## 4 Flight Load Prediction Case Study
### Comparison with Other Neural Networks  
In order to compare the prediction accuracy with other neural networks, a comparison study is conducted in this section. Apart from the tradition ELM, five well-known neural networks are studied, which are the backpropagation (BP) neural network, radial basis function (RBF) neural network, support vector machines (SVMs), long short-term memory (LSTM) neural network, and gate recurrent unit (GRU) neural network. In all neural networks, a single hidden layer is used as illustrated in Figure 3, and the neuron number in the hidden layer is set as 100. Moreover, all neural networks are trained by the same training dataset using a 5-cross-validation method, and the prediction accuracy for the testing dataset is tabulated in Table 5. In addition, to avoid unfair comparisons, BP, RBF, SVM, LSTM, and GRU are coded based on the neural network toolbox of MATLAB software, where the hyperparameters of those neural networks are set in an optimal way. It is worth noting that the training time of the ELM is 0.12 s, which is the shortest among the studied methods for the proposed problem in this work. Meanwhile, for the GA-enhanced ELM,  
\begin{table}
\begin{tabular}{c c c c} \hline \hline
**Flight Parameter** & **MIV** & **Flight Parameter** & **MIV** \\ \hline Altitude & 0.0390 & Angle of right outer alieron & 0.0312 \\ March number & 0.0826 & Angle of left front flap & 0.0450 \\ Angle of attack & 0.1868 & Angle of left outer alieron & 0.0441 \\ Vertical load factor & 0.4449 & Angle of right inner alieron & 0.0648 \\ Roll rate & 0.0255 & Angle of left inner alieron & 0.0141 \\ Pitch rate & 0.0064 & Pitch angle & 0.0028 \\ Roll angle & 0.0127 & - & - \\ \hline \hline \end{tabular}
\end{table}
Table 4: Normalized mean impact values of 13 flight parameters.  
Figure 10: Wing bending moment prediction accuracy against different neuron number \(K\) of hidden layer: (**a**) mean relative errors and (**b**) mean squared errors.  
it is the longest with a time of 164.30 s due to the optimization process of the generic algorithm with 200 generations.  
From Table 5, it indicates that the LSTM and GRU networks outperform the traditional BP, RBF, and SVM. The reason is that the LSTM and GRU are both recurrent neural networks, which are good at extracting the sequence data features. However, the prediction accuracy of the LSTM and GRU is still lower when compared with that of the proposed GA-enhanced ELM method. The reason is that the Moore-Penrose inverse operation of the ELM is robust to the outlier values or measurement noise of the dataset, which improves the accuracy and noise robustness of the established nonlinear mapping relationship. Moreover, the proposed genetic algorithm further enhances the prediction accuracy of the ELM method by optimizing the weights between the input and hidden layers. However, the performance of the traditional ELM is outstanding as well, and it takes less training time compared with the GA-enhanced ELM. In addition, the GRU possesses high prediction accuracy over the LSTM neural network, which indicates that the flight-parameter-based flight load prediction problem is not a long-term time-series dependency problem.