An Efficient Reliability Method with Multiple Shape Parameters Based on Radial Basis Function
Round 1
Reviewer 1 Report
The article titled "An efficient reliability method with multiple shape parameters based on radial basis function" is well written and well structured. The authors develop the subject in detail, presenting the proposed methodology for reliability analysis based on surrogate models, radial basis functions and Monte Carlo simulation. The application examples shown allow validating the proposed methodology. The conclusions are clear and show the potential of the proposed method. Therefore, it is considered that the work can be published in the Journal of Applied Sciences.Author Response
Point 1: The article titled "An efficient reliability method with multiple shape parameters based on radial basis function" is well written and well structured. The authors develop the subject in detail, presenting the proposed methodology for reliability analysis based on surrogate models, radial basis functions and Monte Carlo simulation. The application examples shown allow validating the proposed methodology. The conclusions are clear and show the potential of the proposed method. Therefore, it is considered that the work can be published in the Journal of Applied Sciences.
Response 1: We have re-checked this article very carefully. Thank you for your valuable comments.
Reviewer 2 Report
Report on the paper “An efficient reliability method with multiple shape parameters based on radial basis function”: applsci-1918055
The authors proposed an effective adaptive metamodel based on the combination of the radial basis function (RBF) model and Monte Carlo simulation (MCS) is presented. They used different shape parameters to generate the weighted prediction variance, and the searching for new training samples is guided by the active learning function that achieves a tradeoff of 1) being close enough to limit state function (LSF) to have high-reliability sensitivity; 2) keeping enough distance to the existing samples to avoid clustering problem; and 3) being in the sensitive region to ensure the effectiveness of obtained information. The performance of the proposed method on nonlinear, non-convex, and high dimensional reliability analysis is validated by three numerical cases. The results indicate the high efficiency and accuracy of the proposed method.
Overall, this is a well-written and well-organized manuscript. The manuscript can be accepted for publication in the Applied Sciences journal.
Author Response
Point 1: Overall, this is a well-written and well-organized manuscript. The manuscript can be accepted for publication in the Applied Sciences journal.
Response 1: We have re-checked this article very carefully. Thank you for your valuable comments.
Reviewer 3 Report
Introduction:
The introduction frames appropriately the goals and the problem addressed by the authors, nevertheless authors should improve the introduction according to the following comments of mine:
1) First, it's not clear why authors wrote the first rows in bold (until line 42).
2) Authors should add relevant references on Monte Carlo Simulation from relevant Reliability Engineering journals, in ordeer to demonstrate the importance of this methodology, like:
- A general framework for dependability modelling coupling discrete-event and time-driven simulation
F Chiacchio, A Iacono, L Compagno, D D'Urso
Reliability Engineering & System Safety 199, 106904
- Luo, Changqi, Behrooz Keshtegar, Shun Peng Zhu, Osman Taylan, and Xiao-Peng Niu. "Hybrid enhanced Monte Carlo simulation coupled with advanced machine learning approach for accurate and efficient structural reliability analysis." Computer Methods in Applied Mechanics and Engineering 388 (2022): 114218.
-Lee, S. (2021). Monte Carlo simulation using support vector machine and kernel density for failure probability estimation. Reliability Engineering & System Safety, 209, 107481.
Section 3:
1) Row 157 :-> Kringing, please use the capital letter.
2) To my understanding, authors are using a learning function for an adaptive model. They claim that it is necessary to launch multiple predictions to obtain the prediction variance.
Therefore, to me, theirs look as an heuristic model where they prepare multiple RBF models with different shape parameters.
I am wondering whether they could use Genetic Algorithm as a complementary approach where the reward function is replaced by the learning function.
3) Section 3.4 should be improved to explain better how they perform the reliability analysis procedure.
For instance, why they can assume the performance function of row 275 (equation 25) ?
The flowchart looks a bit different from their explantion in rows 270-295
4) According to rows 298-299 the Figure 3 shows step 1-5 but hte label of the same figure says that it shows steps 1-4. Please correct this information.
Conclusions
Authors should give more information about the pro and contra of their proposed approach.
For instance, accuracy and time of convergence have not been thoroughly discussed.
For instance, in Table 4, they show the results of example 2 for 10 simulations. How long did the Simulation take to perform 10 simulations (or 10 iterations->10 times the performance function is called?)
Author Response
Response to Reviewer 3 Comments
Point 1: First, it's not clear why authors wrote the first rows in bold (until line 42).
Response 1: The font bold of 1-42 lines has been cancelled.
Point 2: Authors should add relevant references on Monte Carlo Simulation from relevant Reliability Engineering journals, in ordeer to demonstrate the importance of this methodology, like:
- A general framework for dependability modelling coupling discrete-event and time-driven simulation
F Chiacchio, A Iacono, L Compagno, D D'Urso, Reliability Engineering & System Safety 199, 106904
- Luo, Changqi, Behrooz Keshtegar, Shun Peng Zhu, Osman Taylan, and Xiao-Peng Niu. "Hybrid enhanced Monte Carlo simulation coupled with advanced machine learning approach for accurate and efficient structural reliability analysis." Computer Methods in Applied Mechanics and Engineering 388 (2022): 114218.
-Lee, S. (2021). Monte Carlo simulation using support vector machine and kernel density for failure probability estimation. Reliability Engineering & System Safety, 209, 107481.
Response 2: The recommended relevant references on Monte Carlo Simulation (MCS) have been added.
Point 3: Row 157: Kringing, please use the capital letter.
Response 3: Revised as required.
Point 4: To my understanding, authors are using a learning function for an adaptive model. They claim that it is necessary to launch multiple predictions to obtain the prediction variance.
Therefore, to me, theirs look as an heuristic model where they prepare multiple RBF models with different shape parameters.
I am wondering whether they could use Genetic Algorithm as a complementary approach where the reward function is replaced by the learning function.
Response 4: In the method proposed in this paper, the new sample point of every iteration is selected from the MC population, so it is feasible to traverse the MC population to find the one with the smallest learning function value. In addition, using heuristic algorithm (such as GA, PSO, etc) to find the newly added sample point is an alternative way. And the difference between traversal and heuristic algorithm has been already described in row 239-246.
Point 5: Section 3.4 should be improved to explain better how they perform the reliability analysis procedure.
For instance, why they can assume the performance function of row 275 (equation 25) ?
The flowchart looks a bit different from their explantion in rows 270-295
Response 5: For the former question of point 5, the row 271 of the manuscript is revised as: “a simple system with sufficient nonlinearity is taken as…”
For the question 2 of point 5: the description of row 270-295 is revised to agree with the flowchart better.
Point 6: According to rows 298-299 the Figure 3 shows step 1-5 but hte label of the same figure says that it shows steps 1-4. Please correct this information.
Response 6: the mismatch information is corrected.
Point 7: Authors should give more information about the pro and contra of their proposed approach.
For instance, accuracy and time of convergence have not been thoroughly discussed.
For instance, in Table 4, they show the results of example 2 for 10 simulations. How long did the Simulation take to perform 10 simulations (or 10 iterations->10 times the performance function is called?)
Response 7: Due to the differences in computer configuration, the efficiency of reliability analysis methods is generally measured by the number of calls to performance functions, i.e., Ncall in this paper, rather than simulation time.
