scholarly journals Structural optimization considering the probabilistic system response

2004 ◽  
Vol 31 (3-4) ◽  
pp. 361-394 ◽  
Author(s):  
M. Papadrakakis ◽  
N.D. Lagaros ◽  
V. Plevris
Keyword(s):  
Structural Optimization ◽  
Design Optimization ◽  
Robust Design ◽  
Large Scale ◽  
Optimization Problem ◽  
Structural Parameters ◽  
Dominant Role ◽  
Robust Design Optimization ◽  
Design Parameters ◽  
System Response

In engineering problems, the randomness and uncertainties are inherent and the scatter of structural parameters from their nominal ideal values is unavoidable. In Reliability Based Design Optimization (RBDO) and Robust Design Optimization (RDO) the uncertainties play a dominant role in the formulation of the structural optimization problem. In an RBDO problem additional non deterministic constraint functions are considered while an RDO formulation leads to designs with a state of robustness, so that their performance is the least sensitive to the variability of the uncertain variables. In the first part of this study a metamodel assisted RBDO methodology is examined for large scale structural systems. In the second part an RDO structural problem is considered. The task of robust design optimization of structures is formulated as a multi-criteria optimization problem, in which the design variables of the optimization problem, together with other design parameters such as the modulus of elasticity and the yield stress are considered as random variables with a mean value equal to their nominal value. .

A Gaussian Process Modeling Approach for Fast Robust Design With Uncertain Inputs

2018 ◽  
Author(s):  
Kevin M. Ryan ◽  
Jesper Kristensen ◽  
You Ling ◽  
Sayan Ghosh ◽  
Isaac Asher ◽  
...  
Keyword(s):  
Gaussian Process ◽  
Design Optimization ◽  
Robust Design ◽  
Optimization Problem ◽  
Robust Design Optimization ◽  
Design Parameters ◽  
Input Uncertainty ◽  
Single Level ◽  
Output Uncertainty ◽  
Gp Model

Many engineering design and industrial manufacturing applications are tasked with finding optimum designs while dealing with uncertainty in the design parameters. The performance or quality of the design may be sensitive to the input variation, making it difficult to optimize. Probabilistic and robust design optimization methods are used in these scenarios to find the designs that will perform best under the presence of known input uncertainty. Robust design optimization algorithms often require a two-level optimization problem (double-loop) to find a solution. The design optimization outer-loop repeatedly calls a series of inner loops that calculate uncertainty measures of the outputs. This nested optimization problem is computationally expensive and can sometimes render the task infeasible for practical engineering robust design problems. This paper details a single-level metamodel-assisted approach for probabilistic and robust design. An enhanced Gaussian Process (GP) metamodel formulation is used to provide exact values of output uncertainty in the presence of uncertain inputs. The GP model utilizes a squared-exponential kernel function and assumes normally distributed input uncertainty. These two factors together allow for an exact calculation of the first and second moments of the marginal predictive distribution. Predictions of output uncertainty are directly calculated, creating an efficient single-level robust optimization problem. We demonstrate the effectiveness of the single-level GP-assisted robust design approach on multiple engineering example problems, including a beam vibration problem, a cantilevered beam with multiple constraints, and a robust autonomous aircraft flight controller design problem. For the optimization problems investigated in this study, the single-level framework found the robust optimum with a 99.9% savings in function evaluations over the standard two-level approach.

scholarly journals Robust Design Optimization in Computational Mechanics

2008 ◽  
Vol 75 (2) ◽  
Author(s):  
E. Capiez-Lernout ◽  
C. Soize
Keyword(s):  
Cost Function ◽  
Design Optimization ◽  
Robust Design ◽  
Stochastic System ◽  
Optimization Problem ◽  
Probabilistic Approach ◽  
Robust Design Optimization ◽  
Design Parameters ◽  
Random Response ◽  
Numerical Application

The motivation of this paper is to propose a methodology for analyzing the robust design optimization problem of complex dynamical systems excited by deterministic loads but taking into account model uncertainties and data uncertainties with an adapted nonparametric probabilistic approach, whereas only data uncertainties are generally considered in the literature by using a parametric probabilistic approach. The possible designs are represented by a numerical finite element model whose design parameters are deterministic and belong to an admissible set. The optimization problem is formulated for the stochastic system as the minimization of a cost function associated with the random response of the stochastic system including the variability of the stochastic system induced by uncertainties and the bias corresponding to the distance of the mean random response to a given target. The gradient and the Hessian of the cost function with respect to the design parameters are explicitly calculated. The complete theory and a numerical application are presented.

A FRAMEWORK FOR CAPTURING DEGRADATION BEHAVIOR IN RELIABILITY-BASED ROBUST DESIGN OPTIMIZATION

2011 ◽  
Vol 18 (06) ◽  
pp. 531-554 ◽  
Author(s):  
OM PRAKASH YADAV ◽  
SUNIL S. BHAMARE ◽  
AJAY PAL SINGH RATHORE
Keyword(s):  
Design Optimization ◽  
Robust Design ◽  
Degradation Process ◽  
Development Stage ◽  
Robust Design Optimization ◽  
Design Parameters ◽  
Leaf Spring ◽  
Degradation Behavior ◽  
Multi Objective ◽  
Target Values

The increasing customer awareness and global competition have forced manufacturers to capture the entire life cycle issues during product design and development stage. The thorough understanding of product behavior (degradation process) and various uncertainties associated with product performance is paramount to produce reliable and robust design. This paper proposes a multi-objective framework for reliability-based robust design optimization, which captures degradation behavior of quality characteristics to provide optimal design parameters. The objective function of the multi-objective optimization problem is defined as quality loss function considering both desirable and undesirable deviations between target values and the actual results. The degradation behavior is captured by using empirical model to estimate amount of degradation accumulated in time t. The applicability of the proposed methodology is demonstrated by considering a leaf spring design problem.

Robust Design Optimization by Adaptive-Sparse Polynomial Dimensional Decomposition

2016 ◽  
Author(s):  
Xuchun Ren ◽  
Sharif Rahman
Keyword(s):  
Design Optimization ◽  
Robust Design ◽  
Large Scale ◽  
Design Sensitivity ◽  
Robust Design Optimization ◽  
Score Functions ◽  
Design Sensitivities ◽  
Sparse Polynomial ◽  
Dimensional Decomposition ◽  
Polynomial Dimensional Decomposition

This work proposes a new methodology for robust design optimization (RDO) of complex engineering systems. The method, capable of solving large-scale RDO problems, involves (1) an adaptive-sparse polynomial dimensional decomposition (AS-PDD) for stochastic moment analysis of a high-dimensional stochastic response, (2) a novel integration of score functions and AS-PDD for design sensitivity analysis, and (3) a multi-point design process, facilitating standard gradient-based optimization algorithms. Closed-form formulae are developed for first two moments and their design sensitivities. The method allow that both the stochastic moments and their design sensitivities can be concurrently determined from a single stochastic simulation or analysis. Precisely for this reason, the multi-point framework of the proposed method affords the ability of solving industrial-scale problems with large design spaces. The robust shape optimization of a three-hole bracket was accomplished, demonstrating the efficiency of the new method to solve industry-scale RDO problems.

Gradient-based design robustness measure for robust geotechnical design

2014 ◽  
Vol 51 (11) ◽  
pp. 1331-1342 ◽  
Author(s):  
Wenping Gong ◽  
Sara Khoshnevisan ◽  
C. Hsein Juang
Keyword(s):  
Design Optimization ◽  
Robust Design ◽  
Cost Efficiency ◽  
Robust Design Optimization ◽  
System Response ◽  
Robustness Measure ◽  
Gradient Based ◽  
Geotechnical Design ◽  
Safety Constraint ◽  
Noise Factors

This paper presents a gradient-based robustness measure for robust geotechnical design (RGD) that considers safety, design robustness, and cost efficiency simultaneously. In the context of robust design, a design is deemed robust if the system response of concern is insensitive, to a certain degree, to the variation of noise factors (i.e., uncertain geotechnical parameters, loading parameters, construction variation, and model biases or errors). The key to a robust design is a quantifiable robustness measure with which the robust design optimization can be effectively and efficiently implemented. Based on the developed gradient-based robustness measure, a robust design optimization framework is proposed. In this framework, the design (safety) constraint is analyzed using advanced first-order second-moment (AFOSM) method, considering the variation in the noise factors. The design robustness, in terms of sensitivity index (SI), is evaluated using the normalized gradient of the system response to the noise factors, which can be efficiently computed from the by-product of AFOSM analysis. Within the proposed framework, robust design optimization is performed with two objectives, design robustness and cost efficiency, while the design (safety) constraint is satisfied by meeting a target reliability index. Generally, cost efficiency and design robustness are conflicting objectives and the robust design optimization yields a Pareto front, which reveals a tradeoff between the two objectives. Through an illustrative example of a shallow foundation design, the effectiveness and significance of this new robust design approach is demonstrated.

Adaptive Refined-Model-Based Approach for Robust Design Optimization

2018 ◽  
pp. 19-43
Author(s):  
Tanmoy Chatterjee ◽  
Rajib Chowdhury
Keyword(s):  
Design Optimization ◽  
Robust Design ◽  
Large Scale ◽  
Model Building ◽  
Kriging Model ◽  
Robust Design Optimization ◽  
Engineering Systems ◽  
Selection Scheme ◽  
Meta Model ◽  
Systems Implementation

Robust design optimization (RDO) has been noteworthy in realizing optimal design of engineering systems in presence of uncertainties. However, computations involved in RDO prove to be intensive for real-time applications. For addressing such issues, a meta-model-assisted RDO framework has been proposed. It has been further observed in such approximation-based RDO frameworks that accuracy of the meta-model is an important factor and even slight deviation in intermediate iterations may eventually lead to false optima. Therefore, two-tier improvement has been incorporated within existing Kriging model so as to ensure accurate approximation of response quantities. Firstly, the trend portion has been refined so that the model is capable of approximating higher order non-linearity. Secondly, a sequential basis selection scheme has been merged during model building, which reduces computational complexity significantly in case of large-scale systems. Implementation of the proposed approach in a few examples clearly illustrates its potential for further complex problems.

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