-based response surface method, combined with the first-order reliability method (FORM), is developed to calculate the reliability index of tunnel, and implementation of the method is explained briefly. A circular tunnel with analytical solution and horseshoe tunnel with numerical solution are used to demonstrate the proposed method. The obtained reliability index is in excellent agreement with Low and Tang’s (2007) method and traditional RSM. It shows that HDMR-based response surface can approximate well the limit state function, and the proposed method is an efficient and effective approach for reliability analysis in tunnel engineering. It is very useful for reliability analysis of practical large-scale rock engineering.

scholarly journals RPCM: a strategy to perform reliability analysis using polynomial chaos and resampling

2010 ◽  
pp. 795-830
Author(s):  
Alban Notin ◽  
Nicolas Gayton ◽  
Jean Luc Dulong ◽  
Maurice Lemaire ◽  
Pierre Villon ◽  
...  
Keyword(s):  
Reliability Analysis ◽  
Reliability Index ◽  
Polynomial Chaos ◽  
Limit State ◽  
State Function ◽  
Limit State Function ◽  
New Approach ◽  
Stochastic Finite Elements ◽  
Polynomial Chaos Expansions ◽  
Computational Purpose

Using stochastic finite elements, the response quantity can be written as a series expansion which allows an approximation of the limit state function. For computational purpose, the series must be truncated in order to retain only a finite number of terms. In the context of reliability analysis, we propose a new approach coupling polynomial chaos expansions and confidence intervals on the generalized reliability index as truncating criterion.

scholarly journals Gaussian Process-Based Response Surface Method for Slope Reliability Analysis

2019 ◽  
Vol 2019 ◽  
pp. 1-11 ◽  
Author(s):  
Bin Hu ◽  
Guo-shao Su ◽  
Jianqing Jiang ◽  
Yilong Xiao
Keyword(s):  
Gaussian Process ◽  
Reliability Analysis ◽  
Response Surface ◽  
Response Surface Method ◽  
Failure Probability ◽  
Limit State ◽  
State Function ◽  
Limit State Function ◽  
Surface Method ◽  
Gp Model

A new response surface method (RSM) for slope reliability analysis was proposed based on Gaussian process (GP) machine learning technology. The method involves the approximation of limit state function by the trained GP model and estimation of failure probability using the first-order reliability method (FORM). A small amount of training samples were firstly built by the limited equilibrium method for training the GP model. Then, the implicit limit state function of slope was approximated by the trained GP model. Thus, the implicit limit state function and its derivatives for slope stability analysis were approximated by the GP model with the explicit formulation. Furthermore, an iterative algorithm was presented to improve the precision of approximation of the limit state function at the region near the design point which contributes significantly to the failure probability. Results of four case studies including one nonslope and three slope problems indicate that the proposed method is more efficient to achieve reasonable accuracy for slope reliability analysis than the traditional RSM.

Iterative Algorithm for Structure Reliability Analysis Based on Support Vector Classification Method

2007 ◽  
Vol 353-358 ◽  
pp. 1009-1012
Author(s):  
Chao Ma ◽  
Zhen Zhou Lu
Keyword(s):  
Reliability Analysis ◽  
Iterative Algorithm ◽  
Limit State ◽  
Sampling Procedure ◽  
Support Vector ◽  
State Function ◽  
Limit State Function ◽  
Structure Reliability ◽  
Important Region ◽  
Actual Limit

For reliability analysis of structure with implicit limit state function, an iterative algorithm is presented on the basis of support vector classification machine. In the present method, the support vector classification machine is employed to construct surrogate of the implicit limit state function. By use of the proposed rational iteration and sampling procedure, the constructed support vector classification machine can converge to the actual limit state function at the important region, which contributes to the failure probability significantly. Then the precision of the reliability analysis is improved. The implementation of the presented method is given in detail, and the feasibility and the efficiency are demonstrated by the illustrations.

scholarly journals Hybrid Reliability Analysis for Spacecraft Docking Lock with Random and Interval Uncertainty

2017 ◽  
Vol 2017 ◽  
pp. 1-9 ◽  
Author(s):  
Jianguo Zhang ◽  
Jiwei Qiu ◽  
Pidong Wang
Keyword(s):  
Reliability Analysis ◽  
Structural Reliability ◽  
Limit State ◽  
Random Variables ◽  
Simple Problem ◽  
State Function ◽  
Limit State Function ◽  
Interval Variables ◽  
Reliability Method ◽  
Hybrid Reliability

This paper presents a novel procedure based on first-order reliability method (FORM) for structural reliability analysis with hybrid variables, that is, random and interval variables. This method can significantly improve the computational efficiency for the abovementioned hybrid reliability analysis (HRA), while generally providing sufficient precision. In the proposed procedure, the hybrid problem is reduced to standard reliability problem with the polar coordinates, where an n-dimensional limit-state function is defined only in terms of two random variables. Firstly, the linear Taylor series is used to approximate the limit-state function around the design point. Subsequently, with the approximation of the n-dimensional limit-state function, the new bidimensional limit state is established by the polar coordinate transformation. And the probability density functions (PDFs) of the two variables can be obtained by the PDFs of random variables and bounds of interval variables. Then, the interval of failure probability is efficiently calculated by the integral method. At last, one simple problem with explicit expressions and one engineering application of spacecraft docking lock are employed to demonstrate the effectiveness of the proposed methods.

A Random Field Approach to Reliability Analysis With Random and Interval Variables

2015 ◽  
Vol 1 (4) ◽  
Author(s):  
Zhen Hu ◽  
Xiaoping Du
Keyword(s):  
Random Field ◽  
Reliability Analysis ◽  
Extreme Values ◽  
Limit State ◽  
State Function ◽  
Limit State Function ◽  
Response Variable ◽  
Field Approach ◽  
Reliability Bounds ◽  
Interval Variables

Interval variables are commonly encountered in design, especially in the early design stages when data are limited. Thus, reliability analysis (RA) should deal with both interval and random variables and then predict the lower and upper bounds of reliability. The analysis is computationally intensive, because the global extreme values of a limit-state function with respect to interval variables must be obtained during the RA. In this work, a random field approach is proposed to reduce the computational cost with two major developments. The first development is the treatment of a response variable as a random field, which is spatially correlated at different locations of the interval variables. Equivalent reliability bounds are defined from a random field perspective. The definitions can avoid the direct use of the extreme values of the response. The second development is the employment of the first-order reliability method (FORM) to verify the feasibility of the random field modeling. This development results in a new random field method based on FORM. The new method converts a general response variable into a Gaussian field at its limit state and then builds surrogate models for the autocorrelation function and reliability index function with respect to interval variables. Then, Monte Carlo simulation is employed to estimate the reliability bounds without calling the original limit-state function. Good efficiency and accuracy are demonstrated through three examples.

Sequential Multidisciplinary Design Optimization and Reliability Analysis Using an Efficient Third-Moment Saddlepoint Approximation Method

2015 ◽  
Author(s):  
Debiao Meng ◽  
Hong-Zhong Huang ◽  
Huanwei Xu ◽  
Xiaoling Zhang ◽  
Yan-Feng Li
Keyword(s):  
Reliability Analysis ◽  
Limit State ◽  
Saddlepoint Approximation ◽  
Cumulative Distribution ◽  
Multidisciplinary Design ◽  
Sequential Optimization ◽  
State Function ◽  
Limit State Function ◽  
Highly Nonlinear ◽  
Third Moment

In Reliability based Multidisciplinary Design and Optimization (RBMDO), saddlepoint approximation has been utilized to improve reliability evaluation accuracy while sustaining high efficiency. However, it requires that not only involved random variables should be tractable; but also a saddlepoint can be obtained easily by solving the so-called saddlepoint equation. In practical engineering, a random variable may be intractable; or it is difficult to solve a highly nonlinear saddlepoint equation with complicated Cumulant Generating Function (CGF). To deal with these challenges, an efficient RBMDO method using Third-Moment Saddlepoint Approximation (TMSA) is proposed in this study. TMSA can construct a concise CGF using the first three statistical moments of a limit state function easily, and then express the probability density function and cumulative distribution function of the limit state function approximately using this concise CGF. To further improve the efficiency of RBMDO, a sequential optimization and reliability analysis strategy is also utilized and a formula of RBMDO using TMSA within the framework of SORA is proposed. Two examples are given to show the effectiveness of the proposed method.

scholarly journals A New SORM Method for Structural Reliability with Hybrid Uncertain Variables

2020 ◽  
Vol 11 (1) ◽  
pp. 346
Author(s):  
Pidong Wang ◽  
Lechang Yang ◽  
Ning Zhao ◽  
Lefei Li ◽  
Dan Wang
Keyword(s):  
Reliability Analysis ◽  
Structural Reliability ◽  
Limit State ◽  
Random Variables ◽  
State Function ◽  
Strong Nonlinearity ◽  
Limit State Function ◽  
Practical Applications ◽  
Uncertain Variables ◽  
Practical Engineering

(1) Background: in practical applications, probabilistic and non-probabilistic information often simultaneously exit. For a complex system with a nonlinear limit-state function, the analysis and evaluation of the reliability are imperative yet challenging tasks. (2) Methods: an improved second-order method is proposed for reliability analysis in the presence of both random and interval variables, where a novel polar transformation is employed. This method enables a unified reliability analysis taking both random variables and bounded intervals into account, simplifying the calculation by transforming a high-dimension limit-state function into a bivariate state function. The obtained nonlinear probability density functions of two variables in the function inherit the statistic characteristics of interval and random variables. The proposed method does not require any strong assumptions and so it can be used in various practical engineering applications. (3) Results: the proposed method is validated via two numerical examples. A comparative study towards a contemporary algorithm in state-of-the-art literature is carried out to demonstrate the benefits of our method. (4) Conclusions: the proposed method outperforms existing methods both in efficiency and accuracy, especially for cases with strong nonlinearity.

A Nested Extreme Response Surface Approach for RBDO With Time-Dependent Probabilistic Constraints

2012 ◽  
Author(s):  
Zequn Wang ◽  
Pingfeng Wang
Keyword(s):  
Reliability Analysis ◽  
Engineering Design ◽  
Response Surface ◽  
Limit State ◽  
Time Dependent ◽  
Probabilistic Constraints ◽  
State Function ◽  
Limit State Function ◽  
Extreme Response ◽  
Practical Engineering

A primary concern in practical engineering design is ensuring high system reliability throughout a product life-cycle subject to time-variant operating conditions and component deteriorations. Thus, the capability to deal with time-dependent probabilistic constraints in reliability-based design optimization is of vital importance in practical engineering design applications. This paper presents a nested extreme response surface (NERS) approach to efficiently carry out time-dependent reliability analysis and determine the optimal designs. The NERS employs kriging model to build a nested response surface of time corresponding to the extreme value of the limit state function. The efficient global optimization technique is integrated with the NERS to extract the extreme time responses of the limit state function for any given system design. An adaptive response prediction and model maturation mechanism is developed based on mean square error (MSE) to concurrently improve the accuracy and computational efficiency of the proposed approach. With the nested response surface of time, the time-dependent reliability analysis can be converted into the time-independent reliability analysis and existing advanced reliability analysis and design methods can be used. The NERS is integrated with RBDO for the design of engineered systems with time-dependent probabilistic constraints. Two case studies are used to demonstrate the efficacy of the proposed NERS approach.

Seismic Reliability Analysis of Complex Structure

2012 ◽  
Vol 446-449 ◽  
pp. 2321-2325
Author(s):  
Zhi Yong Zhang ◽  
Wen Bo Huang ◽  
Yue Fa Zhou ◽  
Tian Shu Song
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Reliability Analysis ◽  
Structural Reliability ◽  
Limit State ◽  
Complex Structure ◽  
State Function ◽  
Limit State Function ◽  
Seismic Reliability ◽  
Element Method

The seismic reliability analysis of complex structure is carried out based on the response surface method and finite element method. Firstly, the appropriate design points are selected based on the mean values and standard deviations of the basic random variables. Secondly, the finite element method is employed to obtain the values of the limit state function of the complex structure. Thirdly, with selected design points and the obtained values of the limit state function of the complex structure, a polynomial function is constructed to approximate the original implicit limit state function. Then, with the established explicit polynomial limit state function and available methods of structural reliability analysis, the seismic reliability of the complex structure is estimated. Numerical analyses show that the established method is simple to use for the evaluation of the reliability analysis of complex structure.

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