Worst case propagated uncertainty of multidisciplinary systems in robust design optimization

Gu, Xiaoyu; Renaud, John E.; Batill, Stephen M.; Brach, Raymond M.; Budhiraja, Amarjit

doi:10.1007/s001580050148

Cited by 122 publications

(54 citation statements)

References 7 publications

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“…When these works were published, design optimization with stochastic computational model was not still really possible for large scale multiscale computational models. The applications that have been published (see for instance [1,5,11,12,16,22,29] and also [35,54,57,68,70,72,80,99,96]) were devoted to optimization problems under uncertainties for which the computational models had a reasonable number of degrees of freedom, for which the optimizers were based on the use of relatively classical optimization algorithms and/or the introduction of approximations such as surface responses and surrogate models.…”

Section: Stochastic Modeling Of Biological Tissuesmentioning

confidence: 99%

Design optimization under uncertainties of a mesoscale implant in biological tissues using a probabilistic learning algorithm

Soize

2017

Comput Mech

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This paper deals with the optimal design of a titanium mesoscale implant in a cortical bone for which the apparent elasticity tensor is modeled by a non-Gaussian random field at mesoscale, which has been experimentally identified. The external applied forces are also random. The design parameters are geometrical dimensions related to the geometry of the implant. The stochastic elastostatic boundary value problem is discretized by the finite element method. The objective function and the constraints are related to normal, shear, and von Mises stresses inside the cortical bone. The constrained nonconvex optimization problem in presence of uncertainties is solved by using a probabilistic learning algorithm that allows for considerably reducing the numerical cost with respect to the classical approaches.

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Section: Stochastic Modeling Of Biological Tissuesmentioning

confidence: 99%

Design optimization under uncertainties of a mesoscale implant in biological tissues using a probabilistic learning algorithm

Soize

2017

Comput Mech

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“…Additionally, the propagation of uncertainties associated with precision errors of inputs and bias errors of disciplinary analysis have been studied by investigating the worst case uncertainty. The method of worst case estimation of uncertainty is then integrated with a robust optimization framework to obtain robust designs 35 . Reliability Based Design Optimization (RBDO) also provides single-level and multi-level computational methodologies for the mitigation of uncertainties and achieving robust designs [36][37][38] .…”

Section: Figure 3 Solutions Superior To the Nash Equilibriummentioning

confidence: 99%

Decentralized Design Under Uncertainty: Investigating the Impact of Designer Mistakes

Gurnani¹,

Lewis²

2006

11th AIAA/ISSMO Multidisciplinary Analysis and Optimization Conference

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The design of products and processes within a decentralized design framework requires different design teams or distributed subsystems to solve their local optimization problems and pass their optimal designs to the other subsystems. It is common for subsystems to not cooperate with each other by sharing objective or gradient information and the only information communicated between subsystems is the values of coupled design variables. Non local design variables are treated as constraints in local subsystem optimization. The subsystems iterate by communicating design variable values back and forth until they all converge upon a solution. For subsystems with multiple, conflicting objectives, the converged solution lies at the intersection of the Rational Reaction Set and is called the "Nash Equilibrium". It is known that the Nash Equilibrium solution is rarely Pareto optimal, the ideal solution set for multiobjective optimization problems. A common assumption in design decision making is that the designer makes no errors in the selection of the optimal design in the iterative process. In this paper, a framework for distributed design is presented that preserves the general assumptions of non cooperation between subsystems but models mistakes made by designers in the selection of optimal designs. It is assumed that the designers of the initial decision making subsystem within the decentralized design process make errors in selecting the optimal design. A set based approach is used to model these errors which are then propagated through the design process. Subsystems utilize metamodeling techniques to develop approximations of the non local rational reaction sets which are then used to determine a representation of the non local objective functions. It is seen that solutions from this modified decentralized design framework are better than the Nash Equilibrium. The proposed framework includes concepts from game theory, uncertainty modeling, error propagation, set based design and metamodeling techniques.

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“…The sensitivity-based robust optimization method is modified by implementing a worst-case scenario 10 . The worst-case estimation of propagated uncertainty is developed and applied as an alternative means to the estimate function variations.…”

Section: Moreover By Incorporating a Probabilistic Model For Design mentioning

confidence: 99%

Coupled Systems Design in Probabilistic Environments

Halecki¹,

Lewis²

2002

9th AIAA/ISSMO Symposium on Multidisciplinary Analysis and Optimization

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Worst case propagated uncertainty of multidisciplinary systems in robust design optimization

Cited by 122 publications

References 7 publications

Design optimization under uncertainties of a mesoscale implant in biological tissues using a probabilistic learning algorithm

Design optimization under uncertainties of a mesoscale implant in biological tissues using a probabilistic learning algorithm

Decentralized Design Under Uncertainty: Investigating the Impact of Designer Mistakes

Coupled Systems Design in Probabilistic Environments

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