Scarce Sample-Based Reliability Estimation and Optimization Using Importance Sampling
Round 1
Reviewer 1 Report
The paper approximates the probability density function and the cumulative distribution function using kernel functions and employs these approximations to find the parameters of the importance sampling density (ISD) to estimate the reliability eventually. The paper is interesting and well-written. After review, there are some minor revisions that need to be made before the paper can be accepted for publication. The detailed requirements for revision and suggestions are listed below.
1、The authors are suggested to give more comments about how to classify the limit state to the difference between Capacity (C) and Response (R).
2、In the numerical examples, the authors are suggested to present more discussion about how the proposed method improves efficiency compared with traditional methods.
3、In section 6.4, how to determine the number of DoE’s size as 200? Whether the convergence of the sample number is verified？
Author Response
Please see the attachment.
Author Response File: 
Author Response.pdf
Reviewer 2 Report
The manuscript proposes a scarce sample based reliability estimation and optimization method, in which the probability density function and the cumulative distribution function are approximated. The motivation seems interesting. The literature review is sufficient, and the numerical experimental studies are representative. Therefore, I recommend accepting this manuscript after the following questions are well answered.
1. Why can the ISD be assumed to follow normal distribution?
2. The detailed introduction and key parameters for bootstrap should be given.
3. The approximation accuracy of TPNT should be verified or calculated before it used for approximating.
4. In numerical studies, how to define the distribution of all the random variables? How to define the mean and standard deviations of all the random variables?
5. For an unknown problem, how to distinguish the characteristics such as interval or random of all variables?
Author Response
Please see the attachment.
Author Response File: Author Response.pdf
Round 2
Reviewer 1 Report
The authors have reply the reviewer's comments point by point. The quality of the manuscript has been improved surfficently, so the reviewer thinks that the paper can be publised at now.
Reviewer 2 Report
The authors had addressed all comments from reviewers. I think it can be accepted now.
