scholarly journals An efficient method for calculating system non-probabilistic reliability index

2021 ◽  
Vol 23 (3) ◽  
pp. 498-504
Author(s):  
Hui Liu ◽  
Ning-Cong Xiao
Keyword(s):  
Iterative Process ◽  
Reliability Index ◽  
Kriging Model ◽  
Efficient Global Optimization ◽  
Stopping Criteria ◽  
Performance Function ◽  
Learning Function ◽  
Training Samples ◽  
Reliability Methods ◽  
Estimate System

Collecting enough samples is difficult in real applications. Several interval-based non-probabilistic reliability methods have been reported. The key of these methods is to estimate system non-probabilistic reliability index. In this paper, a new method is proposed to calculate system non-probabilistic reliability index. Kriging model is used to replace time-consuming simulations, and the efficient global optimization is used to determine the new training samples. A refinement learning function is proposed to determine the best component (or performance function) during the iterative process. The proposed refinement learning function has considered two important factors: (1) the contributions of components to system nonprobabilistic reliability index, and (2) the accuracy of the Kriging model at current iteration. Two stopping criteria are given to terminate the algorithm. The system non-probabilistic index is finally calculated based on the Kriging model and Monte Carlo simulation. Two numerical examples are given to show the applicability of the proposed method.

scholarly journals A Kriging-Based Active Learning Algorithm for Mechanical Reliability Analysis with Time-Consuming and Nonlinear Response

2019 ◽  
Vol 2019 ◽  
pp. 1-14 ◽  
Author(s):  
Cao Tong ◽  
Jian Wang ◽  
Jinguo Liu
Keyword(s):  
Active Learning ◽  
Reliability Analysis ◽  
Nonlinear Response ◽  
Learning Algorithm ◽  
Limit State ◽  
Kriging Model ◽  
Real Space ◽  
Mechanical Reliability ◽  
Learning Function ◽  
Reliability Methods

When the reliability analysis of the mechanical products with high nonlinearity and time-consuming response is carried out, there will be the problems of low precision and huge computation using the traditional reliability methods. To solve these issues, the active learning reliability methods have been paid much attention in recent years. It is the key to choose an efficient learning function (such as U, EFF, and ERF). The aim of this study is to further decrease the computation and improve the accuracy of the reliability analysis. Inspired from these learning functions, a new point-selected learning function (called HPF) is proposed to update DOE, and a new point is sequentially added step by step to the DOE. The proposed learning function can consider the features like the sampling density, the probability to be wrongly predicted, and the local and global uncertainty close to the limit state. Based on the stochastic property of the Kriging model, the analytic expression of HPF is deduced by averaging a hybrid indicator throughout the real space. The efficiency of the proposed method is validated by two explicit examples. Finally, the proposed method is applied to the mechanical reliability analysis (involving time-consuming and nonlinear response). By comparing with traditional mechanical reliability methods, the results show that the proposed method can solve the problems of large computation and low precision.

Kriging-Based Reliability Analysis and Variance-Based Sensitivity Analysis for an Idler Shaft

2015 ◽  
Author(s):  
Weimin Cui ◽  
Wei Guo ◽  
Zhongchao Sun ◽  
Tianxiang Yu
Keyword(s):  
Sensitivity Analysis ◽  
Influence Factors ◽  
Random Variables ◽  
Kriging Model ◽  
Element Analysis ◽  
Performance Function ◽  
The Finite Element Analysis ◽  
Inner Diameter ◽  
Sensitivity Method ◽  
The Relationship

In order to analyze the reason of failure and improve the reliability of the idler shaft, this paper studies the reliability and sensitivity for the idler shaft based on Kriging model and Variance Methods respectively. The finite element analysis (FEA) of idler shaft is studied in ABAQUS firstly. Then, combining the performance function and various random variables, the Kriging model of idler shaft is established and verified. Based on Kriging model which has been established, the relationship between random variables and the response value is studied, and the function reliability is calculated which explains why the failure of the idler shaft occurred frequently in service. Finally, the variance-based sensitivity method is used for sensitivity analysis of influence factors, the result shows that the reliability of idler shaft is sensitive to the inner diameter of body A and inner diameter of body B, which could contribute for the analysis and further improvement of idler shaft.

Handling of Constraints in Efficient Global Optimization

2020 ◽  
pp. 2050033
Author(s):  
Hu Wang ◽  
Wei Hu ◽  
Enying Li
Keyword(s):  
Global Optimization ◽  
Variable Stiffness ◽  
Kriging Model ◽  
Superior Performance ◽  
Efficient Global Optimization ◽  
Feasible Region ◽  
Support Vector ◽  
Multiple Constraint ◽  
Fiber Path ◽  
Feasible Points

Although the Efficient Global Optimization (EGO) algorithm has been widely used in multi-disciplinary optimization, it is still difficult to handle multiple constraint problems. In this study, to increase the accuracy of approximation, the Least Squares Support Vector Regression (LSSVR) is suggested to replace the kriging model for approximating both objective and constrained functions while the variances of these surrogate models are still obtained by kriging. To enhance the ability to search the feasible region, two criteria are suggested. First, a Maximize Probability of Feasibility (MPF) strategy to handle the infeasible initial sample points is suggested to generate feasible points. Second, a Multi-Constraint Parallel (MCP) criterion is suggested for multiple constraints handling, parallel computation and validation, respectively. To illustrate the efficiency of the suggested EGO-based method, several deterministic benchmarks are tested and the suggested methods demonstrate a superior performance compared with two other constrained algorithms. Finally, the suggested algorithm is successfully utilized to optimize the fiber path of variable-stiffness beam and lightweight B-pillar to demonstrate the performance for engineering applications.

scholarly journals Reliability Estimation for Highway Bridges

2020 ◽  
Author(s):  
Nafiseh Kiani
Keyword(s):  
Reliability Index ◽  
Structural Reliability ◽  
Limit State ◽  
Highway Bridges ◽  
Reliability Estimation ◽  
State Function ◽  
Limit States ◽  
Resistance Factors ◽  
Load And Resistance Factors ◽  
Reliability Methods

Structural reliability analysis is necessary to predict the uncertainties which may endanger the safety of structures during their lifetime. Structural uncertainties are associated with design, construction and operation stages. In design of structures, different limit states or failure functions are suggested to be considered by design specifications. Load and resistance factors are two essential parameters which have significant impact on evaluating the uncertainties. These load and resistance factors are commonly determined using structural reliability methods. The purpose of this study is to determine the reliability index for a typical highway bridge by considering the maximum moment generated by vehicle live loads on the bridge as a random variable. The limit state function was formulated and reliability index was determined using the First Order Reliability Methods (FORM) method.

On Using Kriging Models for Complex Design

2011 ◽  
Author(s):  
Jay D. Martin
Keyword(s):  
Complex Systems ◽  
Robust Design ◽  
Kriging Model ◽  
Response Surfaces ◽  
Optimal System ◽  
System Level ◽  
Design Teams ◽  
Complex Design ◽  
Level Performance ◽  
Estimate System

The design of most modern systems requires the tight integration of multiple disciplines. In practice, these multiple disciplines are often optimized independently, given only fixed values or targets for their interactions with other disciplines. The result is a system that may not represent the optimal system-level design. It may also not be a robust design in the sense that small changes in each subsystem’s performance may have a large impact on the system-level performance. The use of kriging models to represent the response surfaces of subsystems that are then combined to estimate system-level performance can be used as a method to provide collaboration between design teams. The difficulty with this method is the creation of the models given potentially large number of dimensions or observations. This paper presents a method to reduce the dimensionality of the input space for kriging models used for designing of complex systems. The input dimensionality of the kriging model is reduced to only includes the most important factors needed for the prediction of the observed output. A result of using these reduced dimensionality models is the need to no longer force interpolation of all of the observations used to create the models.

RCA-PCK: A new structural reliability analysis method based on PC-Kriging and radial centralized adaptive sampling strategy

2020 ◽  
pp. 095440622095771
Author(s):  
Zhenliang Yu ◽  
Zhili Sun ◽  
Runan Cao ◽  
Jian Wang ◽  
Yutao Yan
Keyword(s):  
Reliability Analysis ◽  
Failure Probability ◽  
Adaptive Sampling ◽  
Structural Reliability ◽  
Sampling Strategy ◽  
Kriging Model ◽  
Strong Nonlinearity ◽  
Analysis Method ◽  
Structural Reliability Analysis ◽  
Training Samples

To improve the efficiency and accuracy of reliability assessment for structures with small failure probability and time-consuming simulation, a new structural reliability analysis method (RCA-PCK) is proposed, which combines PC-Kriging model and radial centralized adaptive sampling strategy. Firstly, the PC-Kriging model is constructed by improving the basis function of Kriging model with sparse polynomials. Then, the sampling region which contributes a great impact on the failure probability is constructed by combining the radial concentration and important sampling technology. Subsequently, the k-means++ clustering technology and learning function LIF are adopted to select new training samples from each subdomains in each iteration. To avoid the sampling distance in one subdomain or the distance between the new training samples in two subdomains being too small, we construct a screening mechanism to ensure that the selected new training samples are evenly distributed in the limit state. In addition, a new convergence criterion is derived based on the relative error estimation of failure probability. Four benchmark examples are given to illustrate the convergence process, accuracy and stability of the proposed method. Finally, the transmission error reliability analysis of thermal-elastic coupled gears is carried out to prove the applicability of the proposed method RCA-PCK to the structures with strong nonlinearity and time-consuming simulation.

Reliability of Gravity Foundation in Coral Sands Subject to Dynamic Wind Load

2013 ◽  
Vol 302 ◽  
pp. 355-358 ◽  
Author(s):  
Zhong Qing Cheng ◽  
Ping Yang ◽  
Hai Bo Jiang
Keyword(s):  
Natural Frequency ◽  
Wind Velocity ◽  
Reliability Index ◽  
Great Influence ◽  
Mechanical Analysis ◽  
Wind Pressure ◽  
Performance Function ◽  
Vibration Equation ◽  
High Rise ◽  
Fluctuating Wind

Taking circular gravity foundation of high-rise structure in coral sands as research object, on the basis of mechanical analysis of foundation during inclination, the inclination vibration equation was established. The amplitude of foundation inclination was calculated. The inclination performance function of foundation was established. JC method is used to calculate the reliability index of foundation. Calculation shows that the amplitude of wind velocity has great influence on the reliability index of foundation when the frequency of sinusoidal wind pressure equals the natural frequency of foundation in inclination vibration. In the design of foundation, the natural frequency of foundation in inclination vibration should be made as far away from the frequency of fluctuating wind pressure as possible.

Non-Probabilistic Reliability and Slope Stability Analysis

2014 ◽  
Vol 578-579 ◽  
pp. 1538-1541
Author(s):  
Huan Sheng Mu
Keyword(s):  
Stability Analysis ◽  
Slope Stability ◽  
Reliability Index ◽  
Mean Value ◽  
Slope Stability Analysis ◽  
Performance Function ◽  
Interval Variables ◽  
Reliability Method ◽  
The Mean ◽  
The Difference

In the present paper, a non-probabilistic reliability method is proposed for slope stability analysis. Soil properties involved in non-probabilistic reliability analysis are viewed as random variables and represented by interval variables. The performance function for slope stability analysis is expressed as the difference between anti-sliding moment and driving moment. The non-probabilistic reliability index is defined as the ratio of the mean value of performance function to deviate. Three examples have illustrated the simplicity and applicability of the method. This method provides a new means for slope stability analysis.

Hybrid reliability-based multidisciplinary design optimization with random and interval variables

2017 ◽  
Vol 232 (1) ◽  
pp. 52-64 ◽  
Author(s):  
Fan Yang ◽  
Zhufeng Yue ◽  
Lei Li ◽  
Dong Guan
Keyword(s):  
Design Optimization ◽  
Multidisciplinary Design Optimization ◽  
Region Of Interest ◽  
Kriging Model ◽  
Collaborative Optimization ◽  
Multidisciplinary Design ◽  
Learning Function ◽  
Design Variables ◽  
Interval Variables ◽  
Hybrid Reliability

This article presents a procedure for reliability-based multidisciplinary design optimization with both random and interval variables. The sign of performance functions is predicted by the Kriging model which is constructed by the so-called learning function in the region of interest. The Monte Carlo simulation with the Kriging model is performed to evaluate the failure probability. The sample methods for the random variables, interval variables, and design variables are discussed in detail. The multidisciplinary feasible and collaborative optimization architectures are provided with the proposed method. The method is demonstrated with three examples.

Probabilistic design of slopes

1987 ◽  
Vol 24 (4) ◽  
pp. 520-535 ◽  
Author(s):  
K. S. Li ◽  
P. Lumb
Keyword(s):  
Reliability Index ◽  
Slip Surface ◽  
Probabilistic Approach ◽  
Probabilistic Design ◽  
Performance Function ◽  
Stability Model ◽  
First Order Second Moment ◽  
The Stability ◽  
Derivatives Of ◽  
Slope Design

This paper discusses some improvements on the first-order second-moment (FOSM) probabilistic approach to slope design. The stability model by Morgenstern and Price is used for the formulation of the performance function, thus enabling the FOSM method to be applied to the probabilistic assessment of a general slip surface. A new solution scheme is also used herein for Morgenstern and Price's method. It does not require iterations for the calculation of the interslice forces and the derivatives of the performance function can be evaluated analytically. The reliability index βHL defined by Hasofer and Lind is used as an index of safety measure. It has the advantage of being "invariant," that is, its value does not depend on the format of the performance function, a property considered lacking in the conventional reliability index. Reference is also made to the probabilistic modelling of soil profiles. The importance of the correlation structure of soil properties is highlighted and its effect on the reliability index βHL is discussed. Key words: slope stability, safety factors, reliability index, probability of failure, general slip surface, rigorous stability model.

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