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.

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 Design Optimization With an Uncertain Vibroacoustic Model

2008 ◽  
Vol 130 (2) ◽  
Author(s):  
E. Capiez-Lernout ◽  
C. Soize
Keyword(s):  
Numerical Model ◽  
Design Optimization ◽  
Optimization Problem ◽  
Acoustic Pressure ◽  
Design Parameters ◽  
Internal Cavity ◽  
Admissible Set ◽  
Acoustic Source ◽  
Model Uncertainties ◽  
Numerical Application

This paper deals with the design optimization problem of a structural-acoustic system in the presence of uncertainties. The uncertain vibroacoustic numerical model is constructed by using a recent nonparametric probabilistic model, which takes into account model uncertainties and data uncertainties. The formulation of the design optimization problem includes the effect of uncertainties and consists in minimizing a cost function with respect to an admissible set of design parameters. The numerical application consists in designing an uncertain master structure in order to minimize the acoustic pressure in a coupled internal cavity, which is assumed to be deterministic and excited by an acoustic source. The results of the design optimization problem, solved with and without the uncertain numerical model, show significant differences.

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.

scholarly journals Robust design optimization of a renewable-powered demand with energy storage using imprecise probabilities

2021 ◽  
Vol 238 ◽  
pp. 10004
Author(s):  
Diederik Coppitters ◽  
Ward De Paepe ◽  
Francesco Contino
Keyword(s):  
Design Optimization ◽  
Robust Design ◽  
Effective Action ◽  
Electricity Price ◽  
Robust Design Optimization ◽  
Design Parameters ◽  
Imprecise Probabilities ◽  
Levelized Cost Of Electricity ◽  
Cost Of Electricity ◽  
Levelized Cost

During renewable energy system design, parameters are generally fixed or characterized by a precise distribution. This leads to a representation that fails to distinguish between uncertainty related to natural variation (i.e. future, aleatory uncertainty) and uncertainty related to lack of data (i.e. present, epistemic uncertainty). Consequently, the main driver of uncertainty and effective guidelines to reduce the uncertainty remain undetermined. To assess these limitations on a grid-connected household supported by a photovoltaic-battery system, we distinguish between present and future uncertainty. Thereafter, we performed a robust design optimization and global sensitivity analysis. This paper provides the optimized designs, the main drivers of the variation in levelized cost of electricity and the effect of present uncertainty on these drivers. To reduce the levelized cost of electricity variance for an optimized photovoltaic array and optimized photovoltaic-battery design, improving the determination of the electricity price for every specific scenario is the most effective action. For the photovoltaic-battery robust design, the present uncertainty on the prediction accuracy of the electricity price should be addressed first, before the most effective action to reduce the levelized cost of electricity variance can be determined. Future work aims at the integration of a heat demand and hydrogen-based energy systems.

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