# A Deep Learning Method for Short-Term Dynamic Positioning Load Forecasting in Maritime Microgrids
## 4 Test Results and Discussions
### Scenario 3: Hourly Load Forecasting  
Another significant characteristic of the DP load profile has shown in Figure 10a which provides the autocorrelation function of the hourly DP demand over four weeks. The peaks of DP profile indicate for thrusting demand at the multiples of 24-h delays at rough to high sea conditions, which shows that the load demand at the identical hours has a high relationship with each other dependent on the sea state and hours of the days as shown in Figure 8a,b. The DP load demand is categorized into hours-day and sea state patterns. The weight vector has approximated at each time intervals by applying the previous DP demand dataset for each pattern as in (15) and (16). When the weights matrix at day n, time t has been determined in (14) and (17), the thrusting force command is predicted with the DP profile data set of previous days as well as the estimated DP demand data by the network for the same day at previous time steps in (16). Hence, the adjustment of the weights vector tolerance is decreased to 0.0006 and the dataset lengths \(Tdx\) and \(Tdy\) are defined to two. Therefore, the sea state and vessel movement parameters (total 7 inputs) into the NARX model at times t, t - 1, and t - 2 of the past two days to predicted DP demand for time t + 1 of the same day. The NN with 25 hidden layers with seven neurons is used in this case.  
The results have analyzed in Table 10 with details on hourly based for one-day ahead forecasting and presented in Figure 12a,b by the performance measurement indicators in (20) and (21). The comparison of \(MAPE\) and \(\delta\) error with the other time-series-NN model schemes indicates which the minimum \(MAPE\) and \(\delta\) have found 0.36% and 0.26 MW, respectively by NARX-NN. The maximum \(\delta\) and error percentage values belong to TDL-NN, which are 0.46 MW and 0.7% respectively. The average error of 1 h to 24 h ahead forecasts with other time series forecasting methods have applied to the same previous network setting and evaluated in Table 10. The proposed method illustrates significant accuracy, minimum error percentage, and reliability in thrust force estimating models compared with other conventional time-series patterns.  
To ensure the performance of the proposed method, the speed of convergence in the NN-training run-time is also tested and compared with those obtained from NAR and TDL-NN methods. Table 5 shows comparisons of training run-time under different scenarios using different methods. Comparisons of Figures 10-12 and Tables 3-5 have shown that in contrast to other NN time series configurations, the NARX based on NN can have a fairly good performance with relatively less computation burden than other methods under different scenarios. For instance, in Scenario 3 the running time of NARX is about 5.2 s which are less than those for the NAR and TDL-NN with their running times are about 6.65 s and 208.5 s respectively. Similar results can be seen for other methods in Scenario 1 and Scenario 2.  
Figure 12: (**a**) The proposed method comparison in SOTLF for with 24 h lead times, and (**b**) error Percentage in MW.