Temporal Convolutional Network-Based Axle Load Estimation from Pavement Vibration Data

Round 1

Reviewer 1 Report

Comments and Suggestions for Authors

The paper aims to present a vibration-based method to estimate axle weights using DOVS and TCN. However, some issues need to be clarified so the paper can be consider for publication.

1.      Please correct grammatical errors and typos.

2.      What is the novelty of this research? Describe your novelty in the last paragraph of introduction.

3.      It is suggested that the results be compared numerically at the end of the abstract.

 

4.      It is suggested that the conclusion section be rewritten and that the results be presented in a practical and comparative. Also, in one case, the practical result of this research should be presented.

 

Comments on the Quality of English Language

The paper aims to present a vibration-based method to estimate axle weights using DOVS and TCN. However, some issues need to be clarified so could paper consider for publication.

1.      Please correct grammatical errors and typos.

2.      What is the novelty of this research? Describe your novelty in the last paragraph of introduction.

3.      It is suggested that the results be compared numerically at the end of the abstract.

4.      It is suggested that the conclusion section be rewritten and that the results be presented in a practical and comparative. Also, in one case, the practical result of this research should be presented.

Author Response

The paper aims to present a vibration-based method to estimate axle weights using DOVS and TCN. However, some issues need to be clarified so the paper can be consider for publication.

Comment 1:

Please correct grammatical errors and typos.

Response:

Thank you so much for your good suggestion. We have revised the manuscript accordingly.

Comment 2:

What is the novelty of this research? Describe your novelty in the last paragraph of introduction.

Response:

Thank you so much for your good suggestion. The paper presents two innovations: Firstly, a pavement vibration acquisition method based on Distributed Optical Vibration Sensors (DOVS) is developed. This method enables distributed and spatially dense monitoring of pavement vibration data. Secondly, a load mapping method tailored for pavement vibration data collected by DOVS is proposed. The mapping method, based on deep learning, is validated for its performance through two on-site experiments. We have revised the manuscript in Line 78-88.

 

Comment 3:

It is suggested that the results be compared numerically at the end of the abstract.

Response:

Thank you so much for your good suggestion. The revised abstract is below.

Measuring the axle loads of vehicles with more accuracy is a crucial step for weight enforcement and pavement condition assessment. This paper proposed a vibration-based method, which has an extended sensing range, high temporal sampling rate, and dense spatial sampling rate, to estimate axle loads in concrete pavement using distributed optical vibration sensing (DOVS) technology. Temporal Convolutional Networks (TCN), which consist of non-causal convolutional layers and a concatenate layer, were proposed and trained by over 6,000 samples of vibration data and ground truth of axle loads. Moreover, the TCN could learn the complex inverse mapping between pavement structure inputs and outputs. The performance of the proposed method is calibrated in two field tests with various conditions. The results demonstrate that the proposed method could obtain estimated axle loads within 11.5% error, under diverse circumstances that consist of different pavement types and loads moving speeds ranging from 0~35 m/s. The proposed method demonstrates significant promise in the field of axle load reconstruction and estimation. Its error, closely approaching the 10% threshold specified by LTPP, underscores its efficacy. Additionally, the method aligns with the standards set by Cost-323, with an error level up to category C. This indicates its capability to provide valuable support for the assessment and decision-making processes related to pavement structure conditions [1].

[1] Jacob, Bernard, and Eugene J. O’Brien. "European specification on weigh-in-motion of road vehicles (COST323)." Proceedings of second European conference on weigh-in-motion of road vehicles, Held Lisbon, Portugal. 1998.

Comment 4:

It is suggested that the conclusion section be rewritten and that the results be presented in a practical and comparative. Also, in one case, the practical result of this research should be presented.

Response:

Thank you so much for your good suggestion. The rewritten conclusion is below.

Accurately measuring vehicle axle loads is a vital component in weight enforcement and pavement condition assessment. Existing WIM technologies are costly, impractical for high-speed vehicle detection due to inadequate time for pressure change registration, and susceptible to installation challenges. The goal of this paper was to develop an inexpensive but accurate DOVS-based WIM system. The vibration of concrete pavement contains valuable information that can identify vehicle load characteristics. But it is difficult to ensure the accuracy of the process, which typically requires complicated mathematical modeling and formula derivation.

The proposed method, characterized by an extended sensing range, high temporal sampling rate, and dense spatial sampling rate, demonstrates promising results in field tests under diverse conditions. The TCN model, trained with over 6,000 samples of vibration data and corresponding ground truth of axle loads, exhibits the ability to learn the intricate inverse mapping between pavement structure inputs and outputs. The method achieves estimated axle loads within an 11.5% error margin, showcasing its efficacy in weight enforcement and pavement condition assessment. Furthermore, the approach aligns closely with specified standards such as those set by LTPP and Cost-323, reinforcing its potential to offer valuable support in assessing and making decisions related to pavement structure conditions. The collection of pavement vibration data is privileged data and is only used for traffic data analysis. The data has been desensitized and will not involve personal privacy.

Future work in this research avenue could focus on several aspects to further enhance the proposed method. Firstly, refining the deep learning-based load reconstruction method to accommodate variations in load conditions and pavement types would contribute to increased robustness. Secondly, exploring the application of the proposed methodology to asphalt pavements, which may present distinct challenges in coordination with fiber optic technology, could broaden its scope. Thirdly,  Lastly, considering the potential integration of real-time monitoring capabilities into the proposed method would provide a dynamic approach to pavement assessment and management. Addressing these aspects would contribute to the continual improvement and applicability of the presented vibration-based method for axle load estimation in diverse pavement scenarios.

Reviewer 2 Report

Comments and Suggestions for Authors

The paper is fine as it is. The authors are honest about the accuracy of the model. I doubt if the accuracy acheived so far is sufficient for weight enforcement, but it is probably sufficient for road planning application.

Comments on the Quality of English Language

Just get a simple workthrough of the language. It's possible to understand, and I see no major mistakes.

Author Response

Comments 1:

The paper is fine as it is. The authors are honest about the accuracy of the model. I doubt if the accuracy acheived so far is sufficient for weight enforcement, but it is probably sufficient for road planning application.

Response:

We appreciate the reviewer’s acknowledgement of the quality of our paper. In future research, we plan to conduct additional on-site experiments to acquire a more diverse set of vibration data for model training. Furthermore, we intend to enhance predictive accuracy by incorporating transfer learning strategies.

Reviewer 3 Report

Comments and Suggestions for Authors

The paper would benefit from a more explicit description of the training process for the Temporal Convolutional Networks, including details on the dataset selection criteria and the architecture specifics.

 

A comparative analysis with other existing methods for axle load estimation would add depth to the paper, providing readers with a clearer understanding of the advantages and limitations of the proposed approach.

It would be valuable to include a sensitivity analysis to explore how the proposed method performs under various conditions, providing a more comprehensive evaluation of its robustness.

Discussing potential sources of error and addressing how the proposed method mitigates or is affected by these sources would enhance the paper's credibility and help readers interpret the reported results.

Consider discussing the real-world applicability of the proposed method, addressing any practical challenges or limitations that may arise when implementing this approach in a broader context.

Elaborate on any challenges faced during the data collection process, such as environmental factors or technical issues, to provide insights into the feasibility and reliability of the proposed method in different scenarios.

Comment on the generalization capability of the trained TCN model. Does it perform equally well across different pavement types and under varying load conditions?

Connect the findings more explicitly to their implications for decision-making in pavement structure conditions, emphasizing how the estimated axle loads can inform weight enforcement and infrastructure maintenance decisions.

Clarify the methodology used to validate the results, including any statistical tests or benchmarks employed to demonstrate the significance and reliability of the reported 11.5% error rate.

Discuss any ethical considerations related to the use of vibration data for axle load estimation, such as privacy concerns or potential unintended consequences, to address the broader impact of the proposed method.

Comments on the Quality of English Language

Minor editing of English language required

Author Response

Comments 1:

The paper would benefit from a more explicit description of the training process for the Temporal Convolutional Networks, including details on the dataset selection criteria and the architecture specifics.

Response:

Thank you so much for your good suggestion. We have revised the manuscript accordingly.

In Site 1, The training set and the test set were divided by a ratio of 4:1. A uniform sampling of 80% of all load level and load speed samples was used as the training set to ensure a balanced sample distribution. Finally, the training set has 5352 samples and the test set has 1338 samples. In Site 2, The training set and the test set were also divided by a ratio of 4:1. The samples were evenly sampled according to vehicle type. The training set has 268 samples and the test set has 70 samples. After preprocessing and augmentation, the training set samples are increased to 804 and the testing set samples are increased to 201.

The proposed TCN network is presented in Figure 3. The TCN model architecture consisted of non-causal convolutional layers and a concatenate layer. The non-causal convolutional layers allowed the model to capture temporal dependencies effectively, while the concatenate layer enabled the integration of information from multiple segments of the input sequence. The first convolutional block (CONV) has N_T filters. There are N_B TCN blocks that use the same number of filters N_T, the same kernel length K_T, and a variable dilation d ∈ {1, 2,4…   }. The default parameter is N_T = 32, K_T = 31, N_B = 12.

Figure 3. TCN architecture processing the number of vibration sensors (N₀) x 700 samples.

Using the PyTorch environment, the model was developed, trained, and tested on an Nvidia GeForce RTX 3060 GPU. In the training process, we optimized the network weights and biases using the mean square error loss (MSE) and uniformly initialized the filter kernels. To minimize the objective loss function, we used the Adam optimizer. The mini-batch size varied from 16 to 128 for different tasks. The initial learning rate was set to 1e-4, and we implemented adaptive adjustment of the learning rate. If the validation loss did not decrease for 15 epochs, we reduced the learning rate by a factor of 10.

Comments 2:

A comparative analysis with other existing methods for axle load estimation would add depth to the paper, providing readers with a clearer understanding of the advantages and limitations of the proposed approach.

Response:

Thank you so much for your good suggestion. In the revised manuscript, we have added a table in Field Application to compare the cost, error and lifetime between different methods for axle load estimation as shown in Table 1 [1,2]. The results show that the proposed method has advantages both in cost and lifetime. However, the accuracy is not as high as other methods. We have revised the manuscript accordingly.

Table 2. Methods for axle load estimation comparation

Methods for axle load estimation	Annual life cycle cost ($)	Error	Expected life (years)
DOVS based (presented)	1000	±11.5%	15
Bending plate	5000	±15%	4
Strip WIM (piezoelectric)	6000	±10%	6
Single load cell	8000	±6%	12

 

[1] Wang J, Han Y, Cao Z, et al. Applications of optical fiber sensor in pavement Engineering: A review[J]. Construction and Building Materials, 2023, 400: 132713.

[2] Zhao, C.; Bian, Z.; Zhao, H.; Ma, L.; Guo, M.; Peng, K.; Gao, E. Identification of Moving Load Characteristic on Pavement Using F-P Cavity Fiber Optical Technology. Sustainability 2022, 14, 2398.

Comments 3:

It would be valuable to include a sensitivity analysis to explore how the proposed method performs under various conditions, providing a more comprehensive evaluation of its robustness.

Response:

Thank you so much for your good suggestion. Among the loading parameters, the load speed has a greater influence on the weighing results [2]. The network model structural hyperparameters have a greater impact on the performance of the load reconstruction model. The sensitivity analysis of network hyperparameters and loading velocities have been presented in the paper.

However, there are currently only two sites with ground truth load. It is difficult to conduct sensitivity analyses in terms of pavement type, size, and temperature. We will conduct more field tests in the future.

[2] Zhao, C.; Bian, Z.; Zhao, H.; Ma, L.; Guo, M.; Peng, K.; Gao, E. Identification of Moving Load Characteristic on Pavement Using F-P Cavity Fiber Optical Technology. Sustainability 2022, 14, 2398.

Comments 4:

Discussing potential sources of error and addressing how the proposed method mitigates or is affected by these sources would enhance the paper's credibility and help readers interpret the reported results.

Response:

Thank you so much for your good suggestion. There are four potential sources of error, which are environmental variability, pavement heterogeneity, traffic composition and model complexity. Environmental variability, pavement heterogeneity, traffic composition increases the diversity of data samples. If the training samples do not cover all conditions, then the robustness of the model decreases. We have revised the manuscript accordingly.

Comments 5:

Consider discussing the real-world applicability of the proposed method, addressing any practical challenges or limitations that may arise when implementing this approach in a broader context.

Response:

Thank you so much for your good suggestion. In the real-world applicability of the proposed method, the limitations of the method are centered on the installation of the DOVS system in the pavement and the labeling of the vibration data. The former can be integrated with precast concrete slab to solve the problem of installation accuracy. The latter can adopt a transfer learning strategy to reduce the amount of labeled data required. We have revised the manuscript accordingly.

Comments 6:

Elaborate on any challenges faced during the data collection process, such as environmental factors or technical issues, to provide insights into the feasibility and reliability of the proposed method in different scenarios.

Response:

Thank you so much for your good suggestion. Challenges encountered in the data collection process encompass several key aspects. Firstly, the acquisition of vibration samples accurately labeled with corresponding load conditions presents a primary obstacle. Secondly, the synchronized processing of vibration data across multiple points poses a significant challenge, particularly given the system's sample frequency of 2500 Hz. Designing a reliable backend program capable of real-time, synchronous processing and efficient storage of substantial data volumes represents a complex undertaking. Lastly, ensuring harmonious deformation alignment with the pavement structure during system installation is crucial. The inherent attributes of high stiffness and minimal deformation in concrete pavements facilitate their compatibility with distributed optical fiber vibration sensing, ensuring the durability of the optical fiber and the efficacy of vibration monitoring. However, for asphalt pavements, additional consideration may be necessary to optimize the coordination of deformation during installation with the deployment of fiber optic technology. We have revised the manuscript accordingly.

Comments 7:

Comment on the generalization capability of the trained TCN model. Does it perform equally well across different pavement types and under varying load conditions?

Response:

Thank you so much for your good suggestion. This study conducted experiments on two sizes of cement concrete pavement. The results indicate that the Temporal Convolutional Networks (TCN) model exhibits excellent load inversion accuracy for both sizes of cement concrete pavement. In Site 2, the TCN model demonstrated robust performance when subjected to natural traffic flow with varying speeds and vehicle types. Hence, it can be concluded that the TCN model performs well under different sizes of cement concrete pavement and varied load conditions. However, the current study lacks experimental design for asphalt pavement. In future research, we plan to expand the investigation to include asphalt roads to validate the model's performance in inverting loads from natural traffic flow on asphalt road. We have revised the manuscript accordingly.

Comments 8:

Connect the findings more explicitly to their implications for decision-making in pavement structure conditions, emphasizing how the estimated axle loads can inform weight enforcement and infrastructure maintenance decisions.

Response:

Thank you so much for your good suggestion. Accurate axle load estimates assist in regulatory compliance, targeted inspections, load-induced pavement damage assessment, pavement design and planning and optimized maintenance scheduling. Specially, the precise information on axle loads enables targeted enforcement efforts. Authorities can focus inspections on vehicles with estimated loads exceeding permissible limits, optimizing resources and enhancing the efficiency of weight enforcement operations. Accurate estimation of axle loads provides insights into the actual stress and strain exerted on the pavement. This information is critical for assessing the potential for load-induced pavement damage and predicting areas that may require maintenance. The data on estimated loads contributes to the refinement of pavement design and planning. It aids in developing infrastructure that can withstand anticipated loads, thereby promoting longevity and reducing the frequency of maintenance interventions. By understanding the load distribution across different sections of the road, maintenance activities can be scheduled more efficiently. Areas experiencing higher loads may be prioritized for timely repairs or upgrades, preventing premature deterioration and minimizing overall maintenance costs. We have revised the manuscript accordingly.

Comments 9:

Clarify the methodology used to validate the results, including any statistical tests or benchmarks employed to demonstrate the significance and reliability of the reported 11.5% error rate.

Response:

Thank you so much for your good suggestion. According to equation (1), all the data results of Site 1 and Site 2 are calculated to get the peak error. N is 1539.

(1)

 

We have revised the manuscript accordingly.

Comments 10:

Discuss any ethical considerations related to the use of vibration data for axle load estimation, such as privacy concerns or potential unintended consequences, to address the broader impact of the proposed method.

Response:

Thank you so much for your good suggestion. The collection of pavement vibration data is privileged data and is only used for traffic data analysis. The data has been desensitized and will not involve personal privacy. We have revised the manuscript accordingly.

Round 2

Reviewer 3 Report

Comments and Suggestions for Authors

Accept in present form

Comments on the Quality of English Language

Minor editing of English language required