• Title/Summary/Keyword: Nonlinear equations

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A Study on the Attributes of Software Reliability Cost Model with Shape Parameter Change of Type-2 Gumbel Life Distribution (Type-2 Gumbel 수명분포의 형상모수 변화에 따른 소프트웨어 신뢰성 비용모형의 속성에 관한 연구)

  • Yang, Tae-Jin
    • The Journal of Korea Institute of Information, Electronics, and Communication Technology
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    • v.12 no.3
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    • pp.211-217
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    • 2019
  • In this study, we compare and analyze the attributes of the software development cost model according to the shape parameters change of the Type-2 Gumbel lifetime distribution using the NHPP model. In order to analyze the software failure phenomena, the parametric estimation is applied to the maximum likelihood estimation method, and the nonlinear equations are calculated using the bisection method. As a result, when the attributes of the cost curves according to the change of shape parameters are compared, it is found that the larger the number of shape parameters, the lower the software development cost and the faster the release time. Through this study, it is expected that it will be helpful for the software developers to search for the development cost according to the software shape parameters change, and also to provide the necessary information for the attributes of the software development cost.

Effect of nonlinear FG-CNT distribution on mechanical properties of functionally graded nano-composite beam

  • Zerrouki, Rachid;Karas, Abdelkader;Zidour, Mohamed;Bousahla, Abdelmoumen Anis;Tounsi, Abdelouahed;Bourada, Fouad;Tounsi, Abdeldjebbar;Benrahou, Kouider Halim;Mahmoud, S.R.
    • Structural Engineering and Mechanics
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    • v.78 no.2
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    • pp.117-124
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    • 2021
  • This work focused on the novel numerical tool for the bending responses of carbon nanotube reinforced composites (CNTRC) beams. The higher order shear deformation beam theory (HSDT) is used to determine strain-displacement relationships. A new exponential function was introduced into the carbon nanotube (CNT) volume fraction equation to show the effect of the CNT distribution on the CNTRC beams through displacements and stresses. To determine the mechanical properties of CNTRCs, the rule of the mixture was employed by assuming that the single-walled carbon nanotubes (SWCNTs)are aligned and distributed in the matrix. The governing equations were derived by Hamilton's principle, and the mathematical models presented in this work are numerically provided to verify the accuracy of the present theory. The effects of aspect ratio (l/d), CNT volume fraction (Vcnt), and the order of exponent (n) on the displacement and stresses are presented and discussed in detail. Based on the analytical results. It turns out that the increase of the exponent degree (n) makes the X-beam stiffer and the exponential CNTs distribution plays an indispensable role to improve the mechanical properties of the CNTRC beams.

Design of Key Sequence Generators Based on Symmetric 1-D 5-Neighborhood CA (대칭 1차원 5-이웃 CA 기반의 키 수열 생성기 설계)

  • Choi, Un-Sook;Kim, Han-Doo;Kang, Sung-Won;Cho, Sung-Jin
    • The Journal of the Korea institute of electronic communication sciences
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    • v.16 no.3
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    • pp.533-540
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    • 2021
  • To evaluate the performance of a system, one-dimensional 3-neighborhood cellular automata(CA) based pseudo-random generators are widely used in many fields. Although two-dimensional CA and one-dimensional 5-neighborhood CA have been applied for more effective key sequence generation, designing symmetric one-dimensional 5-neighborhood CA corresponding to a given primitive polynomial is a very challenging problem. To solve this problem, studies on one-dimensional 5-neighborhood CA synthesis, such as synthesis method using recurrence relation of characteristic polynomials and synthesis method using Krylov matrix, were conducted. However, there was still a problem with solving nonlinear equations. To solve this problem, a symmetric one-dimensional 5-neighborhood CA synthesis method using a transition matrix of 90/150 CA and a block matrix has recently been proposed. In this paper, we detail the theoretical process of the proposed algorithm and use it to obtain symmetric one-dimensional 5-neighborhood CA corresponding to high-order primitive polynomials.

Application of POD reduced-order algorithm on data-driven modeling of rod bundle

  • Kang, Huilun;Tian, Zhaofei;Chen, Guangliang;Li, Lei;Wang, Tianyu
    • Nuclear Engineering and Technology
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    • v.54 no.1
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    • pp.36-48
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    • 2022
  • As a valid numerical method to obtain a high-resolution result of a flow field, computational fluid dynamics (CFD) have been widely used to study coolant flow and heat transfer characteristics in fuel rod bundles. However, the time-consuming, iterative calculation of Navier-Stokes equations makes CFD unsuitable for the scenarios that require efficient simulation such as sensitivity analysis and uncertainty quantification. To solve this problem, a reduced-order model (ROM) based on proper orthogonal decomposition (POD) and machine learning (ML) is proposed to simulate the flow field efficiently. Firstly, a validated CFD model to output the flow field data set of the rod bundle is established. Secondly, based on the POD method, the modes and corresponding coefficients of the flow field were extracted. Then, an deep feed-forward neural network, due to its efficiency in approximating arbitrary functions and its ability to handle high-dimensional and strong nonlinear problems, is selected to build a model that maps the non-linear relationship between the mode coefficients and the boundary conditions. A trained surrogate model for modes coefficients prediction is obtained after a certain number of training iterations. Finally, the flow field is reconstructed by combining the product of the POD basis and coefficients. Based on the test dataset, an evaluation of the ROM is carried out. The evaluation results show that the proposed POD-ROM accurately describe the flow status of the fluid field in rod bundles with high resolution in only a few milliseconds.

Prediction of the shear capacity of reinforced concrete slender beams without stirrups by applying artificial intelligence algorithms in a big database of beams generated by 3D nonlinear finite element analysis

  • Markou, George;Bakas, Nikolaos P.
    • Computers and Concrete
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    • v.28 no.6
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    • pp.533-547
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    • 2021
  • Calculating the shear capacity of slender reinforced concrete beams without shear reinforcement was the subject of numerous studies, where the eternal problem of developing a single relationship that will be able to predict the expected shear capacity is still present. Using experimental results to extrapolate formulae was so far the main approach for solving this problem, whereas in the last two decades different research studies attempted to use artificial intelligence algorithms and available data sets of experimentally tested beams to develop new models that would demonstrate improved prediction capabilities. Given the limited number of available experimental databases, these studies were numerically restrained, unable to holistically address this problem. In this manuscript, a new approach is proposed where a numerically generated database is used to train machine-learning algorithms and develop an improved model for predicting the shear capacity of slender concrete beams reinforced only with longitudinal rebars. Finally, the proposed predictive model was validated through the use of an available ACI database that was developed by using experimental results on physical reinforced concrete beam specimens without shear and compressive reinforcement. For the first time, a numerically generated database was used to train a model for computing the shear capacity of slender concrete beams without stirrups and was found to have improved predictive abilities compared to the corresponding ACI equations. According to the analysis performed in this research work, it is deemed necessary to further enrich the current numerically generated database with additional data to further improve the dataset used for training and extrapolation. Finally, future research work foresees the study of beams with stirrups and deep beams for the development of improved predictive models.

Free vibration of various types of FGP sandwich plates with variation in porosity distribution

  • Aicha Kablia;Rabia Benferhat;Tahar Hassaine Daouadji;Rabahi Abderezak
    • Structural Engineering and Mechanics
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    • v.85 no.1
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    • pp.1-14
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    • 2023
  • The use of functionally graded materials in applications involving severe thermal gradients is quickly gaining acceptance in the composite mechanics community, the aerospace and aircraft industry. In the present study, a refined sandwich plate model is applied to study the free vibration analysis of porous functionally graded material (FGM) sandwich plates with various distribution rate of porosity. Two types of common FG sandwich plates are considered. The first sandwich plate is composed of two FG material (FGM) face sheets and a homogeneous ceramic or metal core. The second one consists of two homogeneous fully metal and ceramic face sheets at the top and bottom, respectively, and a FGM core. The displacement field of the present theory is chosen based on nonlinear variations in the in-plane displacements through the thickness of the sandwich plate. The number of unknowns and equations of motion of the present theory is reduced and hence makes them simple to use. In the analysis, the equation of motion for simply supported sandwich plates is obtained using Hamilton's principle. In order to present the effect of the variation of the porosity distribution on the dynamic behavior of the FGM sandwich plates, new mixtures are proposed which take into account different rate of porosity distribution between the ceramic and the metal. The present method is applicable to study the dynamic behavior of FGM plates and sandwich plates. The frequencies of two kinds of FGM sandwich structures are analyzed and discussed. Several numerical results have been compared with the ones available in the literature.

Filtering Algorithms for Position Evaluation and Tracking of Tactical Objects (전술객체 위치 모의 및 추적을 위한 필터링 알고리즘 연구)

  • Kim, Seok-Kwon;Jin, Seung-Ri;Son, Jae-Won;Park, Dong-Jo
    • Journal of the Korea Society for Simulation
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    • v.19 no.4
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    • pp.199-208
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    • 2010
  • Positions of tactical objects are represented as Time, Space and Position Information(TSPI) in modeling and simulations(M&S). The format and required information record for TSPI is investigated by referring the TSPI object model of the Test and Training Enabling Architecture(TENA), which has been developed by the United States Department of Defense. The most sophisticated tactical data link, Link-16 has a Precise Participant Location and Information (PPLI) message. We study the data format for exchanging TSPI data based on the PPLI message. To evaluate and track positions of tactical objects, we consider the Kalman filter for linear systems, and the extended Kalman filter and the unscented Kalman filter for nonlinear systems. Based on motion equations of a ballistic missile, the tracking performance for the trajectory of the ballistic missile is simulated by the unscented Kalman filter.

Theoretical buckling analysis of inhomogeneous plates under various thermal gradients and boundary conditions

  • Laid Lekouara;Belgacem Mamen;Abdelhakim Bouhadra;Abderahmane Menasria;Kouider Halim Benrahou;Abdelouahed Tounsi;Mohammed A. Al-Osta
    • Structural Engineering and Mechanics
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    • v.86 no.4
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    • pp.443-459
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    • 2023
  • This study investigates the theoretical thermal buckling analyses of thick porous rectangular functionally graded (FG) plates with different geometrical boundary conditions resting on a Winkler-Pasternak elastic foundation using a new higher-order shear deformation theory (HSDT). This new theory has only four unknowns and involves indeterminate integral variables in which no shear correction factor is required. The variation of material properties across the plate's thickness is considered continuous and varied following a simple power law as a function of volume fractions of the constituents. The effect of porosity with two different types of distribution is also included. The current formulation considers the Von Karman nonlinearity, and the stability equations are developed using the virtual works principle. The thermal gradients are involved and assumed to change across the FG plate's thickness according to nonlinear, linear, and uniform distributions. The accuracy of the newly proposed theory has been validated by comparing the present results with the results obtained from the previously published theories. The effects of porosity, boundary conditions, foundation parameters, power index, plate aspect ratio, and side-to-thickness ratio on the critical buckling temperature are studied and discussed in detail.

Negative Turbulent Magnetic 𝛽 Diffusivity effect in a Magnetically Forced System

  • Park, Kiwan;Cheoun, Myung-Ki
    • The Bulletin of The Korean Astronomical Society
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    • v.46 no.2
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    • pp.47.3-48
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    • 2021
  • We studied the large scale dynamo process in a system forced by helical magnetic field. The dynamo process is basically nonlinear, but can be linearized with 𝛼&𝛽 coefficients and large scale magnetic field $\bar{B}$. This is very useful to the investigation of solar (stellar) dynamo. A coupled semi-analytic equations based on statistical mechanics are used to investigate the exact evolution of 𝛼&𝛽. This equation set needs only magnetic helicity ${\bar{H}}_M({\equiv}{\langle}{\bar{A}}{\cdot}{\bar{B}}{\rangle},\;{\bar{B}}={\nabla}{\times}{\bar{A}})$ and magnetic energy ${\bar{E}}_M({\equiv}{\langle}{\bar{B}}^2{\rangle}/2)$. They are fundamental physics quantities that can be obtained from the dynamo simulation or observation without any artificial modification or assumption. 𝛼 effect is thought to be related to magnetic field amplification. However, in reality the averaged 𝛼 effect decreases very quickly without a significant contribution to ${\bar{B}}$ field amplification. Conversely, 𝛽 effect contributing to the magnetic diffusion maintains a negative value, which plays a key role in the amplification with Laplacian ∇2(= - k2) for the large scale regime. In addition, negative magnetic diffusion accounts for the attenuation of plasma kinetic energy EV(= 〈 U2 〉/2) (U: plasma velocity) when the system is saturated. The negative magnetic diffusion is from the interaction of advective term - U • ∇ B from magnetic induction equation and the helical velocity field. In more detail, when 'U' is divided into the poloidal component Upol and toroidal one Utor in the absence of reflection symmetry, they interact with - B • ∇ U and - U • ∇ B from ∇ × 〈 U × B 〉 leading to 𝛼 effect and (negative) 𝛽 effect, respectively. We discussed this process using the theoretical method and intuitive field structure model supported by the simulation result.

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Hysteretic Damage Model for Reinforced Concrete Joints Considering Bond-Slip (부착-슬립을 고려한 철근콘크리트 접합부의 이력 손상 모델 개발)

  • Kim, Do-Yeon;Choi, In-Kil
    • KSCE Journal of Civil and Environmental Engineering Research
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    • v.28 no.4A
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    • pp.517-528
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    • 2008
  • This paper presents a hysteretic damage model for reinforced concrete (RC) joints that explicitly accounts for the bond-slip between the reinforcing bars and the surrounding concrete. A frame element whose displacement fields for the concrete and the reinforcing bars are different to permit slip is developed. From the fiber section concept, compatibility equations for concrete, rebar, and bond are defined. Modification of the hysteretic stress-strain curve of steel is conducted for partial unloading and reloading conditions. Local bond stress-slip relations for monotonic loads are updated at each slip reversal according to the damage factor. The numerical applications of the reinforcing bar embedded in the confined concrete block, the RC column anchored in the foundation, and the RC beam-column subassemblage validate the model accuracy and show how including the effects of bond-slip leads to a good assessment of the amount of energy dissipation during loading histories.