Predictions of Geological Interface Using Relevant Vector Machine with Borehole Data
Round 1
Reviewer 1 Report
The paper presents the prediction of geological interface using relevant vector machine (RVM) with the optimal width parameter being optimized using Particle Swarm Optimization (PSO). The method is applied to a real case from the Dajiang Tunneling project in 2D and 3D. Results show that in the 2D case Gauss kernel functions are best while in the 3D case spline kernel functions are best.
The reviewer thanks the authors for the well presented paper. Its strong point is the clarity of the language and logical organization which makes it easy to follow and understand, the major weak point is that conclusions are formulated based on the application of the method to a single case, this raises questions about generalization. A few comments are given below:
1. In line 143 the use of PSO algorithm is announced. Authors need to justify this choice in the context of metaheuristics and in a more general sense as well, e.g., what are the characteristics of the problem at hand that lead to the use of PSO.
2. PSO is not described at all, authors need to formulate the PSO optimization problem: objective function, optimization variables, as well as the hyperparameters used: swarm size, social and cognitive coefficients, inertia weight, maximum number of iterations, etc. Authors also need to specify which one of the many PSO variants is used: inertia PSO, lbest PSO, gbest PSO… and depending on the case specify the parameters specific to that. The description should have a level of detail that allows reproducibility.
3. Are equations (11) and (13) the same? Variables x_i and y_i defined in line 158 do not appear in equation (13).
4. Is the scale of figure 1 in meters? Please indicate.
5. What are the axes in figure 2? Please explain.
6. “I” in table 1 not defined before, I guess it should have been defined in equation (13).
7. In table 1 there are two columns with the same heading and different values, I guess the second one is for validation (not training) data?
8. Conclusion in lines 309-311 is quite obvious, it can be omitted.
9. Lines312-315: concluding that Gauss kernel function is better when there is more geotechnical data based on one single case seems unjustified. Authors need to highlight that this applies to the present case study, but more tests are needed for this to be generalized. Also check the relevant text in the document (before conclusions).
10. Paragraph in lines 317-323 is very long, the same can be expressed in 1-2 lines.
11. Why spline is best in 3D and Gauss in 2D? What is the intuition behind that? The authors mention that spline function performs better in fast changing geology, but why is this the case in 3D but not 2D?
12. Check if the spelling of “Tunnelling” is correct, I think it’s Tunneling
Author Response
Please see the attachment.
Author Response File: 
Author Response.pdf
Reviewer 2 Report
In this study, the authors employ the machine learning method of relevant vector machine (RVM) to predict the stratigraphic boundary based on limited geotechnical borehole data. The performance was promising, however, some major points should be addressed as follows:
The quality of figures should be improved; it is below the necessary level.
1. The overall objectives, novelty and contribution are not well presented.
2. The quality of figures should be improved; it is below the necessary level.
3. The authors did not explain in detail on the dataset, this section should be improved using reasonable curves such as Pearson, correlation, data distribution and etc.
4. Boxplot, Violin plot and Taylor diagram for models comparison are necessary.
5. A figure of the SVR model should be provided by highlighting the input and output variables.
6. Flowchart of the proposed modeling strategy is needed.
7. Uncertainties of models should be reported.
8. More discussions should be added.
9. Literature review in the introduction should be improved and updated. The utilized Machine learning prediction model and the used optimizer is well-known and have been used in previous studies such as below which can be considered:
- "Predicting triaxial compressive strength and Young’s modulus of frozen sand using artificial intelligence methods." Journal of Cold Regions Engineering 33.3 (2019): 04019007.
- Gong, Yu-Lin, et al. "Research on application of ReliefF and improved RVM in water quality grade evaluation." Water Science and Technology 85.3 (2022): 799-810.
- Li, T., Zhou, M., Guo, C., Luo, M., Wu, J., Pan, F., ... & He, T. (2016). Forecasting crude oil price using EEMD and RVM with adaptive PSO-based kernels. Energies, 9(12), 1014.
- "Nonlinear model predictive control with relevance vector regression and particle swarm optimization." Journal of control theory and applications 11.4 (2013): 563-569.
- "A comparative study on predicting the rapid chloride permeability of self‐compacting concrete using meta‐heuristic algorithm and artificial intelligence techniques." Structural Concrete 23.2 (2022): 753-774.
- "River water level prediction in coastal catchment using hybridized relevance vector machine model with improved grasshopper optimization." Journal of Hydrology 598 (2021): 126477.
- ""Estimation of rapid chloride permeability of SCC using hyperparameters optimized random forest models." Journal of Sustainable Cement-Based Materials (2022): 1-19.
10. Source codes should be provided for replicating the study.
11. From the results, it looks like the model contained under-fitting (differences between training and testing performance). The authors should discuss more on this situation.
12. Running time and complexity of models should be reported.
Author Response
Please see the attachment.
Author Response File: Author Response.pdf
Round 2
Reviewer 1 Report
The reviewer thanks the authors for the reply and the revised manuscript. The concerns are correctly address in the revised version.
Reviewer 2 Report
The authors have made their efforts and completely answered to my comments. Tanks the authors for preparing detailed response letter and reasonable addressing all of my comments. So, I think it is ready to publish and I recommend to accept the paper.
