About this repository

This repository is an optimization algorithm for the following problem:

Finding a function $f$ that minimizes the following expression:

$$ (f(x)-\text{signal})^2 $$

Where $\text{signal}$ is the signal from a flow detector in canalisations.

Moreover $f$ is characterized by the following expression:

$$ f(x) = cx^a(1-x)^b \cos (2\pi \nu x - \phi) $$

Where $c$, $a$, $b$, $\nu$ and $\phi$ are the parameters to be optimized.

Two signals are provided in the file signal.csv and signal2.csv. Two graphical representations of the signals are shown below:

For this problem, an Adam optimizer is used to minimize the expression. The algorithm is implemented in the file main.py.

The results of the optimization are shown below:

How to reproduce the results

To reproduce the results, you can run the file main.py with the following command:

python main.py

You have to install python on your machine to run this command.

Requirements

The requirements for this repository are shown in the file requirements.txt. You can install them with the following command:

pip install -r requirements.txt

Bibliography

This project is inspired by V.Vigon teaching at the University of Strasbourg. The course is available at the following address: https://colab.research.google.com/drive/1Fabl0nLbM5FdXWkIFKH0KRy46BwexvYa