The Harmonious Relationship between Energy Utilization Efficiency and Industrial Structure Development under Carbon Emission Constraints: Measurement, Quantification, and Identification

Abstract

Addressing the challenge of attaining a harmonious balance between energy utilization efficiency and the level of industrial structure development is crucial for promoting regional sustainable development. Aiming at the goal of carbon neutrality, a three-stage method to analyze the relationship between energy utilization and industrial structure development is proposed. The multidimensional input–output index system was augmented with a carbon emission constraint. Additionally, two classical data envelopment analysis models were integrated to establish a dynamic measurement model for energy utilization efficiency, ensuring comparability among all decision-making units. From two perspectives of industrial structure, rational degree and advanced degree, the industrial structure development index was proposed to quantitatively characterize the level of regional industrial structure development. Drawing upon the Tapio decoupling theory, an elaborate model for identifying harmonious relationships was constructed to refine the recognition of the harmonious state between energy utilization efficiency and industrial structural development. A city-scale case study was conducted in Heilongjiang Province, a typical energy province in Northern China. The results revealed that: (a) energy utilization efficiency in various cities has exhibited a consistent upward trend, with the average efficiency rising from 0.54 in 2010 to 0.88 in 2020. Core cities like Daqing and Harbin stand out in energy utilization, and the disparity in energy utilization levels between different cities is progressively diminishing; (b) the overall level of industrial structural development has shown a weak downward trend. Harbin has the best industrial structure development level, with a quantitative index higher than 0.8. For some cities with relatively backward industrial structures, it is necessary to clarify new industrial development positioning and promote deep optimization of industrial structures; and (c) the harmonious relationship between energy utilization efficiency and industrial structural development demonstrates stage characteristics, indicating an overall negative decoupling relationship with limited dynamic coordination. These distinct findings will assist in identifying potential solutions for achieving high-quality development in traditional industrial cities under carbon emission constraints.

1. Introduction

1.1. Background and Motivation

Energy is the source of power for human economic and social development. In 2005, the United Nations Energy Mechanism (UN-Energy) proposed the need to improve efficiency in energy production and use to achieve the Millennium Development Goals (MDGs) [1]. In 2015, the United Nations Sustainable Development Summit released 15 sustainable development goals (SDGs), pointing out that addressing backward energy efficiency is an important challenge to achieve sustainable development [2]. The International Energy Agency (IEA) stated that improving energy efficiency is one of the most effective ways to reduce carbon emissions [3]. In 2020, the Chinese government set the goal of “carbon neutrality” as a long-term strategy for the country to achieve high-quality development, putting forward higher requirements for the efficient utilization of energy resources and green upgrading of industrial structures [4]. After the release of the White Paper on China’s Energy Development in the New Era, building a safe and efficient energy system has become a key task and a solid guarantee for China’s modernization of harmonious coexistence between man and nature [5]. As an important energy and industrial base in China, Heilongjiang Province plays an important role in supporting the stable development of the national economy. However, with the acceleration of the regional development process, the contradiction between the supply and demand for resources and energy in Heilongjiang Province has become more and more significant, and there is still substantial room for improvement in industrial structure upgrading and technological innovation [6]. In the 14th Five-Year Plan, the Chinese government has proposed to improve the level of energy supply security and form an industrial structure with balanced development to achieve breakthroughs in the revitalization of Northeast China [7]. Resolving the intricate energy challenges in Heilongjiang Province hinges on enhancing energy utilization, optimizing the industrial structure, and attaining sustainable economic and social development while minimizing energy consumption. Therefore, quantifying city-scale energy utilization efficiency under the goal of “carbon neutrality”, exploring the development level of industrial structure, and clarifying the dynamic relationship between energy utilization and industrial structure development is of great significance for the sustainable development of the region, and it is also a beneficial undertaking for promoting the comprehensive revitalization of Northeast China.

1.2. Literature Review

Rapid economic and social development has brought about the continuous expansion of energy demand. The contradiction between energy supply and demand in countries around the world, especially in developing countries, has become increasingly prominent. Efficient energy utilization models have gradually become a research hotspot. Many scholars have carried out in-depth exploration in the field of energy utilization and gradually formed a relatively complete method and application system. Life cycle assessment (LCA) [8], stochastic frontier analysis (SFA) [9], and data envelopment analysis (DEA) [10] are all effective methods for quantitative studies of energy utilization efficiency (EUE). Among them, the data envelopment analysis model, as a non-parametric model, is widely used in the field of resource and energy efficiency measurement and has produced rich research results. Relevant studies cover different research scales, such as countries [11,12,13], river basins [14,15], provinces [16,17], and cities [18,19]. For example, Zhang et al. used a three-stage SBM model to evaluate the energy utilization efficiency of RECP countries and its influencing factors [12]; Pan et al. quantitatively calculated the energy utilization efficiency of 30 provincial-level administrative regions in China based on the SBM-DEA model and explored its driving factors using a regression model [20]. In terms of research objects, relevant research covers traditional fossil energy [21]; mature green energy, such as water energy, wind energy, and photovoltaic energy [22,23]; and emerging renewable energy, such as biomass energy and geothermal energy [24]. For instance, Chen et al. combined the DEA model to explore the utilization efficiency of different types of fossil energy in 30 provincial-level administrative regions in China [25]; Meng and Du conducted a quantitative study of green energy efficiency in different provinces of China using the DEA model [26]. Based on the core database of the Web of Science, this study sorted a total of 1000 DEA topic-related studies in the past five years and used the LinLog layout algorithm and the modularity clustering algorithm to construct a high-frequency keyword contribution network (Figure 1) which can reflect key information, such as research objects, fields, research scales, and model methods, related to this topic to a certain extent. A comparison of selected studies related to energy efficiency based on data envelopment analysis is shown in

Table 1. Comparison of selected studies related to energy efficiency based on DEA.

Study	Scope	Method
Wang et al. (2019) [11]	25 countries	SBM model and Malmquist Index
Zhang and Chen (2022) [12]	13 RECP countries	Three-stage SBM model
Jebali et al. (2017) [13]	Mediterranean countries	Two-stage bootstrap DEA model
Ren et al. (2020) [14]	30 provinces, China	Metafrontier DEA model
Ma and Wang (2022) [15]	96 cities, China	Super-EBM model
Zhao et al. (2019) [16]	30 provinces, China	Three-stage DEA model
Li et al. (2022) [17]	30 provinces, China	Bootstrapped DEA model
Wang and Wang (2020) [18]	284 cities, China	Malmquist–Luenberger index
Keirstead (2013) [19]	198 cities, UK	DEA and Regression model
Pan et al. (2020) [20]	30 provinces, China	SBM and Regression model
Eguchi et al. (2021) [21]	Thermal power plant	Multi-hierarchy DEA model
Aldieri et al. (2021) [22]	American companies	DEA model and Malmquist Index
Ślusarz et al. (2021) [24]	Provinces of Poland	CCR-DEA model
Chen et al. (2021) [25]	30 provinces, China	Mixed integer DEA model
Meng and Qu (2022) [26]	29 provinces, China	Super-SBM and GML model

.

On the other hand, the development of industrial structures is an important research topic in industrial economics. In recent years, facing the challenges of sustainable development, scholars in related fields have carried out in-depth discussions on issues such as the optimization of industrial structure [27], the green transformation of industrial structure [28], and the quantification of industrial structure development levels [29]. Relevant research results provide important theoretical references and technical support for the sustainable development of regional industrial structures. Of course, the discussion of industrial structure is not limited to industrial economics but also involves resources, the environment, and other related fields, such that it has a strongly interdisciplinary character [30]. There is a close connection between the level of development of regional industrial structures and the pressure on resources and the environment, and industrial restructuring will have different degrees of backward effects on numerous fields. Therefore, industrial structure development is also an enduring research topic in the fields of resource and energy utilization [31,32], ecological and environmental protection [33,34], etc. In particular, many analyses have been carried out on the relationship between regional industrial structure development and resource and environment consumption, involving water resource utilization [35], energy consumption [36], greenhouse gas emissions [37], land use [38], climate change [39], and many other fields. The research methodology involves a variety of statistical and economic methods, such as optimization models, regression analysis models, system dynamics models, and input–output models. For example, Mi et al. established an optimization model based on the input–output method to explore the potential impact of industrial structure changes on energy consumption and carbon dioxide emissions at the urban scale [40]. Wan et al. combined the double difference model to analyze the impact mechanism of the adjustment of industrial structure at the watershed scale on regional ecological compensation [33].

In general, the above research has resulted in a series of important discoveries which have a high reference value for regional industrial structure development and the sustainable utilization of energy and resources. However, it is undeniable that most current energy efficiency studies based on data envelopment analysis use cross-sectional models, which cannot meet the needs of dynamic calculations. Moreover, some studies often have the problem of the incomparability of effective decision-making units (DMUs), especially when the number of DMUs is large, which will increase the uncertainty of the efficiency measurement results [41]. “Carbon neutrality” has become a major strategic layout for China to actively address climate change. Considering carbon emission constraints, the coordination between energy utilization efficiency and industrial structure development in traditional industrial cities has rarely been analyzed, especially from multiple time scales. Related challenges include achieving a long-term time-series dynamic measurement of energy utilization efficiency while ensuring full comparability of all DMUs, comprehensively quantifying the level of industrial structure development from various perspectives and identifying a harmonious relationship between energy utilization efficiency and industrial structure development. Feasible solutions need to be found for the aforementioned issues.

1.3. Objective and Contributions

This study presents a three-stage analysis method that includes measurement, quantification, and identification modules. The potential contributions of this study are: (a) an integrated data envelopment analysis model, known as the SW-DEA model, developed to dynamically measure energy utilization efficiency by incorporating carbon emission constraints from the input perspective and integrating the advantages of Super-DEA and Window-DEA models; (b) the industrial structure development index (ISDI), which considers both the rational and advanced degrees of an industrial structure. The ISDI offers a novel approach to quantifying the level of industrial structure development; and (c) combined with Tapio decoupling theory, a harmonious relationship identification model constructed to explore the dynamic coordination characteristics of EUE and ISDI across various time scales. The methodological framework described above was applied in a case study of a traditionally energy-rich province in China to develop a systematic understanding of the spatial and temporal distribution characteristics of energy utilization efficiency and industrial structure development levels in traditional industrial cities and then to refine and identify the dynamic harmonious relationship between them. The research findings offer valuable insights for formulating sustainable energy utilization strategies and promoting the high-quality development of industrial structures in traditional industrial cities. Figure 2 illustrates the research framework of this study.

The other parts are arranged as follows. Section 2 introduces the methodology. Section 3 gives an overview of the study area and data sources. The analysis of the results and the discussion make up Section 4, and Section 5 distills the main conclusions and prospects.

2. Methodology

2.1. SW-DEA Model

DEA is a non-parametric efficiency measure that does not assume a functional relationship between input and output indicators and minimizes the influence of subjective factors. Therefore, the method has been widely applied in recent years in the quantification of efficiency studies in different fields of energy [11,12], water resources, carbon emissions, land use, and ecological functions. The traditional DEA model’s calculation results for multiple effective decision-making units on the production frontier are all 1, which makes it impossible to conduct further comparative analysis on effective DMUs. Andersen and Petersen [42] proposed the Super-DEA model based on the traditional DEA model, the principle of which is to remove the evaluated DMU from the reference set and for the effective DMU to still be evaluated as effective after increasing the input in equal proportion while keeping the other DMU input and output values unchanged. The Super-DEA model realizes that the efficiency value of the effective DMU is greater than 1, solves the comparability defect of the traditional DEA model, and can be used for sensitivity and stability analysis of efficiency.

The Super-DEA model is a static DEA model which uses cross-sectional data for a certain period and cannot be directly used for the dynamic calculation of long-term series efficiency values. In a long-term production process, the technology itself is constantly changing (technological progress), and the static DEA model cannot reflect this technological change. If the time-series panel data are decomposed into cross-sectional data and the static DEA model is used for multiple calculations, the calculation results can only be compared horizontally and statically with different DMUs in a specific section; they are not longitudinally comparable in the entire time series. The Window-DEA model can solve this problem well. The model sets multiple reference sets based on the moving average method. In a specific reference set, each DMU can be compared with itself and other DMUs so that the changes in the efficiency value of each DMU within a certain period can be tracked and, finally, the efficiency calculation based on long-term panel data completed [43]. In the Window-DEA model, DMU will correspond to multiple efficiency values under different windows in each period (except the first and last periods), and the average of multiple efficiency values corresponding to a period is the final efficiency value of the period.

Integrating the advantages of the two classic DEA models, a new combination model (SW-DEA) was constructed which can realize the dynamic calculation of energy utilization efficiency under the premise of full DMU comparability. The efficiency value of a DMU at period t under the window a is denoted as θ_(t,a). The final efficiency, θ_t, of this DMU at period t can be expressed as a segmentation function. The efficiency calculation formula of the SW-DEA model can be summarized as follows:

$$\begin{array}{l}\min \theta \hfill \\ \mathrm{s}.\mathrm{t}. \{\begin{array}{l}{\displaystyle \sum _{\begin{array}{c}j=1\\ j\ne k\end{array}}^n{\lambda }_j}{x}_{ij}\le \theta x_{ik}\\ {\displaystyle \sum _{\begin{array}{c}j=1\\ j\ne k\end{array}}^n{\lambda }_j}{y}_{rj}\ge y_{rk}\\ \lambda \ge 0\\ i=1,2\dots ,m;r=1,2\dots ,q;j=1,2\dots ,n\end{array}\hfill \end{array}$$

(1)

$${\theta }_t=\{\begin{array}{l}\frac{1}{t}{\displaystyle \sum _{a=1}^t{\theta }_{(t,a)}}, \hspace{1em} \hspace{1em}\hspace{1em} 1⩽t⩽d\hfill \\ \frac{1}{d}{\displaystyle \sum _{a=t-d+1}^t{\theta }_{(t,a)}},\hspace{1em}\hspace{1em} d<t⩽p-d+1\hfill \\ \frac{1}{p-t+1}{\displaystyle \sum _{a=t-d+1}^{p-d+1}{\theta }_{(t,a)}},\hspace{1em}p-d+1<t⩽p\hfill \end{array}$$

(2)

where X_k = (x_1k, x_2k, …, x_mk), Y_k = (y_1k, y_2k, …, y_rk), θ, and λ are the relative efficiency values and weights of the decision unit. If θ ≥ 1, this means that the decision unit is in the production frontier plane and is an effective DMU. m and q represent the number of input and output indicators, and n is the number of DMUs. θ_t is the efficiency of different DMUs in period t. d is the window width, and p is the length of the time series studied.

2.2. Industrial Structure Development Index

The level of industrial structure development is a concentrated expression of the stability and competitiveness of the national economic system [44]. Therefore, from a dynamic perspective, the quantification of the industrial structure development level should at least cover the two dimensions of “rational” and “advanced”, which are expressed in this study as the industrial structure rational degree (ISRD) and industrial structure advanced degree (ISAD). The industrial structure rational degree can generally be regarded as the degree of aggregation quality between industries, which is used to represent the overall stability of the national economic system. Based on the concept of entropy in information theory, the Theil index can quantify the degree of difference between objects [45]. Compared with other similar indicators, the Theil index can reflect the economic meaning and theoretical basis of structural deviation and increase consideration of the relative importance of industries, which has the advantage of avoiding the calculation of absolute values. It can be considered that this index has applicability in measuring the industrial structure rational degree [46]. Therefore, we redefine the Theil index based on the research needs and quantify ISRD based on Theil entropy. The calculation formula is as follows:

$$\mathrm{ISRD}={\displaystyle \sum _{i=1}^n\left(\frac{Y_i}{Y}\right)}\ln \left(\frac{Y_i}{L_i}/\frac{Y}{L}\right)$$

(3)

where ISRD is the industrial structure rational degree, Y_i is the added value of the i industry (i = 1, 2, 3), Y is the gross regional product, L_i represents the number of employees in the i industry, and L is the total employment in the region. The higher the ISRD, the greater the deviation of the current industrial structure from the equilibrium state and the stronger the irrationality of the industrial structure.

The industrial structure advanced level can be considered as a measure of the upgrading of industrial structure, and it is used to represent the degree of industrial structure at a high level. The upgrading of the industrial structure often follows the law of economic development that gradually shifts from being dominated by the primary industry to being dominated by the secondary industry and the tertiary industry [47]. The proportion of the added value of different industries in terms of GDP is used as a component to form a three-dimensional vector, X = (x_1,0, x_2,0, x_3,0). The angles between X₀ and the three industry vectors X₁ = (1, 0, 0), X₂ = (0, 1, 0), and X₃ = (0, 0, 1) are α₁, α₂, and α₃. Then, the industrial structure advanced degree (ISAD) can be measured as follows:

$${\alpha }_j=\arccos \left(\frac{{\displaystyle \sum _{i=1}^3\left(x_{i,j}\cdot x_{i,0}\right)}}{\left({\displaystyle \sum _{i=1}^3{\left(x_{i,j}^2\right)}^{1/2}}\cdot {\displaystyle \sum _{i=1}^3{\left(x_{i,0}^2\right)}^{1/2}}\right)}\right)j=1,2,3$$

(4)

$$\mathrm{ISAD}={\displaystyle \sum _{k=1}^3{\displaystyle \sum _{j=1}^k{\alpha }_j}}$$

(5)

The industrial structure development index (ISDI) was constructed to quantitatively characterize the level of regional industrial structure development by integrating the two dimensions of rational degree and advanced degree. The CRITIC weighting method is considered to be a more credible objective weighting method than the entropy weight method and the standard deviation method [48]. When setting the weight distribution scheme, we took into account both contrast and conflict and combined the CRITIC method to assign the weights of the two indices. Of course, the weight distribution scheme can be flexibly adjusted according to different research needs. The ISDI is calculated as follows:

$$\mathrm{ISDI}={\omega }_1{\mathrm{ISRD}}^{\prime }+{\omega }_2{\mathrm{ISAD}}^{\prime }$$

(6)

$${\mathrm{ISRD}}^{\prime }=\frac{\max (\mathrm{ISRD})-\mathrm{ISRD}}{\max (\mathrm{ISRD})-\min (\mathrm{ISRD})}$$

(7)

$${\mathrm{ISAD}}^{\prime }=\frac{\mathrm{ISAD}-\min (\mathrm{ISAD})}{\max (\mathrm{ISAD})-\min (\mathrm{ISAD})}$$

(8)

where ω₁ and ω₂ are the weights of ISRD and ISAD based on the CRITIC method, respectively. ISRD and ISAD are the industrial structure rational degree and the industrial structure advanced degree. Due to the difference in dimensions, ISRD and ISAD need to be normalized. ISRD′ and ISAD′ are the results of ISRD and ISAD normalization, respectively.

2.3. Tapio Decoupling Model

The elastic decoupling theory is a theory used to quantitatively determine the relationship between the fitness of different variables on time series, and Tapio developed its refinement to form the Tapio decoupling model [49]. This model can be used to judge the degree of decoupling between different objects at different scales and is widely used in research on carbon emissions [50], resource consumption [51], industrial development [52], energy utilization [50], and other related fields of resources and environment. This study defines the harmonious relationship between energy utilization efficiency and industrial structure development as a dynamic coordination and balance relationship on a time scale which can reflect the dynamic adaptation state of the two in the development process. Based on the basic concept of the Tapio decoupling model, in this study, a harmonious relationship identification model was constructed to further refine the harmonious relationship between energy utilization efficiency and industrial structure development in 13 cities in Heilongjiang Province at multiple time scales, and the model was constructed as follows:

$$\mathrm{TDI}=\frac{\Delta \mathrm{EUE}/{\mathrm{EUE}}_0}{\Delta \mathrm{ISDI}/{\mathrm{ISDI}}_0}=\frac{({\mathrm{EUE}}_t-{\mathrm{EUE}}_0)/{\mathrm{EUE}}_0}{({\mathrm{ISDI}}_t-{\mathrm{ISDI}}_0)/{\mathrm{ISDI}}_0}$$

(9)

where TDI is the Tapio decoupling index between energy utilization efficiency and industrial structure development index which is used to measure the degree of coordination between the two. ∆EUE/∆EUE₀ and ∆ISDI/∆ISDI₀ are the rates of change of energy utilization efficiency and industrial structure development for a certain period. ISDI₀ and EUE₀ are the ISDI and EUE at the beginning of the period; ISDI_t and EUE_t are the ISDI and EUE at the end of the period. Referring to the existing research results [49], the decoupling status definition criteria in this study were determined as shown in

Table 2. Decoupling status definition criteria.

△EUE/EUE0	△ISDI/ISDI0	TDI	Decoupling Status
>0	>0	>1.2	Expansive negative decoupling (END)
>0	<0	<0	Strong negative decoupling (SND)
<0	<0	[0, 0.8)	Weak negative decoupling (WND)
<0	<0	>1.2	Recessive decoupling (RD)
<0	>0	<0	Strong decoupling (SD)
>0	>0	[0, 0.8)	Weak decoupling (WD)
>0	>0	[0.8, 1.2)	Expansive connection (EC)
<0	<0	[0.8, 1.2)	Recessive connections (RC)

. Among them, END, SND, and WND represent the negative decoupling relationship between energy utilization efficiency and industrial structure development to different degrees, indicating poor dynamic synergy; RD, SD, and WD represent EUE and ISDI as achieving different degrees of decoupling; EC and RC represent EUE and ISDI as maintaining different degrees of dynamic synergy and failing to reach decoupling status.

3. Implementation

3.1. The Study Area

Exploring the coordination relationship between energy utilization and industrial structure with traditional energy provinces as the research area can better verify the applicability of the measurement–quantification–identification three-stage analysis method and increase the reference value of research findings for regional development. Heilongjiang Province is an important energy and industrial province in Northern China and plays an important role in China’s energy security [6]. Nonetheless, conspicuous discrepancies in economic progress emerge among the diverse cities nestled within Heilongjiang Province. The divergence is conspicuous when considering per capita GDP. The per capita income of DQ, HRB, and HH is relatively high, while the per capita GDP of QQH, QTH, and SH is at the lower level for the whole province. In terms of industrial structure, Heilongjiang Province is primarily based on the first and third industries, but certain industry-dominated cities, such as DQ and QTH, still have a significant proportion of the second industry. Over the past 70 years, Heilongjiang Province has produced more than 4% of China’s raw coal, 6.2% of its natural gas, and 32.9% of its crude oil, providing vital energy security for China’s economic and social development and ecological civilization construction. Against the backdrop of the “Revitalization of Northeast China” strategy, promoting the optimization and upgrading of the industrial structure, as well as improving energy utilization efficiency, have become pressing bottlenecks that different cities in Heilongjiang Province must overcome to achieve high-quality development. An overview of the study area is presented in Figure 3.

3.2. Data and Implementation

When employing the data envelopment analysis model for efficiency evaluation, the fundamental principle in selecting input–output indicators is to minimize their number while encompassing various dimensions of production factors. This approach enhances the rationality and interpretability of the results [10]. Therefore, referring to relevant research, representative indicators were selected from four dimensions: energy, capital, labor, and ecological environment. In this study, the total energy consumption of the region was used to represent energy input, fixed asset investment represented social capital input, and the number of employees was used as a representation of labor input. As the economic benefits gained from the input of production factors under certain conditions are the most direct reflection of the high efficiency of energy utilization regions, the regional gross domestic product (GDP) was selected as the output variable to represent efficiency.

According to the 14th Five-Year Plan, China aims to achieve carbon neutrality by 2060. Over 80% of China’s carbon emissions come from energy consumption activities [53]. Carbon neutrality is a crucial long-term national strategy for China, and different industries and sectors are actively implementing carbon reduction actions. The energy sector’s efforts to reduce carbon emissions will be a crucial aspect of the carbon neutrality strategy. Therefore, it is necessary to dynamically measure energy utilization efficiency considering carbon emission constraints. In this study, CO₂ emissions were selected as an indicator of environmental function input in the model calculation, which reflects the carbon emission constraints while avoiding the problem of reasonable weight allocation among multiple output indicators. The selected input–output indicators in this study are shown in

Table 3. Input–output indicator system of energy utilization efficiency.

Type	Indicator	Meaning
Input	Total energy consumption	Reflects energy resource input
	Fixed asset investment	Reflects capital factor input
	Number of employees	Reflects human resource input
	Carbon dioxide emissions	Reflect environmental constraint input
Output	Gross domestic product	Reflects economic benefit output

.

The research period spans from 2010 to 2020, and the research unit is 13 cities in Heilongjiang Province. The data for the relevant indicators were obtained from the following sources: the “Statistical Yearbook of Heilongjiang Province,” the “China Energy Statistical Yearbook,” the “China Urban Statistical Yearbook,” the “China Rural and Urban Construction Statistical Yearbook,” and the CEADs Carbon Accounting Database (https://www.ceads.net.cn/, accessed on 25 February 2023). Based on the SW-DEA model, this study integrated the moving average principle to conduct a long-term dynamic calculation of energy utilization efficiency for the cities in Heilongjiang Province from 2010 to 2020. A window width of 3 years was chosen, following the principle of “narrow as possible to improve comparability of results” [43]. The measurement process of energy utilization efficiency based on the SW-DEA model was completed using DEA-Solver 13.1 and DEAP 2.1 software. The calculation of industrial structure development indices and decoupling indices was realized using Matlab R2020a.

4. Results and Discussion

4.1. Energy Utilization Efficiency

The energy utilization efficiency (EUE) for all nine windows can be found in Figure 4. During the study period, DQ consistently reached the production frontier in almost all windows. As the core industrial city of Heilongjiang Province, it exhibited a significant advantage in terms of energy utilization compared to other cities. Most cities showed a year-on-year increase in energy utilization efficiency within the same window, while the efficiency values for the same year decreased as the window shifted. Taking HRB as an example, the efficiency value in 2012 is 1.01 in Window 1 but decreases to only 0.58 in Window 3. This indicates that the energy utilization levels of certain cities are rapidly improving, pushing the production frontier forward. It also confirms the relative nature of the results obtained through the SW-DEA model.

After further processing the EUE for specific years across all windows, the final results for energy utilization efficiency for the 13 cities in Heilongjiang Province from 2010 to 2020 are depicted in Figure 5a. Overall, there has been a significant improvement in energy utilization levels in Heilongjiang Province over the course of 11 years. The average EUE has increased from 0.54 in 2010 to 0.88 in 2020. Notably, the EUE values for the years 2017, 2018, 2019, and 2020 are significantly higher than the multi-year average of 0.71. On one hand, technological progress serves as an endogenous driving force for the improvement of EUE [18,20]. However, these results also reflect to some extent the efforts and determination of China to promote the energy revolution and transform energy utilization patterns in recent years [54]. Another interesting finding is that, in 2010, none of the cities were able to reach the production frontier in terms of energy utilization efficiency (EUE ≥ 1). However, by 2020, the number of effective DMUs had increased to six. Cities like DQ and HRB have achieved leading levels of energy utilization efficiency within the province, continuously pushing the production frontier forward. This finding further illustrates that cities with a strong industrial foundation and robust economic strength play a crucial role in driving the overall improvement of energy utilization levels in their respective provinces or regions. A related study has also reached a similar conclusion [18].

The spatial distribution of the average EUEs for different cities over multiple years is depicted in Figure 5b, revealing significant spatial variations in energy utilization efficiency. The cities of HRB, SH, and DQ, located in the southern part of Heilongjiang Province, exhibit relatively prominent levels of energy utilization, with average EUE values above 0.9 over the years. Among them, DQ consistently operated at the production frontier for 9 out of 11 years, showcasing its outstanding energy utilization performance, which can be attributed to its comprehensive industrial system. In the northern region, cities such as HH and GKM have average EUE values above 0.75, with a noticeable upward trend over the 11 years. In contrast, cities in the central and eastern parts of the province, including YC, QTH, HG, and JX, have average EUE values below 0.6, deviating significantly from the production frontier and exhibiting relatively lower energy utilization efficiency among the 13 cities. During the period from 2010 to 2014, only DQ, SH, and GKM had EUE values exceeding 1 among the 13 cities. However, in the years 2015 to 2020, HRB, HH, and SYS achieved EUE values surpassing 1 and became efficient DMUs. Although the other cities did not reach the production frontier throughout the entire study period, there was an overall upward trend in energy utilization efficiency. These findings suggest that the improvement in energy utilization efficiency among different cities in Heilongjiang Province does not exhibit strong dynamic coordination. However, cities with lower energy utilization levels are gradually narrowing the gap with respect to more efficient cities, leading to an overall enhancement in energy utilization efficiency across the province. This result is similar to Ma’s study on energy utilization efficiency in the Yellow River Basin [15].

4.2. Industrial Structure Development Level

The results of ISRD and ISAD for the 13 cities in Heilongjiang Province from 2010 to 2020 are depicted in Figure 6. From Figure 6a, it is evident that the average ISRD at the urban level is 0.14. Only three years (2010, 2011, and 2018) exhibited ISRD values lower than the average. Among the 13 cities, HRB, JX, HG, YC, QTH, MDJ, HH, and GKM demonstrated a higher level of industrial structure rationalization, with their multi-year average ISRD values below 0.1. However, the cities of SH and SYS displayed ISRD values of 0.59 and 0.35, respectively, indicating a relatively higher degree of industrial structure irrationality. During the research period, there was an increasing trend in the overall ISRD of Heilongjiang Province, indicating a gradual deviation from a balanced state and a certain degree of irrationality in the industrial structure. This can be attributed to the significant outflow of the province’s employed population, particularly high-quality talent, in recent years. Additionally, the aging trend has become more pronounced in the region. Feng’s study has shown that several cities in Heilongjiang have reached varying degrees of aging status [55]. The disproportionate decline in the employed population is the primary cause of the overall increase in ISRD in Heilongjiang Province.

In terms of the advanced degree of industrial structure (Figure 6b), the overall ISAD shows an increasing trend, with a multi-year average of 6.06. Notably, ISAD values for the years 2016, 2017, 2018, and 2019 were above 6.06, indicating that Heilongjiang Province has achieved certain results in optimizing and adjusting its industrial structure in recent years. This finding aligns with Lv’s research on rural economic development in Heilongjiang [56]. Specifically, the cities of HRB, QQH, DQ, QTH, and MDJ have ISAD averages exceeding 6.2, highlighting their significant advantage in the advanced level of industrial structure compared to other cities. The rise in the proportion of the tertiary sector and the shift of industrial focus towards the tertiary sector have contributed to the improvement in the advanced degree of industrial structure. This is the primary reason for the increase in ISAD among most traditional industrial cities. However, HG stands out with a lower ISAD multi-year average of only 5.55, indicating the lowest level of industrial structure advancement among the 13 cities. Further analysis of HG’s industrial system reveals that the primary sector holds a significant position in its industrial layout, while the proportions of the secondary and tertiary sectors have not experienced significant improvement in recent years. This may explain the relatively backward ISAD in HG.

The weighting scheme for ISRD and ISAD was determined using the CIRTIC weighting method with weights of 0.611 and 0.389, respectively. By de-dimensionalization and weighted summation of the two indices, the Industrial Structure Development Index (ISDI) for the 13 cities in Heilongjiang Province from 2010 to 2020 was calculated. The spatial distribution of ISDI and its variations are presented in Figure 7. Over the research period, the overall ISDI for the 13 cities exhibited a declining trend followed by an upward trend, and then a significant decline. While the industrial structure showed some optimization and upgrading in specific years, the overall ISAD showed a slight decrease throughout the entire study period. From 2018 to 2020, except for YC and MDJ, the ISDI of the other 11 cities showed a significant downward trend. Further analysis reveals that the increase in ISRD during this period can be attributed to the loss of the employed population, which in turn led to a decline in the industrial structure development index.

The level of industrial structure development among the 13 cities exhibits significant spatial variations. The cities in the southwest and northwest regions generally demonstrate a higher overall level of industrial structure development, while the cities with relatively lower ISDIs are primarily concentrated in the central part of Heilongjiang Province. Jiamusi stands out as having the most prominent fluctuations in its ISDI over the initial and final years (Figure 7n). HRB, QQH, MDJ, QTH, and GKM have relatively higher ISDI values, with their multi-year averages exceeding 0.8. In particular, HRB, as the provincial capital and economic center of Heilongjiang Province, maintained an ISDI above 0.8 throughout the period of 2010–2020, highlighting its significant advantage in terms of industrial structure development compared to other traditional industrial cities. SH’s level of industrial structure development is relatively lagging among the 13 cities, with an ISDI multi-year average of only 0.33. This necessitates optimizing the regional industrial layout and exploring novel pathways for high-quality industrial development that align with the local conditions. Overall, the industrial structure development level in Heilongjiang Province has shown some improvement during the study period. Cities like HRB and MDJ, as core cities in the Heilongjiang metropolitan area, have played a significant role in radiating and driving the industrial structure development of surrounding cities. Zhang’s study on carbon emission intensity in Chinese cities also arrived at similar conclusions [57]. There is still significant room for improvement in the level of industrial structure development in cities like SH and SYS. Further analysis of the industrial structure layout in these cities reveals that there was an excessive reliance on primary industry accompanied by a noticeable decline in the development pace of secondary industry during the study period. Additionally, the proportion of the tertiary industry remained relatively low for an extended period. These factors contribute to the relatively lagging level of industrial structure development. Going forward, it is crucial for these cities to focus on clarifying their development positioning, accelerating the optimization of industrial structures, and promoting deep-level adjustments in the industrial layout while leveraging their regional industrial characteristics.

4.3. Relationship Identification between EUE and ISDI

Based on the Tapio decoupling model, the dynamic coordination between energy efficiency and industrial structure development at the city level can be identified. To further investigate the decoupling status of the two factors at different time scales, the analysis included the identification of the overall study period (WS) as well as three sub-stages: S1 (2011–2013), S2 (2014–2016), and S3 (2017–2019). This allowed for a more detailed exploration of the decoupling status during different time intervals. First, the TDI was calculated for each city using a 3-year moving window. Then, the overall TDI for the entire study period of 2010–2020 was calculated using the entire duration as the window width. Finally, based on the defined criteria for decoupling status (Table 2), the dynamic coordination between energy efficiency and industrial structure development was determined for different time scales. The results are presented in Figure 8.

Between 2011 and 2013 (Figure 8a), the cities of QQH, DQ, YC, and GKM exhibited a strong decoupling relationship between EUE and ISDI. This means that while their industrial structure development level continued to improve, their energy utilization level decreased, indicating weak dynamic coordination between the two. Conversely, HRB, MDJ, and SH were in a strong negative decoupling state, where their energy utilization level increased while ISDI showed a declining trend. Due to the simultaneous decrease in both EUE and ISDI, with the former declining more significantly, HG and QTH exhibited a deteriorating decoupling relationship during this phase. In contrast, the cities of JX and JMS experienced a simultaneous decrease in energy utilization efficiency and industrial structure development index during this phase, but the decline in ISDI was significantly greater than that in EUE, indicating a weak negative decoupling relationship between the two. Heihe City exemplified a positive growth synergy between EUE and ISDI, with the former growing at a faster pace than the latter, indicating an expansive negative decoupling state. In pursuit of carbon neutrality goals, China has recognized the significance of enhancing energy utilization efficiency and curbing carbon emissions from energy consumption [42]. In this regard, an expansive negative decoupling relationship, as observed in Heihe City, represents an ideal coordination, where energy utilization efficiency increases while carbon emissions decrease. During the period of 2014–2016 (Figure 8b), JX, SYS, and YC transitioned into an expansive negative decoupling state, while JMS and MDJ shifted to a strong decoupling state. QQH, HH, and GKM changed to a strong negative decoupling state, and HG and QTH transitioned from a previous declining decoupling state to an expansive coupling state. Throughout this period, there was an overall improvement in the coordination between energy utilization efficiency and industrial structure development in Heilongjiang Province. From 2017 to 2019 (Figure 8c), QQH, JX, DQ, and QTH transitioned to a weak negative decoupling state, indicating a lack of coordinated development between EUE and ISDI throughout the study period. HG and MDJ shifted to an expansive negative decoupling state, showing a significant improvement in the coordination between EUE and ISDI compared to the previous stage. However, it is undeniable that, compared to the previous period, there was a certain degree of deterioration in the coordination between industrial structure and energy utilization efficiency in most cities during S3.

The analysis of the harmonious relationship between energy utilization efficiency and industrial structure development in the 13 cities throughout the research period using a window width approach (as illustrated in Figure 8d) revealed two types of decoupling states: expansive negative decoupling and strong negative decoupling, from 2010 to 2020. Nine cities, namely, HRB, QQH, JX, HG, SYS, JMS, QTH, HH, and SH, exhibited a strong negative decoupling state, indicating limited coordination between the improvement in industrial structure development and energy utilization efficiency. Therefore, it is imperative to promote the optimization and upgrading of industrial structures in these cities. On the other hand, the remaining four cities demonstrated an expansive negative decoupling state, indicating a continued strong positive correlation between EUE and ISDI. In general, the EUE and ISDI in Heilongjiang Province exhibited a strong negative decoupling state during the period of 2010–2020 (Figure 8e). Upon closer examination of different stages, it was observed that both EUE and ISDI remained in a strong decoupling state during S1 and S3 while experiencing an expansive negative decoupling state during S2. It is evident that there exists a certain degree of negative decoupling between energy utilization and industrial structure development in the 13 cities of Heilongjiang. Over the span of 11 years, the overall coordination between the two factors primarily leaned towards a strong negative decoupling, indicating that the improvement in industrial structure development lagged behind the enhancement of energy utilization efficiency. This signifies a failure to achieve the ideal bidirectional advancement. Notably, this finding aligns with the conclusions drawn from Ma’s research [58]. The aforementioned findings suggest that expediting the upgrading of industrial structure layout in traditional industrial cities like QQH, JX, and HG in China is crucial to achieving carbon neutrality. This process should be accompanied by a consistent improvement in energy utilization levels. Enhancing the dynamic coordination between these two aspects is crucial for facilitating the green transformation and sustainable development of energy-intensive cities.

5. Conclusions

In this study, a three-stage analysis method containing measurement, quantification, and identification modules was proposed for the systematic exploration of the decoupling relationship between energy utilization efficiency and industrial structure development. Specifically, within the measurement module, this study integrated two classical DEA models, developed the SW-DEA model, and incorporated carbon emission constraints from an input perspective. An innovative multidimensional input–output index system was established. Moreover, this study introduced a comprehensive industrial structure development index from two perspectives: rational degree and advanced degree. This provides a novel approach to quantifying the level of industrial structure development. Additionally, the theory of elasticity decoupling was employed to investigate the relationship between energy utilization and industrial structure development within the identification module, enabling the identification of their dynamic coordination across various time scales. The previously mentioned methodological framework was applied in a case study of a traditional energy province in Northern China, yielding the following primary conclusions:

(1)

The energy utilization efficiency at the urban scale in Heilongjiang Province improved overall during the study period, and the average EUE increased from 0.54 in 2010 to 0.88 in 2020. Spatial variations in energy utilization efficiency are evident, with southern cities exhibiting higher levels compared to other regions. However, the disparity among different cities has gradually diminished. Core cities, such as DQ and HRB, have consistently maintained a position at the production frontier, demonstrating remarkable advantages in terms of energy utilization efficiency.

(2)

The overall level of industrial structure development in Heilongjiang Province has experienced a slight downward trend, with the most significant decline observed between 2018 and 2020. The primary factor contributing to this decline is the employment–population factor. Southern cities centered around HRB exhibited a more advanced level of industrial structure development. Cities like SH and SYS showed relatively slower progress in industrial structure development, underscoring the urgency to promptly establish new industrial development orientations and drive profound optimization of the industrial structure.

(3)

The harmonious relationship between energy utilization and industrial structure exhibited distinct stage-based characteristics from 2010 to 2020. Overall, the harmonious relationship was predominantly characterized by strong negative decoupling, with the ISDI lagging behind the improvement in EUE. The dynamic synergy between energy utilization and industrial structure development was weak, resulting in a lack of favorable decoupling. All 13 cities demonstrated varying degrees of negative decoupling. It is essential to ensure the enhancement of energy utilization levels while promptly establishing a sustainable industrial layout and high-quality industrial structure.

It should be noted that this study has certain limitations. Firstly, regarding the quantification of industrial structure development levels, this research solely considered rational degree and advanced degree. The extent to which the constructed industrial structure development index reflects the actual level of industrial structure development in the region requires further investigation. In reality, the quantification of industrial structure development involves a wide range of factors, and future research should focus on how to enhance the representativeness of quantitative indicators for actual industrial structures. Furthermore, this study only utilized decoupling models to preliminarily identify the harmonious relationship between energy utilization efficiency and industrial structure development level, without delving into the analysis of their feedback mechanisms. Future research may need to incorporate feedback-mechanism simulation models to explore the deeper interplay between regional energy utilization and industrial structure development. This specialized investigation can better contribute to the achievement of carbon neutrality goals in the energy sector and the sustainable development of the industrial system.