Dynamic Disturbance Propagation Model of Pedestrian Panic Behaviors and Lyapunov-Based Crowd Stability Analysis
Round 1
Reviewer 1 Report
The study aims to model and simulate panic situations, yet it relies on data collected from the waiting hall of Shanghai Hongqiao Railway Station, which represents a normal case. This choice raises concerns about the authors' familiarity with the subject literature. Upon further examination of the article, it becomes apparent that the literature review is lacking in depth, potentially contributing to the authors' limited understanding of the study's subject matter. While the authors demonstrate familiarity with modeling principles, their research appears to lack a solid foundation, leading to inadequate consideration of certain essential principles. Consequently, the reliability of their results comes into question.
Author Response
Re: Response to reviewer 1
To: Applied Science
Manuscript ID: applsci-2645058.R1
Original Article Title: “Dynamic disturbance model of pedestrian panic behaviors and Lyapunov-based crowd stability analysis”
Dear editor and reviewer 1，
Thank you for allowing a resubmission of our manuscript, with an opportunity to address the reviewer 1’s comments on our manuscript ID applsci-2645058.
We upload :(a) the point-by-point responses to the reviewer comments below, (b) an updated manuscript with red highlighting changes (PDF main document).
Thank you very much for your kind consideration!
Best regards,
Rongyong Zhao
PhD. Asso.Prof.
CIMS research center, Tongji University, Shanghai, China
Response to Reviewer 1
Comment 1
Literature review is lacking in depth, potentially contributing to the authors' limited understanding of the study's subject matter.
Author Response: Thank you for the professional comment on this paper. We agree that a reconstruction of introduction can make this paper more readable.
To improve the depth of this study, we reconstructed the section of “1. Introduction” after reviewing more high-quality references, as follows,
“Scientific management of crowd-gathering scenarios are significant issues regarding public safety. Using physics, transportation, and mathematical tools to describe the characteristics of a crowd flow, crowd flow dynamics has been well-known aca-demic hotspot for several decades . It comprises the processes of establishing a mathematical model of a crowd flow and then carrying out numerical simulations and solving.
There were some similarities between crowd flows and continuous fluids. Since Swiss mathematician and mechanics scientist Euler proposed a classical assumption for fluid continuity [1], the irregular thermal motion of molecules in a fluid were simplified as the regular motion of the molecules; i.e., the fluid was considered as a continuous medium. Then fluids was mainly studied based on a macro-mechanical motion theory of a continuous medium.
In general, a crowd flow consists of pedestrians, with physical gaps between them. From a micro point of view, crowd flows are not continuously distributed, but if the distance between pedestrians and the surrounding environment is defined as a pedestrian area, it is feasible to assume a crowd flow as a continuous pedestrian fluid. Therefore, like the continuum hypothesis in fluid dynamics, the macroscopic quantities of crowd flows are the velocities, densities, and flows, which also conform to the physical laws of mass conservation, momentum conservation, and energy conservation. Henderson first proposed a macroscopic model for pedestrian flow [2,3]..
Literatures showed that the distribution functions for crowd densities and velocities were consistent with the results from the Maxwell-Boltzmann theory, except for significant deviations near the frequency mode of each distribution [3].”
Besides, the new literatures were referred to improve this manuscript as,
[R1] A. B. Mabrouk ;E. Zagrouba. Abnormal behavior recognition for intelligent video surveillance systems: A review,” Expert Syst. Appl. 2018, vol. 91. pp. 480–491.
[R2] R.Y.Zhao;D.H.Dong;Y.Wang;C.L.Li;Y.L. Ma;M.Y. Li; V.F.Enríquez. Image-Based Crowd Stability Analysis Using Improved Multi-Column Convolutional Neural Network[J]. IEEE Transactions on Intelligent Transportation Systems. 2022,vol.23(6),pp.5480-55489.
[R3] A. Balasundaram ; C. Chellappan, An intelligent video analytics model for abnormal event detection in online surveillance video,” J. Real-Time Image Process., vol. 17( 4), pp. 915–930.
[R4] R. Zhao; D.Wang;Y. Wang; C.F. Han;P. Jia;C.L. Li; Y.L. Ma. Macroscopic view: Crowd evacuation dynamics at T-shaped street junctions using a modified Aw-Rascle traffic flow model. IEEE Trans. Intell. Transp. Syst., vol. 22( 10), pp. 6612–6621.
Author action: We update this manuscript with reconstructions [lines 28-49].
Comment 2
While the authors demonstrate familiarity with modeling principles, their research appears to lack a solid foundation, leading to inadequate consideration of certain essential principles.
Author Response: Thank you for this professional comment. We agree it is important to clarify a logic foundation of this study as,
“In real pedestrian-gathering scenarios, the panic behavior characteristics of crowd flows were relatively complex. Due to the subjective initiatives of the crowds and ex-ternal environments, once internal panic disturbances due to emergencies such as pedestrian falls, stampedes, shootings, terrorist attacks, explosions, fires, etc. occur, the stop-and-go phenomena of crowds can cause a chaotic phenomenon of the sudden acceleration and deceleration of pedestrians. In this context, more complex crowd trampling and other accidents often easily occur [5].
It was significant to keep a pedestrian crowd stable considering that a large-scale crowd (including more than 2000 pedestrians) system consisted of a large number of autonomous individual pedestrians, movement rules, and the scene environment [6]. As a continuous flow, a large-scale crowd flow also had three typical system states: stability, critical stability, and instability.
Large-scale crowd trample disasters were typical phenomena of crowd instability owing to internal disturbances. Most existing literatures about crowd stability were based on traffic flow theory and lacked systematic consideration. Owing to the panic characteristics of pedestrian self-organization behaviors and crowd merging flow layouts, they were more complex in crowd flows. While, few studies helped conduct on the propagation characteristics of sudden panic disturbances in crowd flows, which motivate us to study this issue further.
The main contributions of this study are: (1) we proposed a dynamic disturbance model of crowd panic behaviors, considering the anisotropy of crowd movements based on the conservation law of fluid dynamics. (2) the anisotropy property of the disturb-ance propagation was proved with theoretical derivations and simulation experiments. (3) a crowd stability criterion was put forward under internal disturbances based on the Lyapunov theory.”
Author action: We update this manuscript with solid logic and academic contribution descriptions [lines 61-85].
Comment 3
The reliabilityof their results comes into question.
Author Response: Thank you for the comment on the experiment results. We response this comment as follows,
1) To investigate the topic of “Dynamic disturbance propagation model of pedestrian panic behaviors”, this paper mainly focuses theoretical novelties and simulation experiment methods. Thereby, “the main contributions of this study are: (1) we proposed a dynamic disturbance model of crowd panic behaviors, considering the anisotropy of crowd movements based on the conservation law of fluid dynamics. (2) the anisotropy property of the disturbance propagation was proved with theoretical derivations and simulation experiments. (3) a crowd stability criterion was put forward under internal disturbances based on the Lyapunov theory.”
2) In fact, it does not affect the correctness of the theoretical model proposed in the previous verification, as long as the initialization settings of the simulation experimental data are consistent with the actual situation, and the assumptions and change logic are reasonable.
3) The reliability of experimental data can be continuously improved by increasing the measurement of actual data to correct existing experiments and theoretical models, as description of future work as,
“Further work on model calibration based on measured data, with more complex scenarios are suggested to be conducted, which can support more pedestrian flow control in the public places.”
Author action: We update this manuscript with new descriptions [lines 80-85, lines 541-543].
Author Response File: 
Author Response.pdf
Reviewer 2 Report
References [12,13,38] are lost; they are not in the paper.
Lines 102, 104. “FruiT” -> FruiN
Line 104. Reference [8] is a reference on Helbing, not Fruin. It is necessary a reference on Fruin here.
Line 410. “According to the literature, assuming that the pedestrian walking acceleration range is …”. It is necessary some references after “According to the literature”
Line 512. It is not clear from the paper, how a direction of flow affects panic disturbance pressure in a crowd.
Author Response
Re: Response to reviewer 2
To: Applied Science
Manuscript ID: applsci-2645058.R1
Original Article Title: “Dynamic disturbance model of pedestrian panic behaviors and Lyapunov-based crowd stability analysis”
Dear editor and reviewer 2，
Thank you for allowing a resubmission of our manuscript, with an opportunity to address the reviewer 2’s comments on our manuscript ID applsci-2645058.
We upload :(a) the point-by-point responses to the reviewer comments below, (b) an updated manuscript with red text indicating changes (PDF main document).
Thank you very much for your kind consideration!
Best regards,
Rongyong Zhao
PhD. Asso.Prof.
CIMS research center, Tongji University, Shanghai, China
Response to Reviewer 2
Comment 1
References [12,13,38] are lost; they are not in the paper.
Author Response: We are sorry for this mistake caused by citation-missing. We cite them as follows,
“W. Qin [12] constructed a distributed parameter system to describe the disturbed crowd dynamics based on the conservation law of mass. Unit sliding mode control was used to eliminate disturbances and stabilize the crowd dynamic system to a reference density; J. Wei [13] improved the social force model by introducing disturbance fluctuation force, to characterize the disturbance fluctuation of pedestrian flow caused by the disturbance during evacuation and the state change of pedestrian flow.”
“Based on the three experiments above, we can find that the propagation of the crowd disturbance pressure and changes in crowd stability is based the wave theory, consistent with the indications in references [10,36,37] , i.e., that any disturbance in the crowd will propagate in the form of a wave. Therefore, the panic disturbance pressure in a crowd would be enlarged then the pedestrian flow direction was consistent with the current panic disturbance pressure, and vice versa.”
Author action: We update this manuscript with necessary citation of these three references in the text [lines 117-123, lines 500-505].
Comment 2
Lines 102, 104. “FruiT” -> FruiN
Author Response: Thank you for this careful checking! We correct it as follows,
“ For example, in order to investigate the causes of crowd disasters and to propose preven-tive measures and possible methods for mitigating disasters. J. J. Fruin stated that turbulent waves were experienced in dozens of crowd-intensive events each year all over the world [7]. Once a pedestrian was able to pass the narrowing, pedestrians with the same walking direction can easily follow. Hence, the number and “pressure” of waiting, “pushy” pedestrians on one side of the bottleneck becomes less than on the other side [8].”
Author action: We update this manuscript with correction [lines 104-108].
Comment 3
Line 104. Reference [8] is a reference on Helbing, not Fruin. It is necessary a reference on Fruin here.
Author Response: We are sorry for this citation missing! Exactly, we update it with a necessary reference as follows,
“J. J. Fruin stated that turbulent waves were experienced in dozens of crowd-intensive events each year all over the world [7]. “
[7] J. J. Fruin, in R. A. Smith and J. F. Dickie (eds.) Engineering for Crowd Safety, (Elsevier, Amsterdam, 1993), pp. 99–108.”
Author action: We update this manuscript with related reference [lines 104-105,563].
Comment 4
“According to the literature, assuming that the pedestrian walking acceleration range is …”. It is necessary some references after “According to the literature”
Author Response: Thank you for this kind suggestion. We agree that related literature should be cited to support this assumption as follows,
“According to the reference [37], assuming that the pedestrian walking acceleration range is …”.
Author action: We update this manuscript with a supporting literature [lines 424-425].
Comment 5
It is not clear from the paper, how a direction of flow affects panic disturbance pressure in a crowd.
Author Response: Thank you for this professional comment. Actually, there should be a necessary description about how the direction of flow affects panic disturbance pressure in a pedestrian crowd. We explain this point as follows,
In the section of related work, a literature explained this point as
“ W. Qin [25] established a cold dynamics model based on a conservation law, and the relationship between density and speed was expressed using a diffusion model. The feedback linearization method of a partial differential equation was used to design a feedback controller for controlling crowd stability so that pedestrians could evacuate in a certain direction and at a fixed speed.”
In the section of “4.2. Stability analysis of crowd flow with internal disturbances”, we explained that according to the Eq.s (36) and (37), the acceleration direction of a crowd could affect the disturbance pressure as,
“Assuming that in Fig. 2, is the slope of the wavefront at position P. The solution of the Bernoulli equation is . Therefore, the Bernoulli equation can show the evolution of the wavefront slope. In the case of a disturbance, generally, the crowd density increases sharply and the crowd velocity decreases sharply , and , , so the stable range is . Then, we can determine as follows:
In the above, "-" indicates the direction, and is the relaxation factor. Let . is the critical acceleration function, and is related to the disturbance pressure in the crowd.”
In the section of “5 Experiment and Discussion” we explain this point further as,
“Based on the three experiments above, we can find that the propagation of the crowd disturbance pressure and changes in crowd stability is based on the wave theory, consistent with the indications in references [10,36,37] , i.e., that any disturbance in the crowd would propagate in the form of a wave. Therefore, the panic disturbance pressure in a crowd would be enlarged then the pedestrian flow direction was consistent with the current panic disturbance pressure, and vice versa.”
Author action: We explain this point and update this manuscript with additional and red-highlighted descriptions [lines 167-172,500-505].
Author Response File: Author Response.pdf
Reviewer 3 Report
In this article, the authors propose a dynamic disturbance model of crowd panic behaviors, considering the anisotropy of crowd movements based on the conservation law of fluid dynamics.
However, I will comment on some aspects and the changes must be highlighted:
- Section, Figure, Table, Algorithm and Equation must be written with the first capital letter.
- The acronyms are misspelled. The correct way is to write the meaning of the acronym with its first capital letter, for example, "Force, Information, Space, Time" (FIST)". It is an error that must be corrected in all the acronyms in the document.
- Figure 1 does not have significant value for this investigation since something needs to be demonstrated.
- Authors must not use Phrasal Verbs in a scientific article.
- Is the data synthetic or real? And where have they based themselves to obtain the data?
- Why was the total number of step simulations 500?
- In Line 408, it is a bibliographic citation and must not be in superscript.
- The Figures must be larger to be observed in greater detail.
- The authors must improve the conclusions and add future work.
In this article, the authors propose a dynamic disturbance model of crowd panic behaviors, considering the anisotropy of crowd movements based on the conservation law of fluid dynamics.
However, I will comment on some aspects and the changes must be highlighted:
- Section, Figure, Table, Algorithm and Equation must be written with the first capital letter.
- The acronyms are misspelled. The correct way is to write the meaning of the acronym with its first capital letter, for example, "Force, Information, Space, Time" (FIST)". It is an error that must be corrected in all the acronyms in the document.
- Figure 1 does not have significant value for this investigation since something needs to be demonstrated.
- Authors must not use Phrasal Verbs in a scientific article.
- Is the data synthetic or real? And where have they based themselves to obtain the data?
- Why was the total number of step simulations 500?
- In Line 408, it is a bibliographic citation and must not be in superscript.
- The Figures must be larger to be observed in greater detail.
- The authors must improve the conclusions and add future work.
Author Response
Re: Response to reviewer 3
To: Applied Science
Manuscript ID: applsci-2645058.R1
Original Article Title: “Dynamic disturbance model of pedestrian panic behaviors and Lyapunov-based crowd stability analysis”
Dear editor and reviewer 3，
Thank you for allowing a resubmission of our manuscript, with an opportunity to address the reviewer 3’s comments on our manuscript ID applsci-2645058.
We upload :(a) the point-by-point responses to the reviewer comments below, (b) an updated manuscript with red text indicating changes (PDF main document).
Thank you very much for your kind consideration!
Best regards,
Rongyong Zhao
PhD. Asso.Prof.
CIMS research center, Tongji University, Shanghai, China
1 Response to Reviewer 3
Comment 1
Section, Figure, Table, Algorithm and Equation must be written with the first capital letter.
Author Response: Thank you for the professional suggestion. We agree that Section, Figure, Table, Algorithm and Equation must be written with the first capital letter. All the correction were conducted, typically as follows,
“2.1. Internal Disturbances of Drowd Panic Behaviors
3.1. Dynamic Model of Internal Crowd Disturbance
4.1. Lyapunov-based Crowd Stability Analysis
5.1. Numerical Simulation for Dynamic Model of Disturbance Propagation in a Crowd”
“It can be concluded from Equation(30) that , which is substituted into Equations (31) and (33) to obtain the Bernoulli equation,”
“The total number of simulation steps was 500. The characteristics of the propagation of the disturbance pressure in the crowd when the simulation step was 150 are shown in Figure 3.”
Author action: We update this manuscript with necessary capital letters [lines 92,225,319,383, 366-368].
Comment 2
The acronyms are misspelled. The correct way is to write the meaning of the acronym with its first capital letter, for example, "Force, Information, Space, Time" (FIST)". It is an error that must be corrected in all the acronyms in the document.
Author Response: Thank you for this check of acronyms. We checked all acronyms through the manuscript again, and corrected them in this revised version.
Author action: We update this manuscript with acronym corrections.
Comment 3
Figure 1 does not have significant value for this investigation since something needs to be demonstrated.
Author Response: Thank you for this comment on Figure 1. Actually, we should supplement some necessary explanation for this figure. It is useful to demonstrate the 2D and 3D distribution of a disturbance at a given moment, as new description as,
“To construct the dynamic model of a disturbance caused by an abnormal behavior in a pedestrian crowd, we assume that the disturbance burst point is , then the crowd pressure at this point is the largest, and the crowd pressure around it decays exponentially in the form of e, with same character of a Gaussian distribution in Figure 1. This result showed a single disturbance without damping from the neighboring pedestrians. Therefore, under the influence of random disturbances in the crowd, an equivalent pressure at ,”
In order to make this paper more readable, we take this figure as demonstrating result of a single disturbance without damping from the neighboring pedestrians in 3D space, then showed the simulation experiments with damping from the neighboring pedestrians, e.g. , the Figures 9,10, and 11 in the following section-“5. Experiments and Discussion”.
Author action: We update this manuscript with additional explanations about the value of Figure 1[lines 254-260].
Comment 4
Authors must not use Phrasal Verbs in a scientific article.
Author Response: Thank you for this professional suggestion. We checked this problem through the manuscript with necessary corrections, e.g. substituted with one-word alternatives.
Author action: We update this manuscript with necessary corrections.
Comment 5
Is the data synthetic or real? And where have they based themselves to obtain the data?
Author Response: Thank you for these questions. Actually, we supplemented it as follows,
“Some scenario data was from the waiting hall of Shanghai Hongqiao Railway Station. The simulated scenario was a 40 × 40 m rectangular area. It was assumed that the internal disturbance position was (11,11) and that a sudden disturbance occurred when the simulation step was step = 310, i.e., time t = 3.09 min. Special restrictions on the directions of crowd movements were not mentioned in the following experiments. “Experiment data was synthetic as,
“Experiment 1: The initial density of crowd was set as , and the disturbance pressure ; the propagation of the disturbance pressure and the probability distribution of the crowd flow instability are shown in Figure 9. The Z-axis represents the crowd pressure, and the graph color represents the probability of crowd instability.
Experiment 2: The initial density of the crowd was still and disturbance pressure increased to . The propagation of the disturbance pressure and probability distribution of the crowd flow instability are shown in Figure 10.
Experiment 3: The initial density of the crowd was increased to , and the disturbance pressure was still . The propagation of disturbance pressure and probability distribution of the crowd flow instability are shown in Figure 11.”
Author action: We update this manuscript with additional descriptions [lines 484-499].
Comment 6
Why was the total number of step simulations 500?
Author Response: Thank you for this professional question. We should describe the stopping condition of simulation experiments clearly as follows,
“The simulation stopped when the pressure of observation point P reached to the maximum value of 7, indicating with yellow color, at the step=150. The specific characteristics of the propagation of the disturbance pressure were shown in Figure 3.”
Author action: We update the manuscript with a clear description [lines 395-397].
Comment 7
In Line 408, it is a bibliographic citation and must not be in superscript.
Author Response: Thank you for this professional correction. We check and correct this mistake through the text, for an example as
“It is worth noting that the value of the critical stability function in the criterion should vary with the duration of the disturbance and distance from the disturbance center [35,36].”
Author action: We update the manuscript with bibliographic citation corrections description [lines 420-422].
Comment 8
The Figures must be larger to be observed in greater detail.
Author Response: Thank you for this kind suggestion. We check and enlarge all the small Figures in this revised version.
Author action: We update the manuscript with lager figures, e.g., Figures 10,11.
Comment 9
The authors must improve the conclusions and add future work.
Author Response: Thank you for this professional suggestion! We improve the section of conclusions and future work as,
“In this study, a dynamic disturbance model of crowd panic behaviors was proposed based on fluid dynamics to investigate the disturbance dynamics of pedestrian panic behaviors quantitatively. Further, the anisotropy property of this model was proven to keep consistent with ground truth of real pedestrian movement.
In addition, based on the Lyapunov stability theory, a criterion of crowd stability for sudden internal disturbances was proposed; Experiment results in Hongqiao railway station showed that the equivalent pressure was related to the pedestrian density, du-ration of the disturbance, and distance from the center of the disturbance. In the Lyapunov-based crowd stability analysis, two main conclusions were drawn out:
(1) The dynamic propagation of panic disturbance pressure in a crowd was mainly affected by the density, direction of flow, and obstacles, indicating the heterogeneous characteristics of the propagation.
(2) Regardless of the limitations on crowd movement directions, the dynamic disturbance of crowd behaviors changed in crowd stability revealing the characteristics of wave diffusion.
Further study on model calibration based on measured data, with more complex scenarios are suggested to be conducted, which can support more pedestrian flow control in the public places.”
Author action: We update the manuscript with reconstructed section of “6. Conclusions and Future Work” [lines 526-543].
Author Response File: Author Response.pdf
Round 2
Reviewer 1 Report
The manuscript has been significantly improved.
Reviewer 3 Report
Thank you for performing the changes suggested by the reviewers. Before publication, a minor English spelling is recommended.
Thank you for performing the changes suggested by the reviewers. Before publication, a minor English spelling is recommended.
