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.

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.

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

2009 ◽  
Author(s):  
Po Ting Lin ◽  
Hae Chang Gea ◽  
Yogesh Jaluria
Keyword(s):  
Reliability Index ◽  
Reliability Based Design Optimization ◽  
Convergence Problem ◽  
Analysis Problem ◽  
Numerical Examples ◽  
Reliability Based Design ◽  
Index Approach ◽  
Convergence Problems ◽  
Definition Of ◽  
Performance Constraint

RBDO problems have been intensively studied for many decades. Since Hasofer and Lind 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, a reliability analysis problem is formulated to find the reliability index 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 based on this definition is developed. Numerical examples using both the traditional RIA and the modified RIA are compared and discussed.

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.

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.

Reliability-based design optimization of electromagnetic shielding structure using neural networks and real-coded genetic algorithm

2014 ◽  
Vol 228 (18) ◽  
pp. 3471-3481 ◽  
Author(s):  
Heeralal Gargama ◽  
Sanjay K Chaturvedi ◽  
Awalendra K Thakur
Keyword(s):  
Genetic Algorithm ◽  
Neural Networks ◽  
Artificial Neural Networks ◽  
Design Optimization ◽  
Electromagnetic Shielding ◽  
Optimization Approach ◽  
Reliability Based Design Optimization ◽  
Reliability Based Design ◽  
Design Variables ◽  
Real Coded Genetic Algorithm

The conventional approaches for electromagnetic shielding structures’ design, lack the incorporation of uncertainty in the design variables/parameters. In this paper, a reliability-based design optimization approach for designing electromagnetic shielding structure is proposed. The uncertainties/variability in the design variables/parameters are dealt with using the probabilistic sufficiency factor, which is a factor of safety relative to a target probability of failure. Estimation of probabilistic sufficiency factor requires performance function evaluation at every design point, which is extremely computationally intensive. The computational burden is reduced greatly by evaluating design responses only at the selected design points from the whole design space and employing artificial neural networks to approximate probabilistic sufficiency factor as a function of design variables. Subsequently, the trained artificial neural networks are used for the probabilistic sufficiency factor evaluation in the reliability-based design optimization, where optimization part is processed with the real-coded genetic algorithm. The proposed reliability-based design optimization approach is applied to design a three-layered shielding structure for a shielding effectiveness requirement of ∼40 dB, used in many industrial/commercial applications, and for ∼80 dB used in the military applications.

Stochastic Response Analysis and Reliability-Based Design Optimization of Nonlinear Electromechanical Energy Harvesters with Fractional Derivative Elements

2020 ◽  
Author(s):  
Ioannis Petromichelakis ◽  
Apostolos F. Psaros ◽  
Ioannis A. Kougioumtzoglou
Keyword(s):  
Fractional Derivative ◽  
Design Optimization ◽  
Response Analysis ◽  
Reliability Based Design Optimization ◽  
Stochastic Response ◽  
Energy Harvesters ◽  
Reliability Based Design ◽  
Singular Diffusion ◽  
Electromechanical Energy ◽  
Definition Of

Abstract A methodology based on the Wiener path integral technique (WPI) is developed for stochastic response determination and reliability-based design optimization of a class of nonlinear electromechanical energy harvesters endowed with fractional derivative elements. In this regard, first, the WPI technique is appropriately adapted and enhanced to account both for the singular diffusion matrix and for the fractional derivative modeling of the capacitance in the coupled electromechanical governing equations. Next, a reliability-based design optimization problem is formulated and solved, in conjunction with the WPI technique, for determining the optimal parameters of the harvester. It is noted that the herein proposed definition of the failure probability constraint is particularly suitable for harvester configurations subject to space limitations. Several numerical examples are included, while comparisons with pertinent Monte Carlo simulation data demonstrate the satisfactory performance of the methodology.

The Response Surface Single Loop Reliability-Based Design Optimization Method With Reliability Requirement on System Failure

2016 ◽  
Author(s):  
Rami Mansour ◽  
Mårten Olsson
Keyword(s):  
Design Optimization ◽  
Response Surface ◽  
Optimization Problem ◽  
Optimization Method ◽  
Reliability Based Design Optimization ◽  
Single Loop ◽  
Reliability Based Design ◽  
Design Variables ◽  
Reliability Method ◽  
Deterministic Solution

In reliability-based design optimization (RBDO), an optimal design which minimizes an objective function while satisfying a number of probabilistic constraints is found. As opposed to deterministic optimization, statistical uncertainties in design variables and design parameters have to be taken into account in the design process in order to achieve a reliable design. In the most widely used RBDO approaches, the First-Order Reliability Method (FORM) is used in the probability assessment. This involves locating the Most Probable Point (MPP) of failure, or the inverse MPP, either exactly or approximately. If exact methods are used, an optimization problem has to be solved, typically resulting in computationally expensive double loop or decoupled loop RBDO methods. On the other hand, locating the MPP approximately typically results in highly efficient single loop RBDO methods since the optimization problem is not necessary in the probability assessment. However, since all these methods are based on FORM, which in turn is based on a linearization of the deterministic constraints at the MPP, they may suffer inaccuracies associated with neglecting the nonlinearity of deterministic constraints. In a previous paper presented by the authors, the Response Surface Single Loop (RSSL) Reliability-based design optimization method was proposed. The RSSL-method takes into account the non-linearity of the deterministic constraints in the computation of the probability of failure and was therefore shown to have higher accuracy than existing RBDO methods. The RSSL-method was also shown to have high efficiency since it bypasses the concept of an MPP. In RSSL, the deterministic solution is first found by neglecting uncertainties in design variables and parameters. Thereafter quadratic response surface models are fitted to the deterministic constraints around the deterministic solution using a single set of design of experiments. The RBDO problem is thereafter solved in a single loop using a closed-form second order reliability method (SORM) which takes into account all elements of the Hessian of the quadratic constraints. In this paper, the RSSL method is used to solve the more challenging system RBDO problems where all constraints are replaced by one constraint on the system probability of failure. The probabilities of failure for the constraints are assumed independent of each other. In general, system reliability problems may be more challenging to solve since replacing all constraints by one constraint may strongly increase the non-linearity in the optimization problem. The extensively studied reliability-based design for vehicle crash-worthiness, where the provided deterministic constraints are general quadratic models describing the system in the whole region of interest, is used to demonstrate the capabilities of the RSSL method for problems with system reliability constraints.

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