• Title/Summary/Keyword: linear approximation

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A Study on the Optimal Design of Automotive Gas Spring (차량용 가스스프링의 최적설계에 관한 연구)

  • Lee, Choon Tae
    • Journal of Drive and Control
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    • v.14 no.4
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    • pp.45-50
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    • 2017
  • The gas spring is a hydropneumatic adjusting element, consisting of a pressure tube, a piston rod, a piston and a connection fitting. The gas spring is filled with compressed nitrogen within the cylinder. The filling pressure acts on both sides of the piston and because of area difference it produces an extension force. Therefore, a gas spring is similar in function compare to mechanical coil spring. Conversely, optimization is a process of finding the best set of parameters to reach a goal while not violating certain constraints. The AMESim software provides NLPQL (Nonlinear Programming by Quadratic Lagrangian) and GA (genetic algorithm) for optimization. The NLPQL method builds a quadratic approximation to the Lagrange function and linear approximations to all output constraints at each iteration, starting with the identity matrix for the Hessian of the Lagrangian, and gradually updating it using the BFGS method. On each iteration, a quadratic programming problem is solved to find an improved design until the final convergence to the optimum design. In this study, we conducted optimization design of the gas spring reaction force with NLPQL.

Recognition of Occluded Objects by Fuzzy Inference (FUZZY 추론에 의한 중복물체 인식)

  • 김형근;박철하;윤길중;최갑석
    • The Journal of Korean Institute of Communications and Information Sciences
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    • v.16 no.1
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    • pp.23-34
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    • 1991
  • This paper is studied for the recognition of occluded objects by fuzzy inference. The images are transformed a group of linear line segments, which is formed local features extracted from curvature points, using polygonal approximation. The features extracted from images are representes to the fuzzified data which is mapped into fuzzy concepts to represent the fuzziness, and the recognition of a model from scenes is performed by fuzzy inference using the production rulse which is generated from the model image. It is considered that the recognition results according to the change of degree of fuzziness in the experiments, and the experimental results for 30 scenes contained 120 models is obtained 92.5% of recognition rate.

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Flapwise and non-local bending vibration of the rotating beams

  • Mohammadnejad, Mehrdad;Saffari, Hamed
    • Structural Engineering and Mechanics
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    • v.72 no.2
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    • pp.229-244
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    • 2019
  • Weak form integral equations are developed to investigate the flapwise bending vibration of the rotating beams. Rayleigh and Eringen nonlocal elasticity theories are used to investigate the rotatory inertia and Size-dependency effects on the flapwise bending vibration of the rotating cantilever beams, respectively. Through repetitive integrations, the governing partial differential equations are converted into weak form integral equations. The novelty of the presented approach is the approximation of the mode shape function by a power series which converts the equations into solvable one. Substitution of the power series into weak form integral equations results in a system of linear algebraic equations. The natural frequencies are determined by calculation of the non-trivial solution for resulting system of equations. Accuracy of the proposed method is verified through several numerical examples, in which the influence of the geometry properties, rotatory inertia, rotational speed, taper ratio and size-dependency are investigated on the natural frequencies of the rotating beam. Application of the weak form integral equations has made the solution simpler and shorter in the mathematical process. Presented relations can be used to obtain a close-form solution for quick calculation of the first five natural frequencies of the beams with flapwise vibration and non-local effects. The analysis results are compared with those obtained from other available published references.

Capabilities of 1D CUF-based models to analyse metallic/composite rotors

  • Filippi, Matteo;Carrera, Erasmo
    • Advances in aircraft and spacecraft science
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    • v.3 no.1
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    • pp.1-14
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    • 2016
  • The Carrera Unified Formulation (CUF) is here extended to perform free-vibrational analyses of rotating structures. CUF is a hierarchical formulation, which enables one to obtain refined structural theories by writing the unknown displacement variables using generic functions of the cross-section coordinates (x, z). In this work, Taylor-like expansions are used. The increase of the theory order leads to three-dimensional solutions while, the classical beam models can be obtained as particular cases of the linear theory. The Finite Element technique is used to solve the weak form of the three-dimensional differential equations of motion in terms of "fundamental nuclei", whose forms do not depend on the adopted approximation. Including both gyroscopic and stiffening contributions, structures rotating about either transversal or longitudinal axis can be considered. In particular, the dynamic characteristics of thin-walled cylinders and composite blades are investigated to predict the frequency variations with the rotational speed. The results reveal that the present one-dimensional approach combines a significant accuracy with a very low computational cost compared with 2D and 3D solutions. The advantages are especially evident when deformable and composite structures are analyzed.

Kinetics of nitrification and acrylamide biodegradation by Enterobacter aerogenes and mixed culture bacteria in sequencing batch reactor wastewater treatment systems

  • Madmanang, Romsan;Jangkorn, Siriprapha;Charoenpanich, Jittima;Sriwiriyarat, Tongchai
    • Environmental Engineering Research
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    • v.24 no.2
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    • pp.309-317
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    • 2019
  • This study evaluated the kinetics of acrylamide (AM) biodegradation by mixed culture bacteria and Enterobacter aerogenes (E. aerogenes) in sequencing batch reactor (SBR) systems with AQUASIM and linear regression. The zero-order, first-order, and Monod kinetic models were used to evaluate the kinetic parameters of both autotrophic and heterotrophic nitrifications and both AM and chemical oxygen demand (COD) removals at different AM concentrations of 100, 200, 300, and 400 mg AM/L. The results revealed that both autotrophic and heterotrophic nitrifications and both AM and COD removals followed the Monod kinetics. High AM loadings resulted in the transformation of Monod kinetics to the first-order reaction for AM and COD removals as the results of the compositions of mixed substrates and the inhibition of the free ammonia nitrogen (FAN). The kinetic parameters indicated that E. aerogenes degraded AM and COD at higher rates than mixed culture bacteria. The FAN from the AM biodegradation increased both heterotrophic and autotrophic nitrification rates at the AM concentrations of 100-300 mg AM/L. At higher AM concentrations, the FAN accumulated in the SBR system inhibited the autotrophic nitrification of mixed culture bacteria. The accumulation of intracellular polyphosphate caused the heterotrophic nitrification of E. aerogenes to follow the first-order approximation.

A simple prediction procedure of strain-softening surrounding rock for a circular opening

  • Wang, Feng;Zou, Jin-Feng
    • Geomechanics and Engineering
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    • v.16 no.6
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    • pp.619-626
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    • 2018
  • A simple prediction procedure was investigated for calculating the stresses and displacements of a circular opening. Unlike existed approaches, the proposed approach starts each step with a radius increment. The stress for each annulus could be obtained analytically, while strain increments for each step can be determinate numerically from the compatility equation by finite difference approximation, flow rule and Hooke's law. In the successive manner, the distributions of stresses and displacements could be found. It should be noted that the finial radial stress and displacement were equal to the internal supporting pressure and deformation at the tunnel wall, respectively. By assuming different plastic radii, GRC and the evolution curve of plastic radii and internal supporting pressures could be obtained conveniently. Then the real plastic radius can be calculated by using linear interpolation in the evolution curve. Some numerical and engineering examples were performed to demonstrate the accuracy and validity for the proposed procedure. The comparisons results show that the proposed procedure was faster than that in Lee and Pietrucszczak (2008). The influence of annulus number and dilation on the accuracy of solutions was also investigated. Results show that the larger the annulus number was, the more accurate the solutions were. Solutions in Park et al. (2008) were significantly influenced by dilation.

Shear behaviour of RC beams retrofitted using UHPFRC panels epoxied to the sides

  • Al-Osta, Mohammed A.
    • Computers and Concrete
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    • v.24 no.1
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    • pp.37-49
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    • 2019
  • In this study, the shear behaviour of reinforced concrete (RC) beams that were retrofitted using precast panels of ultra-high performance fiber reinforced concrete (UHPFRC) is presented. The precast UHPFRC panels were glued to the side surfaces of RC beams using epoxy adhesive in two different configurations: (i) retrofitting two sides, and (ii) retrofitting three sides. Experimental tests on the adhesive bond were conducted to estimate the bond capacity between the UHPFRC and normal concrete. All the specimens were tested in shear under varying levels of shear span-to-depth ratio (a/d=1.0; 1.5). For both types of configuration, the retrofitted specimens exhibited a significant improvement in terms of stiffness, load carrying capacity and failure mode. In addition, the UHPFRC retrofitting panels glued in three-sides shifted the failure from brittle shear to a more ductile flexural failure with enhancing the shear capacity up to 70%. This was more noticeable in beams that were tested with a/d=1.5. An approach for the approximation of the failure capacity of the retrofitted RC beams was evolved using a multi-level regression of the data obtained from the experimental work. The predicted values of strength have been validated by comparing them with the available test data. In addition, a 3-D finite element model (FEM) was developed to estimate the failure load and overall behaviour of the retrofitted beams. The FEM of the retrofitted beams was conducted using the non-linear finite element software ABAQUS.

High accurate three-dimensional neutron noise simulator based on GFEM with unstructured hexahedral elements

  • Hosseini, Seyed Abolfazl
    • Nuclear Engineering and Technology
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    • v.51 no.6
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    • pp.1479-1486
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    • 2019
  • The purpose of the present study is to develop the 3D static and noise simulator based on Galerkin Finite Element Method (GFEM) using the unstructured hexahedral elements. The 3D, 2G neutron diffusion and noise equations are discretized using the unstructured hexahedral by considering the linear approximation of the shape function in each element. The validation of the static calculation is performed via comparison between calculated results and reported data for the VVER-1000 benchmark problem. A sensitivity analysis of the calculation to the element type (unstructured hexahedral or tetrahedron elements) is done. Finally, the neutron noise calculation is performed for the neutron noise source of type of variable strength using the Green function technique. It is shown that the error reduction in the static calculation is considerable when the unstructured tetrahedron elements are replaced with the hexahedral ones. Since the neutron flux distribution and neutron multiplication factor are appeared in the neutron noise equation, the more accurate calculation of these parameters leads to obtaining the neutron noise distribution with high accuracy. The investigation of the changes of the neutron noise distribution in axial direction of the reactor core shows that the 3D neutron noise analysis is required instead of 2D.

Monte Carlo burnup and its uncertainty propagation analyses for VERA depletion benchmarks by McCARD

  • Park, Ho Jin;Lee, Dong Hyuk;Jeon, Byoung Kyu;Shim, Hyung Jin
    • Nuclear Engineering and Technology
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    • v.50 no.7
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    • pp.1043-1050
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    • 2018
  • For an efficient Monte Carlo (MC) burnup analysis, an accurate high-order depletion scheme to consider the nonlinear flux variation in a coarse burnup-step interval is crucial accompanied with an accurate depletion equation solver. In a Seoul National University MC code, McCARD, the high-order depletion schemes of the quadratic depletion method (QDM) and the linear extrapolation/quadratic interpolation (LEQI) method and a depletion equation solver by the Chebyshev rational approximation method (CRAM) have been newly implemented in addition to the existing constant extrapolation/backward extrapolation (CEBE) method using the matrix exponential method (MEM) solver with substeps. In this paper, the quadratic extrapolation/quadratic interpolation (QEQI) method is proposed as a new high-order depletion scheme. In order to examine the effectiveness of the newly-implemented depletion modules in McCARD, four problems in the VERA depletion benchmarks are solved by CEBE/MEM, CEBE/CRAM, LEQI/MEM, QEQI/MEM, and QDM for gadolinium isotopes. From the comparisons, it is shown that the QEQI/MEM predicts ${k_{inf}}^{\prime}s$ most accurately among the test cases. In addition, statistical uncertainty propagation analyses for a VERA pin cell problem are conducted by the sensitivity and uncertainty and the stochastic sampling methods.

Robust Secure Transmit Design with Artificial Noise in the Presence of Multiple Eavesdroppers

  • Liu, Xiaochen;Gao, Yuanyuan;Sha, Nan;Zang, Guozhen;Wang, Shijie
    • KSII Transactions on Internet and Information Systems (TIIS)
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    • v.15 no.6
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    • pp.2204-2224
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    • 2021
  • This paper studies secure wireless transmission from a multi-antenna transmitter to a single-antenna intended receiver overheard by multiple eavesdroppers with considering the imperfect channel state information (CSI) of wiretap channel. To enhance security of communication link, the artificial noise (AN) is generated at transmitter. We first design the robust joint optimal beamforming of secret signal and AN to minimize transmit power with constraints of security quality of service (QoS), i.e., minimum allowable signal-to-interference-and-noise ratio (SINR) at receiver and maximum tolerable SINR at eavesdroppers. The formulated design problem is shown to be nonconvex and we transfer it into linear matrix inequalities (LMIs). The semidefinite relaxation (SDR) technique is used and the approximated method is proved to solve the original problem exactly. To verify the robustness and tightness of proposed beamforming, we also provide a method to calculate the worst-case SINR at eavesdroppers for a designed transmit scheme using semidefinite programming (SDP). Additionally, the secrecy rate maximization is explored for fixed total transmit power. To tackle the nonconvexity of original formulation, we develop an iterative approach employing sequential parametric convex approximation (SPCA). The simulation results illustrate that the proposed robust transmit schemes can effectively improve the transmit performance.