PV forecasting benchmark¶
Example created by Wilson Rocha Lacerda Junior
Note¶
The following example is not intended to say that one library is better than another. The main focus of these examples is to show that SysIdentPy can be a good alternative for people looking to model time series.
We will compare the results obtained against neural prophet library.
For the sake of brevity, from SysIdentPy only the MetaMSS, AOLS and FROLS (with polynomial base function) methods will be used. See the SysIdentPy documentation to learn other ways of modeling with the library.
We will compare a 1-step ahead forecaster on solar irradiance data (that can be a proxy for solar PV production). The config of the neuralprophet model was taken from the neuralprophet documentation (https://neuralprophet.com/html/example_links/energy_data_example.html)
The training will occur on 80% of the data, reserving the last 20% for the validation.
Note: the data used in this example can be found in neuralprophet github.
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from warnings import simplefilter
import matplotlib.pyplot as plt
import numpy as np
import pandas as pd
from sysidentpy.model_structure_selection import FROLS, AOLS, MetaMSS
from sysidentpy.basis_function import Polynomial
from sysidentpy.parameter_estimation import LeastSquares
from sysidentpy.utils.plotting import plot_results
from sysidentpy.neural_network import NARXNN
from sysidentpy.metrics import mean_squared_error
from neuralprophet import NeuralProphet
from neuralprophet import set_random_seed
simplefilter("ignore", FutureWarning)
np.seterr(all="ignore")
%matplotlib inline
loss = mean_squared_error
data_location = r".\datasets"
from warnings import simplefilter import matplotlib.pyplot as plt import numpy as np import pandas as pd from sysidentpy.model_structure_selection import FROLS, AOLS, MetaMSS from sysidentpy.basis_function import Polynomial from sysidentpy.parameter_estimation import LeastSquares from sysidentpy.utils.plotting import plot_results from sysidentpy.neural_network import NARXNN from sysidentpy.metrics import mean_squared_error from neuralprophet import NeuralProphet from neuralprophet import set_random_seed simplefilter("ignore", FutureWarning) np.seterr(all="ignore") %matplotlib inline loss = mean_squared_error data_location = r".\datasets"
FROLS¶
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files = ["\SanFrancisco_PV_GHI.csv", "\SanFrancisco_Hospital.csv"]
raw = pd.read_csv(data_location + files[0])
df = pd.DataFrame()
df["ds"] = pd.date_range("1/1/2015 1:00:00", freq=str(60) + "Min", periods=(8760))
df["y"] = raw.iloc[:, 0].values
df_train, df_val = df.iloc[:7008, :], df.iloc[7008:, :]
y = df["y"].values.reshape(-1, 1)
y_train = df_train["y"].values.reshape(-1, 1)
y_test = df_val["y"].values.reshape(-1, 1)
x_train = df_train["ds"].dt.hour.values.reshape(-1, 1)
x_test = df_val["ds"].dt.hour.values.reshape(-1, 1)
basis_function = Polynomial(degree=1)
sysidentpy = FROLS(
order_selection=True,
ylag=24,
xlag=24,
info_criteria="bic",
basis_function=basis_function,
model_type="NARMAX",
estimator=LeastSquares(),
)
sysidentpy.fit(X=x_train, y=y_train)
x_test = np.concatenate([x_train[-sysidentpy.max_lag :], x_test])
y_test = np.concatenate([y_train[-sysidentpy.max_lag :], y_test])
yhat = sysidentpy.predict(X=x_test, y=y_test, steps_ahead=1)
sysidentpy_loss = loss(
pd.Series(y_test.flatten()[sysidentpy.max_lag :]),
pd.Series(yhat.flatten()[sysidentpy.max_lag :]),
)
print(sysidentpy_loss)
plot_results(y=y_test[-104:], yhat=yhat[-104:])
files = ["\SanFrancisco_PV_GHI.csv", "\SanFrancisco_Hospital.csv"] raw = pd.read_csv(data_location + files[0]) df = pd.DataFrame() df["ds"] = pd.date_range("1/1/2015 1:00:00", freq=str(60) + "Min", periods=(8760)) df["y"] = raw.iloc[:, 0].values df_train, df_val = df.iloc[:7008, :], df.iloc[7008:, :] y = df["y"].values.reshape(-1, 1) y_train = df_train["y"].values.reshape(-1, 1) y_test = df_val["y"].values.reshape(-1, 1) x_train = df_train["ds"].dt.hour.values.reshape(-1, 1) x_test = df_val["ds"].dt.hour.values.reshape(-1, 1) basis_function = Polynomial(degree=1) sysidentpy = FROLS( order_selection=True, ylag=24, xlag=24, info_criteria="bic", basis_function=basis_function, model_type="NARMAX", estimator=LeastSquares(), ) sysidentpy.fit(X=x_train, y=y_train) x_test = np.concatenate([x_train[-sysidentpy.max_lag :], x_test]) y_test = np.concatenate([y_train[-sysidentpy.max_lag :], y_test]) yhat = sysidentpy.predict(X=x_test, y=y_test, steps_ahead=1) sysidentpy_loss = loss( pd.Series(y_test.flatten()[sysidentpy.max_lag :]), pd.Series(yhat.flatten()[sysidentpy.max_lag :]), ) print(sysidentpy_loss) plot_results(y=y_test[-104:], yhat=yhat[-104:])
3869.3472912979273
MetaMSS¶
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set_random_seed(42)
files = ["\SanFrancisco_PV_GHI.csv", "\SanFrancisco_Hospital.csv"]
raw = pd.read_csv(data_location + files[0])
df = pd.DataFrame()
df["ds"] = pd.date_range("1/1/2015 1:00:00", freq=str(60) + "Min", periods=(8760))
df["y"] = raw.iloc[:, 0].values
df_train, df_val = df.iloc[:7008, :], df.iloc[7008:, :]
y = df["y"].values.reshape(-1, 1)
y_train = df_train["y"].values.reshape(-1, 1)
y_test = df_val["y"].values.reshape(-1, 1)
x_train = df_train["ds"].dt.hour.values.reshape(-1, 1)
x_test = df_val["ds"].dt.hour.values.reshape(-1, 1)
basis_function = Polynomial(degree=1)
estimator = LeastSquares()
sysidentpy_metamss = MetaMSS(
basis_function=basis_function,
xlag=24,
ylag=24,
estimator=estimator,
maxiter=10,
steps_ahead=1,
n_agents=15,
loss_func="metamss_loss",
model_type="NARMAX",
random_state=42,
)
sysidentpy_metamss.fit(X=x_train, y=y_train)
x_test = np.concatenate([x_train[-sysidentpy_metamss.max_lag :], x_test])
y_test = np.concatenate([y_train[-sysidentpy_metamss.max_lag :], y_test])
yhat = sysidentpy_metamss.predict(X=x_test, y=y_test, steps_ahead=1)
metamss_loss = loss(
pd.Series(y_test.flatten()[sysidentpy_metamss.max_lag :]),
pd.Series(yhat.flatten()[sysidentpy_metamss.max_lag :]),
)
print(metamss_loss)
plot_results(y=y_test[-104:], yhat=yhat[-104:])
set_random_seed(42) files = ["\SanFrancisco_PV_GHI.csv", "\SanFrancisco_Hospital.csv"] raw = pd.read_csv(data_location + files[0]) df = pd.DataFrame() df["ds"] = pd.date_range("1/1/2015 1:00:00", freq=str(60) + "Min", periods=(8760)) df["y"] = raw.iloc[:, 0].values df_train, df_val = df.iloc[:7008, :], df.iloc[7008:, :] y = df["y"].values.reshape(-1, 1) y_train = df_train["y"].values.reshape(-1, 1) y_test = df_val["y"].values.reshape(-1, 1) x_train = df_train["ds"].dt.hour.values.reshape(-1, 1) x_test = df_val["ds"].dt.hour.values.reshape(-1, 1) basis_function = Polynomial(degree=1) estimator = LeastSquares() sysidentpy_metamss = MetaMSS( basis_function=basis_function, xlag=24, ylag=24, estimator=estimator, maxiter=10, steps_ahead=1, n_agents=15, loss_func="metamss_loss", model_type="NARMAX", random_state=42, ) sysidentpy_metamss.fit(X=x_train, y=y_train) x_test = np.concatenate([x_train[-sysidentpy_metamss.max_lag :], x_test]) y_test = np.concatenate([y_train[-sysidentpy_metamss.max_lag :], y_test]) yhat = sysidentpy_metamss.predict(X=x_test, y=y_test, steps_ahead=1) metamss_loss = loss( pd.Series(y_test.flatten()[sysidentpy_metamss.max_lag :]), pd.Series(yhat.flatten()[sysidentpy_metamss.max_lag :]), ) print(metamss_loss) plot_results(y=y_test[-104:], yhat=yhat[-104:])
2157.7700127350877
AOLS¶
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set_random_seed(42)
files = ["\SanFrancisco_PV_GHI.csv", "\SanFrancisco_Hospital.csv"]
raw = pd.read_csv(data_location + files[0])
df = pd.DataFrame()
df["ds"] = pd.date_range("1/1/2015 1:00:00", freq=str(60) + "Min", periods=(8760))
df["y"] = raw.iloc[:, 0].values
df_train, df_val = df.iloc[:7008, :], df.iloc[7008:, :]
y = df["y"].values.reshape(-1, 1)
y_train = df_train["y"].values.reshape(-1, 1)
y_test = df_val["y"].values.reshape(-1, 1)
x_train = df_train["ds"].dt.hour.values.reshape(-1, 1)
x_test = df_val["ds"].dt.hour.values.reshape(-1, 1)
basis_function = Polynomial(degree=1)
sysidentpy_AOLS = AOLS(
ylag=24, xlag=24, k=2, L=1, model_type="NARMAX", basis_function=basis_function
)
sysidentpy_AOLS.fit(X=x_train, y=y_train)
x_test = np.concatenate([x_train[-sysidentpy_AOLS.max_lag :], x_test])
y_test = np.concatenate([y_train[-sysidentpy_AOLS.max_lag :], y_test])
yhat = sysidentpy_AOLS.predict(X=x_test, y=y_test, steps_ahead=1)
aols_loss = loss(
pd.Series(y_test.flatten()[sysidentpy_AOLS.max_lag :]),
pd.Series(yhat.flatten()[sysidentpy_AOLS.max_lag :]),
)
print(aols_loss)
plot_results(y=y_test[-104:], yhat=yhat[-104:])
set_random_seed(42) files = ["\SanFrancisco_PV_GHI.csv", "\SanFrancisco_Hospital.csv"] raw = pd.read_csv(data_location + files[0]) df = pd.DataFrame() df["ds"] = pd.date_range("1/1/2015 1:00:00", freq=str(60) + "Min", periods=(8760)) df["y"] = raw.iloc[:, 0].values df_train, df_val = df.iloc[:7008, :], df.iloc[7008:, :] y = df["y"].values.reshape(-1, 1) y_train = df_train["y"].values.reshape(-1, 1) y_test = df_val["y"].values.reshape(-1, 1) x_train = df_train["ds"].dt.hour.values.reshape(-1, 1) x_test = df_val["ds"].dt.hour.values.reshape(-1, 1) basis_function = Polynomial(degree=1) sysidentpy_AOLS = AOLS( ylag=24, xlag=24, k=2, L=1, model_type="NARMAX", basis_function=basis_function ) sysidentpy_AOLS.fit(X=x_train, y=y_train) x_test = np.concatenate([x_train[-sysidentpy_AOLS.max_lag :], x_test]) y_test = np.concatenate([y_train[-sysidentpy_AOLS.max_lag :], y_test]) yhat = sysidentpy_AOLS.predict(X=x_test, y=y_test, steps_ahead=1) aols_loss = loss( pd.Series(y_test.flatten()[sysidentpy_AOLS.max_lag :]), pd.Series(yhat.flatten()[sysidentpy_AOLS.max_lag :]), ) print(aols_loss) plot_results(y=y_test[-104:], yhat=yhat[-104:])
2361.561682547365
Neural Prophet¶
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set_random_seed(42)
# set_log_level("ERROR")
files = ["\SanFrancisco_PV_GHI.csv", "\SanFrancisco_Hospital.csv"]
raw = pd.read_csv(data_location + files[0])
df = pd.DataFrame()
df["ds"] = pd.date_range("1/1/2015 1:00:00", freq=str(60) + "Min", periods=(8760))
df["y"] = raw.iloc[:, 0].values
m = NeuralProphet(
n_lags=24,
ar_sparsity=0.5,
# num_hidden_layers = 2,
# d_hidden=20,
)
metrics = m.fit(df, freq="H", valid_p=0.2)
df_train, df_val = m.split_df(df, valid_p=0.2)
m.test(df_val)
future = m.make_future_dataframe(df_val, n_historic_predictions=True)
forecast = m.predict(future)
# fig = m.plot(forecast)
print(loss(forecast["y"][24:-1], forecast["yhat1"][24:-1]))
set_random_seed(42) # set_log_level("ERROR") files = ["\SanFrancisco_PV_GHI.csv", "\SanFrancisco_Hospital.csv"] raw = pd.read_csv(data_location + files[0]) df = pd.DataFrame() df["ds"] = pd.date_range("1/1/2015 1:00:00", freq=str(60) + "Min", periods=(8760)) df["y"] = raw.iloc[:, 0].values m = NeuralProphet( n_lags=24, ar_sparsity=0.5, # num_hidden_layers = 2, # d_hidden=20, ) metrics = m.fit(df, freq="H", valid_p=0.2) df_train, df_val = m.split_df(df, valid_p=0.2) m.test(df_val) future = m.make_future_dataframe(df_val, n_historic_predictions=True) forecast = m.predict(future) # fig = m.plot(forecast) print(loss(forecast["y"][24:-1], forecast["yhat1"][24:-1]))
WARNING: nprophet - fit: Parts of code may break if using other than daily data.
04-26 20:16:52 - WARNING - Parts of code may break if using other than daily data.
INFO: nprophet.utils - set_auto_seasonalities: Disabling yearly seasonality. Run NeuralProphet with yearly_seasonality=True to override this.
04-26 20:16:52 - INFO - Disabling yearly seasonality. Run NeuralProphet with yearly_seasonality=True to override this.
INFO: nprophet.config - set_auto_batch_epoch: Auto-set batch_size to 32
04-26 20:16:52 - INFO - Auto-set batch_size to 32
INFO: nprophet.config - set_auto_batch_epoch: Auto-set epochs to 7
04-26 20:16:52 - INFO - Auto-set epochs to 7
87%|████████▋ | 87/100 [00:00<00:00, 617.37it/s] INFO: nprophet - _lr_range_test: learning rate range test found optimal lr: 1.23E-01
04-26 20:16:52 - INFO - learning rate range test found optimal lr: 1.23E-01
Epoch[7/7]: 100%|██████████| 7/7 [00:02<00:00, 2.61it/s, SmoothL1Loss=0.00415, MAE=58.8, RegLoss=0.0112] INFO: nprophet - _evaluate: Validation metrics: SmoothL1Loss MAE 1 0.003 48.746
04-26 20:16:55 - INFO - Validation metrics: SmoothL1Loss MAE 1 0.003 48.746 4642.234763049609
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plt.plot(forecast["y"][-104:], "ro-")
plt.plot(forecast["yhat1"][-104:], "k*-")
plt.plot(forecast["y"][-104:], "ro-") plt.plot(forecast["yhat1"][-104:], "k*-")
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[<matplotlib.lines.Line2D at 0x2618e76ebe0>]
