3.1. Construction of An Improved RCNN algorithm Based on Fuzzy Theory

RCNN is a classic object detection algorithm that detects target objects in images through two stages: candidate region extraction and convolutional neural network feature extraction ^[15]. RCNN has a broad range of applications in fault identification. But RCNN also has some shortcomings ^[16]. Firstly, RCNN requires separate convolutional feature extraction and classification on each candidate region, resulting in a huge computational load and slow speed. Secondly, the selection of candidate regions in RCNN is independent of the model, which increases computational and time costs ^[17]. Therefore, to address the shortcomings of RCNN, Faster RCNN was proposed in 2015. The basic architecture and principle of this network are shown in Fig. 1.

As shown in Fig. 1, Faster RCNN introduces a region scheme network based on RCNN, and generates candidate regions by sharing convolutional feature extraction steps, thereby achieving the functions of target classification and bounding box regression. Therefore, Faster RCNN not only reduces computational and time costs, but also optimizes the entire object detection system end-to-end during the training. However, traditional Faster RCNN also has certain shortcomings. In traditional Faster RCNN, the generation of candidate boxes is usually achieved through selective search and other methods. However, the candidate boxes generated by this method may have some inaccuracies or redundancy, leading to a decrease in diagnostic performance in fuzzy faults of transmission lines. Therefore, the study sorts and filters candidate boxes by calculating the similarity score between each candidate box and the target. Fuzzy modular logic algorithm is a method that combines fuzzy logic and pattern recognition, which can improve the quality of Faster RCNN candidate boxes, reduce redundant and inaccurate candidate boxes, and thus improve the performance of object detection. Meanwhile, fuzzy logic can adjust the generation strategy of candidate boxes based on specific application scenarios and target characteristics by designing membership functions reasonably. The calculation of fuzzy logic is denoted in Fig. 2.

As shown in Fig. 2, the calculation of fuzzy logic includes five steps: fuzzification, rule expression, inference, aggregation, and deblurring. Firstly, in the fuzzification calculation step, it is studied to use fuzzy membership functions to fuzzify the input Faster RCNN variables. Then, the fuzzy set is defined using ordinal pair representation and mapped to a fuzzy set. The expression for defining fuzzy sets is shown in Eq. (1).

In Eq. (1), u represents any subset in a given domain space. U represents the domain of discourse. Subsequently, it proceeds to the fuzzification calculation step. Research uses fuzzy membership functions to fuzzify input variables and map them to a fuzzy set. The calculation for the membership function is shown in Eq. (2).

In Eq. (2), x, x, and x respectively represent any element in the domain X, Y, and Z. R and S represent the fuzzy relationship between X and Y, and Y and Z, respectively. × represents the binomial product operator. The selected synthesis operation method for the study is the maximum minimum synthesis, and its calculation is shown in Eq. (3).

Subsequently, in the rule expression stage, the IF-THEN rule is studied to express the relationship between the input and output of the fuzzy set. Each rule includes a condition section and a conclusion section. The process of reasoning is to calculate the corresponding fuzzy output based on the input fuzzy set and rule expression. Finally, the study aggregates all fuzzy outputs to obtain the final output, which then enters the deblurring stage to achieve the transformation of fuzzy sets into clear data. Common deblurring algorithms include centroid method, equal area method, and extremum method. The center of gravity method was used in the study, and its calculation is shown in Eq. (4).

In Eq. (4), d represents the center of gravity. Through the above fuzzy and deblurring operations, the fuzzy logic algorithm can process uncertain information through fuzzy reasoning and fuzzy rules, thereby reducing the computational cost of generating candidate regions and target classification for Faster RCNN, and improving detection speed. In addition, the fuzzy logic algorithm can also improve the generation of Faster RCNN candidate regions. Through methods such as fuzzy rules and fuzzy clustering, candidate boxes can be generated more accurately, improving the accuracy of object detection. The ultimate goal is to improve the accuracy and precision of Faster RCNN in diagnosing faults in transmission lines. The TLFD algorithm that integrates fuzzy logic theory and RCNN is shown in Fig. 3.

In Fig. 3, the TLFD algorithm constructed by integrating fuzzy logic theory and RCNN includes feature extraction network, region suggestion network, bounding box regression network, and classification regression network. In the TLFD algorithm, the study utilizes multi task loss functions to calculate the loss function. The calculation for the loss function is shown in Eq. (5).

In Eq. (5), {p_i} represents the set of output values of the classification layer. {t_i} refers to the set of output values of the bounding box regression layer. N_cls represents the number of predicted samples. p_i represents the predicted result. p_i* represents the sample label. In the regional recommendation network, the calculation for the classification loss function is shown in Eq. (6).

In Eq. (6), β represents the weight matrix. In bounding box regression networks, research first utilizes mapping relationships to perform regression operations on the bounding boxes. The calculation for its mapping relationship is shown in Eq. (7).

In Eq. (7), (P_x, P_y, P_w, P_h) means the candidate box. ( G x ^ , G y ^ , G w ^ , G h ^ ) denotes the prediction box. (G_x, G_y, G_w, G_h) expresses the calibration box. The translation and scaling calculation for the mapping relationship is shown in Eq. (8).

The calculation for the loss function of bounding box regression is shown in Eq. (9).

In Eq. (9), λ means the balance weight of classification loss and bounding box regression loss. N_reg represents the size of the feature map, while t_i and t_i* represent the borders before and after translation.

3.2. Construction of a Transmission Lines Fault Diagnosis Model Based on Improved RCNN Algorithm

After completing the construction of the TLFD algorithm, research is conducted on constructing a TLFD model based on this algorithm. Prior to this, research first collected fault signals from transmission lines. Traditional transmission line detection methods often require manual inspection or the use of wired sensors, which is not only time-consuming and labor-intensive, but also costly ^[18]. Therefore, the study proposed the use of wireless sensors or monitoring devices to collect parameters such as current, voltage, and temperature on transmission lines, and record signals when faults occur. In addition, the study also constructed a common transmission line fault signal database through literature and transmission line fault signal data from power plants, to cover different types and degrees of fault situations. The basic architecture of the transmission line signal acquisition and preprocessing model proposed in the study is shown in Fig. 4.

In Fig. 4, the transmission line signal acquisition and preprocessing model constructed in the study includes two functions: data acquisition and preprocessing. In data collection, research is conducted on the use of wireless sensors to collect signals from transmission lines, including current, voltage, temperature, etc. Subsequently, the sensor sends the collected transmission line data to the intelligent acquisition unit. The intelligent acquisition unit selected for the study is a high-precision 14 bit module conversion unit, which can ensure the accuracy and clarity of the collected signal. Subsequently, the study conducts preprocessing operations on the collected transmission line signals to reduce noise interference and data bias, and improve the accuracy of fault diagnosis. The preprocessing operations used in the study include denoising, filtering, and normalization. The denoising can reduce the impact of high-frequency or low-frequency noise, and normalization can unify the data range of different parameters into a suitable range for subsequent feature extraction and model training. After preprocessing operations such as filtering, these collected data are transmitted to the monitoring platform through wireless communication technology to construct a transmission line fault database. Subsequently, the study utilizes a TLFD model to extract features and detect faults in the signals of transmission lines, ultimately achieving monitoring of the operational status and fault warning of transmission lines. To construct a database of transmission line faults, this study summarizes the common types and causes of transmission line faults using existing literature and maintenance records of power plant transmission lines. The common types and causes of faults in transmission lines are shown in Table 1.

In Table 1, common faults in transmission lines include wire breakage, short circuit, and looseness. Research extracts features of transmission line signals with different fault causes, and trains TLFD algorithms based on fuzzy theory and RCNN to build a TLFD model based on this. The basic architecture of the TLFD model based on fuzzy theory and RCNN is shown in Fig. 5.

As shown in Fig. 5, the TFDM model based on fuzzy theory and RCNN constructed in the study includes four modules: fault data acquisition, data processing, algorithm training, fault diagnosis, and model validation. Firstly, the signal acquisition module is used to study the repair records and laboratory data of power plant transmission lines, construct a transmission line fault dataset, and obtain a transmission line image dataset containing normal and fault states. Subsequently, it enters the data processing stage, where the data is preprocessed, including denoising, data standardization, etc. Finally, the collected dataset is applied to train the constructed TLFD algorithm, and the performance is evaluated and optimized using a validation set. The performance evaluation indicators used in the study are accuracy, recall, F1 value, etc. The accuracy indicates the ratio of correct predictions made by the model during fault diagnosis. The accuracy calculation is shown in Eq. (10).

In Eq. (10), TP means the true rate. FP means false positive rate. The recall rate denotes the ratio of fault samples detected by the model, and the expression for calculating the recall rate is shown in Eq. (11).

In Eq. (11), FP denotes the false reflectance. In addition, to comprehensively reflect the performance of the fault identification model, a comprehensive analysis of accuracy and recall is conducted, using the Precision-Recall (PR) curve for performance analysis. The offline area of this curve is the average accuracy. The calculation is indicated in Eq. (12).

In Eq. (12), p(r) represents the PR curve with the meaning of the offline area. After completing the training of the algorithm, the collected transmission line signals will be studied for fault diagnosis. In the fault diagnosis module, research is conducted on using feature extraction networks to model the sequence and understand the context of the features extracted from transmission line data, to better diagnose transmission line faults. Subsequently, the study utilizes fully connected networks to classify and diagnose the extracted features, distinguishing and identifying different fault situations. Based on the output outcomes of the model, it can be determined that the fault point is at the specific location of the transmission line, so that maintenance personnel can repair and maintain it in a timely manner. In addition, the study also validates the effectiveness and feasibility of the constructed fault diagnosis model.

4.1. Validation of the Effectiveness of the Improved RCNN Algorithm Based on Fuzzy Logic Algorithm

To assess the effectiveness of the proposed TLFD algorithm based on improved RCNN, a performance comparison experiment was curried out using the IEEE 39-Bus system fault dataset. The comparative algorithms were fault diagnosis algorithms based on Faster RCNN, Particle Swarm Optimization Faster RCNN (PSO-Faster RCNN), and Genetic Algorithm Faster RCNN (GA-Faster RCNN). The performance comparison indicators included accuracy, precision, PR curve, F1 value, error, and running time. The experimental environment was CPU (Intel Core i7-9700 CPU @ 3.00GHz ×8). The server operated on Windows 10. The accuracy and precision comparison results of each comparison algorithm are indicated in Fig. 6.

Fig. 6(a) expresses the accuracy comparison results of various fault diagnosis algorithms. In Fig. 6(a), the accuracy of the fault diagnosis algorithm based on optimized RCNN proposed in the study was 98.7%, which is much higher than other comparative algorithms. Meanwhile, the accuracy curve of this algorithm was smoother than other algorithms, and its diagnostic stability was higher. Fig. 6(b) denotes the precision comparison results. In Fig. 6(b), the diagnostic precision of each algorithm increased with the iteration times. The precision of the improved RCNN fault diagnosis algorithm proposed in the study was 87.2%, far higher than other comparative models. With these results, the fault diagnosis model based on improved RCNN had better precision and stability performance than other comparative models, and its precision and stability performance were better than other comparative algorithms. The PR curves and F1 value comparison results of each comparison algorithm are shown in Fig. 7.

Fig. 7(a) illustrates the PR curves of each comparison algorithm. From Fig. 7(a), the offline area of the PR curve of the proposed algorithm based on optimized RCNN was higher than that of other comparison algorithms, with a value of 0.83, indicating that the average precision of the algorithm was better. Fig. 7(b) indicates the F1 value comparison results of various comparison algorithms. In Fig. 7(b), the F1 value of the proposed algorithm based on optimized RCNN was higher than other comparative algorithms, which was 0.81, indicating that the algorithm had better performance. Based on the above results, the proposed fault diagnosis algorithm based on optimized RCNN had better accuracy and reliability in fault diagnosis. The error and running time comparison results of various fault diagnosis algorithms are expressed in Fig. 8.

Fig. 8(a) denotes the error comparison findings of various comparison algorithms. In Fig. 8(a), the error value of the proposed improved RCNN TLFD algorithm was 1.7, which was 6.6 lower than the error value of the PSO-Faster RCNN TLFD algorithm and much lower than other comparative algorithms. As shown in Fig. 8(b), the proposed improved RCNN fault diagnosis algorithm had a running time of 1.0 seconds, which was 0.04 seconds shorter than the PSO-Faster RCNN fault diagnosis algorithm. On the ground of above results, the improved RCNN-based TLFD algorithm had better diagnostic performance and operating speed performance than other comparative algorithms, and had practical application value.

4.2. Effectiveness Analysis of Transmission Line Fault Diagnosis Model Based on Improved RCNN Algorithm

To prove the effectiveness of the proposed TLFD model based on the improved RCNN algorithm, an empirical analysis was curried out. The dataset utilized in this empirical analysis experiment was the IEEE 39-Bus system fault dataset. The comparative models were fault diagnosis models based on Faster RCNN, PSO-Faster RCNN, and GA-Faster RCNN. The performance comparison indicators included accuracy, loss function value, precision, Mean Absolute Error (MAE), Root Mean Square Error (RMSE), and confusion matrix. The experimental environment was CPU (Intel®Core™i7-9700 CPU @ 3.00GHz ×8). The server operated on Windows 10. The accuracy and loss function comparison outcomes of each comparison model are expressed in Fig. 9.

In Fig. 9 (a), the diagnostic accuracy of each model increased with the iteration times until it stabilized. The accuracy of the TLFD model was 0.94, which was bigger than other comparative models. In Fig. 9 (b), the loss function value of the proposed TLFD model was 0.06, which was smaller than other comparative models. With these results, the TLFD model performed better than other comparative models. The accuracy, MAE, and RMSE comparison outcomes of each comparison model are denoted in Fig. 10.

Fig. 10(a) illustrates the accuracy curves of each comparison model. In Fig. 10(a), the accuracy curve of the fault diagnosis model proposed in the study was 96.2% higher than other comparative models. Fig. 10(b) illustrates the comparison results of MAE and RMSE for each comparison model. From Fig. 10(b), the MAE and RMSE values of the raised fault diagnosis model were significantly lower than those of other comparison models, with MAE values of 1.64 ∗ 10⁻² and RMSE values of 1.78 ∗ 10⁻². With the above results, the evaluation accuracy performance of the proposed fault diagnosis model was superior to other comparative models, and it had practical application value. The research divided the causes of fault diagnosis in transmission lines into six stages: wire breakage, loosening, single-phase grounding fault, two-phase short circuit fault, two-phase short circuit grounding fault, and three-phase short circuit fault. Fig. 11 shows the cause prediction confusion matrix of the fault diagnosis model.

In Fig. 11, the columns in the matrix represent the diagnostic results, the rows represent the true results, and the diagonal numbers represent the accuracy of fault diagnosis. In Fig. 11, the study found that the model's average prediction accuracy was 90%. The TLFD model proposed in this study has excellent effectiveness and can be used in practical applications of TLFD.