• Transactions of the Korean Society of Mechanical Engineers A
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• v.26 no.9
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• pp.1931-1942
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• 2002

In this paper a formulation of robust optimization is presented and illustrated by a design example of vibratory micro gyroscopes in order to reduce the effect of variations due to uncertainties in MEMS fabrication processes. For the vibratory micro gyroscope considered it is important to match the resonance frequencies of the vertical (sensing) and lateral (driving) modes as close as possible to attain a high sensing sensitivity. A deterministic optimization in which the difference of both the sensing and driving natural frequencies is minimized as an objective function results in highly enhanced performance but apt to be very sensitive to fabrication errors. The formulation proposed is to attain robustness of the performance by including the sensitivity of the response with respect to uncertain variables as a term of objective function to be minimized. This formulation is simple and practically applicable since no detail statistical information on fabrication errors is required. The geometric variables, beam width, length and thickness of vibratory micro gyroscopes are adopted as design variables and at the same time considered as uncertain variables because here occur the fabrication errors. A robustness test in terms of a percentage yield by using the Monte Carlo simulation has shown that the robust optimum produces twice more acceptable designs than the deterministic optimum. Improvement of robustness becomes bigger as the amount of fabrication errors is assumed larger. Considering that the magnitude of fabrication errors and uncertainties in a MEMS structure are comparatively large, the present method is illustrated to be a viable approach for a robust MEMS design.

• Journal of Industrial Technology
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• v.22 no.A
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• pp.19-28
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• 2002

The Nelder-Mead simplex algorithm has been one of the most widely used methods for the nonlinear unconstrained optimization, since 1965. Recently, the new algorithm, (so-called the Fuzzy Simplex Algorithm), with fuzzy logic controllers for the expansion, reflection and contraction process of this algorithm has been proposed. In this paper, this new algorithm is developed. And, the formulation for the optimum design of the power screw's efficiency is made. And then, the developed fuzzy simplex algorithm as well as the original one is applied to this optimum design problem. The Fuzzy simplex algorithm results in a faster convergence in this problem, as reported in other study, too.

• Structural Engineering and Mechanics
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• v.26 no.2
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• pp.191-210
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• 2007

The three different approaches (reformulations) of evolution strategies (ESs) have been proposed in the literature as extensions of the technique for solving discrete problems. This study implements an extensive research on application, evaluation and comparison of them in discrete optimum design of steel frames. A unified formulation is first developed to explain these approaches, so that differences and similarities between their inherent search mechanisms can clearly be identified. Two examples from practical design of steel frames are studied next to measure their performances in locating the optimum. Extensive numerical experimentations are performed in both examples to facilitate a statistical analysis of their convergence characteristics. The results obtained are presented in the histograms demonstrating the distribution of the best designs located by each approach. In addition, an average improvement of the best design during the course of evolution is plotted in each case to compare their relative convergence rates.

• Culinary science and hospitality research
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• v.23 no.5
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• pp.87-91
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• 2017

This study was conducted to investigate the quality characteristics of sun-dried salt prepared with added Cheongyang hot pepper juice(CPJ). The moisture, crude protein, crude lipid, and crude ash contents of the CPJ were 84.36%, 2.27%, 1.41%, and 0.67% respectively. The moisture content, yellowness, capsaicin, and dihydrocapsaicin of sun-dried salt increased according to the level of added CPJ, whereas the NaCl, pH, lightness, and redness value increased. The sensory evaluation results showed that preferences for the sun-dried salt increased as CPJ, approached their optimum value and decreased as they exceeded optimum levels. Consequently, the proposed optimum level in the ingredient formulation for manufacture of the standard sun-dried salt was 30% CPJ, as based on analyses. Ultimately, this study was expected to contribute to the commercialization of sun-dried salt of high quality.

• Structural Engineering and Mechanics
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• v.54 no.4
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• pp.665-691
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• 2015

This study aims at comparing the optimum design of two common types open web expanded beams: with hexagonal openings, also called castellated beams and beams with circular openings referred to as cellular beams. The minimum weights of both beams are taken as the objective functions while the design constraints are respectively implemented from The Steel Construction Institute Publication Numbers 5 and 100. The design methods adopted in these publications are consistent with BS5950 parts. The formulation of the design problem considering the limitations of the above mentioned turns out to be a discrete programming problem. Improved harmony search algorithm is suggested to compare the optimum design of mentioned web-expanded beams to analysis the performance of both beams. The design algorithms based on the technique select the optimum Universal Beam sections, dimensional properties of hexagonal and circular holes and total number of openings along the beam as design variables.

• Journal of electromagnetic engineering and science
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• v.16 no.2
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• pp.126-133
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• 2016

Wireless power transfer (WPT) efficiencies for multiple-input multiple-output (MIMO) systems are formulated with a goal of achieving their maximums using Z matrices. The maximum efficiencies for any arbitrarily given configurations are obtained using optimum loads, which can be determined numerically through adequate optimization procedures in general. For some simpler special cases (single-input single-output, single-input multiple-output, and multiple-input single-output) of the MIMO systems, the efficiencies and optimum loads to maximize them can be obtained using closed-form expressions. These closed-form solutions give us more physical insight into the given WPT problem. These efficiencies are evaluated theoretically based on the presented formulation and also verified with comparisons with circuit- and EM-simulation results. They are shown to lead to a good agreement. This work may be useful for construction of the wireless Internet of Things, especially employed with energy autonomy.

• Computers and Concrete
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• v.24 no.2
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• pp.117-123
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• 2019

Optimization is an important subject which is widely used in engineering problems. In this paper, an analytical method is developed for optimum design of reinforced concrete beams considering both flexural and shear effects. A closed-form formulation is derived for optimal height and rebar of beams. The total material cost of steel and concrete is considered as the objective function which is minimized during the optimization process. The ultimate flexural and shear capacities of the beam are considered as the main constraints. The ultimate limit state is considered for deriving the relations for flexural capacity of the beam. The design requirements are considered according to the item 9 of the Iranian National Building. Analytical formulas and some curves are proposed to be used for optimum design of RC beams. The proposed method can be used to perform the optimization of RC beams without the need of any prior knowledge in optimization. Also, the results of the studied numerical example show that the proposed method results in a better design comparing with the other methods.

• Structural Engineering and Mechanics
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• v.52 no.2
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• pp.351-368
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• 2014

This study presents a hunting search based optimum design algorithm for engineering optimization problems. Hunting search algorithm is an optimum design method inspired by group hunting of animals such as wolves, lions, and dolphins. Each of these hunters employs hunting in a different way. However, they are common in that all of them search for a prey in a group. Hunters encircle the prey and the ring of siege is tightened gradually until it is caught. Hunting search algorithm is employed for the automation of optimum design process, during which the design variables are selected for the minimum objective function value controlled by the design restrictions. Three different examples, namely welded beam, cellular beam and moment resisting steel frame are selected as numerical design problems and solved for the optimum solution. Each example differs in the following ways: Unlike welded beam design problem having continuous design variables, steel frame and cellular beam design problems include discrete design variables. Moreover, while the cellular beam is designed under the provisions of BS 5960, LRFD-AISC (Load and Resistant Factor Design-American Institute of Steel Construction) is considered for the formulation of moment resisting steel frame. Levy Flights is adapted to the simple hunting search algorithm for better search. For comparison, same design examples are also solved by using some other well-known search methods in the literature. Results reveal that hunting search shows good performance in finding optimum solutions for each design problem.

• Journal of the Computational Structural Engineering Institute of Korea
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• v.13 no.1
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• pp.1-11
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• 2000

In this paper, optimum design problem of R.C. continuous beam is considered and GUI system is developed for using at the practical design. Objective function lot formulation of optimum design problem is made up of the costs of concrete, reinforcing steel and formwork. Design variables are width, effective depth of the beam and steel ratio and design constraints are considered on the strength, serviceability, durability and geometrical conditions. The optimum design problem is solved by using sequential linear programming(SLP), sequential convex programming(SCP) and compared their effectiveness. Also this paper shows the application at practical design work according to the development of GUI system using visual basic.

• Proceedings of the Computational Structural Engineering Institute Conference
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• 2002.04a
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• pp.123-130
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• 2002

A general formulation for shape design sensitivity analysis over three dimensional beam structure is developed based on a variational formulation of the beam in linear elasticity. Sensitivity formula is derived based on variational equations in cartesian coordinates using the material derivative concept and adjoint variable method for the displacement and Von-Mises stress functionals. Shape variation is considered for the beam shape in general 3-dimensional direction as well as for the orientation angle of the beam cross section. In the sensitivity expression, the end points evaluation at each beam segment is added to the integral formula, which are summed over the entire structure. The sensitivity formula can be evaluated with generality and ease even by employing piecewise linear design velocity field despite the bending model is fourth order differential equation. For the numerical implementation, commercial software ANSYS is used as analysis tool for the primal and adjoint analysis. Once the design variable set is defined using ANSYS language, shape and orientation variation vector at each node is generated by making finite difference to the shape with respect to each design parameter, and is used for the computation of sensitivity formula. Several numerical examples are taken to show the advantage of the method, in which the accuracy of the sensitivity is evaluated. The results are found excellent even by employing a simple linear function for the design velocity evaluation. Shape optimization is carried out for the geometric design of an archgrid and tilted bridge, which is to minimize maximum stress over the structure while maintaining constant weight. In conclusion, the proposed formulation is a useful and easy tool in finding optimum shape in a variety of the spatial frame structures.