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

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.

Automated summary

PDFs of wind speeds at pedestrian levels are important for wind environment assessments, but calculating them from time-series data is challenging due to the large data volume. In this study, the Gram-Charlier series (GCS) was applied to analyze the probability density and low-occurrence strong wind speeds using flow field data obtained from large-eddy simulation. The GCS-nth model, which modifies the Gaussian distribution by incorporating higher-order moments, was used to predict PDFs. The results show that GCS can accurately estimate skewed PDFs and percentile values compared to a Gaussian distribution.