# Illustrative test cases Discrete Dynamic#

## Temperature forecasting#

This is one of the dynamic data sets provided with the NeurEco installation. The goal of this test case is to predict the temperature at time t, using weather variables from a weather station.

The input and output features of this test case are as follows:

Inputs

Outputs

p (mbar) at time t

T (deg C) at time t

Tpot(K) at time t

Tdew(deg C) at time t

rh(%) at time t

VPmax(mbar) at time t

VPact(mbar) at time t

VPdef(mbar) at time t

sh(g/kg) at time t

H2OC(mmol/l) at time t

rho (g/m^3) at time t

wv (m/s) at time t

max wv (m/s) at time t

wd(deg) at time t

The test case is provided with the following files:

• Training data set containing one trajectory, $$526$$ time steps long:

• x_first_year.npy: first year of measurements of the input features

• y_first_year.npy: first year of measurements of temperature (the output feature)

• Testing data set containing one trajectory, $$526$$ time steps long:

• x_second_year.npy: second year of measurements of the input features

• y_second_year.npy: second year of measurements of temperature (the output feature)

## Nonlinear oscillator#

This is one of the dynamic data sets provided with the NeurEco installation. This test case describes a Duffing oscillator governed by the following equation:

$\ddot{x} + \delta \dot{x} + \alpha x + \beta x^3 = f(t)$

where:

$\delta = 0.22$
$\alpha = 1$
$\beta = 875$

The choice of the equation parameters were made arbitrarily to give it a strong non linearity.

The input features are: the trajectories of $$f(t)$$.
The output features are: the corresponding $$x(t)$$ with added noise.

This test case is provided with the following files:

• Training data set containing two trajectories:

• train_exc_1.csv: the training inputs file - part 1, $$750$$ time steps long

• train_out_1.csv: the training targets file - part 1

• train_exc_2.csv: the training inputs file - part 2, $$750$$ time steps long

• train_out_2.csv: the training targets file - part 2

• Validation data set containing one trajectory:

• valid_exc_1.csv: the validation inputs file, $$1501$$ time steps long

• valid_out_1.csv: the validation targets file

• Testing data set containing one trajectory:

• test_exc_1.csv: the testing inputs file, $$1501$$ time steps long

• test_out_1.csv: the testing targets file

## Electric Motor Temperature#

This is one of the dynamic data sets provided with the NeurEco installation. The goal is to predict the temperature of the permanent magnet inside an electrical synchronous motor at time t, using its excitations. The motor is excited by hand-designed driving cycles denoting a reference motor speed and a reference torque. Currents in d/q-coordinates (columns “id” and iq”) and voltages in d/q-coordinates (columns “ud” and “uq”) are a result of a standard control strategy trying to follow the reference speed and torque. Columns “motor_speed” and “torque” are the resulting quantities achieved by that strategy, derived from set currents and voltages.

The data set and its detailed description can be found here: Kaggle: Electric Motor Temperature.

Note: This test case uses 1 time step in every 100 time steps found on the website (1% of the data)

Seven input features:

u_q: Voltage q-component measurement in dq-coordinates (in V). coolant: Coolant temperature (in °C). u_d: Voltage d-component measurement in dq-coordinates (in V). motor_speed: Motor speed (in rpm). i_d: Current d-component measurement in dq-coordinates. i_q: Current q-component measurement in dq-coordinates. ambient: Ambient temperature (in °C)

One output feature: pm: Permanent magnet temperature (in °C) measured with thermocouples and transmitted wirelessly via a thermography unit.

This test case is provided with the following files:

• Training data set containing 20 trajectories:

• train_exc_n.csv: the $$n^{th}$$ training inputs file

• train_out_n.csv: the $$n^{th}$$ training targets file

• Validation data set containing 20 trajectories:

• valid_exc_n.csv: the $$n^{th}$$ validation inputs file

• valid_out_n.csv: the $$n^{th}$$ validation targets file

• Testing data set containing 21 trajectories:

• test_exc_n.csv: the $$n^{th}$$ testing inputs file

• test_out_n.csv: the $$n^{th}$$ testing targets file