Modeling probability density functions of instantaneous velocity components at the pedestrian levels of a building array by Gram–Charlier series

Abstract

Probability density distributions (PDFs) of wind speeds at pedestrian levels are required to predict gusts for wind environment assessments. However, the time-series data are extremely large in data volume for calculating the PDFs. Therefore, we applied the Gram–Charlier series (GCS) to the dataset of the flow fields at the pedestrian level around a simplified block array obtained by a large-eddy simulation to analyze the probability density and low-occurrence strong wind speeds. PDFs are predicted using the GCS-nth model, in which the distribution is modified from the Gaussian distribution by incorporating third to nth-order moments. The GCS can estimate the skewed PDFs of pedestrian winds and more accurately predict the percentile values compared to a Gaussian distribution. In addition, at most locations, the higher-order GCS estimates the probability densities and percentiles more accurately than the lower-order models. In contrast, the accuracy of GCS-6th is not always better than that of GCS-5th or lower models in some locations because of the large values of the coefficient in the polynomial function that modifies a Gaussian distribution. This study proves that using GCS to predict PDFs from statistics is a newly discovered and useful approach for wind environmental assessment.