• Title/Summary/Keyword: closed form expressions

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System model reduction by weighted component cost analysis

  • Kim, Jae-Hoon;Skelton, Robert-E.
    • 제어로봇시스템학회:학술대회논문집
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    • 1993.10b
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    • pp.524-529
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    • 1993
  • Component Cost Analysis considers any given system driven by a white noise process as an interconnection of different components, and assigns a metric called "component cost" to each component. These component costs measure the contribution of each component to a predefined quadratic cost function. One possible use of component costs is for model reduction by deleting those components that have the smallest component cost. The theory of Component Cost Analysis is extended to include finite-bandwidth colored noises. The results also apply when actuators have dynamics of their own. When the dynamics of this input are added to the plant, which is to be reduced by CCA, the algorithm for model reduction process will be called Weighted Component Cost Analysis (WCCA). Closed-form analytical expressions of component costs for continuous time case, are also derived for a mechanical system described by its modal data. This is very useful to compute the modal costs of very high order systems beyond Lyapunov solvable dimension. A numerical example for NASA's MINIMAST system is presented.presented.

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Green Cooperative Sensing Scheme in Heterogeneous Networks

  • Shen, Lifei;Liu, Jian;Tan, Xinxin;Wang, Lei
    • KSII Transactions on Internet and Information Systems (TIIS)
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    • v.12 no.2
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    • pp.550-565
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    • 2018
  • Cognitive radio technology is still the key technology of future mobile communication systems. Previous studies have focused on improving spectrum utilization and less energy consumption. In this paper, we propose an Overhead Reduced Scheme (ORS) for green cooperative spectrum sensing. Compared to traditional cooperative sensing scheme, ORS scheme divides the sensing time into three time slots and selects the best multi-mode user to report decisions. In consideration of reporting channel deviation, we derive closed-form expressions for detection probability and false alarm probability of ORS scheme based on Rayleigh fading channel. Simulation results show that ORS scheme can improve the perception accuracy while reducing the perceived delay and energy consumption in the process of perception, so as to realize the green communication.

Multiple Eavesdropper-Based Physical Layer Security in SIMO System With Antenna Correlation

  • Sun, Gangcan;Liu, Mengge;Han, Zhuo;Zhao, Chuanyong
    • KSII Transactions on Internet and Information Systems (TIIS)
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    • v.14 no.1
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    • pp.422-436
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    • 2020
  • In this paper, we investigate the impact of antenna correlation on secure transmission in a multi-eavesdropper single-input multiple-output (SIMO) system, where the receiver and eavesdroppers are equipped with correlated antennas. Based on the practical passive eavesdropping system, the new closed-form expressions of secrecy outage probability (SOP) and non-zero secrecy capacity probability are derived to explore the effect of antenna correlation on the system with multiple eavesdroppers. To further analyze the secrecy performance of the investigated system, we theoretically derive the expression of asymptotic SOP to clearly show the diversity order and array gain. Finally, Monte Carlo simulations verify the effectiveness of our theoretical results.

Effect of the rotation on a non-homogeneous infinite cylinder of orthotropic material with external magnetic field

  • Hussein, Nahed S.;Bayones, F.S.;Mahmoud, S.R.
    • Structural Engineering and Mechanics
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    • v.54 no.1
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    • pp.135-148
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    • 2015
  • The present investigation is concerned with a study effect of magnetic field and non-homogenous on the elastic stresses in rotating orthotropic infinite circular cylinder. A certain boundary conditions closed form stress fields solutions are obtained for rotating orthotropic cylinder under initial magnetic field with constant thickness for three cases: (1) Solid cylinder, (2) Cylinder with a circular hole at the center, (3) Cylinder mounted on a circular rigid shaft. Analytical expressions for the components of the displacement and stress fields in different cases are obtained. The effect of rotation and magnetic field and non-homogeneity on the displacement and stress fields are studied. Numerical results are illustrated graphically for each case. The effects of rotating and magnetic field and non-homogeneity are discussed.

Closed form ultimate strength of multi-rectangle reinforced concrete sections under axial load and biaxial bending

  • da Silva, V. Dias;Barros, M.H.F.M.;Julio, E.N.B.S.;Ferreira, C.C.
    • Computers and Concrete
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    • v.6 no.6
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    • pp.505-521
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    • 2009
  • The analysis of prismatic members made of reinforced concrete under inclined bending, especially the computation of ultimate loads, is a pronounced non-linear problem which is frequently solved by discretizing the stress distribution in the cross-section using interpolation functions. In the approach described in the present contribution the exact analytical stress distribution is used instead. The obtained expressions are integrated by means of a symbolic manipulation package and automatically converted to optimized Fortran code. The direct problem-computation of ultimate internal forces given the position of the neutral axis-is first described. Subsequently, two kinds of inverse problem are treated: the computation of rupture envelops and the dimensioning of reinforcement, given design internal forces. An iterative Newton-Raphson procedure is used. Examples are presented.

Effect of fractional order on energy ratios at the boundary surface of elastic-piezothermoelastic media

  • Kumar, Rajneesh;Sharma, Poonam
    • Coupled systems mechanics
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    • v.6 no.2
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    • pp.157-174
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    • 2017
  • In the present investigation reflection and transmission of plane waves at an elastic half space and piezothermoelastic solid half space with fractional order derivative is discussed. The piezothermoelastic solid half space is assumed to have 6 mm type symmetry and assumed to be loaded with an elastic half space. It is found that the amplitude ratios of various reflected and refracted waves are functions of angle of incidence, frequency of incident wave and are influenced by the piezothermoelastic properties of media. The expressions of amplitude ratios and energy ratios are obtained in closed form. The energy ratios are computed numerically using amplitude ratios for a particular model of graphite and Cadmium Selenide (CdSe). The variations of energy ratios with angle of incidence are shown graphically. The conservation of energy across the interface is verified. Some cases of interest are also deduced from the present investigation.

Noncoherent Detection of Orthogonal Modulation Combined with Alamouti Space-Time Coding

  • Simon, Marvin K.;Wang, Ji-Bing
    • Journal of Communications and Networks
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    • v.5 no.2
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    • pp.124-134
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    • 2003
  • In this paper, we investigate the error probability performance of noncoherently detected orthogonal modulation combined with Alamouti space-time block coding. We find that there are two types of pair-wise error probabilities that characterize the performance. We employ methods that allow a direct evaluation of exact, closed-form expressions for these error probabilities. Theoretical as well as numerical results show that noncoherent orthogonal modulation combined with space-time block coding (STBC) achieves full spatial diversity. We derive an expression for approximate average bit error probability for-ary orthogonal signaling that allows one to show the tradeoff between increased rate and performance degradation.

Eigenvalue analysis of structures with flexible random connections

  • Matheu, E.E.;Suarez, L.E.
    • Structural Engineering and Mechanics
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    • v.4 no.3
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    • pp.277-301
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    • 1996
  • A finite element model of a beam element with flexible connections is used to investigate the effect of the randomness in the stiffness values on the modal properties of the structural system. The linear behavior of the connections is described by a set of random fixity factors. The element mass and stiffness matrices are function of these random parameters. The associated eigenvalue problem leads to eigenvalues and eigenvectors which are also random variables. A second order perturbation technique is used for the solution of this random eigenproblem. Closed form expressions for the 1st and 2nd order derivatives of the element matrices with respect to the fixity factors are presented. The mean and the variance of the eigenvalues and vibration modes are obtained in terms of these derivatives. Two numerical examples are presented and the results are validated with those obtained by a Monte-Carlo simulation. It is found that an almost linear statistical relation exists between the eigenproperties and the stiffness of the connections.

Performance Analysis of Multi-Hop Decode-and-Forward Relaying with Selection Combining

  • Bao, Vo Nguyen Quoe;Kong, Hyung-Yun
    • Journal of Communications and Networks
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    • v.12 no.6
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    • pp.616-623
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    • 2010
  • In this paper, exact closed-form expressions for outage probability and bit error probability (BEP) are presented for multi-hop decode-and-forward (DF) relaying schemes in conjunction with cooperative diversity, in which selection combining technique is employed at each node. We have shown that the proposed protocol offers remarkable diversity advantage over direct transmission as well as the conventional DF relaying schemes with the same combining technique. We then investigate the system performance when different diversity schemes are employed. It has been observed that the system performance loss due to selection combining relative to maximal ratio combining is not significant. Simulations are performed to confirm our theoretical analysis.

Linear Diversity Analysis for M-ary Square Quadrature Amplitude Modulation over Nakagami Fading Channels

  • Yoon, Dong-Weon;Chang, Dae-Ig;Kim, Nae-Soo;Woo, Hoon-Shik
    • ETRI Journal
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    • v.25 no.4
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    • pp.231-237
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    • 2003
  • We derive and analyze the exact closed-form expression for the average bit error probability (BEP) of M-ary square quadrature amplitude modulation (QAM) for diversity reception in frequency-nonselective Nakagami fading. A maximal ratio combining (MRC) diversity technique with independent or correlated fading cases are considered. Numerical results demonstrate error performance improvement with the use of MRC diversity reception. The presented new expressions offer a convenient way to evaluate the performance of M-ary square QAM with an MRC diversity combiner for various cases of practical interest.

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