A General Approach for Robust Optimal Design

1993 ◽  
Vol 115 (1) ◽  
pp. 74-80 ◽  
Author(s):  
A. Parkinson ◽  
C. Sorensen ◽  
N. Pourhassan
Keyword(s):  
Statistical Analysis ◽  
Optimal Design ◽  
Design Optimization ◽  
Design Problem ◽  
Optimization Process ◽  
Worst Case ◽  
Rigorous Approach ◽  
Design Variables ◽  
Robust Optimal Design ◽  
And Control

This paper describes a general, rigorous approach for robust optimal design. The method allows a designer to explicitly consider and control, as an integrated part of the optimization process, the effects of variability in design variables and parameters on a design. Variability is defined in terms of tolerances which bracket the variation of fluctuating quantities. A designer can apply tolerances to any model input and can analyze how the tolerances affect the design using either a worst case or statistical analysis. As part of design optimization, the designer can apply the method to find an optimum that will remain feasible when subject to variation, and/or the designer can minimize or constrain the effects of tolerances as one of the objectives or constraints of the design problem.

Robust Optimal Design for Worst-Case Tolerances

1994 ◽  
Vol 116 (4) ◽  
pp. 1019-1025 ◽  
Author(s):  
G. Emch ◽  
A. Parkinson
Keyword(s):  
Nonlinear Programming ◽  
Optimal Design ◽  
Worst Case ◽  
New Approach ◽  
Robust Designs ◽  
Design Variables ◽  
Robust Optimal Design ◽  
Programming Techniques ◽  
Engineering Models ◽  
Analytical Tools

Engineering models can and should be used to understand the effects of variability on a design. When variability is ignored, brittle designs can result that will not function properly or that will fail in service. By contrast, robust designs function properly even when subjected to off-nominal conditions. There is a need for better analytical tools to help engineers develop robust designs. In this paper we present a new approach for developing designs that are robust to variability induced by worst-case tolerances. An advantage of this approach is that tolerances may be placed on any or all model inputs, whether design variables or parameters. The method adapts nonlinear programming techniques in order to determine how a design should be modified to account for variability. We tested the method under relatively severe conditions on 13 problems, with excellent results. Using this approach, a designer can account for the effects of worst-case tolerances, making it possible to build robustness into an engineering design.

Tolerances and Robustness in Engineering Design Optimization

1990 ◽  
Author(s):  
Alan Parkinson ◽  
Carl Sorensen ◽  
Joseph Free ◽  
Bradley Canfield
Keyword(s):  
Statistical Analysis ◽  
Optimal Design ◽  
Design Optimization ◽  
Engineering Design ◽  
Tolerance Allocation ◽  
Worst Case ◽  
Engineering Design Optimization ◽  
New Strategy ◽  
Transmitted Variation

Abstract This paper describes a new strategy for incorporating tolerances as part of engineering design optimization. The tolerance problem is defined in a general way that allows for tolerances on all model variables and parameters and includes worst case and statistical analysis. Two methods are described for taking tolerances into account during optimization such that an optimal design will remain feasible despite fluctuations in variables or parameters. Methods are also presented for directly controlling transmitted variation, and a framework for optimal tolerance allocation is proposed.

Shape-design optimization of hull structures considering thermal deformation

2013 ◽  
Vol 228 (13) ◽  
pp. 2266-2277
Author(s):  
Myung-Jin Choi ◽  
Min-Geun Kim ◽  
Seonho Cho
Keyword(s):  
Optimal Design ◽  
Design Optimization ◽  
Thermal Deformation ◽  
Parametric Design ◽  
Optimization Method ◽  
Optimization Process ◽  
Design Parameters ◽  
Shape Design ◽  
Shape Design Optimization ◽  
Modified Method

We developed a shape-design optimization method for the thermo-elastoplasticity problems that are applicable to the welding or thermal deformation of hull structures. The point is to determine the shape-design parameters such that the deformed shape after welding fits very well to a desired design. The geometric parameters of curved surfaces are selected as the design parameters. The shell finite elements, forward finite difference sensitivity, modified method of feasible direction algorithm and a programming language ANSYS Parametric Design Language in the established code ANSYS are employed in the shape optimization. The objective function is the weighted summation of differences between the deformed and the target geometries. The proposed method is effective even though new design variables are added to the design space during the optimization process since the multiple steps of design optimization are used during the whole optimization process. To obtain the better optimal design, the weights are determined for the next design optimization, based on the previous optimal results. Numerical examples demonstrate that the localized severe deviations from the target design are effectively prevented in the optimal design.

Optimal Design and Control of a Rotating Flexible Arm With ACLD Treatment

Aerospace ◽  
2003 ◽  
Author(s):  
E. H. K. Fung ◽  
D. T. W. Yau
Keyword(s):  
Optimal Control ◽  
Optimal Design ◽  
Shear Modulus ◽  
Optimal Control Problem ◽  
Control Problem ◽  
Performance Index ◽  
Flexible Arm ◽  
Design Variables ◽  
And Control ◽  
Optimal Design And Control

In this paper, the optimal design and control of a rotating clamped-free flexible arm with fully covered active constrained layer damping (ACLD) treatment are studied. The arm is rotating in a horizontal plane in which the gravitational effect and rotary inertia are neglected. The piezo-sensor voltage is fed back to the piezo-actuator via a PD controller. Finite element method (FEM) in conjunction with Hamilton’s principle is used to derive the governing equations of motion of the system which takes into account the effects of centrifugal stiffening due to the rotation of the beam. The damping behavior of the viscoelastic material (VEM) is modeled using the complex shear modulus method. The design optimization objective is to maximize the sum of the first three open-loop modal damping ratios divided by the weight of the damping treatment. A genetic algorithm, differential evolution (DE), combined with a gradient-based algorithm, sequential quadratic programming (SQP), is used to determine the optimal design variables such as the thickness and storage shear modulus of the VEM core. Next for the determined optimal design variables, the optimal control problem is performed to determine the optimal control gains which minimize a quadratic performance index. The control performance index is normalized with respect to the initial conditions and the optimal control problem is posed to solve a min-max optimization problem. The results of this study will be useful in the optimal design and control of adaptive and smart rotating structures such as rotorcraft blades or robotic arms.

scholarly journals Reliability-Based Robust Design Optimization of Structures Considering Uncertainty in Design Variables

2015 ◽  
Vol 2015 ◽  
pp. 1-8 ◽  
Author(s):  
Shujuan Wang ◽  
Qiuyang Li ◽  
Gordon J. Savage
Keyword(s):  
Sensitivity Analysis ◽  
Design Optimization ◽  
Robust Design ◽  
Structural Reliability ◽  
Computational Cost ◽  
Optimization Process ◽  
Robust Design Optimization ◽  
Global Approximation ◽  
Design Variables ◽  
Uncertainty In Design

This paper investigates the structural design optimization to cover both the reliability and robustness under uncertainty in design variables. The main objective is to improve the efficiency of the optimization process. To address this problem, a hybrid reliability-based robust design optimization (RRDO) method is proposed. Prior to the design optimization, the Sobol sensitivity analysis is used for selecting key design variables and providing response variance as well, resulting in significantly reduced computational complexity. The single-loop algorithm is employed to guarantee the structural reliability, allowing fast optimization process. In the case of robust design, the weighting factor balances the response performance and variance with respect to the uncertainty in design variables. The main contribution of this paper is that the proposed method applies the RRDO strategy with the usage of global approximation and the Sobol sensitivity analysis, leading to the reduced computational cost. A structural example is given to illustrate the performance of the proposed method.

Robust MDSDO for Co-Design of Stochastic Dynamic Systems

2019 ◽  
Vol 142 (1) ◽  
Author(s):  
Saeed Azad ◽  
Michael J. Alexander-Ramos
Keyword(s):  
Dynamic System ◽  
Design Optimization ◽  
System Design ◽  
Design Problem ◽  
Integrated Design ◽  
Problem Formulation ◽  
Robust Design Optimization ◽  
Design Problems ◽  
Embodiment Design ◽  
And Control

Abstract Optimization of dynamic engineering systems generally requires problem formulations that account for the coupling between embodiment design and control system design simultaneously. Such formulations are commonly known as combined optimal design and control (co-design) problems, and their application to deterministic systems is well established in the literature through a variety of methods. However, an issue that has not been addressed in the co-design literature is the impact of the inherent uncertainties within a dynamic system on its integrated design solution. Accounting for these uncertainties transforms the standard, deterministic co-design problem into a stochastic one, thus requiring appropriate stochastic optimization approaches for its solution. This paper serves as the starting point for research on stochastic co-design problems by proposing and solving a novel problem formulation based on robust design optimization (RDO) principles. Specifically, a co-design method known as multidisciplinary dynamic system design optimization (MDSDO) is used as the basis for an RDO problem formulation and implementation. The robust objective and inequality constraints are computed per usual as functions of their first-order-approximated means and variances, whereas analysis-based equality constraints are evaluated deterministically at the means of the random decision variables. The proposed stochastic co-design problem formulation is then implemented for two case studies, with the results indicating the importance of the robust approach on the integrated design solutions and performance measures.

Multidisciplinary Design Optimization of Actuator Arrangements, Lay-Up Configurations and Control Systems for Smart Laminated Composite Structures

2010 ◽  
Author(s):  
Shinya Honda ◽  
Itsuro Kajiwara ◽  
Yoshihiro Narita
Keyword(s):  
Design Optimization ◽  
Control Systems ◽  
Multidisciplinary Design Optimization ◽  
Composite Structures ◽  
Vibration Suppression ◽  
Laminated Composite ◽  
Piezoelectric Actuators ◽  
Multidisciplinary Design ◽  
Design Variables ◽  
And Control

Structures and control systems of smart laminated composites consisting of graphite-epoxy composites and piezoelectric actuators are designed optimally for the vibration suppression. Placements of piezoelectric actuators, lay-up configurations of laminated composite plates and the H2 control system are employed as design variables and are optimized simultaneously by a simple genetic algorithm (SGA). An objective function is H2 performance with assuming that the state feedback is available. A multidisciplinary design optimization is performed with above three design variables and then the output feedback system is reconstructed with the dynamic compensator based on the linear matrix inequality (LMI) approach. Optimization results show that the optimized smart composite successfully realizes vibration suppression of the system and it is confirmed that the present multidisciplinary design optimization technique is quite efficient to the smart composites.

Trajectory Pattern Based Simultaneous Kinematic and Dynamic Optimal Design of High Speed Manipulators

1996 ◽  
Author(s):  
M. Tai ◽  
J. Rastegar
Keyword(s):  
Optimal Design ◽  
High Speed ◽  
High Performance ◽  
Current Approach ◽  
Operating Conditions ◽  
Control Problems ◽  
Structure And Motion ◽  
Design Variables ◽  
Trajectory Pattern ◽  
And Control

Abstract An integrated structure and motion pattern specific design approach is proposed for optimal design of high speed and accuracy computer controlled machines including robots. The approach is based on the Trajectory Pattern Method (TPM). The current approach to the design of such machines is to assume that the machine will be required to perform more or less any arbitrary and often unrealistic tasks. This assumption nearly always leads to designs based on the worst operating conditions. The proposed trajectory pattern based design methodology presented in this paper stems from a fundamentally new design philosophy. The philosophy behind the proposed approach is that machines in general and ultra-high performance machines in particular must only be designed to perform a class or classes of motions effectively. And that trajectory patterns, i.e., classes of parametric trajectories, exist with which high speed motions can be synthesized with minimal ensuing vibration and control problems. In the proposed approach, given the kinematic structure of the machine, its kinematic and dynamic parameters are optimized simultaneously with the parameters that describe a selected trajectory pattern. The controller parameters may also be included as design variables. In the present study, the optimality criterion employed is based on minimizing the higher harmonic portion of the actuating forces (torques) required for performing the selected class(es) of motion patterns. Trajectories that do not demand high frequency actuating torque harmonics are desirable since they reduce vibration and control problems in high performance systems and reduce settling time. Examples of the application of the proposed approach are presented.

A Sequential Algorithm for Possibility-Based Design Optimization

2006 ◽  
Author(s):  
Jun Zhou ◽  
Zissimos P. Mourelatos
Keyword(s):  
Design Optimization ◽  
Optimization Algorithm ◽  
Computational Cost ◽  
Possibility Theory ◽  
Sequential Optimization ◽  
Sequential Algorithm ◽  
Computationally Efficient ◽  
Worst Case ◽  
Reliability Based Design ◽  
Design Variables

Deterministic optimal designs that are obtained without taking into account uncertainty/variation are usually unreliable. Although reliability-based design optimization accounts for variation, it assumes that statistical information is available in the form of fully defined probabilistic distributions. This is not true for a variety of engineering problems where uncertainty is usually given in terms of interval ranges. In this case, interval analysis or possibility theory can be used instead of probability theory. This paper shows how possibility theory can be used in design and presents a computationally efficient sequential optimization algorithm. After, the fundamentals of possibility theory and fuzzy measures are described, a double-loop, possibility-based design optimization algorithm is presented where all design constraints are expressed possibilistically. The algorithm handles problems with only uncertain or a combination of random and uncertain design variables and parameters. In order to reduce the high computational cost, a sequential algorithm for possibility-based design optimization is presented. It consists of a sequence of cycles composed of a deterministic design optimization followed by a set of worst-case reliability evaluation loops. Two examples demonstrate the accuracy and efficiency of the proposed sequential algorithm.

Structural Topology Design Considering Reliability

2005 ◽  
Vol 297-300 ◽  
pp. 1901-1906 ◽  
Author(s):  
Seung Jae Min ◽  
Seung Hyun Bang
Keyword(s):  
Topology Optimization ◽  
Design Optimization ◽  
Optimization Problem ◽  
Performance Measure ◽  
Topology Design ◽  
Optimization Process ◽  
Programming Algorithm ◽  
Probabilistic Design ◽  
Most Probable Point ◽  
Design Variables

In the design optimization process design variables are selected in the deterministic way though those have uncertainties in nature. To consider variances in design variables reliability-based design optimization problem is formulated by introducing the probability distribution function. The concept of reliability has been applied to the topology optimization based on a reliability index approach or a performance measure approach. Since these approaches, called double-loop singlevariable approach, requires the nested optimization problem to obtain the most probable point in the probabilistic design domain, the time for the entire process makes the practical use infeasible. In this work, new reliability-based topology optimization method is proposed by utilizing single-loop singlevariable approach, which approximates searching the most probable point analytically, to reduce the time cost and dealing with several constraints to handle practical design requirements. The density method in topology optimization including SLP (Sequential Linear Programming) algorithm is implemented with object-oriented programming. To examine uncertainties in the topology design of a structure, the modulus of elasticity of the material and applied loadings are considered as probabilistic design variables. The results of a design example show that the proposed method provides efficiency curtailing the time for the optimization process and accuracy satisfying the specified reliability.

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