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.

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

2010 ◽  
Author(s):  
Yoojeong Noh ◽  
Kyung K. Choi ◽  
Ikjin Lee ◽  
David Gorsich
Keyword(s):  
Standard Deviation ◽  
Statistical Model ◽  
Confidence Intervals ◽  
Confidence Level ◽  
Bootstrap Method ◽  
Reliability Based Design Optimization ◽  
Gaussian Distributions ◽  
Reliability Based Design ◽  
Input Variables ◽  
Non Gaussian

For reliability-based design optimization (RBDO), generating an input statistical model with confidence level has been recently proposed to offset the inaccurate estimation of the input statistical model with Gaussian distributions. For this, the confidence intervals of mean and standard deviation are calculated using the Gaussian distributions of input random variables. However, if the input random variables are non-Gaussian, the use of the Gaussian distributions of input variables will provide inaccurate confidence intervals, and thus, yield undesirable confidence level of the reliability-based optimum design meeting the target reliability βt. In this paper, the RBDO method using the bootstrap method, which does not use the Gaussian distributions of input variables to calculate the confidence intervals of mean and standard deviation, are proposed to obtain the desirable confidence level of output performance for non-Gaussian distributions.

Reliability-Based Design Optimization With Confidence Level Under Input Model Uncertainty

2009 ◽  
Author(s):  
Yoojeong Noh ◽  
K. K. Choi ◽  
Ikjin Lee ◽  
David Gorsich ◽  
David Lamb
Keyword(s):  
Standard Deviation ◽  
Confidence Interval ◽  
Design Optimization ◽  
Optimum Design ◽  
Upper Bound ◽  
Confidence Level ◽  
Limited Data ◽  
Reliability Based Design Optimization ◽  
Reliability Based Design ◽  
Input Model

For obtaining correct reliability-based optimum design, an input model needs to be accurately estimated in identification of marginal and joint distribution types and quantification of their parameters. However, in most industrial applications, only limited data on input variables is available due to expensive experimental testing costs. The input model generated from the insufficient data might be inaccurate, which will lead to incorrect optimum design. In this paper, reliability-based design optimization (RBDO) with the confidence level is proposed to offset the inaccurate estimation of the input model due to limited data by using an upper bound of confidence interval of the standard deviation. Using the upper bound of the confidence interval of the standard deviation, the confidence level of the input model can be assessed to obtain the confidence level of the output performance, i.e. a desired probability of failure, through the simulation-based design. For RBDO, the estimated input model with the associated confidence level is integrated with the most probable point (MPP)-based dimension reduction method (DRM), which improves accuracy over the first order reliability method (FORM). A mathematical example and a fatigue problem are used to illustrate how the input model with confidence level yields a reliable optimum design by comparing it with the input model obtained using the estimated parameters.

Confidence-Based Method for Reliability-Based Design Optimization

2014 ◽  
Author(s):  
Hyunkyoo Cho ◽  
K. K. Choi ◽  
David Lamb
Keyword(s):  
Design Optimization ◽  
Confidence Level ◽  
Probabilistic Model ◽  
Input Data ◽  
Mathematical Problem ◽  
Design Sensitivity ◽  
Conditional Probabilities ◽  
Probabilistic Constraint ◽  
Reliability Based Design Optimization ◽  
Reliability Based Design

An accurate input probabilistic model is necessary to obtain a trustworthy result in the reliability analysis and the reliability-based design optimization (RBDO). However, the accurate input probabilistic model is not always available. Very often only insufficient input data are available in practical engineering problems. When only the limited input data are provided, uncertainty is induced in the input probabilistic model and this uncertainty propagates to the reliability output which is defined as the probability of failure. Then, the confidence level of the reliability output will decrease. To resolve this problem, the reliability output is considered to have a probability distribution in this paper. The probability of the reliability output is obtained as a combination of consecutive conditional probabilities of input distribution type and parameters using Bayesian approach. The conditional probabilities that are obtained under certain assumptions and Monte Carlo simulation (MCS) method is used to calculate the probability of the reliability output. Using the probability of the reliability output as constraint, a confidence-based RBDO (C-RBDO) problem is formulated. In the new probabilistic constraint of the C-RBDO formulation, two threshold values of the target reliability output and the target confidence level are used. For effective C-RBDO process, the design sensitivity of the new probabilistic constraint is derived. The C-RBDO is performed for a mathematical problem with different numbers of input data and the result shows that C-RBDO optimum designs incorporate appropriate conservativeness according to the given input data.

Reliability-Based Design Optimization on Qualitative Objective With Limited Information

2018 ◽  
Vol 140 (12) ◽  
Author(s):  
Khaldon T. Meselhy ◽  
G. Gary Wang
Keyword(s):  
Objective Function ◽  
Design Optimization ◽  
Probability Distributions ◽  
Random Variables ◽  
Limited Information ◽  
Reliability Based Design Optimization ◽  
Mathematical Formula ◽  
Reliability Based Design ◽  
Design Structure ◽  
Design Variables

Reliability-based design optimization (RBDO) algorithms typically assume a designer's prior knowledge of the objective function along with its explicit mathematical formula and the probability distributions of random design variables. These assumptions may not be valid in many industrial cases where there is limited information on variable variability and the objective function is subjective without mathematical formula. A new methodology is developed in this research to model and solve problems with qualitative objective functions and limited information about random variables. Causal graphs and design structure matrix are used to capture designer's qualitative knowledge of the effects of design variables on the objective. Maximum entropy theory and Monte Carlo simulation are used to model random variables' variability and derive reliability constraint functions. A new optimization problem based on a meta-objective function and transformed deterministic constraints is formulated, which leads close to the optimum of the original mathematical RBDO problem. The developed algorithm is tested and validated with the Golinski speed reducer design case. The results show that the algorithm finds a near-optimal reliable design with less initial information and less computation effort as compared to other RBDO algorithms that assume full knowledge of the problem.

scholarly journals Reliability Based Design Optimization of Reinforced Concrete Frames Using Genetic Algorithm

2021 ◽  
Author(s):  
Mohammadreza Seify Asghshahr
Keyword(s):  
Genetic Algorithm ◽  
Reinforced Concrete ◽  
Design Optimization ◽  
Reliability Index ◽  
Random Variables ◽  
Probabilistic Constraints ◽  
Rc Frame ◽  
Reliability Based Design Optimization ◽  
Form Analysis ◽  
Reliability Based Design

This paper introduces a new framework for reliability based design optimization (RBDO) of the reinforced concrete (RC) frames. This framework is constructed based on the genetic algorithm (GA) and finite element reliability analysis (FERA) to optimize the frame weight by selecting appropriate sections for structural elements under deterministic and probabilistic constraints. Modulus of elasticity of the concrete and steel bar, dead load, live load, and earthquake equivalent load are considered as random variables. Deterministic constraints include the code design requirements that must be satisfied for all the frame elements according to the nominal values of the aforementioned random variables. On the other hand, this framework provides the minimum required reliability index as the probabilistic constraint. The first-order reliability method (FORM) using the Newton-type recursive relationship will be used to compute the reliability index. The maximum inter-story drift is considered as an engineering demand parameter to define the limit-state function in FORM analysis. To implement the proposed framework, a mid-rise five-story RC frame is selected as an example. Based on the analysis results, increasing the minimum reliability index from 6 to 7 causes an 11 % increase in the weight of the selected RC frame as an objective function. So, we can obtain a trade-off between the optimized frame weight and the required reliability index utilizing the developed framework. Furthermore, the high values of the reliability index for the frame demonstrate the conservative nature of code requirements for interstory drift limitations based on the linear static analysis method.

Time-Dependent Concurrent Reliability-Based Design Optimization Integrating the Time-Variant B-Distance Index

2019 ◽  
Vol 141 (9) ◽  
Author(s):  
Zhonglai Wang ◽  
Zhihua Wang ◽  
Shui Yu ◽  
Xiaowen Cheng
Keyword(s):  
Experimental Data ◽  
Design Optimization ◽  
Confidence Level ◽  
Moment Method ◽  
Extreme Values ◽  
Time Dependent ◽  
Reliability Based Design Optimization ◽  
Reliability Based Design ◽  
Speed Up ◽  
High Computational Efficiency

This paper presents a time-dependent concurrent reliability-based design optimization (TDC-RBDO) method integrating the time-variant B-distance index to improve the confidence level of design results with a small amount of experimental data. The time-variant B-distance index is first constructed using the extreme values of responses. The Hist Loop CDF (HLCDF) algorithm is then presented to calculate the time-variant B-distance index with high computational efficiency. The TDC-RBDO framework is provided by integrating the time-variant B-distance index and time-dependent reliability. The extreme value moment method (EVMM) is implemented to speed up the procedure of the TDC-RBDO. The case of a harmonic reducer is employed to elaborate on the proposed method.

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