Investigation of Following Vehicles’ Driving Patterns Using Spectral Analysis Techniques

Round 1

Reviewer 1 Report

This paper describes an investigation of multi-vehicle driving pattern using spectral analysis techniques. The homogeneity of sustainable transportation operations can result in various advantages. To optimize the driving behavior of autonomous vehicles, the authors present a methodology by analyzing the driving behavior of following vehicles using spectrum analysis. It is expected that by using this methodology, sustainable traffic management will be possible in the mixed scenario of autonomous vehicles and human drivers.

Some modifications are however needed to improve the paper.

1) What are CVs? The abbreviation is never explained in the text.

2) Figures quality is not good. Fig. 2 background can be chosen as transparent in Matlab figure options for better presentation.

3) The proposed technique is not compared with other algorithms such as HMM for comparative performance.

4) References are very few. Some recent references should be included. Many important works are missing. For example:

[1] Zou, Y., Zhu, T., Xie, Y., Zhang, Y., & Zhang, Y. (2022). Multivariate analysis of car-following behavior data using a coupled hidden Markov model. Transportation research part C: emerging technologies, 144, 103914.

[2]Colmenares, J. A. R., Uriarte, E. A., & del Campo, I. (2023). Driving-Style Assessment from a Motion Sickness Perspective Based on Machine Learning Techniques. Applied Sciences, 13(3), 1510.

[3]Du, Y., Chen, J., Zhao, C., Liu, C., Liao, F., & Chan, C. Y. (2022). Comfortable and energy-efficient speed control of autonomous vehicles on rough pavements using deep reinforcement learning. Transportation Research Part C: Emerging Technologies, 134, 103489.

 

Several typos are found in the paper. For example:

1) Page1. Line 41, 'withe' should be replaced by 'with'

2) Page4. Line 178, 12 's' for second should be in small letter.

3) Caption of Fig. 3 has extra ) on line 261.

 

Please improve the quality of English.

Author Response

• All authors appreciate the reviewer's professional review comments. Modified parts according to the reviewer's comments are highlighted in blue in the manuscript.

 

Point 1: What are CVs? The abbreviation is never explained in the text.

 

Response 1: Description of CVs was added in line 40.

 

 

Point 2: Figures quality is not good. Fig. 2 background can be chosen as transparent in Matlab figure options for better presentation.

 

Response 2: If the background of the figure is changed to transparent, it is difficult to distinguish it from the graph area, so the background is grayed out.

 

 

Point 3: The proposed technique is not compared with other algorithms such as HMM for comparative performance.

 

Response 3: The authors completely agree with the reviewer’s comment regarding the importance of highlighting the usefulness of this study through a comparison with existing studies. However, it should be noted that data from this study into existing models such as HMM (Hidden Markov Model) needs extensive data processing, which would take longer than 10 days allowed for paper revision. Therefore, a performance comparison with other algorithms was recommended as a topic for future research, as mentioned in the Conclusion section. [line 423-424]

 

 

Point 4: References are very few. Some recent references should be included. Many important works are missing.

 

Response 4: The authors are grateful for the valued recommendation to include important research relevant for this study. The recommended research cases were reviewed, and the findings were incorporated into the literature review section. [line 105-110]

 

Point 5: Several typos are found in the paper. For example:

1) Page1. Line 41, 'withe' should be replaced by 'with'

2) Page4. Line 178, 12 's' for second should be in small letter.

3) Caption of Fig. 3 has extra ) on line 261.

 

Response 5: All typos were corrected.

Reviewer 2 Report

Dear authors,

it was a pleasure to read your manuscript, which I find very interesting.

The topic and the methodology applied are up-to-date and I think the paper is suitable for publication in this journal. Nevertheless, I have some minor comments, that I would like to mention you:

1)      The abstract should be improved. Lines 11-14 are not clear. In line 16, since it has not been exactly defined the topic of the paper, it is not clear what you mean with “following vehicle” (it becomes clearer in the paper itself).

2)      Introduction: line 27 – crash à among motorized users. Please reference sentence at line 37-38. Line 41 “with” instead of “with the”. Line 42: abbreviation CV not defined. Lines 49-51: please, reference them. Line 58: “following vehicles” is here intended CVs?

3)      Literature review: Nice literature review, but I lack some references. E.g. at the end of lines 71, 73, 81.

4)      Methodology: in this section, methodology and results are mixed together. I suggest you to keep them separated and to rather create some sub-sections in the section results, which can address the results of the methodology, the validation results and the discussion. Lines 132-136: these sentences should be referenced. Line 138: personally I wouldn’t use the term “powerful”. Lines 142-143: please, mention the issues/limitations that should be considered, when using a 13-year-old set of data.

5)      Section 4.1. : lines 178-188 pay attention to the font.

6)      Section 4.2. : lines 203-204: if this sentence is referred to your case, please, be more specific.

Lines 237-243: this is a repetition. I think you can merge the information reported here and earlier.

7)      Section 4.4. : “DevelopmEnt”. Lines 292-293: please, define reaction time and stimulus compliance index and CRAI. Lines 299: please, define the symbols of the equations. 

8)      Results and discussion: as suggested, here there should be all the results, maybe divided in sub-sections. Figure 8: The columns “Increase Average travel speed”, “Increase Average relative speed”, “Decrease Average headway” are a bit confusing. Please, rename them or explain them better. Line 382: references are lacking here.

 

9)      Conclusions: this section should be improved. At this point, it is not at the level of the rest of the manuscript, which is quite well and clearly written.

 

I hope you will find my comments and suggestions useful. 

Best regards

Some minors typos are present, but overall the paper is clear and easy to read.

Author Response

• All authors appreciate the reviewer's professional review comments. Modified parts according to the reviewer's comments are highlighted in scarlet in the manuscript.

 

Point 1: The abstract should be improved. Lines 11-14 are not clear. In line 16, since it has not been exactly defined the topic of the paper, it is not clear what you mean with “following vehicle” (it becomes clearer in the paper itself).

 Response 1: The abstract was modified to make the background and purpose of the study clearer. [line 9-19]

 

Point 2: Introduction: line 27 – crash à among motorized users. Please reference sentence at line 37-38. Line 41 “with” instead of “with the”. Line 42: abbreviation CV not defined. Lines 49-51: please, reference them. Line 58: “following vehicles” is here intended CVs?

Response 2: All points noted have been corrected. [line 25, 35-37, 40]

CVs means conventional vehicles, and the following vehicles also fall under CVs.

 

Point 3: Literature review: Nice literature review, but I lack some references. E.g. at the end of lines 71, 73, 81.

 Response 3: References about fluid-dynamic model and cellular automata model were added to the thesis. [References 5, 6]

 

Point 4: Methodology: in this section, methodology and results are mixed together. I suggest you to keep them separated and to rather create some sub-sections in the section results, which can address the results of the methodology, the validation results and the discussion. Lines 132-136: these sentences should be referenced. Line 138: personally I wouldn’t use the term “powerful”. Lines 142-143: please, mention the issues/limitations that should be considered, when using a 13-year-old set of data.

Response 4:

ⅰ. The modified TTC and PSD calculation results included in the methodology are examples of application rather than research results on methodology. Therefore, it is judged that it is more appropriate to describe methodology and results sequentially rather than separating them.

ⅱ. A reference to the description contained in lines 136-137 is shown in Fig. 1 has been supplemented.

ⅲ. The term “powerful” was corrected to “useful”. [line 144]

ⅳ. The assumption and limitation of using old data was mentioned in Line 149-151.

- Despite 13-year gap since the data collection period, the findings of this study are applied with the assumption that driver behavior is closely linked to human nature and is not expected to change significantly over time.

 

Point 5: Section 4.1. : lines 178-188 pay attention to the font.

 Response 5: The font was corrected.

 

Point 6: Section 4.2. : lines 203-204: if this sentence is referred to your case, please, be more specific. Lines 237-243: this is a repetition. I think you can merge the information reported here and earlier.

Response 6: In this study, the discrete Fourier transform was applied to apply Fourier transform to computer-based analysis, and it was not the result developed in this study.

 

Point 7: Section 4.4. : “DevelopmEnt”. Lines 292-293: please, define reaction time and stimulus compliance index and CRAI. Lines 299: please, define the symbols of the equations.

 Response 7: The contents of lines 237-243 have been modified to be included in Section 4.3.

 

Point 8: Results and discussion: as suggested, here there should be all the results, maybe divided in sub-sections. Figure 8: The columns “Increase Average travel speed”, “Increase Average relative speed”, “Decrease Average headway” are a bit confusing. Please, rename them or explain them better. Line 382: references are lacking here.

Response 8: Since the results of the study are included in Section 6. Conclusion, the title of Section 5 has been modified to “Validation and discussion” .

Fig 8. was corrected.

The description of Fig. 8 has been modified.

 

Point 9: Conclusions: this section should be improved. At this point, it is not at the level of the rest of the manuscript, which is quite well and clearly written.

Response 9: The purpose, methodology, and research results were supplemented in the conclusion section. [line 400-410]

 

Reviewer 3 Report

Overall:

This is an interesting, novel analysis of real-world car-following behavior from a 2010 dataset, with the computation and validation of a new, spectrum-based measure assessing risk. The main issues for me are:

1.       It was unclear, based on the Introduction, that the focus would be on a single metric (CRAI), and that most of the computational work was leading toward that metric’s development and validation. Describing the measure earlier in the paper (potentially including Figure 4 earlier) would help me understand the flow of the paper better.

2.       It’s unclear to me that CRAI offers much benefit beyond TTC or adjusted TTC. While it’s clear to me, from Fig. 7, that in situations where SCI and RT are controlled for, that differences in CRAI can be associated with safety-relevant distances (i.e., too short headway), it’s unclear to me if that is true when TTC or adjusted TTC are controlled for. If there isn’t a contribution to understanding these scenarios beyond TTC, is that a problem for the new measure? I think the paper can be accepted either way (the measure is interesting and other researchers will likely find use in this approach) but it's unclear to me, as a reader, if I should use this measure or TTC / adjusted TTC.

Specific comments:

Lines 179-180: Do you mean “underestimated,” if you’re referring to the large positive spikes in the unadjusted TTC curve?

Figure 3: It would be useful to include in the text how you’re defining the ratio measure for PSD. Presumably it’s the ratio of the spectrum of interest (e.g., <= .05 Hz) to the entire spectrum, but that isn’t clear to me. This is especially important because it’s the basis for your correlational analyses. But regarding the figure, it would suggest that, given the slopes of the ratio measures appear weaker than the power sum measures, that there is just a lot more energy overall in the PSD for the short TTC conditions—do you have an explanation for this?

280-288: I don’t know if it’s accurate to say that the lowest frequency component is the one most strongly associated with collision risk—in fact, it’s positively correlated with lower risk (higher adjusted TTC), whereas the other components, although showing weaker correlations, are negatively correlated with lower risk (higher adjusted TTC). This would suggest that the energy in those higher frequency components is being contributed by following car maneuvers that do occur at closer TTCs (perhaps in stop-and-go traffic or aggressive car following), whereas the energy in the low frequency component is related, potentially, to healthier, safer car following behavior. I do wonder if there is any value in the other components of the spectrum (i.e., higher frequency components)—perhaps a spectrogram (frequency power over time across the spectrum) would be helpful to plot against certain scenarios?

Equation 9: Isn’t this the same as the ratio score for the low harmonics? (i.e., the top row in Table 1?) Is there a reason you didn’t overlap the waveforms, based on the optimal time T for computing the SCI, and take the average difference in velocity (as Figure 4 suggested to me that you would)? Otherwise, this makes sense, as it’s the measure found in the earlier part that strongly correlates with a positive TTC (although you could have substituted TTC or adjusted TTC, and I’m not sure why). If the paper were re-framed so that it was specifically about this new measure, which is really only being defined as “CRAI” here, it would have been easier to anticipate this section.

Author Response

• All authors appreciate the reviewer's professional review comments. Modified parts according to the reviewer's comments are highlighted in green in the manuscript.

 

Point 1: It was unclear, based on the Introduction, that the focus would be on a single metric (CRAI), and that most of the computational work was leading toward that metric’s development and validation. Describing the measure earlier in the paper (potentially including Figure 4 earlier) would help me understand the flow of the paper better.

 Response 1: A description of the three driving-pattern indices developed through this study was added to section 3 methodology with re-positioning of Figure 4.

 

Point 2: It’s unclear to me that CRAI offers much benefit beyond TTC or adjusted TTC. While it’s clear to me, from Fig. 7, that in situations where SCI and RT are controlled for, that differences in CRAI can be associated with safety-relevant distances (i.e., too short headway), it’s unclear to me if that is true when TTC or adjusted TTC are controlled for. If there isn’t a contribution to understanding these scenarios beyond TTC, is that a problem for the new measure? I think the paper can be accepted either way (the measure is interesting and other researchers will likely find use in this approach) but it's unclear to me, as a reader, if I should use this measure or TTC / adjusted TTC.

Response 2: he authors deeply appreciate the insightful comment provided by reviewer 3, as it forms the crux of this study. The modified TTC proposed in this study serves as an indicator for assessing the collision risk between two vehicles in a car-following situation.

However, it is important to note that the modified TTC discretely calculates the expected collision time between the two vehicles in one-second intervals, focusing on the risk at a specific point in time. It does not include information on the driving behavior of the following vehicle.

On the other hand, CRAI analyzes the response characteristics of the following vehicle to the stimulus of the leading vehicle using wave analysis. It includes information on driving behavior, providing the advantage of identifying potential collision risks.

 

Point 3: Lines 179-180: Do you mean “underestimated,” if you’re referring to the large positive spikes in the unadjusted TTC curve?

Response 3: The term “overestimated” was corrected into “underestimated” . [line 197]

 

Point 4: Figure 3: It would be useful to include in the text how you’re defining the ratio measure for PSD. Presumably it’s the ratio of the spectrum of interest (e.g., <= .05 Hz) to the entire spectrum, but that isn’t clear to me. This is especially important because it’s the basis for your correlational analyses. But regarding the figure, it would suggest that, given the slopes of the ratio measures appear weaker than the power sum measures, that there is just a lot more energy overall in the PSD for the short TTC conditions—do you have an explanation for this?

Response 4: Both the case of frequency above and below 0.05 HZ are found to have a negative correlation with the modified TTC in the case of PSD sum, which indicates a consistent relationship regardless of the frequency domain. On the other hand, in the case of the PSD ratio, frequencies below 0.05Hz show a positive correlation, while frequencies equal to or above 0.05 indicates a negative correlation, indicating a difference in correlation within specific frequency ranges. Based on these characteristics, it has been determined that the PSD ratio is a more suitable indicator for interpreting the risk of collision.

 

Point 5: 280-288: I don’t know if it’s accurate to say that the lowest frequency component is the one most strongly associated with collision risk—in fact, it’s positively correlated with lower risk (higher adjusted TTC), whereas the other components, although showing weaker correlations, are negatively correlated with lower risk (higher adjusted TTC). This would suggest that the energy in those higher frequency components is being contributed by following car maneuvers that do occur at closer TTCs (perhaps in stop-and-go traffic or aggressive car following), whereas the energy in the low frequency component is related, potentially, to healthier, safer car following behavior. I do wonder if there is any value in the other components of the spectrum (i.e., higher frequency components)—perhaps a spectrogram (frequency power over time across the spectrum) would be helpful to plot against certain scenarios?

Response 5: The correlation analysis shows a positive correlation between frequency components below 0.017 Hz and the modified TTC. This implies that as PSD ratio below 0.017 Hz increases, the modified TTC also increases, indicating a reduced risk of collision. Based on these findings, the PSD ratio of the low-frequency components was designated as an indicator to describe collision risk aversion feature. As shown in Figure 7, a smaller CRAI value corresponds to a higher risk of collision. Thus, the relationship between the PSD ratio of low-frequency components and the risk of collision is inversely proportional. This has been added in the paper to avoid confusion for readers [line 295- 296]. Even though reader might think that higher frequency components are directly related to crash risk, the higher frequency components were not set as indicators because the p-value in the correlation analysis was smaller than that of lower frequencies.

 

Point 6: Equation 9: Isn’t this the same as the ratio score for the low harmonics? (i.e., the top row in Table 1?) Is there a reason you didn’t overlap the waveforms, based on the optimal time T for computing the SCI, and take the average difference in velocity (as Figure 4 suggested to me that you would)? Otherwise, this makes sense, as it’s the measure found in the earlier part that strongly correlates with a positive TTC (although you could have substituted TTC or adjusted TTC, and I’m not sure why). If the paper were re-framed so that it was specifically about this new measure, which is really only being defined as “CRAI” here, it would have been easier to anticipate this section.

Response 6: The equation 9 calculates the ratio of the sum of the PSDs below 0.017 Hz and the top row in Table 1 shows the correlation coefficient between PSD ratio below 0.017 Hz and modified TTC.

The reaction time and stimulus compliance index are indicators that provide insight into driving behavior at a specific time t. On the other hand, CRAI is calculated by transforming the domain from time to frequency using Fourier transform. Due to the distinct domains of these indicators, it was not possible to assemble them directly into a single indicator. That is why driving pattern indices were suggested individually in this study.

 

Round 2

Reviewer 1 Report

The revised version of the manuscript is sufficiently improved and necessaery references and details have been added as per the reviewer's guidelines.

Author Response

Point 1: The revised version of the manuscript is sufficiently improved and necessary references and details have been added as per the reviewer's guidelines.

 

Response 1: Thank you for your review.

Author Response File: Author Response.docx