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An elegant probability model for the joint distribution of wind speed and direction.
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readme.md

A Probability Model for the Joint Distribution of Wind Speed and Direction (Gaussian Mixture Models, GMM)

What is this?

This is a Python program for modeling the joint distribution of wind speed and direction.

The method is based on:

  1. Harris, Cook, The parent wind speed distribution: Why Weibull?, http://www.sciencedirect.com/science/article/pii/S0167610514001056

  2. Gaussian Mixture Models, http://scikit-learn.org/stable/modules/mixture.html

Fitting Effect

Take Shanghai Hongqiao Intl as an example

1. PDF (Probability Density Function) Comparison

Left: Empirical PDF, Right: Model PDF

2. Speed and Direction Distribution Comparison

Histogram vs. Model

3. Sectoral Comparison

Left: Histogram vs. Model, Right: Empirical vs. Model CDF

4. Live Demo

The above results are available at https://cdn.rawgit.com/cqcn1991/Wind-Speed-Analysis/master/output_HTML/hongqiao_intl.html , along with other analysis.

Applications

This model can be used to obtain the wind speed distribution, wind direction distribution and the joint distribution of wind speed and direction distribution with good accuracy.

Its potential applications include:

  1. Wind energy evaluation, wind resource assessment (long term). For example, the optimization of wind farm layout.

  2. Wind load analysis on structures, such as fatigue analysis. For example, the wind load on highrise buidings.

  3. Pedestrian-level wind environment assessment.

Gallery

Here is how the method applies to different places across the world. The Weibull distribution is listed as the traditional model for comparison.

1. North America

Minneapolis, USA

Boston 16 NM East, USA (Offshore)

2. Europe

Tiree, UK

Pau Pyrenees, France

Landsberg Lech, Germany

3. East Asia

Luogang, China

4. Mid East

Al Maktoum Intl, United Arab Emirates

You can use the code toggle button and sidebar to navigate these reports.

The Probability Model

The model I'm using is Gaussian Mixture Model, or simply put, the sum of some normal distributions. The idea is very simple:

1. For a certain wind character, the wind vector (speed and direction) follows the normal distribution:

2. For specific location, its wind speed direction distribution is composed of several such wind characters, and hence the sum of several normal distributions:

fi is the PDF of normal distribution component, pi is its weight.

The chief beauty of this model is its elegance (simplicity). You can use such a simple model (GMM) to describe wind, contrary to previous Weibull combination and others.

For a complete explanation of how GMM fit the joint distribution of wind speed and direction, you can read

Harris, Cook, The parent wind speed distribution: Why Weibull?, http://www.sciencedirect.com/science/article/pii/S0167610514001056

And I'm also working on a paper about it, this is my Master Thesis. And if you have any interest (question, collaboration...) feel free to ask me. I open source the project is meant to help you try it.

How to use it

1. Install Anaconda

Download at https://www.continuum.io/downloads

This repo use Python 3, so you should use the 3 as well.

2. Download the code

3. Additional Environment Configuration

After installing Anaconda, there are still some additional packages you need to install:

Just run these in your command line to install them

pip install -r requirements.txt

4. GMM Fitting

If you have any question, you could post it at issue, or mail me at 38306608#qq.com

5. R configuration (optional)

The program now uses some R packages to fit von Mises mixture model. You can either delete related code, or install R and Rpy 2 to enable this feature. Specifically:

6. Jupyter Extention config (Optional)

Install extentions from https://github.com/ipython-contrib/jupyter_contrib_nbextensions

pip install jupyter_contrib_nbextensions
jupyter contrib nbextension install --user --skip-running-check
jupyter nbextension enable toc2/main

Acknowledgement

This work would be impossible without the help from Cook and Harris. Thank you!

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