A Coupling Mechanism and the Measurement of Science and Technology Innovation and Rural Revitalization Systems

Abstract

Under the concept of scientific and technological progress and new rural development, the relationship between scientific and technological innovation and rural revitalization is becoming closer and closer. The purpose of this study is to reveal the coupling coordination mechanism between the two and promote agricultural and rural construction and regional high-quality development through quantitative analysis and scientific decision making. This paper analyzes the systematic coupling mechanism of scientific and technological innovation and rural revitalization. An evaluation index system coupled with a coordination measure model and grey prediction GM (1,1) model are constructed. We demonstrate the implementation process of these models using data from Hebei province from 2010 to 2019. According to the application results, some suggestions for policy and measures are put forward. The results verify the coupling and coordination relationship between the two and the feasibility of the method. The results show that the state of coupling coordination of scientific and technological innovation and rural revitalization systems in Hebei province has transitioned from a mild imbalance to the primary coordination stage, and it is predicted that it will reach good coordination in 2024. This study provides theoretical and methodological support for the coupling coordination between regional scientific and technological innovation and rural revitalization and can serve as a useful reference for similar regional rural construction.

1. Introduction

In the context of comprehensively deepening agricultural reform and continuously improving rural construction, scientific and technological innovation has become an important means for improving the level of agricultural productivity and realizing rural revitalization. It is also an inevitable requirement to realize the innovation-driven and green development of regional economies in the new era. Some of the following policy documents related to agricultural and rural development also illustrate that rural revitalization needs to rely on scientific and technological innovation. Following the proposal of the “rural revitalization” strategy, the “implementation plan of science and technology support action for rural revitalization” introduced in 2018 proposed focusing on industrial technology, strengthening technological innovation and the application of achievements, and promoting the revitalization of rural science and technology [1,2]. In order to achieve a breakthrough in agricultural core technology, the No. 1 Central Document of 2021 clearly strengthens the support for modern agricultural science and technology and material equipment. The Ministry of Science and Technology proposed that innovation-driven rural revitalization and development is an inevitable requirement to accelerate agricultural and rural modernization. It is expected that the rate of contribution of progress in agricultural science and technology will reach 61.5% in 2022. In the 14th Five-Year Plan for Promoting Agricultural and Rural Modernization, it is also proposed to promote the transformation of agricultural scientific and technological achievements into productive forces and to clarify the development of rural revitalization driven by agricultural science and technology. Against the background of building a new development pattern, the development of agriculture and rural areas has entered a critical period. In implementing scientific and technological innovation to drive rural revitalization, accelerating smart agriculture and digital rural construction have become the primary methods of realizing agricultural and rural economic transformation and green innovation development in the new era.

Previous studies have rarely analyzed the coupling mechanism of science and technology innovation and the rural revitalization system in depth, with a particular lack of model research on the measurement of the system’s coupling coordination state and development trend prediction at a certain regional level, which also seriously restricts the speed and effect of rural construction and development. Therefore, exploring the mechanism and state measurement of the coordinated development of science and technology innovation and rural revitalization is of great significance and has become the focus of academic attention. This study investigates the coordinated development of science and technology innovation and rural revitalization from the perspective of the coupling mechanism and its measurement, which contributes to the literature and is expected to encourage a breakthrough in the field. This study elaborates on the coupling and coordination mechanism of science and technology innovation and rural revitalization, and it constructs a systematic coupling and coordination evaluation index system. The coupling coordination degree model is used to measure the coupling development status, and a grey mathematical prediction model is introduced to predict the development trend of coordination between the two and propose development strategies. Through the analysis of the mechanism and the quantitative evaluation of the state of the coordinated development of science and technology innovation and rural revitalization, the research on the theory and evaluation related to this topic is expected to be enriched. Under the Beijing–Tianjin–Hebei synergistic development strategy, Hebei province, as a large agricultural province, has a difficult and complex task in terms of rural construction, and the research results obtained using Hebei as an example have important practical application value for promoting the synergistic development of science and technology innovation and rural revitalization.

The rest of the article is presented below. We first review the literature related to science and technology innovation and agricultural and rural development. Next, an in-depth analysis of the mechanism of the coupled development of science and technology innovation and rural revitalization is presented. Then, the relevant evaluation models and prediction methods are introduced. Taking Hebei province in China as an example, we construct an evaluation index system for the coupled and coordinated development of science and technology innovation and rural revitalization and validate the model. Finally, the results are analyzed, and development strategy suggestions and conclusions are discussed.

2. Literature Review

The essence of the study of science and technology innovation-driven rural revitalization is to use advanced production technology in the production system and improve the modernization of agricultural and rural areas [3]. The focus of this process is to grasp the core strengths of “people, things and industry”, with “things” being characteristic industries and modern technical facilities. The prerequisite for the effective construction of a rural wisdom system is also the support of agricultural technology [4,5,6].

Academic research on technology and rural issues can be broadly divided into three categories. The first is research on rural revitalization from a technological perspective. Tripathi et al. [7], Wiredu et al. [8] and Belova et al. [9] described the importance of information technology and innovation centers for the development of rural areas. Lucero et al. [10] and Dirierzhe [11] identified innovative systems as an important tool for improving the economic situation of farmers. Michail et al. [12], Blasch et al. [13] and Long [14] argued that precision farming techniques are key to promoting economic efficiency in agriculture. Zhang et al. suggested three main reasons for the weak development of science and technology innovation today: the lack of motivation for agricultural innovation, the uneven distribution of resources and the low rate of application and transformation of science and technology results [15,16,17]. A great amount of adequate research on science and technology has been conducted in the countryside, and in-depth discussions have been conducted on the development of science and technology and rural revitalization, mainly for enhancing the integration of science and technology industries and optimizing resource allocation.

The second category is studies on the relevance of science and technology to the countryside. Ibitoye [18] analyzed the relevance of science and technology to agricultural production by using poultry incubators as an example. Aryal et al. [19] analyzed the concept and factors of agricultural modernization. In addition, scholars have conducted research on the integration of agricultural energy technology and sustainable rural development using field research mostly in urban areas [20,21]. Wu et al. [22] proposed new ideas and responses to the development of agricultural science and technology in China scholars’ research, mainly focusing on the study of agricultural modernization and sustainable rural development, but only a few works have explored the coupling and coordination interaction between the two from the perspective of the coupling mechanism.

The third is quantitative research on the level of innovation and degree of integration of agricultural science and technology. At present, most scholars measure the level of agricultural science and technology with multi-dimensional and multi-index evaluation systems using models such as the entropy-weighted TOPSIS method, CPM, Moran’s I index and vector autoregressive model to conduct quantitative research [23,24,25]. Most scholars have focused on measuring the level of agricultural science and technology, but there is a lack of development trend predictions for a particular provincial level. There are few quantitative studies on the use of the entropy value method and coupling coordination model. Therefore, based on the existing research results, the coupling between science and technology innovation and rural revitalization is further quantitatively analyzed from the provincial level.

3. Mechanism of the Coupling Effect of Science and Technology Innovation and Rural Revitalization

Coupling coordination is the transformation of two or more systems to interact and form a benign correlation. This benign correlation turns a simple and disorderly subsystem into a complex and orderly integrated system, completing the upgrading of the integrated system and exerting an overall effect [26]. At present, rural revitalization is facing many development challenges in areas such as industry, technology, ecology and governance, and it is urgent to support scientific and technological innovation. At the same time, the demand for and development of rural construction will also force the continuous improvement of scientific and technological innovation. From the perspective of resource factors, rural revitalization, in a sense, is the reorganization and optimization of agricultural and rural resources. The essence of scientific and technological innovation is to act on the rural revitalization system through land, talent, technology and other media resources. The two have a close dynamic coupling relationship to a certain extent and are manifested as an input and output mechanism, connection mechanism, action mechanism and feedback mechanism, as shown in Figure 1.

3.1. Input and Output Mechanism

The scientific and technological innovation system is mainly composed on the basis of scientific and technological innovation, the input of scientific and technological resources, the output of scientific and technological achievements, the system of scientific and technological innovation and the platform of scientific and technological innovation. Through the input of innovation system elements and the role of media resources, scientific and technological innovation drives the development of agricultural and rural modernization so as to realize the output goal of rural revitalization. (1) The foundation of scientific and technological innovation is the source of rural revitalization. Capital and labor are the foundation of innovation. The improvement of the economic level can accelerate the aggregation of talents, technology and capital in the field of agriculture. The positive externalizations generated by the agglomeration of resource factors promote the spillover of knowledge and technology between regions [27,28], improve the output of scientific and technological achievements, drive the integration of rural industry, create more employment opportunities and help realize prosperity. (2) The input of scientific and technological resources is the premise of driving rural revitalization. It is often accompanied by investment in infrastructure, digital technology and supporting services, which lay the foundation for scientific and technological research and development. Artificial intelligence, cloud computing and big data technology are integrated into rural construction to reduce social conflicts, improve the quality and efficiency of public services such as education, health care and rehabilitation and promote effective rural governance [29]. (3) The output of scientific and technological achievements is a driver of rural revitalization. Through the transformation of scientific research achievements such as invention patents, projects and papers into productivity, they can provide high-tech and high-value-added products or services for the development of agriculture, rural areas and farmers so as to promote agricultural technological progress, the sustainable behavior of farmers and a livable rural ecology. (4) A scientific and technological innovation system guarantees rural revitalization. The government promotes the upgrading of traditional technology and inherent modes through financial subsidies and tax incentives, accelerates the integration and optimization of industries, promotes the formation of new models, new formats and new technologies and realizes industrial prosperity. (5) Science and technology innovation platforms provide support for rural revitalization. Relevant technological innovation platforms such as engineering and technology centers, research centers, key laboratories and innovation strategic innovation alliances can maximize the agglomeration advantages of equipment, talent and intellectual capital, provide advanced technical guidance and experimental conditions for agricultural production, promote the joint research of core technologies such as the modern seed industry, agricultural machinery and equipment, accelerate the popularization and application of agricultural science and technology and carry out research, production and service in the fields of green industry, smart agriculture and the digital countryside.

3.2. Connection Mechanism

In the coupled system of rural revitalization and scientific and technological innovation, land, talent and technology, as media resources, play a connecting role in the interaction between the two. (1) Land is fundamental to farmers’ productivity, and agricultural technology is used to improve land use and productivity and raise farmers’ incomes [30,31]. (2) Talent is the core of scientific and technological innovation and rural revitalization. It is exemplified by the role played by local experts, returning entrepreneurs and new professional farmers and cultivates a group of modern agricultural science and technology talents with local feelings, as well as talents in rural planning engineering, rural e-commerce logistics and agricultural product sales management. It provides knowledge support for the development of agricultural science and technology, the industrial chain, agricultural science and technology progress and rural ecological construction. (3) Agricultural technology is an important engine for rural revitalization. New technologies optimize production resources, associate other industries with each other, connect industries, promote intelligent production, provide digital management and convenient service and realize industrial transformation and economic benefits. (4) The government plays a guiding role in organization, providing guidance for rural development and scientific and technological innovation, taking low-carbon, intelligent and digital systems as the baseline, embedding the new development concept into the elements of rural development and technological innovation and transforming the single production and management system for the realization of supply chain management through technological change. (5) The environment includes the natural environment and social environment, which are not only the objects of scientific and technological innovation but also the carriers of rural revitalization. A livable ecology and a comfortable life are promoted through scientific and technological innovation to reduce the number of pesticides and fertilizers and reduce environmental pollutants, the promotion of industrial green transformation and scientific and technological innovation to implement digital rural construction. (6) The application of advanced technology and the improvement of the level of science and culture complement each other. By guiding farmers to learn traditional cultural knowledge and modern information technology, the shortcomings of rural scientific knowledge and rural civilization construction can be addressed [32].

3.3. Mechanism of Action

Scientific and technological innovation will lead to rural revitalization and development. In turn, this will lead to the application of new agricultural technologies, the development of industrial chains and supply chains and the high-quality development of agricultural production, farmers’ lives and rural ecology. Scientific and technological innovation also play a supporting role in rural revitalization. Relying on technology-based resources, we will boost industrial upgrading in the county, transform current agricultural technology into intelligent, low-carbon and green technology, improve the rate of resource utilization and create an ecological and livable rural environment. We will strengthen the popularization and application of science and technology, stimulate farmers’ enthusiasm for learning science, culture and information technology and improve the efficiency and benefits of agricultural production. The application of information technologies such as cloud computing, the Internet of Things, big data technology and artificial intelligence to social services such as farming, breeding, cooperative medical care and education in rural areas will not only improve the scientific and technological content of agricultural products but also facilitate greater production and a higher quality of life, promote rural spiritual civilization construction and improve social governance.

3.4. Feedback Mechanism

The effect of scientific and technological innovation driving rural revitalization can be evaluated by measuring the development status of rural revitalization, and the scientific and technological innovation policy can be constantly improved through the feedback of evaluation results, thus forming a benign interaction relationship. Agricultural rural modernization development cannot be separated from the innovation of science and technology. The emergence of new industries will effectively promote improvement in technical innovation [33], promote innovation efficiency in the formation of spatial spillover effects [34] and enable the diversification of industry transformation and the upgrading of leading consumer demand, in turn driving regional economic growth. The emergence of these new industries has provided a broad space for the development of agricultural technology innovation. Rural construction requires clear water and green mountains, soil remediation, energy conservation and a reduction in emissions, which are also inseparable from agricultural scientific and technological innovation. The continuous improvement of the overall quality and educational level of new professional farmers will guarantee knowledge for agricultural technological innovation, promote the rapid promotion of advanced production technology in rural areas and force scientific and technological progress and continuous innovation through the dynamic scientific evaluation of the application effect.

4. Research Methods

4.1. Coupled Coordination Model

4.1.1. Standardization of Raw Data

When ${\mathrm{x}}_{\mathrm{ij}}^{\prime }$ is a positive indicator, we have

(1)${\mathrm{x}}_{\mathrm{ij}}^{\prime }=\frac{{\mathrm{x}}_{\mathrm{ij}}-\min \left({\mathrm{x}}_{\mathrm{ij}}\right)}{\max \left({\mathrm{x}}_{\mathrm{ij}}\right)-\min \left({\mathrm{x}}_{\mathrm{ij}}\right)}\times 0.99+0.01$

When ${\mathrm{x}}_{\mathrm{ij}}^{\prime }$ is a reverse indicator, we have

(2)${\mathrm{x}}_{\mathrm{ij}}^{\prime }=\frac{\max \left({\mathrm{x}}_{\mathrm{ij}}\right)-{\mathrm{x}}_{\mathrm{ij}}}{\max \left({\mathrm{x}}_{\mathrm{ij}}\right)-\min \left({\mathrm{x}}_{\mathrm{ij}}\right)}\times 0.99+0.01$

where ${\mathrm{x}}_{\mathrm{ij}}$ is the original value for the ith year under the jth indicator in a system and ${\mathrm{x}}_{\mathrm{ij}}^{\prime }$ is the normalized value, where i = 1, 2, …, n; j = 1, 2, …, m. $\max \left({\mathrm{x}}_{\mathrm{ij}}\right)$ and $\min \left({\mathrm{x}}_{\mathrm{ij}}\right)$ are the maximum and minimum values of ${\mathrm{x}}_{\mathrm{ij}}$, respectively.

4.1.2. Calculation of the Index Weight

The calculation formula of the normalized value of the original data is as follows:

(3)$p_{\mathrm{ij}}=\raisebox{1ex}{${\mathrm{y}}_{\mathrm{ij}}^{\prime }$}\!\left/ \!\raisebox{-1ex}{${{\displaystyle \sum }}_{\mathrm{i}=1}^{\mathrm{n}}{\mathrm{y}}_{\mathrm{ij}}^{\prime }$}\right.$

the calculation formula for determining the entropy value of evaluation index is as follows:

(4)${\mathrm{e}}_{\mathrm{j}}=-\frac{1}{\ln \mathrm{m}}{\displaystyle \sum }_{\mathrm{i}=1}^{\mathrm{n}}{p}_{\mathrm{ij}}·\ln p_{\mathrm{ij}}$

the calculation formula for determining the weight of each indicator is as follows:

(5)${\mathsf{\beta }}_{\mathrm{j}}=\raisebox{1ex}{$\left(1-{\mathrm{e}}_{\mathrm{j}}\right)$}\!\left/ \!\raisebox{-1ex}{${{\displaystyle \sum }}_{\mathrm{j}=1}^{\mathrm{m}}\left(1-{\mathrm{e}}_{\mathrm{j}}\right)$}\right.$

where $p_{\mathrm{ij}}$ is the weight of indicator j, ${\mathrm{e}}_{\mathrm{j}}$ is the entropy value of indicator j and ${\mathsf{\beta }}_{\mathrm{j}}$ is the weight of indicator j.

4.1.3. Calculation of the Comprehensive Development Index

On the basis of weight calculation, the comprehensive development index of each subsystem is calculated to reflect the development status between systems. As Equation (6), we have:

(6)${\mathrm{U}}_{\mathrm{k}}={\displaystyle \sum }_{\mathrm{j}=1}^{\mathrm{m}}{\mathsf{\beta }}_{\mathrm{j}}·{\mathrm{y}}_{\mathrm{ij}}^{\prime }$

the calculation formula for determining the composite coordination index is as follows:

(7)$\mathrm{T}={\mathsf{\alpha }\mathrm{U}}_1+{\mathsf{\beta }\mathrm{U}}_2$

where ${\mathrm{U}}_{\mathrm{k}}$ is the comprehensive development index of the k subsystem and ${\mathrm{U}}_1$ and ${\mathrm{U}}_2$ are the comprehensive development index of scientific and technological innovation and rural revitalization, respectively. Referring to the existing research [35], this paper assigns $\mathsf{\alpha }$ and $\mathsf{\beta }$ to 0.4 and 0.6, respectively, and T is the composite coordination index.

4.1.4. Calculation of the Synergistic Development Coefficient

The formula for calculating the synergistic development coefficient is as follows:

(8)$\mathrm{E}=\frac{{\mathrm{U}}_1}{{\mathrm{U}}_2}$

where E is the synergistic development coefficient, which can evaluate the relative development status of both science and technology innovation and rural revitalization [36]. The division is shown in Table 1.

4.1.5. Calculation of Coupling Coordination

The coupling coordination model is applied to the sustainable development evaluation of the system. As Equations (9) and (10), we have:

(9)$\mathrm{C}=2\sqrt{\frac{{\mathrm{U}}_1{\mathrm{U}}_2}{{({\mathrm{U}}_1+{\mathrm{U}}_2)}^2}}$

(10)$\mathrm{D}=\sqrt{\mathrm{C}\times \mathrm{T}}$

where C is the degree of coupling and D is the degree of coupling coordination. The degree of coupling reflects the extent to which each subsystem contributes to the total system. Due to the differences in the respective development levels of the subsystems, there can be situations where the development levels of the subsystems are all low, while the calculated coupling degree is high. To avoid such problems, the coupling coordination degree is further used to measure the coupling coordination development level between the systems. The larger the D value, the higher the coupling coordination degree, and the better the coupling coordination development of the two systems. The classification of the coupling and coupling coordination types is shown in Table 2 and Table 3.

4.2. Grey Prediction Model

Grey forecasting is used to predict data with a high degree of uncertainty by identifying differences in trends between the various components of the system and then analyzing the interconnections and processing the raw data to create a more ordered set of data, thus forming the corresponding differential equation model, which is used to predict the future trends of the system [37].

4.2.1. Data Processing

This study provides a predictive model of coupling coordination. Before the GM (1,1) modeling, a cascade test was performed on the data to determine the suitability of this data series for use in the grey prediction model. For those data that did not pass the cascade test, a certain symmetric shift transformation was performed so that the processed data fell within the standard range for GM (1,1) modeling.

4.2.2. Model Solving

The original sequence ${\mathrm{x}}^{\left(0\right)}=\left\{{\mathrm{x}}^{\left(0\right)}\left(1\right),{\mathrm{x}}^{\left(0\right)}\left(2\right),\cdots ,{\mathrm{x}}^{\left(0\right)}\left(\mathrm{n}\right)\right\}$ is a non-negative data sequence. A new sequence ${\mathrm{x}}^{\left(1\right)}$ is obtained by the first-order accumulation of the series ${\mathrm{x}}^{\left(0\right)}$, where ${\mathrm{x}}^{\left(1\right)}\left(\mathrm{k}\right)={\displaystyle \sum }_{\mathrm{i}=1}^{\mathrm{k}}{\mathrm{x}}^{\left(0\right)}\left(\mathrm{i}\right)$ and k = 1, 2, $\cdots$, n as follows:

• (1). Establish the first-order differential linear equation, namely the original equation of GM (1,1):

(11) ${\mathrm{x}}^{\left(0\right)}\left(\mathrm{k}\right)+{\mathsf{\alpha }\mathrm{x}}^{\left(1\right)}\left(\mathrm{k}\right)=\mathsf{\mu }$

The whitening differential equation is

(12)$\frac{{\mathrm{dx}}^{\left(1\right)}}{\mathrm{dt}}+{\mathrm{x}}^{\left(1\right)}=\mathsf{\mu }$

where $\mathsf{\alpha }$ is the development coefficient and $\mathsf{\mu }$ is the amount of grey action.

• (2). Create a sequence of tight neighborhood mean generation:

${\mathrm{z}}^{\left(1\right)}=\left({\mathrm{z}}^{\left(1\right)}\left(2\right),{\mathrm{z}}^{\left(1\right)}\left(3\right),\cdots ,{\mathrm{z}}^{\left(1\right)}\left(\mathrm{n}\right)\right)$

among which

(13)${\mathrm{z}}^{\left(1\right)}\left(\mathrm{k}\right)=\gamma {\mathrm{x}}^{\left(1\right)}\left(\mathrm{k}\right)+\left(1-\mathsf{\gamma }\right){\mathrm{x}}^{\left(1\right)}\left(\mathrm{k}-1\right)$

where $\gamma$ is a weighting factor usually specified as 0.5 and $\mathrm{k}=2,3,\cdots ,\mathrm{n}$. The value of $\gamma$ can be determined by an optimization algorithm [38]. In order to simplify the calculation, through software simulation, 0.5 is appropriate in this paper.

We can shift the original equation toward

(14)$-{\mathsf{\alpha }\mathrm{z}}^{\left(1\right)}\left(\mathrm{k}\right)+\mathsf{\mu }={\mathrm{x}}^{\left(0\right)}\left(\mathrm{k}\right),\mathrm{k}=2,3$

Written in matrix form, this is expressed as

$\left[\begin{array}{cc}-{\mathrm{z}}^{\left(1\right)}\left(2\right)& 1\\ -{\mathrm{z}}^{\left(1\right)}\left(3\right)& 1\end{array}\right]\left[\begin{array}{c}\mathsf{\alpha }\\ \mathsf{\mu }\end{array}\right]=\left[\begin{array}{c}{\mathrm{x}}^{\left(0\right)}\left(2\right)\\ {\mathrm{x}}^{\left(0\right)}\left(3\right)\end{array}\right]$

• (3). The least squares solution for the grey parameter $\hat{\mathsf{\alpha }}$ is

(15)$\hat{\mathsf{\alpha }}={\left[\mathsf{\alpha }\mathsf{\mu }\right]}^{\mathrm{T}}={\left({\mathrm{B}}^{\mathrm{T}}\mathrm{B}\right)}^{-1}{\mathrm{B}}^{\mathrm{T}}\mathrm{Y}$

among which

$$\begin{gathered} \mathrm{B}=\left[\begin{array}{cc}-{\mathrm{z}}^{\left(1\right)}\left(2\right)& 1\\ \begin{array}{c}-{\mathrm{z}}^{\left(1\right)}\left(3\right)\\ ⋮\\ -{\mathrm{z}}^{\left(1\right)}\left(\mathrm{n}\right)\end{array}& \begin{array}{c}1\\ ⋮\\ 1\end{array}\end{array}\right] \\ \mathrm{Y}={\left[{\mathrm{x}}^{\left(0\right)}\left(2\right){\mathrm{x}}^{\left(0\right)}\left(3\right)\cdots {\mathrm{x}}^{\left(0\right)}\left(\mathrm{n}\right)\right]}^{\mathrm{T}} \end{gathered}$$

• (4). Establish the corresponding sequence of whitening differential equations:

  (16)${\hat{\mathrm{x}}}^{\left(1\right)}\left(\mathrm{k}\right)=\left({\mathrm{x}}^{\left(0\right)}\left(1\right)-\frac{\mathsf{\mu }}{\mathsf{\alpha }}\right){\mathrm{e}}^{-\mathsf{\alpha }\left(\mathrm{k}-1\right)}+\frac{\mathsf{\mu }}{\mathsf{\alpha }}$

• (5). A cumulative reduction is carried out, and the prediction of the original data is obtained after the cumulative reduction:

  (17)${\hat{\mathrm{x}}}^{\left(0\right)}\left(\mathrm{k}\right)={\hat{\mathrm{x}}}^{\left(1\right)}\left(\mathrm{k}\right)-{\hat{\mathrm{x}}}^{\left(1\right)}\left(\mathrm{k}-1\right)=\left(1-{\mathrm{e}}^{\mathsf{\alpha }}\right)\left({\mathrm{x}}^{\left(0\right)}\left(1\right)-\frac{\mathsf{\mu }}{\mathsf{\alpha }}\right){\mathrm{e}}^{-\mathsf{\alpha }\left(\mathrm{k}-1\right)}$

4.2.3. Model Testing

The model test is carried out through the posteriori error test, and the accuracy of the model is determined by the C value and p value.

(18)$\mathsf{\epsilon }\left(\mathrm{k}\right)={\mathrm{x}}^{\left(0\right)}\left(\mathrm{k}\right)-{\hat{\mathrm{x}}}^{\left(0\right)}\left(\mathrm{k}\right)$

(19)${\Delta }_{\mathrm{k}}=\frac{\mathsf{\epsilon }\left(\mathrm{k}\right)}{{\mathrm{x}}^{\left(0\right)}\left(\mathrm{k}\right)}$

(20)${\mathrm{S}}_1^2=\frac{1}{\mathrm{n}}{{\displaystyle \sum }}_{\mathrm{k}=1}^{\mathrm{n}}{\left[{\mathrm{x}}^{\left(0\right)}\left(\mathrm{k}\right)-\frac{1}{\mathrm{n}}{{\displaystyle \sum }}_{\mathrm{k}=1}^{\mathrm{n}}{\mathrm{x}}^{\left(0\right)}\left(\mathrm{k}\right)\right]}^2$

(21)${\mathrm{S}}_2^2=\frac{1}{\mathrm{n}}{{\displaystyle \sum }}_{\mathrm{k}=1}^{\mathrm{n}}{\left[\mathsf{\epsilon }\left(\mathrm{k}\right)-\frac{1}{\mathrm{n}}{{\displaystyle \sum }}_{\mathrm{k}=1}^{\mathrm{n}}\mathsf{\epsilon }\left(\mathrm{k}\right)\right]}^2$

(22)$\mathrm{C}=\frac{{\mathrm{S}}_2}{{\mathrm{S}}_1}$

(23)$p=\{\mathsf{\epsilon }\left(\mathrm{k}\right)-\frac{1}{\mathrm{n}}{{\displaystyle \sum }}_{\mathrm{k}=1}^{\mathrm{n}}\mathsf{\epsilon }\left(\mathrm{k}\right)<0.6745{\mathrm{S}}_1\}$

where $\mathsf{\epsilon }\left(\mathrm{k}\right)$ is the residual, ${\Delta }_{\mathrm{k}}$ is the relative error rate, ${\mathrm{S}}_1$ and ${\mathrm{S}}_2$ are the standard deviations of the original series and residuals, respectively, C is the posterior difference ratio value and p is the small error probability value. The model accuracy classification levels are shown in Table 4.

5. Empirical Analysis

5.1. Index Selection and Weight Determination

According to the principle of being systematic, concise and practical, and on the basis of previous research results, this article selected 11 indicators related to science and technology innovation base knowledge, investment and output and 15 indicators related to prosperous industry, livable ecology, local custom civilization, effective governance and a high quality of life in order to construct a system of two coupled coordination evaluation indexes [39,40,41,42]. The original data were obtained from the 2010–2019 China Statistical Yearbook, Hebei Economic Yearbook, Hebei Rural Statistical Yearbook, China Science and Technology Statistical Yearbook and previous statistical bulletins on the national economic and social development of Hebei province. To handle the missing data of some years, SPSS software was used to complete the data through the linear trending method of using proximity points with the missing data processing function. According to Equations (1)–(5), the weight coefficients of each indicator were calculated, as shown in Table 5.

As can be seen from Table 2, the weightings of the indicators of scientific and technological innovation and rural revitalization systems were different. In the system of innovation in science and technology, indicators such as the proportion of the added value of the tertiary industry to the GDP, the turnover of the technology market, the ratio of internal expenditure of R&D funds to business income and the total power of agricultural machinery had relatively larger weights, indicating a strong influence on the comprehensive development index of the science and technology innovation system, while indicators such as GDP per capita and the proportion of investment in education to the GDP had relatively smaller weights and a smaller impact on the comprehensive development index. The weighting of indicators such as GDP per capita and investment in education as a proportion of the GDP was relatively small, having a smaller impact on the overall development index of the scientific and technological innovation system. In the rural revitalization system, the weighting of indicators such as the growth rate of the per capita income of rural residents, the value added by the primary industry, the area of soil erosion control and the number of village committees was relatively large, indicating a higher impact on the comprehensive development index of the rural revitalization system. On the other hand, indicators such as the number of cultural stations in townships, the proportion of machine-harvested area to total sown area and the income disparity ratio between urban and rural residents had a relatively small weighting, which had a smaller impact on the comprehensive development index of the rural revitalization system.

5.2. The Overall Development Level of the Scientific and Technological Innovation System and Rural Vitalization System

According to Equations (6) and (7), the overall development index and overall coordination index of the scientific and technological innovation system and the rural revitalization system in Hebei province from 2010 to 2019 were obtained, as shown in Figure 2.

It can be seen from Figure 2 that the comprehensive development indexes of innovation in science and technology and rural revitalization in Hebei province both showed a steady increase, and the development trend of the comprehensive coordination index was between the development trend of the two systems, increasing from 0.109 in 2010 to 0.4162 in 2019. Overall, the comprehensive level of the development of science, technology and innovation was lagging behind, with the comprehensive development index being only 0.076 in 2010. With the increase in the intensity of science and technology, the intensity of investment in innovation increased, and both per capita consumption expenditure and the value added by the tertiary industry rose year by year until 2019, when the comprehensive development index steadily increased to 0.334, an increase of 339%. The “13th Five-Year Plan” for National Science and Technology Innovation was released in 2016, which called for attaching great importance to innovation in science and technology and accelerating the pace of innovation, and it is the main reason for the rising rate of science and technology innovation development from 2016 onward. In terms of the development of the rural revitalization system, the Composite Development Index was only 0.131 in 2010 and steadily increased to 0.471 in 2019, an increase of 259%. The growth from 2018 to 2019 was particularly rapid, mainly due to the Hebei Provincial Rural Work Conference held in early 2018. The conference emphasized the unwavering pursuit of rural revitalization and the implementation of policies to adhere to the priority development of agriculture and rural areas. In general, compared with rural revitalization, the comprehensive development level of scientific and technological innovation was low. This was due to the prominent contradiction between the development of science and technology and resources and the environment, as well as the unclear path for the integration of science and technology into economic, ecological, cultural and social construction, leading to the low development index of science and technology innovation. In addition, the increase in the comprehensive development index of the two systems indirectly reflects the existence of a complementary interaction between the two systems. In the future, it will continue to evolve in the direction of coordination and common progress.

5.3. Analysis of the Level of Coordination of System Coupling between Science and Technology Innovation and Rural Revitalization

According to Equations (8)–(10), the coupling degree, coupling coordination degree and coefficient of synergistic development of science and technology innovation and the rural revitalization system in Hebei province from 2010 to 2019 were obtained, and the results are shown in Table 6.

As can be seen from Table 3, the coupling degree of science and technology innovation and rural revitalization in Hebei province was stable, being maintained between 0.9 and 1, and the coefficient of synergistic development and the coupling coordination degree generally exhibited an upward trend. As the coupling degree reflects the degree of interconnection between the two systems of science and technology innovation and rural revitalization, it indicates that the mutual influence between the two systems is strong. Describing the degree of synergy and interdependence between the systems also requires reference to the coupling coordination degree and the coefficient of synergistic development, which were analyzed as follows.

In terms of the synergistic development of the two systems, the synergistic development coefficient was less than 0.8 and tended to increase during 2010–2017, indicating that the pressure on science and technology innovation increased in parallel with the development of rural revitalization. In 2018, the synergistic development coefficient was between 0.8 and 1.2, reaching the simultaneous development of rural revitalization and science and technology innovation. Under the guidance of policies such as the “13th Five-Year Plan for National Science and Technology Innovation”, the momentum of science and technology development was strong, and the growth rate of the comprehensive development level of science and technology innovation was accelerating. In 2019, the coordinated development coefficient was less than 0.8, and scientific and technological innovation lagged behind the development of rural construction, especially in terms of ecological and environmental protection, resource development and construction, as well as industrial model innovation. Although both systems are constantly moving toward high-speed development, rural revitalization has a particularly urgent need for scientific and technological innovation.

In terms of overall coupling coordination trends, there are four stages. The first stage is the period of mild dissonance from 2010 to 2011, increasing from 0.324 in 2010 to 0.399 in 2011, which indicates that the level of both scientific and technological innovation and rural revitalization is obviously low, and the degree of interrelationship is at a high level of coupling, but the degree of synergy and dependence between systems is low. The second stage is the near-imbalance stage, which exhibited an increase from 0.407 in 2012 to 0.468 in 2014. This period is in the “Twelfth Five-year Plan” period. Under the guidance of the national development strategy, agricultural modernization develops rapidly, technological innovation capacity construction receives great attention, and the coupling coordination level is improved with the first stage. The third stage is the barely coordinated period, which showed an increase from 0.532 in 2015 to 0.592 in 2018. One of the reasons for the improvement in this stage that occurred in 2014–2015 is that in 2014, the People’s Government of Hebei Province issued the “Implementation Opinions on Improving Rural Habitat Environment”, which put forward the guiding idea of accelerating the creation of a modern countryside and formulated 12 projects around rural revitalization. In order to develop the countryside more quickly, emerging agricultural technologies are needed as support, and under the new normal of rural development, importance is attached to the relationship between rural development and technological development. The fourth stage is the primary coordination period in 2019, with the coupling coordination degree increasing from 0.592 in 2018 to 0.640 in 2019. The main reason for this lies in the “rural revitalization” strategy proposed by the 19th National Congress of the Communist Party of China and the influence of the 2018 Hebei Province Rural Work Conference, which further increased the level of attention to rural economic development and promoted the coordinated development of scientific and technological innovation and rural revitalization through modern agricultural technological innovation and business model optimization.

6. Grey Prediction of the Coupled and Coordinated Development of the Regional Innovation System and Rural Revitalization

Based on the time series data of the coupling and coordination degree of science and technology innovation and the rural revitalization system from 2010 to 2019, this paper examined the actual and predicted values of coupling and coordination development in Hebei province from 2010 to 2019 by constructing a GM (1,1) grey model. If the relative error rate was less than 0.2, this meant that the requirements were met, and if it was less than 0.1, this meant that the requirements were higher. According to Equations (11)–(17), the predicted value of coupling coordinated development is obtained. The relative error rate, posterior difference ratio value and small error probability value are calculated according to Equations (18)–(23). The results show that the relative error rate between the actual and predicted values of coupled and coordinated development were between 0 and 0.05 (p = 0.98, C = 0.0147), indicating that the model was scientific and reasonable and could predict the development trend of coupled and coordinated development in Hebei province in 2020 and the 14th Five-Year Plan period more accurately. The specific results are shown in Table 7 and Table 8.

As can be seen from Table 8, the prediction results show that the coupling coordination degree of scientific and technological innovation and the rural revitalization system in Hebei province in 2020–2025 shows a steady upward trend, indicating that the two systems are in a state of dynamic coupling development and that the coordinated development of rural revitalization is improving, driven by scientific and technological innovation in Hebei province.

The forecasts show a new phase of system coupling beginning in 2022 from primary coordination to intermediate coordination, achieving good coordination by 2024. In recent years, under the guidance of the national “14th Five-Year Plan” and the No. 1 Central Document of the People’s Republic of China, agriculture, rural areas and farmers have made continuous achievements in terms of scientific and technological innovation and have applied them to rural revitalization, which has played a certain role in promoting the optimization and characteristic development of the agricultural industrial structure, rural infrastructure, ecological civilization construction, rural governance system and low-carbon life construction.

7. Conclusions

With the continuous improvement in the level of information technology and, more generally, science and technology, science and technology innovation and rural revitalization are becoming increasingly closely linked. In this study, a coupling mechanism between science and technology innovation and rural revitalization was proposed, and the coupling coordination degree model and grey prediction model were introduced. The aim was to measure and predict the trends of the coupled and coordinated development statuses of science and technology innovation and rural revitalization in Hebei province in China. Based on the application results, development strategies were suggested for relevant government departments. The main conclusions derived from this study are as follows:

• (1). Technological innovation and the rural revitalization system have a dynamic coupling relationship. Rural revitalization is driven by scientific and technological innovation, which is also the core of implementing the strategy for strengthening agricultural science and technology. The coupling mechanism of the two is mainly manifested as an input and output mechanism, connection mechanism, action mechanism or feedback mechanism. The coupling effect is dynamic in regard to regional rural construction and development.

• (2). Innovation in science and technology lags behind the development of rural revitalization. The comprehensive coordination index of science and technology innovation and rural revitalization in Hebei province from 2010 to 2019 showed a steady upward trend and good momentum while the rural index showed a phase increase, and the science and technology index increased more regularly and at a faster rate than the rural index. In general, however, the comprehensive development level of science and technology innovation is lagging behind.

• (3). The synergistic development trend of science and technology innovation and rural revitalization is obvious. In terms of the development trend of coupling coordination, from 2010 to 2019, the coupling coordination level of the two systems gradually transitioned from mild imbalance to primary coordination, which means that the relationship between the science and technology innovation system and the rural revitalization system was becoming increasingly close, and the mutual promotion effect was gradually being enhanced. The synergistic development trend of the two systems is also obvious.

• (4). The forecasted trend of scientific and technological innovation and the rural revitalization system exhibited good coordination. The application results of the prediction model show that the grey prediction GM (1,1) model had a good fitting effect. From 2020 to 2025, the coupling coordination degree of scientific and technological innovation and the rural revitalization system in Hebei province shows a steady upward trend, predicting a transition from intermediate coordination in 2022 to good coordination in 2024.

Based on the above analysis, this paper argues that the relevant government departments in Hebei province in China should take the following measures to strengthen rural revitalization:

• (1). The government’s science and technology departments should increase their support of science and technology policies for rural revitalization. From the perspective of rural revitalization, the science and technology departments should implement policies related to rural planning and rural construction and focus their support on rural education, rural medical care and public services to make up for the shortcomings and deficiencies in the development of the rural revitalization strategy. From the perspective of science and technology innovation, the relevant departments need to formulate measures such as agricultural insurance services, financial and taxation support, practical training, the introduction of talent and a connection between farmers and enterprises. In addition, they should set up a special fund for agricultural technology to guide investments in agricultural technology, enhance the value of the agricultural industry chain, and guide the transformation to digital agricultural production, operation and services.

• (2). Local governments should improve the construction of the infrastructure of the technology-enabled countryside. The government of Hebei province should improve the board overseeing the construction of rural network facilities, upgrade and extend the rural network, increase the rural network’s coverage, encourage the enthusiasm of rural residents to use the network and create conditions for technology-enabled digital rural development. The agricultural and rural sectors should strengthen the construction of infrastructure such as rural road projects, intelligent logistics and intelligent water and fertilizer machines. They should create a complete digital infrastructure regarding rural transportation, logistics, electricity and water conservancy to promote both the penetration of agricultural technology into the countryside and the development of agricultural modernization.

• (3). Local governments should optimize industrial and supply chains for green development. The agricultural and rural departments in Hebei province should strengthen agricultural mechanization and the rate of self-sufficiency of seed research and development, establish a whole domestic industrial chain and speed up agricultural scientific and technological innovation. Industries with regional advantages and characteristics should be expanded and strengthened according to local conditions. At present, with the gradual improvement of the sales momentum of agricultural products, in the export process, both the product itself and the resource allocation of the whole industry chain have higher requirements. The government of Hebei province should focus on cultivating leading industries with regional characteristics, building a modern agricultural production and management system, increasing the added value of local specialty agricultural products and activating the vitality of rural science and technology development. Hebei province should also make full use of its geographical advantages to create distribution bases and transit logistics storage centers for special agricultural products in the east and central parts of the country in order to improve the delivery efficiency of agricultural products, reduce transportation costs and accelerate the improvement of the logistics system. The concept of high-quality green development should be upheld to ensure the sales of agricultural products, agricultural economic development and the promotion of the use of agricultural technology for cash crops to achieve agricultural prosperity.

• (4). Government departments should apply big data technology to empower rural science and technology development. The Hebei government’s science and technology departments should guide the application of the Internet of Things, artificial intelligence and other scientific and technological means to strengthen the intelligent research of large and efficient combine harvesters, seeders and other equipment. The agricultural and rural sectors should improve the information-sharing platform for logistics services through big data technology, making logistics information more transparent and enabling timely responses to problems. The development and reform department should establish an emergency response mechanism and coordinate monitoring for coupling science and technology with rural areas, strengthen the scientific social governance mechanism and informationization of means and cooperate to promote the high-quality development of science and technology innovation and rural revitalization in Hebei province.

However, the coupled and coordinated development of science and technology innovation and rural revitalization is a complex project, and there are some shortcomings in this study. Since the composite system of science and technology innovation and rural revitalization is influenced by a variety of factors, the index system of the composite system needs to be further improved in future research. The next step may be to further explore the integration and development of AI technology and rural revitalization under the digital economy. More effective methodological measures will be proposed to promote the coordinated development and innovation of the regional economy.

Author Contributions

Conceptualization, C.G. and Z.L.; data curation, Y.Z.; formal analysis, N.L.; investigation, Y.Z.; methodology, Z.L.; supervision, C.G.; validation, N.L.; writing—original draft, Z.L.; writing—review and editing, Z.L. and Y.Z. All authors have read and agreed to the published version of the manuscript.

Institutional Review Board Statement

Not applicable.

Informed Consent Statement

Not applicable.

Data Availability Statement

Data are available upon request from the corresponding author.

Conflicts of Interest

The authors declare that they have no conflict of interest.

Publisher’s Note: MDPI stays neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Figures and Tables

Figure 1. Mechanism of the coupling effect of science and technology innovation and rural revitalization.

Figure 2. Trend of comprehensive development level in Hebei province from 2010 to 2019.

Table 1

Synergistic development coefficient status classification.

0 < E ≤ 0.8	0.8 < E ≤ 1.2	E > 1.2
Relative lag in technological development	Simultaneous development of the two systems	Relative lag in rural development

Table 2

Classification of coupling types.

0 < C ≤ 0.3	0.3 < C ≤ 0.5	0.5 < C ≤ 0.8	0.8 < C ≤ 1
Low-level coupling type	Type of fly down	Type of break-in	High-level coupling type

Table 3

Classification of coupling coordination types.

Coupling Coordination Type Classification	0.0 ≤ D < 0.1	0.1 ≤ D < 0.2
	Extreme disorders	Severe disorders
	0.2 ≤ D < 0.3	0.3 ≤ D < 0.4
	Moderate disorders	Mild disorders
	0.4 ≤ D < 0.5	0.5 ≤ D < 0.6
	On the verge of disorder	Reluctantly coordinated
	0.6 ≤ D < 0.7	0.7 ≤ D < 0.8
	Primary coordination	Intermediate coordination
	0.8 ≤ D < 0.9	0.9 ≤ D ≤ 1.0
	Good coordination	Quality coordination

Table 4

Accuracy table for grey prediction models.

p	C	Accuracy	Grade
p > 0.95	C < 0.35	Good	Grade I
0.80 < p < 0.95	0.35 < C < 0.50	Qualified	Grade II
0.70 < p < 0.80	0.50 < C < 0.65	Barely passable	Grade III
p < 0.70	C > 0.65	Failure	Grade IV

Table 5

Indicators and weights of scientific and technological innovation and rural revitalization.

System	Level Indicators	The Secondary Indicators	Weight
Science and technologyinnovation system	Foundation of scientific and technological innovation (X1)	GDP per capita (X12)	0.0342
		The proportion of education spending in GDP (X12)	0.0342
		The proportion of added value of tertiary industry in GDP (X13)	0.0449
	Input in scientific and technological innovation (X2)	Full-time equivalent of R&D personnel (X21)	0.0353
		R&D expenditure (X22)	0.0373
		Ratio of internal expenditure of R&D expenditure to operating revenue (X23)	0.0407
		Ratio of agricultural technology to professional and technical personnel (X24)	0.0392
	Output of scientific and technological innovation (X3)	Number of patents granted (X31)	0.0396
		Number of scientific papers published (X32)	0.0355
		Technology market turnover (X33)	0.0425
		Total power of agricultural machinery (X34)	0.0406
Rural revitalization system	Prosperous industry(Y1)	Total output value of agriculture, forestry, animal husbandry and fishery (Y11)	0.0352
		Added value of the primary industry (Y12)	0.0439
		Water-saving irrigation area (Y13)	0.0375
	Ecologically livable (Y2)	Rural electricity consumption (Y21)	0.0360
		Tap water-benefitting village (Y22)	0.0375
		Number of villages connected to cable TV (Y23)	0.0371
	Local custom civilization (Y3)	Number of cultural stations in townships (Y31)	0.0330
		Rural workers with college education or above (Y32)	0.0391
	Effective governance (Y4)	Proportion of machine-harvesting area to total sown area (Y41)	0.0332
		Soil erosion control area (Y42)	0.0404
		Number of village committees (Y43)	0.0402
	Rich life (Y5)	The income gap between urban and rural residents (Y51)	0.0338
		Engel’s coefficient of rural households (Y52)	0.0364
		Incidence of rural poverty (Y53)	0.0371
		Growth rate of per capita income of rural residents (Y54)	0.0449

Table 6

The degree of coupling and coordination between science and technology innovation and rural revitalization in Hebei province from 2010 to 2019.

Year	The Coupling	Coupling Type	The Synergistic Development Coefficient	Coupling Coordination	Coupling Coordination Type
2010	0.963	High-level coupling	0.580	0.324	Mild maladjustment of science and technology development lag
2011	0.936	High-level coupling	0.481	0.399	Mild maladjustment of science and technology development lag
2012	0.983	High-level coupling	0.688	0.407	Endangered disorder type of science and technology development lag
2013	0.988	High-level coupling	0.737	0.445	Endangered disorder type of science and technology development lag
2014	0.988	High-level coupling	0.734	0.468	Endangered disorder type of science and technology development lag
2015	0.989	High-level coupling	0.738	0.532	Barely coordinated science and technology development lag type
2016	0.972	High-level coupling	0.620	0.523	Barely coordinated science and technology development lag type
2017	0.989	High-level coupling	0.742	0.565	Barely coordinated science and technology development lag type
2018	0.996	High-level coupling	0.836	0.592	Barely coordinated type of technology and rural synchronization
2019	0.985	High-level coupling	0.709	0.64	Primary coordination science and technology development lag type

Table 7

Grey prediction error table in Hebei province from 2010 to 2019.

Year	2010	2011	2012	2013	2014	2015	2016	2017	2018	2019
Actual value	0.324	0.399	0.407	0.445	0.468	0.532	0.523	0.565	0.592	0.640
Predicted value	0.324	0.389	0.418	0.446	0.476	0.506	0.536	0.568	0.600	0.632
Residuals	0.000	0.009	−0.011	−0.001	−0.008	0.026	−0.013	−0.003	−0.007	0.008
Relative error rate	0.00%	2.38%	2.70%	0.30%	1.76%	4.96%	2.48%	0.49%	1.24%	1.30%

Table 8

Grey prediction of coupled and coordinated development in Hebei province from 2020 to 2025.

Year	2020	2021	2022	2023	2024	2025
Predicted value	0.665	0.699	0.734	0.769	0.805	0.842

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