• Title/Summary/Keyword: function approximation

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Multi-objective optimization of anisogride composite lattice plate for free vibration, mass, buckling load, and post-buckling

  • F. Rashidi;A. Farrokhabadi;M. Karamooz Mahdiabadi
    • Steel and Composite Structures
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    • v.52 no.1
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    • pp.89-107
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    • 2024
  • This article focuses on the static and dynamic analysis and optimization of an anisogrid lattice plate subjected to axial compressive load with simply supported boundary conditions. The lattice plate includes diagonal and transverse ribs and is modeled as an orthotropic plate with effective stiffness properties. The study employs the first-order shear deformation theory and the Ritz method with a Legendre approximation function. In the realm of optimization, the Non-dominated Sorting Genetic Algorithm-II is utilized as an evolutionary multi-objective algorithm to optimize. The research findings are validated through finite element analysis. Notably, this study addresses the less-explored areas of optimizing the geometric parameters of the plate by maximizing the buckling load and natural frequency while minimizing mass. Furthermore, this study attempts to fill the gap related to the analysis of the post-buckling behavior of lattice plates, which has been conspicuously overlooked in previous research. This has been accomplished by conducting nonlinear analyses and scrutinizing post-buckling diagrams of this type of lattice structure. The efficacy of the continuous methods for analyzing the natural frequency, buckling, and post-buckling of these lattice plates demonstrates that while a degree of accuracy is compromised, it provides a significant amount of computational efficiency.

The Prime Counting Function (소수계량함수)

  • Lee, Sang-Un;Choi, Myeong-Bok
    • Journal of the Korea Society of Computer and Information
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    • v.16 no.10
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    • pp.101-109
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    • 2011
  • The Riemann's zeta function $\zeta(s)$ has been known as answer for a number of primes $\pi$(x) less than given number x. In prime number theorem, there are another approximation function $\frac{x}{lnx}$,Li(x), and R(x). The error about $\pi$(x) is R(x) < Li(x) < $\frac{x}{lnx}$. The logarithmic integral function is Li(x) = $\int_{2}^{x}\frac{1}{lnt}dt$ ~ $\frac{x}{lnx}\sum\limits_{k=0}^{\infty}\frac{k!}{(lnx)^k}=\frac{x}{lnx}(1+\frac{1!}{(lnx)^1}+\frac{2!}{(lnx)^2}+\cdots)$. This paper shows that the $\pi$(x) can be represent with finite Li(x), and presents generalized prime counting function $\sqrt{{\alpha}x}{\pm}{\beta}$. Firstly, the $\pi$(x) can be represent to $Li_3(x)=\frac{x}{lnx}(\sum\limits_{t=0}^{{\alpha}}\frac{k!}{(lnx)^k}{\pm}{\beta})$ and $Li_4(x)=\lfloor\frac{x}{lnx}(1+{\alpha}\frac{k!}{(lnx)^k}{\pm}{\beta})}k\geq2$ such that $0{\leq}t{\leq}2k$. Then, $Li_3$(x) is adjusted by $\pi(x){\simeq}Li_3(x)$ with ${\alpha}$ and error compensation value ${\beta}$. As a results, this paper get the $Li_3(x)=Li_4(x)=\pi(x)$ for $x=10^k$. Then, this paper suggests a generalized function $\pi(x)=\sqrt{{\alpha}x}{\pm}{\beta}$. The $\pi(x)=\sqrt{{\alpha}x}{\pm}{\beta}$ function superior than Riemann's zeta function in representation of prime counting.

Design, Analysis, and Equivalent Circuit Modeling of Dual Band PIFA Using a Stub for Performance Enhancement

  • Yousaf, Jawad;Jung, Hojin;Kim, Kwangho;Nah, Wansoo
    • Journal of electromagnetic engineering and science
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    • v.16 no.3
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    • pp.169-181
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    • 2016
  • This work presents a new method for enhancing the performance of a dual band Planer Inverted-F Antenna (PIFA) and its lumped equivalent circuit formulation. The performance of a PIFA in terms of return loss, bandwidth, gain, and efficiency is improved with the addition of the proposed open stub in the radiating element of the PIFA without disturbing the operating resonance frequencies of the antenna. In specific cases, various simulated and fabricated PIFA models illustrate that the return loss, bandwidth, gain, and efficiency values of antennas with longer optimum open stub lengths can be enhanced up to 4.6 dB, 17%, 1.8 dBi, and 12.4% respectively, when compared with models that do not have open stubs. The proposed open stub is small and does not interfere with the surrounding active modules; therefore, this method is extremely attractive from a practical implementation point of view. The second presented work is a simple procedure for the development of a lumped equivalent circuit model of a dual band PIFA using the rational approximation of its frequency domain response. In this method, the PIFA's measured frequency response is approximated to a rational function using a vector fitting technique and then electrical circuit parameters are extracted from it. The measured results show good agreement with the electrical circuit results. A correlation study between circuit elements and physical open stub lengths in various antenna models is also discussed in detail; this information could be useful for the enhancement of the performance of a PIFA as well as for its systematic design. The computed radiated power obtained using the electrical model is in agreement with the radiated power results obtained through the full wave electromagnetic simulations of the antenna models. The presented approach offers the advantage of saving computation time for full wave EM simulations. In addition, the electrical circuit depicting almost perfect characteristics for return loss and radiated power can be shared with antenna users without sharing the actual antenna structure in cases involving confidentiality limitations.

At-site Low Flow Frequency Analysis Using Bayesian MCMC: I. Theoretical Background and Construction of Prior Distribution (Bayesian MCMC를 이용한 저수량 점 빈도분석: I. 이론적 배경과 사전분포의 구축)

  • Kim, Sang-Ug;Lee, Kil-Seong
    • Journal of Korea Water Resources Association
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    • v.41 no.1
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    • pp.35-47
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    • 2008
  • The low flow analysis is an important part in water resources engineering. Also, the results of low flow frequency analysis can be used for design of reservoir storage, water supply planning and design, waste-load allocation, and maintenance of quantity and quality of water for irrigation and wild life conservation. Especially, for identification of the uncertainty in frequency analysis, the Bayesian approach is applied and compared with conventional methodologies in at-site low flow frequency analysis. In the first manuscript, the theoretical background for the Bayesian MCMC (Bayesian Markov Chain Monte Carlo) method and Metropolis-Hasting algorithm are studied. Two types of the prior distribution, a non-data- based and a data-based prior distributions are developed and compared to perform the Bayesian MCMC method. It can be suggested that the results of a data-based prior distribution is more effective than those of a non-data-based prior distribution. The acceptance rate of the algorithm is computed to assess the effectiveness of the developed algorithm. In the second manuscript, the Bayesian MCMC method using a data-based prior distribution and MLE(Maximum Likelihood Estimation) using a quadratic approximation are performed for the at-site low flow frequency analysis.

Economic Evaluation Algorithm of Energy Storage System using the Secondary Battery (이차전지를 이용한 전기저장장치(BESS)의 경제성 평가 알고리즘)

  • Song, Seok-Hwan;Kim, Byung-Ki;Oh, Seung-Teak;Lee, Kye-Ho;Rho, Daeseok
    • Journal of the Korea Academia-Industrial cooperation Society
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    • v.15 no.6
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    • pp.3813-3820
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    • 2014
  • Recently, with the increase in electrical consumption and the unbalanced power demand and supply, the power reserve rate is becoming smaller and the reliability of the power supply is deteriorating. Under this circumstance, a Battery Energy Storage System (BESS) is considered to be an essential countermeasure for demand side management. On the other hand, an economic evaluation is a critical issue for the introduction of a power system because the cost of BESS is quite high. Therefore, this paper presents economic evaluation method for utility use by considering the best mix method and successive approximation method, and an economic evaluation method for customer use by considering the peak shaving function based on the real time price. From a case study on a model power system and educational customer, it was confirmed that the proposed method is a practical tool for the economic analysis of BESS.

Two Class Approximation of TLB (Tomato Late Blight) Activity Data (토마토 역병균 항균 활성 데이터의 이분번 근사모델링)

  • Hahn, Hoh-Gyu;M.D., Ashek Ali;Cho, Seung-Joo
    • The Korean Journal of Pesticide Science
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    • v.9 no.2
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    • pp.140-145
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    • 2005
  • Quantitative Structure Activity Relationship (QSAR) assumes the relatedness between physical property and biological activity. However, activity data measured at single concentration such as percent activity have not been used extensively for modeling purpose. This probably comes from the fact that these values are qualitative instead of quantitative. To utilize percent activity data for molecular modeling, we classified the whole data into two classes. One class represents the active while the other signifies the inactive. The percent activity data of ${\beta}$-Ketoacetoanilides measured for TLB (Tomato Late Blight) were investigated. CoMFA (Comparative Molecular Field Analysis) was used as a discriminant function. Using CoMFA provides 3D (three dimensional) information, which is crucial for chemical insight. It can also serve as a predictive model. The resultant model classified the given data correctly (98%). When LOO (leave-one-out) crossvalidation procedure was applied, the classification accuracy was 69%. Therefore two class approximation of percent activity data with CoMFA can be utilized to understand the relationship between chemical structure and biological activity and design subsequent chemical analogs.

Skin Region Detection Using Histogram Approximation Based Mean Shift Algorithm (Mean Shift 알고리즘 기반의 히스토그램 근사화를 이용한 피부 영역 검출)

  • Byun, Ki-Won;Joo, Jae-Heum;Nam, Ki-Gon
    • Journal of the Institute of Electronics Engineers of Korea SP
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    • v.48 no.4
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    • pp.21-29
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    • 2011
  • At existing skin detection methods using skin color information defined based on the prior knowldege, threshold value to be used at the stage of dividing the backround and the skin region was decided on a subjective point of view through experiments. Also, threshold value was selected in a passive manner according to their background and illumination environments in these existing methods. These existing methods displayed a drawback in that their performance was fully influenced by the threshold value estimated through repetitive experiments. To overcome the drawback of existing methods, this paper propose a skin region detection method using a histogram approximation based on the mean shift algorithm. The proposed method is to divide the background region and the skin region by using the mean shift method at the histogram of the skin-map of the input image generated by the comparison of the similarity with the standard skin color at the CbCr color space and actively finding the maximum value converged by brightness level. Since the histogram has a form of discontinuous function accumulated according to the brightness value of the pixel, it gets approximated as a Gaussian Mixture Model (GMM) using the Bezier Curve method. Thus, the proposed method detects the skin region by using the mean shift method and actively finding the maximum value which eventually becomes the dividing point, not by using the manually selected threshold value unlike other existing methods. This method detects the skin region high performance effectively through experiments.

Design of Multi-FPNN Model Using Clustering and Genetic Algorithms and Its Application to Nonlinear Process Systems (HCM 클러스처링과 유전자 알고리즘을 이용한 다중 FPNN 모델 설계와 비선형 공정으로의 응용)

  • 박호성;오성권;안태천
    • Journal of the Korean Institute of Intelligent Systems
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    • v.10 no.4
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    • pp.343-350
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    • 2000
  • In this paper, we propose the Multi-FPNN(Fuzzy Polynomial Neural Networks) model based on FNN and PNN(Polyomial Neural Networks) for optimal system identifacation. Here FNN structure is designed using fuzzy input space divided by each separated input variable, and urilized both in order to get better output performace. Each node of PNN structure based on GMDH(Group Method of Data handing) method uses two types of high-order polynomials such as linearane and quadratic, and the input of that node uses three kinds of multi-variable inputs such as linear and quadratic, and the input of that node and Genetic Algorithms(GAs) to identify both the structure and the prepocessing of parameters of a Multi-FPNN model. Here, HCM clustering method, which is carried out for data preproessing of process system, is utilized to determine the structure method, which is carried out for data preprocessing of process system, is utilized to determance index with a weighting factor is used to according to the divisions of input-output space. A aggregate performance inddex with a wegihting factor is used to achieve a sound balance between approximation and generalization abilities of the model. According to the selection and adjustment of a weighting factor of this aggregate abjective function which it is acailable and effective to design to design and optimal Multi-FPNN model. The study is illustrated with the aid of two representative numerical examples and the aggregate performance index related to the approximation and generalization abilities of the model is evaluated and discussed.

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Calculation of Pump Light Power in Wideband Optical Phase Conjugator with Highly-Nonlinear Dispersion Shifted fiber (HNL-DSF를 이용한 광대역 광 위상 공액기의 펌프 광 전력 계산)

  • 이성렬;이하철
    • The Journal of Korean Institute of Communications and Information Sciences
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    • v.29 no.5A
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    • pp.473-483
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    • 2004
  • In this paper, we numerically investigated the optimum pump light power best compensating for pulse distortion due to both chromatic dispersion and self phase modulation (SPM) as a function of channel input power in 8 channel ${\times}$ 40 Gbps wavelength division multiplexing (WDM systems. Also we investigated the allowable maximum channel input power dependence on modulation format and fiber dispersion coefficient in the various pump light power of OPC. The considered WDM transmission system is based on path-averaged intensity approximation (PAIA) mid-span spectral inversion (MSSI) compensation method, which has highly-nonlinear dispersion shifted fiber (HNL-SDF) as nonlinear medium of optical phase conjugator (OPC) in the mid-way of total transmission line. We confirmed that optimal pump light power of HNL-DSF OPC depend on modulation format, initial channel input power, total transmission length and fiber dispersion. But optimal pump light power of HNL-DSF OPC must be selected to make power conversion ratio to almost unity. And we confirmed that, if we allow a 1 dB eye opening penalty (EOP), the tolerable maximum channel input power is increased by using RZ than NRZ as modulation format when pump light power of HNL-DSF OPC is not optimal value but another values.

Numerical Modeling of a Short-range Three-dimensional Flash LIDAR System Operating in a Scattering Atmosphere Based on the Monte Carlo Radiative Transfer Matrix Method (몬테 카를로 복사 전달 행렬 방법을 사용한 산란 대기에서 동작하는 단거리 3차원 플래시 라이다 시스템의 수치적 모델링)

  • An, Haechan;Na, Jeongkyun;Jeong, Yoonchan
    • Korean Journal of Optics and Photonics
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    • v.31 no.2
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    • pp.59-70
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    • 2020
  • We discuss a modified numerical model based on the Monte Carlo radiative transfer (MCRT) method, i.e., the MCRT matrix method, for the analysis of atmospheric scattering effects in three-dimensional flash LIDAR systems. Based on the MCRT method, the radiative transfer function for a LIDAR signal is constructed in a form of a matrix, which corresponds to the characteristic response. Exploiting the superposition and convolution of the characteristic response matrices under the paraxial approximation, an extended computer simulation model of an overall flash LIDAR system is developed. The MCRT matrix method substantially reduces the number of tracking signals, which may grow excessively in the case of conventional Monte Carlo methods. Consequently, it can readily yield fast acquisition of the signal response under various scattering conditions and LIDAR-system configurations. Using the computational model based on the MCRT matrix method, we carry out numerical simulations of a three-dimensional flash LIDAR system operating under different atmospheric conditions, varying the scattering coefficient in terms of visible distance. We numerically analyze various phenomena caused by scattering effects in this system, such as degradation of the signal-to-noise ratio, glitches, and spatiotemporal spread and time delay of the LIDAR signals. The MCRT matrix method is expected to be very effective in analyzing a variety of LIDAR systems, including flash LIDAR systems for autonomous driving.