1. Introduction
Product design is a continuously innovative process [
1]. As the physical embodiment of the product, the product form carries both material and spiritual functions, serving as a crucial medium of communication between users and designers [
2]. Over time, the advancement of Internet technology [
3], the rapid development of production technology, and various other factors [
4] have led to shifts in users’ perceptions [
5], designers’ perceptions [
6], and the market environment. To maintain product competitiveness, companies must innovate, which leads to evolving product forms. However, it is not feasible for companies to produce only conceptual design solutions due to factors such as branding, production costs, and mass production cycles. Traditionally, designers determine the direction of product form evolution based on their own experience. Yet, shifts in designers, decision-makers, and other stakeholders introduce uncertainty in the design outcome, exposing companies’ products to various risks. Therefore, balancing the interplay between product innovation and inheritance, as well as between previous and new-generation product forms, is a key issue. The study of product evolution has become a central focus in product design. In recent years, many researchers have focused their research primarily on genealogical analysis, evolutionary computation, and design evolution mechanisms.
In terms of genealogical analysis, for example, the research in [
7] collated and summarized Audi’s 100-year design history and the development process of the brand using the evolution of design styles and styling features as data to construct a spectrum of relationships between styling features in different periods. The work in [
8] identified the product generation and genealogy phenomena concepts by collecting historical product data, conducted a comparative analysis of the design of genealogical products, and discussed their different cognitive recognition models. The work in [
9] used shape grammar to study the pan-family product design process and built a product form derivation system to generate a new generation of product derivation solutions. The work in [
10] systematically evaluated the concept of an open product architecture and analyzed its evolution and intrinsic motivation in terms of the architecture development mode, architecture development strategy, and architecture organization and management. The research in [
11] analyzed the analogous relationship between biological evolution and product innovation. They explained how environmental factor changes drive product innovation and variation from an evolutionary perspective. This will help to support product developers in creating innovative products.
In terms of evolutionary computation, a method based on historical data was proposed in [
12] for predicting the evolutionary trends of automobile form features by quantifying the features and constructing an evolutionary data series of the form features. A dual-objective integer programming model based on the aspects of user satisfaction and product series evolution was established in [
13] to adapt to the complex product development module configuration scheme. The research in [
14] proposed the application of differential evolutionary algorithms to the study of the complex constraint control of robots with the objective of developing a Sun follower and a four-degree Cartesian robot that meet the requisite performance standards. The research in [
15] modelled and analyzed the evolution of product competition from the perspective of the product market and proposed a dynamic method based on networks to help designers understand the change relationships in the product’s competitive stage to support product design decisions. The work in [
16] proposed an evolutionary design system for product forms based on back propagation neural networks and nondominated ranking genetic algorithms. A nonlinear complex relationship between Kansei images and the form elements was obtained and fitted to consumers’ Kansei images, and the form features were obtained to satisfy complex consumer needs. The logistic regression models and relative entropy theory were adopted in [
17] to construct a balanced evaluation model by analyzing the cognitive differences between users, designers and engineers, and established a Kansei image style-oriented product form design evolution method based on genetic algorithms. The research in [
18] explored the evolutionary characteristics of user knowledge in the product evolution process from the perspective of the users. This information can be used, to a certain extent, to map the product evolutionary process. Additionally, they conducted a case study on modeling the iPhone’s evolutionary process, visualized the product evolutionary process and inferred the product evolutionary mode and mechanisms. The research in [
19] quantified product forms from the esthetic preference perspective and proposed a practical design method based on a graph neural network approach that incorporated fuzzy inference theory.
In the study of design evolution mechanisms, a framework for analyzing the evolution process of products using sales big data was proposed in [
20] to explore the evolution mechanism of products. The work in [
21] observed the evolutionary trajectory of product design behavior from a philosophical point of view and explored the interrelationships of the internal factors by analyzing the design behavior, before and after product iteration during an industry paradigm shift, to provide product iteration guidance. The research in [
22] constructed a multi-objective-driven tractor product family-form gene evolutionary design model by extracting and analyzing the coefficients of variation of tractor product family shape genes and the three-objective-driven product family-form gene evolutionary design process of brand identity; the user imagery and social context were also analyzed. A decision model based on Stackelberg game theory was proposed in [
23] to simulate the interaction between product family configuration design and suppliers for the planning of next-generation product families. To eliminate the contradiction between users’ psychological expectations and product engineering needs, the work in [
24] transformed the contradiction of the two factors into a general theory of inventive problem solving (TRIZ) problem, thus simplifying the product form evolution process. The research in [
25] analyzed the evolution of knowledge engineering in design research. They examined the mechanisms of knowledge evolution and knowledge reuse characteristics in design through bibliometrics, providing a theoretical foundation for product design evolution.
Analysis shows that when considering the design evolution of a product from a generational perspective, there are a variety of data on previous product forms that can guide the development of new generations of products [
26]. Learning from the valuable experiences of our predecessors can guide future design developments, although predicting the future with great accuracy is not possible. Early research on the evolution of product forms focused on collecting historical data on the evolutionary process and exploring the product form trends in an inductive and deductive qualitative way. The study of the evolution of product forms has changed from an initial qualitative study of the product development process to an in-depth exploration of the design evolution process. For a particular series of product developments, the initial designers and decision-makers define the design philosophy, and the subsequent evolutionary processes all inherit this design philosophy while incorporating new technical, functional, and cultural elements to produce new product forms [
27]. This process has a high similarity to the logic of evolutionary algorithms. However, importantly, the designers and decision-makers may change during the product evolution process. Existing studies have not adequately addressed the issue of designer and decision-maker change, specifically regarding the effective transmission and innovation of design concepts. Consequently, the simulation of the product evolution process can be achieved by optimizing the evolutionary algorithm, which in turn addresses the aforementioned issues.
This study proposes an evolutionary design method of product form based on the gray Markov model and evolutionary algorithms. We use quadratic curvature entropy, gray Markov models, and evolutionary algorithms to describe the evolution of product forms in the time dimension based on available data on product forms over time. This method focuses on simulating designers’ understanding of previous generations’ design concepts to achieve the stable inheritance of these concepts during product iteration. It predicts the evolutionary trends of new-generation product forms and provides design inspiration or design constraints for designers involved in the development of new products. This study offers new research ideas for the intelligent design of product forms.
The research framework of this paper is as follows.
Section 2 describes, in detail, the evolutionary design method of product forms based on the gray Markov model and evolutionary algorithms. In
Section 3, this study describes the application process of the method using the side outer contour of the Audi A4 automobile as an example. A discussion and analysis of the results are presented in
Section 4. Finally, this study concludes with a summary of the findings.
4. Discussion
In the actual design process, designers usually produce innovative designs of new forms based on their own experience and user needs after understanding the design concepts of previous generations of product forms. This process essentially involves the inheritance and innovation of product design concepts [
47]. The product form contains the designer’s design ideas. In the long-term iterative development of products, different designers and decision-makers lead to different product form evolution directions. Therefore, the product form evolution process is analyzed to reveal the product form evolution design law by quantifying and fitting historical product forms. The impact of these results on future product form design is reflected in two aspects. On the one hand, predictive modeling based on historical data can provide manufacturers with valuable insights into the stable inheritance of design concepts throughout a product’s evolution, thus aiding design decisions; on the other hand, it can also reduce the impact of changes and cognitive differences in design subjects, mainly that of the designers and decision-makers, on the evolution of product forms.
To demonstrate the validity of the model, a design style assessment survey was conducted through the Kansei engineering method [
48]. Firstly, the five design options in
Figure 8 are product forms that can inspire designers’ creative thinking. We let the designers randomly select a design scheme and extract the side profile curve (the third scheme in
Figure 8 is selected here), which together with the eight generations of form curve samples in
Figure 3 constitute nine samples of the imagery style survey and are numbered according to the order of the generations. Then, we can see from the websites of automobile companies that the style of A4 series cars is “sporty”. Therefore, we designed a five-point Likert scale questionnaire based on the sample pictures (curves) and the “sporty” imagery style. The order in which each sample picture appeared in the questionnaire was randomized to avoid the influence of thinking inertia on the evaluators. Ten designers and ten automobile consumers were invited to evaluate each of the nine samples. Finally, the mean values of 20 evaluations were counted and a design style evaluation graph was drawn (see
Figure 9).
As shown in
Figure 9, the value of the “sporty” style tends to increase with each iteration of the product form, and the value of a new generation of the product form style is significantly greater than that of the previous generations of product form style evaluations. The survey results reveal that the possibility of abrupt changes in design concepts and design styles due to changes in designers and decision-makers can be reduced by fitting historical sample data and predicting future trends.
However, it is important to discuss the limitations of the methodology proposed in this study. This study involved five steps, which include the acquisition of study samples, the deconstruction of form features, the quantization of quadratic curvature entropy, prediction by GM(1, 1) fitting, and the generation of product forms by an evolutionary algorithm. There are multiple computational processes in these five steps. There is bound to be some error that accumulates during this time. The accumulated error may have some impact on the accuracy of the model. For example, in the acquisition of product form curves, there are small errors in perspective, even though the pictures collected are all from the same viewpoint. Additionally, the extraction of form feature curves is performed manually in the Illustrator vector software (Adobe Illustrator CC 2018), which also generates small errors. In the quantification of the product form feature, neglecting the variation in the axis distance will lead to some differences in the lengths of the curves obtained by equal division, resulting in some errors in the locations of the equal-division points. There are also some errors in the fitting and prediction of serial data when GM(1, 1) is used for fitting forecasts. These errors cannot be avoided, and in the future, future efforts will be made to reduce these errors so that keep them within a reasonable range. In addition, the predicted product forms generated in this study are not intended to be directly implemented as design solutions for the next generation of products. Instead, these predicted forms provide design inspiration or set design constraints for designers, helping to prevent abrupt changes in the design concepts of the product family caused by the personal cognitive biases of the designers responsible for developing the new generation of products. The final design of new-generation products also depends on user needs, technological advancements, strategic planning, and processing costs.
This study examines the inheritance of design styles during the product evolution process, specifically the gradual evolution of product forms. Disruptive changes occur when the design environment undergoes significant transformations, resulting in a product form that differs significantly from that of previous generations. This evolution requires analyzing changes in the design environment and identifying the main factors that influence the evolution of the product forms [
49]. This is the next stage of research.
In generative design, various methods for 3D morphology generation have been proposed (e.g., surface modeling [
50] and point cloud modeling [
51]). These methods require 3D spatial structure data [
52]. However, the most readily available and accurate data are product pictures and CAD dimension data published by companies. This study focuses on exploring the laws of historical product form evolution, which requires early product form data. It is very difficult to obtain data related to 3D models of early product forms. Therefore, in this study, outer contour curves were extracted from images, and the results were quantified to explore the law of product form evolution. In addition, there are discrepancies between the coding of product form curves for different product types. For instance, more points or parameters are required for the coding of products such as automobiles, whereas fewer points or parameters are necessary for products like Coca-Cola bottles. The number of points or parameters should be determined based on the actual product form, with the objective of maximizing the accuracy of the product form curve.
As described in
Section 3.1.2, the side outer contour of an automobile is the first critical step in the actual design of the automobile form. Inspired by the design method of “designing the whole form first, and then designing the local details”, the side outer contour of an automobile was chosen as the object for the preliminary mining of product form history data. From a system perspective, the automobile form is composed of multiple design features, including the outer contour of the automobile, and there is a complex relationship between them [
53]. In future work, this study will explore the complex relationship between multiple localized design features based on the results generated in
Section 3.3.3 (
Figure 8) and model the evolution of local features such as headlights, air-inlet grills, hoods, waistlines, and taillights to assist designers in further refining the local automobile form and generating a more complete design solution. The method proposed in this study is applicable to the design of the outer contour of product forms with significant evolutionary characteristics, such as those of automobiles.
Since the outer contour curves of the front and top views of the automobile do not change significantly in terms of the expression of the design style, this study ignores their changes and directly inherit previous generations of the product forms. When generating the 3D conceptual model, the outer contour curves on the side of the automobile are mainly used as the object of the evolutionary design of the product form. The model is more intuitive in terms of presentation than 2D automobile side outer contour curves and is more conducive to the selection of forms that fit the design style.