Course Evaluation of Advanced Structural Dynamics Based on Improved SAPSO and FAHP

Abstract

Talent cultivation is the fundamental mission of higher education institutions, and the key to improving the quality of talent cultivation lies in enhancing the quality of teaching. In this regard, the Joint Committee recommends that the United Nations Educational, Scientific and Cultural Organization (UNESCO) should be invited to participate in this conference, in accordance with their respective mandates. However, in China, research on course evaluation systems and mechanisms in application-oriented universities is relatively scarce, and the evaluation dimensions are often limited; therefore, the evaluation of graduate courses in universities faces challenges such as a lack of specialized assessment systems, limitation of evaluation methods, and an imbalance between emphasis on outcomes and neglect of the teaching process. In this study, a comprehensive evaluation system for the Advanced Structural Dynamics (ASD) course is constructed based on the context-input-process-product (CIPP) evaluation model. The evaluation was conducted from four perspectives: teaching objectives, teaching inputs, teaching processes, and teaching outcomes. The fuzzy analytic hierarchy process (AHP) and simulated annealing particle swarm algorithm (SAPSO) are employed to study evaluation indicators and weights at various levels for the ASD course, and the proposed method is validated through practical examples. This study combines qualitative and quantitative evaluation indicators to achieve comprehensive assessment and adopts more scientifically rational algorithms for weight calculation, aiming to improve the accuracy and efficiency of weight calculation. The research findings of this study can further enhance the evaluation level of teaching quality and talent cultivation in graduate courses at application-oriented universities.

1. Introduction

Teaching quality is a core component of educational quality, particularly in higher education, where the execution of teaching tasks is crucial for cultivating high-quality talent and serves as a key indicator for measuring the level of university education. Among myriad courses, Advanced Structural Dynamics (ASD), as a foundational subject, has particularly stringent educational quality requirements due to its unique disciplinary characteristics and profound impact on students’ future engineering practices. Virgin [1] enhanced the teaching of structural dynamics through practical experience with 3D-printed structures. When discussing teaching tools and software resources, Brandt’s ABRAVIBE toolbox [2] serves as an example of how software can be integrated into the teaching of vibration analysis and structural dynamics. Panagiotopoulos and Manolis [3] have developed a web-based educational software that provides interactive experiments for teaching structural dynamics. ASD not only requires students to master complex theoretical knowledge, but also demands an ability to apply this knowledge to practical engineering problems, making the application of teaching methods and technology particularly important [4]. However, current ASD teaching still faces numerous challenges, including a disconnect between theory and practice, insufficient teaching resources, and low student engagement, all of which directly affect teaching quality and student learning outcomes. Therefore, establishing a comprehensive indicator evaluation system and employing scientifically accurate calculation methods to determine the weights of indicators are essential for achieving more reasonable and accurate evaluation results. Moreover, the evaluation system for course indicators is influenced by a variety of factors, some of which are difficult to describe quantitatively, and this adds to the complexity of the evaluation system design.

1.1. CIPP Model

The CIPP model is a framework for evaluating and improving projects, policies, programs, and practices that was first proposed by American scholar Stufflebeam in 1966. CIPP stands for context, input, process, and product, which form the core of the CIPP model. The CIPP model provides a comprehensive evaluation perspective, focuses on process and development, promotes multi-party involvement, emphasizes feedback and improvement, and facilitates continuous program improvement. It helps evaluators to gain a comprehensive understanding of the curriculum and to identify problems, and it provides effective improvement measures to enhance the quality and effectiveness of the curriculum. The CIPP model has been widely used in the evaluation of educational teaching programs. Some studies have shown that the CIPP model has the potential to help professionals (teachers and administrators) in Teaching English to Speakers of Other Languages (TESOL) to improve their professional practice, curriculum design, and program assessment [5]. The CIPP model has also been applied to the evaluation of TESOL programs. In addition, CIPP has been applied to English-language teaching quality assessment [6,7,8], the quality assessment of school education [9], training program evaluation [10], evaluation of the practical professions program curriculum [11], character education evaluation [12], policy evaluation of entrepreneurship practice programs [13], and the evaluation of pre-school education programs [14], etc.

1.2. Course Evaluation

The evaluation of teaching and learning curricula plays an important role in the field of education and is significant in providing feedback and opportunities for improvement, optimizing curriculum design, promoting research and innovation in teaching and learning, and supporting decision making and quality assurance, as well as enhancing the transparency and equity of teaching and learning. Through effective evaluation, the quality of education can be continuously improved and upgraded, and students can be provided with better learning opportunities and space for development. Li and Hu [15] constructed a teaching quality assurance index system suitable for colleges and universities, based on the CIPP model, and validated the effectiveness of this system in university teaching evaluation through empirical research. Keskin et al. [16] concluded that there was no significant difference in teachers’ perceptions of the mathematics curriculum according to gender and educational status. In addition, scholars who have conducted research on higher mathematics and high school geography subjects have also conducted teaching evaluation studies. In terms of professional course evaluation, Rooholamini et al. [17] provided data for undergraduate medical students’ course program evaluation. Mahmoudabad et al. [18] used the CIPP model to assess clerkship programs in the public health curriculum at Yazd University. Al-Shanawan [19] applied the CIPP model and used a mixed-method design to evaluate the self-learning curriculum of a kindergarten in Saudi Arabia, which included randomly selecting and surveying teachers, interviewing school inspectors, and conducting content analysis. In the field of civil engineering, Zhang et al. [20] developed an assessment framework based on CIPP to improve interdisciplinary BIM (building information modeling) education in highway engineering. Atmacasoy et al. [21] evaluated the Introduction to Industrial Engineering course at Sabanci University based on the CIPP model.

1.3. Intelligent Algorithms

Intelligent algorithms can provide personalized assessment and feedback based on individual student differences and learning. It can identify students’ areas of weakness and learning needs, and customize evaluation indicators and improvement measures for students. Based on the evaluation results and model analysis of the intelligent algorithm, teachers can understand their teaching strengths and weaknesses and make targeted teaching improvements. This helps to improve the quality and effectiveness of teaching and better meets students’ learning needs. Intelligent algorithms can analyze and mine large-scale educational data to provide data support and decision-making reference for educational decision-makers. This helps to formulate more scientific and reasonable education policies and improvement measures in order to enhance the quality and effectiveness of education.

Currently, simulated annealing algorithms [22,23,24], particle swarm algorithms [25,26,27], hierarchical analysis [28,29,30], genetic algorithm [31], sailfish optimization [32], the technique for order preference by similarity to an ideal solution (TOPSIS) method, artificial intelligence, and deep learning [33,34,35,36,37,38] have all been applied in various fields, such as engineering optimization and curriculum evaluation. Sun et al. [39] developed a deep learning-assisted online intelligent English-teaching system that integrates decision tree algorithms and neural networks, aiming to enhance students’ English-learning efficiency and provide personalized teaching based on students’ knowledge and personalities. Fang [40] developed an intelligent online English-teaching system based on support vector machine algorithms and complex networks to improve teaching activities and enhance teaching quality. Hamsa et al. [41] developed academic performance prediction models using decision trees and fuzzy genetic algorithms for BS and MS students in computer science and electronics and communications.

This paper will be based on a combination of fuzzy hierarchical analysis and a genetic algorithm, which aims to obtain more satisfactory results in evaluating the multi-indicator program and to obtain more accurate weight coefficients of evaluation indexes, in order that this evaluation can reflect the opinions of experts as well as students, thus promoting the construction and development of the discipline of ASD. This paper is structured as follows: Section 2 introduces the construction method of course teaching evaluation system based on CIPP; Section 3 optimizes the weight coefficients based on the simulated annealing particle swarm hybrid algorithm; Section 4 designs the weight coefficient importance survey and the questionnaire for the evaluation of teaching effect; Section 5, in combination with the ASD course, determines the weight values of evaluation indexes and performs the fuzzy comprehensive evaluation of teaching effect; and Section 6 draws the research conclusions of this paper.

2. Construction of CIPP-Based Course Teaching Evaluation System

2.1. CIPP Model

The CIPP evaluation model is based on the outcome-based education (OBE) model, which advocates a goal-driven approach to education and focuses not only on proving results, but also on “continuous improvement” in terms of the purpose of the evaluation, which is to make the work program more effective. The core evaluation meanings and theoretical implications are summarized below:

(1)

Background evaluation: Determines the basic background of each curriculum plan and the implementation of the activities of the management organization, clarifies the objectives of the evaluated objects and their specific needs, clarifies the opportunities to meet the objectives, diagnoses some basic problems that need to be faced, and judges whether the target activities basically solve practical problems.

(2)

Input evaluation: A comprehensive evaluation of alternative curriculum planning options in order to further assist decision-makers in rationally selecting the best means of realizing activities that will meet the curriculum objectives.

(3)

Process evaluation: The main objective is to accurately describe the data of the actual design process of the course and to scientifically determine the scientific problems that will inevitably exist in analysis or scientific prediction in the course teaching design work itself or in the implementation process, so as to provide a scientific and effective evaluation information basis for decision-makers at all levels, all of which aims to correct current curriculum-planning problems.

(4)

Outcome evaluation: Objective measurement, interpretation and evaluation, and fair evaluation of various achievements in the implementation of the existing curriculum plan, which aims to explain the actual value basis and methodological advantages of the evaluation results.

In this paper, the CIPP model is used to evaluate the ASD course. It not only pays attention to the achievement of teaching objectives, but also overcomes the limitations of the traditional target model. It integrates diagnostic evaluation, formative evaluation, and summative evaluation, and thus can form a more scientific and comprehensive evaluation model.

2.2. Construction of Teaching Evaluation System Based on Fuzzy Hierarchical Analysis Method

The fuzzy analytic hierarchical process (FAHP) is a system analysis method combining qualitative and quantitative methods proposed by Prof. T. L. Saaty of American Operations Research in the 1970’s. FAHP improves the problems that face the traditional AHP and improves the reliability of decision making. The teaching evaluation steps based on FAHP are the construction of a hierarchical model, establishment of a fuzzy judgment matrix, establishment of a fuzzy consistency matrix, hierarchical single ranking, hierarchical total ranking, and fuzzy comprehensive evaluation. Chen et al. [42] proposed a novel framework for teaching performance evaluation that combines the fuzzy analytic hierarchy process (FAHP) with the fuzzy comprehensive evaluation method. In this framework, the teaching evaluation hierarchy includes six factors: planning and preparation; communication and interaction; teaching for learning; managing the learning environment; student evaluation; and professionalism. Each of these is further divided into two or more sub-factors. In the AHP hierarchy model proposed by Thanassoulis et al. [43], the criteria for teaching evaluation consist of two aspects: course and teacher. The course is further analyzed through two sub-criteria: overall interest and the perceived practicality of the course from the students’ perspective. The teacher dimension is analyzed into four sub-criteria: preparation, professionalism, presence, and supporting material. Taking the ASD course as the evaluation object, combined with the direction of evaluation of college courses that have appeared in the previous literature, this paper comprehensively unfolds the teaching evaluation index system in order to carry out a division of evaluation indexes in all aspects, and it constructs a multi-level index system of the target layer, criterion layer, and index layer. Based on the CIPP model, the course evaluation index system is divided into four first-level indicators and 14 second-level indicators, as shown in Table 1. The first-level indicators include four items, including teaching background, teaching input, teaching process, teaching results, teaching effect, etc. This indicator involves the main aspects of course construction, and is the main factor affecting the construction of the course and the core objective of course evaluation. There are 14 items in the secondary indicators, which are the further refinement of the corresponding primary indicators and the items to be evaluated in each main aspect. They are the sub-targets of the course evaluation and are a series of basic target layers around the realization of the sub-targets, and they are also the evaluation elements for the specific realization of the sub-targets.

Table 1. Evaluation indicators for the ASD course.

Target Level	Standardized Layer	Indicator Layer	Description of Indicators
Teaching evaluation A	Teaching background B1	Teaching objective C11	To cultivate students’ ability to deeply understand and apply advanced concepts of ASD to solve practical engineering problems
		Learning situation analysis C12	To assess students’ understanding and application of ASD theories, providing feedback for teaching adjustments
		Teaching program C13	To comprehensively cover ASD topics, ensuring students receive systematic guidance and support
	Teaching input B2	Faculty C21	To emphasize students’ abilities to analyze and solve complex ASD problems
		Base and test equipment C22	To deepen students’ understanding of ASD through laboratory practice
		Teaching resources and funding C23	To ensure students have access to necessary experimental equipment, software, and computational resources
	Teaching process B3	Course instructional content C31	To cover advanced concepts, theories, and applications of ASD, reflecting the latest developments
		Teaching methodology C32	To combine theory with practice, enhancing learning outcomes through case analyses and experimental practices
		Student activity C33	To cultivate students’ practical abilities and team work through discussions, projects, and experimental reports
		Teacher activity C34	To influence teaching quality, including teaching methods, resource preparation, and assignment design
	Teaching outcome B4	Course management and assessment C41	To evaluate the effectiveness of the course, ensure content updates, and improve teaching quality
		Student capacity building C42	To assess students’ theoretical grasp and practical application abilities in the field of ASD
		Teacher capacity building C43	Teachers need to possess profound knowledge and teaching abilities in ASD
		Overall effectiveness of the course C44	To reflect students’ learning outcomes and capability enhancement, including knowledge mastery, practical abilities, and innovation capabilities

2.3. Establishment of Fuzzy Consistency Matrix

The basic idea of fuzzy hierarchical analysis is basically the same as the analytical steps of the hierarchical analysis proposed by T. L. Staaty, and the core problem of fuzzy hierarchical analysis is to establish a fuzzy consistency matrix. The core problem of fuzzy hierarchical analysis is to establish a fuzzy consistency matrix, and how to construct a fuzzy consistency matrix easily and objectively is particularly important. Fuzzy hierarchical analysis of the objective existence of uncertainty using an [0, 1] interval for qualitative description, and the fuzzy set theory of fuzzy consistency relations and fuzzy consistency matrix based on the evaluation of multiple indicators, combined with fuzzy program preferences, can obtain more satisfactory results; therefore, it is necessary to provide the definition and properties of a fuzzy consistency matrix and to evaluate it using fuzzy hierarchical analysis.

2.3.1. Definition of a Fuzzy Agreement Matrix

Noting $=\left\{1,2,\cdots ,n\right\}$, the fuzzy consistency matrix is defined as follows:

Definition 1.

Let the matrix $\mathit{R}=(r_{ij}{)}_{n\times n}$ be set, where $r_{ij}$ is the element of the $i$ row and $j$ column of the matrix, and $n$ is the total number of rows or columns of the matrix, and, if the matrix satisfies $0\le r_{ij}\le 1 \left(i,j\in \mathit{\Omega }\right)$, then $\mathit{R}$ is said to be a fuzzy matrix.

Definition 2.

A fuzzy matrix $\mathit{R}$ is said to be a fuzzy complementary matrix if the fuzzy matrix $\mathit{R}=(r_{ij}{)}_{n\times n}$ satisfies $r_{ij}+r_{ji}=1 \left(i,j\in \mathit{\Omega }\right)$, denoting the fuzzy complementary matrix as $\mathit{F}$.

Definition 3.

Fuzzy matrix $\mathit{F}$ is said to be fuzzy consistent if the fuzzy complementary matrix $\mathit{F}=(f_{ij}{)}_{n\times n}$ satisfies $f_{ij}=f_{ik}-f_{jk}+0.5 \left(i,j,k\in \mathit{\Omega }\right)$.

2.3.2. Properties of Fuzzy Consistent Matrices

Theorem 1.

Let the fuzzy matrix $\mathit{R}=(r_{ij}{)}_{n\times n}$ be a fuzzy consistent matrix, then there are $\forall i,j\in \mathit{\Omega }$ and $r_{ii}=0.5$, $r_{ij}+r_{ji}=1 \left(i,j\in \mathit{\Omega }\right),$ and the sum of the elements of the rows of $i$ and the columns of $j$ of $\mathit{R}$ is $n$, and the sub-matrix obtained by removing any rows and their corresponding columns from the matrix $\mathit{R}$ is still a fuzzy consistent matrix. The sub-matrix obtained by removing any row and its corresponding column is still a fuzzy consistent matrix.

Theorem 2.

If the fuzzy complementary matrix $\mathit{R}=(r_{ij}{)}_{n\times n}$ is summed by rows, denoted as

$${\mathbf{r}}_{\mathbf{i}}=\sum _{\mathit{k}=1}^{\mathit{n}}{\mathit{r}}_{\mathit{i}\mathit{k}} (\mathit{i}\in \mathit{\Omega })$$

(1)

the following transformation is implemented:

$${\mathit{f}}_{\mathbf{i}\mathit{j}}={\displaystyle \frac{{\mathit{r}}_{\mathit{i}}-{\mathit{r}}_{\mathit{j}}}{\mathbf{2}\left(\mathit{n}-\mathbf{1}\right)}}+\mathbf{0.5}$$

(2)

then the resulting matrix $\mathit{F}=(f_{ij}{)}_{n\times n}$ is a fuzzy consistent matrix.

2.3.3. Establishment of the Fuzzy Agreement Matrix

Construct a fuzzy complementary judgment matrix based on the mutual comparison of the importance of the elements, which compares the relative importance scores between two factors of each indicator at the same level and with the same affiliation. Perform dimensional sub-division on the use of the 0.1–0.9 scale method, which, from the psychological point of view, is the current method that reflects the maximum number of grading people can accept when grading things. Use the 0.1–0.9 scale method for scoring comparisons, so that any two elements on the relative importance of a criterion can be quantitatively described for the nine-level scale method, as shown in Table 2.

Table 2. Scale 0.1 to 0.9.

Scale	Definition	Clarification
0.5	Equal importance	The two elements are equally important when compared
0.6	Slightly important	Comparing two elements, the former element is slightly more important than the other element
0.7	Clearly important	Comparing two elements, the former element is significantly more important than the other element
0.8	High priority	Comparing two elements, the former element is more strongly important than the other element
0.9	Vital	Comparing two elements, the former element is extremely more important than the other element
0.1~0.4	Inverse comparison	The element $a_i$ is compared with the element $a_j$ to obtain the judgment $r_{ij}$, then the element $a_j$ is compared with the element $a_i$ to obtain the judgment $r_{ji}=1-r_{ij}$

After obtaining the fuzzy judgment matrix $\mathit{R}=(r_{ij}{)}_{n\times n}$, the fuzzy consistency matrix is obtained by transforming it according to the property theorem of fuzzy consistency matrix. The evaluation model establishes the fuzzy matrix as a fuzzy complementary matrix, $\mathit{F}=(f_{ij}{)}_{n\times n}$ is a fuzzy consistent matrix obtained by transforming the fuzzy judgment matrix $\mathit{R}$ according to Theorem 2, and the weights of the indicators are configured based on the fuzzy consistent matrix in order to obtain more accurate results.

2.3.4. Consistency Test

After obtaining the weight values of each indicator, a consistency test is needed in order to judge whether the calculated weight values are reasonable. In this paper, in the consistency test of the fuzzy consistency matrix, the selected indicators are the compatibility indicators of the fuzzy judgment matrix and its feature matrix. The definition of the compatibility index $\mathit{I}\left(\mathit{A},{\mathit{W}}^{\mathrm{*}}\right)$, obtained from the feature matrix ${\mathit{W}}^{\mathrm{*}}$, and the judgment matrix is given below:

Definition: Let the vector $\mathit{W}={(w_1,w_2,\cdots ,w_N)}^T$ be the importance weight vector computed by processing the fuzzy consistency matrix $\mathit{F}$, where $w$ is the importance weight coefficient, ${\sum }_{i=1}^n{w}_i=1, w_i\ge 0, \left(i=1,2,\cdots ,n\right)$, and let $w_{ij}={\displaystyle \frac{w_i}{w_i+w_j}}\left(\forall i,j=1,2,\cdots ,n\right)$, then the identity matrix of the judgment matrix $\mathit{A}$ is the $n$ order matrix:

$${\mathit{W}}^{*}={\left(w_{ij}\right)}_{n\times n}$$

(3)

Let the matrices $\mathit{A}=(a_{ij}{)}_{n\times n}$ and $\mathit{B}=(b_{ij}{)}_{n\times n}$ both be fuzzy judgment matrices, and $\mathit{I}\left(\mathit{A},\mathit{B}\right)$ is called the compatibility index between $\mathit{A}$ and $\mathit{B}$, and its expression is as follows:

$$\mathit{I}\left(\mathit{A},\mathit{B}\right)={\displaystyle \frac{1}{n^2}}\sum _{i=1}^1\sum _{j=1}^n\left|a_{ij}+b_{ij}-1\right|$$

(4)

When the compatibility indicator $\mathit{I}\left(\mathit{A},\mathit{W}\right)\le \alpha$, where $\alpha$ is the attitude of the decision-maker, then the consistency of the fuzzy judgment matrix is considered to meet the requirements. The value $\alpha$ reflects the attitude of the decision-maker, and the smaller the value, the higher the consistency requirement of the decision-maker. If we test the consistency of fuzzy judgment matrix $\mathit{A}$, we need to let $\mathit{I}\left(\mathit{A},{\mathit{W}}^{\mathrm{*}}\right)\le \alpha$, i.e., in general $\alpha$ take 0.1.

3. Optimization of Weight Coefficients Based on Simulated Annealing Particle Swarm Hybrid Algorithm

3.1. Principles of the Hybrid Simulated Annealing Particle Swarm Algorithm

3.1.1. Simulated Annealing Algorithm

The earliest idea of the simulated annealing (SA) algorithm was proposed by N. Metropolis et al. in 1953 and successfully introduced into the field of combinatorial optimization in 1983 by S. Kirkpatrick et al. It is a stochastic optimization algorithm based on the Monte-Carlo iterative solution strategy, and its starting point is based on the similarity between the annealing process of solids in physics and general combinatorial optimization problems. The simulated annealing algorithm starts from a higher initial temperature, accompanied by the decreasing temperature parameter, and combines the probabilistic jumping characteristic in order to randomly search for the global optimal solution of the objective function in the solution space, i.e., the local optimal solution can be probabilistically jumped out of the local optimal solution and ultimately converge with the global optimal solution. The SA algorithm is an optimization algorithm that avoids falling into the serial structure of local minima and eventually converges with the global optimum by giving the search process time varying, and eventually converges to a zero probability of jumping. The SA algorithm updates the solution by accepting the new solution if it is better than the current one; otherwise, SA decides whether to accept the new solution based on the Metropolis criterion.

The acceptance probability $P$ is:

$$P=\left\{\begin{array}{c}1, E_{t+1}<E_t\hfill \\ e^{{\displaystyle \frac{-\left(E_{t+1}-E\right)}{kT}}}, E_{t+1}\ge E_t \hfill \end{array}\right.$$

(5)

where $E_t$ is the energy of the system at the moment of $t$; $E_{t+1}$ is the energy of the system at the moment of $t$ + 1; $k$ is the rate of temperature decrease; and $T$ represents the temperature.

3.1.2. Particle Swarm Optimization

The particle swarm optimization (PSO) algorithm is an optimization algorithm based on group intelligence, developed by J. Kennedy and R. C. Eberhart et al. in 1995. PSO simulates the behavior of a flock of birds foraging for food and finds the optimal solution through collaboration and information sharing among individuals in the flock. PSO originated from the study of bird flock behavior, which uses the sharing of information among individuals in the flock to make the motion of the whole flock evolve from disorder to order in the problem solution space, so as to obtain the optimal solution. In PSO, each solution to the optimization problem is called a particle, which moves in the search space to find the optimal solution. Particles have two attributes: position, which represents their position in the search space, and velocity, which represents how fast they are moving. The process of PSO mainly includes initializing the particle swarm, evaluating the particles, searching for individual extremes, searching for the global optimal solution, and modifying the velocity and position of the particles. PSO demonstrates its superiority in solving practical problems in its advantages in easy implementation, high accuracy, and fast convergence. The particle velocity update formula of particle swarm algorithm is as follows:

$$\begin{gathered} {\mathit{V}}_{i^{\prime }{j}^{\prime }}\left(t+1\right)={\mathit{V}}_{i^{\prime }{j}^{\prime }}\left(t\right)+c_1\times rand\left( \right)\times \left({\mathit{P}}_{best}\left(t\right)-{\mathit{X}}_{i^{\prime }{j}^{\prime }}\left(t\right)\right) \\ +c_2\times rand( )\times \left({\mathit{G}}_{best}\left(t\right)-{\mathit{X}}_{i^{\prime }{j}^{\prime }}\left(t\right)\right) \end{gathered}$$

(6)

where ${\mathit{V}}_{i^{\prime }{j}^{\prime }}$ represents the current velocity of the particle; ${\mathit{P}}_{best}\left(t\right)$ is the distance between the current position of a particle and the optimal position; ${\mathit{G}}_{best}\left(t\right)$ represents the distance between the current position of a particle and the best position of the group; $i^{\prime }$ represents the $i^{\prime }$ particle; $j^{\prime }$ represents the dimensionality of the actual problem; $t$ is the number of iterations; $c_1$ and $c_2$ are the learning factors, which take the value of 2.0; and $rand\left( \right)$ is the random number uniformly distributed in the range of 0–1.

3.2. Hybrid Algorithms

PSO is a process of designing a massless particle to simulate a bird in a flock, at the same time inputting the two attributes of speed and position of the particles, and searching for the optimal solution in the search space individually. SAPSO is based on the basic operation process of PSO, simulated annealing mechanism, self-cognition, the social cognition of the adaptive adjustment of PSO, and aims to achieve the global convergence of the algorithm. In order to improve the performance of the algorithm, the simulated annealing mechanism is introduced to adaptively adjust the self-cognitive and social-cognitive parts of the PSO algorithm to improve the performance of the hybrid algorithm, thus achieving an effective balance between global convergence and local convergence. The execution process is as follows: the initial population is randomly generated, then the random search is started to generate new individuals through the basic PSO algorithm, then the SA is performed on the generated local optimal individuals to judge whether the results can be used as the individuals in the next generation of the population or not, until the optimal results are searched. The introduction of the simulated annealing principle not only enhances the global search ability of PSO, but also solves the refusal non-convergence of the PSO algorithm to a large extent. The position update formula for SAPSO before improvement is shown in Equation (6).

The way of updating the speed of the algorithm before improvement is mainly through the speed of the particle in the previous moment and the current position; however, when the first term of the formula $V_{i^{\prime }}$ is 0, then the updating is only related to the current position and the algorithm at this time can easily fall into the local optimal solution. Therefore, in order to improve the global search ability of the algorithm, the inertia weight of the PSO is improved in this study, and the inertia weight coefficient $H$ is introduced here. $H$ is the proportionality coefficient related to the velocity of the previous moment, and the setting of the inertia weight $H$ has an important influence on the convergence speed and the result of the algorithm. The larger the $H$ weights are, the stronger the global search ability is; on the contrary, a smaller $H$ weight favors the local search. Therefore, in solving practical problems, we can constantly adjust $H$ to achieve the goal of searching the ideal results.

The velocity update equation after adding inertia weights $H$ is

$$\begin{gathered} {\mathit{V}}_{i^{\prime }{j}^{\prime }}\left(t+1\right)=H\times {\mathit{V}}_{i^{\prime }{j}^{\prime }}\left(t\right)+c_1\times rand()\times \left({\mathit{P}}_{best}\left(t\right)-{\mathit{X}}_{i^{\prime }{j}^{\prime }}\left(t\right)\right) \\ +c_2\times rand()\times \left({\mathit{G}}_{best}\left(t\right)-{\mathit{X}}_{i^{\prime }{j}^{\prime }}\left(t\right)\right) \end{gathered}$$

(7)

where the inertia weights are calculated by the following formula:

$$H=H_{\min }+\left(H_{\max }-H_{\min }\right)\times \mathit{tanh}\left(iter\right)$$

(8)

where $H_{\max }$ and $H_{\min }$ represent the maximum and minimum values of the inertia weights, respectively, which generally range from 0.4 to 0.95; $iter$ represents the number of iterations; and $\tan \mathrm{h}$ is the hyperbolic tangent function.

3.3. Validation of the Performance of the Hybrid Algorithm

In order to evaluate the actual optimization performance of the improved SAPSO, common optimization algorithm test functions are introduced for testing. The relevant test functions are as follows:

$${\mathit{f}}_{\mathbf{1}}\left(\mathit{x}\right)={\sum }_{\mathit{i}=\mathbf{1}}^{\mathbf{30}}{\mathit{x}}_{\mathit{i}}^{\mathbf{2}}, {\mathit{x}}_{\mathit{i}}\in \left[-\mathbf{1},\mathbf{1}\right]$$

(9)

$${\mathit{f}}_{\mathbf{2}}\left(\mathit{x}\right)={\sum }_{\mathit{i}=\mathbf{1}}^{\mathbf{30}}[{\mathit{x}}_{\mathit{i}}^{\mathbf{2}}-\mathbf{10}\mathbf{cos}(\mathbf{2}\mathit{\pi }{\mathit{x}}_{\mathit{i}})+\mathbf{10}], {\mathit{x}}_{\mathit{i}}\in \left[-\mathbf{0.01},\mathbf{0.01}\right]$$

(10)

The test function iteration process is shown as Figure 1.

Figure 1. Test function iteration process.

3.4. Weight Calculation of SAPSO Algorithm

The improved simulated annealing particle swarm algorithm is used to solve the objective function, which is the fuzzy consistency matrix established in the evaluation of the ASD course, so as to obtain the weight coefficients of the indicator layer and the program layer, and the process of its solution is realized in Matlab 2023b. The fuzzy consistency matrix is calculated using the improved algorithm in order to solve for the weight coefficients with optimal consistency. The process of evaluating the ASD course is shown in Figure 2.

Figure 2. Evaluation process of the ASD course.

4. Teaching Questionnaire

4.1. Survey of the Importance of Weighting Factors

The survey on the importance of the weighting factors of each indicator layer of the evaluation of the ASD course was conducted by means of an online questionnaire (Questionstar), mainly among the master’s degree students of the class of 2022 taught by Professor Huang Minshu of the Wuhan Institute of Technology, with a total number of 50 students from the civil engineering program, according to the four teaching evaluation guideline layers and the 14 indicator layers under them (Figure 3).

Figure 3. Questionnaire on the importance of weighting coefficients of course evaluation indicators.

The scoring scale is set from 0.1 to 0.9, and each evaluation element and its corresponding scale is shown in Table 1. The specific scoring method refers to Table 2, comparing two evaluation elements. The 0.5 scale is equally important, 0.6 scale is slightly important, 0.7 scale is obviously important, 0.8 scale is strongly important, 0.9 scale is extremely important, and the higher the scale, the higher the importance of the former element represented. 0.1–0.4 scale is for the inverse comparison, i.e., the importance of the latter element over the former element is 1–(0.1~0.4) scale. In order to facilitate statistical calculations, the original scale is enlarged by 10 times when setting the options in the questionnaire, i.e., 5 is used to represent 0.5 scale, and so on. For example, suppose “teaching background” B1 is compared with “teaching results” B4, and the respondents think that “teaching background” is slightly more important than “teaching results”. For example, if “teaching background” B1 is slightly more important than “teaching achievements” B4, the scale is 0.6, corresponding to option 6; if “teaching achievements” is slightly more important than “teaching background”, the scale is 0.4, corresponding to option 4. The design of the questionnaire page is shown in Figure 3.

4.2. Teaching Effectiveness Evaluation Survey

The evaluation survey of teaching effectiveness in the ASD course was also conducted anonymously through an online questionnaire designed by Questionstar, using a method of inviting civil engineering graduate students of the Wuhan Institute of Technology from the class of 2022 who participated in the course, as well as relevant personnel, to evaluate the course, one by one, on each of the 14 indicators evaluated in this course. The evaluation method is to give each indicator a score according to the percentage system: [90, 100] is excellent; [80, 90) is good; [60, 80) is average; and below 60 is poor. The elements of each indicator level and their corresponding descriptions are given in Table 1. The questionnaire design is shown in Figure 4.

Figure 4. Questionnaire for evaluating the effectiveness of course teaching.

5. Evaluation of Teaching Effectiveness

5.1. Determination of Evaluation Indicator Weights

Through the online questionnaire survey (Questionstar), the indicators at all levels in the established teaching evaluation index system were scored according to the 0.1–0.9 scale method (Table 2), the questionnaire survey results of 50 civil engineering graduate students from the class of 2022 at the Wuhan Institute of Technology in the ASD teaching class were collected, and the scoring results of each indicator were normalized to obtain five fuzzy judgment matrices, which are A (teaching evaluation), B1 (teaching background), B2 (teaching input), B3 (teaching process), B4 (teaching results), and the fuzzy judgment matrices are shown in Table 3, Table 4, Table 5, Table 6 and Table 7.

Table 3. Teaching evaluation fuzzy judgment matrix F-A.

Teaching Evaluation A	Teaching Background B1	Teaching Input B2	Teaching Process B3	Teaching Outcome B4
Teaching background B1	0.5	0.4	0.3	0.4
Teaching input B2	0.6	0.5	0.4	0.5
Teaching process B3	0.7	0.6	0.5	0.4
Teaching outcome B4	0.6	0.5	0.6	0.5

Table 4. Teaching context fuzzy judgment matrix F-B1.

Teaching Background B1	Teaching Objective C11	Learning Situation Analysis C12	Teaching Program C13
Teaching objective C11	0.5	0.5	0.4
Learning situation analysis C12	0.5	0.5	0.3
Teaching program C13	0.6	0.7	0.5

Table 5. Fuzzy judgment matrix of teaching inputs F-B2.

Teaching Input B2	Faculty C21	Base and Test Equipment C22	Teaching Resources and Funding C23
Faculty C21	0.5	0.6	0.6
Base and test equipment C22	0.4	0.5	0.4
Teaching resources and funding C23	0.4	0.6	0.5

Table 6. Fuzzy judgment matrix of teaching process F-B3.

Teaching Process B3	Course Instructional Content C31	Teaching Methodology C32	Student Activity C33	Teacher Activity C34
Course instructional content C31	0.5	0.6	0.5	0.6
Teaching methodology C32	0.4	0.5	0.6	0.6
Student activity C33	0.3	0.4	0.5	0.5
Teacher activity C34	0.4	0.4	0.5	0.5

Table 7. Fuzzy judgment matrix for teaching outcomes F-B4.

Teaching Outcome B4	Course Management and Assessment C41	Student Capacity Building C42	Teacher Capacity Building C43	Overall Effectiveness of the Course C44
Course management and assessment C41	0.5	0.1	0.4	0.5
Student capacity building C42	0.9	0.5	0.5	0.5
Teacher capacity building C43	0.6	0.5	0.5	0.4
Overall effectiveness of the course C44	0.5	0.5	0.6	0.5

The fuzzy judgment matrix established from the evaluation results is organized, and the fuzzy judgment matrix is transformed according to the fuzzy consistent matrix Theorem 2, and the results of the fuzzy consistent matrix are shown in Table 8, Table 9, Table 10, Table 11 and Table 12:

Table 8. Teaching evaluation fuzzy agreement matrix R-A.

Teaching Evaluation A	Teaching Background B1	Teaching Input B2	Teaching Process B3	Teaching Outcome B4
Teaching background B1	0.5	0.43	0.4	0.4
Teaching input B2	0.57	0.5	0.47	0.47
Teaching process B3	0.6	0.53	0.5	0.5
Teaching outcome B4	0.6	0.53	0.5	0.5

Table 9. Teaching context fuzzy consistency matrix R-B1.

Teaching Background B1	Teaching Objective C11	Learning Situation Analysis C12	Teaching Program C13
Teaching objective C11	0.5	0.53	0.4
Learning situation analysis C12	0.48	0.5	0.37
Teaching program C13	0.6	0.63	0.5

Table 10. Fuzzy consistency matrix of teaching inputs R-B2.

Teaching Input B2	Faculty C21	Base and Test Equipment C22	Teaching Resources and Funding C23
Faculty C21	0.5	0.6	0.55
Base and test preparation C22	0.4	0.5	0.45
Teaching resources and funding C23	0.45	0.55	0.5

Table 11. Instructional process matrix fuzzy consistency matrix R-B3.

Teaching Process B3	Course Instructional Content C31	Teaching Methodology C32	Student Activity C33	Teacher Activity C34
Course instructional Content C31	0.5	0.51	0.58	0.57
Teaching methodology C32	0.49	0.5	0.57	0.55
Student activity C33	0.42	0.43	0.5	0.48
Teacher activity C34	0.43	0.45	0.52	0.5

Table 12. Fuzzy consistency matrix of instructional outcomes R-B4.

Teaching Outcome B4	Course Management and Assessment C41	Student Capacity Building C42	Teacher Capacity Building C43	Overall Effectiveness of the Course C44
Course management and assessment C41	0.5	0.32	0.38	0.35
Student capacity building C42	0.68	0.5	0.57	0.53
Teacher capacity building C43	0.62	0.43	0.5	0.47
Overall effectiveness of the course C44	0.65	0.47	0.53	0.5

After obtaining the fuzzy consistency matrix, the consistency test is needed. In Matlab, combined with simulated annealing particle swarm algorithm in order to calculate the weights of the indicators, the weights of the indicators are summarized in single sort and total sort, and combined with the calculation of the weight vector $\mathit{W}$. Then, calculate the compatibility index of the fuzzy judgment matrix, and test the consistency of the calculation results. The weights of the indicators are summarized in single sort and total sort, taking the calculation of teaching evaluation A as an example:

According to the fuzzy consistency matrix $\mathit{R}$ of teaching evaluation A, combined with simulated annealing particle swarm algorithm, the weight vector is calculated as

$${\mathit{W}}_{\mathit{A}}=(0.217,0.259,0.262,0.262{)}^T$$

(11)

According to Equation (1), the feature matrix of teaching evaluation A is calculated as

$${\mathit{W}}_A^{*}=\left[\begin{array}{cccc}0.5& 0.456& 0.453& 0.453\\ 0.544& 0.5& 0.497& 0.497\\ 0.547& 0.503& 0.5& 0.5\\ 0.547& 0.503& 0.5& 0.5\end{array}\right]$$

(12)

According to Equation (4), calculate the compatibility index $I\left(\mathit{A},{\mathit{W}}_{\mathit{A}}^{\mathrm{*}}\right)=0.092<0.1$ between the fuzzy judgment matrix F-A and ${\mathit{W}}_{\mathit{A}}^{\mathbf{*}}$, so it can be considered that fuzzy judgment matrix F-A is satisfactorily consistent, and the weight set ${\mathit{W}}_{\mathit{A}}$ reasonableness calculated through the fuzzy consistency matrix, combined with the simulated annealing particle swarm algorithm, is in line with requirements. By calculating and verifying one by one, the weights of each evaluation index are sorted in a single level, and the results are shown in Table 13, Table 14, Table 15, Table 16 and Table 17:

Table 13. Calculation of teaching evaluation A.

Evaluation Indicators	Relative Weight	Compatibility Indicators
Teaching background B1	0.217	$I\left(\mathit{A},{\mathit{W}}_{\mathit{A}}^{*}\right)=0.092<0.1$ Consistency test passed
Teaching input B2	0.259
Teaching process B3	0.262
Teaching outcome B4	0.262

Table 14. Calculation results of teaching context B1.

Evaluation Indicators	Relative Weight	Compatibility Indicators
Teaching objective C11	0.310	$I\left(\mathit{B}\mathbf{1},{\mathit{W}}_{\mathit{B}\mathbf{1}}^{*}\right)=0.042<0.1$ Consistency test passed
Learning situation analysis C12	0.304
Teaching program C13	0.386

Table 15. Calculation of teaching input B2.

Evaluation Indicators	Relative Weight	Compatibility Indicators
Faculty C21	0.268	$I\left(\mathit{B}\mathbf{2},{\mathit{W}}_{\mathit{B}\mathbf{2}}^{*}\right)=0.089<0.1$ Consistency test passed
Base and test preparation C22	0.385
Teaching resources and funding C23	0.347

Table 16. Calculation results of teaching process B3.

Evaluation Indicators	Relative Weight	Compatibility Indicators
Course instructional content C31	0.272	$I\left(\mathit{B}\mathbf{3},{\mathit{W}}_{\mathit{B}\mathbf{3}}^{*}\right)=0.082<0.1$ Consistency test passed
Teaching methodology C32	0.266
Student activity C33	0.229
Teacher activity C34	0.233

Table 17. Calculation of teaching and learning outcome B4.

Evaluation Indicators	Relative Weight	Compatibility Indicators
Course management and assessment C41	0.22	$I\left(\mathit{B}\mathbf{4},{\mathit{W}}_{\mathit{B}\mathbf{4}}^{*}\right)=0.0974<0.1$ Consistency test passed
Student capacity building C42	0.276
Teacher capacity building C43	0.247
Overall effectiveness of the course C44	0.257

After calculation, each fuzzy judgment matrix and its feature matrix compatibility index is less than 0.1; therefore, the consistency test of the fuzzy judgment matrix passes and the reasonableness of the calculated weight allocation is verified. The calculation results are obtained as a single order of the relative weights between the elements in this level relative to the previous level, and the weight indicators are calculated and summarized in the hierarchical analysis structure chart (Figure 5), which can clearly see the relative weights of each element.

Figure 5. Calculation of evaluation indicator weights.

5.2. Fuzzy Integrated Evaluation

The fuzzy comprehensive evaluation method is a comprehensive evaluation method based on fuzzy mathematics, in which fuzzy objects and fuzzy concepts reflecting certain properties of fuzzy objects are treated as a fuzzy set, and qualitative evaluation is converted into quantitative evaluation based on the fuzzy mathematical affiliation function. After deriving the weights of the indicators for each indicator level for the evaluation of the course, for the implementation of the evaluation of the course, a number of students who participated in the course in the current semester, as well as those who participated in the course in previous semesters, were invited to conduct an online questionnaire survey on the course.

5.2.1. Commentary Set Setting

The establishment of a course evaluation indicator system has been determined. The four first-level evaluation indicators and 14 second-level evaluation indicators form the indicator set C of this evaluation, and the composition of the indicator set can be seen in the first-level and second-level indicator layers of this evaluation indicator system:

$$\mathit{A}=\left[\mathrm{B}1,\mathrm{B}2,\mathrm{B}3,\mathrm{B}4\right]$$

(13)

$$\mathit{B}=\left[{\mathrm{C}}_{11},{\mathrm{C}}_{12},{\mathrm{C}}_{13},{\mathrm{C}}_{21},{\mathrm{C}}_{22},\cdots ,{\mathrm{C}}_{44}\right]$$

(14)

Evaluation set, i.e., the collection of evaluation level determination, is in accordance with the general evaluation habit. This paper divides the evaluation set into four levels, and organizes the score interval and assignment of each level as shown in Table 18:

$$\mathit{V}=\{\mathrm{t}\mathrm{a}\mathrm{l}\mathrm{e}\mathrm{n}\mathrm{t}\mathrm{e}\mathrm{d}, \mathrm{f}\mathrm{a}\mathrm{v}\mathrm{o}\mathrm{r}\mathrm{a}\mathrm{b}\mathrm{l}\mathrm{e}, \mathrm{g}\mathrm{e}\mathrm{n}\mathrm{e}\mathrm{r}\mathrm{a}\mathrm{l}, \mathrm{m}\mathrm{e}\mathrm{d}\mathrm{i}\mathrm{o}\mathrm{c}\mathrm{r}\mathrm{e}\}$$

(15)

Table 18. Classification of evaluation indicators and their assigned values.

Rating	Score Range/Points	Assign a Value to Something
Talented	90~100	95
Favorable	80~90	85
General	60~80	70
Mediocre	0~60	30

Through the establishment of the indicator set and evaluation set, the comprehensive evaluation of the ASD course implementation scoring can be performed, and the collected data for the normalization operation can thus obtain the affiliation value of each evaluation indicator, in order to obtain the final score of the course. Evaluation matrix $\mathit{R}$ is indeed a fuzzy insinuation from the indicator set to the evaluation set, and, for the comprehensive evaluation of the course, the final score statistics need to be accomplished by the weight values established for each indicator. The one-dimensional vector composed of the weights of the indicators calculated above is denoted as $\mathit{W}$, and the fuzzy comprehensive evaluation of $\mathit{P}$ is obtained by combining the weights of the second-level evaluation indicators and the first-level indicators, i.e., $\mathit{P}=\mathit{W}\times \mathit{R}$, and the final evaluation grade is calculated by using the principle of maximum affiliation.

5.2.2. Calculation of Integrated Evaluation Results

The evaluation panel for the ASD course was established, inviting course participants and teachers to evaluate each of the indicators in the course evaluation, and the comments were given according to the set of comments identified above. For example, in the evaluation of the teaching objectives C11 in the teaching context B1, 80% of the members of the evaluation team evaluated “talented”, 20% evaluated “favorable”, and no one evaluated “general” or “mediocre”; the score for this indicator is calculated as ${\mathit{R}}_1=\left[0.8,0.2,0,0\right]$, based on the percentage of comments that appear.

The results of this evaluation team’s scoring for each indicator of the course’s evaluation are summarized in Table 19.

Table 19. Results of the evaluation team’s scores for each indicator of the course evaluation.

Level 1 Indicators	Secondary Indicators	Judging Set (Number of People as a Percentage)
		Talented	Favorable	General	Mediocre
B1	C11	0.78	0.22	0	0
	C12	0.79	0.18	0.03	0
	C13	0.71	0.17	0.12	0
B2	C21	0.89	0.11	0	0
	C22	0.78	0.18	0.04	0
	C23	0.71	0.21	0.08	0
B3	C31	0.65	0.29	0	0
	C32	0.78	0.18	0.04	0
	C33	0.82	0.14	0.04	0
	C34	0.79	0.18	0.03	0
B4	C41	0.82	0.14	0.04	0
	C42	0.75	0.21	0.04	0
	C43	0.79	0.18	0.03	0
	C44	0.78	0.17	0.05	0

The evaluation matrix $\mathit{R}$ was obtained:

$$\begin{gathered} {\mathit{R}}_1=\left[\begin{array}{cccc}0.78& 0.22& 0& 0\\ 0.79& 0.18& 0.03& 0\\ 0.71& 0.17& 0.12& 0\end{array}\right] \\ {\mathit{R}}_2=\left[\begin{array}{cccc}0.89& 0.11& 0& 0\\ 0.78& 0.18& 0.04& 0\\ 0.71& 0.21& 0.08& 0\end{array}\right] \\ {\mathit{R}}_3=\left[\begin{array}{cccc}0.65& 0.29& 0& 0\\ 0.78& 0.18& 0.04& 0\\ 0.82& 0.14& 0.04& 0\\ 0.79& 0.18& 0.03& 0\end{array}\right] \\ {\mathit{R}}_4=\left[\begin{array}{cccc}0.82& 0.14& 0.04& 0\\ 0.75& 0.21& 0.04& 0\\ 0.79& 0.18& 0.03& 0\\ 0.78& 0.17& 0.05& 0\end{array}\right] \end{gathered}$$

A weighted average type of comprehensive evaluation model was used to obtain a vector of evaluation results for teaching context B1:

$${\mathit{P}}_1={\mathit{W}}_1\times {\mathit{R}}_1=\left[0.067, 0.066, 0.084\right]\times \left[\begin{array}{cccc}0.78& 0.22& 0& 0\\ 0.79& 0.18& 0.03& 0\\ 0.71& 0.17& 0.12& 0\end{array}\right]$$

$$=\left[0.756, 0.1885, 0.0554, 0\right]$$

The vector of evaluation results for instructional input B2, instructional process B3, and instructional outcomes B4 is derived in the same way:

$$\begin{gathered} {\mathit{P}}_2=\left[0.7974, 0.1868, 0.0385, 0\right] \\ {\mathit{P}}_3=\left[0.7561, 0.2008, 0.0268, 0\right] \\ {\mathit{P}}_4=\left[0.7830, 0.1769, 0.0401, 0\right] \end{gathered}$$

This results in a comprehensive evaluation matrix $\mathit{R}$:

$$\mathit{R}=\left[\begin{array}{c}{\mathit{P}}_1\\ {\mathit{P}}_2\\ {\mathit{P}}_3\\ {\mathit{P}}_4\end{array}\right]=\left[\begin{array}{cccc}0.756& 0.1885& 0.0554& 0\\ 0.7974& 0.1868& 0.0385& 0\\ 0.7561& 0.2008& 0.0268& 0\\ 0.7830& 0.1769& 0.0401& 0\end{array}\right]$$

The final result is calculated by combining the weights of the evaluation indicators at the first level. The calculation gives the evaluation for the ASD course as

$$\mathit{P}=\mathit{A}\times \mathit{R}=\left[0.7738, 0.1882, 0.0395, 0\right]$$

According to the final calculation results and the combination of all the evaluation indicators and weights, it is found that the degree of students and experts recognizing the ASD course as “excellent” reaches 74.35%; the degree of affiliation to “good” is 21.94%; the degree of affiliation to “fair” is only 3.81%; and the degree of affiliation to “poor” is 0. According to the principle of maximum affiliation in fuzzy evaluation, the evaluation result of this course is recognized as “excellent”. According to the principle of maximum affiliation in fuzzy evaluation, the evaluation result of this course is recognized as “excellent”. According to the evaluation set $\mathit{V}$, the value of the composite rating was calculated as 92.273, which is within the range of excellence of the evaluation set.

6. Conclusions

In this paper, a fuzzy hierarchical analysis, integrated with a simulated annealing particle swarm algorithm, was employed to assess the ASD course. As a foundational course within the civil engineering discipline, the course has garnered significant recognition from evaluators following continuous endeavors to develop and enhance its content and teaching conditions. The weighting of the course evaluation indicators reveals that the ASD teaching team at the Wuhan Institute of Technology is relatively outstanding and that the course material is abundant. However, future iterations of the course should focus on improving the teaching environment, as well as upgrading the hardware and software teaching facilities. This study truly exemplifies the principle of “enhancing learning and teaching through evaluation”, offering valuable insights for the future development and construction of this course. The main findings of this study are as follows:

(1)

In indicator C33 (student activity), teamwork involves structural dynamics analysis tasks based on theoretical and numerical methods. Teachers require students to choose methods and write MATLAB programs to conduct structural dynamic analysis after understanding the theory of ASD. Homework statistics show that most students opt to use the finite element method, considering it a superior approach to solving dynamic problems due to its ability to handle complex issues and its high precision, efficiency, and flexibility.

(2)

Essentially, science is derived from experience and practice; yet, it transcends them, and intuitions, being a significant source of innovation, serve as an important bridge from experience and practice to science. In this study, the extension of students’ engineering intuition in structural vibration can be assessed through intuitive perception, logical analysis processes (indicator C42, student capacity building), and experimental operation skills (indicator C22, base and test equipment). Only when students have a deep understanding of the key points of the ASD course and possess engineering intuition can they draw inferences about other matters in subsequent professional courses and have an added advantage in future engineering practice.

Although this study reveals the advantages of the ASD course in terms of the teaching team and course content, the evaluation results also point out areas for improvement, particularly in the teaching environment and facilities, as well as in enhancing students’ engineering intuition. This reflects an important principle in educational evaluation practice: evaluation is not only a summary of past achievements, but also a guide for future development directions. In order to continuously improve the teaching quality of the ASD course, we recommend adopting the following measures:

(1)

Optimization of the teaching environment: Consider introducing more flexible and modern classroom layouts to promote teacher–student interaction and cooperative learning among students. At the same time, increase natural lighting and ventilation in classrooms to create a more comfortable learning atmosphere.

(2)

With the rapid development of civil engineering technology, it is necessary to update the hardware and software facilities required for teaching to ensure that students have access to the latest technical tools. For example, introduce advanced structural analysis software and virtual reality (VR) or augmented reality (AR) technologies to provide more intuitive and engaging learning experiences.

(3)

Establish a regular evaluation mechanism to collect feedback from students, teachers, and industry experts, and adjust course content, teaching methods, and facility configurations in a timely manner. Through continuous evaluation, ensure that the ASD course remains synchronized with industry demands, cultivating more civil engineering talents with practical abilities and innovative spirits.

(4)

To cultivate and enhance students’ engineering intuition, firstly, continuous practice and experience should be used to strengthen intuitive feelings, recognizing that the development of this intuition is a gradual process that requires constant sensation, insight, and reinforcement. Secondly, through experimental teaching, students should be encouraged to conduct structural dynamics experiments themselves to gain hands-on experience, which further clarifies and reinforces the basic theories and concepts taught in class. Lastly, engineering case teaching should be employed to foster students’ attention to relevant engineering cases, which complements the development of engineering intuition.