# A Novel Fault Diagnosis Method for TE Process Based on Optimal Extreme Learning Machine
## 2 Materials and Methods  
### The Proposed BCOA-KELM Model  
Figure 1 shows the variation of the average diagnostic accuracy with the number of training epochs for BCOA and COA, for both the training and test datasets. It can be seen that either curve is steadily converging. It can be seen that the average diagnostic accuracy of BCOA and COA for the training dataset is higher than that of the test dataset, which can indicate a reasonable selection of data. At the same time, the graph clearly shows that BCOA reaches its accuracy maximum at 10 epochs, while COA reaches its accuracy maximum after 20 epochs, which can indicate that BCOA has made a major breakthrough in terms of convergence speed.  
Figure 1: Change of testing ACR with the number of training epochs.  
To increase the model's efficiency and accuracy, individual significance values are obtained using the random forest treebagger [44; 45]. Following that, features are chosen based on the results, with redundant attributes removed to limit the number of network element nodes. Due to the network structure of KELM, the setting of the regularization coefficients \(c\) and kernel function parameters \(S\) will have an impact on the classification performance of KELM. At this point, the BCOA algorithm is an improvement in the emerging intelligent bionic optimization algorithm. Compared with other metaheuristics, BCOA has a unique algorithmic structure, which provides a new mechanism for balancing exploration and exploitation in the optimization process, and BCOA can maintain a high population diversity while improving convergence efficiency. Therefore, the BCOA algorithm can be used to find the most suitable \(c\) and \(S\) to improve the performance of the network.  
The process of the model is presented in Figure 2, and is described as follows:  
Step 1: Input of simulation data from the TE process into RFtb for training and prediction.  
Step 2: RFtb's feature importance values are ranked.  
Step 3: Based on the ranking results, select features and retrieve the dataset for the input network.  
Step 4: Initialize the Kernel Based Extreme Learning Machine and take the random regularization factor \(c\) and kernel function parameter \(S\).  
Step 5: Initialize the numbers of the coyotes: NumCoy, the numbers of packs: NumPac, the maximum number of the coyotes: MaxNumCoy, the fitness function: FitFunc.  
Step 6: Equations (5) and (6) calculate alpha and cultural trend cult for alpha coyotes, and Equation (6) calculates effect size for alpha wolves and groups.  
Step 7: Based on the fitness function, update the current coyote (Equation (10)), compare the adaptive capacity of the coyote before and after the update, and retain the better coyote (Equation (11)).  
Step 8: If the Iteration loop conditions is satisfied, proceed to the next step; otherwise, return to Step 7.  
Step 9: Find the current \(1/N_{c}\) number of worse coyotes and perform a chaotic operation to generate additional coyotes if the threshold is met; otherwise, proceed to the next step.  
Step 10: Proceed to the next step if the maximum iteration condition or preset condition is met; otherwise, return to Step 6.  
Step 11: The optimal KELM diagnostic model is obtained by substituting the optimized regularization coefficients \(c\) kernel function parameters \(S\) into the KELM for training.  
Step 12: The test samples are fed into the trained network to obtain the predicted output.