# A Deep Learning Method for Short-Term Dynamic Positioning Load Forecasting in Maritime Microgrids
## 2 Review of Artificial Neural Networks
### Recurrent Dynamic Neural Network  
The structure of the learning algorithm and weights adjustment at the input layer of MLP feedforward networks for dynamic networks have been so far discussed. The nonlinear autoregressive network with NARX is a recurrent dynamic network, with feedback connections enclosing several layers of the network. The NARX model is defined on the linear ARX model [64], which is used commonly in time-series modeling. ANN is employed in various applications such as smart grids. For example, NN based NARX is implemented in [64] to estimate the electrical load demand, wind speed, and state of battery charging (SOC). Furthermore, a technique is proposed in [65; 66] to predict the PV power generation by applying the NN-NARX in smart grids. Choosing an accurate category of the NN is very essential and it is specified the type of system nature. Especially, the network type is influenced by the correlations between inputs and the outputs system nature. Accordingly, the feedforward neural networks system is applied when the relationship between input and output is static. On the other hand, when the relationships depend on the weather conditions and sea state parameters as external inputs. For this reason, we have proposed the recurring neural network as a proper superior due to memory functions that are embedded in their neurons. The NN-NARX is classified as a recurrent neural network (RNN). To compare with the other conventional RNN such as time series-NN, nonlinear automatic regressive (NAR) prove proposes that NN-NARX has characteristic advantages in  
Figure 4: The EBP computing method for MLP. speed convergence, accuracy, and capability of the deep learning algorithm [67]. Moreover, it should be mentioned that the other types of RNN might be also executing well, but due to environmental disturbances, such as sea conditions as external disturbances, which can affect inaccuracy of the load demand prediction in real-time or online conditions. As a result, it is also important to consider these disturbances as external inputs during neurons weight adjusting as we have noted in Section 3. Moreover, we should mention, the comparative performance of the three different kinds of RNN methods in the paper is investigated. To illustrate that this type of RNN is precise for solving the PMS challenges in DP vessels, we are used the NN-NARX model. For achieving this purpose, we have trained the NN with the offline procedure. Hence, the speed of convergence is not a significant problem in this method but, the convergence speed with minor step size plays a key role to have a successful training process in the NARX application. For many applications, recurrent or operational training processes are not executed, and they are applying offline. Nevertheless, a precise trained NN is anticipated. In the next sections, the deviation error concerning the evaluated and predicted values by the NN-NARX performs initially in the DP controller, then through the communications appears in the PMS system for dispatching economically. Therefore, due to the precision of trained NN, accurate operation of the expert NN, the sea state historical relationship between inputs and the output of the NN-NARX is executed in this work to predict DP power demand in the various weather condition. The results show that the proposed NN-NARX based on LM-BP has a precise operation to approximate the trusting force command as a sensitive load related to weather situations. Therefore, it persuades the concept of employing the NN-NARX in this paper. The initial mathematical correlation of the proposed method in the nonlinear time- amplitude scheme is defined as:  
\[y(n,t)=f(x(n,t-1),\ldots,x(n,t-Td_{x}),y(n,t-1),\ldots,y(n,t-Td_{n})) \tag{15}\]  
where \(y(n,t)\), \(x(n,t)\) and \(F(x)\) represent \(k\)th output sample, \(k\)th input term, and nonlinear activation function, respectively.