IoT and Ensemble Long-Short-Term-Memory-Based Evapotranspiration Forecasting for Riyadh

. 2023 Sep 1;23(17):7583. doi: 10.3390/s23177583

Algorithm 2 Boosted LSTM algorithm for

E T

forecasting.

Require:
Temperature sequence $T = [T_{1}, T_{2}, \dots, T_{n}]$
Humidity sequence $H m = [H m_{1}, H m_{2}, \dots, H m_{n}]$
Wind speed sequence $W s = [W s_{1}, W s_{2}, \dots, W s_{n}]$
Output sequence $E T = [E T_{1}, E T_{2}, \dots, E T_{n}]$
Number of LSTM models M
Number of epochs E
Ensure:
Boosted LSTM model weights $W = [w_{1}, w_{2}, \dots, w_{M}]$

1:
Initialize empty list W
2:
for m in range(M) do
3:
Initialize LSTM model $L S T M_{m}$
4:
Randomly split the data into training and validation sets
5:
Initialize input sequence $X = [(T_{1}, H m_{1}, W s_{1}), (T_{2}, H m_{2}, W s_{2}), \dots, (T_{n}, H m_{n}, W s_{n})]$
6:
Initialize output sequence $Y = [E T_{1}, E T_{2}, \dots, E T_{n}]$
7:
Train $L S T M_{m}$ on the training set for E epochs using the following equations:
8:
for each epoch e in range(E) do
9:
for i in range(n) do
10:
Set the LSTM input sequence $x_{i} = (T_{i}, H m_{i}, W s_{i})$
11:
Set the LSTM target output $y_{i} = E T_{i}$
12:
Calculate the LSTM hidden state $h_{i}$ and cell state $c_{i}$ using the LSTM equations:
13:
$f_{i} = σ (W_{f} \cdot [h_{i - 1}, x_{i}] + b_{f})$
14:
$i_{i} = σ (W_{i} \cdot [h_{i - 1}, x_{i}] + b_{i})$
15:
$o_{i} = σ (W_{o} \cdot [h_{i - 1}, x_{i}] + b_{o})$
16:
${\tilde{c}}_{i} = tanh (W_{c} \cdot [h_{i - 1}, x_{i}] + b_{c})$
17:
$c_{i} = f_{i} \cdot c_{i - 1} + i_{i} \cdot {\tilde{c}}_{i}$
18:
$h_{i} = o_{i} \cdot tanh (c_{i})$
19:
Calculate the LSTM output $y_{p r e d_{i}}$ using the output equation:
20:
$y_{p r e d_{i}} = W_{y} \cdot h_{i} + b_{y}$
21:
Calculate the LSTM loss $L_{i}$ using a suitable loss function (e.g., mean squared error):
22:
$L_{i} = \frac{1}{2} {(y_{p r e d_{i}} - y_{i})}^{2}$
23:
Update the LSTM model parameters $W_{f}, W_{i}, W_{o}, W_{c}, W_{y}, b_{f}, b_{i}, b_{o}, b_{c}, b_{y}$ using back-propagation and gradient descent:
24:
$W_{f} = W_{f} - α \cdot \frac{\partial L_{i}}{\partial W_{f}}$
25:
$W_{i} = W_{i} - α \cdot \frac{\partial L_{i}}{\partial W_{i}}$
26:
$W_{o} = W_{o} - α \cdot \frac{\partial L_{i}}{\partial W_{o}}$
27:
$W_{c} = W_{c} - α \cdot \frac{\partial L_{i}}{\partial W_{c}}$
28:
$W_{y} = W_{y} - α \cdot \frac{\partial L_{i}}{\partial W_{y}}$
29:
$b_{f} = b_{f} - α \cdot \frac{\partial L_{i}}{\partial b_{f}}$
30:
$b_{i} = b_{i} - α \cdot \frac{\partial L_{i}}{\partial b_{i}}$
31:
$b_{o} = b_{o} - α \cdot \frac{\partial L_{i}}{\partial b_{o}}$
32:
$b_{c} = b_{c} - α \cdot \frac{\partial L_{i}}{\partial b_{c}}$
33:
$b_{y} = b_{y} - α \cdot \frac{\partial L_{i}}{\partial b_{y}}$
34:
Evaluate the performance of $L S T M_{m}$ on the validation set
35:
Calculate the weight $w_{m}$ based on the validation performance of $L S T M_{m}$
36:
$w_{m} = \frac{Validation Accuracy of L S T M_{m}}{Total Validation Accuracy}$
37:
Store the weight $w_{m}$ in the list W
38:
Normalize the weights in W
39:
return W