Bayesian optimization for robust design of steel frames with joint and individual probabilistic constraints

2021 ◽  
Vol 245 ◽  
pp. 112859
Author(s):  
Bach Do ◽  
Makoto Ohsaki ◽  
Makoto Yamakawa
Keyword(s):  
Robust Design ◽  
Steel Frames ◽  
Bayesian Optimization ◽  
Probabilistic Constraints

scholarly journals Design of Mechanical Metamaterials via Constrained Bayesian Optimization

2018 ◽  
Author(s):  
Conner Sharpe ◽  
Carolyn Conner Seepersad ◽  
Seth Watts ◽  
Dan Tortorelli
Keyword(s):  
Design Space ◽  
Engineering Problem ◽  
Bayesian Optimization ◽  
Probabilistic Constraints ◽  
Objective Functions ◽  
Bulk Properties ◽  
New Class ◽  
Naturally Occurring ◽  
Design Variables ◽  
Mechanical Metamaterials

Advances in additive manufacturing processes have made it possible to build mechanical metamaterials with bulk properties that exceed those of naturally occurring materials. One class of these metamaterials is structural lattices that can achieve high stiffness to weight ratios. Recent work on geometric projection approaches has introduced the possibility of optimizing these architected lattice designs in a drastically reduced parameter space. The reduced number of design variables enables application of a new class of methods for exploring the design space. This work investigates the use of Bayesian optimization, a technique for global optimization of expensive non-convex objective functions through surrogate modeling. We utilize formulations for implementing probabilistic constraints in Bayesian optimization to aid convergence in this highly constrained engineering problem, and demonstrate results with a variety of stiff lightweight lattice designs.

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.

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.

ERGO: a new Robust Design Optimization Technique combining Multi-Objective Bayesian Optimization with Analytical Uncertainty Quantification

2021 ◽  
pp. 1-22
Author(s):  
Jolan Wauters
Keyword(s):  
Design Optimization ◽  
Uncertainty Quantification ◽  
Robust Design ◽  
Bayesian Optimization ◽  
Robust Design Optimization ◽  
The Novel ◽  
Analytical Uncertainty ◽  
Multi Objective ◽  
Optimization Framework ◽  
Quantities Of Interest

Abstract In this work, robust design optimization (RDO) is treated, motivated by the increasing desire to account for variability the design phase. The problem is formulated in a multi-objective setting with the objective of simultaneously minimizing the mean of the objective and its variance due to variability of design variables and/or parameters. This allows the designer to choose its robustness level without the need to repeat the optimization as typically encountered when formulated as a single objective. To account for the computational cost that is often encountered in RDO problems, the problem is fitted in a Bayesian optimization framework. The use of surrogate modeling techniques to efficiently solve problems under uncertainty has effectively found its way in the optimization community leading to surrogate-assisted optimization-under-uncertainty schemes. The surrogates are often considered cheap-to-sample black-boxes and are sampled to obtain the desired quantities of interest. However, since the analytical formulation of the surrogates is known, an analytical treatment of the problem is available. To obtain the quantities of interest without sampling an analytical uncertainty propagation through the surrogate is presented. The multi-objective Bayesian optimization framework and the analytical uncertainty quantification are linked together through the formulation of the robust expected improvement (REI), obtaining the novel efficient robust global optimization (ERGO) scheme. The method is tested on a series of test cases to examine its behavior for varying difficulties and validated on an aerodynamic test function which proves the effectiveness of the novel scheme.

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.

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