Reliability index function approximation based on adaptive double-loop Kriging for reliability-based design optimization

2021 ◽  
pp. 108020
Author(s):  
Xiaobo Zhang ◽  
Zhenzhou Lu ◽  
Kai Cheng
Keyword(s):  
Design Optimization ◽  
Function Approximation ◽  
Reliability Index ◽  
Double Loop ◽  
Reliability Based Design Optimization ◽  
Index Function ◽  
Reliability Based Design

Barrier Function Method in Reliability Based Design Optimization

2005 ◽  
Vol 297-300 ◽  
pp. 1882-1887
Author(s):  
Tae Hee Lee ◽  
Jung Hun Yoo
Keyword(s):  
Design Optimization ◽  
Barrier Function ◽  
Reliability Index ◽  
Feasible Solution ◽  
Reliability Based Design Optimization ◽  
User Requirement ◽  
Mean Values ◽  
Reliability Based Design ◽  
Design Variables ◽  
Reliability Method

In practical design applications, most design variables such as thickness, diameter and material properties are not deterministic but stochastic numbers that can be represented by their mean values with variances because of various uncertainties. When the uncertainties related with design variables and manufacturing process are considered in engineering design, the specified reliability of the design can be achieved by using the so-called reliability based design optimization. Reliability based design optimization takes into account the uncertainties in the design in order to meet the user requirement of the specified reliability while seeking optimal solution. Reliability based design optimization of a real system becomes now an emerging technique to achieve reliability, robustness and safety of the design. It is, however, well known that reliability based design optimization can often have so multiple local optima that it cannot converge into the specified reliability. To overcome this difficulty, barrier function approach in reliability based design optimization is proposed in this research and feasible solution with specified reliability index is always provided if a feasible solution is available. To illustrate the proposed formulation, reliability based design optimization of a bracket design is performed. Advanced mean value method and first order reliability method are employed for reliability analysis and their optimization results are compared with reliability index approach based on the accuracy and efficiency.

scholarly journals Efficient optimum safety factor approach for system reliability-based design optimization with application to composite yarns

2019 ◽  
Vol 19 (3) ◽  
pp. 221-230 ◽  
Author(s):  
Gh. Kharmanda ◽  
I. R. Antypas
Keyword(s):  
Design Optimization ◽  
Safety Factor ◽  
Reliability Index ◽  
Performance Measure ◽  
Alternative Methods ◽  
Reliability Based Design Optimization ◽  
Implementation Framework ◽  
Reliability Level ◽  
Reliability Based Design ◽  
Convergence Stability

Introduction. The integration of reliability and optimization concepts seeks to design structures that should be both economic and reliable. This model is called Reliability-Based Design Optimization (RBDO). In fact, the coupling between the mechanical modelling, the reliability analyses and the optimization methods leads to very high computational cost and weak convergence stability. Materials andMethods. Several methods have been developed to overcome these difficulties. The methods called Reliability Index Approach (RIA) and Performance Measure Approach (PMA) are two alternative methods. RIA describes the probabilistic constraint as a reliability index while PMA was proposed by converting the probability measure to a performance measure. An Optimum Safety Factor (OSF) method is proposed to compute safety factors satisfying a required reliability level without demanding additional computing cost for the reliability evaluation. The OSF equations are formulated considering RIA and PMA and extended to multiple failure case.Research Results. Several linear and nonlinear distribution laws are applied to composite yarns studies and then extended to multiple failure modes. It has been shown that the idea of the OSF method is to avoid the reliability constraint evaluation with a particular optimization process.Discussion and Conclusions. The simplified implementation framework of the OSF strategy consists of decoupling the optimization and the reliability analyses. It provides designers with efficient solutions that should be economic satisfying a required reliability level. It is demonstrated that the RBDO compared to OSF has several advantages: small number of optimization variables, good convergence stability, small computing time, satisfaction of the required reliability levels.

A New Study on Reliability-Based Design Optimization

1999 ◽  
Vol 121 (4) ◽  
pp. 557-564 ◽  
Author(s):  
J. Tu ◽  
K. K. Choi ◽  
Y. H. Park
Keyword(s):  
Design Optimization ◽  
Reliability Index ◽  
Performance Measure ◽  
Probabilistic Constraints ◽  
Probabilistic Constraint ◽  
Reliability Based Design Optimization ◽  
Performance Measure Approach ◽  
Reliability Based Design ◽  
Index Approach ◽  
Special Cases

This paper presents a general approach for probabilistic constraint evaluation in the reliability-based design optimization (RBDO). Different perspectives of the general approach are consistent in prescribing the probabilistic constraint, where the conventional reliability index approach (RIA) and the proposed performance measure approach (PMA) are identified as two special cases. PMA is shown to be inherently robust and more efficient in evaluating inactive probabilistic constraints, while RIA is more efficient for violated probabilistic constraints. Moreover, RBDO often yields a higher rate of convergence by using PMA, while RIA yields singularity in some cases.

A Modified Reliability Index Approach for Reliability-Based Design Optimization

2011 ◽  
Vol 133 (4) ◽  
Author(s):  
Po Ting Lin ◽  
Hae Chang Gea ◽  
Yogesh Jaluria
Keyword(s):  
Design Optimization ◽  
Reliability Index ◽  
Reliability Based Design Optimization ◽  
Second Moment ◽  
Reliability Indices ◽  
Reliability Based Design ◽  
Design Variables ◽  
Index Approach ◽  
Definition Of ◽  
Code Format

Reliability-based design optimization (RBDO) problems have been intensively studied for many decades. Since Hasofer and Lind [1974, “Exact and Invariant Second-Moment Code Format,” J. Engrg. Mech. Div., 100(EM1), pp. 111–121] defined a measure of the second-moment reliability index, many RBDO methods utilizing the concept of reliability index have been introduced as the reliability index approach (RIA). In the RIA, reliability analysis problems are formulated to find the reliability indices for each performance constraint and the solutions are used to evaluate the failure probability. However, the traditional RIA suffers from inefficiency and convergence problems. In this paper, we revisited the definition of the reliability index and revealed the convergence problem in the traditional RIA. Furthermore, a new definition of the reliability index is proposed to correct this problem and a modified reliability index approach is developed based on this definition. The strategies to solve RBDO problems with non-normally distributed design variables by the modified RIA are also investigated. Numerical examples using both the traditional and modified RIAs are compared and discussed.

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.

scholarly journals Multi-Objective, Reliability-Based Design Optimization of a Steering Linkage

2020 ◽  
Vol 10 (17) ◽  
pp. 5748
Author(s):  
Suwin Sleesongsom ◽  
Sujin Bureerat
Keyword(s):  
Design Optimization ◽  
Double Loop ◽  
Reliability Based Design Optimization ◽  
Case Scenario ◽  
Worst Case ◽  
Multi Objective ◽  
Reliability Based Design ◽  
Linkage Design ◽  
A New Technique ◽  
Optimization Loop

Reliability-based design optimization (RBDO) of a mechanism is normally based on the non-probabilistic model, which is viewed as failure possibility constraints in each optimization loop. It leads to a double-loop nested problem that causes a computationally expensive evaluation. Several methods have been developed to solve the problem, which are expected to increase the realization of optimum results and computational efficiency. The purpose of this paper was to develop a new technique of RBDO that can reduce the complexity of the double-loop nested problem to a single-loop. This involves using a multi-objective evolutionary technique combined with the worst-case scenario and fuzzy sets, known as a multi-objective, reliability-based design optimization (MORBDO). The optimization test problem and a steering linkage design were used to validate the performance of the proposed technique. The proposed technique can reduce the complexity of the design problem, producing results that are more conservative and realizable.

A Hybrid Reliability Approach for Reliability-Based Design Optimization

2010 ◽  
Author(s):  
Po Ting Lin ◽  
Yogesh Jaluria ◽  
Hae Chang Gea
Keyword(s):  
Design Optimization ◽  
Reliability Index ◽  
Optimization Problems ◽  
Performance Measure ◽  
Accurate Solution ◽  
Probabilistic Constraints ◽  
Reliability Based Design Optimization ◽  
Reliability Based Design ◽  
Index Approach ◽  
Hybrid Reliability

Reliability-based Design Optimization problems have been solved by two well-known methods: Reliability Index Approach (RIA) and Performance Measure Approach (PMA). RIA generates first-order approximate probabilistic constraints using the measures of reliability indices. For infeasible design points, the traditional RIA method suffers from inaccurate evaluation of the reliability index. To overcome this problem, the Modified Reliability Index Approach (MRIA) has been proposed. The MRIA provides the accurate solution of the reliability index but also inherits some inefficiency characteristics from the Most Probable Failure Point (MPFP) search when nonlinear constraints are involved. In this paper, the benchmark examples have been utilized to examine the efficiency and stability of both PMA and MRIA. In our study, we found that the MRIA is capable of obtaining the correct optimal solutions regardless of the locations of design points but the PMA is much efficient in the inverse reliability analysis. To take advantages of the strengths of both methods, a Hybrid Reliability Approach (HRA) is proposed. The HRA uses a selection factor that can determine which method to use during optimization iterations. Numerical examples from the proposed method are presented and compared with the MRIA and the PMA.

A Single-Loop Method for Reliability-Based Design Optimization

2004 ◽  
Author(s):  
Jinghong Liang ◽  
Zissimos P. Mourelatos ◽  
Jian Tu
Keyword(s):  
Design Optimization ◽  
Optimization Problem ◽  
Computational Effort ◽  
Side Impact ◽  
Double Loop ◽  
Reliability Based Design Optimization ◽  
Deterministic Optimization ◽  
Single Loop ◽  
Reliability Based Design ◽  
Reliability Assessments

Reliability-Based Design Optimization (RBDO) can provide optimum designs in the presence of uncertainty. It can therefore, be a powerful tool for design under uncertainty. The traditional, double-loop RBDO algorithm requires nested optimization loops, where the design optimization (outer) loop, repeatedly calls a series of reliability (inner) loops. Due to the nested optimization loops, the computational effort can be prohibitive for practical problems. A single-loop RBDO algorithm is proposed in this paper for both normal and non-normal random variables. Its accuracy is the same with the double-loop approach and its efficiency is almost equivalent to deterministic optimization. It collapses the nested optimization loops into an equivalent single-loop optimization process by imposing the Karush-Kuhn-Tucker optimality conditions of the reliability loops as equivalent deterministic equality constraints of the design optimization loop. It therefore, converts the probabilistic optimization problem into an equivalent deterministic optimization problem, eliminating the need for calculating the Most Probable Point (MPP) in repeated reliability assessments. Several numerical applications including an automotive vehicle side impact example, demonstrate the accuracy and superior efficiency of the proposed single-loop RBDO algorithm.

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