## 2 Materials and Methods
### Data Preprocessing and Analysing
#### 2.2.2 Back-Propagation Neural Network Modelling  
A back-propagation (BP) neural network is a multilayer feedforward network characterized by signal forward propagation and error backward propagation. If the expectations are not met, back-propagation is performed, and the weights and thresholds of the network are adjusted according to the prediction error. The network training stops when the output error value reaches the minimum or preset range. Finally, the error and classification results are outputted [25]. Generally, when each node adopts a sigmoid function, the hidden layer is sufficient to realize any decision classification problem, and compared to the number of hidden layers, the number of neural network iterations (i.e., the number of back-propagations to the weights) is more important to the correct rate [26].  
By combining the position, speed, and heading data from the VMS with the fishing time, longitude, and latitude data from the fishing logs of the three sample vessels, the VMS data with casting, hauling, or sailing states were extracted. Each state's 300 VMS data points were randomly selected as the training and test set samples. Two groups of network topology structures were established based on the speed/positioning time (neural network 1) and heading/positioning time (neural network 2), including the number of nodes in the input, hidden, and output layers. There were two nodes in the input layer: speed and positioning time or heading and positioning time. There were three nodes in the output layer: casting, hauling, and sailing. According to Equation (1), proposed by [PERSON] [27], the number of hidden layer nodes was set at 3 to 12. When there were 10 nodes, the identification accuracy was the highest, and the training speed was fast.  
\[J=\sqrt{n+m}+a \tag{1}\]  
where \(J\) is the number of hidden layer nodes, \(n\) is the number of input neurons, \(m\) is the number of output neurons, and \(a\) is a constant between 1 and 10. In this study, the neural network was based on the delta method to adjust the weights to increase the momentum term and the self-adaptive learning rate to address the problems of the BP neural network, such as ease of falling into the local optimal solution, low learning efficiency, and slow convergence speed.  
In MATLAB R2016a, 300 VMS data points of each state were normalized, and all numerical values were controlled between \(-1\) and 1. The corresponding Boolean variables were also established. The classification target values corresponded to 1, while the rest were zero. Therefore, the casting, hauling, and sailing states were [1,0,0], [0,1,0], and [0,0,1], respectively. The transmission functions of the nodes were logsig and purelin. The training function adopted trainingdx, which is the gradient descent self-adaptive learning rate training function. Training and test samples were randomly allocated (80% and 20%, respectively). The maximum number of network training iterations was set to 1000, and the learning rate was 0.02. In addition, the maximum error was 0.001, and the maximum failure verification was six times. Finally, a trained neural network with better performance at identifying the position states was used to identify the position states of all vessels.