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.

Reliability-Based Design Optimization of Complex Problems With Multiple Design Points via Narrowed Search Region

2019 ◽  
Vol 142 (6) ◽  
Author(s):  
Yutian Wang ◽  
Peng Hao ◽  
Zhendong Guo ◽  
Dachuan Liu ◽  
Qiang Gao
Keyword(s):  
Design Optimization ◽  
Risk Function ◽  
Computational Cost ◽  
Reliability Based Design Optimization ◽  
Search Region ◽  
Complex Problems ◽  
Reliability Based Design ◽  
Training Samples ◽  
Gradient Based ◽  
Similar Accuracy

Abstract The expensive computational cost is always a major concern for reliability-based design optimization (RBDO) of complex problems. The performance of RBDO can be lowered by the inaccuracy of reliability analysis (RA) which is caused by multiple local optimums and multiple design points in highly non-linear space. In order to reduce the computational burden and guarantee the accuracy of RA (and thus to improve the RBDO performance), a global RBDO algorithm by adopting an improved constraint boundary sampling (GRBDO-ICBS) method is proposed. Specifically, the GRBDO-ICBS method first narrows the concerned search region by using a Kriging-based global search. The accuracies of the design points are verified by the expected risk function (ERF), and the corresponding inaccurate design points are added into training samples to update Kriging. Then a multi-start gradient-based sequential RBDO is carried out, which tries to find out all multiple design points in the concerned search region. The performance of GRBDO-ICBS is demonstrated by four examples. All results have shown that the proposed method can achieve similar accuracy as Monte Carlo simulation (MCS)-based RBDO but with a much lower computational cost.

Development of a Multistage Reliability-Based Design Optimization Method

2013 ◽  
Vol 136 (1) ◽  
Author(s):  
Eric J. Paulson ◽  
Ryan P. Starkey
Keyword(s):  
Objective Function ◽  
Design Optimization ◽  
Technology Development ◽  
Computational Cost ◽  
Optimization Method ◽  
Comparison Method ◽  
Reliability Based Design Optimization ◽  
Numerical Example ◽  
Reliability Based Design ◽  
System Acquisition

Complex system acquisition and its associated technology development have a troubled recent history. The modern acquisition timeline consists of conceptual, preliminary, and detailed design followed by system test and production. The evolving nature of the estimates of system performance, cost, and schedule during this extended process may be a significant contribution to recent issues. The recently proposed multistage reliability-based design optimization (MSRBDO) method promises improvements over reliability-based design optimization (RBDO) in achieved objective function value. In addition, its problem formulation more closely resembles the evolutionary nature of epistemic design uncertainties inherent in system design during early system acquisition. Our goal is to establish the modeling basis necessary for applying this new method to the engineering of early conceptual/preliminary design. We present corrections in the derivation and solutions to the single numerical example problem published by the original authors, Nam and Mavris, and examine the error introduced under the reduced-order reliability sampling used in the original publication. MSRBDO improvements over the RBDO solution of 10–36% for the objective function after first-stage optimization are shown for the original second-stage example problem. A larger 26–40% improvement over the RBDO solution is shown when an alternative comparison method is used than in the original. The specific implications of extending the method to arbitrary m-stage problems are presented, together with a solution for a three-stage numerical example. Several approaches are demonstrated to mitigate the computational cost increase of MSRBDO over RBDO, resulting in a net decrease in calculation time of 94% from an initial MSRBDO baseline algorithm.

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.

Fatigue Reliability Based Design Optimization of Bending Stiffener

2012 ◽  
Vol 56 (02) ◽  
pp. 120-128
Author(s):  
Hezhen Yang ◽  
Aijun Wang
Keyword(s):  
Design Optimization ◽  
Oil And Gas ◽  
Computational Cost ◽  
Fatigue Analysis ◽  
Gas Production ◽  
Test Case ◽  
Accuracy Evaluation ◽  
Fatigue Reliability ◽  
Reliability Based Design Optimization ◽  
Reliability Based Design

A methodology for fatigue reliability based design optimization is proposed for the design of bending stiffener. Bending stiffener is employed to protect the upper connection of umbilical/flexible riser against damage from overbending. It is prone to cause fatigue failure due to the wave induced vessel motions. Therefore, its fatigue character has a great impact on the safety of oil and gas production and we should pay more attention to it. In addition, the fatigue analysis involves material, geometric, and loading uncertainties, hence the reliability analysis is performed for considering the influence of uncertain factors. In this work, the fatigue reliability based optimization involves the fatigue analysis and complex optimization algorithms the metamodel is used to reduce the computational cost. Threemetamodels are constructed by the optimum Latin hypercube method. Then, the optimum metamodel is selected for the optimization through the accuracy evaluation. The feasibility of the methodology is verified by a test case of beam. Finally, it is applied to the fatigue reliability based design optimization of bending stiffener. The results demonstrate that this methodology is rational and improves the fatigue reliability of bending stiffener. First, compared with deterministic optimization.

High-Dimensional Reliability-Based Design Optimization Involving Highly Nonlinear Constraints and Computationally Expensive Simulations

2019 ◽  
Vol 141 (5) ◽  
Author(s):  
Meng Li ◽  
Mohammadkazem Sadoughi ◽  
Chao Hu ◽  
Zhen Hu ◽  
Amin Toghi Eshghi ◽  
...  
Keyword(s):  
Design Optimization ◽  
Reliability Analysis ◽  
Sequential Sampling ◽  
Computational Cost ◽  
High Dimensional ◽  
Reliability Based Design Optimization ◽  
Reliability Based Design ◽  
Highly Nonlinear ◽  
Modeling Strategy ◽  
Design Cost

Reliability-based design optimization (RBDO) aims at optimizing the design of an engineered system to minimize the design cost while satisfying reliability requirements. However, it is challenging to perform RBDO under high-dimensional uncertainty due to the often prohibitive computational burden. In this paper, we address this challenge by leveraging a recently developed method for reliability analysis under high-dimensional uncertainty. The method is termed high-dimensional reliability analysis (HDRA). The HDRA method optimally combines the strengths of univariate dimension reduction (UDR) and kriging-based reliability analysis to achieve satisfactory accuracy with an affordable computational cost for HDRA problems. In this paper, we improve the computational efficiency of high-dimensional RBDO by pursuing two new strategies: (i) a two-stage surrogate modeling strategy is adopted to first locate a highly probable region of the optimum design and then locally refine the accuracy of the surrogates in this region; and (ii) newly selected samples are updated for all the constraints during the sequential sampling process in HDRA. The results of two mathematical examples and one real-world engineering example suggest that the proposed HDRA-based RBDO (RBDO-HDRA) method is capable of solving high-dimensional RBDO problems with higher accuracy and comparable efficiency than the UDR-based RBDO (RBDO-UDR) and ordinary kriging-based RBDO (RBDO-kriging) methods.

A Reliability Index Based Decoupling Method for Reliability-Based Design Optimization

2012 ◽  
Vol 544 ◽  
pp. 223-228 ◽  
Author(s):  
Zhen Zhong Chen ◽  
Hao Bo Qiu ◽  
Hong Yan Hao ◽  
Hua Di Xiong
Keyword(s):  
Design Optimization ◽  
Reliability Index ◽  
Computational Cost ◽  
Probabilistic Constraints ◽  
Reliability Based Design Optimization ◽  
Decoupling Method ◽  
Practical Applications ◽  
Reliability Based Design ◽  
Structure Reliability ◽  
Comparison Results

Reliability-based design optimization (RBDO) evaluates variation of output induced by uncertainties of design variables and results in an optimal design while satisfying the reliability requirements. However, its use in practical applications is hindered by the huge computational cost during the evaluation of structure reliability. In this paper, the reliability index based decoupling method is developed to improve the efficiency of probabilistic optimization. The reliability index is used to calculate the shifting vector in the decoupling process, due to its efficiency in evaluating violated probabilistic constraints. The computation capability of the proposed method is demonstrated using two examples, which are widely used to test RBDO methods. The comparison results show that the proposed method has the same accuracy as the existing methods, and it is also very efficient.

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