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.. TO MAKE CHANGES, EDIT THE SOURCE PYTHON FILE:
.. "examples/basics/ex2_4_chainfielderrs_disp2d.py"
.. LINE NUMBERS ARE GIVEN BELOW.

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.. _sphx_glr_examples_basics_ex2_4_chainfielderrs_disp2d.py:


Basics: Chaining field errors
================================================================================

In this example we show how field errors can be chained together and accumulated
allowing for successive perturbations in postion, sampling time and orientation.
It is more computationally efficient to provide a single field error object as
this will perform all perturbations in a single step allowing for a single new
interpolation of the underlying physical field. However, in some cases it can
be useful to separate the sensor parameter perturbations to determine which is
contributing most to the total error.

Note that this tutorial assumes you are familiar with the use of `pyvale` for
scalar fields as described in the first set of examples.

Test case: point displacement sensors on a 2D plate with hole loaded in tension

.. GENERATED FROM PYTHON SOURCE LINES 24-30

.. code-block:: Python


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


.. GENERATED FROM PYTHON SOURCE LINES 31-33

We start by building the same displacement sensor array applied to a 2D
solid mechanics simulation that we have analysed previously.

.. GENERATED FROM PYTHON SOURCE LINES 33-60

.. code-block:: Python

    data_path = pyv.DataSet.mechanical_2d_path()
    sim_data = mh.ExodusReader(data_path).read_all_sim_data()
    field_name = "disp"
    field_comps = ("disp_x","disp_y")
    sim_data = pyv.scale_length_units(scale=1000.0,
                                        sim_data=sim_data,
                                        disp_comps=field_comps)

    descriptor = pyv.SensorDescriptorFactory.displacement_descriptor()

    disp_field = pyv.FieldVector(sim_data,field_name,field_comps,elem_dims=2)

    n_sens = (2,3,1)
    x_lims = (0.0,100.0)
    y_lims = (0.0,150.0)
    z_lims = (0.0,0.0)
    sensor_positions = 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)

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

    disp_sens_array = pyv.SensorArrayPoint(sensor_data,
                                            disp_field,
                                            descriptor)


.. GENERATED FROM PYTHON SOURCE LINES 61-67

Now we will build a series of field errors that cause succesive offsets in
sensor sampling time, sensor position and sensor orientation. That way
we should be able to analyse the sensor data object at each point in the
error chain to see how the sensor parameters have accumulated.

We will apply a position offset of -1.0mm in the x and y axes.

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.. code-block:: Python

    pos_offset = -1.0*np.ones_like(sensor_positions)
    pos_offset[:,2] = 0.0 # in 2d we only have offset in x and y so zero z
    pos_error_data = pyv.ErrFieldData(pos_offset_xyz=pos_offset)


.. GENERATED FROM PYTHON SOURCE LINES 72-73

We will apply a rotation offset about the z axis of 1 degree

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.. code-block:: Python

    angle_offset = np.zeros_like(sensor_positions)
    angle_offset[:,0] = 1.0 # only rotate about z in 2D
    angle_error_data = pyv.ErrFieldData(ang_offset_zyx=angle_offset)

    time_offset = 2.0*np.ones_like(disp_sens_array.get_sample_times())
    time_error_data = pyv.ErrFieldData(time_offset=time_offset)


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Now we add all our field errors to our error chain. We add each error
twice to see how they accumulate with each other. We also need to set the
error dependence to `DEPENDENT` so that the sensor state is accumulated
over the error chain as field errors are `INDEPENDENT` by default.

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.. code-block:: Python

    err_chain = []
    err_chain.append(pyv.ErrSysField(disp_field,
                                        time_error_data,
                                        pyv.EErrDep.DEPENDENT))
    err_chain.append(pyv.ErrSysField(disp_field,
                                        time_error_data,
                                        pyv.EErrDep.DEPENDENT))

    err_chain.append(pyv.ErrSysField(disp_field,
                                        pos_error_data,
                                        pyv.EErrDep.DEPENDENT))
    err_chain.append(pyv.ErrSysField(disp_field,
                                        pos_error_data,
                                        pyv.EErrDep.DEPENDENT))

    err_chain.append(pyv.ErrSysField(disp_field,
                                        angle_error_data,
                                        pyv.EErrDep.DEPENDENT))
    err_chain.append(pyv.ErrSysField(disp_field,
                                        angle_error_data,
                                        pyv.EErrDep.DEPENDENT))


.. GENERATED FROM PYTHON SOURCE LINES 108-116

Instead of setting the dependence for each individual error above we could
also just use our error integration options to force all errors to be
`DEPENDENT`. We also set the error integration options to store the errors
for each step in the error chain so we can analyse the sensor data at each
step of chain. This option also allows us to separate the contribution of
each error in the chain to the total error rather than just being able to
analyse the total systematic and total random error which is the default.
Note that this option will use more memory.

.. GENERATED FROM PYTHON SOURCE LINES 116-119

.. code-block:: Python

    err_int_opts = pyv.ErrIntOpts(force_dependence=pyv.EErrDep.DEPENDENT,
                                    store_all_errs=True)


.. GENERATED FROM PYTHON SOURCE LINES 120-122

Now we build our error integrator, add it to our sensor array and then run
our sensor simulation to obtain some virtual measurements.

.. GENERATED FROM PYTHON SOURCE LINES 122-130

.. code-block:: Python

    error_int = pyv.ErrIntegrator(err_chain,
                                    sensor_data,
                                    disp_sens_array.get_measurement_shape(),
                                    err_int_opts)
    disp_sens_array.set_error_integrator(error_int)

    measurements = disp_sens_array.calc_measurements()


.. GENERATED FROM PYTHON SOURCE LINES 131-134

Here we will print to the console the time, position and angle of from the
sensor data objects at each point in the error chain. We should see each
sensor parameter perturbed and accumulated throughout the chain:

.. GENERATED FROM PYTHON SOURCE LINES 134-152

.. code-block:: Python

    sens_data_by_chain = error_int.get_sens_data_by_chain()
    if sens_data_by_chain is not None:
        for ii,ss in enumerate(sens_data_by_chain):
            print(80*"-")
            if ss is not None:
                print(f"SensorData @ [{ii}]")
                print("TIME")
                print(ss.sample_times)
                print()
                print("POSITIONS")
                print(ss.positions)
                print()
                print("ANGLES")
                for aa in ss.angles:
                    print(aa.as_euler("zyx",degrees=True))
                print()
            print(80*"-")


.. GENERATED FROM PYTHON SOURCE LINES 153-159

Try setting all the field errors to be `INDEPENDENT` using the error
integration options above. You should see that the sensor parameters are
not accumulated throughout the error chain.

Here we print the final sampling time, sensor positions and sensor angles
at the end of error chain.

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.. code-block:: Python

    print()
    print(80*"=")
    sens_data_accumulated = error_int.get_sens_data_accumulated()
    print("TIME")
    print(sens_data_accumulated.sample_times)
    print()
    print("POSITIONS")
    print(sens_data_accumulated.positions)
    print()
    print("ANGLES")
    for aa in sens_data_accumulated.angles:
        print(aa.as_euler("zyx",degrees=True))
    print()
    print(80*"=")


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We print the results for one of the sensors so we can see what the errors
are for the last few sampling times.

.. GENERATED FROM PYTHON SOURCE LINES 177-192

.. code-block:: Python

    print(80*"-")

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

    print("ROTATED SENSORS WITH ANGLE ERRORS:")
    print(f"These are the last {time_last} virtual measurements of sensor "
            + f"{sens_print} for {field_comps[comp_print]}:")

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

    print(80*"-")


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Finally, we plot the time traces for all field components.

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.. code-block:: Python

    for ff in field_comps:
        pyv.plot_time_traces(disp_sens_array,ff)

    plt.show()


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