Shock and Vibration

Volume 2018 (2018), Article ID 9213503, 26 pages

https://doi.org/10.1155/2018/9213503

## Comparative Study on Non-Gaussian Characteristics of Wind Pressure for Rigid and Flexible Structures

Correspondence should be addressed to Chun-xiang Li

Received 13 May 2017; Revised 17 August 2017; Accepted 23 October 2017; Published 17 January 2018

Academic Editor: Marco Belloli

Copyright © 2018 Lei Jiang et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

#### Abstract

This paper summarizes a comprehensive study for non-Gaussian properties of wind pressure. The field measurements are implemented on the structure surface of a rigid structure, while a large-span membrane structure is selected as the flexible structure wind pressure contrast group. The non-Gaussian characteristics of measured pressure data were analyzed and discussed through probability density distribution, characteristic statistical parameters, power spectral density function, and the correlations, respectively. In general, the non-Gaussian characteristics of wind pressure present depending on tap location, wind direction, and structure geometry. In this study, the fluctuating wind pressures on the windward side and leeward side of the structures show obvious different degrees of non-Gaussian properties; that is, the surface of rigid structure shows strong non-Gaussian property in leeward, while the roof of flexible structure shows obvious non-Gaussian property in windward. Finally, this paper utilizes the present autospectrum empirical formula to fit the wind pressure power spectrum density of the measured data and obtains the conclusion that the existing empirical formula is not ideal for fitting of the flexible structure.

#### 1. Introduction

Wind loads possess stochastic characteristics, especially the fluctuating component, which may force the engineering structure to flutter, torsional vibration, and other forms of wind-induced random coupling vibration. In the 1970s and 1980s, research on characteristics of wind load on structural has begun; Dalgliesh [1] computed the pressure coefficients of measured wind pressures to better identify potential problem areas on high-rise building. Holmes [2] compared correlations and spectra of pressure fluctuations on the windward and leeward faces of a 43 m high building and found the error of quasi-steady linear theory. Stathopoulos and Surry [3] made a contribution to the question of scaling for low building models in wind-tunnel experiments. Nevertheless, they did not consider the problem of the non-Gaussian characterization of wind pressures. In some separate flow regions, the wind pressure distributions show obvious non-Gaussian characteristics [4–6] due to the influence of air separation, reattachment, and vortex shedding. This kind of wind pressures with asymmetric distribution and sharply pulse peak, which has close correlations with the vortex movement of the wind field, leads easily to the fatigue damage of structure and is the major cause of local structural damage [7]. Compared with the Gaussian wind pressures, the non-Gaussian wind pressures take on the feature of asymmetric and/or leptokurtic distribution, which is the nonnormal distribution. Many researchers have contributed to research on non-Gaussian processes [8–13]. Kumar and Stathopoulos [4, 5] expounded the existence of the non-Gaussian wind pressures on the flat and herringbone roofs of low-rise building and conduct the partitions of the Gaussian and non-Gaussian areas. Through a wind-tunnel test, Ye and Hou [6] tested that wind pressure shows obvious non-Gaussian characteristics on the windward edge area and the corner of long span roof and partitioned the non-Gaussian region of wind pressure using the curve fitting method based on the* K-S* test. Through a wind-tunnel test on rhombus super high-rise buildings along with chamfers, Lou et al. [14] partitioned the Gaussian and non-Gaussian distributions of fluctuating wind pressures on the structural surfaces under consideration of different wind direction angles, respectively, and found that there exist remarkable non-Gaussian wind pressures on the flow separation zone of lateral inlet edge and the incisal angle region of leeward and windward side. The non-Gaussian characteristics of pulsating wind pressures on square high-rise buildings were researched by Han and Gu [15] through a wind-tunnel test; the results show that non-Gaussian characteristics are prominently affected by the wind angle. On the windward surfaces, both positive skewness and negative skewness of the wind pressures are present, and the kurtosis and skewness values are relatively small. On the surfaces impacted by separated flow and wake, only negative skewness is present; both kurtosis and skewness values are relatively large. Recently, a new moment-based polynomial model for coping with hardening non-Gaussian processes with kurtosis less than three was presented in Ding and Chen’s work [16]. Ma et al. [17] presented a hybrid data and simulation-based (HDSB) approach that incorporates simulated data based on an autoregression (AR) model with an inverse Johnson transformation to estimate the extreme values of non-Gaussian wind pressures.

Previous studies on the non-Gaussian characteristics of wind pressures are mainly conducted through wind-tunnel test data, while the field measurement data of non-Gaussian wind pressure is very limited. Li et al. [18] investigated the characteristics of tropical cyclone-generated winds and evaluated the wind effects on a typical low-rise building under tropical cyclone conditions through field measurements.

Large-span membrane structure, as a new appearance structure, has superior mechanical properties and light transmission. Some researchers [19–22] have done research on it. Bartko et al. [19] collected the wind speed, wind direction, and wind pressure field measuring data for extended time periods to analyze the wind interaction with low slope membrane roofs. Zheng et al. [21] simulated the mean wind load on the long-span membrane roof of the EXPO-axis by adopting Realizable - turbulent model and investigated the effects of surrounding buildings on the mean wind pressure distribution on the membrane. Luo et al. [22] presented a zero memory nonlinearity (ZMNL) transformation based method to simulate the stochastic fluctuating wind pressure field acting on a large-span membrane roof, which consists of Gaussian and non-Gaussian regions. However, academics have yet to systematically discuss the non-Gaussian property of the flexible structure; it is thus urgent to investigate.

The power spectrum of pulsating wind pressure is based on a limited data collection to describe the power (on the frequency) distribution of fluctuating wind pressure. Many scholars [23–30] have done some research on fitting the wind pressure autospectra data with empirical formulas. The universal model of wind velocity autospectra has been described by Olesen et al. [31] and Tieleman [32] as follows:where is frequency in Hz; is the variance of wind velocity (or wind pressure); is the fitting parameter; is a feature length in m, which can be selected as the height of the structure or a constant length over the entire height; is mean wind velocity in m/s. Li et al. [29] found that coefficient parameters, , , and , are related to the location of the autospectral curves and index parameters, *α*, *β*, and *γ*, are related to the shape of the curve. Sun [26] and Pan [27] applied (1) in empirical formula of wind pressure autospectral model with identified parameters , , and in Sun [26] and , , and in Pan [27], respectively. With the aim of building an aerodynamic database for engineering application, Sun et al. [33, 34] and Shao [35] have made large amounts of wind-tunnel tests on large-span roofs, and the spectra of these wind pressure data were fitted with the wind pressure autospectral formula as follows:

This paper summarizes a comprehensive study for non-Gaussian properties, in which wind pressure time series is measured at different locations on two types of structure: the structure surface of a rigid structure and the roof of a flexible structure. Probability density distribution, characteristic statistical parameters, and the correlations of the measured pressure data were analyzed and discussed. Finally, this paper utilizes the present autospectrum empirical formula to fit the wind pressure power spectrum density of the measured data.

#### 2. Statistical Parameters of Non-Gaussian Stochastic Process

According to the theory of random process, the first four-order statistical parameters, the mean, variance, skewness, and kurtosis, are the mathematical characteristics of random variables. For the random Gaussian process, the probability density function can be determined by only using the first two-order statistics parameters (i.e., the mean and variance), while it is very difficult for the non-Gaussian stochastic process. It needs high-order statistics parameters such as the third-order, fourth-order, or higher-order ones [36].

The mean is the center of random process, which takes 0 value in the fluctuating random process. And the variance is the degree of the deviation from the center. The third-order and fourth-order statistics parameters, namely, the skewness SK and kurtosis , are used to describe the asymmetry and flatness degree of the distribution centered on the mean value, respectively. They can be stated as follows:where is the probability density function of stochastic process .

Treated as a random process, the discrete random fluctuating wind pressure can be characterized by the following four-order statistics parameters:The skewness and kurtosis of Gaussian stochastic processes are fixed. A skewness value of zero and a kurtosis of 3 mean that the stochastic process follows normal distributions; otherwise it is a non-Gaussian stochastic process. For the skewness value, when it is greater than 0, the distribution curve is positive skewness, and the long tail of the curve is in the positive direction of the horizontal axis; when it is less than 0, the curve is negative skewness, and the long tail is in the negative direction. For the kurtosis value, when it is less than 3, the distribution curve is lower than the normal curve; when it is greater than 3, the curve is steeper than the normal curve.

#### 3. Field Measurement Program and Data Analysis

##### 3.1. Flexible Structure Field Measurement

Yueqing City Sports Center is located in Xu Yang Road, Yueqing City, which is composed of the stadium, swimming pool, and gymnasium. The stadium building is about 229 m from north to south, 211 m from east to west, and about 42 m from the top of the column. The roof is covered with meniscus nonenclosed space cable-truss system. The maximum cantilever span is about 57 m. The wave structure of the membrane structure is supported by the 273 × 10 steel pipe arch of the cable-truss system. Under the structure of the two waves, the rope structure is arranged under the cable. The effect of the stadium is shown in Figure 1.