Recursive Algorithms for Multivariable Output-Error-Like ARMA Systems

Round 1

Reviewer 1 Report

The researchers have proposed a new approach such as  partially-coupled recursive generalized extended least squares algorithm to study a multivariable output systems. Though the work seems to be interesting and significant, there are few concerns: 

(1) In the introduction explain multivariable output error like system and their significance/relevance to the scientific world. This would increase the readability of the work. 

(2) Add few more relevant works and mention how is the current work different from others. 

(3) The researchers have tried to explain the proposed algorithm using a simple example. What is the applicability in real world scenario? It would be interesting to assess the comparative performance of the proposed approach with others in a real world problem. 

(4) What are the limitations of the proposed approach? Also, mention the scope for future work. 

Author Response

The researchers have proposed a new approach such as partially-coupled recursive generalized extended least squares algorithm to study a multivariable output systems. Though the work seems to be interesting and significant, there are few concerns:

The authors’ reply: Thank you for your positive comments.

1. In the introduction explain multivariable output error like system and their significance/relevance to the scientific world. This would increase the readability of the work.

In the revised version, we have enriched Introduction, and indicated that the multivariable

output-error like systems can describe modern industrial process more accurately than

other types of multivariable systems.

2. Add few more relevant works and mention how is the current work different from others.

According to your suggestion, we have added few more relevant works about the identification for multivariable systems and indicated that the differences of the proposed methods in this paper with others. Please see Paragraph 4 on Page 2.

3. The researchers have tried to explain the proposed algorithm using a simple example. What is the applicability in real world scenario? It would be interesting to assess the comparative performance of the proposed approach with others in a real world problem.

At present, the methods proposed in this paper are based on theoretical research, and

applying the methods studied in this paper to solve practical problems is also our main

work in the future.

4. What are the limitations of the proposed approach? Also, mention the scope for future work.

The proposed methods are suitable for multivariable systems and have good estimation

effect for systems with complex parameter types, and can be extended to other fields such

as model industrial processes and network systems by means of some other mathematical

tools and approaches.

Author Response File: Author Response.pdf

Reviewer 2 Report

The paper from  Pan et al. provides a novel approach for improving the algorithms for multivariable output-error-like autoregressive moving average systems. The authors demonstrate it by using the coupling identification concept  and the hierarchical identification principle. The methodology is clearly demonstrated and a useful example application is provided.

The paper can be accepted with minor revisions, given these modifications:

In Figure 3, the authors report the estimation errors versus s. Interestingly, RGELS algorithm leads to the higher estimation error. Can the authors provide an explanation for this?

Minor typos:

-pag. 11 "the prochedures" should be corrected to "the procedures"

-pag. 12 "the parameter vectors of the system is" should be corrected to "the parameter vectors of the system are"

Author Response

The paper from Pan et al. provides a novel approach for improving the algorithms for multivariable output-error-like autoregressive moving average systems. The authors demonstrate it by using the coupling identi fication concept and the hierarchical identi cation principle. The methodology is clearly demonstrated and a useful example application is provided.

The paper can be accepted with minor revisions, given these modi cations:

The authors' reply: Thank you for your positive comments and acceptance for publication.

1. In Figure 3, the authors report the estimation errors versus s. Interestingly, RGELS algorithm leads to the higher estimation error. Can the authors provide an explanation for this?

The RGELS algorithm is aimed at the original M-OEARMA-like system. Because of the

high dimension of the information matrix, the RGELS algorithm simultaneously estimates

the parameter vector and the parameter matrix, which lead to a large amount of compu-

tation and higher parameter estimation errors.

2. -pag. 11 "the prochedures" should be corrected to "the procedures"

According to your suggestion, we have corrected typos.

3. -pag. 12 "the parameter vectors of the system is" should be corrected to "the parameter vectors of the

system are"

Thank you for your careful reading, we have corrected typos.

Author Response File: Author Response.pdf

Reviewer 3 Report

Focus:

This paper addressed the parameter identification problems of multivariable output-error-like (M-OE-like) systems with colored noises which is described by the autoregressive moving average (ARMA) model by means of the decomposition technique and the coupling identification concept.

Strengths :

Well organized and well written

The authors discussed the comparison between the RGELS algorithm and the derived algorithms and found that the PC-S-RGELS and PC-RGELS algorithms have higher computational efficiency than the RGELS algorithm. 

Potential Improvements:

The abstract do not explain well what is explained in rest of the paper. Needs more conciseness.

A number of typos e.g section 6 fund -> found etc. Needs a grammar review.

Author Response

This paper addressed the parameter identification problems of multivariable output-error-like (M-OE-like) systems with colored noises which is described by the autoregressive moving average (ARMA) model by means of the decomposition technique and the coupling identification concept.

Strengths :

Well organized and well written

The authors discussed the comparison between the RGELS algorithm and the derived algorithms and found that the PC-S-RGELS and PC-RGELS algorithms have higher computational efficiency than the RGELS algorithm.

The authors' reply: Thank you for your positive comments.

Potential Improvements:

1. The abstract do not explain well what is explained in rest of the paper. Needs more conciseness.

In the revised version, we have rewritten and enriched Abstract.

2. A number of typos e.g section 6 fund ? > found etc. Needs a grammar review.

Thank you for your careful reading. We have corrected typos and improved the writing of

the paper .

Author Response File: Author Response.pdf