Non-stationary Wind Speed Research Articles

Analysis of non-stationary wind characteristics at an arch bridge using structural health monitoring data

The accurate characterization of the wind characteristics of extreme wind events is crucial to the structural design and safety evaluation. However, the field-measured wind data during typhoons exhibit a strong non-stationary feature with an inherent time-varying trend which deviates from the traditional stationary assumption. This paper presents the study of non-stationary wind characteristics of Typhoon Soudelor at the Jiubao Bridge located in Hangzhou, China, which has been instrumented with a structural health monitoring system. After data classification by the stationary test, the non-stationary wind data are analyzed by both traditional stationary wind model and non-stationary wind model which considers the inherent time–varying mean wind speed. The empirical mode decomposition (EMD) and wavelet multiresolution analysis (MRA) are employed to extract the underlying trend from the original wind data as the time-varying mean wind speed for the non-stationary wind model. Based on two categories of fluctuating wind speeds obtained by removing the constant and time-varying mean wind speed, the wind characteristics including the mean wind speed, turbulence intensity, gust factor, probability distribution and power spectral density are comparatively analyzed. The results indicate that the time-varying mean wind speed can be effectively identified and extracted by the EMD and MRA. The non-stationary wind model is more appropriate than the traditional stationary wind model in the analysis of non-stationary wind speed data during a typhoon.

Analysis of buffeting response of hinged overhead transmission conductor to nonstationary winds

Abstract This paper addresses analysis of dynamic buffeting response of a hinged transmission line (conductor) under nonstationary wind excitations. The nonstationary wind speed is characterized by deterministic time-varying mean and stochastic fluctuating components. The wind load on the conductor is quantified using quasi-steady theory. The wind-induced response of the conductor is decomposed into deterministic time-varying mean and stochastic dynamic components. The time-varying mean response is determined by nonlinear static analysis with an analytical solution. The stochastic dynamic response is determined through quasi-static analysis in terms of influence function around the time-varying mean equilibrium. A closed-form formulation is presented for calculating time-varying standard derivation of response. The cumulative distribution function of the extreme response over a given time duration is then calculate using mean upcrossing rate theory of nonstationary random process. The effectiveness and accuracy of the proposed analytical framework are verified through response time history analysis using a nonlinear finite element model. The response characteristics of conductor under various nonstationary winds are examined through a parametric study.

Temporal-spatial cross-correlation analysis of non-stationary near-surface wind speed time series

Temporal-spatial cross-correlation analysis of non-stationary wind speed time series plays a crucial role in wind field reconstruction as well as in wind pattern recognition. Firstly, the near-surface wind speed time series recorded at different locations are studied using the detrended fluctuation analysis (DFA), and the corresponding scaling exponents are larger than 1. This indicates that all these wind speed time series have non-stationary characteristics. Secondly, concerning this special feature (i.e., non-stationarity) of wind signals, a cross-correlation analysis method, namely detrended cross-correlation analysis (DCCA) coefficient, is employed to evaluate the temporal-spatial cross-correlations between non-stationary time series of different anemometer pairs. Finally, experiments on ten wind speed data synchronously collected by the ten anemometers with equidistant arrangement illustrate that the method of DCCA cross-correlation coefficient can accurately analyze full-scale temporal-spatial cross-correlation between non-stationary time series and also can easily identify the seasonal component, while three traditional cross-correlation techniques (i.e., Pearson coefficient, cross-correlation function, and DCCA method) cannot give us these information directly.

Measurements and analysis of non-stationary wind characteristics at Sutong Bridge in Typhoon Damrey

Recent measurements of the wind field during extreme wind events (tropical and extratropical storms) indicate that the wind speed fluctuations exhibit strong non-stationary features echoing similar observations reported at other locations. In this study, the wind data of Typhoon Damrey recorded by the Structural Health Monitoring System (SHMS) at the Sutong Bridge were analyzed to examine the non-stationary features. Following stationarity test, the wind data were analyzed by both the stationary and non-stationary wind speed models utilizing conventional time- or frequency-domain as well from the time–frequency perspective. Wind characteristics, e.g., the mean wind speed, turbulence intensity, gust factor and power spectral density including the evolutionary power spectral density (EPSD) of the wind were evaluated. The EPSD, which represents the distribution of the local turbulent energy in both time and frequency domains, was estimated using a wavelet-based scheme. The results of this study exhibit strong non-stationary characteristics in the measured wind data at the Sutong Bridge site. The findings of the data at the Sutong Bridge in the tropical storm reaffirm results from earlier studies and emphasize the need to incorporate non-stationary features of winds in the analysis and design of bridges from aerodynamic view point.

Simulation of non-stationary wind speed and direction time series

The simulation of synthetic wind time series is strictly necessary, among others, to assess the risk of structures and systems, to model the dynamic of morphological features like dunes, or to investigate the potential of wind energy in a certain location. For all these applications, a tool able to simulate time series of wind speed and direction is required. In this paper we propose a methodology for the simulation of bivariate non-stationary time series of wind speed and direction. This methodology takes into account the circular nature of the wind direction, as well as the mean annual cycle of both wind speed and direction. For modelling the joint distribution of the two variables, wind speed is modelled conditioned to the wind direction. For modelling short-term self- and cross-dependency among the variables a Vector Autoregressive (VAR) model of order p is used, with an innovation process at time t that depends on the value taken by the variables at time t−1, based on the use of a mixture of multivariate normal distributions. The proposed methodology is applied to a case study, simulating several synthetic series, of the same length as the original series. The simulated series satisfactorily captures the characteristics of averaging or common data (i.e. with low or moderate speed) and, under certain independence conditions, the directional extreme value distribution of the wind speed is also properly reproduced.

An experimental investigation of two Wavelet-MLP hybrid frameworks for wind speed prediction using GA and PSO optimization

Wind speed series show unsteady and nonlinear phenomena. The accurate forecast of wind speed is important for the safety of renewable energy utilization. Compared to the prediction models which use single algorithms, hybrid models always have higher accuracy. Based on the theories of Wavelet, classical time series analysis, genetic algorithm, particle swarm optimization and artificial neural networks, two hybrid forecasting frameworks [the Wavelet-Genetic Algorithm (GA)-Multilayer Perceptron (MLP) and the Wavelet-Particle Swarm Optimization (PSO)-Multilayer Perceptron (MLP)] are proposed to predict non-stationary wind speeds. Comparisons of forecasting performance using different algorithm combinations are provided to investigate the contribution of different components in those two hybrid frameworks. The results based on three experimental cases show that: (1) both of the two proposed hybrid forecasting frameworks are suitable for the diverse accuracy requirements in wind speed predictions, which can be applied to wind power systems; and (2) in both of the two hybrid frameworks, the contribution of the GA and the PSO components in improving the MLP are not statistically significant while that of the Wavelet component is statistically significant.

Multistep Wind Speed Forecasting Based on Wavelet and Gaussian Processes

Accurate wind speed forecasts are necessary for the safety and economy of the renewable energy utilization. The wind speed forecasts can be obtained by statistical model based on historical data. In this paper, a novel W-GP model (wavelet decomposition based Gaussian process learning paradigm) is proposed for short-term wind speed forecasting. The nonstationary and nonlinear original wind speed series is first decomposed into a set of better-behaved constitutive subseries by wavelet decomposition. Then these sub-series are forecasted respectively by GP method, and the forecast results are summed to formulate an ensemble forecast for original wind speed series. Therefore, the previous process which obtains wind speed forecast result is named W-GP model. Finally, the proposed model is applied to short-term forecasting of the mean hourly and daily wind speed for a wind farm located in southern China. The prediction results indicate that the proposed W-GP model, which achieves a mean 13.34% improvement in RMSE (Root Mean Square Error) compared to persistence method for mean hourly data and a mean 7.71% improvement for mean daily wind speed data, shows the best forecasting accuracy among several forecasting models.

Conditional Simulation of Nonstationary Fluctuating Wind Speeds for Long-Span Bridges

This paper presents a computationally efficient method for the conditional simulation of nonstationary fluctuating wind speeds for the buffeting analysis of long-span bridges. The fluctuating wind speeds, with part of their time histories measured at some points, are regarded as a zero-mean nonstationary Gaussian vector process characterized by an evolutionary power spectral density (EPSD) matrix. The Kriging method is then applied to the random vector of the Fourier coefficients of the evolutionary vector process for conditional simulation. A mathematical proof of this conditional simulation is provided. A fast algorithm of the conditional simulation is further derived, by converting the Cholesky decomposition of a large size covariance matrix of the Fourier coefficients into the Cholesky decomposition of a series of small-size coherence matrices with much less computational time. The procedure for implementing the fast algorithm-based conditional simulation method is detailed. Finally, this method is applied for the conditional simulation of typhoon-induced nonstationary wind speed time histories for the buffeting analysis of Stonecutters Bridge in Hong Kong. The time domain buffeting responses of the bridge obtained using the conditionally simulated wind speed time histories indicate that the proposed simulation method is feasible and applicable.

NONSTATIONARITY ANALYSIS IN WIND-RAIN-INDUCED VIBRATION OF STAY CABLES

Wind and wind-rain-induced cable vibration are usually nonstationary. Based on the field measured wind data from the Dongting Lake Bridge (DLB) in China, a wavelet-based method was developed to investigate the wind characteristics of wind-rain-induced cable vibration. By using the wavelet analysis, the time-varying mean wind speed is extracted and a nonstationary wind speed model is proposed. The turbulence intensities and probability distributions of measured wind data are calculated using the proposed nonstationary model and compared with those based on empirical mode decomposition (EMD) and design values. The correlation between wind and wind-rain-induced acceleration response are discussed. At the same time, the relativity of acceleration responses of cable and the wind speed are discussed via calculating root mean square (RMS) averaging and acceleration response peak factors.

Comparison of two new ARIMA-ANN and ARIMA-Kalman hybrid methods for wind speed prediction

Wind speed prediction is important to protect the security of wind power integration. The performance of hybrid methods is always better than that of single ones in wind speed prediction. Based on Time Series, Artificial Neural Networks (ANN) and Kalman Filter (KF), in the study two hybrid methods are proposed and their performance is compared. In hybrid ARIMA-ANN model, the ARIMA model is utilized to decide the structure of an ANN model. In hybrid ARIMA-Kalman model, the ARIMA model is employed to initialize the Kalman Measurement and the state equations for a Kalman model. Two cases show both of them have good performance, which can be applied to the non-stationary wind speed prediction in wind power systems.

Generating wind time series as a hybrid of measured and simulated data

Certain applications, such as analysing the effect of a wind farm on grid frequency regulation, require several years of wind power data measured at intervals of a few seconds. We have developed a method to generate days to years of non-stationary wind speed time series sampled at high rates by combining measured and simulated data. Measured wind speed data, typically 10–15 min averages, capture the non-stationary characteristics of wind speed variation: diurnal variations, the passing of weather fronts, and seasonal variations. Simulated wind speed data, generated from spectral models, add realistic turbulence between the empirical data. The wind speed time series generated with this method agree very well with measured time series, both qualitatively and quantitatively. The power output of a wind turbine simulated with wind data generated by this method demonstrates energy production, ramp rates and reserve requirements that closely match the power output of a turbine simulated turbine with measured wind data. Copyright © 2011 John Wiley & Sons, Ltd.

Multi-step forecasting for wind speed using a modified EMD-based artificial neural network model

In this paper, a modified EMD-FNN model (empirical mode decomposition (EMD) based feed-forward neural network (FNN) ensemble learning paradigm) is proposed for wind speed forecasting. The nonlinear and non-stationary original wind speed series is first decomposed into a finite and often small number of intrinsic mode functions (IMFs) and one residual series using EMD technique for a deep insight into the data structure. Then these sub-series except the high frequency are forecasted respectively by FNN whose input variables are selected by using partial autocorrelation function (PACF). Finally, the prediction results of the modeled IMFs and residual series are summed to formulate an ensemble forecast for the original wind speed series. Further more, the developed model shows the best accuracy comparing with basic FNN and unmodified EMD-based FNN through multi-step forecasting the mean monthly and daily wind speed in Zhangye of China.

Wavelet-Based Nonstationary Wind Speed Model in Dongting Lake Cable-Stayed Bridge

The wind-rain induced vibration phenomena in the Dongting Lake Bridge (DLB) can be observed every year, and the field measurements of wind speed data of the bridge are usually nonstationary. Nonstationary wind speed can be decomposed into a deterministic time-varying mean wind speed and a zero-mean stationary fluctuating wind speed component. By using wavelet transform (WT), the time-varying mean wind speed is extracted and a nonstationary wind speed model is proposed in this paper. The wind characteristics of turbulence intensity, integral scale and probability distribution of the bridge are calculated from the typical wind samples recorded by the two anemometers installed on the DLB using the proposed nonstationary wind speed model based on WT. The calculated results are compared with those calculated by the empirical mode decomposition (EMD) and traditional approaches. The compared results indicate that the wavelet-based nonstationary wind speed model is more reasonable and appropriate than the EMD-based nonstationary and traditional stationary models for characterizing wind speed in analysis of wind-rain-induced vibration of cables.

Wavelet-Based Nonstationary Wind Speed Model in Dongting Lake Cable-Stayed Bridge

The wind-rain induced vibration phenomena in the Dongting Lake Bridge (DLB) can be observed every year, and the field measurements of wind speed data of the bridge are usually nonstationary. Nonstationary wind speed can be decomposed into a deterministic time-varying mean wind speed and a zero-mean stationary fluctuating wind speed component. By using wavelet transform (WT), the time-varying mean wind speed is extracted and a nonstationary wind speed model is proposed in this paper. The wind characteristics of turbulence intensity, integral scale and probability distribution of the bridge are calculated from the typical wind samples recorded by the two anemometers installed on the DLB using the proposed nonstationary wind speed model based on WT. The calculated results are compared with those calculated by the empirical mode decomposition (EMD) and traditional approaches. The compared results indicate that the wavelet-based nonstationary wind speed model is more reasonable and appropriate than the EMD-based nonstationary and traditional stationary models for characterizing wind speed in analysis of wind-rain-induced vibration of cables.

Numerical simulation of extreme winds from thunderstorm downbursts

In (Chen, L., 2005. Vector time-varying autoregressive (TVAR) models and their application to downburst wind speeds. A PhD Dissertation, Texas Tech University, Lubbock, Texas.), a nonparametric deterministic–stochastic hybrid (NDESH) model was proposed for characterizing and simulating nonstationary thunderstorm downburst wind fields, and two sets of full-scale downburst wind speed records were fitted in this model. This paper aims to build an empirical numerical model for downburst wind fields according to the NDESH model and based on the results in (Chen, L., 2005; Chen, L., Letchford, C.W., 2005. Proper orthogonal decomposition of two vertical profiles of full-scale nonstationary downburst wind speeds. Journal of Wind Engineering and Industrial Aerodynamics 93(3), 187–216; Chen, L., Letchford, C.W., 2006. Multi-scale correlation analyses of two lateral profiles of full-scale downburst wind speeds, Journal of Wind Engineering and Industrial Aerodynamics 94(9), 675–696.), so that correlated downburst wind speeds can be synthesized from this empirical model.

Real-time three-dimensional wind simulation for windmill rig tests

This paper deals with the methods of three-dimensional fixed-point wind speed real-time simulation modelled in large band, in order to use them in test rigs for experimental investigation of the wind energy conversion systems. The medium- and long-term components of the non-stationary wind speed are considered as known, being issued from measured data or by adopting a generic model. The spectral characteristics of three-dimensional turbulence are described either by the Kaimal or the von Karman models. The turbulence intensity and the length scale that take part in these models are calculated by the site parameters, using current standards. The basic idea of the methods for large-band three-dimensional wind simulation is to use rational shaping filters that approximate non-integer orders shaping filters issued from the Kaimal and the von Karman models. All the synthesized rational shaping filters use one time constant, automatically adapted to the medium- and long-term components that pilot the other time constants of the shaping filters by a set of parameters practically constant. Some numerical results concerning time series that simulate the non-stationary wind speed with three-dimensional turbulence components based on Kaimal and von Karman models are presented.

A Comparative Study of Stationary and Non-stationary Wind Models Using Field Measurements

We present a comparative study of the conventional stationary wind speed model and a newly proposed non-stationary wind speed model using field measurements. The concept of, and the differences between, the two wind models are briefly reviewed. Wind data recorded by a field measurement system for wind turbulence parameters (FMS-WTP) of 1-year duration are analyzed using the two wind models. Comparisons were made between the wind characteristics obtained from the two models, including hourly mean wind speed, turbulence intensity, the wind spectrum, integral length scale, root coherence function and probability density function. The effects of wind types (monsoon or typhoon), statistical properties (stationary or non-stationary), and surface roughness (open-sea fetch or overland fetch) on wind characteristics are discussed. The comparative study demonstrates that the non-stationary wind model appears to be more appropriate than the conventional stationary wind speed model for characterizing turbulent winds of one-hour duration over complex terrain.

Proper orthogonal decomposition of two vertical profiles of full-scale nonstationary downburst wind speeds[lzcl

The paper proposes a novel analysis framework for nonstationary wind speeds, from which accumulated results can potentially lead to or enhance empirical nonstationary wind speed models such as the hybrid one for downbursts in (Eng. Struct. 26 (2004) 619). This framework is motivated by the proper orthogonal decomposition (POD) technique and consists of four major steps: separation, POD, approximation and property inference. In the first step, the original wind speed time histories are separated into their time-varying mean speeds and fluctuating speeds through wavelet shrinkage, which is a promising new tool for smoothing; fluctuating speeds are further expressed as the product of their time-varying standard deviations and normalized fluctuating speeds with unit variance. In the second step, the POD is applied to the time-varying means, standard deviations and normalized fluctuation. In the third step, by properly selecting the number of retained modes, the original time series can be approximated to a numerical model. Finally, wind properties such as velocity vertical profiles and turbulence vertical profiles can be calculated from the model. The POD employed herein is a specific POD for arbitrary multivariate data representation. The normalized fluctuations are characterized by both their power spectral densities (PSD) and evolutionary power spectral densities (EPSD). The concept of EPSD for nonstationary processes is briefly presented and one EPSD estimator is given. Specifically, the PSD/EPSD of an original process is related to the PSD/EPSD of the principal coordinate process obtained by the POD. This framework is applied to two sets of nonstationary full-scale thunderstorm downburst wind speed time series. Many appealing downburst properties are obtained and the benefit of the POD is demonstrated.

Characterizing Nonstationary Wind Speed Using Empirical Mode Decomposition

This paper explores how to characterize nonstationary wind speed that can be modeled as a deterministic time-varying mean wind speed component plus a stationary random process for the fluctuating wind speed component. The time-varying mean wind speed is naturally extracted from the nonstationary wind data using the empirical mode decomposition (EMD). The proposed approach is then applied to the wind data recorded by the anemometers installed in the Tsing Ma suspension Bridge during Typhoon Victor to find its time-varying mean wind speed, probability distribution of fluctuating wind speed, wind spectrum, turbulence intensity, and gust factor. The resulting wind characteristics are compared with those obtained by the traditional approach based on a stationary wind model. It is found that most of nonstationary wind data can be decomposed into a time-varying mean wind speed plus a well-behaved fluctuating wind speed admitted as a stationary random process with a Gaussian distribution. The time-varying mean wind speed identified by EMD at a designated intermittency frequency level is more natural than the traditional time-averaged mean wind speed over the certain time interval. The proposed approach can also be applied to stationary wind speed with the same output as obtained by the traditional approach. It is concluded that the proposed approach is more appropriate than the traditional approach for characterizing wind speed.