# A Deep Learning Method for Short-Term Dynamic Positioning Load Forecasting in Maritime Microgrids
## 3 The Proposed Method
For instance, environmental disturbances such as wave, wind, and their patterns affect the DP load demand, which leads to vessel movements. Hence, the following dynamic propulsion model is forecasted essential load demand for one hour, one day, and one week for PMS according to the Caspian Sea state, where the data has collected in a DP ship. To make the NARX, NAR, and NN with TDL, as NN-Time Series schemes which are used in the MATLAB deep learning toolbox [70]. Furthermore, the percentage of external inputs as we revealed in Table 1 is defined as 70%, 15%, and 15% for training, validating, and testing, respectively. After the definition of the percentage, the number of hidden layers neurons are adjusted 25. Finally, according to the parameters which we have defined, the NN is trained and implemented offline to predict the desired target. According to the collected data, as shown in Figure 6, we observed a non-linear relationship between the sea state parameters, such as wind, wave, and hourly DP load profile. Therefore, we have modeled the sea disturbances on the DP load profile as shown in Figure 8a,b. Hence, we applied hourly data of wind and wave variations and ship displacement as external inputs (disturbances) in (15) and (16) for high accuracy and speed convergence of the NARX-NN to train weights in MLP based LM-BP in (17) for DP load forecasting. To analyze the performance of the training procedure by using the proposed method, we have validated and tested the trained data set based on actual thruster's power consumption. Figure 9 \begin{table}
\begin{tabular}{c c c c} \hline  & **Weather Conditions** & **Actual Power (MW)** \\ \hline Description & Wind (m/s) & Wave (m) & \\ Calm-Slight & [0–5] & [0–1.25] & [0–1] \\ Moderate & [5–10] & [1.5–3] & [1–3] \\ Rough & [10–15] & [3.25–5.5] & [3–5] \\ High & [15–20] & [5.5–9.5] & [5–7] \\ \hline \end{tabular}
\end{table} 
Table 2: Weather parameters data patterns based on the code of sea states (data from [36]). Figure 8: (**a**). Relationship model between wind speed and wave height as inputs for short terms load forecasting and (**b**) DP load profile for January 2020.  
displays the regression plots of STELF for the hourly, daily, and weekly for training, validation, and testing epochs. The regression results show that the training, validating, and testing are fairly successful where the data sets are trained more than 0.99, validated and tested values of trained parameters are around 0.99 and 0.98 at the 11 iterations. In addition, the majority of the vast data of the training collection produces result output on the edge of the first-order line, which is correlated to the best fitting connection. Accordingly, the relationship between the proposed method and target fitting line has shown that it can have a fairly good performance concerning the actual and predicted DP power demands by using the LM-BP-NARX technique. Regression figures are achieved for every single training process similarly. In our case study, we evaluate LM-NARX, and the others time series NN based on following two performance measurement indicators are defined as follow: (a) mean absolute percentage error (_MAPE_), and (b) error variance (\(\delta\)), given as:  
\[\delta=\sqrt{\frac{1}{N}{\sum_{i=1}^{N}{\left[y(n,t)-\frac{\wedge}{y}(n,t) \right]^{2}}}} \tag{20}\]  
\[\textit{MAPE}=\frac{1}{N}{\sum_{i=1}^{N}{\frac{\left[y(n,t)-\frac{\wedge}{y}(n,t)\right]}{y(n,t)}\times 100}} \tag{21}\]