Non-stationary Wind Fields Research Articles

Characteristics of Fluctuating Wind Speed Spectra of Moving Vehicles under the Non-Stationary Wind Field

To promote energy saving, emission reduction, and sustainable development of high-speed trains, as well as achieve low-carbon operation of these trains. It is necessary to establish a fluctuating wind speed spectra model that can accurately describe the characteristics of the fluctuating wind speed field of the moving vehicle. This will help explore the effects of strong winds on the running resistance, energy consumption, safety, and comfort of trains. In this paper, based on Priestley’s evolutionary power spectral density (EPSD) theory, an efficient method was developed for generating the fluctuating wind speeds at the moving point under the non-stationary wind field. On such basis, the effects of different mean wind speeds, ground clearances, temporal modulation function parameters, and vehicle’s moving speeds on the time-varying correlation function ratio of fluctuating wind speed at fixed and moving points were analyzed. Subsequently, the relationship between the time-varying correlation functions of fluctuating wind speed at the fixed and moving points was established by analyzing the sensitivity of the above parameters, and a theoretical model of fluctuating wind speed spectra of the moving point under the non-stationary wind field was proposed. In addition, the relational expression of fluctuating wind speed spectra of the moving point under stationary and non-stationary wind fields was established, which was further validated using the fluctuating wind speed spectra model at the fixed points with different modulation function forms. The results demonstrated that the direct generation method can avoid n times of POD decomposition and Ns∑j=1nNqjj times of FFT calculation, improve the calculation speed, and save memory. The proposed fluctuating wind speed spectra model at the moving point under the non-stationary wind field is in good agreement with the corresponding target one, indicating the high accuracy of the proposed model. Meanwhile, it is also noted that the fluctuating wind speed spectra at the moving point under the non-stationary wind field can be obtained by modulating the spectra under the stationary wind field using temporal modulation function, which is the same as that of the fluctuating wind speed spectra at fixed points under the non-stationary wind field.

High-efficiency simulation of nonstationary wind velocity using diagonal POD of decomposed time-frequency interpolation node spectrum matrices

The classical spectral representation method (SRM) used extensively to simulate nonstationary wind fields suffers from lower efficiency. Although some tries can already accelerate SRM, the efficiency improvement is restricted when the number of simulation points is large. For this reason, this paper proposed a high-efficiency interpolation scheme to boost the efficiency of SRM. Firstly, the decomposed time-frequency interpolation node spectrum matrices can be approximately decouple into the products of time and frequency functions using diagonal proper orthogonal decomposition (POD). Specifically, the POD operation is just for the diagonal elements, which are low-dimensional matrices. Since Cholesky decomposition is merely needed in the time-frequency interpolation point, the time consumed by spectral decomposition will be significantly reduced. Then, one-dimensional (1D) interpolation is implemented for these decoupling terms in the time and frequency directions, respectively. The decoupling results only contains a few time terms, so the number of 1D interpolation operations can be considerably decreased. Moreover, by exchanging the summation order, very few fast Fourier transform operations are required to accelerate harmonic superposition. Therefore, the proposed method may further enhance the simulation efficiency. Finally, through numerical examples, the accuracy and superiority of the proposed method are demonstrated.

Field measurement analysis of wind parameters and nonstationary characteristics in mountainous terrain: Focusing on cooling windstorms

Cold fronts passing through the mountain areas may produce continuous windstorm and cooling processes, potentially impacting the mountain areas' infrastructure. Cooling windstorms belong to the dynamically-driven wind in the mountain wind system. To accurately estimate the wind field parameters of these storms and provide a basis for structural wind resistance design, cooling windstorms should be extracted and analyzed separately from the wind field observation data. Based on the long-term field measurement in complex mountain terrain, a framework for identifying cooling windstorms is established according to temperature and wind speed features. The mean and fluctuating wind parameters of these intense winds are then obtained. Strong nonstationary is detected for cooling windstorms. This paper focuses on the time-varying regularity of fluctuating parameters during intense wind with cooling based on the evolutionary power spectral density. From the perspective of turbulent energy, the basis for selecting the optimal wavelet decomposition levels is put forward when extracting the time-varying mean wind through discrete wavelet transform in the nonstationary wind speed model. This investigation can provide a reference for studying the nonstationary wind field.

Influence of Phases of Coherence Functions on the Wind Field Simulation Using Spectral Representation Method

The wave passage effect is a measure of the wave passage delay due to the apparent velocity of waves, which is one of spatially varying properties of multivariate random processes. The phase of coherence function reflects the wave passage effect of wind fields. In the wind field, simulation by the spectral representation method, the classical phase formula, is not rigorous. This may affect the accuracy of simulation results and even cause incorrect simulations. In this study, the influences of the phase on stationary and nonstationary wind field simulations are researched and discussed in detail. Two schemes containing the classical phase formula and the separated phase scheme are compared in four types of wind field simulation. The qualitative analysis based on theoretical correlation function formula is first made to study the influence of the phase. Then, four numerical examples are utilized to quantitatively study the magnitude of the influence on the sample time history and correlation function of the simulated wind field. Results show that the classical phase formula will result in considerable simulation error for all four types of wind fields because it cannot completely represent the phase angle of a complex number.

Conditional simulation of 3D nonstationary wind field for sea-crossing bridges

This paper presents a framework for the conditional simulation of a 3D nonstationary wind field for super-long sea-crossing bridges based on wind speed time histories measured by limited anemometers on site. The variations of wind characteristics along the bridge deck with multi-elements are considered in this framework. The wind characteristics, including mean wind speeds, mean wind directions, turbulence intensities, turbulence integral scales, evolutionary wind spectra and spectral parameters, coherence functions and function parameters, at the measurement points are first obtained by analyzing the measured wind speed time histories. The wind characteristics are then extended over all the simulation points along the deck of the sea-crossing bridge using the spatial interpolation method and considering the variation of deck height above the sea level using the profiles of mean wind speeds, turbulence intensities and turbulence integral scales estimated from the measured wind speed time histories. After working out wind cross correlation functions, wind speed time histories at all simulation points over the sea-crossing bridge can be conditionally simulated. The proposed framework is finally applied to a real 22.9 km sea-crossing bridge under Typhoon Higos. The conditionally simulated wind speed time histories at all simulation points of the bridge are acceptable and consist a complete wind field which can be used for the buffeting analysis of the bridge.

Fast simulation of fully non-stationary wind fields using a new matrix factorization assisted interpolation method

The classical spectral representation method and its improved versions have been widely used to generate non-stationary wind fields. However, they are not efficient for the simulation of non-stationary wind fields with time-varying coherence (i.e., fully non-stationary wind fields) due to the extensive computational demand regarding spectral matrix decomposition or harmonic superposition. To this end, this study develops a new matrix factorization assisted interpolation method, which is composed of an improved interpolation scheme and the monotone projected Barzilai-Borwein based non-negative matrix factorization (MPBB-NMF). Specifically, an improved interpolation scheme is firstly developed to quantify the desired distribution of time-frequency interpolation nodes, and only the decomposed spectra at these nodes are calculated by Cholesky decomposition. Then, MPBB-NMF with a fast global convergence is used to decouple these spectra into products of non-negative time- and frequency-dependent functions. Finally, one-dimensional interpolation is performed for these decoupled functions, which makes it possible to accelerate the harmonic superposition using a small amount of fast Fourier transforms (FFTs). Obviously, the proposed method realizes the decomposition of spectral matrix in the decoupling form. Besides reducing of the number of Cholesky decomposition and invoking FFT, its decoupling only aims at the low dimensional matrix and the interpolation merely involves a few decoupled items. Numerical simulation on the fully non-stationary wind field of a long-span bridge demonstrates the effectiveness and superiority of the proposed method.

Fast simulation of nonstationary wind velocity fields by proper orthogonal decomposition interpolation

The classic spectral representation method (SRM) has been extensively utilized in simulating nonstationary wind velocity fields because of its great precision and simplicity. However, this method is computationally expensive when it is applied to the situation with a great number of simulation positions. Although several attempts have been made to alleviate the computational burden, the efficiency improvement may be limited. To this end, this study develops a proper orthogonal decomposition (POD) interpolation-enhanced approach to expedite the simulation of nonstationary wind fields by SRM. Firstly, the Cholesky decomposition is only executed for the spectral matrices at time-frequency interpolation points and the corresponding computational cost is therefore reduced greatly. The POD interpolation is then used to approximately decouple each decomposed spectrum into a small amount of time and frequency functions, thereby invoking the fast Fourier transform to speed up the summing of cosine functions. The POD operation is merely executed for the low-dimensional matrix and the interpolation operation solely aims at the few time and frequency functions. As a result, the proposed approach has the potential to considerably improve the simulation efficiency. Finally, numerical examples with the simulation of two different nonstationary wind fields validate its precision and efficiency.

Fast Hilbert–Wavelet Simulation of Nonstationary Wind Field Using Noniterative Simultaneous Matrix Diagonalization

AbstractThe frequency content and spatial correlation of nonstationary wind fields during extreme events typically present time-variant characteristics. Several effective schemes [e.g., using evolu...

Dynamic Studies on Blade of Wind Turbine Generator, Taking into Account Aerodynamic Interaction with Non-Homogeneous, Non-Stationary Wind Field

Dynamic Studies on Blade of Wind Turbine Generator, Taking into Account Aerodynamic Interaction with Non-Homogeneous, Non-Stationary Wind Field

Efficient simulation of fully non-stationary random wind field based on reduced 2D hermite interpolation

The spectral representation method (SRM) has been widely used to simulate stationary or non-stationary wind fields for engineering structures. Although several attempts have been made to realize the invoking of Fast Fourier Transform (FFT), the SRM is still very inefficient to simulate the fully non-stationary wind field with a time-varying coherence due to the extremely time-consuming Cholesky decompositions and large memory requirement. In this paper, a reduced 2D Hermite interpolation-enhanced approach is developed to further improve the efficiency of SRM in simulating fully non-stationary wind fields. Central to this approach is the interpolation procedure which requires Cholesky decompositions and storage of cross power spectral density matrix (CEPSD) elements only at interpolation knots. Thus the computational costs of Cholesky decompositions and memory requirement are dramatically decreased. The number of Cholesky decompositions is then fixed with no relation to the segments of frequency and duration of wind samples, which eliminates the Cholesky decomposition as a cause that affects the simulation efficiency. Meanwhile, each element in the decomposed CEPSD matrix is decoupled into products of time- and frequency-dependent functions by the reduced 2D Hermite interpolation, so the FFT can be used to expedite the summation of trigonometric terms. Apart from using FFT, another merit of the proposed approach is that an accelerated FFT algorithm can be incorporated to further improve the simulation efficiency based on the specific decoupled expression of frequency-dependent functions. The parametric analysis shows that the proposed approach is very efficient in comparison with the existing method using proper orthogonal decomposition (POD), and it provides a desired level of simulation accuracy when appropriate interpolation interval is selected. The case study in simulating the fully non-stationary wind field of a long-span cable-stayed bridge demonstrates the effectiveness of the proposed approach with verifications on both evolutionary power spectra and correlation functions.

Dynamical stresses in the high class wind turbine blades caused in nonhomogeneous nonstationary wind field. Part 1 Dynamical model

The wind turbines of a high class are with considerable sizes. For this reason, the consideration of the fluid field as a homogeneous when performing the aerodynamic analysis is not quite correct. In addition, due to the gusts and horizontal turbulence, the wind field is also nonstationary. All this causes dynamic, time-varying loads and fatigue. The determination of these loads is a major aim of this publication. The turbine blades are considered as Euler-Bernoulli beams under the impact of the aerodynamic thrust and torque forces as well as from this of the centrifugal force. The finite element method is applied to solve the partial differential equations describing the model under consideration. Two-node elements with four degrees of freedom for each node and a cubic, polynomial approximation of modal shapes were used. The deformations are relatively small in the separated finite elements and this makes it possible to apply the superposition principle.

Dynamical stresses in the high class wind turbine blades caused in nonhomogeneous nonstationary wind field. Part 2 Numerical simulations

In this second part of the publication, numerical results for a specific a wind turbine model of a high class – prototype NREL 5MW are presented. A wind speed model is described, taking into account the vertical speed gradient and longitudinal turbulence. Based on the proposed by the authors a modification of Blade Element Momentum theory, the aerodynamic forces, distributed along the length of turbine blades, are calculated as time functions. As a result of this, according to the results of the first part of the publication, the dynamical loads, stresses, and deformations in the blades are calculated.

Simulation of nonstationary wind in one-spatial dimension with time-varying coherence by wavenumber-frequency spectrum and application to transmission line

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.

INCREASE OF WAVE HEIGHT DUE TO TRANSITION IN WIND DIRECTION – EXAMPLE: RIJEKA BAY

Surface wind wave dynamics were analyzed during wind transition from the third to the fourth quadrant, with the transition from Sirocco to Libeccio used as an example. This research is focused on the deepwater area in front of the Rijeka port. The analyses utilized a numerical model for wave generation, covering the entire Adriatic basin. Numerical simulations were conducted for relevant situations during the period 1998-2001. The numerical model was forced by the wind field obtained from the Aladin-HR atmospheric model. Numerical simulations were conducted in two steps, initially using hypothetical scenarios with homogenous and stationary wind fields, followed by simulations based on nonstationary wind fields from the Aladin-HR atmospheric model. The first step was used to confirm the hypothesis that significant wave heights rise during the transition of wind direction in the analyzed area. Model simulations in step two verified the assumption that the observed phenomenon can also occur in real atmospheric conditions.The results of the model simulations indicate the onset of a significant wave height increase during the transition of wind direction from the SSE to SW in a wider area that includes Kvarner and Rijeka bay. The increase in wind velocity results in a more noticeable significant wave height maximum.

Dynamic response of the tower of a NREL5MW wind turbine generator

Considering the complexity of the aerodynamic interaction between a non-homogeneous, nonstationary wind field and a wind turbine, one can easily establish that the constructive elements of the turbine will be exposed to dynamic loads, which will eventually lead to forced motion and particularly to forced vibrations. One of the most significant elements of every wind turbine is the tower of the generator. The tower is subjected to forced vibrations and transmits all dynamic loads that appear in the wind turbine. That is why a dynamic analysis of the tower is worth executing. In this research such an analysis is made considering the tower of the generator as Euler-Bernoulli beam structure and considering it as a Love-Kirchhoff shell structure.

Fatigue life estimation of existing bridges under vehicle and non-stationary hurricane wind

During hurricane events, additional damages to existing bridge details might be accumulated from the large stress cycles generated by the non-stationary wind and dynamic vehicle loads. The environmental corrosion could also reduce the structural fatigue strength. Based on the non-stationary wind field modeling techniques and the vehicle–bridge–wind dynamic analysis framework, this paper initiates a fatigue damage assessment of existing bridges with corrosion under vehicle and non-stationary extreme hurricane wind loads. The non-stationary hurricane wind is simulated as a summation of time-varying mean and fluctuating non-stationary components with a time-varying spectrum. Dynamic stress histories are obtained by solving the vehicle–bridge–wind dynamic system. The rain flow counting method is used to obtain the stress ranges and numbers of stress cycles. The corrosion induced fatigue strength degradation is included in the analysis. Numerical examples of an existing long span bridge under simulated non-stationary hurricane winds and vehicles are presented to demonstrate the effects of the dynamic loads and corrosions on the fatigue life estimation of existing bridges.

Vulnerability assessment of container cranes under stochastic wind loading

Container cranes, an essential component in any seaport facility system, are highly susceptible to failure during natural disasters such as severe windstorms. Damage or collapse of these structures can lead to significant amount of economic loss in terms of both repair or replacement and downtime. To study how various parameters such as boom position, yaw angle, gradient height and gradient wind speed affect the failure vulnerability of a crane, in this work, a representative container crane has been modelled in a commercial software considering both material and geometric nonlinearities. Stochastic wind fields are simulated as a stationary process by means of the spectral representation method using power spectrum in conjunction with along- and across-wind coherence functions. Wind fields are also simulated as a non-stationary stochastic process utilising the modulation functions from the available literature to consider the situations of thunderstorm downbursts. Nonlinear time history analyses are then performed and a few responses are compared for stationary and non-stationary wind field cases. It is observed that for the given simulation parameters, the responses considering stationary wind fields are larger than those of the non-stationary wind fields. Failure vulnerability of the crane is then assessed in terms of fragility curves. The results of this study show that the failure vulnerability may not be maximum for the set of parameter values for which the aerodynamic forces are maximum. This study provides a better understanding of crane vulnerability that may be utilised to achieve a better crane design.

New frontiers in aerodynamic tailoring of long span bridges: an advanced analysis framework

Significant developments in bridge aeroelastic analysis have been made utilizing realistic aerodynamic force modeling for bridges with bluff sections under turbulent winds. With these developments as a background, this paper highlights state-of-the-art developments in the aeroelastic analysis and identifies new frontiers in aerodynamic tailoring of long span bridges. Challenges in the aeroelastic analysis are pointed out that include: the modeling of aerodynamic forces excited by non-stationary wind fields such as hurricanes and thunderstorms and/or for bridges located in complex topography conditions; consideration of nonlinearities in both structural dynamics and aerodynamics; and the ubiquitous issues related to turbulence. In response to these challenges, an advanced analysis framework is offered that focuses on the needs for modeling of aerodynamic and structural nonlinearities, and the effects of turbulence on long span bridges.