Mixture Model in High-Order Statistics for Peak Factor Estimation on Low-Rise Building

Abstract

To design reliable structures, extreme pressures and peak factors are required. In many applications of Wind Engineering, their statistical analysis has to be performed considering the non-Gaussianity of the wind pressures. With the increasing precision and sampling frequency of pressure sensors, short and local peak events of large amplitude are more usually captured. Their relevance is naturally questioned in the context of a structural design. Furthermore, the increasing computational power allows for accumulation and analysis of larger data sets revealing the detailed nature of wind flows around bluff bodies. In particular, in the shear layers and where local vortices form, it is commonly admitted that the Probability Density Function (PDF) of measured pressures might exhibit two or more significant components. These mixed flows can be modelled with mixture models (Cook 2016). Whenever several processes coexist, and when one of them is leading in the tail of the statistical distribution, as will be seen next in the context of corner vortices over a flat roof, it is natural to construct the extreme value model with this leading process and not with the mixed observed pressures. It is therefore important to separate the different processes that can be observed in the pressure histories. Once this is done, specific analytical formulations of non-Gaussian peak factors can be used to evaluate the statistics of extreme values (Kareem and Zhao 1994; Chen and Huang 2009). The separation of mixed processes is usually done by means of the PDF of the signals (Cook 2016). This information is of course essential to perform an accurate decomposition, but it might be facilitated by considering higher rank information like auto-correlations and higher correlations like the triple or quadruple correlation. Indeed, the two phenomena that need to be separated and identified might be characterized by significantly different timescales, which are not reflected in the PDF. In this paper, the large negative pressures measured on a flat roof are analyzed and decomposed into two elementary processes, namely, the flapping corner vortex and the turbulent flow detaching from the sharp upstream edge. This paper will finally show that an accurate decomposition of the recorded pressures into their underlying modes provides a more meaningful evaluation of the extreme pressures.