The Generative Generic-Field Design Method Based on Design Cognition and Knowledge Reasoning

Abstract

Large language model (LLM) and Crowd Intelligent Innovation (CII) are reshaping the field of engineering design and becoming a new design context. Generative generic-field design can solve more general design problems innovatively by integrating multi-domain design knowledge. However, there is a lack of knowledge representation and design process model in line with the design cognition of the new context. It is urgent to develop generative generic-field design methods to improve the feasibility, innovation, and empathy of design results. This study proposes a method based on design cognition and knowledge reasoning. Firstly, through the problem formulation, a generative universal domain design framework and knowledge base are constructed. Secondly, the knowledge-based discrete physical structure set generation method and system architecture generation method are proposed. Finally, the application tool Intelligent Design Assistant (IDA) is developed, verified, and discussed through an engineering design case. According to the design results and discussion, the design scheme is feasible and reflects empathy for the fuzzy original design requirements. Therefore, the method proposed in this paper is an effective technical scheme of generative generic-field engineering design in line with the design cognition in the new context.

1. Introduction

In modern industry and smart manufacturing, industries are being reshaped by two forces: the power of crowds and artificial intelligence (AI) represented by large language models (LLMs) [1]. Under these two forces, the fields of engineering design and product innovation design are rapidly developing along two paths: crowd intelligence innovation (CII) represented by the Problem–Solution (P-S) Co-evolution Model [2], and AI-Generated Content (AIGC) [3], which utilizes AI technology to generate content.

First of all, we should clarify the following concepts: intra-field design is a process in which a single-field design problem is solved directly in the same field, cross-field design is a process in which a single-field design problem is solved in a multi-field solution space, and generic-field design is a process in which a multi-field design problem is solved in a multi-field solution space. Clearly, cross-field design is a special form of generic-field design. It can be seen that the fundamental basis behind the shift from the intra-field design to generic-field design paradigm is the shift in the product conceptual design process from the traditional sequential model of problem-solving to the P-S Co-evolution Model [4]. Therefore, generic-field design has also become the most fundamental innovation mechanism and the most effective design problem-solving model in the context of CII and AIGC.

In the classical design theory, engineering design is categorized into heuristic design and generative design based on the process and output: heuristic design can output knowledge elements within various design domains such as technical, physical, and functional domains for stimulating the designer’s inspiration, whereas generative design needs to give relevant design solutions, i.e., system architectures that contain the physical structure and their relationships with each other. Compared with heuristic reasoning, generative reasoning needs to consider more dimensional knowledge elements at the technical level, and the technical methods are more complex. The fundamental task of generative reasoning is to provide a physical architecture that meets the conditions based on the input design requirements (including technical domains, functional requirements, etc.).

As shown in Figure 1, this study divides the product concept generation process into two phases: the first phase is responsible for discrete physical structure reasoning, and the second phase is responsible for physical structure relationship reasoning and interpretation to obtain a complete knowledge of the system architecture. In the first phase, the inference engine reasons about the set of discrete physical structures that satisfy the conditions based on the given technical fields and functional requirements. It should be pointed out that although the reasoning result is a discrete set and does not require an explicit expression of the relationship, the organic relationship between the physical structures must still exist implicitly, which means that the reasoning method in the first stage must take this into account. The second stage of the reasoning method is responsible for revealing the implicit correlations in the discrete set of physical structures and interpreting the generated results to a certain extent according to the designer’s needs.

Although generative intra-field design and heuristic generic-field design techniques have been widely used, generative generic-field design methods are still seriously lacking, and their main technical difficulties include the following:

(1) Lack of engineering design knowledge base that contains global coupling correlations: The essence of this problem is that there is no corresponding knowledge representation model based on the design cognitive model of global coupling, which leads to a structural solution set obtained by the heuristic method that shows a lack of systematic correlation and does not conform to the design cognitive model;

(2) Lack of AI method for engineering design with empathy: The essence of this problem is that AI’s understanding of design problems is too limited to the input text, which makes it difficult to form a generic-field problem-solving model, resulting in the lack of feasibility and innovation of the output scheme, and the lack of empathy with users in terms of use situation;

(3) Lack of system-level scheme generation method in line with product conceptual architecture: The causes of this problem are complex, including the lack of global coupling connection of the physical structure solution set obtained in the early stage, the lack of knowledge base to support architecture search, and the difficulty in learning the physical structure connection mode.

In the context of LLM and CII, the unreasonable use of design resources and computing power leads to problems such as low quality of design outputs, repetitive design processes, and difficult convergence of design schemes [5]. Therefore, the lack of appropriate generative methods may lead to new design sustainability problems [6].

To address the generative generic-field design process and the above technical difficulties, this study proposes a method based on design cognition and knowledge reasoning. Firstly, based on the topic model, a statistical model widely used in semantic analysis and text mining, ConceptTM, is proposed to generate a set of physical structures containing implicit connections for a given technical field and functional requirements. Second, in order to represent the hierarchical physical architecture of engineering products, this study proposes the Semantic Graph-based Techspecs Concept Ontology (SG-TCO) model based on semantic graph as the output form of the conceptual design solution, and with this goal in mind, the knowledge base G-Base is improved and constructed to support generic-field design. Based on this, we propose a system architecture generation method, G-Designer, which realizes scheme generation in the form of SG-TCO by finding similar instances from the knowledge base and learning structural connectivity patterns.

This paper will introduce the research progress in related fields in Section 2. Section 3 will clarify the research problem and scope, introduce the knowledge base constructed in the previous stage to support this research, and propose the research framework. Section 4 will introduce the physical structure set solving method ConceptTM, and Section 5 will introduce the system architecture generation method G-Designer. Section 6 will introduce the application platform constructed according to the methodology proposed in this research, and verify and discuss the feasibility and efficiency of the methodology based on a specific case. Finally, the contributions of this research and future research work will be summarized.

2. Literature Review

2.1. Knowledge-Based Design Combined with Design Cognition

Knowledge-based design (KBD) combined with design cognition (DC) mostly utilizes data sources in the form of natural language text [7,8]. It integrates natural language processing (NLP) to conduct heuristic knowledge reasoning that aligns with design cognition. Luo [9] assigns different AI techniques to different design task requirements and proposes a Double Hump Innovation Process Model based on the divergence–convergence cognitive process. Andrade et al. [10] used NLP techniques to alert designers to possible pitfalls in design concepts when appropriate, reducing design iterations. Tan et al. [11] focused on the design work of washing machine products. There are also studies related to design inspiration and knowledge recommendations using online consumer reviews [12] and project work texts [13]. Generic-field design involves a large amount and rich type of knowledge, which can be better utilized with AI technology to play the role of knowledge. With the continuous development of big data and big computing power, a series of emerging AI technologies such as the famous vector model [14], pre-training model [15], contrastive learning [16], generative model [17], and so on, have been derived. The development of AI technology has also contributed to the boom of AI applications in various other fields, and AI4Art [18,19], AI4Game [20,21,22,23], AI4Science [24,25,26], and other related work have emerged. In the field of engineering design, a blueprint for the work of AI4Design is gradually taking shape.

In terms of knowledge representation, knowledge graphs and semantic networks are the most popular approaches among researchers. Li et al. [27] constructed a knowledge graph based on medical requirements and technical documents to provide designers with design algorithms inspired by smart medical devices. Liu et al. [28] constructed a knowledge graph in the field of smart home product design. Wang et al. [29] achieved the goal of providing designers with risk prevention and feasibility analysis at the early design stage based on knowledge graphs. Hao et al. [30] constructed a knowledge graph on supply chain system design. Jia et al. [31] constructed a knowledge graph on mechanical product design. Liu et al. [32] proposed a Functional Structured Concept Network (FSCN) for mining users’ explicit and implicit requirements.

In addition to heuristic reasoning for designing knowledge entities, Chen et al. [33] proposed a method to inspire designers to think (QCue) based on the human reflective process, which mainly promotes thinking by answering users’ questions and asking them rhetorical questions. Jiang et al. [34] proposed a convolutional neural network for extracting the feature vectors of patent images for image classification and retrieval. Bai et al. [35] proposed a DMGAN model for transforming sketch features into real image features to retrieve the realistic counterparts of their design concepts. There are also some technical aspects of research available. For example, Bayesian networks as a form of knowledge representation [36], heuristic design using machine learning and optimization algorithms [37,38,39], manually constructing an expert system using expert experience [40], integrating multiple heuristic reasoning methods to construct a design system [41,42,43,44,45], etc.

2.2. Knowledge-Based Generic-Field Conceptual Design

The complexity of knowledge-based generic-field conceptual design lies in the fact that on the one hand, the knowledge sources used in the generic-field design must cover multiple engineering fields; on the other hand, the generic-field design must support cross-field knowledge fusion and integration, and therefore, needs to abstract the core conceptual elements within each engineering field.

Patents are the best source of knowledge used to support generic-field design. Sarica et al. [46] collected patent data from the USPTO and constructed TechNet, a large semantic network of engineering designs, for designers to perform design concept searches and evaluations. Siddharth et al. [47] improved upon TechNet and constructed a large and extensible knowledge graph for engineering design. Design knowledge characterization methods using semantic networks or knowledge graphs do not need to distinguish the class attributes of entities and can provide a unified description of design concepts in generic fields. However, if a more precise characterization of the conceptual scheme is required, entity category attributes still need to be defined and discerned. In order to clearly describe the connection between technical fields, Luo et al. [48] take IPCs of patents as technical field entities and utilize the citation relationship between patents to construct a technical map InnoGPS, which is used to calculate the knowledge distance between different fields so as to more effectively guide designers in cross-field knowledge integration. Liu et al. [49] built a technical terminology knowledge base based on the IPC of patents and standard terminology of functional flow, which is used to assist designers in searching for design solutions, and Ye et al. [50] also used IPC to classify design concepts into technical fields and realized the retrieval and recommendation of design concepts.

Combining the three domains of generic-field design, KBD and DC, heuristic design based on biological analogies also has a place in the existing research. The starting point of bio-inspired design lies in nature’s biodiversity and evolutionary system; in order to adapt to the requirements of the environment, organisms have evolved diverse coping mechanisms, and in this way, the structures formed are the result of natural selection. If a certain biological structure or mechanism is suitable for solving an engineering problem, it can often bring better results. Chen et al. [51] combined natural language processing technology to extract the structure and function of organisms from biological databases, which was used to inspire the design of wind turbines for noise reduction. Cao et al. [52] assisted in the design of natural resource collection systems in a similar way. In addition to functional–structural analogies, sometimes visual analogies can also provide references for designers. Based on human visual analogical thinking, Zhang et al. [53] proposed a deep clustering model that mines the similarity of visual edges for the visual analogies of sketches to provide inspiration for designers. However, the visual analogy method lacks a principled interpretation of engineering techniques, so applications tend to favor industrial design.

In terms of generic-field design tool development, Design Ideator is a conceptual design toolkit built by Narsale et al. [54] that provides designers with a variety of design inspirations such as context-switching, analogical reasoning, stimulus arousal, and combinatorial constructions, while Linkage is an online tool built by Eliot et al. [55] that provides cross-domain bionic design for design teams. ONPS is an ontology-based intelligent recommendation system for new product development proposed by Hsu et al. [56].

2.3. AI Based Generative Design

AI algorithms such as flow-based models and diffusion models, as well as deep learning methods such as the variable auto-encoder (VAE) and generative against network (GAN), are widely used in generative design. In terms of design objects, due to the simple composition of drug molecules and the availability of a large number of structured databases, studies related to the generative design of drug molecules are more abundant. Mahmood et al. [57] proposed a generative model for mask map modeling to generate drug molecules with similar physicochemical properties to the original data. Zang et al. [58] proposed a generative model based on the reversible flow model. Luo et al. [59] proposed a generative model based on a discrete flow model to accommodate the discrete nature of drug molecules. In terms of output, the generation of drug molecules is often encoded as a graph structure; i.e., a two-dimensional molecular map is used as the output rather than a three-dimensional molecular structure. The architectural domain more often uses 3D structures for generation, which is due to the fact that the structure of buildings is more fixed and regularity is more obvious. Wen et al. [60] achieve the automatic generation of 3D building models based on the structural elements of the line segments. Chang et al. [61] propose a GAN-based method for generating 3D building designs (Building GAN). Sydora et al. [62] proposed an automatic building design generation method based on building information modeling (BIM) rules. Compared to engineering design, which is concerned with functionality and systematicity, building design is more inclined to exterior and industrial design.

In the field of mechanical and structural design, the generative methods are different based on different design representations. Yaroslav et al. [63] use 2D CAD graphics as design representations, extract lines and constraints from them as the basic elements of the design, mimic the natural language generation, and use autoregressive modeling to learn the design. Ayush et al. [64] learn the design from the designer’s behavioral sequences and generate designs by capturing and mimicking the designer’s behavior. Wang et al. [65] proposed a GAN-based generative model for generating the geometrical structure of a crystalline cell that satisfies a given condition. Lee et al. [66] proposed a GAN-based method for generating tire treads using tire performance as the input. Zheng et al. [67] proposed a GAN-based method for generating tire treads in response to standardized program instructions and semantic reasoning mechanisms, and proposed a rule-based robot generation method.

From the studies collated above, it is not difficult to find that most of the current research for generic-field design problems adopt heuristic design methods, and it is difficult to form a methodology that realizes cross-domain knowledge fusion and conceptual program solving for engineering design problems. In the research of generative methods, most of the design problems and schemes belong to the same technical field. On the other hand, studies on generative design require good design characterization methods, large-scale datasets, or explicit generation rules as a prerequisite. Therefore, this study proposes a generative approach for engineering design that is consistent with design cognition, starting from problem formulation, design characterization, and a knowledge base that supports generic-field design.

2.4. Topic Modeling Approaches and Application

Topic model is a method of mining hidden topics in a corpus through modeling, and its essence is a statistical model for clustering the hidden semantic structure of the corpus [68]. The topic model can map words or phrases with the same topic to the same dimension through text dimensionality reduction, and effectively discover the topic structure hidden in large-scale text corpus [69], forming the effect of soft clustering on the vocabulary set. The implementation methods of the topic model mainly include the probabilistic topic model and neural topic model.

2.4.1. Probabilistic Topic Model

The modeling thinking of the probabilistic topic model is to regard the text as the probability distribution of the topic; that is, each text is composed of several topics, and the topic is regarded as the probability distribution of words; that is, each topic is represented by several words.

Blei et al. [70] proposed the first full Bayesian probabilistic topic model Latent Dirichlet Allocation (LDA), which is mainly used to speculate the topic distribution of documents. LDA selects a topic from each document with a certain probability, and then selects a word from this topic with a certain probability, and repeats the above steps continuously to obtain the final whole document. The model structure of LDA mainly contains two distributions; that is, the document is modeled as the distribution of topic, and the topic is modeled as the distribution of words. LDA has greatly promoted the development of the topic model, and a large number of improvements have been proposed based on the LDA model framework. Blei et al. [71] proposed the Correlated Topic Model (CTM) to model the correlation between topics by introducing the covariance matrix. LDA and CTM are both static topic models, which cannot model the timing of text. Therefore, researchers have proposed Dynamic Topic Models (DTMs) [72] and their extension to analyze the evolution of topics in text over time. On the other hand, a collapsed Gibbs Sampling Algorithm for the Dirichlet Multinomial Mixture Model (GSDMM) [73], Biterm Topic Model (BTM) [74], Multi-attribute Latent Dirichlet Allocation (MA-LDA) [75], and other models have also been proposed one after another, which are applied to sparse short text analysis.

Most of the above topic models are unsupervised machine learning models, which pay too much attention to maintaining text data and ignore other predictive information. The topic model based on supervised learning can effectively use text labels [76,77,78,79] to learn the topic distribution implied in documents to train the prediction model and produce more interpretable topics [80]. Representative, such as the Author Topic Model (ATM) [81], is a document generation model based on LDA. It believes that there is a correlation between the polynomial distribution of authors and topics, and models the document as a mixed distribution of topics and authors.

2.4.2. Neural Topic Model

When the data scale is expanded, the complexity of solving the topic model is greatly increased, and the topic model needs to be able to find the multi-level and multi-faceted feature information of the data. In the face of these new challenges, the neural topic model effectively avoids complex model derivation by combining the deep learning method and using the black box mechanism, and is better applied to downstream tasks with the flexibility of neural networks. The neural topic model optimizes the text generation process by combining word embedding [82,83,84,85], Variational Auto-Encoders (VAEs), neural networks, and other frameworks.

Word embedding is a kind of vocabulary vector representation learning technology in natural language processing, which maps the lexical features from high-dimensional space to low-dimensional continuous space into dense vectors. The Topic2Vec model [86] proposes a hybrid method of extracting features from documents. LDA is used to model the global relationship from each document to all topics, and Word2Vec is used to learn target words from the context to capture these relationships so as to realize the integration of context relationships between words.

VAE is a coding–decoding network structure proposed by Kingma et al. [87] that compresses input data into potential features and reconstructs text data distribution. Researchers have proposed a series of VAE-based topic model designs [88,89,90,91,92], providing an extensible and powerful deep generation framework for potential topic modeling [93,94,95,96].

The early neural topic model was based on the multilayer perceptron neural network with forward propagation [97]. Later, aiming at the sparsity of distribution, a neural topic model with sparse constraint was proposed [98,99,100]. The existing neural topic model can learn the complex nonlinear distribution of text and effectively adapt to various natural language processing tasks for mining text topics [101,102]. However, in the face of complex text expression and context dependence, the learned document features still have problems with inconsistent topics and the low utilization of data and knowledge in the text [103,104].

Topic clustering is also common in engineering design. For example, a technical field can be divided into more detailed sub-fields, and the physical structure distribution under each sub-field is different. In this case, a given technical field, divided sub-fields, and all physical structures can be regarded as specific articles, topics, and vocabulary, respectively. Therefore, this study will also use the topic model to reconstruct Bayesian design thinking and build a generative design model.

3. Problem Formulation, Preliminary Preparations, and Research Framework

3.1. Problem Formulation

In the stage of problem formulation, the IPO (Input–Process–Output) model of generic-field generative design should be specified first.

• Input: While the input of generative design is often the functional requirements, in the generic-field design process, the concept of technical fields needs to be introduced as another type of element in the input. Considering that this study uses patents as the knowledge source, IPC code can be used as the input form of technical field class. Many complete functional effect bases have been formed in the field of engineering design, and each term can be used as a functional requirement.
• Process: In this study, it is proposed to realize the generic-field design through two processes: discrete physical structure set generation and system architecture generation.
• Output: In order to specify the output form of the task, a hierarchical characterization of the physical architecture needs to be proposed. An ontology model Techspecs Concept Ontology (TCO) [105] for expressing the hierarchical architecture of engineering products has been proposed in the research related to Product Family Design (PFD) based on a Modular Platform. The architecture of TCO is shown in Figure 2a, including the component layer, Modular Layer, and Product Layer. However, the TCO model ignores the interactive correlations between different units under the same layer, so this study proposes the Semantic Graph-based TCO (SG-TCO) model, as shown in Figure 2b. The SG-TCO model uses a graph structure at the component level to characterize the correlations between physical structures, and the modules at the module level are no longer simple collections of discrete physical structures, but communities or clusters in the semantic graph at the component level.

Figure 2. Difference between TCO and SG-TCO.

Figure 2. Difference between TCO and SG-TCO.

In response to the above generic-field design process, this research also needs to focus on solving the following four problems:

• Problem 1: Global coupling knowledge correlation affecting conceptual scheme generation.

As shown in Figure 3 for a simple lighting system, two models are used here to represent the relationships between the three elements in the system.

Figure 3 shows a directed semantic network consisting of two pieces of knowledge “weather affects lighting” and “light affects lighting”. The information obtained is that both weather and light affect lighting, but this information is still Pair-wise and does not explain the global coupling between the three. In this small lighting system, the coupling of weather and lighting can be accomplished by the designer’s brain; however, once large and complex systems are involved, simple human considerations may ignore these influences, leading to the generation of low-quality design solutions. In the process of solving generic-field design problems, it is necessary to establish joint distributions across different design domains (technical, functional, and structural) for reasoning about physical structure solutions, and thus, it is necessary to understand the coupling and interactions between various elements in the system, which cannot be fulfilled by fragmented modes of knowledge representation, such as knowledge graphs or semantic networks.

In this study, we consider the use of the Probabilistic Graphical Model (PGM) to model the global correlations between conceptual elements and to measure the coupling effects and uncertainties within the system from a quantitative perspective. A Bayesian network, as illustrated in the figure, quantifies the causal relationships and gives the coupling effects of weather and lighting on lighting, providing designers with more comprehensive information.

• Problem 2: A discrete physical structure set solving model in accordance with the designer’s cognitive mode.

Studies in cognitive science and neuroscience have shown that the thinking process of the human brain is likely to follow the Bayesian paradigm, and scholars call this hypothesis the “Bayesian brain” [106,107,108]. The core view of the Bayesian paradigm is that human understanding of things is prior. On the basis of this prior assumption, likelihood assessment is conducted on the various manifestations or products of things. After the assessment, the posterior is obtained by modifying the prior according to the assessment results. This view can be expressed by the famous Bayesian formula as follows:

$$\mathcal{P}\left(x|D\right)\propto \mathcal{P}\left(x\right)\mathcal{P}\left(D|x\right)$$

(1)

where x is the thing or hypothesis to be evaluated, and D is the phenomenon or data obtained from observation or experiment on the thing or hypothesis. The symbol $\propto$ indicates that there is a proportional relationship between the two before and after the symbol. The product concept design process is a thinking process with strong cognitive attributes. Considering the conceptual scheme as a collection of structures, the concept design process is a structure-by-structure sampling process, and the assumption of the “Bayesian brain” is obviously very suitable for this process, which is called Bayesian design thinking (BDT).

In the physical structure set solving process, the goal is to obtain a physical structure that satisfies the conditions based on the given technical fields and functional requirements. From the perspective of BDT, the physical structure is the object to be evaluated, and the a priori and likelihood should be based on the technical fields and functional requirements, respectively. In the general design context, on the one hand, the physical structure is considered to be subordinate to a specific technical field, e.g., a notebook belongs to the field of electronic information, and the concept of “electronic information” provides the a priori technical domain for “notebook”; on the other hand, “structure determines function” has been widely recognized by structure-functionalism [69] in the natural sciences and the FS theory in the design sciences [109], so the likelihood term in the BDT is the likelihood that a particular structure has a particular function.

In summary, the physical structure set solving process based on BDT in this study can be expressed as follows:

$$\mathcal{P}\left(S|T,F\right)\propto \mathcal{P}\left(S|T\right)\mathcal{P}\left(F|S\right)$$

(2)

where S represents the physical structure and T and F are the technical field and functional requirements, respectively.

• Problem 3: Physical structure set solving method.

As described in Problem 2, considering the conceptual design process as a structure-by-structure sampling process, this study considers the topic clustering method for conceptual solution: firstly, a sub-field topic is sampled based on the distribution of sub-field topics under the technical field of the product; secondly, a structure is sampled based on the distribution of the structures under the sub-field topics, and the process is repeated until the generation of the structure set is completed.

Therefore, in the process of solving $\mathcal{P}\left(S|T,F\right)$, $\mathcal{P}\left(S|T\right)$ can be expressed as a topic model based on the above process: construct distributions on all the physical structures as sub-domain topics, and then construct distributions on all these topics as technical domains. Similarly, the $\mathcal{P}\left(F|S\right)$ topic model is constructed. In summary, this study uses a topic model to solve the problem of generating a conceptual scheme—i.e., a collection of discrete physical structures—(the topic model is called ConceptTM), thus capturing the clustering phenomenon in design concepts and reducing the parameters of the model for generalization and computation.

• Problem 4: System architecture generation method.

For generic-field design output in the form of SG-TCO, it is necessary to first establish connections at the physical structure (component) level, and then further cluster the components according to functional modules and construct connections at the module level.

In this study, we first improve the existing knowledge base by constructing structural node connections between the component level and the module level. Based on the knowledge base, for the new generative generic-field design, search-based generation and connect-based generation methods are proposed to construct connections in the discrete physical structure set to generate the system architecture.

3.2. Preliminary Preparations

3.2.1. Knowledge Base Building for Discrete Structure Set Generation

Based on the Function–Behavior–Structure (FBS) model and axiomatic design theory, this study incorporates functional and physical domains into the proposed multi-domain design knowledge representation model. In addition, it is necessary to introduce a technical domain to characterize the relationship between different technical fields, which is the essential requirement of generic-field design.

In summary, this study proposes a three-domain (technical, physical, and functional) generic-field design knowledge representation model consisting of three basic design elements (technical domain, physical structure, and functional effect). Based on the three-domain model, an engineering design product is the sum of the three basic elements, so a design concept can be represented as follows:

$$P_n=\left(\{T_i{\}}_{i=1}^{I_n},\{S_j{\}}_{j=1}^{J_n},\{F_k{\}}_{k=1}^{K_n},R_n\right)$$

(3)

In the formula, $P_n$ represents the design concept described in the nth patent; $T_i$ is the ith technical element that the corresponding design concept has, and $I_n$ is the total number of technical elements; $S_j$ is the jth physical element that the corresponding design concept has, and $J_n$ is the total number of physical elements; $F_k$ is the kth functional element that the corresponding design concept has, and $K_n$ is the total number of functional elements; and $R_n$ and $P_n$ are the original texts of the corresponding patent describing the detailed relationship between $T_i$, $S_j$, and $F_k$. All the existing design concepts constitute a base knowledge base:

$$K_B=\{P_n{\}}_{n=1}^N$$

(4)

In this study, Chinese invention patents are selected as the knowledge source, and the relevant data can be downloaded from the Patent Data Service Pilot System of the State Intellectual Property Office. The three domain elements in the knowledge base can be extracted from the invention patent data using natural language processing techniques:

• In this study, IPC codes are used as the technical domain elements, and each code represents a technical field. The first four bits of the IPC code are taken as the characterization of the technology element; i.e., the technology coverage of the technology element is taken as the degree of the subcategory, e.g., B64C is a technology element representing the technology domain of the flight-related technology.
• Physical domain elements are represented using physical structure terms, and all the terms together constitute the physical domain. In this study, the main physical structure terms referred to in the patent are extracted directly from the illustration section of the accompanying drawings using patent characteristics based on the method of constructing regular expressions.
• Functional domain elements are represented by functional effect terms, and in the patent text, the abstract, the declaration of rights, the content of the invention, and the specific embodiment are the parts on which the functional effect terms are concentrated. In this study, function effect terms are extracted for the above content based on the word division tool and TF-IDF algorithm, and all the terms together constitute the functional domain.

Finally, this study extracts the above design concepts from 39,463 patents to form the technical domain set T (|T| = 582), the physical structural domain set S (|S| = 4420), and the functional domain set F (|F| = 24246). The constructed knowledge base will support the discrete physical structure set solving process.

3.2.2. Construction of SG-TCO Knowledge Base for System Architecture Generation

The base element of the SG-TCO knowledge base (later referred to as G-Base) is SG-TCO instances; in this study, one SG-TCO instance can be extracted from each patent based on constructing correlations at two levels, component and module, to form the G-Base. The G-Base can be expressed by the following equation:

$$\mathrm{G}-\mathrm{B}\mathrm{a}\mathrm{s}\mathrm{e}=\{{\mathrm{SG}-\mathrm{TCO}}_{\mathrm{n}}{\}}_{\mathrm{n}=1}^{\mathrm{N}}$$

(5)

$$\begin{array}{c}\mathrm{SG}-\mathrm{TCO}=\left(G_c,S_m,P\right),\\ G_c=\left(V_c,E_c\right),\\ S_m=\{M_l{\}}_{l=1}^L.\end{array}$$

(6)

In the formula, $G_c$ represents the component semantic graph, $S_m$ represents the set of module subgraphs, and $P$ represents the description of the other attributes of the product such as name and IPC code. $V_c$ represents the set of the nodes of the underlying physical structures, $E_c$ represents the set of the connected edges of the semantic correlation relations between the physical structures, $M_l$ represents the set of underlying physical structures that the module l has, and L is the number of modules.

This study adopts the bottom-up construction method, starting from the component layer to build the component semantic graph, then extracting the corresponding physical modules at the module layer, and finally adding the ancillary information to form a complete SG-TCO instance.

(1) Component level: semantic graph-based relationship recognition.

Component semantic graph refers to the graph relations between interrelated underlying physical structures, and the essence of constructing a component semantic graph under a given patent is the problem of calculating the strength of semantic correlations between the underlying physical structures that the patent has. The physical structure elements in the patent can be used as the component layer nodes of SG-TCO instances. The number of co-occurrences between two nodes is counted by the regular matching method, which is used as the semantic correlation edge of the component semantic graph. During the construction process, the component semantic graph can be constructed into two modes: undirected graph and directed graph.

(2) Module level: module clustering based on community detection algorithm.

In G-Base, module-level physical modules are defined as a subset of more closely connected physical structures in the component semantic graph. In the field of graph computing, the above methods for mining the subset of tightly connected nodes are collectively known as community detection [110,111].

For the undirected graph pattern component semantic graph, Modularity-based Louvain’s algorithm [112] is used to extract physical modules. Modularity is a metric to evaluate the good or bad results of community detection, and its physical meaning is the difference between the sum of the weights of the connected edges of nodes inside the community and the random case, which is calculated as follows:

$$Q={\displaystyle \frac{1}{2m}}\sum _{i,j}\left[A_{i,j}-{\displaystyle \frac{d_i{d}_j}{2m}}\right]\delta \left(c_i,c_j\right).$$

(7)

In the formula, A is the undirected graph adjacency matrix, $d_i\left(d_j\right)$ is the node degree value, $m={\displaystyle \frac{1}{2}}\sum _{i,j}{A}_{i,j}$ is the total weight of all the connected edges, $c_i\left(c_j\right)$ is the community into which the corresponding node is divided, and $\delta \left(c_i,c_j\right)$ is the Dirichlet function:

$$\delta \left(c_i,c_j\right)=\left\{\begin{array}{ll}1,& c_i=c_j\\ 0,& c_i\ne c_j\end{array}\right.$$

(8)

For directed graph schema component semantic graph, the Map Equation-based Infomap algorithm [113] is used to extract the physical modules. The Map Equation is of the following form:

$$\begin{array}{ll}& L\left(C\right)=q_{\curvearrowright }H\left(\mathcal{Q}\right)+{\displaystyle \sum _c}{p}_{cひ}H\left({\mathcal{P}}^c\right),\\ & H\left(\mathcal{Q}\right)=-{\displaystyle \sum _c}{\displaystyle \frac{q_{c\curvearrowright }}{q_{\curvearrowright }}}\mathrm{l}\mathrm{o}\mathrm{g}{\displaystyle \frac{q_{c\curvearrowright }}{q_{\curvearrowright }}},\\ & H\left({\mathcal{P}}^c\right)=-{\displaystyle \frac{q_{c\curvearrowright }}{p_{cひ}}}\mathrm{l}\mathrm{o}\mathrm{g}{\displaystyle \frac{q_{c\curvearrowright }}{p_{cひ}}}-{\displaystyle \sum _{i\in c}}{\displaystyle \frac{p_i}{p_{cひ}}}\mathrm{l}\mathrm{o}\mathrm{g}{\displaystyle \frac{p_i}{p_{cひ}}}.\end{array}$$

(9)

In the formula, $p_i$ is the ith element of the smooth distribution $\mathbf{p}$ with the directed adjacency matrix $B$ as the transfer probability, i.e., the probability of node i appearing in the wandering sequence after an infinitely long period of random wandering. There

$$\mathbf{p}=B^{\mathrm{\top }}\mathbf{p}$$

(10)

The other parameters are calculated as follows:

$$\begin{gathered} q_{c\curvearrowright }=\sum _{i\in c}\sum _{j\notin c}{p}_i{B}_{i,j}, \\ {q}_{\curvearrowright }=\sum _c{q}_{c\curvearrowright }, \\ {p}_{cひ}=q_{c\curvearrowright }+\sum _{i\in c}{p}_i. \end{gathered}$$

(11)

The physical meaning of Map Equation is the information entropy of the sequence obtained by randomly wandering in the network system after performing the community division, so the goal of the Infomap algorithm is to find the optimal community division C-minimization equation.

In addition to physical modules based on the community form, G-Base also focuses on physical modules based on the clique form. A clique is a subgraph that constitutes a complete graph in a graph structure, and any two nodes of these subgraphs have edges. As a supplement to the community form, the clique can improve the recall rate of potential physical modules. In G-Base, both the community and the clique require no less than three component nodes to be recognized as a physical module.

3.3. Research Framework

To address the above problems in the generative generic-field design process, a research framework is proposed as shown in the Figure 4:

4. ConceptTM: Structure Set Generation Method Based on Topic Model

4.1. Graphical Representation of ConceptTM

The infrastructure used by ConceptTM is a directed probability graph, that is, a Bayesian network. More specifically, it is a topic model similar to LDA. As a generative model, ConceptTM describes the generation process of engineering products including technical fields, physical structures, and functional requirements:

(1) Input the technical fields $\{T_{n,i}{\}}_{i=1}^{I_n}$ involved in the nth engineering product;

(2) Sample one of the $T_{n,j}$ from the given technical fields;

(3) Sample technical topics $Z_{n,j}^s$ according to the distribution of technical topics in the technical field ${\theta }_{T_{n,j}}^s$;

(4) Sample the physical structure $S_{n,j}$ according to the distribution of physical structures in the technical topics ${ \beta }_{Z_{n,j}}^s$;

(5) Execute the above physical structure sampling $J_n$ times to complete the sampling of physical structures;

(6) Sample one of the $S_{n,k}$ from a given physical structure;

(7) Sample a physical topic $Z_{n,k}^f$ according to the distribution of physical topics in the physical structures ${\theta }_{S_{n,k}}^f$;

(8) Sample functional requirements $F_{n,k}$ according to the distribution of functional requirements in the physical topics ${\beta }_{Z_{n,k}}^f$;

(9) Execute the above functional structure sampling $K_n$ times to complete the sampling of functional requirements.

Repeat the above generation process N times to obtain engineering product datasets:

$$D=\{\left(\{T_{n,i}{\}}_{i=1}^{I_n},\{S_{n,j}{\}}_{j=1}^{J_n},\{F_{n,k}{\}}_{k=1}^{K_n}\right){\}}_{n=1}^N$$

(12)

For PGM, graph representation implies a predefinition of the model based on a priori knowledge or assumptions, including the definition of the graph structure and of the variable types. Figure 5 illustrates the graph representation of ConceptTM.

The variable elements represented by shaded nodes in the figure are Visible Variables, which are the elements described in the K_B; the variables represented by non-shaded nodes are assumptions of the model, which will not be observed in the actual dataset, and are Latent Variables. The Technical Topic Distributions ${\theta }_t^s$, Topic Distributions ${\beta }_z^s$, Structural Topic Distributions ${\theta }_s^f$, and Functional Topic Distributions ${\beta }_z^f$ are sampled from their respective priors, and are the most important model parameters of ConceptTM. The inference process of ConceptTM describes the joint distribution of elements within an engineering product dataset:

$$\mathcal{P}\left({\theta }_t^s,{\beta }_z^s,T_{n,j},Z_{n,j}^s,S_{n,j},S_{n,k},{\theta }_s^f,{\beta }_z^f,Z_{n,k}^f,F_{n,k}|T_{n,i}\right)$$

(13)

$$=\prod _{t=1}^{\left|T\right|}\mathcal{P}\left({\theta }_t^s\right)\prod _{z=1}^{\left|Z^s\right|}\mathcal{P}\left({\beta }_z^s\right)\prod _{s=1}^{\left|S\right|}\mathcal{P}\left({\theta }_s^f\right)\prod _{z=1}^{\left|Z^f\right|}\mathcal{P}\left({\beta }_z^f\right)$$

(14)

$$\times \prod _{n=1}^N\prod _{j=1}^{J_n}\mathcal{P}\left(T_{n,j}\left|\right\{T_{n,i}{\}}_{i=1}^{I_n}\right)\mathcal{P}\left(Z_{n,j}^s|{\theta }_{T_{n,j}}^s\right)\mathcal{P}\left(S_{n,j}|{\beta }_{Z_{n,j}^s}^s\right)$$

(15)

$$\times \prod _{n=1}^N\prod _{k=1}^{K_n}\mathcal{P}\left(S_{n,k}\left|\right\{S_{n,j}{\}}_{j=1}^{J_n}\right)\mathcal{P}\left(Z_{n,k}^f|{\theta }_{S_{n,k}}^s\right)\mathcal{P}\left(F_{n,k}|{\beta }_{Z_{n,k}^f}^f\right)$$

(16)

Equation (14) is the joint distribution corresponding to the generation process of each topic distribution. Equation (15) is the joint distribution corresponding to the generation process of the physical structure, i.e., the solving process of $\mathcal{P}\left(\mathrm{S}|\mathrm{T}\right)$; Equation (16) is the joint distribution corresponding to the generation process of the functional requirements, i.e., the solving process of $\mathcal{P}\left(\mathrm{F}|\mathrm{S}\right)$. The technical fields $T_{n,i}$ of the individual engineering products are not derived from sampling, but are given by the designer, which facilitates the explicit control of technical field integration.

Due to the architecture of the topic model with the use of latent variables, the individual physical structures are not conditionally independent from each other for a given technical fields and functional requirements, i.e.:

$$\mathcal{P}\left(\left\{S_j{\}}_{j=1}^J\right|T,F\right)\ne \prod _{j=1}^J\mathcal{P}\left(S_j|T,F\right).$$

(17)

This suggests that ConceptTM is capable of mining global coupling connections between physical structures, and can construct sets of discrete physical structures with implicit correlations that are amenable to generative reasoning.

4.2. Training Method of ConceptTM Based on MVI

The mechanism of ConceptTM is Bayesian inference, i.e., the computation of $\mathcal{P}\left(\mathrm{S}|\mathrm{T},\mathrm{F}\right)$. According to Equation (13),${ \theta }_t^s,{\beta }_z^s,{\theta }_s^f,\mathrm{a}\mathrm{n}\mathrm{d} {\beta }_z^f$ need to be estimated by a training method of fitting dataset D.

Mean field Variational Inference (MVI) [114] is an approximation algorithm for solving complex multivariate posterior distributions, which assumes that the posterior distributions are independent among multiple variables. After obtaining the approximate posterior distribution of a variable, the mean of the approximate posterior is often used as the point estimate of the variable, which is how ConceptTM obtains the point estimate of the variable ${\theta }_t^s,{\beta }_z^s,{\theta }_s^f,{\beta }_z^f$. The original true posterior distributions of (${\theta }_t^s,{\beta }_z^s$) are conditionally independent, i.e.,:

$$\mathcal{P}\left({\theta }_t^s,{\beta }_z^s,{\theta }_s^f,{\beta }_z^f|D\right)=\mathcal{P}\left({\theta }_t^s,{\beta }_z^s|D\right)\mathcal{P}\left({\theta }_s^f,{\beta }_z^f|D\right)$$

(18)

And in ConceptTM, $\mathcal{P}\left(\mathrm{S}|\mathrm{T}\right)$ and $\mathcal{P}\left(\mathrm{F}|\mathrm{S}\right)$ obviously have the same structural characteristics, so it is sufficient to apply to (${\theta }_s^f,{\beta }_z^f$) after studying the estimation method of (${\theta }_t^s,{\beta }_z^s$). The graphical representation of the process of estimating the posterior distribution of (${\theta }_t^s,{\beta }_z^s$) by inference from the mean variational field is shown in Figure 6:

In this case, the MVI of variables only plays an auxiliary role in solving, and the results can be discarded after the model training is completed. The approximate posterior distribution of (${\theta }_t^s,{\beta }_z^s$) is expressed using a parameterization as follows (~represents the distribution that the variable follows):

$$\begin{array}{ll}\hfill q\left(T_{n,j}|{\lambda }_{n,j}\right)& \sim \mathbf{C}\mathbf{a}\mathbf{t}\mathbf{e}\mathbf{g}\mathbf{o}\mathbf{r}\mathbf{i}\mathbf{c}\mathbf{a}\mathbf{l}\left({\lambda }_{n,j}\right),\\ \hfill q\left(Z_{n,j}^s|{\gamma }_{n,j}\right)& \sim \mathbf{C}\mathbf{a}\mathbf{t}\mathbf{e}\mathbf{g}\mathbf{o}\mathbf{r}\mathbf{i}\mathbf{c}\mathbf{a}\mathbf{l}\left({\gamma }_{n,j}\right),\\ \hfill q\left({\theta }_t^s|{\alpha }_t^s\right)& \sim \mathbf{D}\mathbf{i}\mathbf{r}\mathbf{i}\mathbf{c}\mathbf{h}\mathbf{l}\mathbf{e}\mathbf{t}\left({\alpha }_t^s\right),\\ \hfill q\left({\beta }_z^s|{\eta }_z^s\right)& \sim \mathbf{D}\mathbf{i}\mathbf{r}\mathbf{i}\mathbf{c}\mathbf{h}\mathbf{l}\mathbf{e}\mathbf{t}\left({\eta }_z^s\right).\end{array}$$

(19)

The MVI is solved with the optimization objective of minimizing the Kullback–Leibler Divergency (KLD) between the true posterior distribution and the approximate posterior distribution, and its equivalent problem is maximizing the Evidence Lower BOund (ELBO):

$${\mathrm{m}\mathrm{a}\mathrm{x}}_{\varphi }\mathrm{E}\mathrm{L}\mathrm{B}\mathrm{O}={\int }_{z}q\left(z|\varphi \right)\mathrm{l}\mathrm{o}\mathrm{g}{\displaystyle \frac{\mathcal{P}\left(x,z\right)}{q\left(z|\varphi \right)}}$$

(20)

$$x=(T_{n,i},S_{n,j})$$

(21)

$$z=(T_{n,j},Z_{n,j}^s,{\theta }_t^s,{\beta }_z^s)$$

(22)

$$\varphi =\left({\lambda }_{n,j},{\gamma }_{n,j},{\alpha }_t^s,{\eta }_z^s\right)$$

(23)

$\varphi$ is the parameter to be solved and has the following:

$$\mathcal{P}\left(x,z\right)=\prod _{t=1}^{\left|T\right|}\mathcal{P}\left({\theta }_t^s|{\alpha }^s\right)\prod _{z=1}^{\left|Z^s\right|}\mathcal{P}\left({\beta }_z^s|{\eta }^s\right)\prod _{n=1}^N\prod _{j=1}^{J_n}\left[\mathcal{P}\left(T_{n,j}\left|\right\{T_{n,i}{\}}_{i=1}^{I_n}\right)\mathcal{P}\left(Z_{n,j}^s|{\theta }_{T_{n,j}}^s\right)\mathcal{P}\left(S_{n,j}|{\beta }_{Z_{n,j}^s}^s\right)\right]$$

(24)

$$\begin{array}{ll}q\left(z|\varphi \right)& \begin{array}{l}={\displaystyle \prod _{t=1}^{\left|T\right|}}q\left({\theta }_t^s|{\alpha }_t^s\right){\displaystyle \prod _{z=1}^{\left|Z^s\right|}}q\left({\beta }_z^s|{\eta }_z^s\right){\displaystyle \prod _{n=1}^N}{\displaystyle \prod _{j=1}^{J_n}}\left[q\left(T_{n,j}|{\lambda }_{n,j}\right)q\left(Z_{n,j}^s|{\gamma }_{n,j}\right)\right]\end{array}\end{array}$$

(25)

Since the model features of ConceptTM are consistent with the Author Topic Model (ATM) [115], training can be performed directly using the algorithm in Gensim [116]. The a posteriori means are calculated as the point estimates of the parameters after the optimization is complete:

$${\widehat{\theta }}_t^s={\displaystyle \frac{{\alpha }_t^s}{\sum _s{\alpha }_t^s}}$$

(26)

$${\widehat{\beta }}_t^s={\displaystyle \frac{{\eta }_z^s}{\sum _s{\eta }_z^s}}$$

(27)

$${\widehat{\theta }}_s^f={\displaystyle \frac{{\alpha }_s^f}{\sum _f{\alpha }_s^f}}$$

(28)

$${\widehat{\theta }}_z^f={\displaystyle \frac{{\eta }_z^f}{\sum _f{\eta }_z^f}}$$

(29)

Furthermore, compute $\mathcal{P}\left(S|T\right)$ and $\mathcal{P}\left(F|S\right)$:

$$\mathcal{P}(\{S_j{\}}_{j=1}^J|\{T_i{\}}_{i=1}^I)={\displaystyle \frac{1}{I^J}}\prod _{S_j\in \{S_j{\}}_{j=1}^J}\left[\sum _{T_j\in \{T_i{\}}_{i=1}^I}\sum _{z\in Z^s}{\widehat{\theta }}_{T_j}^z{\widehat{\beta }}_z^{S_j}\right]$$

(30)

$$\mathcal{P}(\{F_k{\}}_{k=1}^K|\{S_j{\}}_{j=1}^J)={\displaystyle \frac{1}{J^K}}\prod _{F_k\in \{F_k{\}}_{k=1}^K}\left[\sum _{S_k\in \{S_j{\}}_{j=1}^J}\sum _{z\in Z^f}{\widehat{\theta }}_{S_k}^z{\widehat{\beta }}_z^{F_k}\right]$$

(31)

At this point, the generation of a discrete physical structure set with implicit global coupling correlations can be accomplished by Bayesian inference.

4.3. Reasoning Method of ConceptTM Based on Sampling

The core of ConceptTM’s generative inference is the Bayesian formula:

$$\mathcal{P}\left(\left\{S_j{\}}_{j=1}^J\right|\{T_i{\}}_{i=1}^I,\{F_k{\}}_{k=1}^K\right)\propto \mathcal{P}\left(\left\{S_j{\}}_{j=1}^J\right|\{T_i{\}}_{i=1}^I\right)\times \mathcal{P}\left(\left\{F_k{\}}_{k=1}^K\right|\{S_j{\}}_{j=1}^J\right)$$

(32)

In the formula, $\{T_i{\}}_{i=1}^I$ and $\{F_k{\}}_{k=1}^K$ are the given technology fields and functional requirements, and $\{S_j{\}}_{j=1}^J$ is the set of discrete physical structures that possess implicit correlations. The event space of the posterior distribution is a power set of all the physical structures, and if the technical fields and functional requirements that are conditions are also considered, then the total space will be so huge that it will not be possible to accurately obtain the probabilities of each subset. In this case, this study provides two methods for sampling the above distributions, namely Gibbs and Maximum A Posterior (MAP).

4.3.1. ConceptTM’s Gibbs Sampling

Gibbs sampling as an iterative algorithm can greatly reduce the computational complexity to obtain sampled samples that approximately obey the distribution. The specific process is shown in the following Algorithm 1:

Algorithm 1 Gibbs sampling of ConceptTM

$\mathbf{Input}: \mathrm{Posterior} \mathcal{P}\left(\left\{S_j{\}}_{j=1}^1\right|\{T_i{\}}_{j=1}^1,\{F_k{\}}_{k=1}^K\right)$

$\mathbf{Output}: \mathrm{Samples} {\mathcal{S}}_{\mathrm{G}}=\left\{\right\{S_{l,j}{\}}_{j=1}^L{\}}_{i=1}^L$

$\begin{array}{l}1:\hspace{1em}{\mathcal{S}}_{\mathrm{G}}\leftarrow \mathrm{\varnothing }\\ 2:\hspace{1em}\mathrm{S}\mathrm{e}\mathrm{t} \{S_j{\}}_{j=1}^J \mathrm{as} \mathrm{some} \mathrm{random} \mathrm{physical} \mathrm{concepts}\\ 3:\hspace{1em}\mathrm{f}\mathrm{o}\mathrm{r} l \mathrm{in} \mathrm{range}\left(1,\mathrm{L}\right) \mathrm{do}\\ 4:\hspace{1em}\hspace{1em}\mathrm{f}\mathrm{o}\mathrm{r} j \mathrm{in} \mathrm{range}\left(1,\mathrm{J}\right) \mathrm{do}\\ 5:\hspace{1em}\hspace{1em}\hspace{1em}\mathrm{S}\mathrm{a}\mathrm{m}\mathrm{p}\mathrm{l}\mathrm{e} S_{l,j}\sim \mathcal{P}\left(S_j\left|\right\{T_i{\}}_{i=1}^I,\{F_k{\}}_{k=1}^K,\{S_{j\prime }{\}}_{j\prime =1,j\prime \ne j}^J\right)\\ 6:\hspace{1em}\hspace{1em}\hspace{1em}{S}_j\leftarrow S_{l,j}\\ 7:\hspace{1em}\hspace{1em}\mathrm{e}\mathrm{n}\mathrm{d} \mathrm{f}\mathrm{o}\mathrm{r}\\ 8:\hspace{1em}\hspace{1em}\mathrm{A}\mathrm{d}\mathrm{d} {\left\{S_{l,j}\right\}}_{j=1}^J \mathrm{t}\mathrm{o} {\mathcal{S}}_{\mathrm{G}}\\ 9:\hspace{1em}\mathbf{end} \mathbf{for}\\ 10: \mathbf{return} \mathbf{Samples}{\mathcal{S}}_{\mathrm{G}}\end{array}$

4.3.2. ConceptTM’s MAP Sampling

MAP is a point estimation method in Bayesian statistics, and applying maximum a posteriori estimation to ConceptTM implies taking the posterior distribution $\mathcal{P}\left(\left\{S_j{\}}_{j=1}^J\right|\{T_i{\}}_{i=1}^I,\{F_k{\}}_{k=1}^K\right)$ of the set of discrete physical structures as the inference result:

$${\mathcal{S}}_M=arg\underset{\{S_j{\}}_{j=1}^J}{\mathrm{m}\mathrm{a}\mathrm{x}}\mathcal{P}\left(\left\{S_j{\}}_{j=1}^J\right|\{T_i{\}}_{i=1}^I,\{F_k{\}}_{k=1}^K\right)$$

(33)

Again, due to the large size of the event space, the following greedy Algorithm 2 was used for the approximate solution:

Algorithm 2 Greedy MAP Sampling of ConceptTM

$\mathbf{Input}: \mathrm{Posterior} \mathcal{P}\left(\left\{S_j{\}}_{j=1}^1\right|\{T_i{\}}_{j=1}^1,\{F_k{\}}_{k=1}^K\right)$

$\mathbf{Output}: \mathrm{Approximate} \mathrm{MAP} \mathrm{Estimation} {\mathcal{S}}_{\mathrm{G}}=\left\{\right\{S_{l,j}{\}}_{j=1}^L{\}}_{i=1}^L$

$\begin{array}{l}1:\hspace{1em}{\mathcal{S}}_{\mathrm{M}}\leftarrow \mathrm{\varnothing }\\ 2:\hspace{1em}\mathrm{f}\mathrm{o}\mathrm{r} \mathrm{j} \mathrm{i}\mathrm{n} \mathrm{r}\mathrm{a}\mathrm{n}\mathrm{g}\mathrm{e} \left(1,\mathrm{J}\right) \mathrm{d}\mathrm{o}\\ 3:\hspace{1em}\hspace{1em}{\mathrm{S}}_{\mathrm{j}}\leftarrow \mathrm{a}\mathrm{r}\mathrm{g}{\mathrm{m}\mathrm{a}\mathrm{x}}_{{\mathrm{S}}_{\mathrm{j}\prime }}\mathcal{P}\left({\mathcal{S}}_{\mathrm{M}}\cup \left\{S_{j\prime }\right\}\left|\right\{T_i{\}}_{i=1}^I,\{F_k{\}}_{k=1}^K\right)\\ 4:\hspace{1em}\hspace{1em}{\mathcal{S}}_{\mathrm{M}}\leftarrow {\mathcal{S}}_{\mathrm{M}}\cup \left\{S_j\right\}\\ 5:\hspace{1em}\mathrm{e}\mathrm{n}\mathrm{d} \mathrm{f}\mathrm{o}\mathrm{r}\\ 6:\hspace{1em}\mathrm{f}\mathrm{o}\mathrm{r} \mathrm{l} \mathrm{i}\mathrm{n} \mathrm{r}\mathrm{a}\mathrm{n}\mathrm{g}\mathrm{e} \left(1,\mathrm{L}\right) \mathrm{d}\mathrm{o}\\ 7:\hspace{1em}\hspace{1em}\mathrm{f}\mathrm{o}\mathrm{r} \mathrm{j} \mathrm{i}\mathrm{n} \mathrm{r}\mathrm{a}\mathrm{n}\mathrm{g}\mathrm{e} \left(1,\mathrm{J}\right) \mathrm{d}\mathrm{o}\\ 8:\hspace{1em}\hspace{1em}\hspace{1em} S_{l,j}\leftarrow \mathrm{a}\mathrm{r}\mathrm{g}{\mathrm{m}\mathrm{a}\mathrm{x}}_{S_{j\prime }}\mathcal{P}\left(\left\{S_{j\prime }\right\}\cup {\mathcal{S}}_M/\left\{S_j\right\}\left|\right\{T_i{\}}_{i=1}^I,\{F_k{\}}_{k=1}^K\right)\\ 9:\hspace{1em}\hspace{1em}\hspace{1em}\mathrm{U}\mathrm{p}\mathrm{d}\mathrm{a}\mathrm{t}\mathrm{e} {\mathcal{S}}_{\mathrm{M}} \mathrm{w}\mathrm{i}\mathrm{t}\mathrm{h} S_j\leftarrow S_{l,j}\\ 10:\hspace{1em} \mathbf{end} \mathbf{for}\\ 11: \mathbf{end} \mathbf{for}\\ 12: \mathbf{return} \mathbf{Estimation} {\mathcal{S}}_{\mathrm{M}}\end{array}$

At this point, ConceptTM has completed the entire training and reasoning process, realizing the generative design of a discrete physical structure set for products.

5. G-Designer: System Architecture Generation Based on Semantic Graph

5.1. Architecture of G-Designer

As can be seen from problem formulation, G-Designer, as a knowledge-based system architecture generation method, consists of a knowledge base G-Base and a knowledge inference engine G-Infer:

$$\mathrm{G}-\mathrm{Designer}=\{\mathrm{G}-\mathrm{B}\mathrm{a}\mathrm{s}\mathrm{e},\mathrm{G}-\mathrm{I}\mathrm{n}\mathrm{f}\mathrm{e}\mathrm{r}\}$$

(34)

In the formula, the composition and construction method of G-Base has been introduced in the previous section. G-Infer is the executor of knowledge reasoning and is responsible for transforming the collection of discrete physical structures into physical architectures ($\mapsto$ indicates that the left side of the symbol represents the input and the right side represents the output):

$$\mathrm{G}-\mathrm{Infer}:{\mathbf{S}}_i\mapsto \mathrm{S}{\mathrm{G}-\mathrm{TCO}}_i,\mathrm{s}.\mathrm{t}.{\mathbf{S}}_i\subset \mathbf{S}$$

(35)

In the formula, S is the set of physical domains and S_i is a subset of them. G-Infer includes two implementation methods: one is knowledge reuse and the other is knowledge generalize.

Knowledge reuse refers to the feedback of possible physical architectures based on the correlation with the set of input discrete physical architectures by using the existing SG-TCO instances in G-Base as the output. The knowledge reuse-based reasoning method is called G-Searcher. G-Searcher does not generate new instances by itself, but the existing instances have been screened and certified, and its feasibility and reliability are highly guaranteed:

$$\mathrm{G}-\mathrm{Searcher}:{\mathbf{S}}_i\mapsto {\mathrm{SG}-\mathrm{TCO}}_i,\mathrm{s}.\mathrm{t}.{\mathbf{S}}_i\subset \mathbf{S},{\mathrm{SG}-\mathrm{TCO}}_i\in \mathrm{G}-\mathrm{Base}$$

(36)

Knowledge generalization refers to capturing the physical architecture to form patterns by learning patterns from a large number of instances in G-Base so as to complete the complementation of relationships between discrete physical structures and form the system architecture. The knowledge generalization mechanism is based on relational connectivity, so the reasoning method is called G-Connector:

$$\mathrm{G}-\mathrm{Connector}:{\mathbf{S}}_i\mapsto {\mathrm{SG}-\mathrm{TCO}}_i,\mathrm{s}.\mathrm{t}.{\mathbf{S}}_i\subset \mathbf{S},V_c\left({\mathrm{SG}-\mathrm{TCO}}_i\right)={\mathbf{S}}_i$$

(37)

In the formula, Vc(SG TCO_i) represents the set of physical structures at the component level of SG-TCO_i instances. The G-Connector complements the G-Searcher in that it can generate new SG-TCO instances on its own, providing greater potential for innovation.

5.2. Knowledge Infer Method of G-Designer

5.2.1. G-Searcher Based on Knowledge Reuse

G-Searcher is a reasoning method based on knowledge reuse, whose main reasoning task is to find instances corresponding to a given set of discrete physical structures from G-Base, which essentially constructs a correlation between two structures:

$$\{S_i{\}}_{i=1}^I\mapsto \mathrm{SG}-\mathrm{TCO},s.t.\forall i,S_i\in \mathbf{S}, \mathrm{SG}-\mathrm{TCO}\in \mathrm{G}-\mathrm{Base}$$

(38)

In this study, two correlation calculation methods, node symbol similarity and structural semantic similarity, are used.

(1) Node symbol similarity calculation

Calculating the similarity of the set of physical structures contained in an instance to a given set of physical structures can be performed using the Jaccard coefficient:

$$\mathrm{J}\mathrm{a}\mathrm{c}\mathrm{c}\mathrm{a}\mathrm{r}\mathrm{d}(\{S_i{\}}_{i=1}^I,\mathrm{SG}-\mathrm{TCO})={\displaystyle \frac{\left|\right\{S_i{\}}_{i=1}^I\cap \left\{S_j{\}}_{j=1}^J\right|}{\left|\right\{S_i{\}}_{i=1}^I\cup \left\{S_j{\}}_{j=1}^J\right|}}$$

(39)

Or using the Dice factor:

$$\mathrm{D}\mathrm{i}\mathrm{c}\mathrm{e}(\{S_i{\}}_{i=1}^I,\mathrm{SG}-\mathrm{TCO})={\displaystyle \frac{2\left|\right\{S_i{\}}_{i=1}^I\cap \left\{S_j{\}}_{j=1}^J\right|}{\left|\right\{S_i{\}}_{i=1}^I|+|\left\{S_j{\}}_{j=1}^J\right|}}={\displaystyle \frac{2\left|\right\{S_i{\}}_{i=1}^I\cap \left\{S_j{\}}_{j=1}^J\right|}{I+J}}$$

(40)

It can be seen that the node symbol similarity is characterized by precise matching; however, the structural relationship between the underlying physical structures is ignored and the fact that different structures may not contribute the same to the instance as a whole is not taken into account.

(2) Structural Semantic Similarity Calculation

Different underlying physical structures contained in a product play different roles and have different degrees of importance, and this different importance can be calculated through the component semantic graph.

Therefore, the first step in structural semantic similarity computation is to utilize the semantic graph information of instances to assign different contribution weights to different underlying physical structures [117]. In this study, the node degree in the undirected graph model is used as an evaluation metric, which is normalized to obtain the importance weights:

$$\forall j\in [1,\cdots ,J]:w_j={\displaystyle \frac{d_j}{\sum _{j=1}^J{d}_j}}$$

(41)

Second, the semantic correlation of two structures is computed based on semantic correlations. After obtaining the importance weights, the correlation between a given set of physical structures and SG-TCO instances can be calculated as follows:

$$\begin{array}{cc}\hfill \mathrm{R}\mathrm{e}\mathrm{l}\mathrm{e}\mathrm{v}\mathrm{a}\mathrm{n}\mathrm{c}\mathrm{e}\left(\right\{S_i{\}}_{i=1}^I,\mathrm{S}\mathrm{G}-\mathrm{T}\mathrm{C}\mathrm{O})& =\left({\displaystyle \sum _{i=1}^I}{w}_i\mathbf{v}\right(S_i\left){)}^{\mathrm{\top }}\right({\displaystyle \sum _{j=1}^J}{w}_j\mathbf{v}\left(S_j\right))\hfill \\ & ={\displaystyle \sum _{i=1}^I}{\displaystyle \sum _{j=1}^J}{w}_i{w}_{j}v\left(S_i{)}^{\mathrm{\top }}v\right(S_j)\hfill \\ & ={\displaystyle \sum _{i=1}^I}{\displaystyle \sum _{j=1}^J}{w}_i{w}_j\kappa (S_i,S_j).\hfill \end{array}$$

(42)

In the formula, $\kappa (S_i,S_j)$ is the synthesized semantic correlation between two physical elements, including contextual semantic correlation and morphological semantic correlation:

$$\kappa \left(e_i,e_j\right)=\beta {\kappa }_c\left(e_i,e_j\right)+\left(1-\beta \right){\kappa }_m\left(e_i,e_j\right)\in \left[\mathrm{0,1}\right],\beta \in \left[\mathrm{0,1}\right]$$

(43)

• Calculating contextual semantic correlation s${\kappa }_c(e_i,e_j)$ based on Skip-gram.

The principle of the Skip-gram model lies in the use of central words to predict their contextual correlations [118]. In this study, the full text of patent text is utilized to train the Skip-gram model so as to obtain the contextual semantic vectors of all the relevant knowledge elements [119]. After the training is completed, the contextual semantic correlations between the knowledge elements can be calculated based on the following normalized cosine similarity:

$${\kappa }_c(e_i,e_j)=({\displaystyle \frac{{\mathbf{v}}_i^{\mathrm{\top }}{\mathbf{v}}_j}{\parallel {\mathbf{v}}_{\mathbf{i}}\parallel \parallel {\mathbf{v}}_j\parallel }}+1)/2\in [0, 1]$$

(44)

In the formula, e represents the knowledge element and v represents the corresponding contextual semantic vector.

• Computing morphosyntactic correlations ${\mathsf{\kappa }}_{\mathrm{s}}^{\mathrm{n}}(\mathrm{s},\mathrm{t})$ based on string kernel [120].

The construction of terms ensures the existence of morphosyntactic correlations between knowledge elements. String kernel refers to a function that is used to compute the similarity between strings by mapping the substrings of the strings into a high-dimensional feature space, where the similarity between the strings is computed using the inner product in the feature space:

$${\kappa }_s^n(s,t)={\displaystyle \frac{{\varphi }_n\left(s{)}^{\mathrm{\top }}{\varphi }_n\right(t)}{\parallel {\varphi }_n\left(s\right)\parallel \parallel {\varphi }_n\left(t\right)\parallel }}\in [0, 1]$$

(45)

ϕ_n(s) and ϕ_n(t) represent the feature vectors of strings s and t in the feature space constructed by the substrings of length n. Since the length of Chinese terminology vocabulary is usually short and the size of the character set is large, this study will use string kernels with n = 1 and n = 2 and weight both of them to obtain the morphosyntactic correlations between the knowledge elements:

$${\kappa }_m(e_i,e_j)=\alpha {\kappa }_s^1(e_i,e_j)+(1-\alpha ){\kappa }_s^2(e_i,e_j)\in [0, 1]$$

(46)

In the formula, α ∈ [0, 1] is the adjustable weight parameter.

So far, the G-Searcher inference process based on knowledge reuse is completed, and the system architecture search and recommendation of the existing relevant SG-TCO instances is realized.

5.2.2. G-Connector Based on Knowledge Generalization

G-Connector is a knowledge generalization-based reasoning approach that speculates on the system architecture for a given collection of discrete physical structures based on connection patterns between physical structures learned from training data:

$$\{S_i{\}}_{i=1}^I\mapsto \mathrm{S}\mathrm{G}-\mathrm{TCO},s.t.\forall i,S_i\in \mathbf{S},V_c(\mathrm{G}-\mathrm{TCO})=\{S_i{\}}_{i=1}^I$$

(47)

The G-Connector inference generation process is divided into two parts: component semantic graph generation and module division.

The key to constructing the component semantic graph lies in judging the strength of semantic correlations between the underlying physical structures, and this study adopts contextual semantic correlations to calculate the strength of semantic correlations between the underlying physical structures:

$${\widehat{A}}_{i,j}={\widehat{A}}_{j,i}=\left\{\begin{array}{ll}{\kappa }_c(S_i,S_j),& i\ne j,\\ \\ 0,& i=j.\end{array}\right.$$

(48)

Once the semantic component graph is constructed, the community detection algorithm (in Section 3) is utilized to delineate the modules in it, thus constructing a complete example of the system architecture.

6. Platform Development, Case Study, and Discussion

6.1. Training and Case Study of ConceptTM

6.1.1. Training and Evaluation of ConceptTM

In order to obtain the best performance, several ConceptTM models are trained under different hyperparameter settings, and then the best one is selected according to the evaluation index. In ConceptTM, the hyperparameters that have the greatest impact on the performance of the model are the number of topics in the technical–physical part |Z^S| and the number of topics in the physical–functional part |Z^F|. The performance of ConceptTM is evaluated using the degree of perplexity [68] and coherence [115]. The degree of perplexity refers to the degree of unfamiliarity of the model with the data sample set. Coherence refers to the degree to which the model fits the data sample set. The smaller the model perplexity and the higher the coherence, the better the performance. The specific index calculation method can refer to the references. A total of 80% of the data in K_B is used as the model training set, and the remaining 20% is used as the model test set. During the training process, 7 models of the technical–physical part and 7 models of the physical–functional part were obtained, respectively, so a total of 49 ConceptTM models were obtained. All the model instances are trained on the training set, and the evaluation index is calculated on the test set. The results are shown in Figure 7 and Figure 8.

It can be seen from the evaluation results that the concepttm model with the best performance should take |Z^S| = 10 and |Z^F| = 50.

6.1.2. A Case Study of ConceptTM

Take a simple robot design as an example. Firstly, the technical field (IPC code) of the robot is determined as A61B. Secondly, set four related functional requirements, including “robot”, “material”, “grab”, and “move”, to indicate the need to design a mobile robot for grabbing materials. The required discrete physical structure set size is 10. Under the above settings, the reasoning results obtained by ConceptTM through Gibbs sampling and MAP are shown in

Table 1. The outputs of ConceptTM in the design case “a mobile robot for grabbing materials”.

Technical Field	A61B
Functional Requirements	Robot Material Grab Move
Reasoning Methods	Gibbs Sampling			MAP
Physical Structure	Bracket	Protective cover	Horizontal board	Protective cover
	Shell	Feed pipe	Compression spring	Spring
	Storage box	Articulated axis	Rotating axis	Axis
	Water tank	Screw	Slider	Shell
	Protective box	Exhaust port	Piston rod	Slider
	Motor	Servo motor	Guide	Base
	Partition	Ruler	Angle sensor	Motor
	Scroll	Guiding pulley	Driving axis	Fixed board
	Cavity	Charging port	Cavity	Supporting board
	Storage cabinets	Main body	Regulating screw	Assembly table

.

Since a large number of samples can be obtained through Gibbs sampling, the table shows the last three samples taken from 100 rounds of sampling. It can be seen that Gibbs sampling is more diversified, and MAP can provide more stable results. Most of the physical structures obtained belong to mechanical parts (base, support, shell, various “boxes” and “plates”), which can be used to assemble the body of the robot. “Motor”, “servo motor”, and “charging port” can be used as mechanical power and energy sources. The robot posture can be measured by “angle sensor”, and can be adjusted by various driving media (spring, slider, guide rail, etc.). It can be proved that ConceptTM can realize the generation of physical structure, which means that ConceptTM can indeed provide practical design inspiration.

Next, verify that ConceptTM can realize the integration of technical fields. ConceptTM can perform explicit technology field integration, mainly because it clearly divides the technology fields from other design concepts based on the three-domain model. Still taking the robot design as an example, in addition to the basic electromechanical execution ability, the current high-tech robots are expected to have interactive perception ability. Therefore, in addition to the above basic technical fields and functional requirements, we also added the settings related to vision (G06K was added in the technical field, and “vision” and “image” were added in the functional requirements). The results are shown in

Table 2. The outputs of ConceptTM implementation technical field integration.

Technical Field	+G06K
Functional Requirements	+Vision, +Image
PhysicalStructure	Fixed board, protective cover, spring, camera, motor, shell, base, controller, slider, and support column

.

In order to stabilize the results and facilitate comparison, only the knowledge reasoning method based on map estimation is used here. It can be seen that in addition to the general electromechanical components previously obtained, “camera” and “controller” are added to the reasoning results. ConceptTM does add the physical structure of visual processing to the robot as needed, which means that the implementation of technology integration in ConceptTM is successful.

6.2. Platform Development

Intelligent Design Assistant (IDA), a generic-field design knowledge service system, was developed by integrating the knowledge base and the generative generic-field design method obtained in this study into the software, and adopting a convenient user interaction interface design. The main operation interface of the software is shown in Figure 9. Inspired by ChatGPT, IDA adopts the method of “Dialog Interaction, Command Input”, which allows designers to input commands in a certain format to have a dialog with IDA. The main operation interface of IDA mainly consists of two parts: the dialog display part and the command control part.

There are four access objects in IDA, namely:

• Access object @IDA, which is used for the introduction of the system;
• Access object @ConceptTM, which is used to call ConceptTM reasoning interface;
• Access object @GDesigner, for calling GDesigner reasoning interface;
• Access object @PSearcher for patent searching.

6.2.1. @ConceptTM Command System

Entering the command “@ConceptTM: Help”, the system replies are shown in Figure 10. What can be seen is that in addition to the help command, @ConceptTM also gives two other commands, namely the MAP command and the Gibbs command. The results of MAP inference are fixed under the same command, while the results of Gibbs sampling are more diverse.

6.2.2. @G Designer Command System

Entering the command “@GDesigner: Help”, the system replies are shown in Figure 11. What can be seen is that besides the help command, @GDesigner also gives four other commands, which are the Set Mode command, the G-TCO command, the Search command, and the Connect command.

• The “Modes” are the methods used by G-Designer to calculate the correlation between physical structures, and there are three of them: contextual semantic correlation (the default method), morphological semantic correlation, and synthesized semantic correlation.
• The G-TCO command is the retrieval and visualization of SG-TCO instances from G-Base, idx is the number of instances to be viewed, and alg is the module partitioning method used (Louvain/Infomap). The system response to the command will be divided into two parts, the component semantic graph of the instance and the individual module subgraphs.
• An example of G-Seacher reasoning is shown in Figure 12. The system reply contains the number (“#37764”) and the title (“A New All-in-One Microbiological Testing Device”) of the corresponding instance, and the results of the specific SG-TCO instance visualization can be obtained via the instance view command.
• G-Connector inference uses the correlation calculation method set by “Set Mode” to calculate the correlation relationship between the provided physical structures and control a certain threshold (eps), and then utilizes the community detection method to classify the sub-modules therein.

6.2.3. @PSearcher Command System

Entering the command “@PSearcher: Help”, and the system replies are shown in Figure 13. In addition to the help command, @PSearcher also gives two other commands, namely, the patent search command “Search” and the patent content display command “Patent #”.

• The patent search command is used to search for patent documents that contain key conceptual elements. The corresponding patent number, title, and key design concepts are given in the system response.
• Once the number of a particular patent is obtained, designers can use the display command to view the specific contents of the patent, including the textual parts and abstract drawings.

6.3. Case Study

The application of the methodology and software system proposed in this study is demonstrated by the design of “a product that helps people to move objects”. The scope of the original requirement is very broad, and only one basic requirement is mentioned: “to move objects”. The designer can use “moving” as the basic functional requirement concept to explore the requirements and further define the basic function of the product: it can move freely and handle objects, and its corresponding general physical form is a vehicle with robotic arms and manipulators. At the same time, the technical fields of the product to be designed are identified as B25J (mainly related to industrial robots) and B62D (mainly related to vehicle construction).

Based on the acquired basic technical fields, physical structures, and functional requirements, the designer can utilize PSearcher to conduct patent searches. They can run the command “@PSearcher: Search maxn = 10 tech B25J B62D phys robot robot arm vehicle func handling handling robot handling vehicle”, and its system reply is shown in Figure 14.

Based on the above results, the designer can run the command “@PSearcher: Patent #idx” to view the profile of the relevant patent for inspiration. Figure 15 shows the brief introduction and figures for patent #135233. It can be seen that the patent fits the basic features of the product to be designed: an on-board robotic arm and a gripper, thanks to the accuracy of the underlying design concepts derived from the above reasoning.

Patent #135233 can be used as a reference for the basic form of the product to be designed, but it does not describe the physical architecture of the key component, the gripper, so the next step is to consider using a generative approach to complete the design of this component. Using ConceptTM to generate a discrete set of physical structures and running the command “@ConceptTM: MAP maxn = 10 tech B25J func Gripping Release Clamping Driving Torque”, the system response is shown in Figure 16.

Among the 10 physical structures, some of them are selected as the core components. After obtaining the set of discrete physical structures, G-Designer is utilized to generate the architecture by running the command “@GDesigner: Connect eps = 0.8 alg = louvain phys Motor Worm Gear Clamp Claw Fixed Pin Bracket Shaft” and the result is shown in Figure 17.

It can be seen that the “mechanical claw” mainly includes two Louvain modules, one is the power module (“motor”, “shaft”, “worm”, and “bracket”), and the other is the clamping claw module (“clamping claw”, “fixing pin”, and “gear”). The basic working principle of the “mechanical claw” is that the “motor” drives the “shaft” to rotate, the “shaft” drives the “worm”, the “worm” drives the “gear” (according to the general mechanical structure, this actually refers to the “turbine”), the “gear” drives the “clamping claw”, and the “bracket” and “fixing pin” play the role of fixation and support.

In order to show the final product more clearly, Figure 18 shows the Lego3D model of the “mechanical claw” (some connecting and supporting parts on the view side have been removed in order to see the internal structure), and Figure 19 shows the Lego3D model of the final product “Mechanical Moving Trolley” and its three views. It should be noted that the Lego model does not have any obvious “motor” parts, but the first and second transmission parts that should be connected to the motor are marked in red and orange, such as the “shaft”, “worm”, and “gear” (“turbine”) in the “mechanical claw”.

6.4. Discussion

(1) Performance of ConceptTM

ConceptTM adopts the PGM, especially the infrastructure of the topic model, to systematically express the complex and implicit correlations among physical structures. The advantages of ConceptTM’s features and capabilities are summarized as follows:

• Based on the topic model architecture, ConceptTM can express global coupling correlations among knowledge elements, which is superior to general fragmented knowledge representation models.
• With the help of design theory and cognitive theory, ConceptTM reveals the causal relationships among three basic types of design concepts, i.e., technical fields, physical structures, and functional requirements.
• ConceptTM is able to perform the topic clustering of physical structures, thus mining the internal features of design concepts. Further, it is capable of accomplishing the generation of discrete physical structure collections with implicit correlations for the conceptual design of physical architectures.
• ConceptTM is capable of explicitly performing technical field fusion, providing a source of innovation for engineering design.

(2) Performance of G-Designer

G-Base obtained a total of 38,473 SG-TCO instances, 149,270 Louvain community modules, 143,397 Infomap community modules, and 544,714 cluster modules. On average, each SG-TCO instance has 3.88 Louvain community modules, 3.73 Infomap community modules, and 14.16 cluster modules.

In the case study, the ability to obtain a clear division of labor between modules is not only the ability of the community detection algorithm, but also an effect of the component semantic graph that captures the underlying physical structures in a certain way. The successful realization of the generative design example proves the following three points: first, the reasonableness of the SG-TCO representation of the product hierarchical system architecture; second, the effectiveness of the G-Base construction method; and third, the feasibility and innovation of the G-Infer architecture generation method.

7. Conclusions

In summary, this study solved a series of problems of generative generic-field design in the context of large language model (LLM) and Crowd Intelligent Innovation (CII). In addition, by improving the utilization efficiency of data resources and putting forward the innovation mechanism in line with design cognition, this research promotes the sustainable innovation generation mode in the field of engineering design [121].

By analyzing the actual needs of designers, combining cognitive science and knowledge engineering, and based on the design cognitive process model, this study proposes a generative generic-field design method. ConcepttTM is based on the Bayesian brain hypothesis. The technical field provides a priori and functional requirements providing the likelihood to complete Bayesian reasoning, and generates a set of discrete physical structures with implicit systematic correlation. G-Designer constructs the architecture knowledge base of patents based on the improved SG-TCO model using a graph algorithm, and generates the system architecture for a given set of discrete physical structures based on the mechanisms of “knowledge reuse” and “knowledge generalization”.

In the course of this research, the development of AI technology has reached a new level: the emergence of ChatGPT has shown the world that “the future is here”. However, ChatGPT is a general-purpose language model, which only has advantages in general text understanding and generation.

In the field of engineering design, generative design based on LLM still has two shortcomings: the design results are considered to lack feasibility, and the output of the model lacks empathy with the designer and design context. The design process has poor interpretability and lacks support from the design cognitive theory. Compared with related models such as ChatGPT and BingChat, the generative generic-field design method proposed in this study can summarize the following three contributions in terms of originality, theoretical significance, and practical significance:

• In the fields of conceptual design and engineering design, the research gap of generative generic-field design methods has been supplemented.
• Proposed a design framework that conforms to the new context of design cognition, formed a knowledge representation model and process model that supports generative generic-field design, and reflected the completion and empathy of fuzzy original requirements.
• Implemented generative design for generic-field problems, outputting a set of design structures containing modular themes and implicit associations, as well as design result layouts and system architectures that meet engineering feasibility.

This does not mean that similar work cannot be carried out in the field of engineering design; therefore, this paper concludes with the following research outlook:

• The construction of a large professional knowledge base: The knowledge base related to engineering design currently displayed in the academic world is still “too small”, which includes the problem of the type of knowledge in addition to the insufficiency of quantity. Engineering design itself is a task involving rich types of knowledge, including the knowledge of natural language, image visualization, symbolic formulas, computer 2D/3D models, and so on. Therefore, the construction of a large quantity and high-quality multimodal engineering design knowledge base must be a future consideration in this field.
• Realization and innovation of specialized knowledge reasoning methods: At a time when AI technology is so advanced, it has provided relevant researchers with a rich variety of algorithms that can be used; however, generalized methods do not necessarily fully meet the needs of the task of engineering design. Therefore, the development of specialized knowledge reasoning methods in line with engineering design remains a must for future research, with generative methods being a top priority. At the same time, in order to compare and evaluate the advantages and disadvantages of different reasoning methods, the engineering design field also needs to construct the corresponding evaluation index system and benchmark dataset, which lays the foundation for the synergistic development of reasoning methods.
• The development and application of interaction technology: Although engineering designers have certain professional abilities, more convenient interaction technology can completely reduce the issues of engineering designers in the learning of design tools, applications, and other cognitive and use loads [122]. This will greatly improve work efficiency, to a certain extent, due to reducing the burden on the brain which can also stimulate the innovation ability of designers. Based on this consideration, therefore, continuing to explore the development and application of interactive technology in the field of engineering design is also one of the directions that can be continuously focused on in the future.