Dynamic Reliability-Based Robust Design with Time-Variant Probabilistic Constraints

2013 ◽  
Author(s):  
Zequn Wang ◽  
Abdulaziz T. Almaktoom ◽  
Pingfeng Wang
Keyword(s):  
Robust Design ◽  
Probabilistic Constraints ◽  
Dynamic Reliability

Time-Dependent Reliability-Based Robust Design Optimization via Extreme Value Moment Method

2018 ◽  
Author(s):  
Shui Yu ◽  
Zhonglai Wang
Keyword(s):  
Design Optimization ◽  
Reliability Analysis ◽  
Robust Design ◽  
Moment Method ◽  
Time Dependent ◽  
Robust Design Optimization ◽  
Probabilistic Constraints ◽  
Multi Objective Optimization ◽  
Integrated Framework ◽  
Multi Objective

During the product design and development stage, design engineers often encounter reliability and robustness of dynamic uncertain structures. Meanwhile, time-varying and high nonlinear performance are the basic characteristics of reliability analysis and design. Hence, the time-dependent reliability analysis and integrating reliability-based design with robust design become a primary challenge in reliability-based robust design optimization. This paper proposes a multi-objective integrated framework for time-dependent reliability-based robust design optimization and the corresponding algorithms. The multi-objective integrated framework, which minimizes the mean value and coefficient of variation for the objective function at the same time subject to time-dependent probabilistic constraints, is first established. The time-dependent probabilistic constraints are then converted into deterministic constraints using a combination of moment method and the sparse grid based stochastic collocation method. The evolutionary multi-objective optimization algorithm is finally employed for the deterministic multi-objective optimization problem. Several examples are investigated to demonstrate the effectiveness of the proposed method.

Reliability-based robust design of wind turbine’s shrink disk

2017 ◽  
Vol 232 (15) ◽  
pp. 2685-2696 ◽  
Author(s):  
Jianmei Wang ◽  
Ke Ning ◽  
Junliang Xu ◽  
Zhixiong Li
Keyword(s):  
Robust Design ◽  
Design Method ◽  
Minimum Principle ◽  
Reliability Model ◽  
Strength Model ◽  
Interference Fit ◽  
Dynamic Reliability ◽  
Multi Objective ◽  
Traditional Design ◽  
Reliability Sensitivity

Wind turbine’s shrink disk (WTSD), as a component of transmission system, plays a crucial role in the wind turbine work. In this study, the matrix expression of combined pressure and interference magnitude has been derived by analyzing the geometry relationship of interference fit of multi-layer cylinder. The mechanic model is built by simplifying WTSD as interference fit of multi-layer cylinder. The reliability model is established on the basis of pressure-strength model, and the formula regarding reliability sensitivity is derived. In terms of the minimum principle on the square sum of reliability sensitivity and the minimum reliability principle, the reliability-based robust design (RBRD) model is built under the multi-objective conditions, and the dynamic reliability model is established on the basis of reliability model, load model, and residual strength model. Dynamic reliability sensitivity formula is deduced, and the dynamic reliability-based robust design (DRBRD) model is established under the multi-objective conditions. The effects of the coefficient of friction, assembly clearance, and yield strength on the reliability of WTSD are analyzed by RBRD and DRBRD methods. Taking a type of WTSD as an example, the calculating results validate that the reliability changes along with interference magnitude. The comparison of results shows that the above methods and Monte Carlo method have the same tendency and approximately agree well. Moreover, the traditional design method and RBRD method are compared. It turned out that RBRD can improve the reliability of WTSD by 47.6%, the reliability-based sensitivity is less than that from the traditional design method, and the robustness is stronger. The experiment verified that the design methods of this study can better meet the operation requirements.

A Sequential Algorithm for Reliability-Based Robust Design Optimization Under Epistemic Uncertainty

2012 ◽  
Vol 134 (1) ◽  
Author(s):  
Yuanfu Tang ◽  
Jianqiao Chen ◽  
Junhong Wei
Keyword(s):  
Design Optimization ◽  
Robust Design ◽  
Epistemic Uncertainty ◽  
Robust Design Optimization ◽  
Probabilistic Constraints ◽  
Sequential Algorithm ◽  
Practical Applications ◽  
Reliability Based Design ◽  
Design Variables ◽  
Novel Concept

In practical applications, there may exist a disparity between real values and optimal results due to uncertainties. This kind of disparity may cause violations of some probabilistic constraints in a reliability based design optimization (RBDO) problem. It is important to ensure that the probabilistic constraints at the optimum in a RBDO problem are insensitive to the variations of design variables. In this paper, we propose a novel concept and procedure for reliability based robust design in the context of random uncertainty and epistemic uncertainty. The epistemic uncertainty of design variables is first described by an info gap model, and then the reliability-based robust design optimization (RBRDO) is formulated. To reduce the computational burden in solving RBRDO problems, a sequential algorithm using shifting factors is developed. The algorithm consists of a sequence of cycles and each cycle contains a deterministic optimization followed by an inverse robustness and reliability evaluation. The optimal result based on the proposed model satisfies certain reliability requirement and has the feasible robustness to the epistemic uncertainty of design variables. Two examples are presented to demonstrate the feasibility and efficiency of the proposed method.

scholarly journals An Efficient Integrated Framework of Reliability-Based Robust Design Optimization for Computation-Intensive Structures

2021 ◽  
Author(s):  
xiongming lai ◽  
Ju Huang ◽  
Cheng Wang ◽  
Yong Zhang
Keyword(s):  
Design Optimization ◽  
Robust Design ◽  
Optimization Problems ◽  
Trust Region Method ◽  
Performance Measure ◽  
Robust Design Optimization ◽  
Probabilistic Constraints ◽  
Engineering Structures ◽  
Integrated Framework ◽  
Finite Element Software

Abstract When carrying out robust design optimization for complex engineering structures, they are computed by finite element software and are always computation-intensive. Aim at this problem, the paper proposes an efficient integrated framework of Reliability-based Robust Design Optimization (RBRDO). Firstly, the conventional RBRDO problem is changed as percentile form, that is, the improved percentile formulation of computing the objective robustness and probabilistic constraints is presented by resorting to the employment of Performance Measure Approach (PMA). Secondly, the above improved RBRDO problem is simplified by a series of new approximation methods due to the need of reducing computation. An efficient approximation method is proposed to estimate PMA functions of the RBRDO formulation. Based on it, the above improved RBRDO problem can be transformed into a sequence of approximate deterministic sub-optimization problems, whose objective function and constraints are expressed as the approximate explicit form only in relation to the design variables. Furthermore, use the trust region method to solve the above sequence of sub-optimization. Lastly, several examples are used to demonstrate the effectiveness and efficiency of the proposed method.

Applying Robust Design Optimization to Large Systems

2014 ◽  
Author(s):  
Matthew G. McIntire ◽  
Veronika Vasylkivska ◽  
Christopher Hoyle ◽  
Nathan Gibson
Keyword(s):  
Robust Optimization ◽  
Dimension Reduction ◽  
Robust Design ◽  
Large Scale ◽  
Robust Design Optimization ◽  
Probabilistic Constraints ◽  
Operational Control ◽  
Revenue Optimization ◽  
Large Scale Systems ◽  
Uncertainty Space

While Robust Optimization has been utilized for a variety of design problems, application of Robust Design to the control of large-scale systems presents unique challenges to assure rapid convergence of the solution. Specifically, the need to account for uncertainty in the optimization loop can lead to a prohibitively expensive optimization using existing methods when using robust optimization for control. In this work, a robust optimization framework suitable for operational control of large scale systems is presented. To enable this framework, robust optimization uses a utility function for the objective, dimension reduction in the uncertainty space, and a new algorithm for evaluating probabilistic constraints. The proposed solution accepts the basis in utility theory, where the goal is to maximize expected utility. This allows analytic gradient and Hessian calculations to be derived to reduce the number of iterations required. Dimension reduction reduces uncertain functions to low dimensional parametric uncertainty while the new algorithm for evaluating probabilistic constraints is specifically formulated to reuse information previously generated to estimate the robust objective. These processes reduce the computational expense to enable robust optimization to be used for operational control of a large-scale system. The framework is applied to a multiple-dam hydropower revenue optimization problem, then the solution is compared with the solution given by a non-probabilistic safety factor approach. The solution given by the framework is shown to dominate the other solution by improving upon the expected objective as well as the joint failure probability.

A Unified Framework for Integrated Optimization Under Uncertainty

2010 ◽  
Vol 132 (5) ◽  
Author(s):  
Zhonglai Wang ◽  
Hong-Zhong Huang ◽  
Yu Liu
Keyword(s):  
Objective Function ◽  
Robust Design ◽  
Taylor Series Expansion ◽  
Assessment Method ◽  
Optimization Under Uncertainty ◽  
Probabilistic Constraints ◽  
Sequential Optimization ◽  
Design Stage ◽  
Unified Framework ◽  
Reliability Based Design

Reliability and robustness are two main attributes of design under uncertainty. Hence, it is necessary to combine reliability-based design and robust design at the design stage. In this paper, a unified framework for integrating reliability-based design and robust design is proposed. In the proposed framework, the probabilistic objective function is converted to a deterministic objective function by the Taylor series expansion or inverse reliability strategy with accounting for the probabilistic characteristic of the objective function. Therefore, with this unified framework, there is no need to deal with a multiobjective optimization problem to integrate reliability-based design and robust design any more. The probabilistic constraints are converted to deterministic constraints with inverse reliability strategy at the same time. In order to solve the unified framework, an improved sequential optimization and reliability assessment method is proposed. Three examples are given to illustrate the benefits of the proposed methods.

Sequential Optimization and Reliability Assessment Method for Efficient Probabilistic Design

2002 ◽  
Author(s):  
Xiaoping Du ◽  
Wei Chen
Keyword(s):  
Robust Design ◽  
Optimization Design ◽  
Reliability Assessment ◽  
Assessment Method ◽  
Side Impact ◽  
Probabilistic Constraints ◽  
Sequential Optimization ◽  
Probabilistic Design ◽  
Probabilistic Optimization ◽  
Reliability Based Design

Probabilistic optimization design offers tools for making reliable decisions with the consideration of uncertainty associated with design variables/parameters and simulation models. In a probabilistic design, such as reliability-based design and robust design, the design feasibility is formulated probabilistically such that the probability of the constraint satisfaction (reliability) exceeds the desired limit. The reliability assessment for probabilistic constraints often involves an iterative procedure; therefore, two loops are involved in a probabilistic optimization. Due to the double-loop procedure, the computational demand is extremely high. To improve the efficiency of a probabilistic design, a novel method – sequential optimization and reliability assessment (SORA) is developed in this paper. The SORA method employs a single-loop strategy where a serial of cycles of optimization and reliability assessment is employed. In each cycle optimization and reliability assessment are decoupled from each other; no reliability assessment is required within optimization and the reliability assessment is only conducted after the optimization. The key concept of the proposed method is to shift the boundaries of violated deterministic constraints (with low reliability) to the feasible direction based on the reliability information obtained in the previous cycle. Hence the design is quickly improved from cycle to cycle and the computational efficiency is improved significantly. Two engineering applications, the reliability-based design for vehicle crashworthiness of side impact and the integrated reliability and robust design of a speed reducer, are presented to demonstrate the effectiveness of the SORA method.

Time-Dependent Reliability-Based Robust Design Optimization Using Evolutionary Algorithm

2019 ◽  
Vol 5 (2) ◽  
Author(s):  
Shui Yu ◽  
Zhonglai Wang ◽  
Zhihua Wang
Keyword(s):  
Design Optimization ◽  
Robust Design ◽  
Dynamic Properties ◽  
Time Dependent ◽  
Robust Design Optimization ◽  
Probabilistic Constraints ◽  
Multi Objective Optimization ◽  
Engineering Structures ◽  
Integrated Framework ◽  
Multi Objective

Due to the uncertain and dynamic parameters from design, manufacturing, and working conditions, many engineering structures usually show uncertain and dynamic properties. During the product design and development stages, designers often encounter reliability and robustness measures of dynamic uncertain structures. Time-varying and high nonlinear performance brings a new challenge for the reliability-based robust design optimization. This paper proposes a multi-objective integrated framework for time-dependent reliability-based robust design optimization and the corresponding algorithms. The integrated framework is first established by minimizing the mean value and coefficient of variation of the objective performance at the same time subject to time-dependent probabilistic constraints. The time-dependent probabilistic constraints are then converted into deterministic constraints using the dimension reduction method. The evolutionary multi-objective optimization algorithm is finally employed for the deterministic multi-objective optimization problem. Several examples are investigated to demonstrate the effectiveness of the proposed method.

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