• Wind and Structures
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• v.16 no.5
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• pp.517-540
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• 2013

This paper presents applications of proper orthogonal decomposition in both the time and frequency domains based on both cross spectral matrix and covariance matrix branches to analyze multi-variate unsteady pressure fields on prisms and to study spanwise and chordwise pressure distribution. Furthermore, modification of proper orthogonal decomposition is applied to a rectangular spanwise coherence matrix in order to investigate the spanwise correlation and coherence of the unsteady pressure fields. The unsteady pressure fields have been directly measured in wind tunnel tests on some typical prisms with slenderness ratios B/D=1, B/D=1 with a splitter plate in the wake, and B/D=5. Significance and contribution of the first covariance mode associated with the first principal coordinates as well as those of the first spectral eigenvalue and associated spectral mode are clarified by synthesis of the unsteady pressure fields and identification of intrinsic events inside the unsteady pressure fields. Spanwise coherence of the unsteady pressure fields has been mapped the first time ever for better understanding of their intrinsic characteristics.

• 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.

• Wind and Structures
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• v.29 no.6
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• pp.389-403
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• 2019

In this study, two original spectral representations of stationary stochastic fields, say the continuous proper orthogonal decomposition (CPOD) and the frequency-wavenumber spectral representation (FWSR), are derived from the Fourier-Stieltjes integral at first. Meanwhile, the relations between the above two representations are discussed detailedly. However, the most widely used conventional Monte Carlo schemes associated with the two representations still leave two difficulties unsolved, say the high dimension of random variables and the incompleteness of probability with respect to the generated sample functions of the stochastic fields. In view of this, a dimension-reduction model involving merely one elementary random variable with the representative points set owing assigned probabilities is proposed, realizing the refined description of probability characteristics for the stochastic fields by generating just several hundred representative samples with assigned probabilities. In addition, for the purpose of overcoming the defects of simulation efficiency and accuracy in the FWSR, an improved scheme of non-uniform wavenumber intervals is suggested. Finally, the Fast Fourier Transform (FFT) algorithm is adopted to further enhance the simulation efficiency of the horizontal stochastic wind velocity fields. Numerical examplesfully reveal the validity and superiorityof the proposed methods.

• Journal of Industrial Technology
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• v.25 no.B
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• pp.89-97
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• 2005

Application of proper orthogonal decomposition (POD) and continuous wavelet transform (CWT) is introduced to study wind speed and building roof pressures of flow separation region. In this study, a detailed analysis of the approach wind flow, wind-induced building pressure and the relation between the two fields was carried out using the POD technique and CWT analysis. The results show potential of the application of POD and CWT in characterization of spatio-temporal and spectral properties of the approach wind and its induced dynamic pressure events. Some of findings resulting from the application of this analysis can be summarized as follows: (1) The POD first principal coordinate of the roof pressure in the separated shear layer is closely correlated with the longitudinal component of oncoming flow. (2) The CWT analysis suggests that the extreme peak pressure in the separated shear layer is due to condensed large-scale eddy motions.

• Proceedings of the Computational Structural Engineering Institute Conference
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• 2004.10a
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• pp.11-18
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• 2004

In this paper, an efficient model reduction scheme is presented for large scale dynamic systems. The method is founded on a modal analysis in which optimal eigenvalue is extracted from time samples of the given system response. The techniques we discuss are based on classical theory such as the Karhunen-Loeve expansion. Only recently has it been applied to structural dynamics problems. It consists in obtaining a set of orthogonal eigenfunctions where the dynamics is to be projected. Practically, one constructs a spatial autocorrelation tensor and then performs its spectral decomposition. The resulting eigenfunctions will provide the required proper orthogonal modes(POMs) or empirical eigenmodes and the correspondent empirical eigenvalues (or proper orthogonal values, POVs) represent the mean energy contained in that projection. The purpose of this paper is to compare the reduced order model using Karhunen-Loeve expansion with the full model analysis. A cantilever beam and a simply supported plate subjected to sinusoidal force demonstrated the validity and efficiency of the reduced order technique by K-L method.

• 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.

• Wind and Structures
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• v.32 no.3
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• pp.227-238
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• 2021

This study analyzed the pressure patterns and local pressure of tall buildings with corner modifications (recessed and chamfered corner) using wind tunnel tests and proper orthogonal decomposition (POD). POD can distinguish pressure patterns by POD mode and more dominant pressure patterns can be found according to the order of POD modes. Results show that both recessed and chamfered corners effectively reduced wind-induced responses. Additionally, unique effects were observed depending on the ratio of corner modification. Tall building models with recessed corners showed fluctuations in the approaching wind flow in the first POD mode and vortex shedding effects in the second POD mode. With large corner modification, energy distribution became small in the first POD mode, which shows that the effect of the first POD mode reduced. Among building models with chamfered corners, vortex shedding effects appeared in the first POD mode, except for the model with the highest ratio of corner modifications. The POD confirmed that both recessed and chamfered corners play a role in reducing vortex shedding effects, and the normalized power spectral density peak value of modes showing vortex shedding was smaller than that of the building model with a square section. Vortex shedding effects were observed on the front corner surfaces resulting from corner modification, as with the side surface. For buildings with recessed corners, the local pressure on corner surfaces was larger than that of side surfaces. Moreover, the average wind pressure was effectively reduced to 88.42% and 92.40% in RE1 on the windward surface and CH1 on the side surface, respectively.

• Journal of the Korean Society for Industrial and Applied Mathematics
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• v.19 no.2
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• pp.123-135
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• 2015

In this paper, a reduced-order modeling(ROM) of Burgers equations is studied based on pseudo-spectral collocation method. A ROM basis is obtained by the proper orthogonal decomposition(POD). Crank-Nicolson scheme is applied in time discretization and the pseudo-spectral element collocation method is adopted to solve linearlized equation based on the Newton method in spatial discretization. We deliver POD-based algorithm and present some numerical experiments to show the efficiency of our proposed method.

• 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.

• Wind and Structures
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• v.12 no.3
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• pp.239-257
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• 2009

This paper develops and discusses a method by which it is possible to evaluate the Equivalent Static Force (ESF) of wind in the case of long-span bridges. Attention is focused on the alongwind direction. The study herein carried out deals with the classical problems of determining the maximum effects due to the alongwind action and the corresponding ESFs. The mean value of the maximum alongwind displacement of the deck is firstly obtained both by the spectral analysis and the Gust Response Factor (GRF) technique. Successively, in order to derive the other wind-induced effects acting on the deck, the Gust Effect Factor (GEF) technique is extended to long-span bridges. By adopting the GRF technique, it is possible to define the ESF that applied on the structure produces the maximum alongwind displacement. Nevertheless the application of the ESF so obtained does not furnish the correct maximum values of other wind-induced effects acting on the deck such as bending moments or shears. Based on this observation, a new technique is proposed which allows to define an ESF able to simultaneously reproduce the maximum alongwind effects of the bridge deck. The proposed technique is based on the GEF and the POD techniques and represents a valid instrument of research for the understanding of the wind excitation mechanism.