Switch Open-Circuit Fault Diagnosis of the Vienna Rectifier Using the Transformer–BiTCN Network with Improved Snow Geese Algorithm Optimization

 Point-by-point response to Comments and Suggestions for Authors

Comments 1: Consider clarifying the details of the training process.

Response 1: Thank you for pointing this out. In the revision, this part has been added and analyzed, Line 373-384, as follows:

Step 6: The training set is used to train the other hyper-parameters of the Transform-er-BiTCN model with preset parameters via ISGA algorithm. After each training epoch, the validation set is employed to conduct model optimization validation. This ensures the model continuously improves during the training process. Once the training reaches the preset number of iterations, the trained model is saved for subsequent testing.

Step 7: The test set is input into the model saved in step 6 to evaluate the model's performance. If the evaluation results indicate that the model's diagnostic capabilities can not yet reached the optimal level, the process returns to step 6 for further model training and validation. This iterative process continues until the model's performance meets predefined criteria. At this point, the optimally performing model is obtained. Subsequently, this offline trained model can be deployed in the actual working production of the SOCF online diagnostics.

Comments 2: Include the number of epochs, the type of activation function, the optimizer used, and the learning rate change schedule.

Response 2: This part has been demonstrated in the new manuscript, Line 434-449, as follows:

During the training process of this model, we set a total of 500 training epochs. The selection of this number of epochs was determined through multiple experiments and optimizations. According to our tests, it is found that when the number of epochs is too small, the model fails to adequately learn the features and patterns in the data, resulting in suboptimal performance. Conversely, when the number of epochs is excessive, the model may exhibit overfitting, where it performs well on the training set but shows degraded performance on the validation and test sets. After comprehensive evaluation, setting the number of epochs to 500 strikes an appropriate balance. It ensures the model can learn the data sufficiently while effectively preventing overfitting, enabling the model to achieve stable and excellent performance across various datasets.

For the chosen of activation function, the ReLU is computationally efficient and helps mitigate the vanishing gradient problem, serving as the default choice in this paper. The learning rate with exponential decay factor is employed whose decay factor is optimized via ISGA algorithm. During model training stage, the Adam optimizer is employed since it features fast convergence speeds, and strong generalization capabilities, enabling the training of high-performance models in a relatively short time.

Comment 3: Refine the regularization parameters (e.g., L2, dropout) to prevent overfitting.

Response 3: In the new manuscript, the dropout technique has been employed to prevent overfitting, whose value is chosen as 0.10, as shown in Table 6.

Comment 4: Consider adding statistical significance tests (e.g., Student's t-test, ANOVA) to confirm the superiority of the proposed method over other models.

Response 4: We sincerely appreciate the reviewer’s valuable suggestion. The nature of our data is not suitable for t-tests and ANOVA. These tests are mainly designed for continuous data. In our study, the data we collected are non-continuous categorical data. Although t-tests and ANOVA are useful methods for statistical significance testing, our study has already employed cross-validation methods to demonstrate the effectiveness and superiority of our method, which can also reflect the actual situation of our research and provide reliable evidence for the performance of our method.

Comment 5: Consider providing confidence intervals for mean accuracy values.

Response 5: Thank you for your kind suggestion. In this paper, total 20 SOCFs, including single switch fault and double switches fault have been considered, and the per-class accuracy for each SOCF fault is tested to analyze the individual performance of each class. In such classification tasks, accuracy may cluster around a few specific values with distribution of accuracy data is highly skewed, making it difficult to providing confidence intervals for mean accuracy values.

Comment 6: Consider including additional sequential architectures (e.g., GRU, Transformer-LSTM) as benchmarks.

Response 6: The Transformer-GRU and Transformer-LSTM are added as benchmark models, whose test results are shown in Table 9 and Figure 8.

Comment 7: Consider comparing with methods not using hyperparameter optimization to demonstrate the impact of ISGA alone.

Response 7: The comparison has been conducted to demonstrate the impact of ISGA in the revision, Line 517-520, as follows:

       Compare performance of Model 4 and Model 5, the ISGA optimization algorithm can achieve higher SOCF diagnosis accuracy, indicating that automated optimization can avoid human experience and significantly improve diagnostic performance over default or manually tuned models.

Comment 8: Consider providing training and inference times for the proposed method and benchmark models.

Response 8: The training and inference times are closely is related to multiple factors, mainly including sequence length of input data, model parameters, network depth, and hardware computation performance. In this paper, model parameters and network depth are optimized using ISGA algorithm. The hardware computation server is equipped with 2×NVIDIA RTX 4090 GPU and 4×2TB memory.

The training and inference times for the proposed method and benchmark models have been added in Table 7.

Comment 9: Consider specifying hardware requirements (CPU/GPU) and memory usage.

Response 9: The hardware requirements and memory usage are added in the revised manuscript, Line 555-559, as follows:

For on-line testing of SOCF diagnosis, the real-time performance is related to multiple     factors, mainly including sequence length of input data, model parameters, network depth, and hardware computation performance. In this paper, model parameters and network depth are optimized using ISGA algorithm. The hardware computation server is equipped with 2×NVIDIA RTX 4090 GPU and 4×2TB memory.

Comment 10: Consider enlarging fonts and improving contrast in some graphs.

Response 10: The fonts of all figures are checked and enlarged for clearly understanding, and font styles across all figures have been standardized. We also adjusted color schemes in figures with low contrast by using darker colors, and enhanced background/foreground differentiation in multi-color plots.

Comment 11: Consider standardizing the style of tables and figures.

Response 11: The style of tables and figures have been checked and standardized according to the journal template requirements.

Comment 12: Consider identifying limitations of the method (e.g., scalability to other converter topologies, susceptibility to unusual faults).

Response 12: We sincerely appreciate the reviewer’s insightful suggestion to explicitly discuss the limitations of our proposed method. The presented method in this paper is a data-driven method, and it is feasible for other converter topologies or unusual faults once training datasets are available and sufficient. The limitation of the method is that as the number of fault categories increases, the real-time performance of the model declines. For future work, transfer learning can be combined with our proposed method to response to increased fault categories.

Comment 13: Consider suggesting research directions: adapting the model to real-time operation in embedded systems, testing in industrial environments.

Response 13: Thank you for this insightful suggestion. We fully agree that extending our work to real-time embedded systems and industrial environments presents valuable future research opportunities. This part has been added in the new manuscript in Conclusions part in the revision, Line 616-618, as follows:

In the future, we will try to adapt the proposed model for real-time operation on resource-constrained embedded platforms and further validate model robustness in industrial settings by testing under noisy sensor data, variable latency conditions, and so on.

Comment 14: Consider adding scenarios with rare, random faults or combinations of several fault types.

Response 14: Constrained by KCL and KVL principles, for the Vienna rectifier, some switch faults can operate continuously with distorted voltages and currents without irreversible damage within a certain period of time. During this time interval, our proposed method can be adopted to locate faulted switches. Moreover, for Vienna rectifier, it is well known that the probability of a single-switch fault is significantly higher than that of a multi-switches fault, including double switches fault, three switches fault, and so on. Here, total 20 SOCFs, including single switch fault and double switches fault have been considered in this paper. However, some switch faults may cause irreversible damage and tremendous economic losses immediately. These faults can be recognized by triggering hardware protect circuit and interrupt power supply, which are not considered in this paper.

In general, most faults, including single switch fault and double switches fault, have been considered in this paper. In the future, we will invest efforts to seek rare, random faults or combinations of several fault types according to KCL and KVL principles. In theory, it is feasible to employ our proposed method to establish the non-linear relationship between input data and the SOCF diagnosis results once the training dataset related to rare, random faults or combinations of several fault types are provided.

Comment 15: Consider testing the model's performance over longer operating cycles, taking into account component aging.

Response 15: We fully agree that evaluating the model’s long-term reliability under extended operating conditions, including the impact of component aging, is critical for practical deployment. We have extended the evaluation period from original 24 hours to 96 hours of continuous operation. No significant performance degradation was observed over 96 hours, suggesting stable performance and strong robustness to short-term aging. In this paper, testing is conducted under controlled lab condition, it is a little difficult to test component aging. However, in the future, we will test the model's performance over longer operating cycles, taking into account component aging, and this part has been added in Conclusions part in the revision, Line 616-620, as follows:

In the future, we will try to adapt the proposed model for real-time operation on resource-constrained embedded platforms and further validate model robustness in industrial settings by testing under noisy sensor data, variable latency conditions, and so on. During this process, we will also test the model's performance over longer operating cycles, taking into account component aging.

 Response to Comments on the Quality of English Language

Point 1: Recommended language improvements:

Simplification and shortening of sentences – e.g.,

Original: "The original measured currents and DC voltage, without any prior knowledge or manual threshold selection, can be directly used for feature extraction with high diagnostic accuracy and strong robustness."

Revised: "The measured currents and DC voltage can be directly used for feature extraction, without prior knowledge or manual threshold selection, achieving high diagnostic accuracy and robustness."

Response 1: We sincerely appreciate the reviewer’s constructive suggestion to improve the clarity and readability of our manuscript by simplifying and shortening sentences. We have broken down overly complex or compound sentences into shorter, logically connected statements. Redundant phrases have been removed or replaced with more direct alternatives.

Point 2: Grammatical improvements – corrections to singular/plural forms, verb forms, and prepositions.

Avoiding redundancy – e.g., multiple repetitions of "Vienna rectifier" in a single paragraph, which can be replaced with a pronoun or abbreviation after being defined.

Response 2: Thanks for the reviewer’s meticulous feedback regarding grammatical refinements and the elimination of redundancy. We have conducted a comprehensive grammar check across the whole manuscript to address issues related to singular/plural forms, verb conjugation, and preposition usage. Unnecessary repetition also has been checked and eliminated in the revision.

Point 3: Consistency in terminology – standardization of technical abbreviations and their formatting.

Response 3: We thank the reviewer for highlighting this critical aspect, which significantly enhances the manuscript’s professionalism and readability. Revisions have been made to ensure that all technical terms and abbreviations are presented in a clear, consistent, and standardized manner.

Point 4: Improving logical consistency – in some places, the order of information presentation can be changed to smooth the transition from theoretical background to methods.

Response 4: We sincerely appreciate the reviewer’s valuable observation regarding the logical flow of our manuscript. The suggestion to optimize the order of information presentation—particularly to smooth the transition from theoretical background to methods—is entirely justified and aligns with our goal of enhancing readability and coherence.

Point-by-point response to Comments and Suggestions for Authors

Comments 1: The motivation to use Vienna Rectifier is unclear. A simple 2L-VSR has six IGBTs too and it is very well known in the literature. In fact, many papers appears in the literature to detect open circuits faults. Please, improve the motivation to use Vienna Rectifier instead of 2L-VSR or 3L-NPC rectifiers.

Response 1: Thank you for pointing this out. Compared with two-level voltage source rectifiers (2L-VSR) and three-level neutral point clamped rectifiers (3L-NPC), Vienna rectifiers have the advantages of high power factor, efficiency, reliability, and lower voltage stress of switching devices, making Vienna rectifiers especially suitable for scenarios with high requirements for power density and power quality, such as grid integration of new energy sources, industrial high-performance power center, electric vehicle charging system, and so on. The motivation to use Vienna Rectifier instead of 2L-VSR or 3L-NPC rectifiers has been described in the revision, Line 40-45, as follows:

Compared with two-level voltage source rectifiers (2L-VSR) and three-level neutral point clamped rectifiers (3L-NPC), Vienna rectifiers have the advantages of high power factor, efficiency, reliability, and lower voltage stress of switching devices, making Vienna rectifiers especially suitable for scenarios with high requirements for power density and power quality, such as grid integration of new energy sources, industrial high-performance power center, electric vehicle charging system, and so on [3]-[4].

Comments 2: A strong comparison between the proposed method and other simple methods, based on linear or gradients approaches, are totally missing. Note that, the idea is totally solved in the industry.

Response 2: The comparison between the proposed method and other simple methods has been added in the revised manuscript in Subsection 5.5, Line 541-552, as follows:

To further verify the diagnostic accuracy of the proposed hybrid model via improved Transformer and Bi-TCN with ISGA under non-stationary open-circuit faults in Vienna rectifiers, a comparative analysis has been conducted between the present-ed model and other linear or gradients approaches, including Bayesian Network, Linear Support Vector Machine, Shallow Gradient Boosting Decision Tree and Random Forests. During our testing, the average values of 50 results have been analyzed for comparative analysis, and the corresponding results are shown in Table 9. Here, it can be seen that the proposed method achieves the highest fault diagnosis accuracy with a fault diagnosis accuracy rate of 99.69%, a precision rate of 99.76%, and a recall rate of 99.71%. This indicates that the proposed method better fits the probability distribution of fault features, and therefore exhibits superior fault diagnosis accuracy when dealing with fault signals characterized by periodic non-stationarity.

We respectfully clarify that while certain industrial applications may have adopted basic or generalized fault diagnosis solutions (e.g., rule-based systems, conventional machine learning models), the specific challenges addressed in our work is to solve time-varying and non-stationary characteristics of SOCF signal with no universally optimal industrial solution.

Comment 3: The justification to use ISGA optimized Transformer-BiTCN algorithm is totally missing. Please, compare this method with other simple methods already included in the literature.

Response 3: For the SOCF diagnosis tasks, especially under non-stationary, multi-scale, and periodic signal conditions require models that can capture long-range temporal dependencies via the Transformer’s self-attention mechanism and can preserve local pattern details and directional features via BiTCN. Therefore, the hybrid Transformer-BiTCN algorithm benefits from the complementary advantages of both architectures. In detail, the Transformer excels at global signal sequence modeling but may struggle with localized temporal features or computation efficiency. The BiTCN, on the other hand, is effective in extracting local and multi-scale time-series features. By combining them together, the hybrid Transformer-BiTCN can result in a more robust and accurate SOCF diagnostic results. This part also has been added in the revision, Line 159-167, as follows:

For the SOCF diagnosis tasks, especially under non-stationary, multi-scale, and peri-odic signal conditions require models that can capture long-range temporal dependencies via the Transformer’s self-attention mechanism and can preserve local pattern details and directional features via BiTCN. Therefore, the hybrid Transformer-BiTCN algorithm bene-fits from the complementary advantages of both architectures. In detail, the Transformer excels at global signal sequence modeling but may struggle with localized temporal features or computation efficiency. The BiTCN, on the other hand, is effective in extracting local and multi-scale time-series features. By combining them together, the hybrid Trans-former-BiTCN can result in a more robust and accurate SOCF diagnostic results.

Moreover, the ISGA is an intelligent optimization strategy designed to efficiently search the hyperparameter space and structural configurations of above deep hybrid model. In detail, the ISGA is employed to optimize key hyperparameters and network structure parameters. This data-driven, automated optimization helps to achieve a more efficient, accurate, and generalized model, avoiding human bias in design and significantly improving diagnostic performance over default or manually tuned models. This part also has been added in the new manuscript, Line 258-263, as follows:

Here, the ISGA is an intelligent optimization strategy designed to efficiently search the hyperparameter space and structural configurations of above deep hybrid model. In detail, the ISGA is employed to optimize key hyperparameters and network structure parameters. This data-driven, automated optimization helps to achieve a more efficient, accurate, and generalized model, avoiding human bias in design and significantly improving diagnostic performance over default or manually tuned models.

Typical simple methods, based on linear or gradients approaches, including Bayesian Network, Linear Support Vector Machine, Shallow Gradient Boosting Decision Tree and Random Forests are compared and tested in the new manuscript, as shown in in Table 9. It can be seen that the proposed method achieves the highest fault diagnosis accuracy with a fault diagnosis accuracy rate of 99.69%, a precision rate of 99.76%, and a recall rate of 99.71%. This indicates that the proposed method better fits the probability distribution of fault features, and therefore exhibits superior fault diagnosis accuracy when dealing with fault signals characterized by periodic non-stationarity.

Comment 4: Equation (6) is unclear, please use a formal definition based in matrixes or vectors.

Response 4: You are absolutely right that Equation (6) would benefit from a more rigorous and formal presentation using matrix/vector notation to enhance clarity and precision. To address this, we have completely revised Equation (6) in the revision.

Comment 5: The implementation of the proposed algorithm is totally missing, how is ensured the operation in real time? Please, comment about the experimental hardware set-up used in this implementation.

Response 5: T The implementation of the proposed algorithm has been added in the new revision, Subsection 4.3, Line 390-402, as follows:

       Once the hyperparameters of model proposed in Fig.4 is trained well, the obtained model can be applied for open-circuit fault diagnosis in a practical field. The whole flowchart for Vienna open-circuit fault diagnosis is illustrated in Fig. 6.

Step 1: The input currents ia, ib, ic and DC voltage udc1, udc2 of Vienna rectifier from experimental platform under different SOCF faults are sampled and employed as the raw signal for diagnosing.

Step 2: The raw current sampled data collected in Step 1 are pre-processed including normalization and abnormal values removal.

Step 3: The pre-processed data is then directly introduced to the well-trained SOCF diagnosis model with optimized parameters and structure.

Step 4: The SOCF diagnosis results are recognized and the faulted switches are located via looking up Table 1.

Meanwhile, both the real-time operation and experimental hardware set-up used in this implementation have been added in the revised manuscript, Line 555-563, as follows:

For on-line testing of SOCF diagnosis, the real-time performance is related to multiple factors, mainly including sequence length of input data, model parameters, network depth, and hardware computation performance. In this paper, model parameters and network depth are optimized using ISGA algorithm. The hardware computation server is equipped with 2×NVIDIA RTX 4090 GPU and 4×2TB memory. To ensure the operation in real time, the following two different strategies are adopted: 1) Parallel inference strategies across multiple GPUs are adopted to accelerate batch processing; 2) Except for the optimized hyperparameters in Table 6, other parameters, such as sequence length of input data, are manually tested for satisfied real-time performance.

Comment 6: Convergence of the proposed method must be investigated.

Response 6: The convergence of the proposed method has been added in the revision, Line 475-480, as follows:

From Figure 7, it can be observed that as the number of iterations increases, the Loss of the Transformer-BiTCN model using the ISGA optimization algorithm achieves the smallest value and exhibits a convergent state. In contrast, the Loss of the Transformer-BiTCN model via other optimization algorithms are relatively larger or converge more slowly. The con-vergence performance of the ISGA optimization algorithm is superior to that of optimization algorithms such as ABC, RBMO, TOC, traditional SGA.

And meanwhile, the performance comparison between different optimization algorithms, including convergence, also has been added in Table 7, Line 483-488, as follows:

From Table 7, it can be conducted that our proposed ISGA optimized Transformer-                           BiTCN can achieve highest diagnosis accuracy while maintaining the lowest loss value, the shortest processing time and the minimum number of parameters. The main reason is that the ISGA optimization algorithm with Bloch initialization strategy and Rime search mechanism can enhance exploration capability to escape local optima and converge to the global optimum.

Comment 7: Convergence, number of parameters, real-time operation, processing time and other features of methods in Table 5 must be included in a table.

Response 7: In the revised manuscript, the performance comparison between different optimization algorithms, including convergence, number of parameters, processing time and average accuracy has been carried out in Table 7, Line 483-488, as follows:

   From Table 7, it can be conducted that our proposed ISGA optimized Transformer-      BiTCN can achieve highest diagnosis accuracy while maintaining the lowest loss value, the shortest processing time and the minimum number of parameters. The main reason is that the ISGA optimization algorithm with Bloch initialization strategy and Rime search mechanism can enhance exploration capability to escape local optima and con-verge to the global optimum.

 Response to Comments on the Quality of English Language

Point 1: The English could be improved to more clearly express the research along introduction and conclusion part.

Response 1: We sincerely appreciate the reviewer’s constructive suggestion. Clear communication of research objectives, contributions, and implications is critical, and we fully refine these sections for better readability and impact in the new manuscript.

Comments 1: The manuscript “Switch Open-circuit Fault Diagnosis of Vienna Rectifier Using Transformer-BiTCN Network With Improved Snow Geese Algorithm Optimization” presents a novel methodology for open switch fault diagnosis.

The paper is well-structured, and the authors provide a detailed and clear explanation of the proposed methodology, supported by simulations and experimental validation. The technical contribution is significant, and the results demonstrate the effectiveness and robustness of the approach.

I find the manuscript suitable for publication in its present form.

Response 1: We are truly grateful to the reviewer for your highly positive and encouraging assessment of our manuscript. These kind words regarding the structure, clarity of the methodology, and the significance of our technical contribution mean a great deal to us.

Your feedback validates the rigorous efforts we put into this work, and we are delighted that the simulations and experimental validation successfully supported the presentation of our proposed methodology. We will carefully incorporate any minor formatting to ensure the highest quality of the published version. Once again, thank you for your time, expertise, and invaluable support.