Support Vector Machine-Assisted Importance Sampling for Optimal Reliability Design

Round 1

Reviewer 1 Report

This paper proposed effective population-based greedy  algorithm to solve optimal reliability designs (ORD) by  combining the support vector machine  (SVM) and importance sampling (IS). 

- Authro should provde the clear advantage of the imrpved algorith compared to the traditional or existing algorithms described in references.

- The proposed exampless are not good enought to show in science area, but valid for mathematical area.

After Author provide more clear and concrete results by showing the advatages of this alogrothm, I would like to suggest this paper to mathematics or computational mathematic related journals.

Author Response

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Author Response File: Author Response.docx

Reviewer 2 Report

The paper is interesting and well written and organized. I have some comments before recommending accepting the papers.

1. It appears from equation (2) that p(u) is a function of u and the integration for u also. Then, how did the authors get equation (3) by writing the p(t) outside the integration? 

2. The summation in equation (3) depends on j, how p_j(t) written outside the summation? The same thing for equation (39). 

3. I have tried to get the result of the integration in (5), but I have a different result. More details in this regard will be helpful.

4. After equation (19), how to reduce the variance to zero?

5. Is the proposed method valid for any model or the exponential model only?

6. Some future topics and extensions of the current work should be added in the conclusions.

Author Response

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Author Response File: Author Response.docx

Reviewer 3 Report

The submitted manuscript proposes a resultant approach, combining the importance sampling and support vector machine, to solve the optimal reliability design. The utilization of importance sampling can keep the sample diversity and avoid local optima. In addition, the support vector machine used in the proposed approach can alleviate the computational burden. The innovation and contribution of this manuscript are evident. The presented numerical results fully demonstrate the feasibility of the proposed approach. The concrete comments and suggestions are as follows:

1.      To construct the IS PDF, it has to determine a priori distribution of variables. Which distribution is used in this study. Is the result sensitive to the choice of the priori distribution?

2.      Add list of notations.

3.      Add more detailed explanations to the constraints, such as the cost unit.

4.      How to generate the initial population to capture more information of the design space. Please clarify it concretely.

5.      It is seen that the proposed approach has two termination conditions. So, how to determine the maximal number of iterations?

6.      The proposed approach uses SVM to construct the classification hyperplane. Is this classification plane generated at one time or updated iteratively?

7.      The defects or key points (affecting efficiency or accuracy) of the proposed algorithm also need to be mentioned.

Author Response

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Author Response File: Author Response.docx

Reviewer 4 Report

This paper (applsci-2014248) proposes a novel support vector machine assisted importance sampling for optimal reliability design. A population-based optimization algorithm, combining the support vector machine (SVM) and importance sampling (IS), is proposed to achieve a global solution of the optimal reliability design. The paper is well organized, and this reviewer supports the publication of this paper in applied sciences. But the following main comments and suggestions need to be addressed before it is accepted for publication.

Some major revisions

1. In introduction, this paper proposes a new population-based greedy algorithm that is able to reach the (near) global optimum in a relatively short time. But in example 1, the algorithm takes longer time compared to other algorithms. It is suggested that the authors carefully consider and revise it.

2. In introduction, the authors propose a greedy algorithm, but do not describe the greedy algorithm carefully. It is suggested that the authors supplement the corresponding content.

3. The innovation of using IS to construct a new target distribution without the need to set a series of parameters is relatively simple and has been proposed. Please clarify and explain the innovation and contribution of this part.

4. In Example 1, when and , the reliability of the system obtained by the genetic algorithm is better than the proposed algorithm and does not satisfy the claims of this paper. It is suggested that the authors further explain the effectiveness of the method.

5. In Example 1, when and , the reliability results of the genetic algorithm and the proposed algorithm are approximately equal, but the proposed algorithm has a longer computational time. It is suggested to be further demonstrated the superiority of the proposed method.

Some minor revisions

- It is suggested to add “Start” and “End” to the flowchart of the proposed method to increase calculation process integrity.

- In Section 3, some formula numbers are not aligned and it is suggested that the authors double check formula numbers. For example, Eq. (32).

- In Section 3, there are some diagrams without legends and it is suggested that the authors check the legends carefully. For example, Fig. 8.

- Please carefully check and modify the symbols in this paper to ensure the readability.

Comments for author File: Comments.docx

Author Response

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Author Response File: Author Response.docx