Modelling probability density functions based on the Gram–Charlier series with higher-order statistics: Theoretical derivation and application

Abstract

This study focused on the low-occurrence wind events at pedestrian levels. The probability density functions (PDFs) are reliable statistical information. However, instantaneous velocity datasets are required to determine PDFs. In this study, theoretical methods were derived to model PDFs, based on the Gram–Charlier series (GCS methods) and higher-order statistics. The time-series data of the wind velocity components and speed at the pedestrian level around an isolated building from a large-eddy simulation (LES) database were used to validate GCS methods. Results showed that all GCS methods showed enhanced flexibility than the Gaussian distribution for modelling PDFs. For the low-occurrence values, the estimation accuracy of the GCS method gradually increased as the modelling order increased, at most probe points. The GCS-A method was developed to adaptively remove the large-error points based on thresholds of the fifth- and sixth-order moments. For global accuracy, the GCS-4th and GCS-A methods have higher estimation accuracy than other methods. The present model provides a new framework to estimate the low-occurrence wind events at pedestrian levels using only turbulence statistics, yielding to the expansion of the application of LESs for pedestrian-level wind assessments.