Reliability-Based Design Optimization Concerning Objective Variation Under Mixed Probabilistic and Interval Uncertainties

2016 ◽  
Vol 138 (11) ◽  
Author(s):  
Jianhua Zhou ◽  
Min Xu ◽  
Mian Li
Keyword(s):  
Design Optimization ◽  
Performance Measure ◽  
Interval Uncertainty ◽  
Reliability Based Design Optimization ◽  
Worst Case ◽  
Reliability Based Design ◽  
Matrix Operations ◽  
Interval Uncertainties ◽  
Treat All ◽  
Objective Robustness

Uncertainties, inevitable in nature, can be classified as probability based and interval based uncertainties in terms of its representations. Corresponding optimization strategies have been proposed to deal with these two types of uncertainties. It is more likely that both types of uncertainty can occur in one single problem, and thus, it is trivial to treat all uncertainties the same. A novel formulation for reliability-based design optimization (RBDO) under mixed probability and interval uncertainties is proposed in this paper, in which the objective variation is concerned. Furthermore, it is proposed to efficiently solve the worst-case parameter resulted from the interval uncertainty by utilizing the Utopian solution presented in a single-looped robust optimization (RO) approach where the inner optimization can be solved by matrix operations. The remaining problem can be solved utilizing any existing RBDO method. This work applies the performance measure approach to search for the most probable failure point (MPFP) and sequential quadratic programing (SQP) to solve the entire problem. One engineering example is given to demonstrate the applicability of the proposed approach and to illustrate the necessity to consider the objective robustness under certain circumstances.

Reliability Based Design Optimization Concerning Objective Variation Under Mixed Probabilistic and Interval Uncertainties

2016 ◽  
Author(s):  
Jianhua Zhou ◽  
Min Xu ◽  
Mian Li
Keyword(s):  
Design Optimization ◽  
Performance Measure ◽  
Interval Uncertainty ◽  
Optimization Approach ◽  
Reliability Based Design Optimization ◽  
Worst Case ◽  
Reliability Based Design ◽  
Interval Uncertainties ◽  
Treat All ◽  
Objective Robustness

Uncertainties, inevitable in nature, can be classified as probability based and interval based uncertainties, in terms of its representations. Corresponding optimization strategies have been proposed to deal with these two types of uncertainties individually. However, it is more likely that both types of uncertainty occur in one single problem and so it is trivial to treat all uncertainties the same. In this paper a novel formulation for reliability based design optimization (RBDO) under mixed probability and interval uncertainties is proposed, in which the objective variation or the objective robustness is also concerned. Furthermore, it is proposed to efficiently solve the worst case parameter resulted from the interval uncertainty by utilizing the Utopian solution presented in a single-looped robust optimization approach, in which the inner optimization problem can be solved by performing matrix operations. The remaining problem can be solved utilizing any existing RBDO method. This work applies the performance measure approach to search for the most probable failure point (MPFP) and sequential quadratic programming (SQP) to solve the entire problem. Two engineering examples are given to demonstrate the applicability of the proposed approach and to illustrate the necessity to consider the objective robustness under certain circumstances.

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 Robotic System Dynamic Performance

2006 ◽  
Vol 129 (4) ◽  
pp. 449-454 ◽  
Author(s):  
Alan P. Bowling ◽  
John E. Renaud ◽  
Jeremy T. Newkirk ◽  
Neal M. Patel ◽  
Harish Agarwal
Keyword(s):  
Design Optimization ◽  
Reference Point ◽  
High Reliability ◽  
Dynamic Performance ◽  
Performance Measure ◽  
Robotic System ◽  
Reliability Based Design Optimization ◽  
End Effector ◽  
Reliability Based Design ◽  
Reliable Design

In this investigation a robotic system’s dynamic performance is optimized for high reliability under uncertainty. The dynamic capability equations (DCE) allow designers to predict the dynamic performance of a robotic system for a particular configuration and reference point on the end effector (i.e., point design). Here the DCE are used in conjunction with a reliability-based design optimization (RBDO) strategy in order to obtain designs with robust dynamic performance with respect to the end-effector reference point. In this work a unilevel performance measure approach is used to perform RBDO. This is important for the reliable design of robotic systems in which a solution to the DCE is required for each constraint call. The method is illustrated on a robot design problem.

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.

Reliability-Based Design Optimization of Microstructures With Analytical Formulation

2018 ◽  
Vol 140 (11) ◽  
Author(s):  
Pinar Acar
Keyword(s):  
Design Optimization ◽  
Material Properties ◽  
Optimization Problem ◽  
Optimization Under Uncertainty ◽  
Reliability Based Design Optimization ◽  
Case Scenario ◽  
Worst Case ◽  
Analytical Formulation ◽  
Reliability Based Design ◽  
Safe Approach

Microstructures are stochastic by their nature. These aleatoric uncertainties can alter the expected material performance substantially and thus they must be considered when designing materials. One safe approach would be assuming the worst case scenario of uncertainties in design. However, design under the worst case conditions can lead to over-conservative solutions that provide less effective material properties. Here, a more powerful design approach can be developed by implementing reliability constraints into the optimization problem to achieve superior material properties while satisfying the prescribed design criteria. This is known as reliability-based design optimization (RBDO), and it has not been studied for microstructure design before. In this work, an analytical formulation that models the propagation of microstructural uncertainties to the material properties is utilized to compute the probability of failure. Next, the analytical uncertainty solution is integrated into the optimization problem to define the reliability constraints. The presented optimization under uncertainty scheme is exercised to maximize the yield stress of α-Titanium and magnetostriction of Galfenol, respectively.

Reliability-Based Design Optimization for Design Problems with Random Fuzzy and Interval Uncertainties

2019 ◽  
Vol 17 (06) ◽  
pp. 1950018 ◽  
Author(s):  
Li-Xiang Zhang ◽  
Xin-Jia Meng ◽  
He Zhang
Keyword(s):  
Design Optimization ◽  
Mechanical Design ◽  
Computational Cost ◽  
Reliability Based Design Optimization ◽  
Design Problems ◽  
Main Obstacle ◽  
Reliability Based Design ◽  
Interval Uncertainties ◽  
Mixed Uncertainties ◽  
Measurement Approach

Reliability-based design optimization (RBDO) has been widely used in mechanical design. However, the treatment of various uncertainties and associated computational burden are still the main obstacle of its application. A methodology of RBDO under random fuzzy and interval uncertainties (RFI-RBDO) is proposed in this paper. In the proposed methodology, two reliability analysis approaches, respectively named as FORM-[Formula: see text]-URA and interpolation-based sequential performance measurement approach (ISPMA), are developed for the mixed uncertainties assessment, and a parallel-computing-based SOMUA (PCSOMUA) method is proposed to reduce the computational cost of RFI-RBDO. Finally, two examples are provided to verify the validity of the methods.

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