• Transactions of the Korean Society of Mechanical Engineers A
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• v.24 no.12
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• pp.3053-3060
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• 2000

Alternative formulation is presented for robust optimization problems and an efficient computational scheme for reliability estimation is proposed. Both design variables and design parameters considered as random variables about their nominal values. To ensure the robustness of objective performance a new cost function bounding the performance and a new constraint limiting the performance variation are introduced. The constraint variations are regulated by considering the probability of feasibility. Each probability constraint is transformed into a sub-optimization problem and then is resolved with the modified advanced first order second moment(AFOSM) method for computational efficiency. The proposed robust optimization method has advantages that the mean value and the variation of the performance function are controlled simultaneously and the second order sensitivity information is not required even in case of gradient based optimization. The suggested method is examined by solving three examples and the results are compared with those for deterministic case and those available in literature.

• Communications for Statistical Applications and Methods
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• v.21 no.2
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• pp.161-168
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• 2014

In mixture experiments with process variables, we consider the case that some of process variables are either uncontrollable or hard to control, which are called noise variables. Given the such mixture experimental data with process variables, first we study how to search for candidate models. Good candidate models are screened by the sequential variables selection method and checking the residual plots for the validity of the model assumption. Two methods, which use numerical optimization methods proposed by Derringer and Suich (1980) and minimization of the weighted expected loss, are proposed to find a cost-effective robust optimal condition in which the performance of the mean as well as the variance of the response for each of the candidate models is well-behaved under the cost restriction of the mixture. The proposed methods are illustrated with the well known fish patties texture example described by Cornell (2002).

• 제어로봇시스템학회:학술대회논문집
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• 1995.10a
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• pp.348-351
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• 1995

This note proposes a robust LQR method for systems with structured real parameter uncertainty based on Riccati equation approach. Emphasis is on the reduction of design conservatism in the sense of quadratic performance by utilizing the uncertainty structure. The class of uncertainty treated includes all the form of additive real parameter uncertainty, which has the multiple rank structure. To handle the structure of uncertainty, the scaling matrix with block diagonal structure is introduced. By changing the scaling matrix, all the possible set of uncertainty structures can be represented. Modified algebraic Riccati equation (MARE) is newly proposed to obtain a robust feedback control law, which makes the quadratic cost finite for an arbitrary scaling matrix. The remaining design freedom, that is, the scaling matrix is used for minimizing the upper bound of the quadratic cost for all possible set of uncertainties within the given bounds. A design example is shown to demonstrate the simplicity and the effectiveness of proposed method.

• Transactions of the Korean Society of Mechanical Engineers A
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• v.27 no.7
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• pp.1234-1242
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• 2003

In this paper we present a simple and efficient robust optimal design formulation for MEMS structures and its application to a resonant-type micro probe. The basic idea is to use the gradient index (GI) to improve robustness of the objective and constraint functions. In the robust optimal design procedure, a deterministic optimization for performance of MEMS structures is followed by design sensitivity analysis with respect to uncertainties such as fabrication errors and change of operating conditions. During the process of deterministic optimization and sensitivity analysis, dominant performance and uncertain variables are identified to define GI. The GI is incorporated as a term of objective and constraint functions in the robust optimal design formulation to make both performance and robustness improved. While most previous approaches for robust optimal design require statistical information on design variations, the proposed GI based method needs no such information and therefore is cost-effective and easily applicable to early design stages. For the micro probe example, robust optimums are obtained to satisfy the targets for the measurement sensitivity and they are compared in terms of robustness and production yield with the deterministic optimums through the Monte Carlo simulation. This method, although shown for MEMS structures, may as well be easily applied to conventional mechanical structures where information on uncertainties is lacking but robustness is highly important.

• The Transactions of The Korean Institute of Electrical Engineers
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• v.57 no.8
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• pp.1429-1433
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• 2008

In this paper, we consider the design method of robust guaranteed cost controller for discrete-time singular systems with norm-bounded time-varying parameter uncertainty. In order to get the optimum(minimum) value of guaranteed cost, an optimization problem is given by linear matrix inequality (LMI) approach. The sufficient condition for the existence of controller and the upper bound of guaranteed cost function are proposed in terms of strict LMIs without decompositions of system matrices. Numerical examples are provided to show the validity of the presented method.

• Transactions of the Korean Society of Mechanical Engineers A
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• v.36 no.10
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• pp.1109-1114
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• 2012

The performance of a system can be affected by various variables such as manufacturing tolerances, uncertainties of material properties, and environmental factors acting on the system. Robust design optimization has attracted much attention in the design of products because it can find the best design solution that minimizes the variance of the response while considering the distribution of the variables. However, the computational cost and accuracy of optimization have thus far been a challenging problem. In this study, robust design optimization using the multiplicative decomposition method is proposed in order to solve these problems. Because the proposed method calculates the mean and variance of the system directly from the kriging metamodel using the multiplicative decomposition method, it can be used to search for a robust optimum design accurately and efficiently. Several mathematical and engineering examples are used to demonstrate the feasibility of the proposed method.

• Transactions of the Society of Information Storage Systems
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• v.1 no.2
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• pp.137-142
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• 2005

In this paper, we propose a new servo system design strategy to reduce the position error signal(PES) and track mis-registration(TMR) in magnetic disk drive systems. The proposed method provides a systematic design procedure based on the plant model and an optimal solution via an optimization with a 'Robust Random Neighborhood Search(RRNS)' algorithm. In addition, it guarantees the minimum PES level as well as stability to parametric uncertainties. Furthermore, the proposed method can be used to estimate the performance at the design stage and thus can reduce the cost and time for the design of the next generation product. The reduction of PES as well as robust stability is demonstrated by simulation and experiments.

• Journal of the Korean Society of Manufacturing Process Engineers
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• v.21 no.7
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• pp.43-52
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• 2022

Design of a controller for a high-precision servo control system has been a popular topic while finding optimal parameters for multiple controllers is still a challenging subject. In this paper, we propose a practical scheme to optimize multi-parameters for the robust servo controller design by introducing a new cost function and optimization scheme. The proposed design method provides a simple and practical tool for the systematic servo design to reduce the control error with guaranteeing robust stability of the overall system. The reduction of the position error by 24% along with a faster convergence rate is demonstrated using a typical hard disk drive servo controller with 41 parameters.

• Structural Engineering and Mechanics
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• v.81 no.1
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• pp.93-102
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• 2022

The optimum design of reinforced concrete cantilever retaining walls subjected to seismic loads is an extremely important challenge in structural and geotechnical engineering, especially in seismic zones. This study proposes an adaptive sperm swarm optimization algorithm (ASSO) for economic design of retaining structure under static and seismic loading. The proposed ASSO algorithm utilizes a time-varying velocity damping factor to provide a fine balance between the explorative and exploitative behavior of the original method. In addition, the new method considers a reasonable velocity limitation to avoid the divergence of the sperm movement. The proposed algorithm is benchmarked with a set of test functions and the results are compared with the standard sperm swarm optimization (SSO) and some other robust metaheuristic from the literature. For seismic optimization of retaining structures, Mononobe-Okabe method is employed for dynamic loading conditions and total construction cost of the structure is considered as the single objective function. The optimization constraints include both geotechnical and structural restrictions and the design variables are the geometrical dimensions of the wall and the amount of steel reinforcement. Finally, optimization of two benchmark retaining structures under static and seismic loads using the ASSO algorithm is presented. According to the numerical results, the ASSO may provide better optimal solutions, and the designs obtained by ASSO have a lower cost by up to 20% compared with some other methods from the literature.

• Advances in Computational Design
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• v.8 no.4
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• pp.295-307
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• 2023

This paper presents an optimization of the reinforced concrete ribbed slab in terms of minimum CO₂ emissions and an economic justification of the final optimal design. The design variables are six geometry variables including the slab thickness, the ribs spacing, the rib width at the lower and toper end, the depth of the rib and the bar diameter of the reinforcement, and the seventh variable defines the concrete strength. The objective function is considered to be the minimum amount of carbon dioxide gas (CO₂) emission and at the same time, the optimal design is economical. Seven significant design constraints of American Concrete Institute's Standard were considered. A robust metaheuristic optimization method called improved dolphin echolocation and ant colony optimization (IDEACO) has been used to obtain the best possible answer. At optimal design, the three most important sources of CO₂ emissions include concrete, steel reinforcement, and formwork that the contribution of them are 63.72, 32.17, and 4.11 percent respectively. Formwork, concrete, steel reinforcement, and CO₂ are the four most important sources of cost with contributions of 67.56, 19.49, 12.44, and 0.51 percent respectively. Results obtained by IDEACO show that cost and CO₂ emissions are closely related, so the presented method is a practical solution that was able to reduce the cost and CO₂ emissions simultaneously.