Multiple-mixed Statistical Model of Random Variables and Optimal Estimation of Distribution Parameters

2003 ◽  
Author(s):  
Xiang Gao ◽  
Changgao Xia ◽  
Maotao Zhu
Keyword(s):  
Statistical Model ◽  
Random Variables ◽  
Optimal Estimation ◽  
Distribution Parameters ◽  
Estimation Of Distribution

Confidence-Based Design Optimization Under Data Uncertainty Using Most Probable Point-Based Approach

2019 ◽  
Author(s):  
Yongsu Jung ◽  
Hyunkyoo Cho ◽  
Ikjin Lee
Keyword(s):  
Statistical Model ◽  
Design Optimization ◽  
Performance Measure ◽  
Cumulative Distribution ◽  
Data Uncertainty ◽  
Normal Space ◽  
Most Probable Point ◽  
Input Distribution ◽  
Design Variables ◽  
Distribution Parameters

Abstract An accurate input statistical model has been assumed in most of reliability-based design optimization (RBDO) to concentrate on variability of random variables. However, only limited number of data are available to quantify the input statistical model in practical engineering applications. In other words, irreducible variability and reducible uncertainty due to lack of knowledge exist simultaneously in random design variables. Therefore, the uncertainty in reliability induced by insufficient data has to be accounted for RBDO to guarantee confidence of reliability. The uncertainty of input distributions is successfully propagated to a cumulative distribution function (CDF) of reliability under normality assumptions, but it requires a number of function evaluations in double-loop Monte Carlo simulation (MCS). To tackle this challenge, reliability measure approach (RMA) in confidence-based design optimization (CBDO) is proposed to handle the randomness of reliability following the idea of performance measure approach (PMA) in RBDO. Input distribution parameters are transformed to the standard normal space for most probable point (MPP) search with respect to reliability. Therefore, the reliability is approximated at MPP with respect to input distribution parameters. The proposed CBDO can treat confidence constraints employing the reliability value at the target confidence level that is approximated by MPP in P-space. In conclusion, the proposed method can significantly reduce the number of function evaluations by eliminating outer-loop MCS while maintaining acceptable accuracy.

scholarly journals INSPECTION PROGRAM DEVELOPMENT FOR FATIGUE CRACK GROWTH MODEL WITH TWO RANDOM PARAMETERS/APŽIŪRŲ PROGRAMOS KŪRIMAS NUOVARGIO PLYŠIO AUGIMO MODELIUI SU DVIEM ATSITIKTINIAIS PARAMETRAIS

Aviation ◽  
2008 ◽  
Vol 12 (2) ◽  
pp. 33-40 ◽  
Author(s):  
Yuri Paramonov ◽  
Andrey Kuznetsov
Keyword(s):  
Critical Size ◽  
Fatigue Cracks ◽  
Random Variable ◽  
Fatigue Curve ◽  
Exponential Approximation ◽  
Random Parameters ◽  
Distribution Parameters ◽  
Estimation Of Distribution ◽  
Set Function ◽  
Crack Growth Model

To keep the fatigue failure probability of an aircraft fleet at or below a certain level, an inspection program is appointed to discover fatigue cracks before they decrease the residual strength of some structurally significant item of the airframe lower than the level allowed by regulations. In this article, the p‐set function for random vector, which, in fact, is a generalization of p‐bound for random variable, and minimax approach to the problem of inspection number choice are used. It is supposed that the exponential approximation of a fatigue curve with two random parameters can be used in the interval when the fatigue curve becomes detectable and then grows to critical size. For estimation of distribution parameters, results of an approval test are used. A numerical example is given. Santrauka Šiame tyrime nagrinėtas apžiūrų, skirtų surasti nuovargio įtrūkimus jėginiuose elementuose iki liekamojo stiprumo sumažėjimo žemiau leistinos ribos, programos planavimas. Čia apžiūrų skaičiui nustatyti buvo naudojamas mini-maksimalus statistinis sprendinys ir atsitiktinio vektoriaus p-aibės sąvoka, kuri yra atsitiktinio vektoriaus p-ribos apibendrinta sąvoka. Taikyta prielaida, kad nuovargio įtrūkimo didėjimo kreivę galima aproksimuoti eksponentiškai laiko intervale nuo to momento, kai plyšys tampa matomas ir iki kritinio dydžio. Parametrų pasiskirstymo įvertinimui naudoti bandymo rezultatai. Daroma prielaida, kad jei bandymo rezultatai yra nepatenkinami, tuomet turi būti ruošiamas naujas, labai pagerintas bandomojo gaminio projektas. Pateikti ir skaitiniai pavyzdžiai.

Reliability-Based Design Optimization With Confidence Level for Non-Gaussian Distributions Using Bootstrap Method

2011 ◽  
Vol 133 (9) ◽  
Author(s):  
Yoojeong Noh ◽  
Kyung K. Choi ◽  
Ikjin Lee ◽  
David Gorsich ◽  
David Lamb
Keyword(s):  
Statistical Model ◽  
Design Optimization ◽  
Confidence Intervals ◽  
Confidence Level ◽  
Bootstrap Method ◽  
Random Variables ◽  
Reliability Based Design Optimization ◽  
Gaussian Distributions ◽  
Reliability Based Design ◽  
Non Gaussian

For reliability-based design optimization (RBDO), generating an input statistical model with confidence level has been recently proposed to offset inaccurate estimation of the input statistical model with Gaussian distributions. For this, the confidence intervals for the mean and standard deviation are calculated using Gaussian distributions of the input random variables. However, if the input random variables are non-Gaussian, use of Gaussian distributions of the input variables will provide inaccurate confidence intervals, and thus yield an undesirable confidence level of the reliability-based optimum design meeting the target reliability βt. In this paper, an RBDO method using a bootstrap method, which accurately calculates the confidence intervals for the input parameters for non-Gaussian distributions, is proposed to obtain a desirable confidence level of the output performance for non-Gaussian distributions. The proposed method is examined by testing a numerical example and M1A1 Abrams tank roadarm problem.

scholarly journals Learning and Searching Pseudo-Boolean Surrogate Functions from Small Samples

2020 ◽  
Vol 28 (2) ◽  
pp. 317-338 ◽  
Author(s):  
Kevin Swingler
Keyword(s):  
Statistical Model ◽  
Fitness Function ◽  
Small Samples ◽  
Benchmark Problems ◽  
Estimation Of Distribution Algorithms ◽  
Fitness Functions ◽  
Estimation Of Distribution ◽  
Surrogate Functions ◽  
Distribution Algorithms ◽  
Linkage Learning

When searching for input configurations that optimise the output of a system, it can be useful to build a statistical model of the system being optimised. This is done in approaches such as surrogate model-based optimisation, estimation of distribution algorithms, and linkage learning algorithms. This article presents a method for modelling pseudo-Boolean fitness functions using Walsh bases and an algorithm designed to discover the non-zero coefficients while attempting to minimise the number of fitness function evaluations required. The resulting models reveal linkage structure that can be used to guide a search of the model efficiently. It presents experimental results solving benchmark problems in fewer fitness function evaluations than those reported in the literature for other search methods such as EDAs and linkage learners.

Estimation of distribution parameters of mixed failure mode data

1997 ◽  
Vol 3 (2) ◽  
pp. 120-135 ◽  
Author(s):  
Rudi H.P.M. Arts ◽  
Anuj Saxena ◽  
Gerald M. Knapp
Keyword(s):  
Failure Mode ◽  
Distribution Parameters ◽  
Estimation Of Distribution
Sign in / Sign up

Export Citation Format

Share Document