# Fuzzy Echo State Network-Based Fault Diagnosis of Remote-Controlled Robotic Arms
## 4 Experiment
### Experimental Results
However, for fault types 2 (communication fault) and 7 (leader sensor 2 fault), there are slight misclassifications, with accuracies of 0.97 and 0.99, respectively. These minor discrepancies suggest that there may be some overlap in the features representing these  
Figure 5: Variation of Mean Squared Error (MSE) during CMA-ES hyperparameter optimization for DFESN, illustrating progressive improvement in model accuracy. \begin{table}
\begin{tabular}{c c c c c c c c c} \hline \hline
**Label** & **1** & **2** & **3** & **4** & **5** & **6** & **7** & **8** & **9** \\ \hline Accuracy & 99.67\% & 99.67\% & 100\% & 100\% & 99.67\% & 100\% & 99.65\% & 100\% & 100\% \\ \hline \hline \end{tabular}
\end{table} 
Table 3: The results of different fault types (accuracy is defined as the percentage of correctly classified samples relative to all test samples.). faults, possibly due to similarities in the observed data patterns under these conditions. The communication fault (type 2) seems particularly challenging for the model, possibly because interruptions in communication can manifest in a manner similar to other faults, making it harder for the model to distinguish. To comprehensively evaluate the robustness of the DFESN model against various real-world conditions, we further analyzed its performance under different types of noise: Gaussian, Uniform, and Impulse noise. Figure 7 shows the classification accuracy across different signal-to-noise ratios (SNRs). At lower SNR levels (e.g., 5 dB), classification accuracy is significantly impacted by noise, dropping to around 60% for all noise types, highlighting the sensitivity of the model in highly noisy environments. However, as SNR increases to 10 dB and above, classification accuracy improves substantially, surpassing 80%. At an SNR of 20 dB and higher, the accuracy approaches nearly 100%, indicating excellent robustness of the DFESN model under typical operational noise conditions. Moreover, the results show no significant difference among Gaussian, Uniform, and Impulse noise types at higher SNR levels, demonstrating that the DFESN method maintains strong performance irrespective of the noise distribution encountered. This analysis confirms the suitability of the proposed DFESN model for practical scenarios where varying noise conditions are common. Table 4 shows the parameter configurations for each approach, which were established through parameter tuning experiments. This ensures that all parameters were optimally adjusted to enable a fair comparison across methods. To further validate the effectiveness of DFESN, we performed comparative studies with commonly used methods including ESN, CNN, LSTM, and BP neural networks. DFESN outperformed these methods in terms of both accuracy and real-time efficiency, as shown in the Table 5. The training time of the ESN method was 1.45 s, which is the shortest of all of the methods. However, this method achieved the lowest accuracy. The LSTM, CNN, BP, and DFESN methods all achieve a mean accuracy exceeding 0.9, yet their training times vary significantly. The LSTM method has the longest training time at 320.59 s. Both the BP and DFESN methods achieve similarly high mean classification accuracies, with the DFESN method slightly outperforming at 0.9947 compared to BP's 0.9925. Notably, the DFESN method has the shortest training time (4.75 s) and online diagnosis time (0.0105 s) among all the compared methods. This indicates that the proposed DFESN method is highly suitable for real-time fault diagnosis applications,  
Figure 6: Confusion matrices for nine types of faults. to missed detections or false positives. Although the presented method is validated for the fault types listed, it can potentially be extended to other fault categories. For instance, the same architecture could be applied to detect faults in additional sensors or actuators not explicitly considered in this study.