• Wind and Structures
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• v.38 no.1
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• pp.1-13
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• 2024

In order to effectively simulate nonstationary stochastic turbulent wind fields, four separation hybrid (SEP-H) models are proposed in the present study. Based on the assumption that the lateral turbulence component at one single-point is uncorrelated with the longitudinal and vertical turbulence components, the fluctuating wind is separated into 2nV-1D and nV1D nonstationary stochastic vector processes. The first process can be expressed as double proper orthogonal decomposition (DPOD) or proper orthogonal decomposition and spectral representation method (POD-SRM), and the second process can be expressed as POD or SRM. On this basis, four SEP-H models of nonstationary stochastic turbulent wind fields are developed. In addition, the orthogonal random variables in the SEP-H models are presented as random orthogonal functions of elementary random variables. Meanwhile, the number theoretical method (NTM) is conveniently adopted to select representative points set of the elementary random variables. The POD-FFT (Fast Fourier transform) technique is introduced in frequency to give full play to the computational efficiency of the SEP-H models. Finally, taking a long-span bridge as the engineering background, the SEP-H models are compared with the dimension-reduction DPOD (DR-DPOD) model to verify the effectiveness and superiority of the proposed models.

• Structural Engineering and Mechanics
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• v.66 no.1
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• pp.139-149
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• 2018

Many practical engineering problems are associated with nonlinear systems subjected to nonstationary random excitations. Equivalent linearization methods are commonly used to seek for approximate solutions to this kind of problems. Compared to various approaches developed in the frequency and mixed time-frequency domains, though directly solving the system equation of motion in the time domain would improve computation efficiency, only limited studies are available. Considering the fact that the orthogonal functions have been widely used to effectively improve the accuracy of the approximated responses and reduce the computational cost in various engineering applications, an orthogonal-function-based equivalent linearization method in the time domain has been proposed in the current paper for nonlinear systems subjected to nonstationary random excitations. In the numerical examples, the proposed approach is applied to a SDOF system with a set-up spring and a SDOF Duffing oscillator subjected to stationary and nonstationary excitations. In addition, its applicability to nonlinear MDOF systems is examined by a 3DOF Duffing system subjected to nonstationary excitation. Results show that the proposed method can accurately predict the nonlinear system response and the formulation of the proposed approach allows it to be capable of handling any general type of nonstationary random excitations, such as the seismic load.

• ETRI Journal
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• v.34 no.6
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• pp.879-884
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• 2012

When the number of users is finite, the performance improvement of the orthogonal random beamforming (ORBF) scheme is limited in high signal-to-noise ratio regions. In this paper, to improve the performance of the ORBF scheme, the user set and transmit power allocation are jointly determined to maximize sum rate under the total transmit power constraint. First, the transmit power allocation problem is expressed as a function of a given user set. Based on this expression, the optimal user set with the maximum sum rate is determined. The suboptimal procedure is also presented to reduce the computational complexity, which separates the user set selection procedure and transmit power allocation procedure.

• KSII Transactions on Internet and Information Systems (TIIS)
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• v.15 no.12
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• pp.4567-4583
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• 2021

This study proposes an analytical approximation algorithm based on extreme value theory (EVT) for the inverse of the power of the incomplete Gamma function. First, the Gumbel function is used to approximate the power of the incomplete Gamma function, and the corresponding inverse problem is transformed into the inversion of an exponential function. Then, using the tail equivalence theorem, the normalized coefficient of the general Weibull distribution function is employed to replace the normalized coefficient of the random variable following a Gamma distribution, and the approximate closed form solution is obtained. The effects of equation parameters on the algorithm performance are evaluated through simulation analysis under various conditions, and the performance of this algorithm is compared to those of the Newton iterative algorithm and other existing approximate analytical algorithms. The proposed algorithm exhibits good approximation performance under appropriate parameter settings. Finally, the performance of this method is evaluated by calculating the thresholds of space-time block coding and space-frequency block coding pattern recognition in multiple-input and multiple-output orthogonal frequency division multiplexing. The analytical approximation method can be applied to other related situations involving the maximum statistics of independent and identically distributed random variables following Gamma distributions.

• Wind and Structures
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• v.7 no.2
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• pp.107-130
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• 2004

This paper presents a time-domain approach for analyzing nonlinear random vibrations of long-span suspended cables under transversal wind. A consistent continuous model of the cable, fully accounting for geometrical nonlinearities inherent in cable behavior, is adopted. The effects of spatial correlation are properly included by modeling wind velocity fluctuation as a random function of time and of a single spatial variable ranging over cable span, namely as a one-variate bi-dimensional (1V-2D) random field. Within the context of a Galerkin's discretization of the equations governing cable motion, a very efficient Monte Carlo-based technique for second-order analysis of the response is proposed. This procedure starts by generating sample functions of the generalized aerodynamic loads by using the spectral decomposition of the cross-power spectral density function of wind turbulence field. Relying on the physical meaning of both the spectral properties of wind velocity fluctuation and the mode shapes of the vibrating cable, the computational efficiency is greatly enhanced by applying a truncation procedure according to which just the first few significant loading and structural modal contributions are retained.

• Structural Engineering and Mechanics
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• v.75 no.4
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• pp.425-434
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• 2020

Practical non-synoptic fluctuating wind often exhibits nonstationary features and should be modeled as nonstationary random processes. Generally, the coherence function of the fluctuating wind field has time-varying characteristics. Some studies have shown that there is a big difference between the fluctuating wind field of the coherent function model with and without time variability. Therefore, it is of significance to simulate nonstationary fluctuating wind field with time-varying coherent function. However, current studies on the numerical simulation of nonstationary fluctuating wind field with time-varying coherence are very limited, and the proposed approaches are usually based on the traditional spectral representation method with low simulation efficiency. Especially, for the simulation of multi-variable wind field of large span structures such as transmission tower-line, not only the simulation is inefficient but also the matrix decomposition may have singularity problem. In this paper, it is proposed to conduct the numerical simulation of nonstationary fluctuating wind field in one-spatial dimension with time-varying coherence based on the wavenumber-frequency spectrum. The simulated multivariable nonstationary wind field with time-varying coherence is transformed into one-dimensional nonstationary random waves in the simulated spatial domain, and the simulation by wavenumber frequency spectrum is derived. So, the proposed simulation method can avoid the complicated Cholesky decomposition. Then, the proper orthogonal decomposition is employed to decompose the time-space dependent evolutionary power spectral density and the Fourier transform of time-varying coherent function, simultaneously, so that the two-dimensional Fast Fourier transform can be applied to further improve the simulation efficiency. Finally, the proposed method is applied to simulate the longitudinal nonstationary fluctuating wind velocity field along the transmission line to illustrate its performances.

• Journal of the Society of Naval Architects of Korea
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• v.42 no.3
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• pp.212-219
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• 2005

Real sea waves in a towing wave basin have been generated using random periodic motion of the segmented wave makers and the wave reflections of sidewalls. Theoretically, the real sea waves can be described by the superposition of many random oblique waves. This paper introduces numerical real sea wave generation in a rectangular wave basin using spectral method that uses a superposition of orthogonal functions which have to satisfy the Laplace equation. Oblique regular waves, long crested irregular waves and real sea waves were simulated and met the requirement of sidewall wave reflection and wave absorption. MLM (Maximum Likelihood Method) and Spatial Fourier Transform were used in order to obtain propagated wave direction characteristics. The estimated results proved the usefulness of the method and the performances showed reasonable directional patterns comparing with generating patterns.

• Journal of IKEEE
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• v.17 no.3
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• pp.339-345
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• 2013

In this paper, the probabilistic exclusion based orthogonal matching pursuit (PEOMP) algorithm for the sparse signal reconstruction is proposed. Some of recent greedy algorithms such as CoSaMP, gOMP, BAOMP improved the reconstruction performance by deleting unsuitable atoms at each iteration. They still often fail to converge to the solution because the support set could not escape from a local minimum. PEOMP helps to escape by excluding a random atom in the support set according to a well-chosen probability function. Experimental results show that PEOMP outperforms several OMP based algorithms and the $l_1$ optimization method in terms of exact reconstruction probability.

• Journal of Communications and Networks
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• v.12 no.3
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• pp.222-230
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• 2010

In this paper, we present a closed-form approximation of the average sum rate of zero-forcing (ZF) beamforming (BF) with semi-orthogonal user selection (SUS). We first derive the survival probability associated with the SUS that absolute square of the channel correlation between two users is less than the orthogonalization level threshold (OLT).With this result, each distribution for the number of surviving users at each iteration of the SUS and the number of streams for transmission is calculated. Secondly, the received signal power of ZF-BF is represented as a function of the elements of the upper triangular matrix from QR decomposition of the channel matrix. Thirdly, we approximate the received signal power of ZF-BF with the SUS as the maximum of scaled chisquare random variables where the scaling factor is approximated as a function of both OLT and the number of users in the system. Putting all the above derivations and order statistics together, the approximated ergodic sum rate of ZF-BF with the SUS is shown in a closed form. The simulation results verify that the approximation tightly matches with the sample average for any OLT and even for a small number of users.

• Journal of Communications and Networks
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• v.7 no.1
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• pp.21-28
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• 2005

In this paper, we analyze the performance of code division multiple access (CDMA) systems with orthogonal frequency division multiplexing (OFDM) that employ random spreading sequences in an additive white Gaussian noise (AWGN) channel. We obtain the probability density function (pdf) of the multiple access interference and extend the results to OFDM-CDMA systems to determine the pdf of multiple access and inter-carrier interference in terms of the number of users, the spreading length, the number of sub-carriers, and the frequency offset. We consider the synchronous downlink of cellular multi-carrier CDMA and derive a Gaussian approximation of the multiple access and inter-carrier interference. Overall the effect of frequency offset is shown to vary with the system loading. The analysis in this paper is critical for further development into fading channels and frequency selective multipath channels.