Exploring Primary Aluminum Consumption: New Perspectives from Hybrid CEEMDAN-S-Curve Model

Round 1

Reviewer 1 Report

Please see attachment.

Comments for author File: Comments.pdf

Author Response

Thanks to the paper reviewers for your professional and constructive feedback. These opinions can not only help to improve the model of primary aluminum consumption greatly, but also improve the application value of society and promote public awareness. At the same time, the opinions of reviewers play an important role in improving the quality of papers.

Based on this, the structure, content, and method of the paper have been revised. More detailed information is described below.

Comments 1. Do the sample countries and test country in this study have standards? Why these countries are selected as sample countries and China as test country? Whether China is similar to the sample countries.

(1) Australia, Canada, France, Italy, Japan, Spain, the United States and the United Kingdom are developed countries and have completed industrialization. The history of primary aluminum consumption in these countries has exceeded 100 years. The curve of per capita primary aluminum consumption in these countries will be generally observed. This curve shows a trend of low growth - rapid growth - decelerated growth – stagnation (Gao et al., 2018; Wang et al., 2015). This pattern can be described by S-curve. At present, most countries in the world are developing countries. Therefore, considering the level of economic development and the integrity of the primary aluminum consumption curve, these countries are very representative.

(2) The main reasons for China being analyzed as a reference country are as follows: (1) At present, China is the largest developing country. The analysis of China's primary aluminum consumption pattern has high reference value for other developing countries; (2) China's primary aluminum industry has become an important part of the world. In 2020, the production and consumption of primary aluminum in China has exceeded half of the world. (3) China is also the largest CO₂ emission country of primary aluminum. Studying the consumption pattern of primary aluminum in China is also of high reference value for achieving global emission reduction.

(3) The consumption patterns of bulk commodities, such as crude oil and iron ore, are basically the same in different countries. The main difference lies in the specific values. According to the comparison results of consumption curves between China and developed countries, China's primary aluminum consumption should also follow this rule (Wang et al., 2021). In addition, some institutions and scholars have successfully analyzed other developing countries by applying the consumption patterns of primary aluminum in developed countries (IAI, 2020).

Comments 2 Why 0.3 and 0.9 were chosen as the boundaries? References or reasons for determining these values should be indicated.

Lempel-Ziv complexity (LZC) is an important detection metric that reflects the rate at which a new pattern emerges in a time series, and is often used to determine the complexity of a time series (Li et al.,2022). In this paper, LZC can reflect the complexity of the IMF. The larger the value of LZC, the shorter the period and the higher the frequency. After calculating the LZC value of the sample country, the range of LZC is 0~1.2. Therefore, CEEMDAN decomposition results are divided into high frequency (>0.9), intermediate frequency (0.3~0.9) and low frequency (<0.3) based on the boundary of 0.3 and 0.9.

Comments 3 The heading in Table 2 is incorrectly formatted and should all be above the table.

Table 2 has been modified.

Comments 4 Page 10, lines 289. The PC value of 0.97 for USA in Table 2 is not significant, is it wrong? If not, the reason for the insignificance should be explained.

This is a marking error, which has been modified.

Comments 5 Although this model has been able to fit the past information well, it is more valuable to predict the future development trend.

Furthermore, the possibility of applying the model to prediction is further discussed. The forecast model of primary aluminum consumption can generally be divided into inflow-driven and stock-driven. The inflow-driven model directly establishes the relationship between consumption and socio-economic indicators (i.e., urbanization rate and GDP), while the stock-driven model establishes the relationship between per capita consumption and socio-economic indicators, and then predicts consumption indirectly. In this paper, both the inflow-driven and stock-driven approaches are utilized. The decomposition results of CEEMDAN-S-curve are low-frequency, medium-frequency and high-frequency component. These three components were established links with different indicators, such as low-frequency component and GDP per capita, medium-frequency component and typical events, high-frequency component and market imbalance. Based on this connection, the CEEMDAN-S-curve can be used to predict primary aluminum consumption in different countries. For example, in 2020, China's per capita primary aluminum consumption was 27.75kg. And the values of low-frequency component, medium-frequency and high-frequency component were 17.60kg, 7.72kg and 2.43kg, respectively. This level is roughly equivalent to that of Japan in 1980. In this period, social development was still the main driving force determining the primary aluminum consumption. Considering the difference between the economic cycles (medium-frequency component) and market fluctuations (high-frequency component) of both countries, it can be expected that the consumption of primary aluminum will continue to increase in the next five years until the consumption level of industrialized countries reaches its peak. Therefore, CEEMDAN, which combines the inflow-driven model and the stock-driven model, will be a better model to analyze the consumption of primary aluminum in different countries.

Comments 6 Is the content of 4.2 closely related to the primary aluminum consumption model? It is better to point out its connection with primary aluminum consumption.

In the life cycle of aluminum, consumption drives the development of the aluminum industry chain. For different countries, it is necessary to obtain sufficient aluminum resources to meet the needs of social and economic development. Generally, the main source of aluminum is the production of primary aluminum and the recycling of recycled aluminum. Primary aluminum production is extremely energy and emissions intensive, thus mitigation strategies from material side have already attracted a lot of attention (Dai et al., 2019). Therefore, it is very necessary to discuss primary aluminum consumption, CO₂ emission and recovery for economic development and industry emission reduction (Figure 1).

Comments 7 The applicability of the model should be indicated in the conclusion and whether the model can be used to analyze primary aluminum consumption in other countries.

The conclusion has been revised, and the applicability and generalizability of the CEEMDAN-S-curve model have been further summarized. In addition, the possibility of using the model to analyze other countries is also further discussed in the discussion section.

Author Response File: Author Response.pdf

Reviewer 2 Report

The paper is interesting, good, and also well written but it lacks novelty.

 

It lacks a clear overview and the description of the structure of the paper at the end of the introduction.

Some improvements are required before paper acceptance. In particular, a revision of the abstract is required since the second part [preparing...... road map] is completely unreadable and could mislead the reader on the real objective of this paper.

I think that this paper requires a few improvements and revisions before the reconsideration as below:

 

1.        First of all the paper is too long. (30 pages)

2.        Some of the diagrams are not visible and their quality need to get improved.

3.        The abstract needs to get improved. In this case the first part of the abstract is actually a part that could be included in the paragraph of Introduction.

4.        It is necessary to highlight the novelty and contribution of the paper in the introduction.

5.        Please add some information about methodology and key results to make them clear

6.        I think the authors need to improve the results, discussion and conclusion parts based on the academic paper.

7.        The introduction needs to improve, I am thinking about lacking theoretical background of the study. This should be located in the Introduction or in independent section.

8.        Please, references also previous studies in the field.

9.        The results should be gathered independently so that authors‘ contribution is clear. Please follow standardized structure of academic papers, It makes orientation in the paper for international reader easier.

Author Response

Thanks to the paper reviewers for your professional and constructive feedback. These comments are of great benefit to improve the structure and quality of the paper.

I modified and processed the structure of the paper make it clearer. It adds the overview and the description of the structure of the paper at the end of the introduction. The abstract part has also been revised. I hope these improvements and revisions make the paper more attractive to the public. More detailed information is described below.

1. In the revised version, many tables and pictures are as supplementary material. Then, the text was compressed from 30 pages to 20 pages to make it more concise and clearer.
2. The diagrams of the paper have been improved.
3. The abstract has been revised. The structure of the abstract is modified according to the purpose, method, result and conclusion. The broader issues related to chromium ore consumption are summarized.

Abstract: Aluminum is the globally most used non-ferrous metal. Clarifying the consumption of primary aluminum is vital to economic development and emission reduction. In this paper, a new hybrid complete ensemble empirical mode decomposition with adaptive noise (CEEMDAN)-S-curve model is proposed to analyze primary aluminum consumption of different countries for the last 100 years The results led to that: (1) Per primary aluminum consumption is composed of low-frequency, medium-frequency, and high-frequency components, explaining over 70%, 2%-17%, and less than 9% of variability, respectively. This can be interpreted as a long-term trend of economic development, effect of a shock from significant events, and short-term fluctuations caused by normal sup-ply-demand disequilibrium, respectively; (2) The CEEMDAN-S-curve exhibits good applicability and generalizability to analyze and predict the primary aluminum consumption in different countries. Furthermore, some major topics related to primary aluminum consumption are discussed, such as CO₂ emission and recovery. Based on the discussion results, in order to meet economic development and achieve sustainable development goals, some measures should be adopted, such as making policies, encouraging resource recovery and developing new technologies

4. In the introduction, the innovation and contribution of the paper are further explained.

The purpose of this paper is to build a new hybrid model to explore the consumption mechanism of primary aluminum. It analyzes the different factors driving the consumption of primary aluminum. Further, the primary aluminum consumption is discussed in a broader context, such as CO2 emission and recovery

The originality and highlights of this paper are: (1) This analysis of primary aluminum consumption covers nine typical countries and a time span of one hundred years. (2) The consumption mechanism of primary aluminum is explained, and various driving factors are quantified. (3）The applicability of the model has been proved ,and can be used to predict future consumption trends.

5. In the methodology, the application of the model, the core content is introduced. The key results are also summarized in the paper. More details in the revised version.
6. The results, discussion and conclusion of the paper have been revised. More details in the revised version.

Result

(1) The standard of sample countries and test countries is introduced.

Australia, Canada, France, Italy, Japan, Spain, the United States and the United Kingdom are developed countries and have completed industrialization. The history of primary aluminum consumption in these countries has exceeded 100 years. The curve of per capita primary aluminum consumption in these countries will be generally observed. This curve shows a trend of low growth - rapid growth - decelerated growth – stagnation (Gao et al., 2018; Wang et al., 2015). This pattern can be described by S-curve. At present, most countries in the world are developing countries. Therefore, considering the level of economic development and the integrity of the primary aluminum consumption curve, these countries are very representative.

The main reasons for China being analyzed as a reference country are as follows: (1) At present, China is the largest developing country. The analysis of China's primary aluminum consumption pattern has high reference value for other developing countries; (2) China's primary aluminum industry has become an important part of the world. In 2020, the production and consumption of primary aluminum in China has exceeded half of the world. (3) China is also the largest CO₂ emission country of primary aluminum. Studying the consumption pattern of primary aluminum in China is also of high reference value for achieving global emission reduction.

(2) In 3.3, the reason for choosing 0.3 and 0.9 as boundaries is explained.

Lempel-Ziv complexity (LZC) is an important detection metric that reflects the rate at which a new pattern emerges in a time series, and is often used to determine the complexity of a time series (Li et al.,2022). In this paper, LZC can reflect the complexity of the IMF. The larger the value of LZC, the shorter the period and the higher the frequency. After calculating the LZC value of the sample country, the range of LZC is 0~1.2. Therefore, CEEMDAN decomposition results are divided into high frequency (>0.9), intermediate frequency (0.3~0.9) and low frequency (<0.3) based on the boundary of 0.3 and 0.9.

Discussion

(1) The possibility of applying the model to prediction is further discussed.

Furthermore, the possibility of applying the model to prediction is further discussed. The forecast model of primary aluminum consumption can generally be divided into inflow-driven and stock-driven. The inflow-driven model directly establishes the relationship between consumption and socio-economic indicators (i.e., urbanization rate and GDP), while the stock-driven model establishes the relationship between per capita consumption and socio-economic indicators, and then predicts consumption indirectly. In this paper, both the inflow-driven and stock-driven approaches are utilized. The decomposition results of CEEMDAN-S-curve are low-frequency, medium-frequency and high-frequency component. These three components were established links with different indicators, such as low-frequency component and GDP per capita, medium-frequency component and typical events, high-frequency component and market imbalance. Based on this connection, the CEEMDAN-S-curve can be used to predict primary aluminum consumption in different countries. For example, in 2020, China's per capita primary aluminum consumption was 27.75kg. And the values of low-frequency component, medium-frequency and high-frequency component were 17.60kg, 7.72kg and 2.43kg, respectively. This level is roughly equivalent to that of Japan in 1980. In this period, social development was still the main driving force determining the primary aluminum consumption. Considering the difference between the economic cycles (medium-frequency component) and market fluctuations (high-frequency component) of both countries, it can be expected that the consumption of primary aluminum will continue to increase in the next five years until the consumption level of industrialized countries reaches its peak. Therefore, CEEMDAN, which combines the inflow-driven model and the stock-driven model, will be a better model to analyze the consumption of primary aluminum in different countries.

(2) The content of 4.2 closely related to the primary aluminum consumption model is discussed.

In the life cycle of aluminum, consumption drives the development of the aluminum industry chain. For different countries, it is necessary to obtain sufficient aluminum resources to meet the needs of social and economic development. Generally, the main source of aluminum is the production of primary aluminum and the recycling of recycled aluminum. Primary aluminum production is extremely energy and emissions intensive, thus mitigation strategies from material side have already attracted a lot of attention (Dai et al., 2019). Therefore, it is very necessary to discuss primary aluminum consumption, CO₂ emission and recovery for economic development and industry emission reduction.

Conclusion

The conclusion has been revised, and the applicability and generalizability of the CEEMDAN-S-curve model have been further summarized.

7. In the introduction, we have added and improved a series of background items of primary aluminum consumption to attract readers, such as the consumption structure and proportion, consumption trend and importance of aluminum.

(1) The basic properties and geological background of aluminum are briefly supplemented.

Aluminum (Al), chemical element, a lightweight silvery white metal of main Group 13 (IIIa, or boron group) of the periodic table. Aluminum is the most abundant metallic element in Earth’s crust and the most widely used nonferrous metal. Because of its chemical activity, aluminum never occurs in the metallic form in nature, but its compounds are present to a greater or lesser extent in almost all rocks, vegetation, and animals.

(2) The theoretical background of the study is further supplemented in the paper. The application of EMD and S-curve and the construction of the model are further supplemented in the section 3.

EMD was initially proposed for the study of ocean waves, and then successfully ap-plied in many areas, such as biomedical engineering, structured health monitoring, earthquake engineering, and global primary productivity evolution. However, these applications are mainly limited to studies of natural science and engineering. The S-curve model is mainly used to analyze the consumption and trends of energy and mineral resources. It is a semi-quantitative analysis model.

8. There is a broader connection between this paper and previous literatures. More details are shown in the revised version.
9. The results of the paper have been reorganized and analyzed. Relevant structures have also been revised according to the standardized structure of academic papers. More details are shown in the revised version.

Author Response File: Author Response.pdf

Round 2

Reviewer 2 Report

1. In conclusion part, the practical recommendations and limitations of the research should be clear

2. In the introduction, the gap in previous studies about the subject of the article and the contribution of the article to the research should be mentioned,

3. In the introduction, needs to explain why you used these methods in your paper

7. The sources related to previous studies should be added

8. please bold the novality of your paper

Author Response

Thanks to the paper reviewers for your constructive feedback again. These comments benefit in improving the quality of paper. This paper has been revised again according to the comments of reviewers. The grammar and expression of the paper have also been revised. At the same time, Other parts of the manuscript have also been revised.

More detailed information is as follow.

Comment 1. In conclusion part, the practical recommendations and limitations of the research should be clear.

The conclusion has been revised and the practical suggestions and limitations of the study have been explained.

limitations of the study:

However, there are some limitations in this paper. (1) CEEMDAN-S-curve model is data-intensive, making analysis complex and difficult to obtain relevant data. (2) Due to the different development levels of countries, the relevant parameters of the application model often need to be adjusted according to the specific status.

practical suggestions:

Furthermore, the research results are linked with broader issues, and some practical suggestions are put forward. (1) The consumption of primary aluminum is closely related to the goal of zero net industrial emissions. Therefore, it is essential to take some measures to promote the efficient use of primary aluminum, such as the government and investors to increase the support of research and development technology, using material efficiency strategies to reduce the demand for raw aluminum, and the aluminum industry prioritizes the development of production plans. (2) Compared with the high energy consumption of primary aluminum, secondary resources can save 93 % of energy. Some measures should also be taken to strengthen the use and re-cycling of scrap, such as government and related companies invest more funds into recycling technology development, the public awareness of recycling can be improved by making laws and regulations.

Comment 2. In the introduction, the gap in previous studies about the subject of the article and the contribution of the article to the research should be mentioned,

The gap in the previous research on the topic of the article and the contribution of the article to the research are also analyzed

the gap in previous studies about the subject of the article:

Many scholars and institutions have studied aluminum consumption and achieved fruitful results. These literature topics mainly focus on demand forecasting, consumption and carbon emissions, consumption and resource recovery, consumption and energy(Yi et al., 2022; Yta et al, 2022; Chen et al., 2012; Chen et al., 2010). Yi et al. (2022) analyzed global carbon emissions and transfers from aluminum production, consumption, and trade from 2000 to 2018, then revealed the carbon distribution across regions and countries. Monica et al. (2010) analyzed the consumption status of aluminum resources in India, and used the MARKAL model to predict the energy demand of the aluminum industry from 2010 to 2031. Li et al. (2021) used dynamic material flow analysis (MFA), regression analysis, and normal life distribution to estimate the domestic consumption, scrap generation, and in-use stock of aluminum from 1990 to 2030 in China. Du et al. (2010) describes a life cycle assessment (LCA) methodology and the general modeling assumptions used to evaluate the impact of Al intensive vehicle on GHG emissions and energy consumption.

The rich theoretical and methodological basis are provided by previous literatures in this paper. However, there are still some gaps: (1) The time span of consumption data in the existing literature is relatively short, generally less than 30 years. Therefore, there is a gap in the study of long-term data of primary aluminum consumption. (2) The existing literature on consumption is mostly based on statistical data, and does not explain the consumption mechanism of primary aluminum. And, some critical questions have not been answered, such as what factors determine the consumption of primary aluminum， and how these factors contribute to consumption.

the contribution of this article:

The contributions of this paper are as follows: (1) The consumption data of primary aluminum for a hundred years in typical countries are analyzed. This makes up for the literature gap in the study of the long-term law of primary aluminum consumption.. (2) A new method is used to explain the consumption mechanism of primary aluminum. The factors affecting the consumption of primary aluminum are clarified and quantified.

Comment 3 In the introduction, needs to explain why you used these methods in your paper.

In the introduction, why these methods are used is also explained

In this paper，based on the signal decomposition tool and S-curve model, a new hybrid complete ensemble empirical mode decomposition with adaptive noise (CEEMDAN)-S-curve model is proposed to study aluminum consumption. Compared with other model, CEEMDAN is a classical tool for analyzing nonlinear series. It can capture data features more accurately and is not limited by stationarity of data. S-curve model demonstrates the consumption law of mineral resources. Moreover, this model quantifies various affecting factors of primary aluminum consumption in the form of formula. The CEEMDAN-S-curve model can quantitatively and directly evaluate the various effect factors, which solves the problem that linear and nonlinear characteristics are difficult to express together. There, CEEMDAN-S-curve is a better model to analyze primary aluminum consumption.

Comment 4 The sources related to previous studies should be added

Previous research has been added to the introduction, results and discussion, and the specific details are in the revised manuscript.

Comment 5 please bold the novality of your paper

The novelty and highlights of the paper are revised and explained again.

The purpose of this paper is to explore the consumption mechanism of primary aluminum using a new hybrid CEEMDAN-S-curve model. The originality and high-lights of this paper are:

(1) more than a century of data research. This analysis of primary aluminum consumption covers nine typical countries and a time span of one hundred years.

(2) consumption mechanism analysis quantitatively and directly. The consumption mechanism of primary aluminum is explained, and various driving factors are quantified.

(3) good stability and applicability of new model. The CEEMDAN-S-curve combines both the simple understanding and the data logicality. and it can be used to predict future consumption trends.

 

Reference:

Yi, X.J.; Lu, Y.L.; He, G.Z.; Li, H.K.; Chen, C.C.; Cui, H.T. Global carbon transfer and emissions of aluminum production and consumption. J. Cleaner Prod., 2022, 362, 132513. [CrossRef]

Yta, B.; Ct, C. An assessment of using aluminum and magnesium on co2 emission in european passenger cars - sciencedirect. Cleaner Prod, 247,119120. [CrossRef]

Chen, W.Q.; Shi, L. Analysis of aluminum stocks and flows in mainland China from 1950 to 2009: exploring the dynamics driving the rapid increase in China's aluminum production. Resour. Conserv. Recycl., 2012, 68, 18-28. [CrossRef]

Chen, W.Q.; Shi, L.; Qian, Y. Substance flow analysis of aluminum in mainland China for 2001, 2004 and 2007: exploring its initial sources, eventual sinks and the pathways linking them. Resour. Conserv. Recycl., 2010, 54, 557-570. [CrossRef]

Monica, D.; Saptarshi, M. An outlook into energy consumption in large scale industries in India: The cases of steel, aluminium and cement. Energ policy., 2010, 11, 7286-7298. [CrossRef]

Li, S.; Zhang, T.; Niu, L.; Yue, Q. Analysis of the development scenarios and greenhouse gas (ghg) emissions in china's aluminum industry till 2030. J. Cleaner Prod., 2021, 290, 125859. [CrossRef]

Du, J. D.; Han, W.J.; Peng, Y.H.; Gu, C.C.. Potential for reducing ghg emissions and energy consumption from implementing the aluminum intensive vehicle fleet in china. Energy, 2010, 35, 4671-4678. [CrossRef]

Author Response File: Author Response.doc

Round 3

Reviewer 2 Report

Dear Authors,

You have already revised your paper based on the reviwers' comments, but still you need to do minor revision as below before final acceptance:

1. the novality of the paper

2. improving results, discussion and conclusion (the practical recommendations and limitations of the research should be clear)

3. the gap in previous studies about the subject of the article

4. theoretical part of article should get clear and improve in Background

5. Research method, tools and steps should be clear

 

Best wishes

Doost

 

Author Response

Dear Reviewer,

Thank you for taking the time to provide feedback on our paper. We appreciate your constructive comments and suggestions, which have helped us to improve the quality of our research. We have carefully considered each of your comments and revised the paper accordingly.

More detailed information is as follow.

Comment 1. the novality of the paper

The novelty and contributions of the paper have been further elaborated.

The purpose of this paper is to explore the consumption mechanism of primary aluminum using a new hybrid CEEMDAN-S-curve model. Thus, this paper makes several notable contributions to the field of primary aluminum consumption research.

Firstly, the study is unique in its comprehensive and extensive data analysis, spanning a time frame of over 100 years and examining the primary aluminum consumption of nine representative countries. This extensive research approach allows for a thorough understanding of the long-term trends and patterns of primary aluminum consumption and provides a foundation for future research in this area.

Secondly, it presents a quantitative and direct analysis of the consumption mechanism of primary aluminum. By decomposing the primary aluminum consumption series using the CEEMDAN-S-curve model, this study is able to quantify the contribution of various driving factors to the volatility of the original series. Specifically, this analysis explains the impact of economic development, significant events, and normal market activities on primary aluminum consumption, providing valuable in-sights into the complex factors influencing primary aluminum consumption.

Finally, the study demonstrates the good stability and applicability of the CEEMDAN-S-curve model in the analysis of primary aluminum consumption. This model provides a clear and simple understanding of the data, while also maintaining a high level of data logicality. Moreover, this model can be used to predict primary aluminum consumption, making it a valuable tool for demand forecasting.

Comment 2 improving results, discussion and conclusion (the practical recommendations and limitations of the research should be clear)

Results: We have re-improved the results, including grammar and contents. The limitations of the results are added in Section 3.7.

Discussion: We have revised the discussion sections to provide more practical recommendations, including model comparison and broader background research.

Conclusions: We revised the conclusion, summarized and improved the content of the paper, and explained the main conclusions, limitations and the practical recommendations. More details in the revised manuscript

More details are shown in manuscript.

Comment 3. the gap in previous studies about the subject of the article

We have added a section in the introduction to discuss the gaps in previous studies related to our research topic, specifically highlighting the lack of research on long-term trends and future predictions of primary aluminum consumption, the limited research scope, and the lack of a unified and comprehensive framework to integrate the various factors that affect primary aluminum consumption.

Previous studies have provided valuable insights into the primary aluminum consumption. However, there are still some research gaps that need to be addressed.

Firstly, most existing studies have focused on analyzing the current state and short-term trends of primary aluminum consumption, which has led to a lack of re-search on long-term trends and future predictions. Long-term trends and future pre-dictions are essential for decision-making and planning, as they provide insights into the direction of primary aluminum consumption.

Secondly, many studies have been limited in their scope, with some focusing solely on specific countries or regions, without providing a comprehensive analysis of global aluminum consumption. A comprehensive analysis of global aluminum consumption is necessary to understand the factors that affect primary aluminum consumption on a global scale.

In addition, despite some studies using different modeling techniques, a unified and comprehensive framework that integrates the various factors influencing primary aluminum consumption is still lacking. Furthermore, existing methods for analyzing primary aluminum consumption have limitations, such as difficulty in revealing the nonlinear characteristics of the data.

Therefore, there is a need for research to focus on the long-term trends and future predictions of primary aluminum consumption, alongside a more comprehensive analysis of global aluminum consumption. Additionally, a unified framework should be developed to integrate the various factors affecting primary aluminum consumption. Research methods must be continuously improved to reveal the nonlinear characteristics of the data, and multiple methods, such as mixed models.

Comment 4. Theoretical part of article should get clear and improve in Background

We have revised theoretical part of our study in background, specifically discussing the key concepts related to primary aluminum consumption and the factors that affect it.

Per capita primary aluminum consumption is a complex indicator that reflects the interplay of multiple economic, technological, and environmental factors, in addition to market dynamics and consumer behavior. Capturing the nonlinear and intricate features of such a series poses a challenge for researchers. To address this, this study introduces a novel hybrid model that combines the complete ensemble empirical mode decomposition with adaptive noise (CEEMDAN) and the S-curve model. By utilizing this model, the per capita primary aluminum consumption series is decomposed, re-constructed, and interpreted, thus providing a better understanding of the primary aluminum consumption mechanism.

CEEMDAN is a signal decomposition tool that decomposes a non-stationary time series into a finite number of intrinsic mode functions (IMFs) and a residue. It is an ex-tension of the original EEMD (Empirical Mode Decomposition) algorithm and improves its performance by adding a white noise layer to the input data and adaptively adjusting the amplitude of the noise layer. By using this tool, the complex nonlinear data series can be decomposed into simpler and more meaningful components, making it easier to analyze the characteristics and patterns of the data.

The S-curve model is a mathematical model that describes the relationship be-tween primary aluminum consumption and various influencing factors. The S-curve model assumes that per capita primary aluminum consumption starts with a slow-growing trend, transitions to a relatively fast-growing trend, then changes to a declining growth trend, and finally reaches a stagnant trend. The model quantifies the influence of different factors on the consumption process by using a formula that de-scribes the relationship between the consumption and the factors. Then, this formula can also be used to predict the future consumption trend.

The combination of CEEMDAN and the S-curve model in the proposed hybrid model can overcome the limitations of using a single method to analyze primary alu-minum consumption. By decomposing the nonlinear data series into simpler compo-nents with CEEMDAN, the hybrid model can accurately capture the features of the data and identify the patterns and trends of the consumption process. By using the S-curve model to quantify the influence of different factors on the consumption process, the hybrid model can provide a more comprehensive and accurate analysis of primary aluminum consumption and its driving factors. More details of the CEEMDAN–S-curve are shown in Section 2.

The purpose of this paper is to develop an effective hybrid CEEMDAN-S-curve method to explore the consumption mechanism of primary aluminum and quantify different influencing factors. This study focuses on the global consumption pattern of primary aluminum. The proposed hybrid model is expected to overcome the limitations of single models and provide a deeper understanding of the consumption mechanism of primary aluminum.

Comment 5. Research method, tools and steps should be clear.

We have added a section to provide a detailed description of the data processing methods, and modeling tools used in our study.

This section provides a detailed introduction to the CEEMDAN and S-curve mod-els, including their development, applications, and usage. Based on these two methods, the CEEMDAN-S-curve model framework is constructed, and the application steps of the model are elaborated in detail. The data processing, analysis, and result statistics tools used in this study are mainly implemented through Matlab and Excel.

The research steps of CEEMDAN – S-curve are further clarified.

The CEEMDAN–S-curve model can be separated into six steps:

Step 1: Data processing.

The data used in this study are related to the production, consumption, trade volume (import and export volume), population, and other economic and social factors of the world. The consumption data are sourced from: (1) the direct use of apparent consumption; and (2) the equation of apparent consumption = domestic production +imports- exports- inventory.

Step 2: CEEMDAN decomposition.

Using EEMDAN to decompose the consumption series into IMFs and a residue. Each IMF component represents the local characteristic time scale by itself. The result of this step are k IMFs (k is the number of IMFs) and a residue 

Step 3: Components reconstruction.

All components are reconstructed based on the Lempel-Ziv complexity values of each IMF to improve the reliability of the model. The Lempel-Ziv complexity values represent the periodicity, variability, and randomness of the components, where a higher value of the component indicates fewer periodic components, lower regularity of change, and more randomness. [38]. The results of component reconstruction are low-frequency, medium-frequency, and high-frequency components.

Step 4: S-curve analysis.

The reconstructed components are analyzed and explained based on the S-curve model, taking into account the data characteristics of each component.

Step 5: Model test.

The reliability and stability of the CEEMDAN–S-curve are tested by selecting the test country and repeating the above steps.

Step 6: Results output

The analysis results of primary aluminum consumption are summarized and presented.

 

Thanks for your time and valuable feedback again.

Author Response File: Author Response.doc