Teaching Design Model of Bridge Aesthetics Course Facing Ecological Landscape Sustainable Development

Abstract

In recent years, ecological building of bridges has gradually begun to appear in cities, and this trend is conducive to the sustainable development of urban bridges and an ecological environment, promoting the development of emerging industries around cities and driving the development of the urban economy. Bridges’ ecological aesthetic design cannot be separated from ecological aesthetics, and the relationship between these two factors is complementary and inseparable. This paper focuses on the relationship between the teaching of a bridge aesthetic design course and ecological landscape sustainable development. Based on a visual impression hierarchy deep learning model and a statistical analysis of a questionnaire, including reliability and validity analyses, a teaching model for the design of landscape bridge structure systems was constructed. Landscape bridge structure systems combine the dimensions of function, form, mechanics, and culture, and the teaching design model of landscape bridges must include non-professional students, undergraduate students, graduate students, and graduates working in enterprises. Investigations were performed of the urban block landscape, water environment landscape, urban garden landscape, and landscape bridges within natural mountain landscapes. The results showed that: (1) the influence and role of landscape aesthetics related to the water environment and urban garden landscapes are the most important; (2) in the teaching of a bridge aesthetics course, sustainable ecological development must consider the aesthetic value of landscape bridges while ensuring function and safety; and (3) for students at different learning stages, the focus in terms of bridge aesthetic system elements is different. Both the bridge structural landscape configuration and the ecological aesthetics must be considered together during the teaching of bridge aesthetics design courses. To achieve such a goal, students at different levels must have a good understanding of ecologically sustainable development and bridge aesthetics.

1. Introduction

The development of ecological aesthetics has evolved through several stages, and research on this topic is being increasingly promoted considering the increasingly serious ecological crisis [1,2]. “Ecology” has become a main concern of society, and aesthetic theory has also introduced a new era of change. In the research area of environmental aesthetics, people have gradually begun to advocate for the construction of an ecological civilization that balances humans, nature, and society [3,4,5]. With the expansion of the city and the improvement of municipal public utilities, the environmental conditions of landscape architecture have gradually attracted people’s attention. The aesthetic requirements that people have of the landscape environment are increasing, placing increased value on very beautiful and distinctive urban parks, street green spaces, and scenic spots. People’s demand for beauty in their living environments is also increasing. Combining the utilization of some bridge spaces and the different aesthetic features of different urban landscape spaces, ecological aesthetics in the bridge landscape are developing, and isolated bridge spaces are being integrated into the overall urban landscape environment, ultimately making the living environment more beautiful. At the same time, the construction of bridge landscape spaces via the simultaneous development of economic and environmental factors, to the end of developing an ecological civilization, enriches the urban bridge landscape’s ecological beauty.

Landscape bridges are ornamental bridges. Landscape ecology is one of the three core theories of Chinese landscape architecture. Chang suggested integrating landscape ecology into landscape design to meet the needs of planning and design practice [6]. Matos used scientometric methods to map dive gun research, synthesizing datasets from the literature, describing the scientific state of diving, and ultimately identifying existing knowledge groups, historical trends, and new topics in gun research [7]. Municipal land use plans generally place few restrictions on land use planning and allow substantial changes and modifications to existing topographic and landscape drainage patterns. The process of developing a residential or industrial area includes the preparation of a drainage master plan. Cuthbert focused on collecting and transporting rainwater or snowmelt runoff from roads and buildings through drainage pipes and ditches [8]. Geographic feature-based image analysis is the most important remote sensing method for land cover mapping and change detection. Chmielewski introduced the theoretical concept of the prospect as a landscape capacity indicator via a multi-domain land cover case study and explained how to interpret this indicator [9]. The above scholars have all conducted research on bridges, but no specific experimental processes have been offered.

Sustainable development is an important contemporary development strategy. Broman presented the Framework for Sustainable Development Strategy (FSSD), the result of 25 years of work by researchers and practitioners. He highlighted and validated the main features of FSSD that contribute to the sustainability of systems science [10]. Sustainability is understood as an environmental concept, but Plessis believes that some cultural concepts can be further integrated into the sustainability formula. Research has shown that, due to the variability and relevance of culture, it may be necessary to distinguish between the role of culture itself and the role of cultural governance in sustainable development [11]. Shapira used a strategic sustainability framework to analyze design thinking. This approach concerns not only human needs but also social sustainability [12]. Yan proposed an urban sustainability assessment framework based on actual natural resource constraints and human needs, taking China’s urban sustainability assessment approach as an example [13]. Although these scholars have performed experiments using sustainable development, their approaches still lack applicability to transportation infrastructure, and this lack is especially true for bridges designed with the goal of ecological aesthetic sustainability.

The role of bridge infrastructure engineering in urban construction is generally studied from three main points of view. The first is studying the mechanical characteristics of structures via mechanical analyses, including static, dynamic, wind resistance, and earthquake resistance properties [14,15,16]. The second involves studying structures from the perspective of sustainable development, including such issues as low-carbon environmental protection, durability, life cycles, and operation and maintenance [17]. The third perspective is landscape aesthetics, including such considerations as shape selection, shape optimization, and aesthetic value evaluation [18]. Bridge aesthetics combines structure, aesthetics, and landscape. It is necessary to study bridge aesthetics from the perspective of ecologically sustainable development and to establish systematic teaching models that can apply to different levels of learning. This need has important theoretical and practical significance to the aesthetic value evaluation and ecologically sustainable development of landscape bridges.

This article is organized as follows. First, the visual depth learning model is introduced, which is the core theory of landscape aesthetics, laying a theoretical foundation for the selection and evaluation of bridge aesthetics. Second, the questionnaire statistical analysis method is used to evaluate the aesthetic value of landscape bridges. Then, we establish the teaching model of landscape bridge aesthetics. Next, based on the ecologically sustainable development of a landscape bridge design teaching model, we design a questionnaire and undertake statistical analysis of its results. Finally, the conclusions are presented.

2. Visual Impression Hierarchy Deep Learning Model

In the field of computer vision, the task of object recognition has been widely considered by researchers for a long time [19]. Deep learning has recently shown superior image classification performance in large-scale visual recognition challenges. Compared with the hand-designed low-level image features used in some image classification algorithms, various models of deep learning have demonstrated their advantages (autoencoders, restricted Boltzmann machines, and convolutional and neural networks) in learning rich intermediate-level image representations. However, many parameters need to be estimated in deep neural networks for the final recognition process to be successful. Learning such a large set of parameters requires a very large set of image samples, annotated with labels [20]. In the context of limited training data sets, this requirement has undoubtedly become a key problem that prevents deep learning models from efficiently completing recognition tasks.

To incorporate Lie group impressions as prior knowledge into the learning rules of a neural network, the geometric structure of the network’s parameter space is restricted to the Lie group manifold during neural network design. This process requires that the weight matrices between the constrained input space and hidden neurons be obtained in an unsupervised manner, with Lie group space constraints [21]. To formally illustrate the learning of weights in a single-layer network with the Lie group impression constraint, the following set of matrices is defined:

$$F_n^{q\times p}\stackrel{\Delta }{=}\left\{N\in T^{q\times p}|N^{R}N=n^2{L}_p\right\}$$

(1)

Here, $L_p$ represents the identity matrix of size p × p, and p ≤ q. n is defined as a first-order differentiable function that can vary with time; that is, n = n(r). Additionally, n(r) ≠ 0 is required. N(r) is regarded as the connection matrix of a certain layer of the neural network. $N\in T^{q\times p}$ means that this connection matrix connects q inputs to p neurons. Constraining the parameter space of a neural network on the connection matrix means that the connection matrix N(r) always belongs to a nonlinear manifold space $F_n^{q\times p}$, with some geometrical properties. This outcome is expressed as

$$H\stackrel{\Delta }{=}\left\{K_U\left(N\right)|\forall r\in R:N(r)\in F_{n\left(r\right)}^{q\times p}\right\}$$

(2)

Here, $K_U\left(N\right)$ represents a specific learning algorithm acting on this layer of the neural network for a given connection matrix N. r represents the time interval for which the learning algorithm $K_U\left(N\right)$ acts on the network, and the subscript U expresses the objective formula used for optimizing the parameters of the entire network. By iteratively optimizing U, the network can find a suitable optimal solution [22].

According to the nonlinear neuron action mechanism, the calculation model for the fth neuron in layer j + 1 is

$$x_f=sign\left({\sum }_{i=1}^n{w}_{if}{y}_i\right),f=1,\dots m$$

(3)

Therefore, the total output of layer j + 1 can be modeled as

$$\left(\begin{array}{l}{x}_1\\ x_2\\ \dots \\ x_m\end{array}\right)=sign\left(\left(\begin{array}{l}{w}_{11}\dots w_{1n}\\ \dots \\ w_{m1}\dots w_{mn}\end{array}\right)\left(\begin{array}{l}y\\ y_2\\ \dots \\ y_n\end{array}\right)\right)$$

(4)

The above formula can be abbreviated as

$$X=sign\left(N^{R}Y\right)$$

(5)

Here, N is an (n × m)-order weight matrix. Following previous assumptions, the weight matrix can define a set of matrices. This set of matrices defines a submanifold in the (n × m)-dimensional Euclidean space $T^{n\times m}$, which is called the Stiefel manifold [23]. With no other constraints, the problem is transformed to consider the geometry of the set of restricted matrices into

$$N\in Sr(n,m)=\{W\in B_{n\times m}|W^{R}W=L_m\}$$

(6)

Here, $Sr(n,m)$ is the Stiefel manifold, and $B_{n\times m}$ represents all (n×m)-order matrices. $L_m$ is the identity matrix of order m. A specific layer in a neural network is expressed as follows:

$$x=sign[N^{R}y+n_0]$$

(7)

Any learning or optimization algorithm using the aforementioned definition of H can be characterized via a very basic characteristic of the network parameters. The optimization problem is expressed as

$$h\left(N\right)=G\left[u\right(Y,X,N\left)\right]$$

(8)

where h(N) represents the training objective function, and $G[\cdot ]$ represents the mathematical expectation inside the parentheses. $u(\cdot ,\cdot ,\cdot )$ represents a measure used to illustrate the performance of the current content of Y, X, and N, which are the criteria by which the neural network assesses the completion of the current task after training [24].

The Li subgroup is essentially a group of orthogonal matrices. According to the increasingly abstract features extracted during the training process, dimensionality gradually decreases from the input layer to the output layer, assuming m ≤ n. In the general gradient algorithm, the following updated formula can be obtained:

$$\frac{dW\left(r\right)}{dr}=-\eta gradh(W(r))$$

(9)

$$W_{m+1}=W_m-\eta gradh\left(W_m\right)$$

(10)

In the above-updated formula, we define the Stiefel manifold (N,W)→NW under the action of the Lie group $D=O\left(n\right)$. For two given points $W_0,W_j\in Sr(n,m,T)$, there exists an element $M_j\in F$ that satisfies $W_j=M_j{W}_0$.

$$F=\{M\in D(n\left)\right|M{W}_0=W_0\}$$

(11)

It is assumed that $W_0=\left(\begin{array}{l}{L}_n\\ D(n-m,n)\end{array}\right)=(s_1,\dots s_n)$. $s_j$ represents the basis vector, the jth element of which is 1 and in which the other elements are 0. Therefore, using the properties of the stabilizer, F can be expressed as the following formula:

$$F=\left\{\left(\begin{array}{cc}{L}_n& D(m,n-m)\\ D(n-m,n)& U\end{array}\right)\right\},U\in D(n-m)$$

(12)

In the Stiefel form, the two orthogonal matrices $N_1,N_2$ represent the same point if, and only if, their first m column vectors are identical. In other words, the Stiefel manifold is the quotient space obtained by dividing the group K = D(n) and its ambivalent subgroup F = D(n − m) [25]. In the following, we outline the method used to obtain the geodesics from a certain point $W\in Sr(n,m,T)$ in the parameter space when moving in the tangential direction $V\in R_{W}Sr(n,m,T)$. First, the weight matrix W is embedded into $D\left(n\right)$ by adding (n − m) orthogonal column vectors $(v_1,\dots ,v_{n-m})$, namely

$$W\to \tilde{W}=(w_1,\dots ,v_m,v_1,\dots ,v_{n-m})$$

(13)

Point $D\left(n\right)$ from the Lie group is mapped to a point on the Stiefel manifold, which can be expressed as $W\left(\begin{array}{l}{L}_n\\ D(n-m,n)\end{array}\right)$. Since this mapping is linear, the corresponding tangential mapping outputs the same form [26]. Since D(n) is a Lie group, tools such as Lie algebra and exponential mapping can be used to ensure convenient calculation, and the following updated weight formula is thus obtained:

$$N_{j+1}={\tilde{N}}_j\mathit{exp}(-\mu {\tilde{N}}_j^R{\tilde{V}}_F)\left(\begin{array}{l}{L}_m\\ D_{(n-m,m)}\end{array}\right)$$

(14)

$${\tilde{V}}_F=gradh(N_j)=\frac{1}{2}(\Delta h(N_j)-N_j\Delta h(N_j)N_j)$$

(15)

The above gives the formula solving $N_j$ under the condition of a known matrix $N_{j+1}$, following the gradient method. Here, ${\tilde{N}}_j=(w_1,\dots w_m,v_1,\dots v_{n-m})\in D(n)$ represents $N_j=(w_1,...w_m)\in Sr(n,m)$, and $v_1,\dots v_{n-m}$ is used to translate $N_j$ into an orthogonal matrix. $D_{(n-m,m)}$ is an all-zero matrix with n-m rows and m columns, and $\mu >0$ is the learning step size. $\Delta h\left(N_j\right)$ is the Euclidean gradient of the optimization function h at $N_j$.

3. Statistical Analysis of Questionnaire

3.1. Validity Analysis

Before the factor analysis, the KMO test and Bartley’s sphericity test were performed. The KMO test and Bartlett’s sphericity test methods are used to test the correlation between the variables used in principal component analysis [27]. The formula for calculating the KMO value is

$$\mathrm{K}\mathrm{M}\mathrm{O}=\frac{\sum \sum _{i\ne j}{r}_{ij}^2}{\sum \sum _{i\ne j}{r}_{ij}^2+\sum \sum _{i\ne j}{p}_{ij}^2}$$

(16)

where $r_{ij}^2$ is the simple correlation coefficient between variables i and j, and $p_{ij}^2$ is the partial correlation coefficient between variables i and j.

The KMO value is close to 1, indicating that the square sum of the simple correlation coefficients between all item variables is far greater than the square sum of the partial correlation coefficients, which can thus be used for principal component analysis.

Suppose there are n groups, and the standard deviation of each group is $s_1^2$, $s_2^2$,…$s_n^2$; in this case, the statistics approximately adhere to the chi-square distribution of n − 1,

$$K^2=\frac{1}{c}[(n-r)(lnMSE-ln{s}_i^2)]$$

(17)

$$c=1+\frac{1}{3(r-1)}[\frac{r^2}{n-r}-\frac{1}{n-r}]$$

(18)

where MSE is the mean square error and n = r n_i.

The degree of freedom of the statistics refers to the number of independent or freely changeable data points in the sample when the parameters of the population are estimated by the statistics of the sample. In the factor analysis undertaken via the Bartley sphericity test, if the p value is less than 0.05, the data are taken to be spherical, indicating that there is a correlation between the original data variables and that the data are suitable for use in factor analysis.

3.2. Reliability Analysis

After factor analysis, we should continue to test the reliability of the scale at all levels individually and the total scale. The reliability refers to the reliability or stability of the scale. The method most commonly used to test the reliability of the attitude scale is the α coefficient, created by Cronbach [28], the formula of which is

$$\mathsf{\alpha }=\frac{K}{K-1}(1-\frac{\sum S_i^2}{s^2})$$

(19)

where $K$ is the total number of questions in the scale, $\sum S_i^2$ is the sum of variance of the items in the scale, and $s^2$ is the variance of the sum of items in the scale.

4. Teaching Design Model of Landscape Bridge Structural System

A landscape bridge structure system combines the dimensions of function, form, mechanics, and culture (

Table 1. Landscape bridge structure system.

Four Dimensions	Concept Connotation
Function	Railways, highways, pedestrians, cities, gardens
Form	Beam, arch, cable-stayed, suspension and composite structures
Mechanics	External constraints, connection form, stiffness distribution
Culture	Regional, unique, and the spiritual core

). Bridge structures enable people and objects to cross obstacles (rivers, valleys, etc.) and thus mainly feature crossing structures. The function applications of landscape bridges mainly include railways, highways, pedestrian crossings, cities, gardens, etc. The shape refers to how the structural system is formed by its designers, and it represents an external performance factor that relates to resistance against external forces. The forms of landscape bridges mainly include beam, arch, cable-stayed, suspension, and composite structures (Figure 1). The force pattern is the mode of transfer between internal loads and the balanced internal force state, and it is crucial to a structure’s resistance to external forces. The mechanics dimension of a landscape bridge mainly includes external constraints placed on the structural system, the form of connection among internal stressed members, and the stiffness distribution among the main members. Landscape bridges also have ornamental functions. Ethnic and cultural groups in different regions form unique cultural expectations that they attach to bridges. The cultural dimension of landscape bridges combines cultural elements with modern architectural concepts and technologies, making the bridge regionally identifiable and unique and representing the spiritual core of the bridge.

The teaching model represents the core element of an aesthetic evaluation of landscape bridges. In the context of ecologically sustainable development, the goal of bridge aesthetic evaluation is the integration of aesthetics and ecology. The ecological aesthetics of a landscape bridge may be affected by the culture, environment, and cognitive abilities of different learning groups. Our model for teaching the design of landscape bridges comprises four levels and considers non-professional students, undergraduate students, graduate students, and graduates working in enterprises. Student groups of different levels pay attention to different aspects in the aesthetic evaluation of ecological and aesthetic landscape bridges. The main reason for this difference is that the cognitive evaluation of the visual depth learning mechanism that is applied to the aesthetic appearance of bridges depends on the established aesthetic system. Students at different levels have different concerns relating to the structural systems of landscape bridges, as shown in

Table 2. Cognitive characteristics of aesthetic value evaluators.

Four Levels	Distribution of Concerns
Non-professional students	Function, Form−, Mechanics−, Culture
Undergraduate students	Function, Form, Mechanics+, Culture
Graduate students	Function+, Form+, Mechanics+, Culture+
Graduates working in enterprises	Function+, Form+, Mechanics, Culture+

Note: “+”means the cognitive tendency is enhanced; “−”means the cognitive tendency is decreased.

.

5. Teaching Design of Bridge Aesthetics Course Based on the Principle of Combination of Force and Form with Shape and Deformation

The basic idea of bridge aesthetics teaching is as follows: to construct a mechanical model classification of landscape bridges based on the basic principle of force shape combination, to establish a structural system of landscape bridges from the relationship between structural modeling and stress, to establish teaching strategies for the bridge aesthetics course, and finally to conduct a questionnaire based on evaluation of the effect of the landscape bridge course.

5.1. Principle of Combination of Force and Form with Shape and Deformation

The qualitative analysis method based on the idea of “combination of force and form with shape and deformation” proposed in this paper aims to break the boundary between statically determinate structures and statically indeterminate structures, to conduct logical reasoning through the deformation characteristics of the structure under external action, to draw a structural bending moment diagram using qualitative analysis, and to unify the deformation characteristics and stress characteristics of the structure. The qualitative analysis method is based on the idea of “combination of force and form with deformation and shape” namely the concept of “visualization”: deriving the structural bending moment diagram by observing the structural deformation characteristics.

According to structural mechanics, the bending moment diagram is generally drawn on the tensile side of the structure, while the bending characteristics of the structure are compression on the concave side and tension on the convex side, and the bending moment diagram is drawn on the convex side. Therefore, it is possible to quickly draw a structural bending moment diagram by observing the concavity and convexity of the deformation curve of the structure under external forces and using key characteristic points of the bending moment diagram characteristics (such as the structural bending moment diagram under concentrated forces being straight lines, etc.).

Structural shape analysis is an important step in quickly drawing structural bending moment diagrams. The structure shape can be composed of two parts: internal composition and external constraints. The same internal composition of the structure has different mechanical characteristics under different external constraints. For the deformation analysis of a structure under external forces, it is necessary to analyze the linear displacement and angular displacement of the structure under external forces. The displacement of the structure can be determined by analyzing the movement trend of the structure under external forces. The overall motion trend of a structure can be compared to rigid body motion, while the local motion trend of the structure is judged based on the rigid body motion trend with degree of freedom constraints.

To draw a bending moment diagram of a structure under external forces, it is necessary to analyze the concave and convex sides of the structure under external forces and to draw the bending moment diagram on the convex side (tensile side). At the same time, combining the characteristics of hinge constraints that do not transfer bending moments, fixed constraints that transfer bending moments, and semi-fixed constraints that also transfer bending moments, it is possible to quickly draw a bending moment diagram of the structure. For example,

Table 3. Bending moment diagram of single beam model under external force.

Model
Deformation
Bending moment
Constraint	(a) hinge + hinge	(b) fixed + freedom	(c) fixed + hinge	(d) fixed + fixed

and

Table 4. Bending moment of rigid frame and arch model under external force.

Model
Deformation
Bending moment
Rigid constraint	(a) single hinge	(b) two hinges	(c) three hinges	(d) no hinge
Model
Deformation
Bending moment
Arch constraint	(e) single hinge	(f) two hinges	(g) three hinges	(h) no hinge

show the bending moment diagram of a single beam model under external force and the bending moment of a rigid frame and arch model under external force, and the mechanical performance of the cable-stayed bridge and the suspension bridge both can be derived from the beam, rigid, and arch bridge structures.

5.2. Landscape Bridge Structural System

Based on the principle of combination of force and form with shape and formation, we can construct the structural system of beam bridge, arch bridge, cable-stayed bridge, suspension bridge and the combination bridge from the mechanics of landscape bridge aesthetics, which can be seen in

Table 5. Landscape bridge aesthetics types from the perspectives of force and form. Note: Reprinted/adapted with permission from Ref. [29]. 2021, Jianming Ding.

Beam			[29]
Arch			[29]
Cable-stayed
Suspension	[29]	[29]
Combination
Aesthetic Types	Integration of force and form	Separation of force and form	Form without force

. From the perspective of force and form, the landscape bridge structural system can be divided into about three types, integration of force and form, separation of force and form, and form without force for the five bridge structures including beam, arch cable-stayed, suspension and combination system.

5.3. Teaching Design Scheme for Bridge Aesthetics Courses

With the increasing updating of national infrastructure construction technology and in the context of building a powerful transportation country, the updating and upgrading of bridge landscape design concepts have been highly valued by transportation departments. Education and transportation ministries have also issued opinions on effectively strengthening the aesthetic education work of colleges and universities in the new era. The “Bridge Aesthetics Course “ is designed to meet the needs of this industry and talent cultivation. “Bridge Aesthetics” is a professional course that emphasizes both artistry and technology, which can enhance students’ aesthetic and innovative abilities and improve the adaptability of relevant graduates to the bridge landscape design market.

The main content of the “Bridge Aesthetics Course” includes the basic principles of bridge aesthetics, aesthetic images and modeling of bridges, landscape bridge structural systems, landscape modeling of bridge components, and evaluation criteria for bridge aesthetics, which can be seen in

Table 6. The teaching design scheme of the “Bridge Aesthetics Course”.

Title	Content
Philosophical basis of bridge aesthetics	Origin and development of bridge aesthetics; world view and methodology of bridge aesthetics; expressions and basic principles of bridge aesthetics
Aesthetic images and modeling of bridges	Physical and spiritual attributes of bridges; images and colors of bridges
Landscape bridge structural systems	Principle of combination of force and form shape; components and systems of conceptual analysis; bridge engineers and architects
Landscape modeling of bridge components	Tension, compression, bending of force; modeling of component landscape
Beam system landscape bridges	Force characteristics; landscape modeling; expression of intention; case collection
Arch system landscape bridges
Cable-stayed system landscape bridges
Suspension system landscape bridges
Combination system landscape bridges
Evaluation criteria for bridge aesthetics	Elements of bridge aesthetic evaluation; bridge aesthetic evaluation levels; bridge aesthetic evaluation methods
Completion of landscape bridges	Competitive scheme design for actual projects; university student bridge design competition; structural design competition

.

5.4. Evaluation of Landscape Bridge Course Effect

Evaluating the teaching effectiveness of bridge aesthetics courses requires consideration from the following aspects: evaluation criteria, evaluation methods, evaluation significance, and teaching evaluation. The bridge aesthetics course evaluation system should be able to provide positive feedback about students’ learning effects and teachers’ teaching effects and promote the improvement and enhancement of teachers’ and students’ abilities based on questionnaires, as shown in

Table 7. The teaching evaluation dimension of the “Bridge Aesthetics Course”.

Evaluation Dimension	Evaluation Content
Evaluation criteria	1. Students’ interest and understanding in the bridge aesthetics course 2. Improvement of students’ ability and innovative thinking level in bridge design 3. Students’ understanding of bridge culture and its historical background 4. Student satisfaction with bridge aesthetics courses
Evaluation methods	1. Questionnaire survey: Through a questionnaire survey aimed at students, they learn about their understanding, interest, and mastery of the bridge aesthetics course, as well as their evaluation of teaching effectiveness. 2. Course design evaluation: We analyze whether the course design scheme is scientific, reasonable, and effective by evaluating the teaching methods, curriculum settings, and homework design during the teaching process. 3. Evaluation of academic achievements: We evaluate students’ achievements and innovation levels through their papers, work presentations, and other methods.
Evaluation significance	1. By evaluating the teaching effect of the bridge aesthetics course, we continuously optimize the course content and teaching methods and improve students’ learning interest and mastery. 2. By evaluating students’ innovative thinking and ability improvement, we guide students to develop an innovative spirit and explore diversified development paths for aesthetic design. 3. By evaluating students’ understanding of bridge culture and history, we cultivate students’ humanistic literacy and historical awareness and enhance the cultural connotation of aesthetic design.
Teaching evaluation	1. Students: combination of peers, questionnaires, design work, and competition effects 2. Teachers: combination of students, peers, and businesses

.

5.5. The Workflow of the Teaching Design Assessment of Bridge Aesthetics Course

This investigation was conducted with questionnaire groups. The research process structure is shown in Figure 2. First, a questionnaire was designed and sent to the respondents including non-professional students, undergraduate students, graduate students, and graduates working in enterprises, through questionnaire, wechat and tencent QQ, etc. Second, the reliability and validity of the recovered questionnaire were tested. Next, the results of the questionnaire were grouped according to the landscape bridges in the perspective of ecological aesthetics, and the importance of landscape aesthetics to the teaching design of landscape bridge forms under different landscape types was analyzed. Finally, the effect of the bridge aesthetics course was evaluated.

6. Teaching Design and Competition of Ecological Landscapes Based on Bridge Aesthetics Course

6.1. Emergence and Development of Urban Bridges

Every bridge is the product of human beings’ ability to overcome hardships and dangers. Bridges illustrate humans’ ability to control nature and yield a sense of pride in self-realization, engendering a special emotional connection to bridges. Therefore, the process of building bridges often attracts special attention from society, and many cultural and emotional factors accumulate in association. Bridges are not only an important part of the transportation system, but they are also a part of urban culture [30]. The development and promotion of urban bridge design are inseparable from the dual influence of the material and spiritual civilization of an era.

(1)

The concept of urban bridges

With rapid economic development, large numbers of people gather in cities. With the continuous progress of society, the increasingly severe problem of urban expansion has led to rapid changes in urban space, and traditional urban streets have been dismantled and rebuilt to create new spaces. With the rapid development of road and rail transportation, to expand the overall transportation system of a city and ensure its efficiency and safety, bridge design has adopted various structural forms, and different forms of urban space have been developed to expedite the connection between important parts of a city. Moreover, bridges themselves become important parts of a city [31].

(2)

Form types of urban bridges

With the continuous elevation of human ambition, urban development has seen spatial forms with diverse contents and complex structures continuously being formed. Bridges are an example of this formation.

   (1)

City Viaduct

In the limited space of a city, due to the lack of long-term and holistic planning and management, high-density populations can lead to overwhelming traffic. To improve urban efficiency, the scope for the rapid construction of viaducts expands urban roads in three-dimensional space and relieves the pressure of urban traffic, allowing more traffic to pass effectively through crowded cities [32]. The advantages of viaducts have meant that they are naturally the preferred solution to continuous urban expansion, as shown by the specific analysis in Figure 3.

   (2)

City overpasses

Overpasses are generally located in the main traffic lanes of a city. According to the different space types, they can be divided into four categories: fully separated, semi-separated, semi-interconnected, and fully interconnected. Figure 4 analyzes these structures explicitly.

   (3)

Pedestrian bridges

Pedestrian bridges are also called pedestrian overpasses. As the urban traffic network becomes increasingly complex, to avoid traffic jams caused by the interaction between people and vehicles and to address all aspects of pedestrian safety, pedestrian bridges are often built in densely crowded places, thus protecting pedestrians and maintaining the smooth flow of vehicles [33]. They are mainly built on high-traffic roads in cities. With the development of three-dimensional transportation, more and more pedestrian bridges will appear across roads, rivers, etc. The pedestrian bridge form is shown in Figure 5.

   (4)

Large-span urban bridges across rivers and seas

The basic structural forms of modern river-crossing and sea-crossing urban bridges can be divided into suspension bridges, cable-stayed bridges, arch bridges, and beam bridges. Landscape urban bridges are shown in Figure 6.

6.2. Questionnaire for Bridges in Landscape Aesthetics Class

(1)

Scale questionnaire design

(1)

Select the survey object

The purpose of the questionnaire is to understand the differences in the important aesthetic features of landscape bridges in different environments. Respondents are required to have a basic understanding of the environment and landscape bridges. To ensure the quality of the questionnaire and facilitate the selection of a broad sample, students at different levels (shown in Table 2) were selected for the survey.

  (2)

Questionnaire test method

In this study, paper questionnaires were provided, while online questionnaires were constructed as follows: they were imported onto the online data research platform “Questionnaire Star” and then input into the pool provided by the platform for questionnaire collection. At the same time, the questionnaires were spread on social media platforms such as WeChat and Tencent QQ for nine to 10 days by sharing links, and 2000 questionnaires were collected. The questionnaires were sorted, and the completed questionnaires were imported into SPSS (data processing software) for analysis.

  (3)

Questionnaire recovery

To ensure that the recovered questionnaires had highly reliable results, some invalid questionnaires were excluded. Quantitative statistical analyses were performed on the completed questionnaires, and the validity and reliability were calculated using SPSS software to determine whether the questionnaires had been effective. If the validity of a questionnaire was greater than 75%, its results were eligible for use as the research basis. Through the online questionnaire platform and the distribution of offline paper questionnaires, a total of 2500 questionnaires were distributed, and 2000 were returned. Therefore, our research was conducted using the questionnaire results.

(2)

Questionnaire reliability survey

Since separate questionnaires were designed to address the four types of landscape environments, the four questionnaires had to be tested separately for validity and reliability.

  (1)

Validity testing

The validity test is used to investigate whether each item is reasonable and meaningful. The validity is mainly judged via the KMO value, as shown in

Table 8. KMO value description.

Sequence Number	KMO Value Range	Validity
1	Greater than 0.8	High validity
2	Between 0.7 and 0.8	Good validity
3	Between 0.6 and 0.7	Acceptable validity
4	Less than 0.6	Poor validity

. The four categories of questionnaire validity can be calculated according to Table 8, and the results are shown in

Table 9. Four questionnaire types’ KMO values and Bartlett’s test results.

Questionnaire Classification	KMO Value	Bartlett Sphericity Test
		Approximate Chi-Square	Degrees of Freedom (df)	p-Value
Landscape bridge form in urban block landscape	0.926	1104.576	567	0.000
Landscape bridge form in water environment landscape	0.908	1247.918	567	0.000
Landscape bridge form in urban garden landscape	0.891	1398.577	567	0.000
Landscape bridge form in mountain natural landscape	0.911	1401.225	567	0.000

.

It can be seen from Table 9 that the KMO value of the questionnaire concerning the importance of landscape bridge morphology and landscape aesthetics in an urban block landscape is 0.926. The KMO value of the questionnaire on the importance of landscape bridge morphology and landscape aesthetics in a water environment landscape is 0.908, and the KMO value of the questionnaire on the importance of landscape bridge morphology and landscape aesthetics in an urban garden landscape is 0.891. The KMO value of the questionnaire on the importance of landscape bridge morphology and landscape aesthetics in a mountainous landscape is 0.911, and the KMO values of the four questionnaires have all been shown to be greater than 0.85, or near 0.9 and close to 1, indicating that the questionnaire has high construct validity and is very suitable for use in analysis.

  (2)

Reliability testing

Reliability testing is widely used in the comprehensive evaluation of scientific research. The Cronbach’s reliability coefficient (Cronbach’s alpha coefficient value) is generally used to test the reliability of a scale, as shown in

Table 10. Description of Cronbach’s alpha coefficient values.

Sequence Number	Cronbach’s α Coefficient Value Range	Reliability
1	Greater than 0.8	The scale reliability is very good
2	Between 0.7 and 0.8	The scale is acceptable
3	Between 0.6 and 0.7	The scale should be revised
4	Less than 0.6	The scale needs to be redesigned

. Following the calculations in Table 10, the reliability analysis of each landscape type is illustrated in

Table 11. Cronbach’s alpha reliability analysis of four types of questionnaires.

Questionnaire Classification of the Importance of Landscape Aesthetics	Number of Items	Sample Size	Cronbach’s α Coefficient
Landscape bridge form in urban block landscape	18	2000	0.932
Landscape bridge form in water environment landscape	18	2000	0.945
Landscape bridge form in urban garden landscape	18	2000	0.927
Landscape bridge form in mountain natural landscape	18	2000	0.965

.

It can be seen in Table 11 that the Cronbach’s α coefficient of the questionnaire on the importance of landscape bridge morphology and landscape aesthetics in an urban block landscape is 0.932 > 0.9. The Cronbach’s alpha coefficient of the questionnaire on landscape bridge morphology in a water environment is 0.945 > 0.9. The Cronbach’s alpha coefficient of the questionnaire on the importance of landscape bridge morphology and landscape aesthetics in an urban garden landscape is 0.927 > 0.9. The Cronbach’s alpha coefficient of the questionnaire on the importance of landscape bridge morphology and landscape aesthetics in a natural landscape of mountains is 0.965 > 0.9. All of the above indicators show that the four questionnaires, when taken as a whole, can be used to effectively investigate the issues under analysis. The results of the comparison of the importance of landscape aesthetics to landscape bridge morphology in different environments are valid and have high reliability, making them suitable for further data analysis.

6.3. Results and Discussion

(1)

Attribute analysis of respondents

(1)

The respondents were all students at different levels or office workers. The male-to-female ratio was 42.78% male and 57.22% female.

(2)

The educational level of the respondents ranged from junior college to postgraduate, and the respondents all had a basic higher educational level.

(3)

The distribution of respondents between different industries and majors was generally balanced.

(2)

Analysis of the importance of landscape aesthetics to the teaching design of landscape bridge forms under different landscape types

This study was analyzed using the total scores obtained from the questionnaires. The total score of a questionnaire was between 18 and 36, which is the lowest score range for all questionnaires addressing the impact of landscape aesthetics on the importance of landscape bridge morphology, indicating that the respondents believed that the importance of landscape aesthetics in landscape bridge morphology design is low. A total score of 36–54 points indicates that the respondents believed that the role of landscape aesthetics in landscape bridge design is of low importance. The influence and function of the bridge shape were considered more important. If the total score obtained was between 72 and 90 points, the respondents believed that the role of landscape aesthetics in the forming of landscape bridges is of high importance.

Through the statistical analysis of the total score frequency results of the four questionnaires, the following conclusions are drawn.

 (1)

The mean total score regarding the importance of landscape aesthetics to bridge morphology in an urban block landscape type is 64.567, which is in the range of 54–72. Most of the samples yielded a total score ranking at the importance level III, representing a high degree of importance. The maximum sample values were 54–72 points.

 (2)

The total score regarding the importance of landscape aesthetics to the form of landscape bridges in a water environment landscape is 71.868, which is between 54 and 72. Most of the samples yielded a total importance level of III, representing a higher degree of importance. The maximum total score values were near 90, in the range of 72–90;

 (3)

The total score regarding the importance of landscape aesthetics to the form of landscape bridges in an urban garden landscape environment is 69.334, which is between 54 and 72, and most of the samples yielded a total score of importance of level III, indicating a higher degree of importance. The maximum values were near 90 and thus in in the range of 72–90;

 (4)

The total score regarding the importance of landscape aesthetics to the form of landscape bridges in the natural landscape environment of mountains is 68.522, which is between 54 and 72, and most of the samples yielded a total score of importance level III, representing a higher degree of importance. The total scores reached a maximum at 72 points.

This outcome shows that the respondents had a certain understanding of the importance of landscape aesthetics to the forms of bridges in different environments. There was a high degree of recognition of the importance of the aesthetics of landscape bridges in the four types of landscape environments. Among the four types of landscape environment, the highest average value was earned by the landscape bridge form in a water environment (71.868). Next was the landscape bridge form in an urban garden landscape (69.334). Then came the landscape bridge form (64.567) in an urban block landscape. Last was the landscape bridge form (68.522) in a mountainous natural landscape. This order shows that the influence and function of landscape aesthetics in relation to a water environment and the landscape bridge form in an urban garden landscape are more important.

(3)

Analysis of the importance of landscape aesthetics’ three-dimensionality to the teaching design of landscape bridge form for different landscape types

This study defines 18 factors according to the three dimensions of environmental factors of functional beauty, formal beauty, and harmonious beauty. According to the average scores of the three-dimensional rules, the average values of the three aspects can be calculated. The three-dimensional approach to landscape aesthetics analyzes the morphological features of bridges of different landscape types in two ways: comparison among the three aesthetic dimensions of a single landscape bridge type; and comparison of the three dimensions between different landscape bridge types.

(1)

Comparison of the average value of the three-dimensional features of a single landscape bridge type

The 18 rules are set out as follows: A1, the overall and local structure proportions are unified; A2, the shape and geometric elements are unified; A3, the building materials and colors are unified; B1, the form and surroundings are coordinated; B2, the form, road plane, and elevation are coordinated; B3, symmetrical balance; B4, a harmonious match between form and function; C1, stationary beauty and dynamic beauty; C2, visual security; D1, the point of view effect; D2, the expressiveness of the space on the bridge; D3, the visual effect of the perspective and the environment under the bridge; D4, the visual effect of the surroundings of the bridge; D5, the coordination of the view from the bridge and the environment; E1, daylight projection; E2, landscape lighting; F1, the historical value of the construction technology; and F2, artistic rendering.

① Figure 7a shows an average value map of the urban block form, function, and beauty rules. Figure 7b shows a graph of the average value of the urban block form and beauty rules. Figure 7c shows the average values of rules concerning the coordination of urban block morphological and environmental factors.

Figure 7 shows that people strongly recognize the importance of functional beauty to the overall form of landscape bridges in an urban block landscape, as well as of the harmonious beauty of environmental factors, although the recognition of the importance of formal beauty is the lowest.

② Figure 8a shows a mean value map of the water environment form, function, and beauty rules. Figure 8b shows a graph of the average values of the detailed rules regarding the form of the water environment, and Figure 8c shows a graph of the average values of the rules regarding the coordination of the formal and environmental factors of a water environment.

Figure 8 shows that, regarding the overall shape of a landscape bridge in a water environment, the importance of the coordination and beauty of environmental factors is highly recognized, followed by functional beauty, while formal beauty is taken to be the least important.

③ Figure 9a shows a map of the average values of the rules regarding urban garden form, function, and beauty. Figure 9b shows a graph of the average values of the urban garden form and beauty rules. Figure 9c shows the average values of the rules regarding the coordination and beauty of urban garden morphological and environmental factors.

Figure 9 shows that people highly recognize the importance of the coordination and beauty of environmental factors in relation to the overall shape of a bridge in an urban garden landscape, followed by formal beauty, and functional beauty is taken to be the least important.

④ Figure 10a is a mean value map of the rules regarding the beauty of a mountain landscape, as well as its form and function. Figure 10b shows a mean value of the rules regarding the form of mountain landscapes. Figure 10c shows the average values of the rules regarding the coordination and beauty of landscape morphological and environmental factors in mountainous areas.

It can be seen from Figure 10 that people highly recognize the importance of the coordination and beauty of the environmental factors of a landscape bridge in a mountainous landscape. This importance is followed by the recognition of functional beauty, and the importance of formal beauty is the least recognized.

(2)

Three-dimensional comparative analysis between different types of landscape bridges

As shown in Figure 11, the questionnaires on the four types of landscape bridges with different landscape types are compared considering the three dimensions of functional beauty (a), formal beauty (b), and environmental factor coordination beauty (c).

  ①

Among the aesthetic elements comprising functional beauty, the average value of the landscape bridge form in an urban block landscape is the highest, followed by the bridge form in a water environment and the bridge form in an urban garden landscape. The lowest average value is assigned to the landscape bridge form in a natural mountain landscape. This outcome shows that the aesthetic elements relating to the functional beauty of a landscape bridge in an urban block landscape and in the water environment are more important than those of a bridge in an urban garden landscape and in a natural mountain landscape.

  ②

Regarding the aesthetic elements of formal beauty, the average value received by the landscape bridge in a water landscape is the highest, followed by that in an urban garden landscape and that in a natural mountain landscape. The mean value of the landscape bridge shape in an urban block landscape is the lowest. Among the four types of landscape bridges, that in a water environment and that in an urban garden landscape were acknowledged as the most important in terms of formal beauty, while a bridge in an urban block landscape was assigned the lowest degree of importance. This outcome shows that the importance of the landscape aesthetics of a bridge in an urban block environment with a strong traffic function is lower than that of a bridge in a water environment and of one in an urban garden landscape with significance within the landscape. More attention is paid to the functional beauty of the bridge. In a water environment, most landscape bridges have symbolic meanings or become landmarks, thus placing higher requirements of formal beauty on the bridge.

  ③

Regarding the elements of the harmonious beauty of environmental factors, the average value given to bridges in an urban garden landscape is the highest, followed by water environment bridges and natural mountain landscape bridges, and the lowest average value is given to landscape bridges in urban block landscapes. Because the form of the landscape bridge in an urban garden landscape is closely related to the features of the surrounding environment, the landscape elements and components that it shows and the responsibilities that it undertakes are different. The combination of visual effects presented would change as the tour route changes. Therefore, the harmonious beauty of the environmental factors of a landscape bridge in an urban garden landscape is the most important.

6.4. Experimental Summary

In this experimental study, we performed a longitudinal comparison of the total scores on the questionnaires, landscape aesthetics and its elements, and the differences in the average scores received by the four types of landscape bridge forms. By comparing the differences among the four types of landscape bridge forms, the following can be concluded:

(1)

The morphological importance of landscape aesthetics for different types of bridges is different—landscape bridges in water environment landscapes > landscape bridges in urban garden landscape > landscape bridges in urban block landscapes > landscape bridges in natural mountain landscapes; and

(2)

Horizontally comparing the three dimensions of and the average differences between landscape aesthetic elements in relation to the four types of landscape bridge forms, it can be seen that the design of bridges in urban block landscapes pays the most attention to functional beauty. Landscape bridges in water environments, urban gardens, and mountain landscapes pay attention to the harmonious beauty of bridge form and environment.

Regarding the elements of landscape aesthetics, bridges in urban block landscapes pay more attention to the coordination of form, and the other three types of bridges pay more attention to the unity of form. In addition, the technical and artistic treatment of the auxiliary structure of a bridge in an urban garden landscape and a water environment is more important than the aesthetic elements, except for unity. The technical and artistic treatment of the morphological structure of a landscape bridge in a natural mountain landscape is the least important compared to the other aesthetic elements.

(3)

A longitudinal comparison of the three main dimensions of the four types of landscape bridge and the average differences between landscapes’ aesthetic elements was performed. Of the three dimensions of landscape aesthetics, functional beauty is the most important for frequently used bridges in urban block landscapes. Regarding formal beauty, bridges in a water environment with specific symbolic significance consider this factor to be the most important compared to the three other types of landscape bridge forms. Regarding the harmonious beauty of environmental factors, landscape bridges in an urban garden landscape with certain aesthetic requirements consider this factor more important than the other types of bridges do.

7. Conclusions

Bridge research is a multidisciplinary field, involving architecture, sociology, art, landscape architecture, philosophy, and mechanics. The ecological nature of landscape bridges is reflected in aesthetic evaluation, which integrates ecological aesthetics into landscape bridge design, provides theoretical guidance in relation to ecological aesthetics, and promotes the development of bridge aesthetics courses and the sustainable design of bridges in the context of ecological aesthetics. This paper has established a model for teaching landscape bridge structure design based on the visual impression hierarchy deep learning model and a statistical analysis of questionnaires, including reliability and validity analyses. Landscape bridge structure systems combine the dimensions of function, form, mechanics, and culture, and the model for teaching the design of landscape bridges can be extended to non-professional students, undergraduate students, graduate students, and graduates working in enterprise. Questionnaires were designed regarding four types of landscape bridges in different environments, and we proposed that bridges within different types of environments have different aesthetic values. It is thus necessary to consider sustainable ecological development in the teaching of bridge aesthetics courses, and the focus of students in terms of aesthetic elements differs at different learning stages. Our purpose is to arouse students’ interest in the aesthetic value of landscape bridges in the context of ecologically sustainable development.