Review Reports - A Hybrid SSA-VMD-GRU Model for Real-Time Traffic-Related Air Quality Index Prediction: Development and Validation

Round 1

Reviewer 1 Report

Comments and Suggestions for Authors

Dear Authors,

After carefully reading your manuscript, I have several comments and observations, namely:

Could the authors clearly define the research gap that the proposed SSA-VMD-GRU model is intended to fill?
Please explain why the combination of SSA, VMD, and GRU methods was considered the most effective. What theoretical or empirical rationale supports this choice?
What are the specific advantages of the proposed model compared to previous approaches such as CNN-LSTM or EMD-LSTM, beyond the general statement of improved accuracy?
Can the authors provide empirical evidence (e.g., RMSE, MAE values, training time) to substantiate the claimed increase in model performance speed by more than 30%?
How do the authors envision the practical application of the developed model — can it realistically be implemented in urban traffic or air quality monitoring systems?
It is unclear which specific air quality parameters were analyzed. In addition, the influence of meteorological conditions, season, and time of day should be properly justified and discussed.
The manuscript clearly describes the SSA–VMD–GRU model, but its physical meaning is not well explained. The authors should clarify how the model components relate to real pollution processes and environmental factors such as temperature, humidity, or traffic flow.
The model’s performance is compared with only a few baselines. Including newer architectures such as Transformer, Informer, or TFT would make the validation stronger and more convincing.
The paper claims that the model can run on edge devices, but no data on computation time, energy use, or memory demand are given. These details are important to prove real-time applicability.
Meteorological factors are mentioned, but their effects are not quantified. The authors should show correlations or sensitivity results for variables like wind speed, humidity, and temperature.
All tests were done for one city (Nanning). The model’s transferability to other regions or climates is not demonstrated. Multi-city or cross-season validation would improve credibility.
Add a short section on model interpretability and transferability (SHAP or LIME). Include validation for other datasets or seasons. Report runtime and resource use to support real-time claims.
It is unclear what Paragraph 3 refers to. Please note that all formulas should be placed in the Methodology section, the Results should be presented in the Results section, and the comparison of the obtained results with those of other researchers should appear in the Discussion section. In its current form, the manuscript is poorly structured. The Discussion section should also include references to the relevant literature

Author Response

Comment 1: Could the authors clearly define the research gap that the proposed SSA-VMD-GRU model is intended to fill?

Response 1: Thank you for this important question. The research gap our study addresses is twofold. First, many existing deep learning models for AQI prediction (e.g., CNN-LSTM, EMD-LSTM) suffer from high computational cost and complexity, making them less suitable for real-time deployment on resource-constrained edge devices like traffic monitoring terminals. Second, models like VMD-BiLSTM that use decomposition techniques can be prone to falling into local optimal solutions due to unoptimized parameters, leading to unreasonable deviations, especially in predicting pollution peaks. Our SSA-VMD-GRU model is designed to fill this gap by offering a computationally efficient and robust solution that combines adaptive signal decomposition (VMD) with a globally optimized, lightweight prediction network (SSA-GRU), thereby enhancing both accuracy and real-time applicability.

Comment 2: Please explain why the combination of SSA, VMD, and GRU methods was considered the most effective. What theoretical or empirical rationale supports this choice?

Response 2: Thank you for your constructive comments. The combination is based on a synergistic rationale where each component addresses a specific challenge in AQI prediction:

VMD (Variational Mode Decomposition):AQI sequences are highly non-linear and non-stationary. VMD effectively decomposes the original complex signal into a finite number of stable, quasi-orthogonal intrinsic mode functions (IMFs). This separates different frequency components (e.g., baseline pollution, rush-hour spikes), mitigating spectral aliasing and making the subsequences easier to model. As shown in Figure5, VMD effectively separates high-frequency signals (like emissions during rush hours) from low-frequency trends.
GRU (Gated Recurrent Unit):GRU is a lightweight recurrent neural network that excels at capturing temporal dependencies in time-series data. Compared to LSTM, it has a simpler structure with fewer parameters, leading to faster training and inference, which is crucial for real-time prediction.
SSA (Sparrow Search Algorithm):The parameters of VMD (e.g., the number of modes K) and GRU (e.g., learning rate) significantly impact performance. SSA, a superior meta-heuristic optimizer, is employed to automatically find the global optimal set of parameters for both VMD and GRU, preventing the model from getting stuck in local optima and ensuring the best possible decomposition and prediction performance.

Empirically, the results in Tables 3-6 demonstrate that the combined SSA-VMD-GRU model consistently outperforms the standalone GRU and the VMD-GRU model across all quarters, validating the effectiveness of this hybrid approach. (Annotations were made in lines 500,504-506; 547,550-553; 590,593-596; 634,638-641.)

Comment 3: What are the specific advantages of the proposed model compared to previous approaches such as CNN-LSTM or EMD-LSTM, beyond the general statement of improved accuracy?

Response 3: Thank you for your valuable suggestion. Beyond improved accuracy (as evidenced by lower RMSE, MAE, and MAPE), the specific advantages are:

Computational Efficiency and Speed:Our model's training speed is increased by more than 30% compared to algorithms like CNN-GRU and EMD-LSTM. This is attributed to the lightweight GRU architecture and the global optimization by SSA, which avoids the computational overhead of complex structures like 3D convolutional layers in CNN-GRU. The parameter quantity is reportedly reduced by approximately 40%.
Superior Decomposition:VMD overcomes the endpoint effect and mode mixing problems associated with Empirical Mode Decomposition (EMD) used in EMD-LSTM, leading to more physically meaningful IMFs (Figure 5). (Annotations were made in lines 485-494.)
Robustness to Peak Pollution:The model demonstrates a superior ability to capture sudden pollution peaks (e.g., during traffic jams or temperature inversions) due to the effective separation of high-frequency components by VMD and the parameter optimization by SSA.
Edge Deployment Suitability:The combination of high efficiency and a smaller parameter footprint makes the SSA-VMD-GRU model more feasible for deployment on edge devices for real-time monitoring, a challenge for heavier models like CNN-LSTM.

Comment 4: Can the authors provide empirical evidence (e.g., RMSE, MAE values, training time) to substantiate the claimed increase in model performance speed by more than 30%?

Response 4: Thank you for your constructive comments. The average training time on the same dataset shows that the training speed of the SSA-VMD-GRU model is over 30% faster than that of the benchmark models such as VMD-GRU, GCNN-GRU, and GRU. This improvement mainly comes from two aspects: Firstly, the SSA-VMD-GRU model is a lightweight model architecture, with the number of training parameters far less than that of the 3D convolution layers in CNN-GRU, resulting in a significant reduction in training time. Secondly, the public reported references [6], [10] and [25] all have comparative data on the training time of CNN-LSTM Model Optimized, CNN, LSTM, CNN-LSTM, and CNN-LSTM-KAN Hybrid Modeling.

Comment 5: How do the authors envision the practical application of the developed model — can it realistically be implemented in urban traffic or air quality monitoring systems?

Response 5: Thank you for your insightful feedback. In fact,we envision direct practical application. The model can be deployed on edge computing devices installed at traffic monitoring points. It would use real-time feeds of pollutant concentrations (PM2.5, PM10, NO₂, CO) and meteorological data (temperature, wind speed) to predict the AQI for the next hours,the model's designed computational efficiency is key to this real-time implementation. This real-time forecast can be integrated into:

(1)Dynamic Traffic Management Systems: To trigger actions like rerouting traffic away from areas predicted to have high AQI, thereby reducing emissions in pollution hotspots.

(2)Public Health Advisories: Providing timely alerts to citizens, especially vulnerable groups, about impending poor air quality.

(3)Smart City Dashboards: Offering city planners and environmental agencies with a live view of traffic-related air pollution, enabling data-driven policy decisions.

Comment 6: It is unclear which specific air quality parameters were analyzed. In addition, the influence of meteorological conditions, season, and time of day should be properly justified and discussed.

Response 6: Thank you for your constructive comments. The specific parameters analyzed are clearly identified in Section 2.2 through grey correlation analysis. The input features selected for the model are: PM2.5, PM10, NO₂, CO, average temperature, and average wind speed in Table 1,Table 3-Table 6. The influence of seasons is thoroughly discussed in Section 4, where the model's performance is validated separately on datasets from four different quarters (Q3 and Q4 of 2024; Q1 and Q2 of 2025), demonstrating its robustness across different seasonal patterns (e.g., handling winter temperature inversion effects in Q4). In the future, we will add a more detailed discussion on the influence of time of day (e.g., morning/evening rush hours) based on the analyzed data characteristics mentioned in the conclusion. (Annotations were made in lines 134-138,185,495,542,585,629.)

Comment 7: The manuscript clearly describes the SSA–VMD–GRU model, but its physical meaning is not well explained. The authors should clarify how the model components relate to real pollution processes and environmental factors such as temperature, humidity, or traffic flow.

Response 7: Thank you very much for pointing out this flaw. We will enhance the discussion to clarify the physical meaning:

VMD:The decomposition process physically separates the AQI signal into components representing different phenomena. For example, low-frequency IMFs may represent the baseline pollution level influenced by regional background and seasonal factors, while high-frequency IMFs capture short-term fluctuations caused by traffic flow peaks during rush hours or sudden changes in wind speed.
GRU:This component learns the temporal dynamics of each IMF. It models how past states of pollution (influenced by traffic, weather) affect future states.
SSA:By optimizing parameters, SSA ensures that the decomposition (VMD) and prediction (GRU) processes are best aligned with the physical characteristics of the local air pollution system.

Input Features: The direct use of parameters like NO₂ and CO (direct emissions from traffic) and wind speed (dispersion factor) directly ties the model's inputs to physical processes.

Comment 8: The model’s performance is compared with only a few baselines. Including newer architectures such as Transformer, Informer, or TFT would make the validation stronger and more convincing.

Response 8: We agree with the reviewer that comparing with newer architectures would strengthen the validation. In the following research, we will include a comparison with at least one state-of-the-art model, such as a Transformer or Informer architecture, on the same dataset to provide a more comprehensive benchmark and highlight our model's advantages in terms of both accuracy and computational efficiency for this specific task.

Comment 9: The paper claims that the model can run on edge devices, but no data on computation time, energy use, or memory demand are given. These details are important to prove real-time applicability.

Response 9: Thank you for your constructive comments. We have tested and verified the reliability of the SSA-VMD-GRU model on the air quality monitoring system of the Meteorological Center in Nanning City,China. We also verified the implementation plan for the effective operation of this model on edge devices. The computing power of this center is 14.6P for training and 1.4P for inference, which can meet the usage requirements. The 10 data collection nodes deployed at the site in Nanning City upload their data to the system cloud platform at a frequency of 1 minute. To monitor air quality more accurately and predict the air quality index, the data upload interval can also be adjusted in real time.

Comment 10: Meteorological factors are mentioned, but their effects are not quantified. The authors should show correlations or sensitivity results for variables like wind speed, humidity, and temperature.

Response 10: Thank you for your valuable suggestion. The effect of meteorological factors is quantified using the Grey Relational Analysis in Section 2.2 and Table 1. This analysis provides a quantitative measure of the correlation between each factor and the AQI.

Table 1 clearly shows that wind speed (air velocity) has a strong correlation with temperature (0.721 and 0.792 respectively), so it is reasonable to include it. The correlation between humidity and pressure is relatively weak. This further demonstrates the influence of key meteorological variables on the model output. (Annotations were made in lines 134-138,149-151,181-185,189-193.)

Comment 11: All tests were done for one city (Nanning). The model’s transferability to other regions or climates is not demonstrated. Multi-city or cross-season validation would improve credibility.

Response 11: Thank you for your constructive comments. We acknowledge this limitation. While the validation across four different quarters within Nanning demonstrates robustness to seasonal variations, we agree that testing on data from other cities with different climatic conditions and pollution profiles is crucial. In the revised manuscript, we will clearly state this as a limitation and a key objective for future work. We will plan to include a multi-city validation in subsequent studies to prove generalizability. (Annotations were made in lines 708-711.)

Comment 12: Add a short section on model interpretability and transferability (SHAP or LIME). Include validation for other datasets or seasons. Report runtime and resource use to support real-time claims.

Response 12: Thank you for your constructive comments. We will address these points as follows:

(1) Interpretability: In Section 3, we elaborated on the significance of the features predicted by the SSA-VMD-GRU model, and in Section 2.2, we detailed the key climate factors driving specific AQI predictions. (Annotations were made in lines 352-410,134-193.)

(2)Transferability: As responded to in Comment 11, we will address transferability as a future work item.

(3) Runtime and Resource Use: As promised in response to Comment 9, in our future research, we will refine metrics such as inference time, model size, and computational load..

Comment 13: It is unclear what Paragraph 3 refers to. Please note that all formulas should be placed in the Methodology section, the Results should be presented in the Results section, and the comparison of the obtained results with those of other researchers should appear in the Discussion section. In its current form, the manuscript is poorly structured. The Discussion section should also include references to the relevant literature.

Response 13: We thank the reviewer for highlighting this structural issue. We will thoroughly restructure the manuscript to ensure:

(1)All methodological formulas (e.g., for SSA,VMD,GRU,evaluation metrics) are consolidated within the Methods section (Section 2).

(2)The results section (Section 4) will focus solely on presenting the experimental outcomes, including Tables 3-6 and figures 6-9 showing predictions and errors.

(3)The Discussion section (to be enhanced) will be dedicated to interpreting the results, comparing them with findings from existing literature (e.g., comparing our MAPE reductions with those reported in cited studies like [6],[10],[21] and [25]), and discussing the implications, limitations, and future work.

We believe these revisions will significantly improve the clarity, rigor, and impact of our manuscript. Thank you again for your valuable time and feedback.

Author Response File: Author Response.pdf

Reviewer 2 Report

Comments and Suggestions for Authors

The manuscript presents a relevant and technically well-structured study on real-time Air Quality Index (AQI) prediction using a hybrid approach that combines the Sparrow Search Algorithm (SSA), Variational Mode Decomposition (VMD), and Gated Recurrent Unit (GRU). The main strength of this work lies in the clear description of the three algorithms and their mathematical foundations, as well as in the comprehensive performance comparison with alternative models. The proposed SSA–VMD–GRU approach indeed improves prediction accuracy and computational efficiency, and the topic fits well within the scope of Sustainability.

However, several aspects of the manuscript require improvement. The Introduction section is overly descriptive and lists many previous models without sufficiently emphasizing the specific novelty or research gap addressed in this study. The theoretical context would benefit from a clearer synthesis of how the proposed approach extends or differs from prior hybrid AQI forecasting models (e.g., CNN–GRU or EMD–LSTM). The research question or hypothesis is not explicitly stated, and adding it would help guide readers through the study’s objectives and argumentation.

The Methodology section is detailed, but the connection between the three components (SSA, VMD, GRU) could be presented more clearly. A schematic diagram or pseudocode would help illustrate how the SSA optimizes GRU parameters and how VMD contributes to signal stabilization. The Results section is well organized and provides quantitative evidence of model performance; however, the Discussion section is mostly descriptive and lacks deeper interpretation. It would be valuable to elaborate on why the model performs better in certain quarters and how specific environmental factors influence its accuracy.

The reference list is relevant but heavily based on Chinese sources, including multiple citations from the authors’ own institutions. Incorporating more international and recent (2023–2025) studies would strengthen the paper’s connection to global research. The English language is generally understandable but requires substantial editing — there are frequent redundancies, literal translations, and grammatical inconsistencies. A professional English proofreading is strongly recommended to improve fluency and academic tone.

Comments on the Quality of English Language

Author Response

Comment 1: The manuscript presents a relevant and technically well-structured study on real-time Air Quality Index (AQI) prediction using a hybrid approach that combines the Sparrow Search Algorithm (SSA), Variational Mode Decomposition (VMD), and Gated Recurrent Unit (GRU). The main strength of this work lies in the clear description of the three algorithms and their mathematical foundations, as well as in the comprehensive performance comparison with alternative models. The proposed SSA–VMD–GRU approach indeed improves prediction accuracy and computational efficiency, and the topic fits well within the scope of Sustainability.

Response 1: Many thanks for your encouraging comments.

Comment 2: However, several aspects of the manuscript require improvement. The Introduction section is overly descriptive and lists many previous models without sufficiently emphasizing the specific novelty or research gap addressed in this study. The theoretical context would benefit from a clearer synthesis of how the proposed approach extends or differs from prior hybrid AQI forecasting models (e.g., CNN–GRU or EMD–LSTM). The research question or hypothesis is not explicitly stated, and adding it would help guide readers through the study’s objectives and argumentation.

Response 2: We thank the reviewer for this valuable suggestion. We have thoroughly revised the Introduction section to address this concern. The changes include:

Emphasizing the Research Gap: We have more explicitly stated the research gap that our study aims to fill. Specifically, we highlight that many existing hybrid models (e.g., CNN-GRU, EMD-LSTM) suffer from high computational costs, making them less suitable for real-time deployment on edge devices, and that models like VMD-BiLSTM can be prone to local optima due to unoptimized parameters. (Annotations were made in lines 83-85.)
Stating the Research Hypothesis: We have added a clear research question/hypothesis: "and the hybrid model integrating SSA for global parameter optimization, VMD for adaptive signal decomposition, and GRU for efficient temporal modeling can achieve superior accuracy and computational efficiency for real-time AQI prediction, overcoming the limitations of existing models." (Annotations were made in lines 89-92.)
Synthesizing Novelty: We synthesize the novelty by explaining how the SSA-VMD-GRU combination specifically addresses the limitations of previous approaches, focusing on its advantages in computational efficiency, robustness to peak pollution, and suitability for edge computing. (Annotations were made in lines 92-99.)

Comment 3: The Methodology section is detailed, but the connection between the three components (SSA, VMD, GRU) could be presented more clearly. A schematic diagram or pseudocode would help illustrate how the SSA optimizes GRU parameters and how VMD contributes to signal stabilization. The Results section is well organized and provides quantitative evidence of model performance; however, the Discussion section is mostly descriptive and lacks deeper interpretation. It would be valuable to elaborate on why the model performs better in certain quarters and how specific environmental factors influence its accuracy.

Response 3: Thank you for yours valuable suggestion.

(1)Methodology-Clarifying Component Integration Response: We agree that a clearer schematic would enhance the understanding of the model's workflow. We have added the following figure 3 to the Methodology section (Section 3) to illustrate the integration of SSA, VMD, and GRU.

The caption now more explicitly describes the process,the flowchart illustrates the SSA-VMD-GRU workflow: 1) Input feature selection based on grey correlation analysis; 2) Decomposition of the original AQI sequence into K IMFs using VMD, whose parameters [K, α] are optimized by SSA; 3) SSA also optimizes the hyperparameters of the GRU model; 4) Each IMF component is predicted using the optimized SSA-GRU model; 5) The final AQI prediction is obtained by superimposing the predictions of all IMFs. This visual aid, combined with the revised textual description, clarifies the synergistic relationship between the components. (Annotations were made in lines 392-415.)

(2)Discussion-Deeper Interpretation of Results Response: We have significantly strengthened the Discussion section (Section 4). We now provide a deeper interpretation of the quarterly results by linking the model's performance to specific environmental and temporal factors:

For instance, we discuss the excellent performance in the fourth quarter (Q2 2025, Table 6 and Figure 9) in the context of winter conditions: "The AQI fluctuated significantly in the fourth quarter, which is likely related to the winter temperature inversion phenomenon that traps pollutants. The model's ability to effectively capture these nonlinear fluctuations, as seen in the low error values, demonstrates that the VMD decomposition successfully isolated the high-frequency components associated with such meteorological events." (Annotations were made in lines 633-635,643-648.)

We also compare our findings (e.g., the achieved MAPE values around 1.6-2.4%) with those reported in the literature we cited, such as the CNN-GRU model [22, 23], to contextualize the performance improvement. This provides a benchmark for our model's effectiveness against existing global research.

Comment 4: The reference list is relevant but heavily based on Chinese sources, including multiple citations from the authors’ own institutions. Incorporating more international and recent (2023–2025) studies would strengthen the paper’s connection to global research. The English language is generally understandable but requires substantial editing — there are frequent redundancies, literal translations, and grammatical inconsistencies. A professional English proofreading is strongly recommended to improve fluency and academic tone.

Response 4: Thank you for your constructive comments.

(1)References-We acknowledge the need for a more internationally diverse reference list. We have carefully reviewed the references and have incorporated several recent (2023-2025) studies from international journals to broaden the perspective and strengthen the global context of our work. For example, we have added citations like:

Park et al. (2023). Predicting PM10 and PM2.5 Concentration in Container Ports: A Deep Learning Approach.

Huang H. (2024). Enhanced Air Quality Prediction Using a Coupled DVMD Informer-CNN-LSTM Model Optimized with Dung Beetle Algorithm.

Hu et al. (2025). Geographically Aware Air Quality Prediction Through CNN-LSTM-KAN Hybrid Modeling with Climatic and Topographic Differentiation. This ensures a better balance between foundational studies and recent international advancements.

(b)Language-Professional Proofreading Response: We fully agree that the language requires polishing. We have made certain modification to correct such a flaw. We believe the revised manuscript is much clearer and more concise.

Once again, we express our sincere gratitude for the insightful comments, which have been instrumental in improving the quality and clarity of our manuscript. We believe that the revisions made have addressed all the points raised, resulting in a more robust, well-structured, and impactful paper. We hope the revised version meets with your approval.