Modeling of Non-stationary Winds in Gust-fronts

The time-varying amplitude and frequency components embedded in random processes make the stationarity assumption inappropriate. Accordingly, non-stationarity of data during passage of hurricanes often precludes utilization of conventional analysis tools. In this study by invoking the Discrete Wavelet Transform (DWT) and empirical mode decomposition (EMD), non-stationary wind speed variations are modeled as a sum of a time-varying mean and a fluctuating component that can be described as a stationary random process. Wind speed data from Hurricane Lili, 2002 was utilized to obtain the turbulence intensity, gust factors, power spectral density and probability density function utilizing the non-stationary model and compared to traditional analysis. Discrepancies between the traditional approach and the new model were noted and discussed. The overall effectiveness of the proposed scheme based on DWT/EMD was demonstrated through detailed data analysis. Introduction The accurate estimation of turbulent wind characteristics during thunderstorms, hurricanes and tornados is difficult as these processes may not be stationary. Most traditional analysis tools are suited for stationary processes, which may not be always appropriate for the analysis of non-stationary data. Therefore, the performance evaluation of structures under transient conditions manifested by non-stationarity has been rather elusive. In order to fully understand the hurricane wind characteristics and their effects on structures, there is clearly a need for analysis tools to analyze non-stationary data. There has been a number of approaches advanced to handle non-stationarity, e.g., parametric time series models with application to earthquake problems. However, with the recent developments in time-frequency analysis, e.g., the Wavelet transform and a combination of empirical mode decomposition and the Hilbert transform, new insights into the signal contents have offered new venues for analysis (Gurley and Kareem, 1999; Huang et al, 1998; Kareem and Kijewski, 2002). This study introduces a new approach based on a time-frequency perspective to analyze and model non-stationary events. An analysis framework that models non-stationary random process as a deterministic time-varying mean wind speed plus a stationary random process as fluctuating component is proposed. The time varying mean wind speed is extracted by two different approaches, i.e., discrete wavelet decomposition and empirical mode decomposition. The wind speed data recorded during Hurricane Lili, 2002 was analyzed to obtain the time-varying mean wind speed, turbulence intensity, spectral density function (psd), probability density function (pdf), gust factors and length scale. The results are then compared to those obtained through traditional approach based on the stationary wind model.