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.. TO MAKE CHANGES, EDIT THE SOURCE PYTHON FILE:
.. "examples/basics/ex1_5_fielderrs_therm3d.py"
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.. _sphx_glr_examples_basics_ex1_5_fielderrs_therm3d.py:


Basics: Field-based systematic errors
================================================================================

In this example we give an overview of field-based systematic errors. Field
errors require additional interpolation of the underlying physical field such as
uncertainty in a sensors position or sampling time. For this example we will
focus on field error sources that perturb sensor locations and sampling times.
In later examples we will analyse sensor orientation for vector and tensor
fields.

Note that field errors are more computationally intensive than basic errors as
they require additional interpolations of the underlying physical field.

Test case: Scalar field point sensors (thermocouples) on a 3D thermal simulation

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.. code-block:: Python


    from pathlib import Path
    import numpy as np
    import matplotlib.pyplot as plt
    import mooseherder as mh
    import pyvale as pyv


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First we use everything we learned from the first three examples to build
a thermocouple sensor array for the same 3D thermal simulation we have
analysed in the previous examples. Then we will look at a new type of
systematic error called a field error which requires additional
interpolation of the underlying physical field to be measured.

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.. code-block:: Python

    data_path = pyv.DataSet.thermal_3d_path()
    sim_data = mh.ExodusReader(data_path).read_all_sim_data()
    sim_data = pyv.scale_length_units(scale=1000.0,
                                        sim_data=sim_data,
                                        disp_comps=None)

    n_sens = (1,4,1)
    x_lims = (12.5,12.5)
    y_lims = (0.0,33.0)
    z_lims = (0.0,12.0)
    sens_pos = pyv.create_sensor_pos_array(n_sens,x_lims,y_lims,z_lims)

    sample_times = np.linspace(0.0,np.max(sim_data.time),50) # | None

    sensor_data = pyv.SensorData(positions=sens_pos,
                                    sample_times=sample_times)

    field_key: str = "temperature"
    tc_array = pyv.SensorArrayFactory \
        .thermocouples_no_errs(sim_data,
                                sensor_data,
                                elem_dims=3,
                                field_name=field_key)

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Now we will create a field error data class which we will use to build our
field error. This controls which sensor parameters will be perturbed such
as: position, time and orientation. Here we will perturb the sensor
positions on the face of the block using a normal distribution and we will
also perturb the measurement times.

We can apply a constant offset to each sensors position in x,y,z by
providing a shape=(num_sensors,coord[x,y,z]) array. Here we apply a
constant offset in the y and z direction for all sensors.

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.. code-block:: Python

    pos_offset_xyz = np.array((0.0,1.0,1.0),dtype=np.float64)
    pos_offset_xyz = np.tile(pos_offset_xyz,(sens_pos.shape[0],1))


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We can also apply a constant offset to the sampling times for all sensors

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.. code-block:: Python

    time_offset = np.full((sample_times.shape[0],),0.1)


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Using the `Gen*` random generators in pyvale we can randomly perturb the
position or sampling times of our virtual sensors.

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.. code-block:: Python

    pos_rand = pyv.GenNormal(std=1.0) # units = mm
    time_rand = pyv.GenNormal(std=0.1) # units = s


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Now we put everything into our field error data class ready to build our
field error object. Have a look at the other parameters in this data class
to geta feel for the other types of supported field errors. We will look
at the orientation and area averaging errors when we look at vector and
tensor fields in later examples.

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.. code-block:: Python

    field_err_data = pyv.ErrFieldData(
        pos_offset_xyz=pos_offset_xyz,
        time_offset=time_offset,
        pos_rand_xyz=(None,pos_rand,pos_rand),
        time_rand=time_rand
    )


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Adding our field error to our error chain is exactly the same as the basic
errors we have seen previously. We can also combine field errors with
basic errors and place them anywhere in our error chain. We can even chain
field errors together which we will look at in the next example. For now
we will just have a single field error so we can easily visualise what
this type of error does.

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.. code-block:: Python

    err_chain = []


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A field error needs to know which field it should interpolate for error
calculations so we provide the field from the sensor array as well as the
field error error data class.

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.. code-block:: Python

    err_chain.append(pyv.ErrSysField(tc_array.get_field(),
                                        field_err_data))
    err_int = pyv.ErrIntegrator(err_chain,
                                sensor_data,
                                tc_array.get_measurement_shape())
    tc_array.set_error_integrator(err_int)


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Now we can run the sensor simulation and display the results to see what
our field error has done.

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.. code-block:: Python

    measurements = tc_array.calc_measurements()

    print(80*"-")

    sens_print = 0
    comp_print = 0
    time_last = 5
    time_print = slice(measurements.shape[2]-time_last,measurements.shape[2])


    print(f"These are the last {time_last} virtual measurements of sensor "
            + f"{sens_print}:")

    pyv.print_measurements(tc_array,sens_print,comp_print,time_print)

    print(80*"-")


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We are going to save some figures to disk as well as displaying them
interactively so we create a directory for this:

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.. code-block:: Python

    output_path = Path.cwd() / "pyvale-output"
    if not output_path.is_dir():
        output_path.mkdir(parents=True, exist_ok=True)


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If we analyse the time traces we can see offsets in the sensor value and
the sampling times which we expect from our field error setup.

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.. code-block:: Python

    (fig,ax) = pyv.plot_time_traces(tc_array,field_key)

    save_traces = output_path/"field_ex1_5_sensortraces.png"
    fig.savefig(save_traces, dpi=300, bbox_inches="tight")
    fig.savefig(save_traces.with_suffix(".svg"), dpi=300, bbox_inches="tight")

    plt.show()


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It is also possible to view the perturbed sensor locations on the
simulation mesh if we create a plot after running the sensor simulation.

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.. code-block:: Python

    pv_plot = pyv.plot_point_sensors_on_sim(tc_array,field_key)
    pv_plot.camera_position = [(59.354, 43.428, 69.946),
                                (-2.858, 13.189, 4.523),
                                (-0.215, 0.948, -0.233)]

    save_render = output_path / "fielderrs_ex1_5_sensorlocs.svg"
    pv_plot.save_graphic(save_render) # only for .svg .eps .ps .pdf .tex
    pv_plot.screenshot(save_render.with_suffix(".png"))

    pv_plot.show()


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We have saved an image of the sensor traces and the perturbed locations of
the sensors to the `pyvale-output` directory in your current working
directory. Analyse these figures side by side to show that the location of
the perturbed sensor locations matches the expected sensor traces.


.. _sphx_glr_download_examples_basics_ex1_5_fielderrs_therm3d.py:

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