# Product Shape Design Scheme Evaluation Method Based on Spatial Data Mining

Authors: Qian Wei
Journal: Mathematical Problems in Engineering
 (2022)

---

## Abstract

The stage of product modeling design implies a lot of complex tacit knowledge, which is the embodiment of the design concept centered on product modeling design and is also the hot spot and difficulty of modern design theory and method research. Aiming at the evaluation and decision of product modeling design scheme, a decision-making method of approaching ideal solution ranking based on grey relational analysis was proposed, which realized the convergence of tacit knowledge. The empty association rule is an important knowledge content of spatial data mining. A fuzzy genetic algorithm can solve the characteristics of random and nonlinear problems and solve the data mining problems of spatial association rules. The fuzzy genetic algorithm of discrete crossover probability and mutation probability is applied to data mining of spatial association rules in a spatial database, the coding method of the fuzzy genetic algorithm and the construction of fitness function are discussed, and the process of mining spatial association rules is given. The results show that the method of mining s association rules with the fuzzy genetic algorithm is feasible and has higher mining efficiency. This paper discusses the construction method of designing a decision support database based on linear regression and neural network and then proposes a decision method combining TOPSIS and grey relational analysis, which comprehensively considers the position and shape of the scheme data curve.


---

## Body

## 1. Introduction

In the network economy, the demand for product modeling design becomes more and more diversified and personalized, and it is more and more difficult for designers and enterprises to accurately grasp the demand, and product modeling design is facing more and more pressure. According to the research, in the process of product modeling design, only one part needs to be completely redesigned, and the other part adopts its own design or improves the existing design. In addition, with the continuous accumulation of product design, a lot of design knowledge and design experience are accumulated; on the one hand, a lot of possible solutions for new design problems are provided; on the other hand, these knowledge and experience are explicit and implicit. Explicit knowledge is easy to organize and use, while tacit knowledge usually has the characteristics of implicit and fuzzy. Therefore, with the increase in this kind of knowledge, it becomes more difficult to solve design problems.The rapid development of modern technology and data acquisition technology has greatly improved the ability of data collection, storage, and processing, and various data resources are increasingly rich. In order to obtain knowledge more automatically and completely, data mining and knowledge discovery, a new subject that is integrated and promoted by multiple subjects, emerged at the end of the 20th century. At present, there are many algorithms applied to data mining. Due to the characteristics of the fuzzy genetic algorithm, it can well solve the problems of chaos, randomness, and nonlinearity, providing a new mathematical model for complex problems that cannot be solved, or are difficult to be solved by other technologies [1, 2]. FGA is applied to the mining of spatial association rules, hoping to put forward new ideas on the extraction method of spatial association rules.Acquisition and Representation of Tacit Knowledge for Product Modeling Design. Three sources of tacit knowledge are studied to provide a basis for tacit knowledge acquisition. The method of acquiring tacit knowledge based on emotion analysis is proposed, and its process is introduced in detail. The tacit knowledge acquisition method based on the cognitive experiment is proposed, and the conceptual design of the machine tool is taken as an example. The method of recessive knowledge analysis is studied, and a method of recessive knowledge reduction based on FA-CA is proposed, which is verified by an example. According to people’s actual cognitive model, a tacit knowledge mapping model based on multidimensional variables was proposed based on the one-dimensional variables kansei engineering model, and the validity and superiority of the model were evaluated through verification experiments and comparative experiments. The tacit knowledge representation method based on graphic semantics and extension relation is proposed.


## 2. Related Work

In view of various problems of genetic algorithm, experts and scholars at home and abroad have proposed various improved algorithms, such as static genetic algorithm, sorting genetic algorithm, multipoint crossover genetic algorithm, mutation rate genetic algorithm, and variable parameter genetic algorithm [3, 4]. Most of these improved algorithms are put forward in view of the disadvantage of premature genetic algorithm, which still belongs to the category of accurate solution. However, when faced with the proposed fuzzy problem, most of the previously improved genetic algorithms are difficult to work [5]. As a new research hotspot, fuzzy genetic algorithm has not been systematically studied and applied. At present, although there are some studies on fuzzy genetic algorithms, such studies do not take fuzzy problems as the starting point, but only introduce fuzzy control rules into genetic operators (crossover, mutation), and try to make the parameters of genetic operation change adaptively in the iterative process through rule control [6].It is the accumulation of information obtained in the whole product life cycle. It includes the generation of design knowledge, acquisition of design knowledge, integration of design knowledge, sharing of design knowledge, reuse of design knowledge, renewal of design knowledge, and selection and release of design knowledge [7]. In the whole process of product design, there will be many types of design knowledge, with multisource and multiconstruction, and the main categories include the knowledge of design itself, design experience, design methods, and other product information conducive to later product design. At present, many researchers have studied the classification of product design knowledge based on many aspects, and the classification of design knowledge is also different. Basic concepts, standards, and specifications as well as application tools of product design are studied in detail [8]. The classification of product design knowledge is studied according to background and foreground. The former refers to what the product is (what), and the latter refers to the basis of product design (How) [9]. Design knowledge is classified from the narrow definition and source of design information. Product design knowledge can be divided into explicit knowledge that can be stored in a certain form of coding and tacit knowledge that cannot be read directly in the human brain according to whether it can be formally coded or not [10]. From the perspective of knowledge reuse and combination with the characteristics of the product design process, the classification of product design process knowledge is studied, including process knowledge, substantive knowledge, relational knowledge, and factual knowledge. On the basis of knowledge sources, combined with design-related personnel and process, the classification of design knowledge is studied from the characteristics of knowledge descriptiveness and judgment structure [11]. For the method of neural network modeling, the acquisition of design knowledge, such as cognitive process, decision formation, and supporting information, was studied [12]. A manufacturing design knowledge acquisition method based on human thinking was proposed, and the effectiveness of the method was verified by taking a sprayer as an example [13]. A method of product configuration design is proposed, which uses knowledge modularization in the whole concept design. The process and method of machine-structure symmetry knowledge discovery based on example were proposed to acquire the knowledge of machine-structure symmetry design [14]. From the perspective of process innovation, the technology system of knowledge acquisition is constructed by using computer-aided technology. By using the physical model, the framework of design knowledge and the expression of QOC were established, and the accumulated knowledge was extracted [15]. Through the acquisition and satisfaction evaluation of multidisciplinary design knowledge, a platform supporting multidisciplinary product design knowledge was established, and the integration ability of multidisciplinary design knowledge was improved.Fuzzy genetic algorithm (FGA) mining spatial association design knowledge reuse research refers to the reuse methods and technologies of explicit and implicit knowledge such as product design process knowledge, object knowledge, and design principle through knowledge management methods and technologies. Representation, acquisition, organization, and retrieval of design knowledge are the main contents of knowledge reuse research. Firstly, the classification, representation, and storage of design knowledge are studied, and then, the reuse of design knowledge is realized according to the new design constraints [16]. The design knowledge reuse technology for integrated product rapid development is studied, and an integrated product development system scheme based on design knowledge reuse is proposed on the basis of in-depth research on key technologies such as design knowledge representation, management, and reuse [17]. Different knowledge units are obtained by object-oriented technology and then described by corresponding knowledge representation methods. A multilevel and multitype knowledge representation model and a conceptual model of product design knowledge reuse are proposed [18]. The process knowledge acquisition method in computer-aided process design (CAPP) is studied, and the process model of knowledge discovery is established [19, 20]. At the same time, the key technologies of design knowledge reuse based on CBR and WEB sharing technology are studied. In recent years, because many scholars devote themselves to the research of fuzzy control, this field has developed by leaps and bounds. Especially with the development of other control subjects, fuzzy control and other control methods, such as neural network, genetic algorithm, and chaos theory of the fusion of new subjects, are showing its great application potential. From the structure and function of the network, it is a large-scale parallel nonlinear dynamic system. Strictly speaking, neural network should be called artificial neural network. It has the advantages of distributed information storage, parallel processing, and self-learning ability. Therefore, it has a broad application prospect in information processing, pattern recognition, intelligent control, and other fields. Neural network-based control is called neural network control [22–25]. Intelligent simulation based on a neural network is used for control and is an important form of intelligent control, which has achieved rapid development in recent years. A system has the ability to learn from its surroundings, process information automatically to reduce its uncertainty, plan, generate, and perform control functions safely and reliably.


## 3. Spatial Association Rule Algorithm Based on Fuzzy Genetic Algorithm

### 3.1. Fuzzy Genetic Algorithm Mining Spatial Association Rules

The convergence speed and quality are affected by crossover probability and mutation probability. The purpose of the FGA is to determine values dynamically. A fuzzy control method called “query table” is used to dynamically determine the value and realize the fuzzy control mechanism. This mechanism converts the fuzzy control rules into a query table and stores the numerical correspondence between input and output discretely. In the actual application process, the required output quantity can be directly determined by looking up the table according to the specific situation of the input, instead of fuzzy, fuzzy reasoning, and then clear calculation. This method greatly reduces the time of the fuzzy control process and has the characteristics of simple structure and convenient operation.The first step of establishing the model is to initialize the fuzzy inference system model and set the membership function of each variable. In this study, there are two fuzzy variables: the amount of input and the rate of change of input. After dimensionless treatment, their value theory domain is in the interval of [0 1]. As for their fuzzy division, they are divided into five fuzzy subsets, which are “high investment,” “high investment,” “medium investment,” “low investment,” “low investment,” and “large change rate,” “large change rate,” “medium change rate,” “small change rate,” and “small change rate.” At present, the commonly used membership functions are linear (triangle or trapezoid) and various nonlinear membership functions. Considering the smoothness of the membership function, the Gaussian function is adopted here as the membership function:(1)Ty,β,t=expy−t2β2.Figure1 shows the model structure of the mining method based on the fuzzy genetic algorithm in the proposed association rules.Figure 1
Product design structure diagram of fuzzy genetic algorithm mining spatial association rules.In Figure1, the data to be mined in the modeling design of network products are input into the association rule mining method model based on the fuzzy genetic algorithm. The processing chip in the model begins to calculate the support of the data to be mined using association rules, and the data list displays this calculation as a numerical code.The support given in the fuzzy genetic algorithm is used to calculate the fitness of data 1 to be mined in network product modeling design. The fitness calculation formula can be expressed as(2)Fy=cy+αTy,t,TX=CICmax+Tx,tTmax.First of all, obtain the product modeling design requirements, and after determining the design objectives and product modeling design requirements, the designer integrates all aspects of knowledge and their own professional knowledge, the design concept into the product conceptual design scheme, including product form, color, texture, and symbol, to provide a design for product modeling design. Product modeling design is based on their own needs combined with the cognitive information of their own products and the understanding and cognition of new products, forming the cognition of products. When the design provided by the designer is consistent with the understanding of the product by the product modeling design, it indicates that the design scheme is an appropriate design. When the two are inconsistent, the design scheme does not meet the requirements of the product modeling design and cannot satisfy the product modeling design, and it needs to be revised or redesigned. In the process of knowledge transfer, the designer’s design process is actually a process of information coding and problem-solving; that is, the designer is searching for the conceptual design scheme to achieve the satisfaction of product modeling design. As the receiver and participant of the knowledge process, product modeling design is actually a process of information decoding and problem evaluation. During knowledge transfer process, product modeling design is the medium of communication between designers.


### 3.2. Mining Spatial Association Rules

According to the characteristics of the proposed FGA, FGA parameters are integrated mining spatial association rules, and the fuzzy genetic algorithm is started. The flow chart is shown in Figure2.Figure 2
Flowchart of mining spatial association rules with fuzzy genetic algorithm.Fuzzy selection of population size: for different objects, we usually cannot know in advance what the appropriate population size is, and therefore, a large number of experiments are often required. Not only does this require considerable experience but it is also time-consuming, which makes it difficult for practical engineering applications. In order to facilitate application, a fuzzy concept is used to select the size of the population in FGA, in order to select the population size with the power of calculation and achieve the purpose of selecting the population reasonably.Fuzzy dynamic regulation of crossover rate and mutation rate: according to the building block hypothesis, individuals with the high fit degree can be obtained by constantly extracting and matching patterns (gene fragments) with high fit degree and short length. The convergence rate of the genetic algorithm is related to the crossover rate and mutation rate. If the selection is not appropriate, the algorithm will not be able to find the global optimal solution. However, the traditional method of selecting fixed crossover rate and mutation rate has been proved to be unsatisfactory in many cases. Therefore, in FGA, we dynamically change the crossover rate and mutation rate of the genetic algorithm according to the population size of the fuzzy selection. The specific methods are as follows: when the population size is smaller, a smaller mutation rate is adopted, but a larger crossover rate is adopted; when the population size is small, the larger variation rate is adopted, while the smaller crossover rate is adopted, so as to realize the dynamic control of genetic algorithm parameters. The algorithm structure of fuzzy_GA (genetic algorithm) can be expressed as shown in Table1.Table 1
Algorithm structure of fuzzy_GA.
Fuzzy_GA(){year = 0Fuzzy selection benefit, group size;Objective function and constraint conditions of each individual in fuzzy uncentering group:Evaluation of individuals in the population;Fuzzy;While does not satisfy the termination condition do{year++;Blur;According to the adaptive function values generated by the fuzzy objective function and constraint conditions of each individual, the offspring were selected to be put into the mating pool and marked individually with the help of multi-target fuzzy optimization technology.Fuzzy adjustment of bamboo crossover rate and variation rate according to population size;Give rise to new progeny;Evaluation of individual offspring;Fuzzy;The population size was changed according to the evaluation results and chronological ambiguity.}


## 3.1. Fuzzy Genetic Algorithm Mining Spatial Association Rules

The convergence speed and quality are affected by crossover probability and mutation probability. The purpose of the FGA is to determine values dynamically. A fuzzy control method called “query table” is used to dynamically determine the value and realize the fuzzy control mechanism. This mechanism converts the fuzzy control rules into a query table and stores the numerical correspondence between input and output discretely. In the actual application process, the required output quantity can be directly determined by looking up the table according to the specific situation of the input, instead of fuzzy, fuzzy reasoning, and then clear calculation. This method greatly reduces the time of the fuzzy control process and has the characteristics of simple structure and convenient operation.The first step of establishing the model is to initialize the fuzzy inference system model and set the membership function of each variable. In this study, there are two fuzzy variables: the amount of input and the rate of change of input. After dimensionless treatment, their value theory domain is in the interval of [0 1]. As for their fuzzy division, they are divided into five fuzzy subsets, which are “high investment,” “high investment,” “medium investment,” “low investment,” “low investment,” and “large change rate,” “large change rate,” “medium change rate,” “small change rate,” and “small change rate.” At present, the commonly used membership functions are linear (triangle or trapezoid) and various nonlinear membership functions. Considering the smoothness of the membership function, the Gaussian function is adopted here as the membership function:(1)Ty,β,t=expy−t2β2.Figure1 shows the model structure of the mining method based on the fuzzy genetic algorithm in the proposed association rules.Figure 1
Product design structure diagram of fuzzy genetic algorithm mining spatial association rules.In Figure1, the data to be mined in the modeling design of network products are input into the association rule mining method model based on the fuzzy genetic algorithm. The processing chip in the model begins to calculate the support of the data to be mined using association rules, and the data list displays this calculation as a numerical code.The support given in the fuzzy genetic algorithm is used to calculate the fitness of data 1 to be mined in network product modeling design. The fitness calculation formula can be expressed as(2)Fy=cy+αTy,t,TX=CICmax+Tx,tTmax.First of all, obtain the product modeling design requirements, and after determining the design objectives and product modeling design requirements, the designer integrates all aspects of knowledge and their own professional knowledge, the design concept into the product conceptual design scheme, including product form, color, texture, and symbol, to provide a design for product modeling design. Product modeling design is based on their own needs combined with the cognitive information of their own products and the understanding and cognition of new products, forming the cognition of products. When the design provided by the designer is consistent with the understanding of the product by the product modeling design, it indicates that the design scheme is an appropriate design. When the two are inconsistent, the design scheme does not meet the requirements of the product modeling design and cannot satisfy the product modeling design, and it needs to be revised or redesigned. In the process of knowledge transfer, the designer’s design process is actually a process of information coding and problem-solving; that is, the designer is searching for the conceptual design scheme to achieve the satisfaction of product modeling design. As the receiver and participant of the knowledge process, product modeling design is actually a process of information decoding and problem evaluation. During knowledge transfer process, product modeling design is the medium of communication between designers.


## 3.2. Mining Spatial Association Rules

According to the characteristics of the proposed FGA, FGA parameters are integrated mining spatial association rules, and the fuzzy genetic algorithm is started. The flow chart is shown in Figure2.Figure 2
Flowchart of mining spatial association rules with fuzzy genetic algorithm.Fuzzy selection of population size: for different objects, we usually cannot know in advance what the appropriate population size is, and therefore, a large number of experiments are often required. Not only does this require considerable experience but it is also time-consuming, which makes it difficult for practical engineering applications. In order to facilitate application, a fuzzy concept is used to select the size of the population in FGA, in order to select the population size with the power of calculation and achieve the purpose of selecting the population reasonably.Fuzzy dynamic regulation of crossover rate and mutation rate: according to the building block hypothesis, individuals with the high fit degree can be obtained by constantly extracting and matching patterns (gene fragments) with high fit degree and short length. The convergence rate of the genetic algorithm is related to the crossover rate and mutation rate. If the selection is not appropriate, the algorithm will not be able to find the global optimal solution. However, the traditional method of selecting fixed crossover rate and mutation rate has been proved to be unsatisfactory in many cases. Therefore, in FGA, we dynamically change the crossover rate and mutation rate of the genetic algorithm according to the population size of the fuzzy selection. The specific methods are as follows: when the population size is smaller, a smaller mutation rate is adopted, but a larger crossover rate is adopted; when the population size is small, the larger variation rate is adopted, while the smaller crossover rate is adopted, so as to realize the dynamic control of genetic algorithm parameters. The algorithm structure of fuzzy_GA (genetic algorithm) can be expressed as shown in Table1.Table 1
Algorithm structure of fuzzy_GA.
Fuzzy_GA(){year = 0Fuzzy selection benefit, group size;Objective function and constraint conditions of each individual in fuzzy uncentering group:Evaluation of individuals in the population;Fuzzy;While does not satisfy the termination condition do{year++;Blur;According to the adaptive function values generated by the fuzzy objective function and constraint conditions of each individual, the offspring were selected to be put into the mating pool and marked individually with the help of multi-target fuzzy optimization technology.Fuzzy adjustment of bamboo crossover rate and variation rate according to population size;Give rise to new progeny;Evaluation of individual offspring;Fuzzy;The population size was changed according to the evaluation results and chronological ambiguity.}


## 4. Acquisition and Representation of Tacit Knowledge of Product Modeling Design Based on Fuzzy Genetic Algorithm

Product modeling value refers to the value contained in product design, including product modeling value, aesthetic value, innovation value, and functional value. For product modeling design, the value of product modeling design is the basic value of product modeling. Product aesthetic value is a value standard reflected in the product form characteristics, including product form, material, color, texture, style, and other factors. Innovation value refers to the originality, uniqueness, and difference of product in function, form and use mode. Product functional value refers to the value of product structure, constraints, and functions. In some design cases, the structure of the product is largely determined by the function of the product and thus determines the overall shape of the product. Each element of product modeling value is shown in Table2.Table 2
Product modeling value connotation.
ElementsContentTargetProduct modeling designProduct modeling design behavior, interaction mode, use environmentMeet the basic needs of product modeling designAestheticProduct form, material, color, texture, styleSatisfy the emotional needs of product modeling design preference and sensibilityInnovationUniqueness and difference of form and use modeDesign new concepts and new productsFunctionProduct structure, constraints, functions, production technologyProduct implementabilityVector space model (VSM) is widely used, simple, and effective. In this method, the similarity between vectors is measured by cosine distance, as shown in Figure3.Figure 3
Schematic diagram of VSM.The more attention product styling design pays to product features, and the more probability and frequency it appears. Therefore, the frequent pattern mining method of the association rule algorithm is first used to extract product features, and feature objects omitted by high-frequency filtering are selected to improve the recall rate. Then, the initial feature set is screened and filtered to improve the accuracy. The detailed process of commodity feature mining is shown in Figure4.Figure 4
Process of commodity feature mining.Normalized Google distance (NGD) is used to calculate semantic similarity to filter the third problem. Any two words Google distance NGD can be expressed as(3)NGD=maxlogft,fxminlogft,fx.According to the feature candidate set, all the extracted features are composed of a product candidate feature set. In order to extract more accurate product features from reviews, a calculation method based on the mutual information value of features and products was proposed. The specific formula is as follows:(4)PMI=hitproduct,featurehitproduct,feature.


## 5. Example Verification

The first collection of 1000 products, through the initial assessment, to delete the modeling of similar and inappropriate samples left invited 5 with more than 5 years of design experience of professional designers using the KJ method for the experiment, finally selected 40 design cypress products, and then divided them into 6 groups. In order to determine the most appropriate dimension, MDS was used to set the dimension as 2–10, and the stress coefficients corresponding to the lie were obtained, respectively. The results showed that when the dimension = 6, the stress coefficient = 0. 03572 was the minimum, so the Ward clustering tree of 40 NC machine tool products whose dimension was set as 60 and MDS results were shown in Figure5. In order to select representative samples in each cluster, k-means clustering was carried out, and the distance between each sample and its cluster center was calculated and sorted, as shown in Table 3.Figure 5
Cluster tree of 1000 products.Table 3
Distance of sample to geometric center of each cluster.
SampleDistanceClusteringSampleDistance260.9434260.942371.135241.031281.153311.108321.5325321.152351.57160.845412.04270.992The simulation-optimization results of spatial association rules of data mining based on a fuzzy genetic algorithm are shown in Figure6. It can be seen from the genetic algorithm optimization results that by optimizing the total air volume, the mining crossover rate is smaller, and the inverse balance method is used to calculate the efficiency, so as to achieve the highest efficiency and to optimize the product modeling design.Figure 6
Optimization of spatial association rule simulation of data mining based on paste genetic algorithm.In the experiment, processing chips with the same specification and mode are used to compare the noise characteristics and noise data clustering generated by the three methods of mining large nature, as well as the comparison of mining accuracy and output curves of the three methods (unit: 1), as shown in Figure7. Meanwhile, the timer is used to time the mining work of the three methods, which is recorded in Table 4.Figure 7
Comparison curves of mining accuracy of the three methods.Table 4
Statistical table of mining time for the three methods.
Three waysMining  timeSpatial association rule mining with fuzzy genetic algorithm37.8Based on structured research43.4Based on feature weighting73.2RKE and LSA-KE methods were used to match all 85 product modeling designs, and the actual selection ranking of product modeling designs was counted. The abscissa is the ranking, and the ordinate is the percentage of the ranking people. The results in Figure8 show that in the LSA-KE method, 71.7% of actual product modeling designs ranked 1–5 in matching, while in the RKE method, only 50.6% of product modeling designs ranked 1–5. Therefore, the lSA-KE method has higher matching accuracy than the RKE method.Figure 8
Percentage ranking of styling design results for all products.


## 6. Conclusion

Mining spatial association rules from the spatial database is an effective method to transform data into knowledge. In this paper, the mining model of the fuzzy genetic algorithm is constructed, and the association rules are combined with the algorithm. By comparing the mining performance of the improved method in this paper, the mining method based on structured research of association rules, and the mining method based on feature weighting of association rules, the experiment proves that the improved method in this paper has a higher mining performance. The application of tacit knowledge in product conceptual design mainly includes auxiliary modeling design, functional design, and structural design, which will be the focus of future research.



---

*Source: 3231357-2022-07-20.xml*