Reliability Analysis for Differential Expansion of Steam Turbine by Saddlepoint Approximation

2011 ◽  
Vol 105-107 ◽  
pp. 1077-1080
Author(s):  
Le Xin Li ◽  
Chang Qing Su ◽  
Ya Juan Jin
Keyword(s):  
Reliability Analysis ◽  
Steam Turbine ◽  
Approximation Method ◽  
Cumulative Distribution Function ◽  
Saddlepoint Approximation ◽  
State Equation ◽  
Cumulative Distribution ◽  
Ultimate State ◽  
The Monte Carlo Method ◽  
Differential Expansion

The reliability analysis for differential expansion of steam turbine is discussed extensively. The ultimate state equation of differential expansion of steam turbine is proposed according to stress-strength interference theory. Based on the premise that the probability distribution of random parameters has been known, the differential expansion of steam turbine is analyzed by saddlepoint approximation method. The probability density function and cumulative distribution function of the ultimate state equation are accurately and quickly obtained by the way of saddlepoint approximation and, as a result, the saddlepoint approximation method is proved accurate with high computing speed in comparison with the Monte-Carlo method. Therefore, the application of the saddlepoint approximation method is accurate and efficient.

Reliability Sensitivity Analysis for Differential Expansion of Steam Turbine by Saddlepoint Approximation

2012 ◽  
Vol 479-481 ◽  
pp. 1018-1022
Author(s):  
Le Xin Li ◽  
Chang Qing Su ◽  
Ya Juan Jin
Keyword(s):  
Sensitivity Analysis ◽  
Steam Turbine ◽  
Approximation Method ◽  
Saddlepoint Approximation ◽  
Analysis Method ◽  
Random Parameters ◽  
Reliability Sensitivity ◽  
Reliability Sensitivity Analysis ◽  
Sensitivity Analysis Method ◽  
Differential Expansion

Based on Saddlepoint Approximation method and sensitivity analysis method, reliability sensitivity analysis for differential expansion of steam turbine with random parameters are studied. On the premise of the probability distribution of random parameters, using Saddlepoint Approximation method, probability density function of limit state function of differential expansion of steam turbine is obtained. The result of Saddlepoint Approximation method is very close to the one of Monte-Carlo, and the computing speed is fast. Then, the sensitivity analysis method and probability density function were employed to discuss the variation regularities of reliability sensitivity and the effect of design parameters on reliability of differential expansion of steam turbine is analyzed.

Saddlepoint approximations for bivariate distributions

1990 ◽  
Vol 27 (03) ◽  
pp. 586-597 ◽  
Author(s):  
Suojin Wang
Keyword(s):  
Monte Carlo ◽  
Distribution Function ◽  
Normal Distribution ◽  
Cumulative Distribution Function ◽  
Saddlepoint Approximation ◽  
Monte Carlo Study ◽  
Cumulative Distribution ◽  
Normal Distribution Function ◽  
Sample Mean ◽  
Saddlepoint Approximations

A saddlepoint approximation is derived for the cumulative distribution function of the sample mean of n independent bivariate random vectors. The derivations use Lugannani and Rice's saddlepoint formula and the standard bivariated normal distribution function. The separate versions of the approximation for the discrete cases are also given. A Monte Carlo study shows that the new approximation is very accurate.

Reliability Analysis of Alumina-Based Ceramic Cutting Tool's Wear Life by Saddle Point Approximation

2013 ◽  
Vol 395-396 ◽  
pp. 979-984
Author(s):  
Xin Gang Wang ◽  
Ya Juan Jin ◽  
Yi Min Zhang
Keyword(s):  
Saddle Point ◽  
Normal Distribution ◽  
Approximation Method ◽  
Cutting Tools ◽  
State Equation ◽  
Ultimate State ◽  
Saddle Point Approximation ◽  
Point Approximation ◽  
Wear Life ◽  
Tools Wear

Under continuous cutting conditions, the reliability of alumina-based ceramic cutting tools wear life with abrasion wear was discussed extensively. An ultimate state equation of alumina-based ceramic cutting tools wear life was proposed according to stress-strength interference theory. Based on the premise that the probability distribution of random parameters has been known, the fracture toughnessKICand the hardnessHwhich obey Weibull distribution were transformed into normal distribution by means of the equivalent normal distribution method, and then the reliability of alumina-based ceramic cutting tools wear life was analyzed by saddle point approximation method. The probability density function and cumulative distribution function of the ultimate state equation were accurately and quickly obtained by way of saddle point approximation, as a result, the saddle point approximation method was proved accurate with high computing speed in comparison with the Monte-Carlo method. Therefore, the application of the saddle point approximation method developed the reliability analysis theory of alumina-based ceramic cutting tools wear life.

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 Improved Method for Approximating the Hazard Rate for Convolution Poisson Random Variables

2021 ◽  
Author(s):  
Andrei Volodin ◽  
ALYA AL MUTAIRI
Keyword(s):  
Hazard Rate ◽  
Cumulative Distribution Function ◽  
Random Variables ◽  
Saddlepoint Approximation ◽  
Mass Function ◽  
Rate Function ◽  
Cumulative Distribution ◽  
Probability Mass Function ◽  
Complicated Model ◽  
Probability Mass

In this study, we investigate the performance of the saddlepoint approximation of the probability mass function and the cumulative distribution function for the weighted sum of independent Poisson random variables. The goal is to approximate the hazard rate function for this complicated model. The better performance of this method is shown by numerical simulations and comparison with a performance of other approximation methods.

Saddlepoint approximations for bivariate distributions

1990 ◽  
Vol 27 (3) ◽  
pp. 586-597 ◽  
Author(s):  
Suojin Wang
Keyword(s):  
Monte Carlo ◽  
Distribution Function ◽  
Normal Distribution ◽  
Cumulative Distribution Function ◽  
Saddlepoint Approximation ◽  
Monte Carlo Study ◽  
Cumulative Distribution ◽  
Normal Distribution Function ◽  
Sample Mean ◽  
Saddlepoint Approximations

A saddlepoint approximation is derived for the cumulative distribution function of the sample mean of n independent bivariate random vectors. The derivations use Lugannani and Rice's saddlepoint formula and the standard bivariated normal distribution function. The separate versions of the approximation for the discrete cases are also given. A Monte Carlo study shows that the new approximation is very accurate.

scholarly journals Structural reliability analysis of a planar truss in case of limited statistical data

2021 ◽  
Vol 247 ◽  
pp. 01073
Author(s):  
Sergey A. Solovyev ◽  
Anastasia A. Solovyeva
Keyword(s):  
Reliability Analysis ◽  
Cumulative Distribution Function ◽  
Structural Reliability ◽  
Statistical Data ◽  
Reliability Assessment ◽  
Cumulative Distribution ◽  
Structural Elements ◽  
Structural Reliability Analysis ◽  
Design Loads

Trusses are common structural elements in many industrial and civil buildings. The article describes the approach to planar trusses reliability analysis in case of limited statistical data. The proposed approach can be used when it is complicated to determine a cumulative distribution function for design loads and physical/mechanical properties of the material of structural elements. The proposed method for structural reliability analysis requires only estimates of mathematical expectations and standard deviations. The article also presents the equation for planar truss reliability assessment as a system of structural elements. The result of a planar truss reliability analysis is obtained at an interval of non-failure probabilities. If the resulting reliability interval is too wide for decision-making, it is necessary to improve the quality of statistical data for a more accurate assessment of reliability (non-failure probability).

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