Quantitative Modeling and Standardized Representation of Hierarchical Product Gene Structures for New Energy Vehicles

Abstract

Complex products continue to face low iterative-design efficiency and poor cross-generation data compatibility, while existing product-gene research is still constrained by the predominance of qualitative approaches, ambiguous representations of hierarchical associations, and insufficient standardization. Based on the principles of decomposition and reconstruction and the systems thinking of genetic engineering, this study develops a generic three-level framework for product genes at the platform, assembly, and component levels. Hierarchical mapping functions and parameter-constraint equations are introduced to enable quantitative representation, and a quantitative product-gene information system is established, including a core-parameter quantification model and inter-/intra-level association-strength models. By integrating multiple international standards, the study further constructs a tripartite standardized description system covering metadata, semantics, and format, and proposes a mathematical mapping method from product information to standardized formats. A case study of Company A’s Platform B and Concept Vehicle C shows that the association-strength model achieves the required adaptation threshold, thereby validating the proposed framework. This study provides quantitative theoretical support for the platform-based and intelligent development of complex products and offers an implementable technical solution for product-gene reuse and data sharing, particularly in the new energy vehicle industry.

1. Introduction

Against the ongoing background of intelligent manufacturing and digital transformation, new energy vehicle (NEV) product development increasingly exhibits a product-family genealogy characterized by the rapid derivation of multiple variants and configurations under platform-based and modular development in response to fast iteration cycles and diversified market demand [1]. This trend has significantly increased the complexity of knowledge inheritance, cross-generation reuse, and cross-team collaboration in product development.

Enterprises must not only reuse structures and parameters across vehicle models and variants, but also maintain consistency in design intent, constraint relationships, and interface logic across heterogeneous software systems and organizational boundaries.

Research on product families and modular design has evolved from early structural decomposition toward systematic frameworks for architecture planning and reuse, thereby forming a relatively complete foundation for module partitioning, architecture organization, and product-family design [2]. However, high-value knowledge such as design intent, parameter constraints, and associative logic remains difficult to abstract into unified, computable, and reusable knowledge units. As a result, engineering practice continues to face problems such as semantic loss, unclear reuse boundaries, and limited verifiability of consistency [3]. To address the challenge of unified knowledge reuse, product-gene theory organizes design knowledge into structured reusable units, thereby providing a new perspective for the representation and reuse of complex product knowledge [4]. Yet when it is applied to highly coupled and complex engineering products such as NEVs, three key challenges remain. First, although product-family and modular-architecture research has produced relatively systematic frameworks and methods, the division of platform, assembly, and component levels still tends to rely on structural decomposition or experiential conventions, while verifiable and reusable quantitative boundary definitions and cross-level constraint representations remain insufficient. This makes it difficult for the same knowledge to be transferred and reused stably across different platforms [5]. Second, because interfaces, parameters, and constraints are intricately coupled both within and across hierarchical levels, the absence of computable association-strength models hinders the establishment of consistent and repeatable criteria for compatibility assessment, reuse decision-making, and change-impact analysis [6]. Third, the lack of a unified standardized description system for cross-platform sharing results in low interoperability, leaving design data isolated across software systems and enterprises and creating significant barriers to data sharing [7].

To address these issues, this study takes new energy vehicles as an example and proposes a quantitative modeling and standardized description method for hierarchical product-gene structures in complex products. The proposed method is further validated through empirical analysis to demonstrate its effectiveness in compatibility assessment for complex systems and in cross-platform interaction.

2. Related Work

Existing studies can generally be summarized into two interrelated streams. One focuses on product modular organization and explores the representation, recombination, and evaluation of reusable knowledge units. The other focuses on product-data exchange, standard implementation, and cross-system interoperability, gradually advancing engineering practice from structural connectivity toward semantic interoperability. The former determines how knowledge content is represented and organized, whereas the latter determines how knowledge objects can be reliably exchanged, validated, and reused across systems. Together, they constitute the foundational framework for the reuse and sharing of complex product knowledge.

2.1. Current Research Status on Product-Gene Representation and Quantitative Modeling

With continuing advances in parameter quantification and association representation, product-gene theory has gradually moved from its initial concept—originally inspired by biological genetics—toward engineering implementation, and has been explored in a variety of representative engineering tasks [8]. For example, in quality tracking and closed-loop quality management, Xu et al. abstracted key knowledge of complex products into reusable gene units and applied them to quality tracking and comprehensive evaluation in equipment manufacturing, thereby demonstrating a feasible path from gene-based representation and computation to practical application [9]. In remanufacturing contexts, some researchers have introduced knowledge-graph approaches to model retired mechanical-product genes in an integrated manner. By characterizing gene units and their combinational relationships, these studies strengthened cross-stage information organization and associative representation, thereby supporting closed-loop lifecycle management [10].

In innovation-design scenarios oriented toward iterative development and continuous evolution, researchers have increasingly focused on the digital representation of functional knowledge, gene coding, and the construction of association networks, so that cross-domain knowledge can be identified, retrieved, and recombined in a computable manner [11]. Some studies have concentrated on the digital representation and identification of functional genes, thereby promoting the transition of design knowledge from empirical description to structured and computable expression [12]. Others, working within the framework of technological parasitism, have reconstructed the product innovation-design process from the perspective of recombination between host and target genes, thus providing methodological support for the recombination, invocation, and transfer of gene units in innovation tasks [13].

These engineering applications indicate that product-gene research is shifting its focus from whether knowledge can be represented to how hierarchical gene structures can be represented in a measurable, computable, and reusable manner, while also attempting to systematize the extraction, construction, and innovation of functional genes [14]. However, when applied to complex product engineering, existing methods remain insufficient in several respects, particularly in the unified quantitative description of hierarchical structures, the coordinated representation of cross-level constraints, and the effective integration of standardized exchange semantics. Most current approaches still concentrate on task-specific or local-feature-level representation and application, and a general modeling framework for multi-level collaborative analysis of complex products has yet to emerge. This limitation is especially evident in highly coupled systems such as NEVs, which involve multiple interdependent subsystems and architectural decisions and therefore make it difficult to support coordinated analysis of platform-level transfer, assembly-level adaptation, and component-level parameter linkage [15]. Accordingly, establishing a quantitative model with clear boundaries, explicit constraints, and measurable associations across the platform–assembly–component hierarchy remains a critical step in translating product-gene theory into practical applications for complex product engineering [16].

2.2. Research Status on Standardized Description and Interoperability of Product Data

To meet the collaborative requirements of complex product engineering, the ISO 10303 (STEP) series provides a systematic framework for product-data representation and exchange, with application protocols such as AP242 serving as key standards for the exchange of model-based three-dimensional engineering data [17]. In parallel, to support conformance verification and interoperability testing in practical standard implementation, the U.S. National Institute of Standards and Technology (NIST) has continuously released tools for STEP parsing, visualization, and consistency checking, thereby providing an operational engineering pathway for validating data exchange and integration across heterogeneous system environments [18]. Overall, research and practice have established relatively mature capabilities for data exchange at the format and structural levels; however, support remains limited for the explicit representation of multi-level constraints, cross-level parameter linkages, and rule semantics in complex products.

Recent studies and industrial practice further indicate a shift from mere data exchange toward semantic interpretability, alignability, and reuse. Knowledge-graph-based methods, for instance, have been employed to integrate lifecycle data across design and inspection stages, thereby enhancing semantic association, traceability, and consistency verification [19]. Moreover, semantic-enhancement studies of STEP product models have begun to map STEP schemas and instances into computable semantic representations through ontology-based transformation, thereby strengthening semantic integration and knowledge reuse across heterogeneous system environments [20]. Nevertheless, systematic methodologies for establishing a unified mapping between high-level, design-reuse-oriented knowledge—such as product genes—and international standard formats and semantic description mechanisms remain lacking, particularly in relation to the multi-level constraints and rules embodied in complex products. Therefore, constructing an expressive framework for complex product-gene structures that simultaneously supports hierarchical quantitative modeling and alignment with standardized representations has clear theoretical significance and practical engineering value.

2.3. Research Contributions

Building on the above review, this study introduces the systems thinking of genetic engineering to systematically justify the hierarchical framework in terms of both theoretical connotation and feature compatibility, thereby strengthening the theoretical foundation of product-gene research. A generic three-tier quantitative hierarchy of platform, assembly, and component genes is constructed, together with hierarchical sets, mapping functions, and explicit quantitative boundary constraints, so as to shift hierarchical delineation from qualitative judgment to quantitative definition. A full-hierarchy core-parameter quantification system and a dual-dimensional association-strength model (inter-level and intra-level) are then established to characterize constraints and collaborative relationships through mathematical formulations, thereby overcoming the limitations of traditional qualitative association analysis. By integrating international standards, the study further develops a tripartite standardized description system consisting of metadata, semantics, and format, together with a mathematical mapping method from product-gene information to standardized data formats, thereby addressing cross-platform sharing challenges. Finally, an empirical study based on Company A’s Platform B validates the effectiveness of the proposed system in complex-system compatibility assessment and cross-platform interaction.

3. Model Construction and Analysis

3.1. Problem Description

The core idea of genetic engineering is to achieve directed improvement of biological traits through hierarchical analysis, hereditary regulation, and evolutionary optimization of biological information at the genome-gene-nucleotide levels. Its essential characteristics include hierarchy, heredity, evolvability, and systemicity. In this study, however, the term product gene is not treated as a direct transplantation of biological genetic mechanisms into engineering systems. Instead, it is used as an engineering knowledge-organization concept inspired by the ideas of hierarchical organization, information carrying, stable inheritance, and controllable variation [21]. The focus of this study is therefore to transform complex product design knowledge into engineering objects with hierarchical boundaries, parameter constraints, and standardized descriptive capability, rather than to establish a strict biological genetic model. The correspondence is shown in

Table 1. Product-gene concept mapping.

Biological-Gene Concept	Engineering Meaning in Product Genes	Implementation in This Model
Heredity	Reuse of platform architectures, interface rules, and core parameters across vehicle models	Constraint mapping from platform genes to assembly genes
Variation	Adjustment of assembly or component parameters within the allowable constraint range	Deviation of cost-type, benefit-type, and interval-type indicators
Selection	Elimination of schemes that fail to satisfy threshold requirements	Association-strength threshold judgment
Adaptation	Matching between assemblies/components and platform requirements	Inter-level compatibility judgment
Evolution	Iteration and updating of platforms and assemblies with technological development	Version number, lifecycle, and parameter-update mechanism

.

From the perspective of theoretical-content adaptability, the design and iterative evolution of complex products can be understood as the inheritance, adjustment, and recombination of core design knowledge [22]. This process has a certain structural similarity to biological genes in terms of hierarchical organization, information inheritance, and variation-selection logic. The biological genome can be used as a heuristic analogy for the product platform gene, which describes the top-level architecture and core technological boundary of a product family; the biological gene can correspond to the assembly gene, which describes a functionally aggregated unit that inherits platform constraints and realizes subsystem functions; and the nucleotide can correspond to the component gene, which describes the minimal structural and parameter unit supporting functional realization. This correspondence provides a heuristic basis for the hierarchical organization of complex product design knowledge, while the subsequent modeling in this study is mainly grounded in engineering logic such as product architecture, parameter constraints, and interface compatibility [23].

From the perspective of feature alignment, the fundamental characteristics of genetic engineering closely correspond to the core attributes of product genes. (1) Heredity: biological genes stably transmit parental traits through genetic material, whereas product genes enable the cross-generational reuse of core technological features through key parameters and architectural design (e.g., shared platform-gene architecture parameters across different NEV models). (2) Evolvability: biological genes adapt to environmental changes through mutation, whereas product genes respond to market upgrading and technological breakthroughs through parameter optimization and architectural iteration (e.g., iterative improvements in the energy density of power-battery genes). (3) Systemicity: hierarchical biological genes work synergistically to sustain organismal function, whereas product genes achieve functional coordination and overall performance optimization through bidirectional constraint–feedback associations. (4) Hierarchicity: The layered organization of biological genes ensures orderly information transmission, while the three-tier platform–assembly–component structure of product genes ensures efficient reuse and iteration of core information. Moreover, the systemic regulatory logic of genetic engineering helps inform the organization of hierarchical associations in product-gene research and provides a useful theoretical reference for full-lifecycle management of product genes [24].

Based on the above rationale and following the principles of system decomposition, functional aggregation, and hierarchical association, a complex product system can be organized into a three-tier generic framework characterized by mutual constraints and coordinated evolution: the platform-gene layer (top level), the assembly–gene layer (middle level), and the component-gene layer (bottom level). This arrangement forms a hierarchical system in which the top level dominates, the middle level inherits, and the bottom level supports (Figure 1). The framework is applicable to a wide range of complex products, including mechanical, electronic, and electromechanical systems, and therefore has generalizable characteristics.

Explanation of Figure 1: The top-level platform gene defines the core technological boundaries of a product family and is characterized by cross-model shareability and long-term stability. The middle-level assembly gene represents a subsystem-level decomposition of platform-gene functions and provides modular adaptability. The bottom-level component gene serves as the minimal functional unit and supports the evolution of higher-level genes through standardized reuse. Bidirectional constraint–feedback relationships among the hierarchical levels establish a closed-loop evolutionary mechanism.

3.2. Quantitative Definitions of Hierarchical Structure

To overcome the limitations of purely qualitative hierarchical partitioning, the following quantitative definitions are proposed on the basis of set theory and function theory, thereby providing an explicit method for characterizing hierarchical boundaries and constraint relationships quantitatively.

Definition 1.

Product-gene hierarchical set. Let the product-gene hierarchical set be $\mathrm{G}=\{{\mathrm{G}}_0,{\mathrm{G}}_1,{\mathrm{G}}_2\}$, where $G_0$ denotes the platform-gene layer, $G_1$ denotes the assembly–gene layer, and ${\mathrm{G}}_2$ denotes the component-gene layer. The parameter space of genes at level $\mathrm{i}$ is ${\mathsf{\Omega }}_{\mathrm{i}}$ (${\mathsf{\Omega }}_{\mathrm{i}}\subseteq {\mathbb{R}}^{{\mathrm{n}}_{\mathrm{i}}}(\mathrm{i}=0,1,2)$, the set of all admissible values of the core parameters of level $\mathrm{i}$ genes, with dimensionality ${\mathrm{n}}_{\mathrm{i}}$). The hierarchy satisfies ${\mathsf{\Omega }}_2\subseteq {\mathsf{\Omega }}_1^{\ast }\subseteq {\mathsf{\Omega }}_0^{\ast }$, and ${\mathsf{\Omega }}_{\mathrm{i}}^{\ast }$ is the closure of the parameter space at level $\mathrm{i}$.

This definition quantitatively specifies the key relationship that the parameter space of lower-level genes is constrained by that of upper-level genes, thereby providing a quantitative basis for hierarchical compatibility.

Definition 2.

Hierarchical mapping function. The constraint imposed by an upper-level gene on a lower-level gene is represented by a hierarchical mapping function ${\mathrm{f}}_{\mathrm{i}}:{\mathrm{G}}_{\mathrm{i}}\to 2^{{\mathrm{G}}_{\mathrm{i}+1}}$ ($\mathrm{i}=\mathrm{0,1}$), where $2^{{\mathrm{G}}_{\mathrm{i}+1}}$ is the power set of ${\mathrm{G}}_{\mathrm{i}+1}$.

Based on Definition 2, the mapping relation satisfies Equation (1).

$${\mathrm{f}}_{\mathrm{i}}\left({\mathrm{g}}_{\mathrm{i}}\right)=\left\{{\mathrm{g}}_{\mathrm{i}+1}\in {\mathrm{G}}_{\mathrm{i}+1}|\forall \mathrm{p}\in {\mathrm{P}}_{\mathrm{i}+1}({\mathrm{g}}_{\mathrm{i}+1}),\hspace{0.33em}\exists \mathrm{q}\in {\mathrm{P}}_{\mathrm{i}}({\mathrm{g}}_{\mathrm{i}}),\mathrm{s}.\mathrm{t}.\hspace{0.33em}\mathrm{p}\in [\mathrm{q}-\mathsf{\Delta }\mathrm{q},\hspace{0.17em}\mathrm{q}+\mathsf{\Delta }\mathrm{q}]\right\}$$

(1)

In Equation (1), ${\mathrm{P}}_{\mathrm{i}}\left({\mathrm{g}}_{\mathrm{i}}\right)$ denotes the set of core parameters of the gene ${\mathrm{g}}_{\mathrm{i}}$ and $\mathsf{\Delta }\mathrm{q}$ denotes the constraint threshold of upper-level gene parameters, which is determined by product-design tolerances and technical specifications. Through parameter-threshold-based screening, the function quantitatively identifies compatible lower-level genes and thus enables precise representation of hierarchical constraints.

4. Construction of Product-Gene Information Quantitative Models

4.1. Core-Parameter Quantification System

Following the principles of functional dominance, parsimony and efficiency, quantifiability, and verifiability, a core-parameter quantification system covering all three hierarchical levels is constructed. For each level, parameters are defined with explicit quantitative indicators, units, and value ranges to ensure operational feasibility and engineering applicability.

4.1.1. Core Parameters Quantification System

Focusing on the architectural and system levels, the quantified parameters include: (1) architectural parameters, such as the architecture compatibility coefficient $\mathsf{\lambda }$ (range of 0–1, representing the number of adaptable product types, with values determined on the basis of national, industry, and enterprise standards) and the core dimensional interval $\mathrm{L}\in \left[{\mathrm{L}}_{\mathrm{m}\mathrm{i}\mathrm{n}},{\mathrm{L}}_{\mathrm{m}\mathrm{a}\mathrm{x}}\right]$ (mm); (2) performance parameters, such as the system efficiency $\mathsf{\eta }$ (range 0–1); and (3) integration parameters, such as the degree of interface standardization σ (range 0–1, indicating the degree of conformity between interfaces and international standards). To quantitatively represent parameter constraints, the core-parameter constraint equations for platform genes are formulated as Equation (2).

$$\left\{\begin{array}{c}\mathsf{\lambda }\ge {\mathsf{\lambda }}_{\mathrm{t}\mathrm{h}}\\ {\mathrm{L}}_{\mathrm{m}\mathrm{i}\mathrm{n}}\le \mathrm{L}\le {\mathrm{L}}_{\mathrm{m}\mathrm{a}\mathrm{x}}\\ \mathsf{\eta }\ge {\displaystyle \frac{{\mathrm{E}}_{\mathrm{o}\mathrm{u}\mathrm{t}}}{{\mathrm{E}}_{\mathrm{i}\mathrm{n}}}} \\ \mathsf{\sigma }\ge {\mathsf{\sigma }}_{\mathrm{t}\mathrm{h}}\end{array}\right.$$

(2)

In Equation (2), ${\mathsf{\lambda }}_{\mathrm{t}\mathrm{h}}$ denotes the threshold of architecture compatibility, $\mathrm{L}$ denotes the actual core dimension of the product, ${\mathrm{E}}_{\mathrm{i}\mathrm{n}}$ and ${\mathrm{E}}_{\mathrm{o}\mathrm{u}\mathrm{t}}$ denote the system input and output energies, and ${\mathsf{\sigma }}_{\mathrm{t}\mathrm{h}}$ denotes the threshold of standardization. The equation quantifies the constraint boundaries of platform genes from four dimensions: compatibility, dimension, energy efficiency, and standardization.

4.1.2. Core Parameters of Assembly Genes

Assembly genes primarily focus on the subsystem functional realization. Their quantifiable parameters include: (1) interface parameters, such as interface compatibility accuracy $\mathsf{\delta }$ (mm) and signal transmission latency $\mathsf{\tau }$ (ms); (2) performance parameters, such as subsystem power density $\mathsf{\rho }$ (kW/kg) and operating temperature interval ${\{\mathrm{T}}_{\mathrm{m}\mathrm{i}\mathrm{n}},{\mathrm{T}}_{\mathrm{m}\mathrm{a}\mathrm{x}}\}$ (°C); and (3) reliability parameters, such as mean time between failures (MTBFs, h) and failure rate ${\mathsf{\lambda }}_{\mathrm{f}}$ (times/h).

4.1.3. Core Parameters of Component Genes

Component genes mainly focus on individual performance and manufacturing attributes. Their quantified parameters include: (1) structural parameters, such as dimensional tolerance $\pm \mathsf{\epsilon }$ (mm) and mass $\mathrm{m}$ (kg); (2) material parameters, such as material strength ${\mathsf{\sigma }}_{\mathrm{m}}$ (MPa) and corrosion-resistance grade $\mathrm{C}$ (levels 1–5); (3) performance parameters, such as operating efficiency ${\mathsf{\eta }}_{\mathrm{c}}$ (range 0–1) and response speed ${\mathrm{v}}_{\mathrm{r}}$ (m/s); and (4) process parameters, such as machining precision $\mathsf{\gamma }$ (μm) and assembly tolerance $\pm \mathsf{\zeta }$ (mm).

4.2. Quantitative Model of Association Rules

To address the limitations of qualitative association analysis, quantitative models of inter-level and intra-level association strength are established to enable precise evaluation of association adaptability. Engineering compatibility is generally not a purely linear relationship: when the deviation is small, compatibility decreases slowly; when the deviation approaches or exceeds the engineering tolerance boundary, compatibility decreases rapidly; and when the deviation is far beyond the threshold, the marginal effect of additional deviation tends to stabilize. Therefore, compared with linear and step functions, the logistic function is more suitable for describing the engineering compatibility characteristics of rapid change near the threshold and slower marginal attenuation away from the threshold.

Definition 3.

Inter-level association strength. Let the association strength between the upper-level gene ${\mathrm{g}}_{\mathrm{i}}\in {\mathrm{G}}_{\mathrm{i}}$ and lower-level gene ${\mathrm{g}}_{\mathrm{i}+1}\in {\mathrm{G}}_{\mathrm{i}+1}$ be denoted by $\mathrm{S}({\mathrm{g}}_{\mathrm{i}},{\mathrm{g}}_{\mathrm{i}+1})$.

It is used to measure the extent to which the lower-level gene satisfies the upper-level gene constraints in terms of interfaces, performance, reliability, and other engineering requirements. According to indicator attributes, the indicators involved in the computation of inter-level association strength are divided into cost-type, benefit-type, and interval-type indicators. Their calculation methods are specified as shown in Equation (3a–c).

(1) Cost-type indicators. For this class, the difference between the actual value of the indicator and the platform constraint parameter is preferred to be as small as possible. The deviation degree can be expressed as $\mathrm{d}=(\mathrm{p}-{\mathrm{q}}_{\mathrm{p}})/△{\mathrm{q}}_{\mathrm{p}}$. Indicators such as compatibility accuracy and transmission latency fall into this category, and the association strength is defined by Equation (3a).

$$\mathrm{S}\left({\mathrm{g}}_{\mathrm{i}},{\mathrm{g}}_{\mathrm{i}+1}\right)={\displaystyle \frac{1}{1+{\mathrm{e}}^{-\mathsf{\alpha }\left(1-(\mathrm{p}-{\mathrm{q}}_{\mathrm{p}})/△{\mathrm{q}}_{\mathrm{p}}\right)}}}$$

(3a)

(2) Benefit-type indicators. For this class, the larger the difference between the actual value and the platform constraint parameter, the better. The deviation degree can be expressed as $\mathrm{d}=({\mathrm{q}}_{\mathrm{p}}-\mathrm{p})/△{\mathrm{q}}_{\mathrm{p}}$. Indicators such as power density and MTBF belong to this category, and the association strength is defined by Equation (3b).

$$\mathrm{S}\left({\mathrm{g}}_{\mathrm{i}},{\mathrm{g}}_{\mathrm{i}+1}\right)={\displaystyle \frac{1}{1+{\mathrm{e}}^{-\mathsf{\alpha }\left(1-\left({\mathrm{q}}_{\mathrm{p}}-\mathrm{p}\right)/△{\mathrm{q}}_{\mathrm{p}}\right)}}}$$

(3b)

(3) Interval-type indicators. These indicators are considered appropriate when their values fall within a specified interval. Attenuation begins only when one of the interval bounds is exceeded. The deviation degree can be expressed as $\mathrm{d}=\mathrm{m}\mathrm{a}\mathrm{x}({|\mathrm{q}}_{\mathrm{L}}-{\mathrm{p}}_{\mathrm{L}}|,{|\mathrm{p}}_{\mathrm{U}}-{\mathrm{q}}_{\mathrm{U}}\left|\right)$. If the lower bound is lower than the platform requirement, it is denoted by (${\mathrm{q}}_{\mathrm{L}}-{\mathrm{p}}_{\mathrm{L}}$); if the upper bound is higher than the platform requirement, it is denoted by (${\mathrm{p}}_{\mathrm{U}}-{\mathrm{q}}_{\mathrm{U}}$). Temperature-related indicators belong to this category, and the association strength is defined by Equation (3c).

$$\mathrm{S}\left({\mathrm{g}}_{\mathrm{i}},{\mathrm{g}}_{\mathrm{i}+1}\right)=\sum _{\mathrm{p}\in {\mathrm{P}}_{\mathrm{i}+1}\left({\mathrm{g}}_{\mathrm{i}+1}\right)} {\displaystyle \frac{1}{1+{\mathrm{e}}^{-\mathsf{\alpha }\left(\mathrm{d}/△{\mathrm{q}}_{\mathrm{p}}\right)}}}$$

(3c)

In Equation (3a–c), ${\mathrm{q}}_{\mathrm{p}}$ denotes the constraint parameter in the upper-level gene corresponding to $\mathrm{p}$, $\mathsf{\Delta }{\mathrm{q}}_{\mathrm{p}}$ denotes the threshold of ${\mathrm{q}}_{\mathrm{p}}$, and $\mathsf{\alpha }$ denotes the attenuation coefficient. According to parameter importance, α takes values from 2 to 5: 5 for core parameters and 2 for general parameters, with the choice calibrated through engineering practice. $\mathrm{S}\left({\mathrm{g}}_{\mathrm{i}},{\mathrm{g}}_{\mathrm{i}+1}\right)\in [0,{\mathrm{n}}_{\mathrm{i}+1}]$. When $\mathrm{S}\ge {\mathrm{S}}_{\mathrm{t}\mathrm{h}}$ (where ${\mathrm{S}}_{\mathrm{t}\mathrm{h}}=0.7\hspace{0.17em}{\mathrm{n}}_{\mathrm{i}+1}$) is the association threshold, determined with reference to industry norms for product-compatibility assessment, the two genes are judged to be compatible.

Definition 4.

Intra-level association strength. Let the intra-level association strength between two genes ${\mathrm{g}}_{\mathrm{i},\mathrm{j}},{\mathrm{g}}_{\mathrm{i},\mathrm{k}}$ at level i be denoted by ${\mathrm{S}}_{\mathrm{i}\mathrm{n}\mathrm{t}\mathrm{r}\mathrm{a}}({\mathrm{g}}_{\mathrm{i},\mathrm{j}},{\mathrm{g}}_{\mathrm{i},\mathrm{k}})$.

It is used to characterize the correlation between same-level genes in terms of parameter variation, functional synergy, or structural coupling. Based on the correlation between core parameter sets and functional weights, the intra-level association strength can be expressed by Equation (4).

$${\mathrm{S}}_{\mathrm{i}\mathrm{n}\mathrm{t}\mathrm{r}\mathrm{a}}\left({\mathrm{g}}_{\mathrm{i},\mathrm{j}},{\mathrm{g}}_{\mathrm{i},\mathrm{k}}\right)=\mathrm{C}\mathrm{o}\mathrm{r}\mathrm{r}\left({\mathrm{P}}_{\mathrm{j}},{\mathrm{P}}_{\mathrm{k}}\right)·{\mathsf{\omega }}_{\mathrm{j}}·{\mathsf{\omega }}_{\mathrm{k}}$$

(4)

In Equation (4), $\mathrm{C}\mathrm{o}\mathrm{r}\mathrm{r}({\mathrm{P}}_{\mathrm{j}},{\mathrm{P}}_{\mathrm{k}})$ denotes the Pearson correlation coefficient of the core-parameter sets of the two genes [25], with a value range of [−1, 1], and ${\mathsf{\omega }}_{\mathrm{j}},{\mathsf{\omega }}_{\mathrm{k}}$ are the weight coefficients of the two genes, determined according to functional importance under the constraint ${\mathsf{\omega }}_{\mathrm{j}}+{\mathsf{\omega }}_{\mathrm{k}}=1$. Their values are obtained by Delphi scoring from five industry experts. When ${\mathrm{S}}_{\mathrm{i}\mathrm{n}\mathrm{t}\mathrm{r}\mathrm{a}}\ge {\mathrm{S}}_0$, the two genes are considered to exhibit a synergistic relationship, where ${\mathrm{S}}_0$ is determined on the basis of practical experience in collaborative product design.

5. Standardized Description System for Product-Gene Information

By integrating international standards such as ISO 10303 (STEP) and ISO 15531 [26], a tripartite standardized description system based on metadata, semantics, and format is established to enable cross-platform sharing and reuse of product-gene information.

5.1. Standardized Metadata Definition

As data labels for product-gene information, metadata are classified by level into platform-gene metadata, assembly–gene metadata, and component-gene metadata. Each category contains three dimensions, including basic attributes, functional attributes, and relational attributes, which are defined in strict accordance with ISO metadata specifications, as shown in

Table 2. Standardized metadata classification and core dimensions of product genes.

Gene Level	Basic Attributes (Required)	Functional Attributes (Required)	Relational Attributes (Required)
Platform gene	Gene ID, name, version number, product family, release date	Architecture function type, system-integration level, technology-route code	List of sub-assembly gene IDs, association-rule ID, enterprise ID (unified social credit code)
Assembly gene	Gene ID, name, version number, parent platform-gene ID, compatible product model	Subsystem function code, modular compatibility grade, performance assurance grade	Parent platform-gene ID, list of child component-gene IDs, association-rule ID
Component gene	Gene ID, name, version number, parent assembly–gene ID, manufacturer ID	Individual function code, assembly-function grade, performance-support grade	Parent assembly–gene ID, associated component-gene ID, process-standard ID

.

5.2. Standardized Semantic Description Specification

By integrating ISO international standards, this study constructs a product-gene semantic ontology model to unify parameter naming, definition scopes, and modes of expression, thereby eliminating cross-enterprise misunderstandings. For example, power density is uniformly defined as the output power per unit mass of a product, with the unit kW/kg. Semantic relations are also standardized, including contains (a platform gene contains assembly genes), compatible with (an assembly gene is compatible with a platform gene), and supports (a component gene supports an assembly gene). In addition, the expression of parameter values is standardized; for instance, temperature intervals are uniformly represented in the format ${\{\mathrm{T}}_{\mathrm{m}\mathrm{i}\mathrm{n}},{\mathrm{T}}_{\mathrm{m}\mathrm{a}\mathrm{x}}\}$ °C.

5.3. Standardized Data-Format Model

XML is adopted as the core data format, and an XML Schema definition is formulated on the basis of ISO standards to establish a mathematical mapping model between product-gene information and standardized data formats. Let the product-gene information set be $\mathrm{I}=\{\mathrm{M},\mathrm{P},\mathrm{R}\}$, where M denotes metadata, P denotes core parameters, and R denotes association rules. The mapping relation is $\phi :\mathrm{I}\to \mathrm{T}\times \mathrm{V}$, where $\mathrm{T}=\{{\mathrm{T}}_{\mathrm{M}},{\mathrm{T}}_{\mathrm{P}},{\mathrm{T}}_{\mathrm{R}}\}$ is the set of standardized tags and $\mathrm{V}=\{{\mathrm{v}}_{\mathrm{m}}$,${\mathrm{v}}_{\mathrm{p}},{\mathrm{v}}_{\mathrm{r}}\}$ is the value set. The mapping is defined by Equation (5).

$$\begin{array}{c}\phi \left(\mathrm{m}\right)=\left({\mathrm{t}}_{\mathrm{m}},{\mathrm{v}}_{\mathrm{m}}\right),\forall \mathrm{m}\in \mathrm{M};\phi \left(\mathrm{p}\right)=\left({\mathrm{t}}_{\mathrm{p}},{\mathrm{v}}_{\mathrm{p}}\right),\\ \forall \mathrm{p}\in \mathcal{P};\phi \left(\mathrm{r}\right)=\left({\mathrm{t}}_{\mathrm{r}},{\mathrm{v}}_{\mathrm{r}}\right),\forall \mathrm{r}\in \mathrm{R}\end{array}$$

(5)

In Equation (5), ${{\mathrm{t}}_{\mathrm{m}}\in \mathrm{T}}_{\mathrm{m}}$, ${\mathrm{t}}_{\mathrm{p}}\in {\mathrm{T}}_{\mathrm{p}}$, and ${\mathrm{t}}_{\mathrm{r}}\in {\mathrm{T}}_{\mathrm{r}}$ denote standardized tags defined with reference to ISO standards, whereas ${\mathrm{v}}_{\mathrm{m}}$, ${\mathrm{v}}_{\mathrm{p}}$, and ${\mathrm{v}}_{\mathrm{r}}$ denote quantified values. The model establishes a one-to-one correspondence between product-gene information and standardized formats, supports conversion to JSON, and thus accommodates the requirements of different design software systems.

6. Case Study

Company A’s Platform B and Concept Vehicle C are selected as the empirical case, and the theoretical model developed in the preceding sections is validated step by step.

6.1. Case Background and Data Sources

To verify the proposed quantitative modeling and standardized description system for hierarchical product genes, a representative pure electric vehicle platform and its three core electric subsystems are selected as the case object. At the platform level, publicly available technical information on Company A’s Platform B is used to construct the platform-gene parameter set. At the assembly level, the battery, motor, and electronic-control assemblies are selected as the three core assembly–gene objects. At the component level, key components that significantly affect performance and compatibility within each assembly are further selected. Following the principles of inspectability, reproducibility, and traceability, the data sources are divided into three categories: (1) standards and normative documents, used to define parameter semantics, units, constraint criteria, and threshold-setting rules; (2) publicly available enterprise technical information, used to obtain key parameters at the platform and system levels; and (3) authoritative third-party evaluation and teardown data, used to supplement and cross-validate parameters at the assembly and component levels.

6.2. Hierarchical Decomposition and Validation Based on the Theoretical Model

6.2.1. Platform-Gene Decomposition and Validation of Parameter Constraints

According to the hierarchical-set definition in Section 3.2 and the parameter-constraint equations in Section 4.1.1, the core parameters of Platform B are decomposed and verified against the proposed constraints.

(1) Hierarchical set and parameter space: ${\mathrm{G}}_0=\{\mathrm{e} \mathrm{P}\mathrm{l}\mathrm{a}\mathrm{t}\mathrm{f}\mathrm{o}\mathrm{r}\mathrm{m}3.0\mathrm{g}\mathrm{e}\mathrm{n}\mathrm{e}\}$, with parameter space ${\mathsf{\Omega }}_0\subseteq {\mathbb{R}}^6$, corresponding to six core parameter dimensions: architecture compatibility coefficient, wheelbase range, system efficiency, lifecycle, degree of interface standardization, and data transmission rate. The detailed assignments are listed in

Table 3. Assigned values of the core parameters of the platform gene.

Parameter Name	Parameter Value	Basis for Assignment	Remarks
Architecture compatibility coefficient $\lambda$	0.85	Official technical white paper of Company A’s Platform B
Wheelbase range $[L_{\mathrm{m}\mathrm{i}\mathrm{n}},L_{\mathrm{m}\mathrm{a}\mathrm{x}}]$	[2700, 3200] mm	Official technical white paper of Company A’s Platform B	Generic wheelbase interval covering mainstream NEV dimensions
System efficiency $\eta$	0.92	Official technical white paper of Company A’s Platform B	Integrated efficiency of the battery–motor–control system
Lifecycle $T$	8 years	Official technical white paper of Company A’s Platform B	Consistent with industry norms for platform technical iteration cycles
Degree of interface standardization $\sigma$	0.88	Calculated from ISO-based interface-conformity assessment	Conformity with ISO standards; satisfies the threshold σ ≥ 0.8
Data transmission rate $v$	8 Mbps	Determined from ISO high-speed CAN specifications and Platform B real-time communication requirements	Supports real-time vehicle-control requirements

, while parameter sources, support for formula rationality, and calculation procedures are provided in Appendix A,

Table A1. Detailed assignment of platform-gene core parameters.

Parameter	Value	Source/Basis	Explanation
Architecture compatibility coefficient λ	0.85	Official technical white paper of Company A’s Platform B	Calculated with reference to GB/T 30555-2014. Four common NEV body types were considered; Platform B explicitly supports three of them, and the maturity coefficient derived from technical documents is 1.13. Thus, λ ≈ (3/4) × 1.13 = 0.85.
Wheelbase range	[2700, 3200] mm	Official technical white paper of Company A’s Platform B	Generic wheelbase interval covering mainstream NEV dimensions.
System efficiency η	0.92	Official technical white paper of Company A’s Platform B	Overall efficiency of the battery–motor–control system.
Lifecycle T	8 years	Official technical white paper of Company A’s Platform B	Consistent with the lifecycle norms of vehicle platforms.
Degree of interface standardization σ	0.88	Calculated from ISO-based interface-conformity assessment	Obtained by comparing Company A’s interface specifications with five ISO-oriented dimensions: label consistency, semantic compatibility, format compatibility, protocol matching, and extensibility. The result satisfies σ ≥ 0.8.
Data transmission rate v	8 Mbps	Determined from ISO high-speed CAN requirements and Platform B real-time control demand	Selected within the ISO-recommended 5–10 Mbps interval and calibrated using a 20% redundancy margin for three-electric-system real-time communication.

.

(2) Constraint-equation verification: substituting the parameter values into Equation (2) shows that $\mathsf{\lambda }=0.85\ge 0.7$ (${\mathsf{\lambda }}_{\mathrm{t}\mathrm{h}}=0.7$, based on GB/T 30555-2014 [27]), the actual platform dimensions satisfy the design requirements, $\mathsf{\eta }=0.92\ge {\displaystyle \frac{{\mathrm{E}}_{\mathrm{o}\mathrm{u}\mathrm{t}}}{{\mathrm{E}}_{\mathrm{i}\mathrm{n}}}}=0.90$ (${\displaystyle \frac{{\mathrm{E}}_{\mathrm{o}\mathrm{u}\mathrm{t}}}{{\mathrm{E}}_{\mathrm{i}\mathrm{n}}}}=0.90$ is the baseline energy-efficiency threshold extracted from Company A’s official technical documentation), and $\mathsf{\sigma }=0.88\ge 0.8$ (${\mathsf{\sigma }}_{\mathrm{t}h}=0.8$), also satisfies the corresponding standardization threshold. All parameters, therefore, meet the proposed constraints, confirming the rationality of the platform-gene parameter assignments.

6.2.2. Assembly–Gene Decomposition and Validation of Inter-Level Association Strength

The three-electric core assemblies (battery, motor, and electric control) are selected as the assembly–gene objects ${\mathrm{G}}_1$. Their association strengths with the platform gene are computed using the model in Section 4.2 to verify compatibility.

The assigned values of the three-electric core assembly–gene parameters and the corresponding platform constraint parameters are presented in

Table 4. Core parameters of assembly genes and platform constraint parameters.

Assembly Type	Core Parameter	Indicator Type	Assembly Value	Platform Constraint Parameter ${\mathit{q}}_{\mathit{p}}$	Threshold ${△\mathit{q}}_{\mathit{p}}$
Battery assembly	Compatibility accuracy $\delta$	Cost-type	0.05 mm	0.08 mm	0.012 mm (0.15 × 0.08)
Battery assembly	Transmission latency $\tau$	Cost-type	5 ms	10 ms	1.5 ms (0.15 × 10)
Battery assembly	Power density $\rho \left(P\right)$	Benefit-type	2.1 kW/kg	2.0 kW/kg	0.3 kW/kg (0.15 × 2.0)
Battery assembly	Temperature range	Interval-type	[−30, 60] °C	[−30, 60] °C	10 °C (0.15 × 60, rounded)
Battery assembly	MTBF	Benefit-type	15,000 h	12,000 h	1800 h (0.15 × 12,000)
Motor assembly	Compatibility accuracy $\delta$	Cost-type	0.06 mm	0.08 mm	0.012 mm (0.15 × 0.08)
Motor assembly	Transmission latency $\tau$	Cost-type	6 ms	10 ms	1.5 ms (0.15 × 10)
Motor assembly	Power density $\rho \left(P\right)$	Benefit-type	3.2 kW/kg	3.0 kW/kg	0.45 kW/kg (0.15 × 3.0)
Motor assembly	Temperature range	Interval-type	[−30, 65] °C	[−30, 60] °C	10 °C (0.15 × 60, rounded)
Motor assembly	MTBF	Benefit-type	14,000 h	12,000 h	1800 h (0.15 × 12,000)
Electric-control assembly	Compatibility accuracy $\delta$	Cost-type	0.07 mm	0.08 mm	0.012 mm (0.15 × 0.08)
Electric-control assembly	Transmission latency $\tau$	Cost-type	4 ms	10 ms	1.5 ms (0.15 × 10)
Electric-control assembly	Power density $\rho \left(P\right)$	Benefit-type	1.8 kW/kg	1.8 kW/kg	0.27 kW/kg (0.15 × 1.8)
Electric-control assembly	Temperature range	Interval-type	[−40, 85] °C	[−30, 80] °C	12 °C (0.15 × 80, rounded)
Electric-control assembly	MTBF	Benefit-type	16,000 h	12,000 h	1800 h (0.15 × 12,000)

; the detailed basis for value assignment is omitted here and provided in Appendix A,

Table A2. Detailed assembly–gene parameters and platform constraint parameters.

Assembly Type	Core Parameter	Assembly Value	Platform Constraint Parameter	Threshold	Source/Basis
Battery assembly	Compatibility accuracy δ	0.05 mm	0.08 mm	0.012 mm	Assembly: Company A Concept Vehicle C technical white paper; Platform: Platform B technical white paper; Threshold: GB/T 1804-2000 [28].
Battery assembly	Transmission latency τ	5 ms	10 ms	1.5 ms	Same as above.
Battery assembly	Power density ρ	2.1 kW/kg	2.0 kW/kg	0.3 kW/kg	Same as above.
Battery assembly	Temperature range	[−30, 60] °C	[−30, 60] °C	10 °C	Same as above.
Battery assembly	MTBF	15,000 h	12,000 h	1800 h	Same as above.
Motor assembly	Compatibility accuracy δ	0.06 mm	0.08 mm	0.012 mm	Assembly: Concept Vehicle C white paper; Platform: Platform B white paper; Threshold: GB/T 1804-2000.
Motor assembly	Transmission latency τ	6 ms	10 ms	1.5 ms	Same as above.
Motor assembly	Power density ρ	3.2 kW/kg	3.0 kW/kg	0.45 kW/kg	Same as above.
Motor assembly	Temperature range	[−30, 65] °C	[−30, 60] °C	10 °C	Same as above.
Motor assembly	MTBF	14,000 h	12,000 h	1800 h	Same as above.
Electric-control assembly	Compatibility accuracy δ	0.07 mm	0.08 mm	0.012 mm	Company A public information and third-party evaluation; threshold based on GB/T 1804-2000.
Electric-control assembly	Transmission latency τ	4 ms	10 ms	1.5 ms	Third-party response-speed testing and Platform B control-system design norms; compliant with real-time communication requirements.
Electric-control assembly	Power density ρ	1.8 kW/kg	1.8 kW/kg	0.27 kW/kg	Company A public technical data and third-party testing.
Electric-control assembly	Temperature range	[−40, 85] °C	[−30, 80] °C	12 °C	Third-party thermal-management testing and Platform B thermal-management norms; consistent with GB/T 21437-2021 [29].
Electric-control assembly	MTBF	16,000 h	12,000 h	1800 h	Company A reliability-test data and Platform B reliability norms; calibrated against core-component reliability datasets.

. The association-strength calculation results are reported in

Table 5. Validation results for inter-level association strength.

Assembly Type	Parameter-Wise Association Scores	Overall Association Strength $\mathit{S}$	Threshold ${\mathit{S}}_{\mathit{t}\mathit{h}}$	Compatibility Judgment	Explanation
Battery assembly	1.000, 1.000, 0.999, 0.993, 1.000	4.992	3.5	Compatible	All deviations are smaller than the threshold; scores are close to 1
Motor assembly	1.000, 1.000, 0.999, 0.924, 1.000	4.923	3.5	Compatible	The temperature interval slightly exceeds the basic threshold; mild attenuation occurs
Electric-control assembly	1.000, 1.000, 0.993, 0.697, 1.000	4.690	3.5	Compatible	Low-temperature tolerance exceeds the range; the score decreases slightly but remains above threshold

Note: parameter-wise association scores are rounded to three decimal places; a value of 1.000 indicates that the calculated value is close to 1 rather than absolutely equal to 1.

.

Based on Equation (3a–c), the attenuation coefficient is set to $\mathsf{\alpha }=5$ for core parameters in accordance with engineering practice, and the association threshold is set to ${\mathrm{S}}_{\mathrm{t}\mathrm{h}}=0.7\times 5({\mathrm{n}}_{\mathrm{i}+1}=5)$ for five core parameters per assembly. The calculated inter-level association strengths are presented in Table 5.

As shown in Table 5, the association strengths between all three assemblies and the platform gene are higher than the threshold of 3.5, indicating that the original case samples are compatible.

6.2.3. Component-Gene Decomposition and Validation of Intra-Level Association Strength

Representative key components corresponding to the three core electric subsystems, namely the battery cell, motor stator, and electronic-control IGBT module, are selected as the elements ${\mathrm{G}}_2$ for analysis. Their assigned core parameters are listed in

Table 6. Assigned values of the core parameters of component genes.

Parent Assembly	Component Name	Core Parameters and Assigned Values
Battery assembly	Battery cell	Dimensional tolerance ±0.02 mm; material strength 350 MPa; operating efficiency 0.99; machining precision 5 μm
Battery assembly	Battery management module (BMS)	Dimensional tolerance ±0.03 mm; material strength 200 MPa; operating efficiency 0.98; machining precision 8 μm
Motor assembly	Stator (hairpin winding)	Dimensional tolerance ±0.01 mm; material strength 400 MPa; operating efficiency 0.97; machining precision 3 μm
Motor assembly	Rotor (permanent magnet)	Dimensional tolerance ±0.02 mm; material strength 380 MPa; operating efficiency 0.96; machining precision 4 μm
Electric-control assembly	IGBT module	Dimensional tolerance ±0.04 mm; material strength 180 MPa; operating efficiency 0.95; machining precision 10 μm
Electric-control assembly	Control chip	Dimensional tolerance ±0.01 mm; material strength 150 MPa; operating efficiency 0.99; machining precision 2 μm

(the detailed basis for value assignment is provided in Appendix A,

Table A3. Detailed assignment of component-gene parameters and data sources.

Parent Assembly	Component Name	Core Parameters and Assigned Values	Data Source
Battery assembly	Blade battery cell	Dimensional tolerance ±0.02 mm; material strength 350 MPa; operating efficiency 0.99; machining precision 5 μm	Autohome special technical evaluation.
Battery assembly	Battery management module (BMS)	Dimensional tolerance ±0.03 mm; material strength 200 MPa; operating efficiency 0.98; machining precision 8 μm	Same source as above.
Motor assembly	Stator (hairpin winding)	Dimensional tolerance ±0.01 mm; material strength 400 MPa; operating efficiency 0.97; machining precision 3 μm	Dongchedi technical analysis.
Motor assembly	Rotor (permanent magnet)	Dimensional tolerance ±0.02 mm; material strength 380 MPa; operating efficiency 0.96; machining precision 4 μm	Same source as above.
Electric-control assembly	IGBT module	Dimensional tolerance ±0.04 mm; material strength 180 MPa; operating efficiency 0.95; machining precision 10 μm	Company A official technical parameter release plus Autohome evaluation, cross-validated.
Electric-control assembly	Control chip	Dimensional tolerance ±0.01 mm; material strength 150 MPa; operating efficiency 0.99; machining precision 2 μm	Same source as above.

). The intra-level association strength among components within the same assembly is then calculated using Equation (4) to verify synergistic relationships.

Using Equation (4), the intra-level association strengths are calculated with weight coefficients assigned according to functional importance, and the synergy threshold is set to 0.2. The results are shown in

Table 7. Computation results of intra-level association strength among component genes.

Parent Assembly	Component Pair	Pearson Correlation Coefficient	Weight Coefficients ω_j and ω_k	Association Strength	Synergy Judgment
Battery assembly	Battery cell—BMS	0.999718	0.6, 0.4	0.24	Synergistic
Motor assembly	Stator—Rotor	0.999996	0.5, 0.5	0.25	Synergistic
Electric-control assembly	IGBT module—Control chip	0.999147	0.7, 0.3	0.21	Synergistic

.

The results show that the association strengths among component genes within the same assembly are all greater than or equal to 0.2, indicating significant synergistic relationships. This finding verifies the rationality of the intra-level association-strength model and also corroborates the hierarchical logic that component collaboration supports assembly-level functionality.

6.2.4. Validation of the Standardized Description System

Using the standardized system proposed in Section 5, a tripartite validation based on metadata, semantics, and format is carried out with the Platform B gene as an example.

(1) Metadata standardization: Platform-gene metadata are defined according to Table 2, including a gene ID and version number as basic attributes, “pure-electric dedicated platform architecture” as a functional attribute, and a list of the IDs of the three-electric assembly genes as relational attributes. The resulting metadata conform to the relevant ISO specifications.

(2) Semantic standardization: parameter semantics are unified, for example, by expressing data transmission rate in the form defined in Section 5.2, thereby eliminating ambiguity and maintaining consistency with international standard semantics.

(3) Format standardization: based on the mapping model in Equation (5), an ISO-compatible XML fragment can be generated and directly imported into design software such as CATIA for cross-platform reuse. The validation results show that product-gene information can be shared across software platforms and enterprises through standardized mapping, thereby overcoming data-silo problems.

6.3. Integrated Analysis of the Case-Validation Results

The effectiveness of the proposed theoretical model can be examined from three aspects. First, with respect to hierarchical partitioning, the platform–assembly–component structure can accurately decompose Platform B, and the parameter spaces satisfy the quantitative constraints whereby the component level is constrained by the assembly level and the assembly level by the platform level. Second, in terms of association strength, the comprehensive association strengths between the three assemblies and the platform gene are all higher than the compatibility threshold of 3.5, while the intra-level association strengths of the three component pairs are all higher than the synergy threshold of 0.2. These results indicate that the model can provide computable representations of hierarchical compatibility and local synergy in the case object. Because the current validation is still based on a single platform case, this study no longer uses an overall applicability rate to generalize the external validity of the model. Third, in terms of standardization, the proposed method enables accurate mapping between product-gene information and ISO standards and supports cross-platform reuse. Taken together, the results show that the proposed quantitative modeling and standardized representation system can support hierarchical management and compatibility assessment of complex product genes.

6.4. Model Discrimination Capability and Robustness Analysis

To examine whether the model can distinguish compatible, boundary-compatible, and incompatible states, this study uses the actual battery assembly in Table 4 as the benchmark sample. Keeping the platform constraint parameters unchanged, boundary-compatible, boundary-incompatible, and clearly incompatible threshold-perturbation samples are constructed according to the corresponding battery-assembly constraint parameters and thresholds. These samples are compared with the actual battery assembly in

Table 8. Threshold-perturbation validation of the battery assembly.

Sample	Sample Nature	Parameter Setting	Five Association Scores	Overall Association Strength S	Threshold	Judgment
Actual battery assembly	Original case sample	0.05 mm, 5 ms, 2.1 kW/kg, [−30, 60] °C, 15,000 h	1.000, 1.000, 0.999, 0.993, 1.000	4.992	3.5	Compatible
Boundary-compatible perturbation sample A	Threshold-perturbation sample	0.092 mm, 11.5 ms, 2.0 kW/kg, [−30, 65] °C, 12,000 h	0.500, 0.500, 0.993, 0.924, 0.993	3.911	3.5	Compatible
Boundary-incompatible perturbation sample B	Threshold-perturbation sample	0.092 mm, 11.5 ms, 1.7 kW/kg, [−30, 65] °C, 12,000 h	0.500, 0.500, 0.500, 0.924, 0.993	3.417	3.5	Incompatible
Clearly incompatible perturbation sample C	Threshold-perturbation sample	0.110 mm, 15 ms, 1.5 kW/kg, [−45, 85] °C, 9000 h	0.001, 0.000, 0.034, 0.001, 0.034	0.070	3.5	Incompatible

.

It should be noted that the perturbation samples in Table 8 are not additional enterprise-measured samples and are not used as new independent cases. Rather, they are counterfactual validation samples designed to test the discrimination capability of the association-strength model under compatible, boundary-compatible, boundary-incompatible, and clearly incompatible states.

Specifically, for cost-type indicators, the platform constraint parameter ${\mathrm{q}}_{\mathrm{j}}$ is used as the benchmark: ${\mathrm{q}}_{\mathrm{j}}+△{\mathrm{q}}_{\mathrm{j}}$ is used to set the boundary state, and ${\mathrm{q}}_{\mathrm{j}}+\mathrm{k}△{\mathrm{q}}_{\mathrm{j}}$ is used to set the out-of-bound state. For benefit-type indicators, ${\mathrm{q}}_{\mathrm{j}}-△{\mathrm{q}}_{\mathrm{j}}$ is used to set the performance-decline boundary, and ${\mathrm{q}}_{\mathrm{j}}-\mathrm{k}△{\mathrm{q}}_{\mathrm{j}}$ is used to set the clearly degraded state. For interval-type indicators, perturbation levels are set according to the extent to which the value exceeds the allowable platform interval. Here, Δqp denotes the constraint threshold and k denotes the perturbation multiplier.

The results show that sample A remains above the compatibility threshold, sample B falls below the threshold after a key benefit-type indicator is reduced, and sample C is clearly incompatible. These results indicate that the model is not limited to producing high scores for compatible samples, but can also produce differentiated judgments for boundary and incompatible states.

Table 9. Robustness analysis of the battery-assembly perturbation samples under different α values.

Sample	α = 2	α = 3	α = 4	α = 5	Judgment Change
Actual battery assembly	4.810, compatible	4.934, compatible	4.977, compatible	4.992, compatible	No
Boundary-compatible perturbation sample A	3.493, incompatible	3.723, compatible	3.845, compatible	3.911, compatible	Yes
Boundary-incompatible perturbation sample B	3.112, incompatible	3.270, incompatible	3.363, incompatible	3.417, incompatible	No
Clearly incompatible perturbation sample C	0.521, incompatible	0.261, incompatible	0.135, incompatible	0.070, incompatible	No

shows that the actual battery assembly and the clearly incompatible perturbation sample maintain stable judgments under α = 2, 3, 4, and 5. By contrast, the boundary-compatible sample is sensitive to α, indicating that α regulates the strictness of model discrimination for near-threshold cases. This behavior is consistent with engineering expectations: clearly compatible and clearly incompatible states should remain stable, whereas boundary states are more sensitive to penalty intensity.

7. Conclusions and Future Work

7.1. Main Conclusions

To address the challenges of qualitative dominance, ambiguous hierarchical associations, and insufficient standardization in complex product-gene research, this study constructs an integrated theoretical framework spanning hierarchical framework design, quantitative modeling, and standardized description. On the basis of validation through a new energy vehicle case, the following main conclusions are drawn.

(1)

A generic three-level framework covering platform, assembly, and component genes is proposed. By defining hierarchical sets and mapping functions on the basis of set theory and function theory, the quantitative boundary-constraint mechanism is clarified, and hierarchical partitioning is advanced from qualitative judgment to quantitative delineation, thereby resolving the problem of ambiguous hierarchical boundaries.

(2)

A full-level core-parameter quantification system and a dual-dimensional association-strength model are established. Through constraint equations and mathematical formulations, parameter constraints, inter-level relationships, and intra-level collaborative relationships can be accurately represented, thereby overcoming the limitations of traditional qualitative association analysis and enabling precise compatibility assessment.

(3)

By integrating international standards such as ISO 10303 and ISO 15531, a tripartite standardized description system based on metadata, semantics, and format is constructed. The proposed mathematical mapping method between product-gene information and standardized data formats enables cross-platform and cross-software sharing of gene information, thereby helping to eliminate barriers to data sharing.

(4)

The new energy vehicle case shows that the comprehensive association strengths between the three-electric assemblies and the platform gene are all higher than the compatibility threshold, and the intra-level association strengths of the three component pairs are all higher than the synergy threshold. Further threshold-perturbation validation shows that the model can form differentiated judgments for compatible, boundary-compatible, and incompatible states, indicating that the proposed quantitative modeling method has certain engineering applicability.

7.2. Limitations and Future Prospects

This study still has several limitations. First, the hierarchical partitioning focuses on the three levels of platform, assembly, and component genes and does not incorporate non-structural gene types such as functional genes and process genes. Second, the case validation is mainly based on a single new energy vehicle platform, and the applicability of the proposed theoretical framework to other complex-product domains, such as aerospace and high-end equipment manufacturing, remains to be further verified. Third, the association-strength model does not yet consider the influence of parameter variation under dynamic operating conditions on association relationships. Fourth, because enterprise platform-level parameters are not always publicly available and may involve commercial sensitivity, this study has not yet conducted cross-platform or cross-vehicle comparative validation.

Future research may proceed in five directions. First, the hierarchical framework can be extended to incorporate functional genes, process genes, and other gene types, thereby constructing a multidimensional and comprehensive product-gene hierarchy. Second, cross-industry case validation can be conducted to optimize model parameters and improve the generalizability and universality of the theoretical framework. Third, a dynamic parameter-evolution mechanism can be introduced to establish a dynamic association-strength model that accounts for full-lifecycle operating conditions, further enhancing the engineering applicability of the framework. Fourth, big data and artificial intelligence technologies can be integrated to develop intelligent matching and optimization algorithms for product genes, thereby supporting intelligent design for complex products. Fifth, future studies can introduce additional vehicle platforms and other complex-product industry cases to statistically calibrate the parameter values, threshold settings, and stability of compatibility judgments.