China’s shipbuilding industry has been in the forefront of the world for a long time in history, and data show that since 2003, China’s shipbuilding industry has entered the track of rapid development [1, 2]. The scale of the industry continues to grow, the output of shipbuilding continues to increase and the number of existing orders and completed orders ranks among the best in the world. The country’s high attention and continuous technological improvement and innovation have made China the third largest shipbuilding country in the world [3]. However, China’s shipbuilding industry is largely only technological progress and leadership, and its exploration in design fields such as styling and interiors is far less than that of Europe and the United States. Design should have played an important role [4–6]. In particular, the interior design of Chinese ships is a basic set, and in many cases, it only meets the functional requirements of specific types of ships, and the exploration in terms of design and living experience is still very simple. The independent design work often needs to be carried out along with the construction process. There is no clear style orientation. The design of each type of ship is relatively messy. There is no set of sound design methods [7–9]. The proportion of space design cost in China’s shipbuilding cost is shown in Table 1 [10, 11]. It can be seen from Table 1 that the proportion of cost is relatively small, which means that due to the reduction of design cost and the imperfect construction level, the quality and design sense of marine supporting facilities are much inferior to those of similar ships in other countries, which is not only passive in construction. The number of production has also dropped significantly [12].

The proportion of space design cost in China’s shipbuilding cost

Boat type | The proportion of space design cost (%) |
---|---|

Yacht | 13 |

Passenger ship | 34 |

Engineering ship | 31 |

Fishing boat | 28 |

However, the foreign ship interior design has become mature, and before the ship is manufactured, there will be a relatively clear positioning and design for the interior [13–15]. On the one hand, the fundamental reason for this gap is that China has always paid little attention to ship design. The focus of ship manufacturing is often on the side of technology, and the investment in design is very lacking. When it comes to the design process, only basic man-machine is often considered. On the other hand, it is the difference in the user groups. The types of Chinese ships are generally military ships and ordinary passenger and cargo ships, and the users are generally professional personnel such as crew members [16, 17]. In contrast, in the United States, there is one boat (including small boats) for every 15 people. The foreign ship ownership rate is so high that foreign ships seem to have changed from a means of transportation to a tool of life [18]. Wang [19], a boat research scholar, mentioned that in boat space design, the sense of experience and design ideas must work together and cannot exist independently. There is interaction between the two, and they cannot exist independently of behaviour. Kang [20] and Bell et al. [21] believe that space design should be regarded as the core content of boat manufacturing, and it has also become an element that needs to be taken seriously in other manufacturing industries. Gross [22] proposed that the research content of boat space design is the relationship between related elements and people. Cowen [23] expounded the basic characteristics of the beauty of ship architecture, analysed the formal beauty of ship architecture and the art of ship architecture in detail and analysed examples, which provided a strong basis for the analysis of the aesthetics of this text. Combined with the above discussion, the content of boat space design theory is relatively complicated. It is worth discussing that the research centre of boat space design is different sense of space and the interaction between space and people. While discussing the space design, it is also necessary to study the changes in the comfort level and behaviour of people in the indoor environment [24, 25].

As a two-dimensional figure, the application of this graphic art to space is a transformation from the two-dimensional form to the three-dimensional form [26–28]. Using the hollowing technique of paper-cut art, it is applied to the space design of boats, forming an art form mainly based on the visual experience of emptiness and virtual reality [29–31]. Incorporating paper-cut elements into the design of boat space can effectively combine the characteristics of boat space and traditional Chinese culture to develop a boat accommodation space with characteristics and paper-cut cultural characteristics, which provides dual benefits for boat space design issues and Chinese traditional culture publicity. As an artistic treasure in traditional national culture, paper-cut art is one of the oldest folk arts in my country [32]. The art of paper cutting has been continuously inherited and developed and has its own unique national cultural heritage. Papercuts in different forms have their own language connotations and rich meanings, which reflect people’s production and life, enrich people’s spiritual life and express people’s yearning and pursuit for a better life.

With the development of the times, the space design of boats has become the demand and development trend of the society and is loved by the public. In today’s boat space design, the focus is on the functional design, and the boat space design is the unity of function and style, and the humanized design cannot be separated from the particularity required by people [33–35]. In view of this situation, this paper, based on Chinese folk paper-cut art, combines theoretical analysis with empirical research, deeply analyses the artistic expression of paper-cut elements in the design of boat space and mainly studies the decorative effects of paper-cut elements in boats. There is artistic fusion in design and the artistic fusion of paper-cut elements in the practical design of boats.

For the design of boat space, the integration and applicability of paper-cut elements in boats are the difficulty and the key point, which is related to the aesthetics of boat space design and the use of other functions. Fusion and applicability establish a deep analysis model based on the SAE algorithm.

The SAE adds sparsity constraints to the objective function and forces the feature layer (hidden layer) to be sparse by means of sparsity penalty, so as to better discover the hidden information in the data. ‘Sparse’ means limiting neurons to 0 or close to 0 values. KL divergence can measure the similarity between two probability distributions and is often used as a sparse penalty term. KL divergence is defined as follows:

The corresponding objective function is as follows:

In order to improve the robustness of AE to disturbance and noise, the contractive autoencoder (CAE) adds a Jacobian penalty term to the objective function, which is defined as follows:

The paper-cut element analysis model based on the SAE algorithm includes two main steps: cluster analysis of training samples by K-means and calculation of similarity between classes.

First, the cluster analysis of the paper-cut element analysis model is studied. K-means is a simple and commonly used cluster analysis method, which is very suitable for the clustering of convex clusters. Because of its simplicity and effectiveness, this chapter uses K-means to perform cluster analysis on training samples. Assuming that the training sample set is

According to the real label and index value of the sample, a C-order matrix A can be calculated, where A is the distribution of the sample in each cluster. Any element

First, the computational inter-class similarity of the SAE-paper-cut element profiling model is studied. According to experience, samples belonging to the same cluster have similar characteristics; so, the similarity between cluster

In Eq. (8), _{m}_{n}_{m}_{n}_{m}_{n}

The numerator calculates the total number of similar samples in cluster _{mn}_{nm}

Based on the SAE algorithm assignments obtained in Section 2.1, a SAE-paper-cut elemental profiling model is proposed to automatically extract discriminative fault features from high-dimensional sensor data. The Gaussian mixture model (GMM) is used to fit the probability distribution between the features and the sample labels to realise feature identification and fault mode diagnosis.

Assume that the samples and labels in the subset _{SXj}

In Eq. (10),

By setting _{ij}

In order to fine-tune the SAE-paper-cut element analysis model, an output layer is added after the hidden layer, as shown in Eq. (12); the output vector

In Eq. (12),

The error between the output value

In Eq. (13),

Note that

In Eq. (18), _{cur} and _{pre} represent the error values of the current iteration and the previous iteration, respectively.

The fine-tuning of the SAE-paper-cut element analysis model is an iterative process; in this paper, the number of iterations is set to 100, and the initial learning rate is 0.1. According to the change of the error

From ^{(i)}, ^{(i)} is the characteristic of the sample ^{(i)}.

Theoretically, the SAE-paper-cut element analysis model can fit any nonlinear model. In view of this advantage, the SAE-paper-cut element analysis model is used to fit the probability distribution between features and sample labels to realise feature identification and fault diagnosis. After obtaining the eigenvectors

In Eqs (20)–(22), π_{i}_{i}_{i}

For each type of sample, a SAE-paper-cut element analysis model is fitted, and

Since the parameter setting has a great influence on the performance of the SAE-paper-cut element analysis model, in order to obtain a reasonable parameter configuration, the particle swarm optimisation (PSO) algorithm is used to optimise the key parameters. The reasons for choosing PSO are as follows: the PSO algorithm has few preset parameters, the algorithm is simple and effective, can quickly converge to the optimal or local optimal solution and has a solid foundation in the research of the PSO algorithm. The following key parameters are selected for optimization: weight coefficient

In Eqs (24) and (25), _{1}, _{2} represents the acceleration factor, which is taken as 0.5 in this paper; _{1}, _{2} represents the random quantity subject to the uniform distribution of [0, 1]; up(·) represents the rounding up.

In the face of the current development status of China’s boating industry, the folk theme of folk paper-cut art is also unsatisfactory in the design of boat space. Folk paper cutting, as a folk art culture of thousands of years in China, has been used for reference and application, but it is not always seen. As a result, it is still more difficult to make Chinese boats with paper-cut elements as the theme go to the world, to classics, and out of taste. This requires designers to find some design principles, design methods and expressions in future design works to adapt to the market structure and marketing mode of the hotel industry. Therefore, on the basis of summarising the previous research, this paper uses the SAE algorithm model to deeply analyse the artistic expression of paper-cut elements in the design of boat space.

Paper-cut elements have the characteristics of innocence, simplicity and folklore. It has unique decorative properties in the decorative design of boats. The pattern elements are extracted from the papercut and applied to the boat decoration. At the same time, these elements are combined in a modern way so that the traditional paper-cut art and modular space can be better integrated. This paper takes curtains, tablecloths, wallpapers and lighting as comparative parameters and brings them into the SAE-paper-cut element model for comparative analysis. The analysis results are shown in Figure 1.

The comparative analysis results show that the decorative integration of paper-cut elements in wallpaper is 82%, which is higher than that of traditional materials (24%). The reason for this result is that the formal sense of the paper-cut element can form a virtual and solid effect when it is used in the boat wallpaper. The hollow part is virtual, the reserved part is solid and the combination of virtual and solid forms a certain sense of rhythm. As a dense form, the hollowing out will form a contrast with the surrounding clean surface environment. In terms of the appearance of decorative materials, the pure white periphery and the hollowed-out line decoration form a contrast between the virtual and the solid. The wallpaper at the entrance is used as a decorative material for the boat space. The dense part and the surrounding blank walls combine virtual and solid to highlight the characteristics of paper-cut elements. And the decorative fusion of paper-cut elements in lighting is far superior to that of traditional materials. The main reason is that with the improvement of people’s aesthetics, lamps are no longer just lighting appliances but also an indispensable decoration in modern home decoration. The elements to be considered in lighting design are more diversified, not only from safety but also from material, type, style, taste and energy saving. Designers began to look for innovative points from different arts, and paper-cut elements became the source of this innovation. The diversification of lighting materials provides strong material support for the application of paper-cut elements in lighting design. At the same time, more and more attention is paid to contemporary national culture. Through the decorative language of paper-cut elements, it can not only increase the aesthetics of lighting but also explore new ways of lighting design, which is conducive to the inheritance and development of paper-cut art. Therefore, the inheritance and development of national culture provides an opportunity for the application of paper-cut elements in lighting design.

Through the theoretical analysis and practical investigation of the folk papercut and the practical space of boats in the early stage, the inheritance, nationality and cultural value of paper-cut elements, as well as the development status of the boat space design industry, are combined with theory and practice, and paper-cut elements are applied to practice. The practical design of the boat mainly includes decks, cabins, consoles and guest rooms. The above design parameters are brought into the SAE-paper-cut element model for comparative analysis, and the analysis results are shown in Figure 2.

It can be seen from Figure 2 that the integration of paper-cut elements in the space design of cabins and guest rooms is as high as 97% and 94%, respectively, which is far better than the integration of traditional materials in the space design of cabins and guest rooms. This shows that the application of folk paper-cut elements to the space design of boats not only highlights the theme of boats but also enhances the cultural value of boats. In a novel way of expression, folk paper-cut art and boat space design are combined. The combined design improves the public’s cognitive ability to folk culture, determines the development direction of boat space design and enriches the language symbols of contemporary boat space design. Selecting traditional paper-cut themes and composition forms, extracting and summarising traditional paper-cut design elements and making them perfectly integrated with modern design, not only using paper-cut art in space composition, but also in other detail designs. It can truly inherit the tradition and accommodate all rivers, providing reference for the space design of the same type of boats.

According to the above analysis results and case studies, it can be seen that the integration of paper-cut elements in the space design of cabins and guest rooms is much better than that of traditional materials in the space design of cabins and guest rooms. This shows that the application of folk paper-cut elements to the space design of boats not only highlights the theme of boats but also enhances the cultural value of boats. Folk paper-cut art has been passed down in China for thousands of years, and the generation and development of boat space design has a long history. With the improvement and development of living standards, people have higher and higher requirements for the space environment of boats. The cultural heritage of thematic design is becoming more and more significant. The significance of in-depth research on the expression of paper-cut elements in the design of boat space mainly includes the following three points:

The boat space design based on paper-cut elements can make better use of the sea space and enhance the industrial added value of Chinese boats. To build a well-configured boat space and improve the versatility of the maritime space, the paper-cut element symbols can be used as much as possible to reflect the diversity of the paper-cut element space. At the same time, the development of boats based on paper-cut elements is conducive to increasing the value-added space of boats and the exploration of China’s shipbuilding industry. In the long run, it will bring more economic benefits to China and more employment opportunities for the local area.

The boat space design based on paper-cut elements breaks through the limitations of low utilisation and low adaptability of traditional boat space design. Combined with movable paper-cut element technology and space construction technology, the boat space can realise flexible movement and high adaptability to the environment, effectively expand the space for human activities and provide reference for the future development of boat space resources.

There are three forms of application of the air-through feature of paper-cut art in space. One is for space division, such as curtains, etc. In the living space and office space, curtains are used to divide the area, which divides the space; second, it is used for decoration, mainly reflected in wallpapers and tablecloths; third, starting from the characteristics of permeation, the combination of hollow and lighting produces a unique visual beauty, forming light and shadow effects in the space, creating a virtual space. In the space design, the papercut is presented in three dimensions. The air-permeable partition can not only divide the space but also play the effect of ‘separation without blocking’. At the same time, the light and shadow effect generated in the interior under the action of light enriches the space environment and makes the boat decoration innovative and sublimated.

Incorporating paper-cut elements into the design of boat space is a new form of paper-cut application and an innovation to the space design of boat space. In the use of paper-cut elements and features, the combination of element symbols and space is carried out according to the modular characteristics of the boat space. This modular design provides a reference paradigm for the general public. This boat space design is an optimisation of the boat space form, which is conducive to improving the quality of life of the occupants; the boat space design serves people and undertakes the mission of promoting and developing Chinese national culture; at the same time, the combination of the traditional folk paper-cut elements and modern boat space is the collision of tradition and modernity, pioneering and innovating on the basis of not forgetting the Chinese tradition. In response to this social hotspot, this paper deeply analyses the artistic expression of paper-cut elements in the design of boat space. The specific conclusions are as follows:

In order to meet people’s pursuit of traditional Chinese culture, it is of advanced reference significance and value to design a boat space with traditional Chinese culture. Incorporating the elements of paper-cut art into the interior space design of boats can meet people’s needs for modern mass production and meet people’s personalised pursuit of space. Creating this type of cultural space can promote the use of paper-cut elements in boat space design.

The decorative integration of paper-cut elements in wallpaper is 82%, which is higher than that of traditional materials (24%). The reason for this result is that the formal sense of the paper-cut element can form a virtual and solid effect when it is used in the boat wallpaper. The hollow part is virtual, the reserved part is solid and the combination of virtual and solid forms a certain sense of rhythm. And the decorative fusion of paper-cut elements in lighting is far superior to that of traditional materials. The main reason is that with the improvement of people’s aesthetics, the elements to be considered in lighting design are more diversified, not only from safety but also from material, type, style, taste and energy saving. The diversification of lighting materials provides strong material support for the application of paper-cut elements in lighting design.

The integration of paper-cut elements in the space design of cabins and guest rooms is as high as 97% and 94%, respectively, which is far better than the integration of traditional materials in the space design of cabins and guest rooms. This shows that the application of folk paper-cut elements to the space design of boats not only highlights the theme of boats but also enhances the cultural value of boats. In a novel way of expression, folk paper-cut art and boat space design are combined, improving the public’s cognitive ability to folk culture, determining the development direction of boat space design and enriching the language symbols of contemporary boat space design. Not only the paper-cut art is used in the space composition but also in other details design; the symbols of the paper-cut art can be used to provide reference for the same type of boat space design.

#### The proportion of space design cost in China’s shipbuilding cost

Boat type | The proportion of space design cost (%) |
---|---|

Yacht | 13 |

Passenger ship | 34 |

Engineering ship | 31 |

Fishing boat | 28 |

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Index Evaluation Based on Logistic Distribution Fitting Transition Probability Function Children's Educational Curriculum Evaluation Management System in Mathematical Equation Model Query Translation Optimization and Mathematical Modeling for English-Chinese Cross-Language Information Retrieval The Effect of Children’s Innovative Education Courses Based on Fractional Differential Equations Fractional Differential Equations in the Standard Construction Model of the Educational Application of the Internet of Things Optimization research on prefabricated concrete frame buildings based on the dynamic equation of eccentric structure and horizontal-torsional coupling Optimization in Mathematics Modeling and Processing of New Type Silicate Glass Ceramics Green building considering image processing technology combined with CFD numerical simulation Research on identifying psychological health problems of college students by logistic regression model based on data mining Abnormal Behavior of Fractional Differential Equations in Processing Computer Big Data Mathematical Modeling Thoughts and Methods Based on Fractional Differential Equations in Teaching Research on evaluation system of cross-border E-commerce platform based on the combined model A mathematical model of PCNN for image fusion with non-sampled contourlet transform Nonlinear Differential Equations in Computer-Aided Modeling of Big Data Technology The Uniqueness of Solutions of Fractional Differential Equations in University Mathematics Teaching Based on the Principle of Compression Mapping Financial customer classification by combined model Influence of displacement ventilation on the distribution of pollutant concentrations in livestock housing Recognition of Electrical Control System of Flexible Manipulator Based on Transfer Function Estimation Method Automatic Knowledge Integration Method of English Translation Corpus Based on Kmeans Algorithm Real Estate Economic Development Based on Logarithmic Growth Function Model Design of Tennis Mobile Teaching Assistant System Based on Ordinary Differential Equations Financial Crisis Early Warning Model of Listed Companies Based on Fisher Linear Discriminant Analysis High Simulation Reconstruction of Crowd Animation Based on Optical Flow Constraint Equation Construction of Intelligent Search Engine for Big Data Multimedia Resource Subjects Based on Partial Least Squares Structural Equation 3D Animation Simulation of Computer Fractal and Fractal Technology Combined with Diamond-Square Algorithm Analysis of the Teaching Quality of Physical Education Class by Using the Method of Gradient Difference The Summation of Series Based on the Laplace Transformation Method in Mathematics Teaching Optimal Solution of the Fractional Differential Equation to Solve the Bending Performance Test of Corroded Reinforced Concrete Beams under Prestressed Fatigue Load Animation VR scene mosaic modeling based on generalized Laplacian equation Radial Basis Function Neural Network in Vibration Control of Civil Engineering Structure Optimal Model Combination of Cross-border E-commerce Platform Operation Based on Fractional Differential Equations The influence of accounting computer information processing technology on enterprise internal control under panel data simultaneous equation Research on Stability of Time-delay Force Feedback Teleoperation System Based on Scattering Matrix BIM Building HVAC Energy Saving Technology Based on Fractional Differential Equation Construction of comprehensive evaluation index system of water-saving irrigation project integrating penman Montei the quation Human Resource Management Model of Large Companies Based on Mathematical Statistics Equations Data Forecasting of Air-Conditioning Load in Large Shopping Malls Based on Multiple Nonlinear Regression Analysis of technical statistical indexes of college tennis players under the win-lose regression function equation Automatic extraction and discrimination of vocal main melody based on quadratic wave equation Analysis of wireless English multimedia communication based on spatial state model equation Optimization of Linear Algebra Core Function Framework on Multicore Processors Application of hybrid kernel function in economic benefit analysis and evaluation of enterprises Research on classification of e-commerce customers based on BP neural network The Control Relationship Between the Enterprise's Electrical Equipment and Mechanical Equipment Based on Graph Theory Mathematical Modeling and Forecasting of Economic Variables Based on Linear Regression Statistics Nonlinear Differential Equations in Cross-border E-commerce Controlling Return Rate 3D Mathematical Modeling Technology in Visualized Aerobics Dance Rehearsal System Fractional Differential Equations in Electronic Information Models BIM Engineering Management Oriented to Curve Equation Model Leakage control of urban water supply network and mathematical analysis and location of leakage points based on machine learning Analysis of higher education management strategy based on entropy and dissipative structure theory Prediction of corporate financial distress based on digital signal processing and multiple regression analysis Mathematical Method to Construct the Linear Programming of Football Training Multimedia sensor image detection based on constrained underdetermined equation The Size of Children's Strollers of Different Ages Based on Ergonomic Mathematics Design Application of Numerical Computation of Partial Differential Equations in Interactive Design of Virtual Reality Media Stiffness Calculation of Gear Hydraulic System Based on the Modeling of Nonlinear Dynamics Differential Equations in the Progressive Method Knowledge Analysis of Charged Particle Motion in Uniform Electromagnetic Field Based on Maxwell Equation Relationship Between Enterprise Talent Management and Performance Based on the Structural Equation Model Method Term structure of economic management rate based on parameter analysis of estimation model of ordinary differential equation Influence analysis of piano music immersion virtual reality cooperation based on mapping equation Chinese painting and calligraphy image recognition technology based on pseudo linear directional diffusion equation Label big data compression in Internet of things based on piecewise linear regression Animation character recognition and character intelligence analysis based on semantic ontology and Poisson equation Design of language assisted learning model and online learning system under the background of artificial intelligence Study on the influence of adolescent smoking on physical training vital capacity in eastern coastal areas Application of machine learning in stock selection Comparative analysis of CR of ideological and political education in different regions based on improved fuzzy clustering Action of Aut( G ) on the set of maximal subgroups ofp -groupsResearch on loyalty prediction of e-commerce customer based on data mining Algebraic Equations in Educational Model of College Physical Education Course Education Professional English Translation Corpus Under the Binomial Theorem Coefficient Geometric Tolerance Control Method for Precision Machinery Based on Image Modeling and Novel Saturation Function Retrieval and Characteristic Analysis of Multimedia Tester Based on Bragg Equation Semiparametric Spatial Econometric Analysis of Household Consumption Based on Ordinary Linear Regression Model Video adaptive watermark embedding and detection algorithm based on phase function equation English Learning Motivation of College Students Based on probability Distribution Scientific Model of Vocational Education Teaching Method in Differential Nonlinearity Research on mobile Awareness service and data privacy Protection based on Linear Equations computing protocol Vocal Music Teaching Model Based on Finite Element Differential Mathematical Equations Studying a matching method combining distance proximity and buffer constraints The trend and influence of media information Propagation based on nonlinear Differential equation Research on the construction of early warning model of customer churn on e-commerce platform Evaluation and prediction of regional human capital based on optimised BP neural network Study on inefficient land use determination method for cities and towns from a city examination perspective A study of local smoothness-informed convolutional neural network models for image inpainting Mathematical Calculus Modeling in Improving the Teaching Performance of Shot Put Application of Nonlinear Differential Equation in Electric Automation Control System Higher Mathematics Teaching Curriculum Model Based on Lagrangian Mathematical Model Computational Algorithm to Solve Two–Body Problem Using Power Series in Geocentric System Decisions of competing supply chain with altruistic retailer under risk aversion Optimization of Color Matching Technology in Cultural Industry by Fractional Differential Equations The Marketing of Cross-border E-commerce Enterprises in Foreign Trade Based on the Statistics of Mathematical Probability Theory Application of Linear Partial Differential Equation Theory in Guiding Football Scientific Training Nonlinear Channel Estimation for Internet of Vehicles Some Necessary Conditions for Feedback Functions of de Bruijn Sequences The Evolution Model of Regional Tourism Economic Development Difference Based on Spatial Variation Function System Model of Shipping Enterprise Safety Culture Based on Dynamic Calculation Matrix Model An empirical research on economic growth from industrial structure optimisation in the Three Gorges Reservoir area The Inner Relationship between Students' Psychological Factors and Physical Exercise Based on Structural Equation Model (SEM) Analysis and Research on Influencing Factors of Ideological and Political Education Teaching Effectiveness Based on Linear Equation Study of agricultural finance policy information extraction based on ELECTRA-BiLSTM-CRF Fractional Differential Equations in Sports Training in Universities Examination and Countermeasures of Network Education in Colleges and Universities Based on Ordinary Differential Equation Model Innovative research of vertical video creation under the background of mobile communication Higher Education Agglomeration Promoting Innovation and Entrepreneurship Based on Spatial Dubin Model Chinese-English Contrastive Translation System Based on Lagrangian Search Mathematical Algorithm Model Genetic algorithm-based congestion control optimisation for mobile data network