.. DO NOT EDIT.
.. THIS FILE WAS AUTOMATICALLY GENERATED BY SPHINX-GALLERY.
.. TO MAKE CHANGES, EDIT THE SOURCE PYTHON FILE:
.. "auto_examples/data_quality/plot_uncertainty.py"
.. LINE NUMBERS ARE GIVEN BELOW.

.. only:: html

    .. note::
        :class: sphx-glr-download-link-note

        Click :ref:`here <sphx_glr_download_auto_examples_data_quality_plot_uncertainty.py>`
        to download the full example code

.. rst-class:: sphx-glr-example-title

.. _sphx_glr_auto_examples_data_quality_plot_uncertainty.py:


===============================
Relative uncertainty estimation
===============================

This example shows how to estimate the relative uncertainty of a non-linear, non-stationary signal using detrending.
We generate a synthetic signal composed of:

    * Three oscillatory signals of different but significant amplitudes
    * Two polynomial functions or trends
    * Data drift

To make the case more realistic, from an industrial perspective, the timestamps are modified to make them nonuniform
and 35% of the data points are randomly removed. Finally, Gaussian noise with a signal-to-noise ratio of 10db and 20db is
are added to the left and right half of the data, respectively.

The figure shows the synthetic signal with and without noise (top), and the estimated relative uncertainty (bottom).
On the left half of the data, where the noise is large, the estimated relative uncertainty increases when the signal
reaches close to 100%. On the right side half of the data, where the noise is small, the relative uncertainty remains closer to 0%.

.. GENERATED FROM PYTHON SOURCE LINES 22-105



.. image-sg:: /auto_examples/data_quality/images/sphx_glr_plot_uncertainty_001.png
   :alt: Signal, Relative uncertainty
   :srcset: /auto_examples/data_quality/images/sphx_glr_plot_uncertainty_001.png
   :class: sphx-glr-single-img





.. code-block:: default


    import matplotlib.pyplot as plt
    import numpy as np
    import pandas as pd

    from indsl.data_quality import uncertainty_rstd
    from indsl.signals import insert_data_gaps, line, perturb_timestamp, sine_wave, white_noise


    seed = 21

    start_date = pd.Timestamp("2022-02-28")
    end_date = pd.Timestamp("2022-03-02")

    # Wave 1: Small amplitude, long wave period
    wave01 = sine_wave(
        start_date=start_date,
        end_date=end_date,
        sample_freq=pd.Timedelta("1m"),
        wave_period=pd.Timedelta("6h"),
        wave_mean=0,
        wave_amplitude=6.5,
        wave_phase=0,
    )
    wave01 = np.exp(wave01)

    # Wave 2: Large amplitude, short wave period
    wave02 = sine_wave(
        start_date=start_date,
        end_date=end_date,
        sample_freq=pd.Timedelta("1m"),
        wave_period=pd.Timedelta("1h"),
        wave_mean=0,
        wave_amplitude=100,
        wave_phase=0,
    )

    # Wave 3: Large amplitude, short wave period
    wave03 = sine_wave(
        start_date=start_date,
        end_date=end_date,
        sample_freq=pd.Timedelta("1m"),
        wave_period=pd.Timedelta("3h"),
        wave_mean=5,
        wave_amplitude=35,
        wave_phase=np.pi,
    )

    # Trends
    trend_01 = (
        line(start_date=start_date, end_date=end_date, sample_freq=pd.Timedelta("1m"), slope=0.00008, intercept=1) ** 3
    )

    trend_02 = (
        line(start_date=start_date, end_date=end_date, sample_freq=pd.Timedelta("1m"), slope=-0.00005, intercept=5) ** 5
    )

    drift = line(start_date=start_date, end_date=end_date, sample_freq=pd.Timedelta("1m"), slope=0.00005, intercept=0)

    signal = wave01 + wave02 + wave03 + trend_01 + trend_02 - drift
    N = len(signal)
    signal_w_noise_high_db = perturb_timestamp(white_noise(signal, snr_db=20, seed=seed))
    signal_w_noise_low_db = perturb_timestamp(white_noise(signal, snr_db=10, seed=seed))
    signal_w_noise = pd.concat([signal_w_noise_low_db[: N // 2], signal_w_noise_high_db[N // 2 :]])

    signal_to_analyse = insert_data_gaps(signal_w_noise, method="Random", fraction=0.35)

    uncertainty = uncertainty_rstd(signal_to_analyse)

    fig, ax = plt.subplots(2, 1, figsize=[9, 7])

    ax[0].plot(signal_to_analyse, label="Signal with noise and perturbation")
    ax[0].plot(signal, label="Synthetic signal")
    ax[0].set_title("Signal")
    ax[0].set_ylabel("Amplitude")
    ax[0].legend()

    ax[1].plot(100 * uncertainty, label="Estimated relative uncertainty", color="r")
    ax[1].set_title("Relative uncertainty")
    ax[1].set_ylabel("Percentage")
    ax[1].legend()

    plt.show()


.. rst-class:: sphx-glr-timing

   **Total running time of the script:** ( 0 minutes  3.386 seconds)


.. _sphx_glr_download_auto_examples_data_quality_plot_uncertainty.py:


.. only :: html

 .. container:: sphx-glr-footer
    :class: sphx-glr-footer-example



  .. container:: sphx-glr-download sphx-glr-download-python

     :download:`Download Python source code: plot_uncertainty.py <plot_uncertainty.py>`



  .. container:: sphx-glr-download sphx-glr-download-jupyter

     :download:`Download Jupyter notebook: plot_uncertainty.ipynb <plot_uncertainty.ipynb>`


.. only:: html

 .. rst-class:: sphx-glr-signature

    `Gallery generated by Sphinx-Gallery <https://sphinx-gallery.github.io>`_