Add comments of Daniel in Wed 2.7
Compare changes
Files
2In this session, you will work with the uncertainty of extreme temperatures in the airport of Barcelona to assess the extreme loads induced by temperature in a steel structure in the area. You have daily observations of the maximum temperature for several years. The dataset was retrieved from the Spanish Agency of Metheorology [AEMET](https://www.aemet.es/es/portada). Your goal is to design the structure for a _lifespan of 50 years_ with a _probability of failure of 0.1_ during the design life.
```
```
```
```
```
```
The observations are NOT identically distributed. We can see in the plot above that there is seasonality. The distribution of temperature during the summer months is not the same as during the winter months so we cannot assume stationarity. Therefore, **we are violating one of the assumptions of EVA and cannot rely on the results**. One possible solution is to move from monthly maxima to yearly maxima, where the problem of seasonality does not occur.
Here, we will continue with the analysis to show the procedure but in practice you should go for a non-stationary method (more advanced, out of the scope of this course), move to a scale when you do not have such seasonality (yearly in this case) or use another sampling approach that does not depend on time windows such as Peak Over Threshold.
```
```
<div style="background-color:#facb8e; color: black; vertical-align: middle; padding:15px; margin: 10px; border-radius: 10px; width: 95%"> <p>Use <a href="https://docs.scipy.org/doc/scipy/reference/stats.html" target="_blank">scipy.stats</a> built in functions (watch out with the parameter definitions!), similar to Week 1.7 and use the DataFrame created in Task 2.
```
The order of the parameters returned from scipy.stats is shape, location, and scale, so shape = 0.32, location = 24.26 and scale = 5.01. Note that the <a html="https://docs.scipy.org/doc/scipy/reference/generated/scipy.stats.genextreme.html" target="_blank">genextreme method of scipy.stats</a> defines the PDF of the distribution with a negative shape parameter $c$, relative to the definition in our book ($\xi$, shown <a html="https://mude.citg.tudelft.nl/book/eva/GEV.html" target="_blank">here</a>). Thus, shape parameter is negative (according to our book) and the obtained GEV is a Reverse Weibull with a upper bound in loc-scale/shape = 24.26 + 5.01/0.32 = 39.92.
```
<div style="background-color:#facb8e; color: black; vertical-align: middle; padding:15px; margin: 10px; border-radius: 10px; width: 95%"> <p>The three missing variables listed below are all type <code>numpy.ndarray</code>; the last is found using your <code>scipy.stats</code> distribution from Task 3.
```
```
© Copyright 2023 <a rel="MUDE Team" href="https://studiegids.tudelft.nl/a101_displayCourse.do?course_id=65595">MUDE Teaching Team</a> TU Delft. This work is licensed under a <a rel="license" href="http://creativecommons.org/licenses/by-nc-sa/4.0/">Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International License</a>.