Analyzing GNSS Measurements to Detect and Predict Bridge Movements Using the Kalman Filter (KF) and Neural Network (NN) Techniques

Round 1

Reviewer 1 Report

• The proposed method used to process GPS measurements in order to evaluate the bridge structure's performance and to monitor its health condition. The last sentence in the abstract mentions "The predicted behavior is then compared with the safety limits known by the bridge’s design to assess its health under usual load". Unfortunately, I couldn't find this in the article. Where is such a comparison mentioned in the paper? Also, What is expected to be detected by this method? What kind of unhealthy behavior of bridge or damage in the structure could be addressed by this method? In that case, I couldn't find a comparison between a damaged and healthy bridge structure. In addition, the monitored bridge is quite a new structure; however, the major use of structural health monitoring is for bridges over 50 years old in which structural health monitoring is used to distinguish between critical damage and negligible ones since we expect from an old bridge to show some extent of deterioration. 

• Line 380-382: The authors mention that "Periodogram diagrams in Figure 9 and dominant frequency values in Table 5 illustrate the similar pattern in frequencies between the station along the bridge and permanent station, which can be considered as a proof that the bridge does not show the irregular high-frequency dynamic behavior.”

  • The question here is that what range of the high-frequency components expected to be received? And how this could be achieved with 30-second samples acquired by the stations?

    For very low frequencies observed in Table 5, what is the minimum sampling rate required? Can it be guaranteed that these frequency components present in the time series? In other work, Nyquist frequency does not see to be satisfied, to what extent the authors are confident that these components are not the aliases of real frequency components? Is only two days of samples enough for the frequency domain analysis

• Section 4.5:

  Training of the NNs is done without presenting evidence that the model fits well and is not overfitted to the training set? What would be the error value compared to epoch numbers? Which portion of the data is used for training and which portion for testing? And is the testing data different than the evaluation one?

Some minor issues and typos also observed in the paper as follows. Please revise them or address them and proofread the paper.

• Line 167: Typo: "the" --> the
• Line 190: Do the authors mean Butterworth filter instead of "Butter". If yes, please also revise in Figure 7.
• Line 204: Please remove the extra bracket from "[22, 23, 27, 29, [40]. "
• Line 342: Typo: "form" --> "from"
• Line 358: Is the unit for correlation "meter" as mentioned after the numbers?
• Line 365: Why the short-period component is used not the dynamic component for frequency domain evaluation?

The paper is suggested for publication upon addressing the above issues.

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Author Response

Detailed response to reviewers

Dear Professor Gao,

Thank you very much for your consideration of our manuscript and request for a revised version. We are grateful to you and the reviewers for providing valuable comments, which are used to improve our manuscript. Herewith, we would like to submit the revised version of geomatics-1078240" Analyzing GPS measurements to detect and predict bridge movements using the Kalman Filter (KF) and Neural Network (NN) techniques ". In the following, you can find the detailed responses to the reviewer’ comments and concerns.  We hope that the revised manuscript would be acceptable in geomatics.

Sincerely Yours,

Ehsan Forootan

Reviewer Comments:

• The proposed method used to process GPS measurements in order to evaluate the bridge structure's performance and to monitor its health condition. The last sentence in the abstract mentions "The predicted behavior is then compared with the safety limits known by the bridge’s design to assess its health under usual load". Unfortunately, I couldn't find this in the article. Where is such a comparison mentioned in the paper? Also, what is expected to be detected by this method? What kind of unhealthy behavior of bridge or damage in the structure could be addressed by this method? In that case, I couldn't find a comparison between a damaged and healthy bridge structure.

Response to Reviewer Comment No. 1:

Thanks for pointing this out. According to the results, we found that the mean deflections of the bridge (the mean of semi-static and short-period components) are 4.2, 3.2, and 5.2 cm in the North, East, and Up, respectively and the norm of three component displacement is 7.4 cm. So, the full behavior of the Tabiat bridge is within the safety limits of the bridge design ([-22 22] ^cm) for the GPS measurements. It can be concluded that the bridge is safe under the traffic load effects. This discussion is reflected in L383-386 of the revised manuscript.

• In addition, the monitored bridge is quite a new structure; however, the major use of structural health monitoring is for bridges over 50 years old in which structural health monitoring is used to distinguish between critical damage and negligible ones since we expect from an old bridge to show some extent of deterioration.

Response to Reviewer Comment No. 2:

It is a good idea and thank you for pointing this matter. In future studies, the old and damaged structures will be considered.

• Line 380-382: The authors mention that "Periodogram diagrams in Figure 9 and dominant frequency values in Table 5 illustrate the similar pattern in frequencies between the station along the bridge and permanent station, which can be considered as a proof that the bridge does not show the irregular high-frequency dynamic behavior.” The question here is that what range of the high-frequency components expected to be received? And how this could be achieved with 30-second samples acquired by the stations?

Response to Reviewer Comment No. 3:

In each phenomenon, we have two types of frequency:

1. Natural Frequency: It is the minimum frequency that can extract from the behavior of a phenomenon and can be calculated as:

Where is the total length of the sampling interval. In this study, the data set was collected in a period of 172770 seconds. So, the Natural frequency for the measurements is 7.61×10^-6 Hz.

2. Nyquist Frequency: It is the maximum frequency that can extract from the Behavior of a phenomenon and can be calculated as:

Where n is the number of samples. In this study, 5760 samples were collected. So, the Nyquist frequency for the measurements is 0.016 Hz.

The dominant frequencies from the measurements should be in the range of Natural frequency and Nyquist frequency. According to Table 5 the dominant frequencies are estimated in this range.

• For very low frequencies observed in Table 5, what is the minimum sampling rate required? Can it be guaranteed that these frequency components present in the time series? In other work, Nyquist frequency does not seem to be satisfied, to what extent the authors are confident that these components are not the aliases of real frequency components? Is only two days of samples enough for the frequency domain analysis

Response to Reviewer Comment No. 4:

Thank you for pointing this matter. According our answer to comment No. 3, the Nyquist frequency can be estimated from Equation (2) and the dominant frequency should be lower than Nyquist frequency, for example, in the North component of Station 1, the sampling interval should be lower than 1000 second. In this study we collect data with 30 second sampling rate, and this sampling rate can be guaranteed that these frequency components present in the time series. As we mentioned in the paper, this study is a short period monitoring approach, and using two days of samples is enough for evaluation the behavior of the bridge. It is obvious that collection data with longer duration lead to the higher accuracy, and reliability of the result. 

• In Section 4.5: Training of the NNs is done without presenting evidence that the model fits well and is not over fitted to the training set? What would be the error value compared to epoch numbers? Which portion of the data is used for training and which portion for testing? And is the testing data different than the evaluation one?

Response to Reviewer Comment No. 5:

In this study, to perform the NN method, the data set is divided into 3 parts randomly: training, validation, and test data. 80%, 10%, and 10% are regarded as training, validation, and test data set, respectively. Also, the dynamic and semi-static components of the bridge are predicted for 15 minutes, which the results are illustrated in Table 6. If an overfitting error occurs, we could not get the proper result in the prediction. This clarification is added to L389-391 of the revised manuscript.

• Line 190: Do the authors mean Butterworth filter instead of "Butter". If yes, please also revise in Figure 7.

Response to Reviewer Comment No. 6:

     Yes, thanks for pointing this out. We corrected this in the revised manuscript.

• Line 358: Is the unit for correlation "meter" as mentioned after the numbers?

      Response to Reviewer Comment No. 7:

      Thanks for pointing this out. We corrected this in the revised manuscript.

• Line 365: Why the short-period component is used not the dynamic component for frequency domain evaluation?

Response to Reviewer Comment No. 8:

The short-period component consists of a dynamic component and noise. To extract the dynamic component, we should remove the noise from the short-period component. The LSHE method is a good tool to eliminate the remaining noise and it can be used to extract the dynamic behavior of the bridge in the frequency domain.

Author Response File: Author Response.docx

Reviewer 2 Report

Dear Authors,

thank you for this submission. I have only few minor remarks.

• Figure 2: I miss the description of different element types. What is the meaning of dashed border, different shapes and colors.
• Figure 5: what is the meaning of the circle size?

Main remark is on the validation of the NN. It is not clear how the performance of the component can be validated without test and/or validation set. The optimization of the number of hidden layers could suffer from overfitting.

Author Response

Detailed response to reviewers

Dear Professor Gao,

Thank you very much for your consideration of our manuscript and request for a revised version. We are grateful to you and the reviewers for providing valuable comments, which are used to improve our manuscript. Herewith, we would like to submit the revised version of geomatics-1078240" Analyzing GPS measurements to detect and predict bridge movements using the Kalman Filter (KF) and Neural Network (NN) techniques ". In the following, you can find the detailed responses to the reviewer’ comments and concerns.  We hope that the revised manuscript would be acceptable in geomatics.

Sincerely Yours,

Ehsan Forootan

Reviewer Comments:

• Figure 2: I miss the description of different element types. What is the meaning of dashed border, different shapes and colors?

Response to Reviewer Comment No. 1:

This figure presents an overview of proposed framework in order to apply the Global Navigation Satellite System (GNSS) data for analyzing and predicting the movements of civil structures such as bridges. The dark blue shapes demonstrate the various filters (Kalman filter, MA filter, and Butterworth filter), the light blue shapes demonstrate the math operation (Difference and Average), and the dashed borders have no special meaning.

• Figure 5: what is the meaning of the circle size?

Response to Reviewer Comment No. 2:

The circles' radius and color are associated with the numerical value of correlation.

• Main remark is on the validation of the NN. It is not clear how the performance of the component can be validated without test and/or validation set. The optimization of the number of hidden layers could suffer from overfitting.

Response to Reviewer Comment No. 3:

In this study, to perform the NN method, the data set is divided into 3 parts randomly: training, validation, and test data. 80%, 10%, and 10% are regarded as training, validation, and test data set, respectively. Also, the dynamic and semi-static components of the bridge are predicted for 15 minutes, which the results are illustrated in Table 6. If an overfitting error occurs, we could not get the proper result in the prediction. This clarification is added to L389-391 of the revised manuscript.

Author Response File: Author Response.docx

Reviewer 3 Report

The paper has a new approach to the phenomenon and I believe that the findings of this study can serve as a basis for advance warning of bridge stability monitoring systems, depending on the GNSS measurement technique.

Author Response

Detailed response to reviewers

Dear Professor Gao,

Thank you very much for your consideration of our manuscript and for your attention to this matter that this study can serve as a basis for advance warning of bridge stability monitoring systems, depending on the GNSS measurement technique. We hope that the manuscript " Analyzing GPS measurements to detect and predict bridge movements using the Kalman Filter (KF) and Neural Network (NN) techniques " could be published in geomatics.

Sincerely Yours,

Ehsan Forootan

Reviewer Comments:

The paper has a new approach to the phenomenon and I believe that the findings of this study can serve as a basis for advance warning of bridge stability monitoring systems, depending on the GNSS measurement technique.

Response to Reviewer Comment No. 1:

Thank you very much!

Author Response File: Author Response.docx