Mixed Variable Optimization Using Taguchi’s Orthogonal Arrays

1995 ◽  
Author(s):  
H.-W. Chi ◽  
C. L. Bloebaum
Keyword(s):  
Orthogonal Array ◽  
Optimization Problem ◽  
Orthogonal Arrays ◽  
Paper Analysis ◽  
Optimal Designs ◽  
Number Of Factors ◽  
The Mean ◽  
Optimal Material ◽  
Structural Optimization Problem ◽  
Mixed Variable

Abstract Taguchi’s orthogonal arrays for Robust Design are used in this paper in a non-taditional way to solve a mixed continuous-discrete structural optimization problem. The factors of an orthogonal array correspond to the members of a structure and the levels of each factor correspond to the material choices of each member. Based on the number of factors to be studied and the number of levels of each factor, an appropriate orthogonal array is selected for each specific problem. The number of rows of the orthogonal array correspond to the number of experiments (i.e. continuous sizing optimizations) to be conducted. The response of these experiments, which are the weight of the optimal designs corresponding to different material settings, are then used to calculate the mean effect of each factor level. Some possible optimal material settings can then be determined. Three examples are presented in this paper. Analysis using Taguchi’s orthogonal arrays was able to isolate several near optimal or optimal designs. The accuracy and efficiency of the proposed method compared to more traditinoal solution methodologies are also discussed.

On the Prediction of Extremal Material Properties and Optimal Material Distribution for Multiple Loading Conditions

1994 ◽  
Author(s):  
Martin P. Bendsøe ◽  
Alejandro R. Díaz ◽  
Robert Lipton ◽  
John E. Taylor
Keyword(s):  
Material Properties ◽  
Optimization Problem ◽  
Simultaneous Optimization ◽  
Elastic Continuum ◽  
Linear Elastic ◽  
Recent Developments ◽  
Multiple Loading ◽  
Optimal Material ◽  
The Cost ◽  
Structural Optimization Problem

Abstract This paper describes some recent developments that treats the simultaneous optimization of material and structure for minimum compliance. The basic idea is to represent the material properties for a linear elastic continuum in the most general form possible namely as the unrestricted set of elements of positive semi-definite constitutive tensors. The cost of resource is measured through certain invariants of the tensors, here the 2-norm or the trace of the tensors. The advantage of this general formulation is that analytical forms for the optimized material properties can be derived and that effective methods for computational solution can be devised for the resulting reduced structural optimization problem.

Identify Generators for 2k - p Experiments Using Taguchi Orthogonal Arrays

1998 ◽  
Vol 05 (04) ◽  
pp. 403-422
Author(s):  
Chuen-Lung Chen ◽  
Muhammad Arshad Khan ◽  
Chyng-Min Wu
Keyword(s):  
Factorial Design ◽  
Fractional Factorial Design ◽  
Orthogonal Arrays ◽  
Fractional Factorial ◽  
Taguchi Methods ◽  
Optimal Designs ◽  
Simple Tool ◽  
Number Of Factors ◽  
Defining Relation ◽  
Taguchi Orthogonal Arrays

Two-level fractional factorial design is an efficient technique for experiments considering a large number of factors. To evaluate the efficiency and analyze the data for such a design, we need to know the generators for the design, so that, using the generators, we can generate its defining relation and alias structure. Although knowing the generators is important for a two-level fractional factorial design, it is not unusual in actual industrial situations for the generators used in the design to be lost or overlooked while the design is performed. Since Taguchi methods has been widely applied in industry, in this research, an efficient algorithm based on Taguchi orthogonal arrays (OA's) and interaction tables is developed to identify the generators for given designs. Furthermore, with the investigation of the insights of Taguchi OA's and interaction tables, this research may provide ideas for making Taguchi methods a simple tool for developing optimal designs for 2k - p experiments.

An Analytical Model to Predict Optimal Material Properties in the Context of Optimal Structural Design

1994 ◽  
Vol 61 (4) ◽  
pp. 930-937 ◽  
Author(s):  
M. P. Bendsoe ◽  
J. M. Guedes ◽  
R. B. Haber ◽  
P. Pedersen ◽  
J. E. Taylor
Keyword(s):  
Material Properties ◽  
Structural Design ◽  
Optimization Problem ◽  
Existence Of Solutions ◽  
Simultaneous Optimization ◽  
Elastic Continuum ◽  
Linear Elastic ◽  
Optimal Material ◽  
Structural Optimization Problem ◽  
Principal Strains

This paper deals with the simultaneous optimization of material and structure for minimum compliance. Material properties are represented in the most general form possible for a (locally) linear elastic continuum, namely the unrestricted set of elements of positive semi-definite constitutive tensors and cost measures based on certain invariants of the tensors. Analytical forms are derived for the optimized material properties. These results, which apply in general, indicate that the optimized material is orthotropic with the directions of orthotropy following the directions of principal strains. The analysis for optimization of the material leads to a reduced structural optimization problem, for which the existence of solutions can be shown and for which effective methods for computational solution can be devised.

scholarly journals Least-thickness symmetric circular masonry arch of maximum horizontal thrust

2021 ◽  
Author(s):  
Giuseppe Cocchetti ◽  
Egidio Rizzi
Keyword(s):  
Optimization Problem ◽  
Research Work ◽  
Complementary Information ◽  
Masonry Arch ◽  
Collapse Mode ◽  
Hinge Position ◽  
Explicit Representations ◽  
Horizontal Thrust ◽  
Structural Optimization Problem ◽  
Typical Solution

AbstractThis analytical note shall provide a contribution to the understanding of general principles in the Mechanics of (symmetric circular) masonry arches. Within a mainstream of previous research work by the authors (and competent framing in the dedicated literature), devoted to investigate the classical structural optimization problem leading to the least-thickness condition under self-weight (“Couplet-Heyman problem”), and the relevant characteristics of the purely rotational five-hinge collapse mode, new and complementary information is here analytically derived. Peculiar extremal conditions are explicitly inspected, as those leading to the maximum intrinsic non-dimensional horizontal thrust and to the foremost wide angular inner-hinge position from the crown, both occurring for specific instances of over-complete (horseshoe) arches. The whole is obtained, and confronted, for three typical solution cases, i.e., Heyman, “CCR” and Milankovitch instances, all together, by full closed-form explicit representations, and elucidated by relevant illustrations.

Qualitative Knowledge and Manufacturing Considerations in Multidisciplinary Structural Optimization of Hybrid Material Structures

2006 ◽  
Vol 10 ◽  
pp. 143-152 ◽  
Author(s):  
Martin Huber ◽  
Horst Baier
Keyword(s):  
Hybrid Material ◽  
Optimization Problem ◽  
Fuzzy Rule ◽  
Optimal Designs ◽  
Design Parameters ◽  
Optimization Approach ◽  
Structural Level ◽  
Design Problems ◽  
Qualitative Knowledge ◽  
Typical Design

An optimization approach is derived from typical design problems of hybrid material structures, which provides the engineer with optimal designs. Complex geometries, different materials and manufacturing aspects are handled as design parameters using a genetic algorithm. To take qualitative information into account, fuzzy rule based systems are utilized in order to consider all relevant aspects in the optimization problem. This paper shows results for optimization tasks on component and structural level.

scholarly journals Orthogonal Arrays with Parameters $OA(s^3,s^2+s+1,s,2)$ and 3-Dimensional Projective Geometries

10.37236/556 ◽  
2011 ◽  
Vol 18 (1) ◽  
Author(s):  
Kazuaki Ishii
Keyword(s):  
Orthogonal Array ◽  
Prime Power ◽  
Orthogonal Arrays ◽  
3 Dimensional ◽  
Projective Geometries ◽  
Finite Spaces ◽  
Alpha Type

There are many nonisomorphic orthogonal arrays with parameters $OA(s^3,s^2+s+1,s,2)$ although the existence of the arrays yields many restrictions. We denote this by $OA(3,s)$ for simplicity. V. D. Tonchev showed that for even the case of $s=3$, there are at least 68 nonisomorphic orthogonal arrays. The arrays that are constructed by the $n-$dimensional finite spaces have parameters $OA(s^n, (s^n-1)/(s-1),s,2)$. They are called Rao-Hamming type. In this paper we characterize the $OA(3,s)$ of 3-dimensional Rao-Hamming type. We prove several results for a special type of $OA(3,s)$ that satisfies the following condition: For any three rows in the orthogonal array, there exists at least one column, in which the entries of the three rows equal to each other. We call this property $\alpha$-type. We prove the following. (1) An $OA(3,s)$ of $\alpha$-type exists if and only if $s$ is a prime power. (2) $OA(3,s)$s of $\alpha$-type are isomorphic to each other as orthogonal arrays. (3) An $OA(3,s)$ of $\alpha$-type yields $PG(3,s)$. (4) The 3-dimensional Rao-Hamming is an $OA(3,s)$ of $\alpha$-type. (5) A linear $OA(3,s)$ is of $\alpha $-type.

scholarly journals AUTHORSHIP PATTERNS AND COLLABORATIVE RESEARCH OF ONCOLOGY RESEARCH OUTPUT IN INDIA: A SCIENTOMETRICS STUDY

2016 ◽  
Vol 3 (2) ◽  
pp. 123-128
Author(s):  
Senthilkumar R ◽  
Muthukrishnan M
Keyword(s):  
Collaborative Research ◽  
Web Of Science ◽  
Research Output ◽  
Paper Analysis ◽  
Research Papers ◽  
Authorship Pattern ◽  
Oncology Research ◽  
Low Profile ◽  
Single Authorship ◽  
The Mean

The paper analysis authorship patterns and collaborative research of oncology research in Indiaas reflected by the research papers listed in Web of Science database for a period of 11 years from 2005-2015. The increased trend towards multiple authorship is predominant as compare to single authorship in case ofoncology in India.In the study, the degree of collaboration was not a constant value, it reveals varies of 0.03 to 0.16 percent and the mean quality as 0.09. The analysis found that single author papers maintained a low profile among oncology research scientists and the multi authorship pattern is expanding slowly in Indian oncology research.

scholarly journals An Improvement of Stochastic Gradient Descent Approach for Mean-Variance Portfolio Optimization Problem

2021 ◽  
Vol 2021 ◽  
pp. 1-10
Author(s):  
Stephanie S. W. Su ◽  
Sie Long Kek
Keyword(s):  
Portfolio Optimization ◽  
Standard Error ◽  
Gradient Descent ◽  
Optimization Problem ◽  
Stochastic Gradient Descent ◽  
Moment Estimation ◽  
The Mean ◽  
Portfolio Optimization Problem ◽  
Mean Variance Portfolio ◽  
Mean Variance

In this paper, the current variant technique of the stochastic gradient descent (SGD) approach, namely, the adaptive moment estimation (Adam) approach, is improved by adding the standard error in the updating rule. The aim is to fasten the convergence rate of the Adam algorithm. This improvement is termed as Adam with standard error (AdamSE) algorithm. On the other hand, the mean-variance portfolio optimization model is formulated from the historical data of the rate of return of the S&P 500 stock, 10-year Treasury bond, and money market. The application of SGD, Adam, adaptive moment estimation with maximum (AdaMax), Nesterov-accelerated adaptive moment estimation (Nadam), AMSGrad, and AdamSE algorithms to solve the mean-variance portfolio optimization problem is further investigated. During the calculation procedure, the iterative solution converges to the optimal portfolio solution. It is noticed that the AdamSE algorithm has the smallest iteration number. The results show that the rate of convergence of the Adam algorithm is significantly enhanced by using the AdamSE algorithm. In conclusion, the efficiency of the improved Adam algorithm using the standard error has been expressed. Furthermore, the applicability of SGD, Adam, AdaMax, Nadam, AMSGrad, and AdamSE algorithms in solving the mean-variance portfolio optimization problem is validated.

Design of 2-DOF Compliant Mechanisms to Form Grip-and-Move Manipulators for 2D Workspace

2010 ◽  
Vol 132 (3) ◽  
Author(s):  
N. F. Wang ◽  
K. Tai
Keyword(s):  
Degrees Of Freedom ◽  
Optimization Problem ◽  
Compliant Mechanisms ◽  
Nonlinear Finite Element ◽  
Optimal Designs ◽  
Structural Topology ◽  
Structural Geometry ◽  
Multiobjective Genetic Algorithm ◽  
Topology And Shape Optimization ◽  
Morphological Representation

This paper demonstrates the design of compliant grip-and-move manipulators by structural optimization using genetic algorithms. The manipulator is composed of two compliant mechanisms (each with two degrees of freedom) that work like two fingers so that the manipulator can grip an object and convey it from one point to another anywhere within a two-dimensional workspace. The synthesis of such compliant mechanisms is accomplished by formulating the problem as a structural topology and shape optimization problem with multiple objectives and constraints to achieve the desired behavior of the manipulator. A multiobjective genetic algorithm is then applied coupled with an enhanced morphological representation for defining and encoding the structural geometry variables. The solution framework is integrated with a nonlinear finite element code for large-displacement analyses of the compliant structures to compute the paths generated by these mechanisms, with the resulting optimal designs used to realize various manipulator configurations.

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