Time Scale Control Using Dynamic GMDH Neural Network Forecasting Based on Real Measurement Data

Round 1

Reviewer 1 Report

Comments and Suggestions for Authors

This paper studies the problem of using dynamic GMDH neural network to predict the measured data. It has certain innovation and application value, and can be considered to be accepted for publication. However, the paper can be improved from the following aspects : 
 
1，The author should briefly introduce the structure of GMDH neural network. 
 
2，The author should give the structural schematic diagram of the method and introduce the method proposed in the paper in detail. 
 
3，The author should give the algorithm flow chart of the method described in the paper, which is convenient for readers to understand the basic principle of the method. 
 
4，The author should compare and analyze the method of the paper with the traditional typical method, and compare the superiority and application scope of the method.

Author Response

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Author Response File: Author Response.pdf

Reviewer 2 Report

Comments and Suggestions for Authors

Please see the attached comments.

Comments for author File: Comments.pdf

Author Response

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Author Response File: Author Response.pdf

Reviewer 3 Report

Comments and Suggestions for Authors

Comments
This paper introduces a novel approach to forecasting the Polish Time Scale (UTC(PL)) by employing a dynamic Group Method of Data Handling (GMDH) neural network. The core contribution lies in the development of a forecasting procedure that leverages real measurement data to predict the differences between UTC(PL) and Coordinated Universal Time (UTC). The authors utilize two time series, TS1 and TS2, derived from real measurement data, and apply the GMDH neural network to forecast these differences. The methodology involves a dynamic selection of neurons within the GMDH architecture, which is a key aspect of their approach. The empirical findings demonstrate that the proposed method achieves high-quality forecasts, with residuals within ±4.4 ns for the year 2024. This level of accuracy is significant for maintaining the stability and reliability of the national time scale. The paper also discusses the potential for broader application of this method to other national time scales and highlights its cost-effectiveness and low complexity compared to traditional methods, such as those relying on expensive caesium fountains. The authors emphasize that the GMDH Shell tool and the developed procedure can be implemented on basic PC computers, making it accessible to various institutions. The research aims to showcase the potential of neural networks as a powerful tool for creating more intelligent and effective systems, using time scale control as a specific example. The paper presents a practical application of neural networks to a specialized domain, demonstrating the potential for improved accuracy and reduced costs in national time scale control. While the paper focuses on a specific application, it also hints at the broader implications of using neural networks for time series forecasting in various scientific and technological fields. The authors position their work as a promising direction for research and development, offering a new perspective on forecasting the differences between national time scales and UTC. The paper's significance lies in its potential to enhance the accuracy and reliability of national time scales, which are crucial for various applications, including navigation, communication, and scientific research. By providing a cost-effective and accurate alternative to traditional methods, the proposed approach could have a significant impact on the field of time scale control and forecasting. The paper also contributes to the growing body of literature on the application of neural networks to time series forecasting, demonstrating the potential of GMDH networks in this context. The authors' focus on a practical application, combined with their discussion of broader implications, makes this paper a valuable contribution to the field.
Strengths:
1. The paper presents a novel application of the GMDH neural network in the field of time scale forecasting, which is a significant strength. This is not a common area for the application of such methods, and the authors' approach offers a fresh perspective on predicting the differences between the Polish Time Scale (UTC(PL)) and Coordinated Universal Time (UTC)
2. The paper also highlights the potential for broader application of the method to other national time scales, suggesting its generalizability and impact on the field. The emphasis on cost-effectiveness and low complexity is a further strength.
3.The paper is well-written and clearly explains the methodology and results. The authors provide a detailed description of the GMDH neural network and the time series preparation procedure.
Comments:
1.To enhance the paper's contribution, the authors should explicitly articulate how their dynamic GMDH neural network approach advances the field of forecasting beyond its application to the Polish Time Scale. This could involve detailing the specific modifications or innovations made to the GMDH architecture, such as the dynamic selection of neurons or the specific structure of the hidden layers, and explaining how these changes address limitations of traditional GMDH networks or other forecasting methods.
2.  How does the dynamic neuron selection mechanism improve the network's ability to adapt to non-stationary time series data? What is the theoretical justification for the chosen network structure and training process, and why are they well-suited for the specific characteristics of the time scale data?

Author Response

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Reviewer 4 Report

Comments and Suggestions for Authors

This study presents a dynamic forecasting approach for the Polish Time Scale UTC(PL) using GMDH neural networks, leveraging real measurement data from UTC and UTC Rapid scales. Before publication, the following issues need to be addressed:

1. The manuscript states forecasts are generated weekly "for the entire upcoming week," but the exact forecasting window is not explicitly defined.
2. The study compares results to linear regression but overlooks modern alternativesInclude a quantitative comparison with at least one contemporary method using the same dataset to substantiate claims of GMDH’s superiority, particularly in handling non-linearities or drift.

  3  The cost advantage of GMDH ($500) versus cesium fountains ($1.5M) is emphasized, but no evidence is provided for operational savings. Quantify practical impacts, such as reduction in UTC(PL) corrections or staff time saved, and cite examples from GUM’s implementation to strengthen this argument.

Author Response

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Author Response File: Author Response.pdf

Round 2

Reviewer 1 Report

Comments and Suggestions for Authors

The author carefully revised the paper according to the reviewers ' comments and suggestions, and the current version of the paper can be accepted for publication.

Reviewer 4 Report

Comments and Suggestions for Authors

The authors have given sufficient explanations and made proper modifications with respect to my comments.