• 전기의세계
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• 제22권1호
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• pp.28-34
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• 1973

This paper treats with the sub-optimal control problem of noninear systems by approximation method. This method involves the approximation by linearization which provides the sub-optimal solution of non-linear control problems. The result of this work shows that, in the problem in which the controlled plant is characterized by an ordinary differential equation of first order, the solution obtained by this method coincides with the exact solution of problem. In of case of the second or higher order systems, it is proved analytically that this method of linearization produces the sub-optimal solution of the given problem. It is also shown that the sub-optimality of solution by the method can be evaluated by introducing the upper and lower bounded performance indices. Discussion is made on the procedure with some illustrative examples whose performance indices are given in the quadratic forms.

• Computers and Concrete
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• 제26권1호
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• pp.1-10
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• 2020

In this paper, a procedure for automated optimized design of reinforced concrete frames has been presented. The procedure consists of formulation and solution of the design problem in the form of an optimization problem. The minimization of total cost of R/C frame has been taken as the objective of optimization problem. In this research, consistent approximation method is applied to explicitly formulate constraints and objective function in terms of the design variables. In the presented method, the primary optimization problem is replaced with a sequence of explicit sub-problems. Each sub-problem is efficiently solved using the Sequential Quadratic Programming (SQP) method. The proposed method is demonstrated through a four-story frame and an eight-story frame, and the optimum results are compared with those in the available literature. It is shown that the proposed method can be easily applied to obtain rational, reliable, economical and practical designs for Reinforced Concrete Moment Resisting Frames (RCMRFs) while it is converged after a few analyses.

• Journal of applied mathematics & informatics
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• 제33권3_4호
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• pp.387-399
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• 2015

In this paper, a new smoothing approximation to the l₁ exact penalty function for constrained optimization problems (COP) is presented. It is shown that an optimal solution to the smoothing penalty optimization problem is an approximate optimal solution to the original optimization problem. Based on the smoothing penalty function, an algorithm is presented to solve COP, with its convergence under some conditions proved. Numerical examples illustrate that this algorithm is efficient in solving COP.

• Structural Engineering and Mechanics
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• 제76권6호
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• pp.799-821
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• 2020

The optimum design of truss structures is one of the significant categories in structural optimization that has widely been applied by researchers. In the present study, new mathematical programming called Consistent Approximation (CONAP) method is utilized for the simultaneous optimization of the size and shape of truss structures. The CONAP algorithm has already been introduced to optimize some structures and functions. In the CONAP algorithm, some important parameters are designed by employing design sensitivities to enhance the capability of the method and its consistency in various optimum design problems, especially structural optimization. The cross-sectional area of the bar elements and the nodal coordinates of the truss are assumed to be the size and shape design variables, respectively. The displacement, allowable stress and the Euler buckling stress are taken as the design constraints for the problem. In the proposed method, the primary optimization problem is replaced with a sequence of explicit sub-problems. Each sub-problem is efficiently solved using the sequential quadratic programming (SQP) algorithm. Several truss structures are designed by employing the CONAP method to illustrate the efficiency of the algorithm for simultaneous shape and size optimization. The optimal solutions are compared with some of the mathematical programming algorithms, the approximation methods and metaheuristic algorithms those reported in the literature. Results demonstrate that the accuracy of the optimization is improved and the convergence rate speeds up.

• Tribology and Lubricants
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• 제38권3호
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• pp.84-92
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• 2022

In Part I, developed was a method to obtain the stress field due to an edge dislocation that locates in an elastic half plane beneath the contact edge of an elastically similar square wedge. Essential result was the corrective functions which incorporate a traction free condition of the free surfaces. In the sequel to Part I, features of the corrective functions, F_kij,(k = x, y;i,j = x,y) are investigated in this Part II at first. It is found that F_xxx(ŷ) = F_xyx(ŷ) where ŷ = y/η and η being the location of an edge dislocation on the y axis. When compared with the corrective functions derived for the case of an edge dislocation at x = ξ, analogy is found when the indices of y and x are exchanged with each other as can be readily expected. The corrective functions are curve fitted by using the scatter data generated using a numerical technique. The algebraic form for the curve fitting is designed as F_kij(ŷ) = $\frac{1}{\hat{y}^{1-{\lambda}}I+yp}$$\sum_{q=0}^{m}{\left}$$\left[A_q\left(\frac{\hat{y}}{1+\hat{y}} \right)^q \right]$ where λ_I=0.5445, the eigenvalue of the adhesive complete contact problem introduced in Part I. To investigate the exponent of F_kij, i.e.(1 - λ_I) and p, Log|F_kij|(ŷ)-Log|(ŷ)| is plotted and investigated. All the coefficients and powers in the algebraic form of the corrective functions are obtained using Mathematica. Method of analyzing a surface perpendicular crack emanated from the complete contact edge is explained as an application of the curve-fitted corrective functions.

• Journal of the Korean Society for Industrial and Applied Mathematics
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• 제23권4호
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• pp.283-300
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• 2019

In this paper, we propose a new semi-analytic approach based on the generalized Taylor series for solving nonlinear differential equations of fractional order. Assuming the solution is expanded as the generalized Taylor series, the coefficients of the series can be computed by solving the corresponding recursive relation of the coefficients which is generated by the given problem. This method is called the generalized differential transform method(GDTM). In several literatures the standard GDTM was applied in each sub-domain to obtain an accurate approximation. As noticed in [19], however, a direct application of the GDTM in each sub-domain loses a term of memory which causes an inaccurate approximation. In this work, we derive a new recursive relation of the coefficients that reflects an effect of memory. Several illustrative examples are demonstrated to show the effectiveness of the proposed method. It is shown that the proposed method is robust and accurate for solving nonlinear differential equations of fractional order.

• Composites Research
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• 제23권6호
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• pp.19-25
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• 2010

본 논문은 유리섬유/에폭시 4-매 주자직 적층 복합재와 PVC 폼 코어로 제작된 철도차량용 복합재 대차프레임의 금속재 체결부 볼트 위치 최적화 연구에 대해 서술했다. 최적화 해석은 APDL(Ansys Parameter Design Language)을 이용한 서브모델링 기법을 적용하였으며 부분문제 근사방법에 의한 최적화를 수행하였다. 이때, 최적화 해석에 적용된 서브모델링 기법은 관심영역을 포함한 부분모델에 대한 계산을 재수행 함으로써 해석에 소요되는 시간을 절약하고 상세한 결과를 도출 할 수 있다. 복합재 대차프레임의 구조해석은 JIS E 4207에 의거하여 수행하였다. 서브모델링 기법을 적용한 복합재 대차프레임의 최적화 해석은 전체모델에 대한 결과에 비해 요소망 밀도의 조절을 통한 해석시간 절약과 상세한 결과를 얻을 수 있으며, 또한 볼트위치의 최적화로 인해 보다 낮은 Von-Mises 응력값이 나타남을 확인하였다.

• KSII Transactions on Internet and Information Systems (TIIS)
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• 제15권8호
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• pp.3086-3101
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• 2021

To supply precise marketing and differentiated service for the electric power service department, it is very important to predict the customers with high sensitivity of electric power failure. To solve this problem, we propose a novel grouped 𝑙_1/2 sparsity constrained logistic regression method for sensitivity assessment of electric power failure. Different from the 𝑙₁ norm and k-support norm, the proposed grouped 𝑙_1/2 sparsity constrained logistic regression method simultaneously imposes the inter-class information and tighter approximation to the nonconvex 𝑙₀ sparsity to exploit multiple correlated attributions for prediction. Firstly, the attributes or factors for predicting the customer sensitivity of power failure are selected from customer sheets, such as customer information, electric consuming information, electrical bill, 95598 work sheet, power failure events, etc. Secondly, all these samples with attributes are clustered into several categories, and samples in the same category are assumed to be sharing similar properties. Then, 𝑙_1/2 norm constrained logistic regression model is built to predict the customer's sensitivity of power failure. Alternating direction of multipliers (ADMM) algorithm is finally employed to solve the problem by splitting it into several sub-problems effectively. Experimental results on power electrical dataset with about one million customer data from a province validate that the proposed method has a good prediction accuracy.

• 한국경영과학회지
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• 제25권4호
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• pp.27-44
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• 2000

In this study we consider a spares provisioning problem for repairable items in which a parts inventory system is incorporated. If a machine fails, a replacement part must be obtained at the parts inventory system before the failed machine enters the repair center. The inventory policy adopted at the parts inventory system is the (S, Q) policy. Operating times of the machine before failure, ordering lead times and repair times are assumed to follow a two-stage Coxian distribution. For this system, we develop an approximation method to obtain the performance measures such as steady state probabilities of the number of machines at each station and the probability that a part will wait at the parts inventory system. For the analysis of the proposed system, we model the system as a closed queueing network and analyze it using a product-form approximation method. A recursive technique as well as an iterative procedure is used to analyze the sub-network. Numerical tests show that the approximation method provides fairly good estimation of the performance measures of interest.

• 한국추진공학회:학술대회논문집
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• 한국추진공학회 2012년도 제38회 춘계학술대회논문집
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• pp.403-407
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• 2012

본 연구의 목적은 최적화 해석 기법을 이용하여 복합재 압력용기의 스커트 치수를 도출하는 것이다. 복합재 압력용기의 스커트 최적화 해석은 부분문제 근사법(sub-problem approximation method) 알고리즘을 사용하였으며, APDL(ANSYS Parametric Design Language)을 이용하여 해석의 모든 과정을 일괄처리(batch processing)하였다. 설계변수로는 압력용기 스커트 부위의 두께와 길이를 선정하였으며, 내압에 의해 발생하는 변위와 무게를 각각 목적함수로 하여 최적화 해석을 통해 최적의 스커트 치수를 도출하였다. 그 결과 복합재 압력용기의 스커트 무게를 최대 4.38% 절감할 수 있었다.