Sensitivity Analysis for Pedestrian-Induced Vibration in Footbridges

Round 1

Reviewer 1 Report

The paper is interesting since global and local sensitivity analyses have been carried out by the authors to determine what parameters of the structure and the pedestrians influence the dynamic response of footbridges. Some details should be revised and some issues must be addressed and I recommend it to be published after suitable revision.

1. The numbers of the sections within the text are not properly defined (Section 0).

2. The numbers of the figures within the document are not properly defined (Error! Reference source not found).

3. In the abstract, the sentence “The damping ratio and natural frequency of human body are found to be the only two insensitive parameters” may not be true for lightweight pedestrian structures susceptible to human-structure interaction phenomenon. Hence, the idea “Therefore, they could be treated as deterministic parameters in stochastic estimation of human-induced vibration” could be misleading. The authors should specify the scenarios (footbridge natural frequency, pedestrian density, pedestrian-to-structure mass ratio, etc.) in which both statements are valid.

4. It may be worthwhile to comment more models that account for HSI besides the mass-damper-spring systems in the Introduction. Also, the term “modal mass” should be clearly defined. Technically, a modal mass is a quantity that depends on the mode shape scale and, thus, it has no direct physical meaning.

5. In Section 3, page 6, a graphic representation of the approach (including the considered variables of the structure and the pedestrians) should be added.

6. In Section 4, page 7, authors should justify the selection of the simply supported beam footbridge of span 50 m as a representative example as it is known that this type of bridge is often used for short spans.

7. A representative result (e.g. mean MTVV of the 10 000 cases or the 95th percentile of the response acceleration of the 10 000 cases) is needed to realize about the levels of vibrations in each performed analysis in Section 4 and Section 5.

8. As the representative structure is heavyweight, why the deterministic loads models in existing guidelines (SETRA, HIVOSS) are not used to predict the dynamic response? It would be interested to compare the predictions (MTVV or response acceleration) from the guidelines and the representative results from the 10,000 simulations, at least for some cases.

9. In Section 6, a summary table of the results of the LSA and GSA performed throughout the document would improve the paper readability.

10. In page 17, the statement about the TMD is just applicable for the heavyweight structures proposed as an example. This is not completely true for lightweight slender pedestrian structures, so authors should mention this fact. Also, the readability of the whole paragraph should be improved.

11. In page 18, the following sentences should be revised:

“… the impact of uncertainties in system…”

“… a representative bridge to two load cases…”

12. The same comment mentioned for the abstract should be addressed in the conclusions.

13. The sentence: "...explains why there are inconsistent results in existing literature..." is not clear. What are the sources of this inconsistency? Authors should provide a better explanation. 

Author Response

Please see the attachment.

Author Response File: Author Response.pdf

Reviewer 2 Report

The paper concerns the problem of sensitivity analysis for pedestrian-excited vibration in footbridges. The manuscript is well organised and discussed. The content is clearly presented. However, some editorial errors cannot be accepted:

1. Everywhere in the text not existing “Section 0” is referred;
2. The lines in the text are not numbered (it is difficult to explain the proper location of the reviewer’s comments);
3. In many places a sentence “Error! Reference source not found” occurs (instead of the Figure number).

Above listed errors cause difficulties in verification of the text and proper reviewing. From the editorial point of view, the text must be improved. Nevertheless, the topic is attractive and the article was verified by the reviewer with interest.

General comments:

1. Many self-citations on the reference list were detected. These articles are obviously valuable, however it is proposed to decrease the number of self-citations and refer also to other works, especially from MDPI base. Here are some recent studies:

- FRP footbridges topic: https://www.mdpi.com/2076-3417/11/14/6654

- Damping topic: https://www.mdpi.com/2073-4360/13/13/2201

- Vibration serviceability topic: https://www.mdpi.com/1996-1944/15/4/1529

- Human-structure interaction topic: https://www.mdpi.com/2076-3417/11/4/1355

- Ground reaction forces topic: https://www.mdpi.com/2076-3417/10/5/1575

- Experimental campaigns topic: https://www.mdpi.com/2076-3417/10/13/4505

2. In Section 4, the representative footbridge is very briefly described. However, the technical drawing is missing. Moreover, from the further part of the text it can be deduced only, that the structure is a FRP footbridge. The reviewer would like to confirm this assumption. The information about the structural material, cross-section of the footbridge should be mentioned in the article.
3. In point 4.1, the characteristics of the footbridge are defined. Are these values defined theoretically only or they refer to the real / designed structure case?
4. The reviewer would like to ask, why the step frequency of exactly 2.0 Hz was defined in Table 2 and further analyses, as it is slightly different from the mean value of a walking pedestrian?
5. Some of conclusions are rather intuitive and obvious (e.g. sensitivity to the modal mass, natural frequency and damping ratio of the bridge). However, the problem was analysed in details, with great scientific attention. Conclusions are important and supported by the results.

In the opinion of the reviewer the paper can be considered for publication after appropriate corrections.

Author Response

Please see the attachment.

Author Response File: Author Response.pdf

Reviewer 3 Report

This is an interesting study into sensitivity analysis of pedestrians under the effect of footbridges forces. Two methods including Sobol’-based global sensitivity and local sensitivity analysis have been utilized for stochastic analysis to consider the effect of uncertainties associated with input parameters on the vibration response of footbridges. From the reviewer's point of view, the manuscript in its presented form needs major revision to make it ready for publication. However, its content is well prepared and it is expected that the following comments help further the authors to improve the quality of the manuscript. My comments are as follows:

• In Page 2, two references [9, 10] are provided for probability-based human-induced vibration estimation in
  More recent research studies have been carried out so far, which need to be mentioned in the introduction.
• In many places, the authors refer to “Section 0” that is not exist. Also, the authors refer to a figure, section, or a reference in which an error “Error! Reference source not found.” is displayed instead, which indicates that the authors did not check these items before submitting the PDF. Please read carefully the manuscript again and try to fix all the mentioned cases.
• In Section 4, the number of people in a crowd is set to be 150. Why this input parameter is considered deterministic? If this parameter is considered probabilistic, what effect is it expected to have on the results? Please comment.
• How is it possible to see a 150% COV of vibration response by considering a maximum 20% COV in the input parameters according to table 2 (see Figure 3)? Does this make sense? Please clarify.
• The authors assume that most of the input parameters are all normally distributed (Table 2), but they do not check the validity of this assumption. This being the case, what is the effect of the probability distribution function type (as an example Log-normal distribution instead of Normal) on the author’s results and conclusion? This requires proper explanation and extension in the revised manuscript. The author can add a new section in the revised manuscript to give an example with lognormal distributions instead of normal ones. https://www.sciencedirect.com/science/article/abs/pii/S0167473017303612

• Due to the nature of the normal density function (which ranges from negative infinity to positive infinity), random parameters generated by the Monte Carlo simulation method may become negative for damping ratio, mass, time, and other parameters that they cannot take negative values. Do the authors consider a special condition on the range of random variables (as an example using truncated normal density function)? In other words, how do the authors ensure that in the Monte Carlo simulation method (given that more than 10,000 simulations are also considered in this study) the randomly generated values were fallen within the appropriate range? Wouldn't it be better to use the log-normal density function instead of the normal density function to make sure that the random numbers are positive? Please comment.
• In stochastic analysis, the model error and its statistical nature will be far more important than other parameters (for example elastic modulus or in this study damping ratio), which is known to have relatively small variability even under high dynamic loads. The reviewer understands that the variability of different input parameters are taken into account, but the uncertainties of the considered model are not included (e,g, SDOF that can be replaced with rigorous FE model or MDOF model). How to include them? Please clarify.
• The authors presented the results based on 10,000 simulations. Why this value is adopted? What confidence level is used to determine this value? Logically a discussion on convergence of MCS should be presented in the revised manuscript (maybe as a new section) to show the effect of simulation number on the outputs. The reference provided in comment 6 may be useful. Moreover, there are a few more sophisticated methods to estimate the statistics with less number of simulations. Why MCS was adopted in the analysis?
• References (on Pages 19-24) should be provided based on the template of the journal.

Author Response

Please see the attachment.

Author Response File: Author Response.pdf

Round 2

Reviewer 1 Report

Authors have addressed the raised queries.

Reviewer 2 Report

All remarks of the reviewer have been taken into consideration and all questions have been answered. The reviewer accepts the article for publication.

Reviewer 3 Report

The paper is well improved and my comments are adequately addressed in the revised file. So, in my point of view, the revised manuscript in its current form is worthwhile to be published.