## 4 Model Construction and Simulation Experiment Results
### Model Construction
\begin{table}
\begin{tabular}{c c c c c c c} \hline \hline \multirow{2}{*}{**Hidden Layer Number**} & \multicolumn{2}{c}{**Training Time**} & \multicolumn{2}{c}{**Training Error**} & \multicolumn{2}{c}{**Test Error**} \\ \cline{2-7}  & **ELM** & **SaDE-ELM** & **ELM** & **SaDE-ELM** & **ELM** & **SaDE-ELM** \\ \hline \(1\) & 0.121 & 3.791 & 0.875 & 0.8 & 1 & 1 \\ \(5\) & 1.342 & 6.522 & 0.275 & 0.125 & 0.275 & 0 \\ \(10\) & 2.527 & 11.357 & 0.125 & 0.1 & 0.125 & 0 \\ \(15\) & 3.712 & 11.388 & 0.075 & 0.05 & 0.075 & 0 \\ \(20\) & 3.855 & 18.767 & 0.065 & 0.05 & 0.065 & 0 \\ \(25\) & 4.521 & 19.032 & 0.025 & 0 & 0.025 & 0 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Quantity of hidden layer impacts on the algorithm. Figure 9: Pressure waveforms for the different states of the marine fuel system. In order to investigate the convergence of the objective function of the extreme learning algorithm and SaDE-ELM to the state recognition process of the marine fuel system, the proposed method is suitable for the fault diagnosis of the marine fuel system. The convergence process can be observed in Figure 10. With the increase of the number of iterations, the ELM algorithm quickly decreases the value of the objective function. However, due to the low precision of the algorithm, the final converged objective function value is close to 0.3, which is still relatively large. In this paper, SaDE-ELM is proposed. The value of the objective function at the initial point is less than 0.2. As the number of iterations increases, the ultimate objective function gradually approaches 0, achieving a better target function minimization effect. At the same time, as the number of iterations continues to increase, the objective function value tends to be stable, close to 0. Based on the experimental results above, the commonly used algorithms for fault diagnosis of marine fuel systems, BP (Back Propagation) neural network, and SVM (support vector machine) algorithm are selected to compare and analyze the experimental results, including the accuracy of fault diagnosis and the time of fault diagnosis. As shown in Table 2.  
Comparing the experimental results in Table 2, it is found that SaDE-ELM has a higher recognition rate for the faults of the marine fuel system than the commonly used algorithm BP neural network and the SVM, and SaDE-ELM is not significantly higher than that of the BP neural network algorithm and the SVM, and the correct rate is obviously higher than other commonly used algorithms. To further demonstrate the recognition status of different fault diagnosis algorithms for 8 types of samples, as shown in Figures 11-14. \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Algorithm** & **Training Time** & **Training Error** & **Test Error** \\ \hline BP neural network & 12.531 & 0.5 & 0.625 \\ SVM & 10.012 & 0.25 & 0.25 \\ SaDE-ELM & 19.032 & 0 & 0 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Performance comparison of different algorithms for fault diagnosis of the marine fuel system. Figure 10: Comparison of the convergence effect of the algorithm. Figure 11: BP neural network algorithm for marine fuel system fault diagnosis. Figure 12: Support vector machine algorithm for marine fuel system fault diagnosis. Figure 13: Extreme learning machine algorithm for marine fuel system fault diagnosis. From Figure 11 to Figure 14, it can be seen that the fault diagnosis method of marine fuel system based on SaDE-ELM proposed in this paper can correctly identify each type of fault, and other three algorithms are certain error rate for the identification of eight types of samples, especially for the fourth type of sample--idle oil identification poor effect, and there have been errors. The reason is perhaps that the characteristics of this kind of sample are close to those of the type 3 sample, so the conventional fault diagnosis algorithm cannot be discriminated. The SaDE-ELM proposed in this paper can better identify the fuzzy faults of this kind of data features.