Research on Field Engineer Cultivation System in Vocational Education-Taking Intelligent Manufacturing Specialty Group as an Example

Intelligent equipment manufacturing is the core development direction of China’s current manufacturing technology, which has become an important symbol for measuring a country’s technical level and comprehensive strength [1–2]. As the domestic manufacturing industry moves forward to the key period of high-quality development, digitalization, networking and intelligence are the distinctive features of new industrialization and the key path to promote the high-quality development of manufacturing industry [3–5].

Vocational education plays an important role in cultivating high-quality talents to meet the market demand. The traditional subject system is gradually difficult to meet the requirements of modern industry for technical proficiency and practical ability, so the importance of vocational education is becoming more and more prominent [6–7]. Compared with traditional engineers and conventional technical skills training, the core work ability of vocational education field engineers is to solve practical problems on site [8–9]. In today’s competitive job market, there is an increasing demand for field engineers with practical skills and adapted to the needs of industrial development. Intelligent manufacturing students are more likely to match the industry demand because of their practical operation and practical experience [10]. However, there are still some challenges in the cultivation of field engineers in the current intelligent manufacturing program, such as the teaching system is not close enough to the actual, and the practical training equipment is not advanced enough [11–12]. By studying the field engineer training system in vocational education, it is expected to promote vocational education to better adapt to the needs of industrial development and provide students with a more practical and efficient training system [13–14].

Jabarullah, N. H. et al. assessed the impact of a problem-based learning approach on engineering students’ learning outcomes by proposing two teaching approaches, namely, traditional classroom-centered teaching approach versus hands-on focused vocational education and training approach (HTVET), and by comparing the students’ learning outcomes in the two classrooms, it was found that an active and experiential approach to learning maximizes both the teaching and the learning experience [15]. Van den Beemt, A. et al. analyzed the learning objectives and challenges of interdisciplinary engineering education and concluded that pedagogical approaches with good organization and team management promote collaborative teamwork, in addition to which, a rich pedagogical and team experience is the basis for the development of interdisciplinary practical teaching [16]. Lantada, A. D. proposes the concept of Engineering Education 5.0, an educational paradigm that expands the application of the ethical and humanistic domains based on technology and principles, and suggests that this emerging educational paradigm will lead and guide engineers in their search for the technological singularity where technological growth is uncontrollable and irreversible [17].

Wang, S. et al. emphasized that the action and orientation of higher education are crucial to the impact of information technology talent education, and that constructing a student-centered training system for interpreting intelligent manufacturing information, and reforming the intelligent manufacturing practical training courses on the basis of analyzing the industry’s structure and talent needs are conducive to supporting the education of modern information technology talents [18]. Lai, Z. H. et al. combined multimodal augmented reality with deep learning networks to propose a worker-centered accessory inspection system that provides on-site guidance through visual image rendering and synthetic data training, which resulted in significant reductions in assembly task time and error in mechanical assembly experiments for CNC engraving machines [19]. Wang, S. et al. constructed a set of mobile robot production line to strengthen the practical experience of intelligent manufacturing engineers, which promotes the synthesis of knowledge and participation of training through the theoretical integration of the manufacturing process and the learning of skills, effectively cultivates their cooperative and adaptive ability, and exercises their critical thinking, which is a set of valuable reference system for engineering management talents [20].

In this paper, for the cultivation of intelligent manufacturing professional group, a two-party evolutionary game model of school-enterprise cooperation between vocational education and enterprises is constructed with the help of evolutionary game theory, and the model is analyzed for the sensitivity factors such as additional cost of cooperation, cooperation benefit, and distribution coefficient of cooperation benefit, etc. The model is also analyzed for sensitivity factors, such as the cost and benefit of cooperation. In order to verify the reliability of the game model results, numerical simulation is carried out with the help of Matlab, and at the same time, the dynamic process of the evolutionary game between the engineer cultivation system and the enterprise to carry out school-enterprise cooperation is shown more intuitively.

2

Research on the training system for field engineers in vocational education

2.1

Cultivation Path of Field Engineers under the View of Industry-Science-Technology-Education Integration

2.1.1

Organization of the College of Field Engineers

First of all, leading enterprises and high-level schools are given priority to form on-site engineer colleges to create a school-enterprise mutual integration and symbiosis community of destiny, and to build a modularized curriculum system focusing on the application of engineering technology, so as to enable students to gain real-world experience that is more closely related to actual work. Secondly, relying on cooperative enterprises and leading by dual-teacher teachers, we should integrate the superior resources of both schools and enterprises, jointly study and formulate on-site engineer training standards, strengthen the construction of practical teaching bases for the integration of industry and education [21], and provide a more practical learning environment for students to strengthen their practical ability and expand their professional quality. Finally, strengthen the "dual-subject" operation mechanism of schools and enterprises, the school and the enterprise jointly assume the responsibility of talent training, establish an interactive mechanism between the school and the enterprise, solve the problems and difficulties in cooperation in a timely manner, participate in the management and decision-making of the college, and ensure the efficient operation and sustainable development of the on-site engineer college.

2.1.2

Create a high-level “dual-teacher” team

First of all, external attraction and internal training cross-border integration, to create a high-level “dual-teacher” team. Open up the organizational boundaries between the teaching team and the research team, work with the university to formulate the “fixed post + mobile post” part-time teacher introduction mechanism, continue to introduce industry and enterprise experts and skilled craftsmen to give part-time lectures in the university, and implement the system of dual professional leaders inside and outside the university. Secondly, the establishment of a mechanism to improve the interaction of multiple subjects “to pass on”, new and old teachers, full-time and part-time teachers in the education and teaching, teaching and research and reform, the application of technology and other aspects of each other as a mentor to pass on their skills and teach, to carry out centralized lesson planning and technical seminars, and to work together to formulate the standards of the curriculum, so as to enhance the overall strength of the teaching force. Finally, optimize the evaluation and incentive mechanisms of teachers to stimulate the vitality of their comprehensive development. The contents of school-enterprise cooperation and technical services are incorporated into the evaluation of teachers’ titles and performance appraisal, so as to stimulate the enthusiasm of team members to carry out applied technology research and development and social services.

2.1.3

Improve the talent training system

Improve the on-site engineer training system, and promote the industry’s “intellectual reform and digital transformation”. “Intelligent Reform and Digital Transformation” refers to the intelligent transformation and digital transformation of the manufacturing industry, helping enterprises to get rid of the big data silos in the industrial chain, so as to promote the innovation of enterprises in operation and business model. First of all, the curriculum of relevant majors should be adjusted and optimized, and courses closely related to cutting-edge technologies such as artificial intelligence, big data, Internet of Things, and cloud computing should be increased. At the same time, it focuses on interdisciplinary integration to cultivate students’ comprehensive quality and cross-field problem-solving ability. Secondly, the importance of practical teaching should be emphasized, and practical links such as experiments, internships, and project training should be strengthened. Establish and enhance the practical training foundations, provide high-quality practical opportunities and equipment conditions, enabling students to interact with and operate intelligent equipment and technology in a realistic manner. Finally, higher vocational colleges and universities should actively take the initiative to establish close cooperative relations with enterprises and promote the combination of production, learning, and research. Higher vocational colleges and universities should follow the trend of industrial intelligent reform and digital transformation in cultivating skilled talents, focusing on the cultivation of practical ability, industry-university-research cooperation and other aspects of practical operation, so as to provide students with skill cultivation more in line with the needs of the industry.

2.1.4

Deepening collaborative education between industry, science and education

Industry-Science-Education Collaborative Education is intended to organically combine industry, scientific research, and education, and guide education through industrial demand, so that students’ learning can be closer to actual demand. First of all, oriented by applied scientific research, we build a mechanism of collaboration among “government, school, industry and enterprise” to create an innovative platform for the integration of industry, science and education, carry out in-depth collaborative innovation between industry, science and education, promote the transformation of achievements, and cultivate students’ innovative ability and practical ability. Secondly, relying on the Field Engineer College jointly established by the university and enterprises, we will combine the common demand and consider the individual demand to form the apprenticeship class, so as to improve the comprehensive ability of the students to solve the field problems. Finally, new technologies, processes, and specifications are dynamically integrated into the entire process of training field engineers to form an educational ecosystem that is industry-chain-oriented. Through innovation and entrepreneurship practice and experience activities, participation in teachers’ on- and off-campus research projects, etc., the first classroom and the second classroom are organically combined to cultivate composite technical and skilled talents with innovative spirit and entrepreneurial ability.

2.2

Evolutionary game model of cooperative cultivation between higher education institutions and enterprises

2.2.1

Relevant Variables and Hypotheses

In order to study the evolution of cooperation behavior between higher education institutions and enterprises, and to simplify the model and calculation. In this paper, we define the relevant variables: ➀ cooperation benefits as R₁, R₂. When one party cooperates and the other does not. ➁ The cost of cooperation is C₁,C₂. The cost to the cooperating party when one party cooperates and the other does not. Expenditures for equipment, personnel, and other costs. ➂ Cooperation gains D. The excess benefits brought about when both parties cooperate. Higher vocational colleges and universities cooperate with enterprises to cultivate high-quality talents, improve the working potential and efficiency of students after joining the workforce, cultivate students who are welcomed by the society, and improve the visibility and reputation of higher vocational colleges and universities; when enterprises cooperate, they provide a milder market environment, such as providing internships, parttime jobs, and other opportunities for students, and improve the motivation of students to learn and improve their comprehensive quality. ➃ The coefficient of excess benefit distribution is a. The rationality of the benefit distribution of school-enterprise cooperation directly affects the success and long-term of school-enterprise cooperation. ➄ Incremental gains P₁, P₂ when one party cooperates and the other does not. The non-cooperating party receives incremental gains P₁, P₂ because it benefits from the other party’s milder market strategy. ➅ The retaliation and punishment will be Q₁, Q₂, when one party cooperates and the other does not. The non-cooperating party will be subject to retaliation and punishment as Q₁, Q₂. ➆ The knowledge level of the other side, expressed by R_i (i =0,1,2), the knowledge reserve of the team members, the more knowledge reserve of each member of the team, the more knowledge benefit of other members will be directly obtained. ➇ M is used to represent the production coefficient of knowledge innovation in higher vocational colleges. Due to the factors of team members’ structure, knowledge will have a certain degree of overlap.

The following hypotheses are proposed: ➀ Limited rationality hypothesis. In the fierce market competition, enterprises and higher vocational colleges and universities have limited cognitive ability and are limited rationality in the choice of strategies. ➁ The existence of two groupgs: higher education institutions and companies. The decisions of these two groups are “cooperative” and “uncooperative”. Cooperation strategies include sharing of equipment, personnel and other resources, joint cultivation, top practice, and cooperative culture building. ➂ When one party cooperates and the other does not, the cooperating party’s benefit impaired cost increases, so assume R₁ < C₁, R₂ < C₂; when both higher vocational colleges and enterprises do not cooperate, higher vocational colleges and universities cultivate talents that are not suitable for the enterprise, and the enterprise can’t find the suitable employees, and has to spend huge costs to re-cultivate, assuming that the benefits are all 0. Without loss of generality, assume that each parameter is greater than 0. ➃ Assume that the probability that a higher education institution adopts cooperation is x and the probability that it adopts non-cooperation is (1–x), where (0 ≤ x ≤ 1). The probability that a firm adopts cooperation is y and the probability that it adopts non-cooperation is (1–y), where (0 ≤ y ≤ 1).

2.2.2

Construction of the cooperation model

Expected Benefits of Selecting Collaborative Strategies for Higher Education Institutions: 1 $u_{11} = y (R_{1} - C_{1} + a D) + (1 - y) (R_{1} - C_{1}) = a y D + R_{1} - C_{1}$

Expected benefits of choosing a non-cooperative strategy in higher education institutions: 2 $u_{12} = y (P_{1} - Q_{1}) + (1 - y) \times 0 = y (P_{1} - Q_{1})$

Expected benefits of firms’ choice of cooperation strategy: 3 $\begin{array}{l} u_{21} & = x (R_{2} - C_{2} + (1 - a) D) + (1 - x) (R_{2} - C_{2}) \\ = (1 - a) x D + R_{2} - C_{2} \end{array}$

Expected returns to a firm’s choice of non-cooperative strategy: 4 $u_{22} = x (P_{2} - Q_{2}) + (1 - x) \times 0 = x (P_{2} - Q_{2})$

Average earnings of higher education institutions: 5 $\bar{u_{1}} = x u_{11} + (1 - x) u_{12} = a x y D + x (R_{1} - C_{1}) + (1 - x) y (P_{1} - Q_{1})$

The average return of the firm: 6 $\begin{array}{l} \bar{u_{2}} & = y u_{21} + (1 - y) u_{2} \neq (1 - a) x y D \\ + y (R_{2} - C_{2}) + (1 - y) \times (P_{2} - Q_{2}) \end{array}$

From the above equation, the equation of replicator dynamics for higher education institutions adopting cooperative strategies is obtained as: 7 $\frac{d x}{d t} = x (u_{11} - \bar{u_{1}}) = x (1 - x) [(Q_{1} + a D - P_{1}) y - (C_{1} - R_{1})]$

Similarly, the equation for the dynamics of the replicator for a firm adopting a cooperative strategy can be obtained as: 8 $\frac{d y}{d t} = y (u_{21} - \bar{u_{2}}) = y (1 - y) [(Q_{2} + (1 - a) D - P_{2}) x - (C_{2} - R_{2})]]$

2.2.3

Evolutionary game process

Set the probability that a firm chooses the participation strategy to be x and the probability that it adopts the non-participation strategy to be 1–x. The probability that a vocational college adopts the advancement strategy is y, and the probability that it adopts the non-advancement strategy is 1–y.

The expected and group average returns for the two strategies (participation and non-participation) that can be adopted by the enterprise are U_1Y, U_1N, and ${\bar{U}}_{1}$ , respectively: 9 $U_{1 Y} = y (C_{1} - C) + (1 - y) (C_{1} - C)$ 10 $U_{1 N} = - y C_{2} - (1 - y) (C_{2} + M)$ 11 ${\bar{U}}_{1} = x (C_{1} - C) + (1 - x) (y M - C_{2} - M)$

The expected and group average gains for the two strategies (advancing and not advancing) available to vocational institutions are U_2Y, U_2N, and ${\bar{U}}_{2}$ , respectively: 12 $U_{2 Y} = x (- R + R_{0}) + (1 - x) (- R + R_{0})$ 13 $U_{2 N} = x (R_{1} - R_{2}) + (1 - x) R_{1}$ 14 ${\bar{U}}_{2} = y (R_{0} - R) + (1 - y) (R_{1} - x R_{2})$ 1)

Building a dynamic equation for replication in the enterprise [22–23]

Construct the replication dynamic equation: 15 $F (x) = \frac{d x}{d t} = x (U_{1 Y} - {\bar{U}}_{1}) = x (1 - x) (C_{1} + C_{2} + M - C - y M)$

Thus, when x = 0,1 or $y = \frac{C_{1} + C_{2} + M - C}{M}$ , $\frac{d x}{d t} = 0$ , the percentage of the business community that adopts the engagement strategy is stable. When $y = \frac{C_{1} + C_{2} + M - C}{M}$ , the state in interval 0 ≤ x ≤ 1 is stable, and the probability of a vocational college choosing due diligence promotion in this state is y. When $y \neq \frac{C_{1} + C_{2} + M - C}{M}$ , then x₁ = 0 or x₂ = 1 are the two possible stable states. When $y < \frac{C_{1} + C_{2} + M - C}{M}$ , then x = 1 is an equilibrium point; when $y > \frac{C_{1} + C_{2} + M - C}{M}$ , then x = 0 is an equilibrium point. Figure 1 is the phase diagram of its corresponding replication dynamic equation.

2)

Constructing the replication dynamic equations for vocational schools

Construct the replication dynamic equation: 16 $F (y) = \frac{d y}{d t} = y (U_{2 γ} - {\bar{U}}_{2}) = - y (1 - y) (R + R_{1} - R_{0} - x R_{2})$

Therefore, when y = 0,1 or $x = \frac{R + R_{1} - R_{0}}{R_{2}}$ , $\frac{d y}{d t} = 0$ , the proportion of vocational colleges and universities adopting the strategy of advancing the integration of industry and education is stable, and when $x = \frac{R + R_{1} - R_{0}}{R_{2}}$ is a steady state for all of any 0 ≤ y ≤ 1, then the probability that the enterprise chooses to participate in the integration of industry and education is x, which can also be regarded as the strength of the enterprise’s participation. When $x \neq \frac{R + R_{1} - R_{0}}{R_{2}}$ y₁ = 0 and y₂ = 1 are two possible stable states respectively.

3)

Stability analysis of the equilibrium point

The phase diagram of the replication dynamic relationship between the two groups is shown in Figure 1.

2.2.4

Evolutionary game analysis

Its Jacobi matrix [24] can be derived from the replication dynamics equation as: 17 ${\begin{matrix} (1 - 2 x) (C_{1} + C_{2} + M - C - y M) & - x M (1 - x) \\ y (1 - y) R_{2} & - (1 - 2 y) (R + R_{1} - R_{0} - x R_{2}) \end{matrix}}$

The immovable points of the system of equations derived from the Jacobi matrix are: (x, y) = (0, 0), (x, y) = (1, 0), (x, y) = (1, 1), (x, y) = (0, 1), $(x, y) = (\frac{R + R_{1} - R_{0}}{R_{2}}, \frac{C_{1} + C_{2} + M - C}{M})$ .

2.3

Analysis of factors influencing the evolutionary system

When $x = \frac{R + R_{1} - R_{0}}{R_{2}}$ , $y = \frac{C_{1} + C_{2} + M - C}{M}$ , the same reason can be obtained that the sign of the value of the determinant is negative, the sign of the trace of the determinant is variable, so this immobile point is also unstable.

(x, y) = (0,0), (x, y) = (1,0) and $(x, y) = (\frac{R + R_{1} - R_{0}}{R_{2}}, \frac{C_{r} + C_{3} + M - C}{M})$ are not stable. Therefore, only (x, y) = (1,1) is the evolutionary stable strategy of the game, that is, vocational colleges actively promote and enterprises fully participate is an evolutionary stable strategy. 1)

Extra cost C

The partial derivation of C can be obtained as 18 $\frac{\partial S_{1}}{\partial C} = \frac{1}{2} [\frac{ε}{R_{3} R + S + G} + \frac{1 - ε}{(1 - R_{3}) R + S + G}] > 0$

Therefore, S₁ is a monotonically increasing function of C. That is, C increases, S₁ increases, and the probability of school-enterprise non-cooperation increases. Therefore, in the case of limited rationality, both parties should formulate a reasonable transaction input cost and establish an effective stabilization mechanism.

2)

Cooperation benefits R

The derivation of R can be obtained as 19 $\frac{\partial S_{1}}{\partial R} = - \frac{1}{2} {\frac{y (ε C - P + W)}{{(y R + S + G)}^{2}} + \frac{(1 - R_{3}) (1 - ε) C - P + W}{{[(1 - R_{3}) R + S + G]}^{2}}} < 0$

Therefore, S₁ is a monotonically decreasing function of R. That is, R increases, S₁ area becomes smaller, and the probability of school-enterprise cooperation increases. So it is necessary to make the overall cooperation the greater the gain, in order to strengthen the feasibility of cooperation.

3)

The coefficient of benefit distribution R₃

By S₁ area formula for R₃derivatives: 20 $\frac{\partial S_{1}}{\partial R_{3}} = \frac{1}{2} {\frac{R [(1 - ε) C - P + W]}{{[(1 - R_{3}) R + S + G]}^{2}} - \frac{R (s C - P + W)}{{(R_{3} R + S + G)}^{2}}}$

Knowing that R₃is non-monotonic with respect to S₁, this is then obtained by taking the second order derivative of S₁ with respect to R₃: 21 $\frac{\partial^{2} S_{1}}{\partial R_{3}^{2}} = \frac{1}{2} {\frac{{(R)}^{2} [(1 - ε) C - P + W]}{{[(1 - R_{3}) R + S + G]}^{2}} - \frac{{(R)}^{2} (ε C - P + W)}{{(R_{3} R + S + G)}^{2}}}$

Let $\frac{\partial S_{1}}{\partial R_{3}} = 0$ , i.e., when $\frac{R [(1 - ε) C - P + W]}{{[(1 - R_{3}) R + S + G]}^{2}} = \frac{R (ε C - P + W)}{{(R_{3} R + S + G)}^{2}}$ , S₁ has a minimal value, when the probability of school-enterprise cooperation is maximum. Therefore, we can find an optimal gain distribution coefficient by solving the evolutionary stability analysis to maximize the probability of school-enterprise cooperation.

4)

Betrayal of gains K

The derivation of K can be obtained: 22 $\frac{\partial S_{1}}{\partial K} = \frac{1}{2} [\frac{ε K}{R_{3} R + S + G} + \frac{(1 - ε) K}{(1 - R_{3}) R + S + G}]$

Therefore, S₁ is a monotonically increasing function of K. That is, as K increases and saddleg point E moves up, the area of region S₁ will increase, the probability that the system tends to uncooperative will increase, and the probability of cooperation will decrease.

5)

The penalty for default P

A partial derivative of P is obtained: 23 $\frac{\partial S_{1}}{\partial P} = - \frac{1}{2} [\frac{1}{{(R_{3} R + S + G)}^{2}} + \frac{1}{(1 - R_{3}) R + S + G}] < 0$

Therefore, S₁ is a monotonically increasing function of P. That is, P increases, saddle point P moves down, the area of region S₁ will decrease, and the probability that the system tends to cooperate will increase. Therefore, an appropriate increase in the amount of liquidated damages can effectively constrain the occurrence of the default situation, which has a positive significance in promoting the cooperation between the institution side and the enterprise side.

6)

Government subsidies G

The derivation of G can be obtained: 24 $\frac{\partial S_{1}}{\partial G} = - \frac{1}{2} [\frac{s C - P + W}{{(R_{3} R + G + S)}^{2}} + \frac{(1 - ε) C - P + W}{{[(1 - R_{3}) R + S + G]}^{2}}] < 0$

Therefore, S₁ is a monotonically decreasing function of G. That is, as G increases, the area of region S₁ will decrease, the probability that the system tends to cooperate will increase, and the greater the probability that the system tends to the Pareto optimal solution C(1,1). That is to say, only when the government invests a large financial subsidies and tax breaks, both parties are willing to actively cooperate to train students, indicating that reasonable government subsidies can effectively promote the development of long-term stable cooperation between the two sides.

3

Results and analysis of the study on the training system for field engineers in vocational education

3.1

Model Numerical Simulation Analysis

3.1.1

Simulation analysis of local stability of the system

The stability of the game model is simulated and based on the assignment principle, the local stability parameters of the system are shown in Table 1.

Table 1.

System local stability parameter

Parameter	Condition 1	Condition 2	Condition 3	Condition 4
R	10	10	10	10
t	0.4	0.4	0.4	0.4
C1	3	4	5	5
C2	2	3	2	4
G1	1.5	1.5	2	2
G2	1.5	2	1.5	2
I1	0.3	0.3	0.3	0.3
I2	0.7	0.7	0.7	0.7
P	0.5	1	0.5	1

The evolved phase diagrams from the Matlab simulation are shown in Fig. 2 (a, b, c, and d represent conditions 1 to 4, respectively). The phase diagram created by the simulation is in line with the theoretical analysis. The validity of the game model is verified. From the stability of the model, (b), (c) and (d) also have ideal evolutionary trends, but the assignment conditions to meet these three evolutionary situations are often difficult to realize in real cooperation. Therefore, this paper focuses on exploring the evolution process of the long-term game of school-enterprise cooperation and the influence of sensitivity factors on the subject’s strategy selection process and results under condition 1.

3.1.2

Initial Strategy Analysis

The simulation results of the evolution simulation of the binary game system are shown in Fig. 3 when the initial willingness to cooperate of one party is at the low (0.2), medium (0.5), and high (0.8) levels and the initial willingness to cooperate of the other party varies in the interval of [0.2,0.8] for the setting of the college of smart manufacturing and the enterprise, respectively, where a, b, and c respectively represent the coefficients of cooperation willingness of the college of smart manufacturing and the enterprise at the low (0.2), medium (0.5) and high (0.8) cooperation willingness coefficients. The results show that when both parties are at a low initial willingness to cooperate, the evolutionary trend of college-enterprise cooperation is constantly converging to the (0,0) point. As enterprises’ initial intentions for cooperation continue to improve, the evolution of the school-enterprise cooperation system towards (1,1) is becoming faster and faster.

3.1.3

Parameter impact analysis

1)

The impact of additional cost

Let the simulation step size be 5, and the initial willingness to participate of both the College of Intelligent Manufacturing and the enterprise be set to 0.5, as shown below. The values of each parameter other than extra cost are set as follows: R=10, t=0.4, I₁=0.3, I₂=0.7, G₁=1.5, G₂=1.5, P=1. The extra cost assignments for both sides are (C1,C2=)(3,2), (4,3), (5,2), (5,4). The simulation results of the system under additional cost variation are shown in Fig. 4.

2)

The effect of cooperation gain

The values of each parameter other than cooperation gains are set as follows: t=0.4, I₁=0.3, I₂=0.7, C₁=5, C₂=5, G₁=2, G₂=2, P=1. The two sides’ cooperation gains are assigned as R=4, 6, 8, 10. The simulation results of the system under the change of cooperation gains are shown in Fig. 5. The increase in cooperation gains plays a positive role in promoting the smooth progress of school-enterprise cooperation. With the rise of cooperation gain, the cooperation system will tend to evolve in the direction of active participation of school-enterprise parties, and the larger the cooperation gain is, the faster the cooperation system goes to coordination. Therefore, when conducting school-enterprise cooperation, in order to ensure that the cooperation system is stable and far-reaching, it is necessary to carry out a rigorous evaluation of the benefits of cooperation.

3)

The effect of the coefficient of distribution of cooperative benefits

The values of each parameter other than the cooperative revenue sharing coefficient are set as follows: R=10, I₁=0.3, I₂=0.7, C₁=5, C₂=5, G₁=2, G₂=2, P=1. The values of the cooperative revenue sharing coefficient of the two parties are assigned as t=(0.1, 0.2, 0.3, 0.4). The simulation results of the system under the variation of cooperative revenue sharing coefficients are shown in Fig. 6. From the simulation results, it can be seen that the change of the cooperative revenue allocation coefficient has a two-way influence on the smooth progress of school-enterprise cooperation. When the coefficient of benefit distribution of cooperation is 0.1 and 0.4, the cooperation system tends to evolve in the direction of negative participation of both parties, and when the coefficient of benefit distribution of cooperation is 0.2 and 0.3, the cooperation system tends to evolve in the direction of active participation of both parties. Therefore, the coefficient of benefit distribution in cooperation does not necessarily have to be high or low, but it should be reasonably divided according to the respective strengths and contributions of the cooperating parties.

4)

Impact of internalized capacity gains

The values of each parameter other than internalized capacity gain are set as R=10, t=0.3, I₁=0.3, I₂=0.7, C₁=5, C₂=5, P=1. The two sides of the internalized capacity gain are assigned as =(G1, G2)(1.5,1.5), (1.5,2), (2,1.5), and (2,2). The simulation results of the system under the variation of internalized capacity gain are shown in Fig. 7. From the simulation results, it can be seen that an increase in the gain of internalized capacity of either party will promote the smooth progress of school-enterprise cooperation, and with the rise of the gain of internalized capacity, the cooperation system will tend to evolve in the direction of active participation of both parties, and the larger the gain of internalized capacity of both parties, the faster the system tends to active cooperation.

5)

The effect of speculative return coefficients

The values of each parameter other than the speculative return coefficient are set as follows: R=10, t=0.3, G₁=2, G₂=2, C₁=5, C₂=5, and P=1. The two sides of the speculative return coefficients are assigned to be =(I₁,I₂)(0.1,0.1), (0.1,0.2), (0.2,0.3), and (0.3,0.3). The simulation results of the system under the variation of speculative gain coefficient are shown in Fig. 8. The speculative gain coefficient has an inhibitory effect on school-enterprise cooperation. The coefficient of speculative gain reacts to the “free-riding” behavior of the cooperation participants who do not comply with the cooperation constraints, which often occurs in the case of large differences in the strengths of the two parties to the cooperation or large business crossover.

6)

Effect of default penalty

The values of each parameter except the default penalty are set as follows: R=10, t=0.3, G₁=2, G₂=2, C₁=5, C₂=5, I₁=0.3, I₂=0.3, P=1, and the default penalty is assigned as P=0.2, 0.5, 0.8, and 1.0. The results of the system under the variation of default penalty are shown in Figure 9. From the simulation results, it can be seen that the default penalty has a facilitating effect on school-enterprise cooperation. The default penalty is about high, and the school-enterprise cooperation system formed by the college of intelligent manufacturing and the enterprise has a more obvious tendency to evolve in the direction of (1,1).

3.2

The results and analysis of the evolutionary game of collaborative co-construction between schools and enterprises

3.2.1

Influence of Different Willingness of Schools and Enterprises on the Process of Strategy Evolution

The initial value (x,y) of school and enterprise strategy takes the values of (0.2,0.2), (0.5,0.5), (0.8,0.8), and the results of the evolutionary game of school-enterprise co-construction are shown in Fig. 10. From the figure, it can be seen that whether the modern industrial college can be successfully constructed is significantly affected by the initial willingness of the two parties, and the lower initial willingness of the two parties will show negative co-construction tendency, and invest less co-construction resources, and their own demand for resource acquisition can’t be satisfied, which ultimately leads to the failure of the co-construction.

3.2.2

Impact of government subsidies on the strategy evolution process

Assuming that the value of government subsidy G is 1.5, 2, 2.5, according to the past industry-university-research cooperation, it can be seen that in the actual construction of the initial stage, the main body is not involved in the enthusiasm, mostly for the guidance of the government’s policy to reach a cooperation, so the two sides of the initial willingness (x,y) to take (0.4,0.4), the government subsidy on the strategy of the evolution of the results shown in Figure 11. With the increase of G the final evolution result is (1,1), the input cost of both sides of the construction is partially shared by the government, both for the enterprise and the university, the reduction of the amount of resource input means that through the cooperation can obtain more resource interaction benefits, so it will tend to actively cooperate to create more economic and social value.

3.2.3

Impact of cooperation benefits on the strategy evolution process

Assuming that the cooperation gain R is 5, 10, 15, the cooperation gain to strategy evolution results are shown in Fig. 12, and the state of the evolutionary system gradually evolves from the stable point (0,0) to (1,1). The higher the gain of active cooperation between the two parties, the faster the two parties choose the active cooperation strategy. At this time, co-construction allows both parties to obtain more external resources to meet their development needs.

3.2.4

Impact of Additional Costs on the Strategy Evolution Process on the University Side

Assuming that the extra cost C of the university side is 2, 4, 5, the result of the extra cost of the university side on the strategy evolution is shown in Fig. 13, and the state of the system gradually evolves from the stable point (1,1) to (0,0). For the university side, the extra input resource cost cannot get enough return, and the speed of choosing negative cooperation increases to avoid more losses. While the university side chooses negative cooperation, reducing the input of additional resources leads to the enterprise can not get enough resources, which further makes the enterprise also choose negative cooperation to ensure that their own interests are not damaged, and ultimately leads to the rupture of the field engineer training system. Thus, it can be seen that the stable operation of the field engineer training system of modern industrial colleges will be negatively affected by the cost of additional resources.

3.2.5

Influence of the distribution of benefits on the evolutionary process of the strategy on the side of the university

Assuming that the positive revenue allocation R3 of the university side is 2, 4, and 5, the result of the university side’s revenue allocation on the strategy evolution is shown in Fig. 14, where the state of the system gradually evolves from the stable point (0,0) to (1,1). With the gradual increase of R3, the distribution of benefits obtained by the university side through co-construction exceeds the cost of resources that need to be additionally invested. Thus, the stability of the institution’s field engineer training system is positively affected by the benefits of positive cooperation.

3.2.6

Impact of Betrayal Gains on Strategy Evolution Processes

Assuming that the betrayal gain K of the university side is 0.5, 1, 1.5, the betrayal gain pair strategy evolution results are shown in Fig. 15, and the system will eventually evolve to (0,0). As K gradually increases, the university side can still enjoy the spillover gain from the resources invested by the enterprise side even without additional investment of corresponding resources. The higher this gain is, the more serious the free-riding phenomenon of the university side will be, and the speed of choosing the negative cooperation strategy will gradually increase. This type of negative cooperation strategy choice by the university will result in the enterprise’s investment of resources not generating enough profit, and may ultimately lead to the company betraying the field engineer training system. Thus, it can be seen that the betrayal gain will restrict the operation of the field engineer training system of modern industrial colleges.

3.3

Revelation of Deep Cooperation between Schools and Enterprises in Vocational Education

3.3.1

Building a community of interest between schools and enterprises

Improve the coordination mechanism for input and benefits to establish a community of interest between schools and enterprises. In the current vocational education school-enterprise cooperation, the high input cost and low expected benefit of enterprises in school-enterprise cooperation seriously restrict their enthusiasm to participate. On the one hand, schools should optimize the approval process of school-enterprise cooperation, improve the efficiency of decision-making, and reduce the time cost in the process of cooperation; at the same time, schools and enterprises should strengthen the communication to avoid the increase in the cost of cooperation due to information asymmetry. On the other hand, vocational colleges and universities should actively promote the transformation of scientific and technological achievements of school-enterprise cooperation, establish a system of resource integration and benefit fusion, so as to enable enterprises to obtain economic benefits from school-enterprise cooperation, and continuously enhance the sense of achievement of enterprises.

3.3.2

Strengthening collaborative education between schools and enterprises

Strengthening the dual-major role of collaborative education between schools and enterprises. Vocational colleges and universities should take the initiative to meet the needs of enterprises, optimize the layout of professions, give priority to the development of emerging professions in industrial demand, eliminate professions with oversupply and low employment rate, cultivate technical and skilled talents who are competent to meet the needs of enterprises’ positions, and realize the matching of supply and demand at both ends of the spectrum of production and education; at the same time, enterprises should strengthen the role of the main body in participating in vocational education and push forward the construction of industrial colleges by schools and enterprises, and the cooperation of internship training bases, and participate in the training of vocational education talents. At the same time, enterprises should strengthen the important role of participating in vocational education, promote the joint establishment of industrial colleges by schools and enterprises, cooperate in building and sharing internship and training bases, and deeply participate in the cultivation of talents in vocational education, so as to avoid free-riding behavior. For the students participating in the top-ranking internship, enterprises should attach importance to the students as if they were their own prospective employees, and strengthen the students’ sense of identification with the enterprise culture, so as to realize the long-term and stable human resources demand of the enterprises.

3.3.3

Improving financial investment and policy incentives

Reflect the government’s leading role and improve the financial input and policy incentive mechanism. Deep cooperation between vocational education schools and enterprises requires the government to play an active leading role and improve the incentive and constraint mechanism for school-enterprise cooperation. 1)

On the enterprise side, local governments can recognize enterprises with outstanding results in school-enterprise cooperation as industry-education integration enterprises, and provide support services in terms of financial support, tax incentives, and land use policies to motivate enterprises to participate in school-enterprise cooperation.

2)

On the school side, government departments should raise the development coordinates of vocational education, tilt the new education funds to vocational education, especially in the teaching instruments and equipment, internship and training base construction and other aspects of support. At the same time, strengthen supervision and evaluation, improve the third-party evaluation mechanism, pay more attention to the evaluation of talent training quality, social services and innovative technological achievements, avoid the superficial and formalized cooperation between schools and enterprises, and promote the formation of a vocational education development pattern with complementary advantages of schools and enterprises and positive interaction between production and education.

4

Conclusion

In this paper, numerical simulation is carried out with the help of Matlab to show more intuitively the dynamic process of the evolutionary game of the engineer cultivation system in which the students of intelligent manufacturing majors and enterprises carry out school-enterprise cooperation. The conclusions obtained are as follows: 1)

The simulation results show that extra costs and speculative gains inhibit school-enterprise cooperation. The benefits of cooperation, the benefits of internalized capacity, and the penalties for breaching contracts have a facilitating effect on school-enterprise cooperation. The performance of the distribution coefficient of cooperation gain on school-enterprise cooperation is not single, and the way of influence has a critical value, but this critical value is not necessarily the more centered the better, it depends on the two sides of the psychological perception of input and output.

2)

The university side and the enterprise side are the two core key subjects of the field engineer cultivation system, and the existence of a reasonable university-enterprise revenue distribution coefficient is conducive to the realization of the effective operation of the field engineer cultivation system. When the cooperation gain under the positive cooperation strategy is increasing, both parties will choose to actively participate in the co-construction for the long-term development; when the positive cooperation strategy needs to pay higher costs, especially when the betrayal gain is also higher, in order to avoid the loss of both parties will choose the negative cooperation to make the field engineer cultivation system rupture. When the subsidy given by the government to stimulate the enthusiasm of the subjects to build together constitutes an important part of the revenue, both parties will choose to cooperate positively in order to obtain this revenue to serve their own development. The higher the liquidated damages for betrayal, the more the two parties will tend to cooperate positively to avoid losses and spillover losses such as damage to the subject’s social image and credibility when the gains from betrayal cannot satisfy the losses.

Język:: Angielski

Częstotliwość wydawania:: 1 razy w roku
Dziedziny czasopisma:: Nauki biologiczne, Nauki biologiczne, inne, Matematyka, Matematyka stosowana, Matematyka ogólna, Fizyka, Fizyka, inne

Kanał RSS czasopisma

Parameter	Condition 1	Condition 2	Condition 3	Condition 4
R	10	10	10	10
t	0.4	0.4	0.4	0.4
C1	3	4	5	5
C2	2	3	2	4
G1	1.5	1.5	2	2
G2	1.5	2	1.5	2
I1	0.3	0.3	0.3	0.3
I2	0.7	0.7	0.7	0.7
P	0.5	1	0.5	1

Parameter	Condition 1	Condition 2	Condition 3	Condition 4
R	10	10	10	10
t	0.4	0.4	0.4	0.4
C1	3	4	5	5
C2	2	3	2	4
G1	1.5	1.5	2	2
G2	1.5	2	1.5	2
I1	0.3	0.3	0.3	0.3
I2	0.7	0.7	0.7	0.7
P	0.5	1	0.5	1

Research on Field Engineer Cultivation System in Vocational Education-Taking Intelligent Manufacturing Specialty Group as an Example

Linlin Zhao

Zhengbo Ji

Tao Wu

Data publikacji: 21 mar 2025

Otrzymano: 14 paź 2024

Przyjęty: 10 lut 2025

DOI: https://doi.org/10.2478/amns-2025-0561

Słowa kluczoweIndustry-teaching integration, School-enterprise cooperation, Evolutionary game theory, Benefit distribution coefficient, Cooperation cost sharing

© 2025 Linlin Zhao et al., published by Sciendo

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.

Słowa kluczowe
Industry-teaching integration, School-enterprise cooperation, Evolutionary game theory, Benefit distribution coefficient, Cooperation cost sharing

Parameter	Condition 1	Condition 2	Condition 3	Condition 4
R	10	10	10	10
t	0.4	0.4	0.4	0.4
C1	3	4	5	5
C2	2	3	2	4
G1	1.5	1.5	2	2
G2	1.5	2	1.5	2
I1	0.3	0.3	0.3	0.3
I2	0.7	0.7	0.7	0.7
P	0.5	1	0.5	1