Monotonicity Analysis of Taguchi’s Robust Circuit Design Problem

1990 ◽  
Author(s):  
Douglass J. Wilde
Keyword(s):  
Circuit Design ◽  
Design Problem ◽  
Recent Article ◽  
Optimization Problem ◽  
Algebraic Function ◽  
Necessary Condition ◽  
Control Range ◽  
Design Variables ◽  
Numerical Iteration ◽  
Monotonicity Analysis

Abstract A recent article showed how to formulate Taguchi’s robust circuit design problem rigorously as an optimization problem. A necessary condition for optimality was found to be that the control range be centered about the target value. This generates a constraint on the two design variables which cannot be solved for either variable. The present article shows that by approximating this unsolvable constraint with a simpler constraint that is solvable, one variable can be eliminated and the problem reduced to an unconstrained one in a single variable. Since this reduced objective turns out to be monotonic in the remaining design variable, its optimum value must be at the limit of its range. The corresponding optimum value of the other variable is then determined exactly from the true, not approximate, constraint. Since no model construction, experimentation, statistical analysis or numerical iteration is needed, this procedure is recommended whenever the input-output relation is known to be a monotonic algebraic function.

Monotonicity Analysis of Taguchi’s Robust Circuit Design Problem

1992 ◽  
Vol 114 (4) ◽  
pp. 616-619 ◽  
Author(s):  
D. J. Wilde
Keyword(s):  
Circuit Design ◽  
Design Problem ◽  
Optimization Problem ◽  
Algebraic Function ◽  
The Other ◽  
Necessary Condition ◽  
Control Range ◽  
Design Variables ◽  
Numerical Iteration ◽  
Monotonicity Analysis

Taguchi’s robust circuit design problem can be formulated rigorously as an optimization problem. A necessary condition for optimality is that the control range be centered about the target value. This generates a constraint on the two design variables which cannot be solved for either variable. The present article shows that by approximating this unsolvable constraint with a simpler constraint that is solvable, one variable can be eliminated and the problem reduced to an unconstrained one in a single variable. Since this reduced objective turns out to be monotonic in the remaining design variable, its optimum value must be at the limit of its range. The corresponding optimum value of the other variable is then determined exactly from the true, not approximate, constraint. Since no model construction, experimentation, statistical analysis, or numerical iteration is needed, this procedure is recommended whenever the input-output relation is known to be a monotonic algebraic function.

Activity Analysis: Simplifying Optimal Design Problems Through Qualitative Partitioning

1995 ◽  
Author(s):  
Brian C. Williams ◽  
Jonathan Cagan
Keyword(s):  
Numerical Analysis ◽  
Optimal Design ◽  
Design Problem ◽  
Optimization Problem ◽  
Activity Analysis ◽  
Design Problems ◽  
Gradient Based ◽  
Monotonicity Analysis

Abstract Activity analysis is introduced as a means to strategically cut away subspaces of a design problem that can quickly be ruled out as suboptimal. This results in focused regions of the space in which additional symbolic or numerical analysis can take place. Activity analysis is derived from a qualitative abstraction of the Karush-Kuhn-Tucker conditions of optimality, used to partition an optimization problem into regions which are nonstationary and qualitatively stationary (qstationary). Activity analysis draws from the fields of gradient-based optimization, conflict-based approaches of combinatorial satisficing search, and monotonicity analysis.

scholarly journals Topology optimization incorporating external variables with metamodeling

2020 ◽  
Vol 62 (5) ◽  
pp. 2455-2466
Author(s):  
Shun Maruyama ◽  
Shintaro Yamasaki ◽  
Kentaro Yaji ◽  
Kikuo Fujita
Keyword(s):  
Topology Optimization ◽  
Design Problem ◽  
Optimization Problem ◽  
Design Domain ◽  
Material Distribution ◽  
Topology Optimization Problem ◽  
Design Variables ◽  
External Variables ◽  
Multi Level ◽  
Dependence Relationship

Abstract The objective of conventional topology optimization is to optimize the material distribution for a prescribed design domain. However, solving the topology optimization problem strongly depends on the settings specified by the designer for the shape of the design domain or their specification of the boundary conditions. This contradiction indicates that the improvement of structures should be achieved by optimizing not only the material distribution but also the additional design variables that specify the above settings. We refer to the additional design variables as external variables. This paper presents our work relating to solving the design problem of topology optimization incorporating external variables. The approach we follow is to formulate the design problem as a multi-level optimization problem by focusing on the dominance-dependence relationship between external variables and material distribution. We propose a framework to solve the optimization problem utilizing the multi-level formulation and metamodeling. The metamodel approximates the relationship between the external variables and the performance of the corresponding optimized material distribution. The effectiveness of the framework is demonstrated by presenting three examples.

Shape Optimization of Hydraulic Structures: an Example of an Optimum Design of a Fish Passage

10.29007/2k64 ◽  
2018 ◽  
Author(s):  
Pat Prodanovic ◽  
Cedric Goeury ◽  
Fabrice Zaoui ◽  
Riadh Ata ◽  
Jacques Fontaine ◽  
...  
Keyword(s):  
Numerical Model ◽  
Shape Optimization ◽  
Objective Function ◽  
Optimum Design ◽  
Optimization Problem ◽  
A Priori ◽  
Coupled System ◽  
Fish Passage ◽  
Hydraulic Structures ◽  
Design Variables

This paper presents a practical methodology developed for shape optimization studies of hydraulic structures using environmental numerical modelling codes. The methodology starts by defining the optimization problem and identifying relevant problem constraints. Design variables in shape optimization studies are configuration of structures (such as length or spacing of groins, orientation and layout of breakwaters, etc.) whose optimal orientation is not known a priori. The optimization problem is solved numerically by coupling an optimization algorithm to a numerical model. The coupled system is able to define, test and evaluate a multitude of new shapes, which are internally generated and then simulated using a numerical model. The developed methodology is tested using an example of an optimum design of a fish passage, where the design variables are the length and the position of slots. In this paper an objective function is defined where a target is specified and the numerical optimizer is asked to retrieve the target solution. Such a definition of the objective function is used to validate the developed tool chain. This work uses the numerical model TELEMAC- 2Dfrom the TELEMAC-MASCARET suite of numerical solvers for the solution of shallow water equations, coupled with various numerical optimization algorithms available in the literature.

Efficient Sensitivity Analysis for Multibody Dynamics Systems Using an Iterative Steps Method With Application in Topology Optimization

2011 ◽  
Author(s):  
Guang Dong ◽  
Zheng-Dong Ma ◽  
Gregory Hulbert ◽  
Noboru Kikuchi ◽  
Sudhakar Arepally ◽  
...  
Keyword(s):  
Sensitivity Analysis ◽  
Topology Optimization ◽  
Multibody Dynamics ◽  
Optimization Problem ◽  
Finite Difference Methods ◽  
Analysis Method ◽  
Topology Optimization Problem ◽  
Design Variables ◽  
Sensitivity Analysis Method ◽  
Rotational Motions

Efficient and reliable sensitivity analyses are critical for topology optimization, especially for multibody dynamics systems, because of the large number of design variables and the complexities and expense in solving the state equations. This research addresses a general and efficient sensitivity analysis method for topology optimization with design objectives associated with time dependent dynamics responses of multibody dynamics systems that include nonlinear geometric effects associated with large translational and rotational motions. An iterative sensitivity analysis relation is proposed, based on typical finite difference methods for the differential algebraic equations (DAEs). These iterative equations can be simplified for specific cases to obtain more efficient sensitivity analysis methods. Since finite difference methods are general and widely used, the iterative sensitivity analysis is also applicable to various numerical solution approaches. The proposed sensitivity analysis method is demonstrated using a truss structure topology optimization problem with consideration of the dynamic response including large translational and rotational motions. The topology optimization problem of the general truss structure is formulated using the SIMP (Simply Isotropic Material with Penalization) assumption for the design variables associated with each truss member. It is shown that the proposed iterative steps sensitivity analysis method is both reliable and efficient.

Engine Mount Optimization for Vibration Isolation in Motorcycles

2006 ◽  
Author(s):  
Sudhir Kaul ◽  
Anoop K. Dhingra ◽  
Timothy G. Hunter
Keyword(s):  
Optimization Problem ◽  
Vibration Isolation ◽  
Total Force ◽  
Engine Mounts ◽  
The Road ◽  
Design Variables ◽  
Swing Arm ◽  
Engine Mount ◽  
Six Degree Of Freedom

This paper presents a comprehensive model to capture the dynamics of a motorcycle system in order to evaluate the quality of vibration isolation. The two main structural components in the motorcycle assembly - the frame and the swing-arm - are modeled using reduced order finite element models; the power-train assembly is modeled as a six degree-of-freedom (DOF) rigid body connected to the frame through the engine mounts and to the swing-arm through a shaft assembly. The engine mounts are modeled as tri-axial spring-damper systems. Models of the front-end assembly as well as front and rear tires are also included in the overall model. The complete vehicle model is used to solve the engine mount optimization problem so as to minimize the total force transmitted to the frame while meeting packaging and other side constraints. The mount system parameters - stiffness, position and orientation vectors - are used as design variables for the optimization problem. The imposed loads include forces and moments due to engine imbalance as well as loads transmitted due to irregularities in the road surface through the tire patch.

Trajectory Optimization Applied to Space Rendezvous

2013 ◽  
Vol 756-759 ◽  
pp. 3466-3470
Author(s):  
Xu Min Song ◽  
Qi Lin
Keyword(s):  
Simulated Annealing ◽  
Optimization Model ◽  
Trajectory Optimization ◽  
Optimization Problem ◽  
Optimization Method ◽  
Nonlinear Constraints ◽  
Design Variables ◽  
Adaptive Simulated Annealing ◽  
Simulation Results

The trajcetory plan problem of spece reandezvous mission was studied in this paper using nolinear optimization method. The optimization model was built based on the Hills equations. And by analysis property of the design variables, a transform was put forward , which eliminated the equation and nonlinear constraints as well as decreaseing the problem dimensions. The optimization problem was solved using Adaptive Simulated Annealing (ASA) method, and the rendezvous trajectory was designed.The method was validated by simulation results.

Bending Stiffener Design Through Structural Optimization

2009 ◽  
Author(s):  
Rafael Loureiro Tanaka ◽  
Lauro Massao Yamada da Silveira ◽  
Joa˜o Paulo Zi´lio Novaes ◽  
Eduardo Esterqui de Barros ◽  
Clo´vis de Arruda Martins
Keyword(s):  
Optimization Problem ◽  
Design Procedure ◽  
Complex Task ◽  
Load Case ◽  
Shear Forces ◽  
Design Variables ◽  
Curvilinear Coordinate ◽  
Regular Design ◽  
Curvature Deformation ◽  
Flexible Risers

Bending stiffeners are very important ancillary equipments of umbilicals or flexible risers, since they protect the lines from overbending. Their design however is a complex task, since many load cases must be taken into account; the structure itself has a section that is variable with curvilinear coordinate. To aid the designer in this task, optimization algorithms can be used to automate the search for the best design. In this work an optimization algorithm is applied to the design of the bending stiffener. First, a bending stiffener model is created, which is capable of simulating different load case conditions and provide, as output, results of interest such as maximum curvature, deformation along the stiffener, shear forces and so on. Then, a bending stiffener design procedure is written as an optimization problem and, for that, objective function, restrictions and design variables defined. Study cases were performed, comparing a regular design with its optimized counterpart, under varying conditions.

Solving a Two-stage Supply Chain Network Design Problem with Fixed Costs by a Hybrid Genetic Algorithm

2021 ◽  
Author(s):  
Ovidiu Cosma ◽  
Petrică C Pop ◽  
Cosmin Sabo
Keyword(s):  
Genetic Algorithm ◽  
Supply Chain ◽  
Network Design ◽  
Design Problem ◽  
Optimization Problem ◽  
Hybrid Genetic Algorithm ◽  
Network Design Problem ◽  
Supply Chain Network Design ◽  
Supply Chain Network ◽  
Fixed Costs

Abstract In this paper we investigate a particular two-stage supply chain network design problem with fixed costs. In order to solve this complex optimization problem, we propose an efficient hybrid algorithm, which was obtained by incorporating a linear programming optimization problem within the framework of a genetic algorithm. In addition, we integrated within our proposed algorithm a powerful local search procedure able to perform a fine tuning of the global search. We evaluate our proposed solution approach on a set of large size instances. The achieved computational results prove the efficiency of our hybrid genetic algorithm in providing high-quality solutions within reasonable running-times and its superiority against other existing methods from the literature.

Frequency optimization of laminated functionally graded carbon nanotube reinforced composite quadrilateral plates using smoothed FEM and evolution algorithm

2017 ◽  
Vol 52 (14) ◽  
pp. 1971-1986 ◽  
Author(s):  
T Vo-Duy ◽  
T Truong-Thi ◽  
V Ho-Huu ◽  
T Nguyen-Thoi
Keyword(s):  
Carbon Nanotube ◽  
Optimization Problem ◽  
Volume Fraction ◽  
Differential Evolution Algorithm ◽  
Composite Plates ◽  
Functionally Graded ◽  
Optimization Approach ◽  
Reinforced Composite ◽  
Design Variables ◽  
Evolution Algorithm

The paper presents an efficient numerical optimization approach to deal with the optimization problem for maximizing the fundamental frequency of laminated functionally graded carbon nanotube-reinforced composite quadrilateral plates. The proposed approach is a combination of the cell-based smoothed discrete shear gap method (CS-DSG3) for analyzing the first natural frequency of the functionally graded carbon nanotube reinforced composite plates and a global optimization algorithm, namely adaptive elitist differential evolution algorithm (aeDE), for solving the optimization problem. The design variables are the carbon nanotube orientation in the layers and constrained in the range of integer numbers belonging to [−900 900]. Several numerical examples are presented to investigate optimum design of quadrilateral laminated functionally graded carbon nanotube reinforced composite plates with various parameters such as carbon nanotube distribution, carbon nanotube volume fraction, boundary condition and number of layers.

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