A Method for Resolving Gene Mutation Conflicts of Retired Mechanical Parts: Generalized Remanufacturing Scheme Design Oriented Toward Resource Reutilization

Abstract

The widespread scrapping of retired mechanical parts has led to severe waste of resources and environmental burdens, posing a significant challenge to sustainable industrial development. To enable efficient recycling of retired mechanical parts and enhance the sustainability of their remanufacturing processes, the concept of biological genes is adopted to characterize the changes in the information of retired mechanical parts during the remanufacturing process as gene mutations of parts, aiming to maximize remanufacturing potential and devise an optimal generalized remanufacturing strategy for extending part life cycles. However, gene mutation of retired mechanical parts is not an isolated event. The modification of local genes may disrupt the original equilibrium of the part’s state, leading to conflicts such as material–performance, structure–function/performance, and function–performance. These conflicts constitute a major challenge and bottleneck in designing generalized remanufacturing schemes. Therefore, we propose a conflict identification and resolution method for gene mutation of retired mechanical parts. First, gene mutation graph of retired mechanical parts is established to express its all-potential remanufacturing pathways. Using discrimination rules and the element representation method from extenics, mutation conflicts are identified, and a conflict problem model is constructed. Then, the theory of inventive problem solving (TRIZ) engineering parameters are reconstructed and mapped to the mutation conflict parameters. The semantic mapping between the inventive principles and the transforming bridges is established by the Word2Vec algorithm, thereby improving the transforming bridge method to generate conflict resolution solutions. A coexistence degree function of transforming bridges is proposed to verify the feasibility of the resolution solutions. Finally, taking the generalized remanufacturing of a retired gear shaft as an example, we analyze and discuss the process and outcome of resolving gene mutation conflicts, thereby verifying the feasibility and effectiveness of the proposed concepts and methodology.

1. Introduction

With the intensification of global industrialization and resource consumption, remanufacturing has become a key strategy for the green transformation of the global manufacturing industry, serving as an essential pathway toward circular economy and sustainable development. As fundamental components in industries such as aerospace, automotive, and engineering, mechanical parts contain substantial reusable resources and energy, including high-quality materials, complex structural designs, and mature manufacturing processes. If directly discarded, these resources not only result in significant material and energy waste but also impose considerable environmental burdens. Traditional remanufacturing mainly focuses on repair, aiming to restore retired products to their original or near-new condition, primarily addressing performance losses caused by part degradation. However, in practical industrial applications, retired mechanical parts often retain considerable residual value. Their reuse potential goes beyond simple restoration and extends to higher-level remanufacturing activities such as structural reconfiguration, functional migration, and performance enhancement. In response to this, our team has proposed the concept of generalized remanufacturing [1,2]. This approach emphasizes maximizing the regeneration of function, performance, lifespan, or value of retired products or components. It does so by means of restoration, upgrading, transformation, or functional reconstruction, while meeting multidimensional objectives related to resources, performance, and demand. Therefore, how to fully discover and harness the remanufacturing potential of retired mechanical parts and design the optimal generalized remanufacturing schemes has become one of the key approaches to enhancing the circular economy benefits of remanufacturing, promoting resource recycling, and fostering the sustainable evolution of industrial systems. However, the anisotropy and uncertainty of information such as material, structure, function, performance, and failure states of retired mechanical parts lead to great variability and flexibility in feasible remanufacturing schemes [3]. To address this, we draw inspiration from genetic engineering and propose a model—referred to as the genes of retired mechanical products—that can comprehensively express both the basic state information of retired mechanical products and the dynamic evolutionary information throughout the generalized remanufacturing process [4,5,6].

Biological genes are the fundamental units of genetic information in living organisms, determining their structure, functions, and characteristics. Similarly, retired mechanical part genes refer to a highly abstracted and encoded representation of key information related to a mechanical component’s structure, function, material, performance, and failure characteristics throughout its life cycle. These can be regarded as genetic units in an engineering context. In biology, gene mutation is a vital mechanism for individuals to adapt to the environment and generate new traits. In the field of engineering, part reconstruction in remanufacturing exhibits similar characteristics. Performance degradation, structural damage, or changes in application scenarios often trigger the need for property adjustments and optimization. The process of transforming a part from its original state through external interventions—such as repair, reconstruction, substitution, or parameter adjustment—toward functional reconstruction or upgrading displays significant mutation-like features. The gene mutation of retired mechanical parts refers to interpreting their state information as genetic data, which undergoes selective inheritance in response to varying customer demands. Through remanufacturing, these parts are guided to mutate and evolve in a favorable direction, enabling either restorative or transformative generalized regeneration. To accurately represent the gene mutation process of retired mechanical parts, each part is viewed as a composite information unit composed of five types of bases: material, structure, function, performance, and failure. By means of base information repair, replacement, and recombination, the part is driven to evolve from a failed state to a target state, thereby enabling the generation of diversified generalized remanufacturing schemes, extending the lifecycle of the part, and supporting the sustainable operation of industrial systems. This study adopts the abstract framework of biological genetic systems to construct a knowledge modeling and evolutionary reasoning paradigm oriented toward remanufacturing. It provides a structured and hierarchical modeling logic for representing part information and its evolution within complex engineering systems. Moreover, it offers a basis for multi-scheme comparison and evaluation in engineering practice, thereby enhancing the scientific rigor and operational stability of remanufacturing design.

However, gene mutation is not an isolated event. Its essence lies in the dynamic interplay of multi-attribute coupling within a complex system. Due to the high interconnectivity of the part genes, the modification of local bases of the part genes may disrupt the original system balance, triggering multi-dimensional conflicts such as material–performance and structure–function contradictions. For instance, the introduction of a high-hardness coating may reduce the toughness of the substrate, or lightweight design may conflict with load-bearing functionality. If such conflicts are not effectively identified and resolved, they will directly lead to the failure of the remanufacturing scheme or even cause cascading system malfunctions. Therefore, there is an urgent need for a conflict resolution method for gene mutation in retired mechanical parts, to support the design of optimal generalized remanufacturing schemes and to provide a theoretical foundation and engineering paradigm for resource circularity.

Current research on conflict issues mainly focuses on fields such as product design, TRIZ, multi-attribute decision-making, and evolutionary game theory. For example, Mao et al. proposed a conflict resolution method for real-time adaptive motion planning under task constraints in unpredictable dynamic environments, which enhanced the task execution capability and flexibility of robotic arms when encountering dynamically unknown obstacles [7]; Wu et al. proposed a collaborative product design–innovation method based on axiom design (AD), theory of inventive problem solving (TRIZ), fuzzy logic, and grey relational analysis, which eliminates various complex conflicts that may arise during the early stages of conceptual design [8]; Wang et al. proposed a new framework combining quality function deployment (QFD) with grey decision-making methods, used for collaborative quality design in large and complex product supply chains [9]; Guo et al. proposed a method to support elastic concept design through functional decomposition and conflict resolution, by defining principles of elastic design and constructing a conceptual design process model to address conflict issues in complex systems [10].

In the context of smart manufacturing, more scholars are focusing on research into intelligent conflict identification and analysis, as well as adaptive and autonomous decision-making mechanisms. Li et al. used current reality tree (CRT) to form a hierarchical representation of conflicts, employed conflict solution tendency network (CSTN) to search for conflict resolution trends, and applied ant colony optimization algorithms to analyze the optimal solution to conflict trends, addressing multi-conflict and efficiency issues in the product development process [11]; Xu et al. proposed a conflict flow network iterative construction process model based on scalable conduction transformation, which resolved conflict issues in the product innovation–design process [12]; Baby et al. considered collaborative design in product design and proposed an informative decision-making framework to model goal guidance, detect potential conflicts between multi-layer decisions, and enhance the performance of target products [13]; Knigd et al. proposed a functional lifecycle energy analysis to address the synergy and conflicts between lightweight design and circular design in products [14]; Mao et al. proposed a product concept design conflict resolution method that integrates deep learning and technological evolution models to solve conflict issues caused by product design constraints, helping designers generate innovative solutions [15]; Huang et al. proposed an intelligent conflict resolution model based on multi-layer knowledge graphs to achieve the correlation and reasoning of multi-domain knowledge, improving the efficiency and reliability of conflict resolution during the conceptual design phase [16].

The aforementioned literature on conflict identification and resolution during the new product design phase each presents unique innovations and applicable scenarios, offering significant inspiration for our research. However, studies specifically addressing conflict issues in the generalized remanufacturing of retired mechanical parts remain relatively scarce. In fact, compared with new product design, the gene mutations of retired mechanical parts are more complex due to uncertainties from their original service life—such as damage, aging, and performance degradation. To address this gap, we propose a conflict resolution method for gene mutation in retired mechanical parts. This method not only enhances the feasibility and adaptability of mutation schemes but also provides theoretical and data support for the realization of generalized remanufacturing of parts. The main contributions of this study are as follows:

(1)

A mutation graph model for retired mechanical parts is proposed. This model systematically characterizes the evolutionary paths of key attributes—such as material, structure, performance, and function—during the remanufacturing process. It provides a basis for accurately identifying remanufacturing value and potential conflicts, thereby effectively supporting resource-efficient remanufacturing design;

(2)

A method for effectively resolving mutation conflicts in retired mechanical parts is developed. This approach enables the decoupling of technical contradictions and the generation of resolution schemes. It aims to extend the service life of mechanical components and indirectly enhances the resource efficiency and ecological feasibility of remanufacturing solutions;

(3)

The proposed method is validated through a case study. The results demonstrate that the method can generate innovative and technically sound conflict resolution strategies, extend the lifecycle of parts, and highlight the potential of remanufacturing design in achieving sustainable development goals.

The remainder of this paper is structured as follows: Section 2 elaborates on the concept of gene mutation in retired mechanical parts and constructs its graph model to integrate gene information. Section 3 proposes a conflict identification and extraction method based on discrimination rules and the element representation method in extenics. It also presents a TRIZ-enhanced transforming bridge method for generating conflict resolution schemes, with a coexistence degree function to evaluate their feasibility. Section 4 presents a case study on the conflict resolution process in the gene mutation of a retired gear shaft, validating the effectiveness of the proposed theory and method. Section 5 discusses the advantages and limitations of the proposed method. Section 6 concludes the paper.

2. The Gene Mutation of Retired Mechanical Parts

2.1. The Concept of Gene Mutation of Retired Mechanical Parts

Retired mechanical part genes ($G_{RMPart}$) refer to the set of part state information that determines the generalized remanufacturing potential and value of retired mechanical parts and evolves dynamically throughout the remanufacturing process. The structure of $G_{RMPart}$ forms the foundation for constructing the part gene model and is represented as a network of part gene bases and their relationships, as illustrated in Figure 1.

The gene base of a retired mechanical part, denoted as ${Gb}_{RMPart}$, is the basic unit that composes the part gene. These bases are categorized into five types: material bases (${Gb}_{RMPart}^M$); structural bases (${Gb}_{RMPart}^S$); functional bases (${Gb}_{RMPart}^F$), such as connection, transmission, steering, etc.; performance bases (${Gb}_{RMPart}^P$), such as strength, impact resistance, corrosion resistance, etc.; failure bases (${Gb}_{RMPart}^D$). To describe the structure of $G_{RMPart}$ more clearly and concisely, the following definitions are provided in this paper:

Definition 1.

The five categories of gene bases are defined as the fundamental elements used to describe $G_{RMPart}$. Each element consists of: a base name, denoted as ${Gb}_{RMPart}^i$ where i = M, S, F, P, D, representing the five categories of bases), a set of characteristics, denoted as $C_{ij}$ where j = 1, 2, …, n, indicating the number of characteristics for that base), and a set of characteristic values, denoted as $V_{ik}$ (where k = 1, 2, …, n, indicating the number of values corresponding to each characteristic). Accordingly, the gene base of a retired mechanical part can be expressed as follows:

$$\begin{array}{c}{Gb}_{RMPart}=\left({Gb}_{RMPart}^i,C_{ij},V_{ik}\right)\end{array}$$

(1)

Thus, the gene bases of retired mechanical parts can be formally represented as follows:

$$\begin{array}{c}{Gb}_{RMPart}=\left\{\left({Gb}_{RMPart}^M,C_{Mj},V_{Mk}\right),\dots ,\left({Gb}_{RMPart}^D,C_{Dj},V_{Dk}\right)\right\}\end{array}$$

(2)

The mutation of $G_{RMPart}$ refers to the process in which a portion of the part’s genetic information is altered through remanufacturing activities, leading to the gradual development of new genes, while the remaining gene information remains unchanged before and after the process. This mutation enables the modified part to meet specific remanufacturing requirements or endows it with new functions or enhanced performance. The objective of remanufacturing retired mechanical parts is to fully utilize their residual value. This may involve restoring dimensions and performance or embedding new modules to enhance functionality and added value. Therefore, the mutation of $G_{RMPart}$ is characterized by uncertainty and diversity.

As a derivation and extension of biological gene theory, $G_{RMPart}$ not only inherits the properties of transmission and mutation characteristic of biological genes, but also transcends them. $G_{RMPart}$ can exist independently of the physical entity of the retired mechanical part, yet it cannot autonomously proliferate or continue without the support of specific manufacturing or remanufacturing processes. Under the support of its generalized growth mechanism, $G_{RMPart}$ inherits homologous genes vertically through parent-offspring genetic transmission, acquires heterologous genes horizontally via non-parental gene transfer, and achieves gene optimization through mutation of base traits, gene fragments, and their combinations. The dynamic process of gene transmission and mutation is characterized by demand orientation, controllability, diversity, and efficiency.

2.2. Gene Mutation Graph Model of Retired Mechanical Parts

The graph model describes various categories of node information and the relationships among these nodes in the form of a graph, offering strong adaptability and representative capability for characterizing the mutation process of $G_{RMPart}$ [17,18,19]. Therefore, a heterogeneous graph is employed to model the $G_{RMPart}$ structure and its remanufacturing process, forming a mutation scheme graph model. This model consists of three main components: the subgraph of the retired mechanical part, the subgraph of the mutated part, and directed relational edges that connect the corresponding nodes.

The subgraph of the retired mechanical part includes five categories of part base-feature nodes. These nodes represent the characteristic information of a specific part in five dimensions: material, structure, function, performance, and failure. Each category of features consists of different types of information. For instance, failure features are described by “failure mode” and “degree of failure”, while material features may include attributes such as “material type”, “stiffness”, and “hardness”. The subgraph of the mutated part is used to represent the base features of the part after mutation. Notably, this subgraph does not contain failure base nodes. Directed relational edges reflect the connection status between nodes in the graph model. They represent the mutation methods by which a part transitions from one state to another. These mutation methods are process-driven, and each edge is annotated with a natural language description of the specific process and records the attribute changes caused by the mutation—for example, “carburizing treatment on the surface to enhance material strength”.

The mutation graph model serves as a highly abstract and structured representation of the $G_{RMPart}$ mutation process. The structure of the graph model is illustrated in Figure 2. By employing knowledge extraction techniques [6], information on materials, structures, functions, performance, failure characteristics, and remanufacturing process activities of retired mechanical parts is extracted from historical remanufacturing case texts. This information is used to enrich the mutation graph model, which is then stored in a Neo4j graph database.

3. Methodology

3.1. Method Framework

Figure 3 illustrates the framework of the $G_{RMPart}$ mutation conflict resolution method, which consists of two stages.

Stage one involves mutation conflict identification and extraction. In this stage, $G_{RMPart}$ information and remanufacturing process activities are extracted from historical case texts. The descriptive language of the process activities is stored as a mutation description set Q, and conflict discrimination rules D are established. Natural language processing (NLP) techniques are then used to identify the mutation description set Q’ that meets the conflict rules D, further constructing a conflict issue model.

Stage two focuses on mutation conflict resolution and evaluation. The Word2Vec technique is employed to achieve semantic mapping between mutation parameters-TRIZ engineering parameters and TRIZ inventive principles-transforming bridges. TRIZ inventive principles are integrated with transforming bridges to propose conflict resolution solutions. Finally, a coexistence evaluation function is constructed to quantitatively analyze the resolution scheme, comprehensively considering the effectiveness of conflict resolution and the rationality of the proposed solution.

3.2. Mutation Conflict Identification and Conflict Problem Model Construction

3.2.1. Identification of Conflict in Gene Mutation of Retired Mechanical Parts

The primary objective of $G_{RMPart}$ mutation is to restore the original functions and performance of a part or to enhance its functionality based on its existing condition, so that it meets technical standards and can be reintroduced into use. A single $G_{RMPart}$ mutation scheme typically affects only a subset of the part’s bases—such as modifying the material or structure—while the remaining bases, such as function or performance, retain their original state. This disrupts the optimized and balanced state of the original part system, potentially triggering conflict issues between the new and original bases. Identifying such conflict problems within $G_{RMPart}$ mutation schemes is therefore a critical aspect of successfully achieving mutation. Mechanical parts are multi-attribute coupled entities, whose material, structural, functional, and performance attributes are balanced through design optimization and exhibit interdependent relationships. Accordingly, we propose that the conflicts within $G_{RMPart}$ mutation schemes can be categorized into four main types:

(1)

Material–Performance Conflict: The physical properties of the part’s material (e.g., strength and heat resistance) fail to meet the required target performance.

(2)

Structure–Performance Conflict: Changes in geometric structure (e.g., lightweight design) result in insufficient mechanical performance (e.g., stiffness and fatigue life) or introduce new stress concentrations.

(3)

Structure–Function Conflict: Physical space constraints or interface mismatches prevent the realization of newly added functions or compromise the original functionality of the part.

(4)

Function–Performance Conflict: The addition of new functions imposes extra loads or interference, leading to the degradation of the part’s original performance.

By extracting and analyzing the attribute change descriptions from the directed relationship edges in the graph model, a set of mutation descriptions is obtained as $Q=\{Q_1,Q_2,\dots ,Q_u\}$. Natural language processing (NLP) tools are employed to evaluate the mutation description set using the rule set $D$, sequentially determining whether each mutation description on the edges meets the keyword-trigger conditions defined by the conflict rules.

$$\begin{array}{c}D=\left\{D_1,D_2,D_3\right\}\end{array}$$

(3)

Among them, $D_1$ indicates that the text contains material-related keywords (e.g., “high-hardness alloy” and “replaced with ceramics”) along with performance-related keywords combined with weakening terms (e.g., “resulting in reduced rigidity”). If these conditions are met, the mutation is identified as a material–performance conflict. $D_2$ indicates that the text contains structural keywords (e.g., “simplified bracket structure” and “modular transformation”) along with performance or functional keywords combined with weakening terms (e.g., “reduced functionality” and “decreased efficiency”). If these conditions are satisfied, the mutation is identified as either a structure–performance conflict or a structure–function conflict. $D_3$ indicates that the text includes functional keywords (e.g., “added gripping module” and “modified control logic”) and performance keywords with weakening terms (e.g., “reduced response speed” and “shortened lifespan”). If these criteria are met, the mutation is identified as a function–performance conflict.

When any mutation description in $Q$ satisfies one of the rule-based criteria in $D$, the corresponding mutation method is regarded as a conflict-containing mutation. By sequentially evaluating each mutation method in $Q$, the conflict mutation set $Q^{\prime }=\{Q_1^{\prime },Q_2^{\prime },\dots ,Q_3^{\prime }\}$ is obtained.

3.2.2. Modeling Conflict Problem in Retired Mechanical Part Gene Mutation

A standardized description of conflict problems facilitates engineers in more accurately identifying the objectives, variables, and constraints involved, thereby enabling the formulation of more targeted solutions. The element representation method in extenics [20,21,22] allows for the clear quantification and logical expression of the core elements of conflict—such as objectives, features, values, and conditions. Moreover, it emphasizes extensible transformation, encouraging the exploration of innovative solutions by expanding the problem domain. Therefore, the element representation method is employed to describe the mutation objectives and conditions of parts, and defines the $G_{RMPart}$ mutation conflict problem as follows.

Definition 2.

Let $P$ represent the conflict problem in the $G_{RMPart}$ mutation process, where $g_1$ and $g_2$ represent the two mutation objectives that need to be achieved, i.e., the new attributes that must be added to the part gene. Let $l$ denote the specific parameters or process conditions (such as material, structure, function, etc.) that the product should have in order to realize these attributes. Assuming that under condition $l$, if objectives $g_1$ and $g_2$ cannot be satisfied simultaneously, the problem $P=(g_1^g_2)\uparrow l$ is defined as the elemental formalization model of a mutation opposition conflict problem, where $g_1$, $g_2$, and $l$ are all n-dimensional elements. The symbol “↑” indicates an opposition relationship, and “↓” indicates a co-existence relationship. Furthermore,

$$\begin{array}{c}{g}_1=\left[\begin{array}{ccc}{O}_1& c_{11}& v_{11}\\ & c_{12}& v_{12}\\ & ⋮& ⋮\\ & c_{1n}& v_{1n}\end{array}\right] g_2=\left[\begin{array}{ccc}{O}_2& c_{21}& v_{21}\\ & c_{22}& v_{22}\\ & ⋮& ⋮\\ & c_{2n}& v_{2n}\end{array}\right] l=\left[\begin{array}{ccc}{O}_l& c_{l1}& v_{l1}\\ & c_{l2}& v_{l2}\\ & ⋮& ⋮\\ & c_{ln}& v_{ln}\end{array}\right]\end{array}$$

(4)

In the formula, $O_1,O_2,and{O}_l$ represent the objects of $g_1$, $g_2$, and$l$, respectively. $C_{11},C_{12},\dots ,C_{1n}$, $C_{21},C_{22},\dots ,C_{2n}$, $C_{l1},C_{l2},\dots ,C_{ln}$ represent the corresponding features of the respective objects. $V_{11},V_{12},\dots ,V_{1n},V_{21},V_{22},\dots ,V_{2n},V_{l1},V_{l2},\dots ,V_{ln}$ represent the values corresponding to the features of the objects.

Taking the remanufacturing of a worn-out gear shaft as an example, when the tooth surface experiences wear failure, engineers aim to improve the gear’s wear resistance ($g_1$) and simultaneously enhance its impact resistance ($g_2$) through surface coating processes. To achieve these two objectives, different coating materials and process conditions may need to be selected ($l$). However, different coating materials may lead to conflicts between wear resistance and impact resistance. For example, using a high-hardness ceramic coating (such as Al₂O₃) can significantly improve the gear’s wear resistance, but this material is relatively brittle and may reduce the gear’s impact resistance. On the other hand, using a more ductile coating material (such as Ni-Co alloy) can enhance impact resistance, but the wear resistance may not be as good as the ceramic coating. In this problem, improving the wear resistance of the gear, improving the impact resistance of the gear, and selecting coating materials and their process parameters.

$$\begin{array}{c}{g}_1=\left[\begin{array}{ccc}\mathrm{W}\mathrm{e}\mathrm{a}\mathrm{r}\mathrm{r}\mathrm{e}\mathrm{s}\mathrm{i}\mathrm{s}\mathrm{t}\mathrm{a}\mathrm{n}\mathrm{c}\mathrm{e}& \mathrm{H}\mathrm{a}\mathrm{r}\mathrm{d}\mathrm{n}\mathrm{e}\mathrm{s}\mathrm{s}& H_1\\ & \mathrm{F}\mathrm{r}\mathrm{i}\mathrm{c}\mathrm{t}\mathrm{i}\mathrm{o}\mathrm{n}\mathrm{c}\mathrm{o}\mathrm{e}\mathrm{f}\mathrm{f}\mathrm{i}\mathrm{c}\mathrm{i}\mathrm{e}\mathrm{n}\mathrm{t}& f_1\end{array}\right]\end{array}$$

(5)

$$\begin{array}{c}{g}_2=\left[\begin{array}{ccc}\mathrm{I}\mathrm{m}\mathrm{p}\mathrm{a}\mathrm{c}\mathrm{t}\mathrm{r}\mathrm{e}\mathrm{s}\mathrm{i}\mathrm{s}\mathrm{t}\mathrm{a}\mathrm{n}\mathrm{c}\mathrm{e}& \mathrm{T}\mathrm{o}\mathrm{u}\mathrm{g}\mathrm{h}\mathrm{n}\mathrm{e}\mathrm{s}\mathrm{s}& T_2\\ & \mathrm{C}\mathrm{r}\mathrm{a}\mathrm{c}\mathrm{k}\mathrm{r}\mathrm{e}\mathrm{s}\mathrm{i}\mathrm{s}\mathrm{t}\mathrm{a}\mathrm{n}\mathrm{c}\mathrm{e}& R_2\end{array}\right]\end{array}$$

(6)

$$\begin{array}{c}l=\left[\begin{array}{ccc}Coatingmaterial& \mathrm{H}\mathrm{a}\mathrm{r}\mathrm{d}\mathrm{n}\mathrm{e}\mathrm{s}\mathrm{s}& H_l\\ & \mathrm{T}\mathrm{o}\mathrm{u}\mathrm{g}\mathrm{h}\mathrm{n}\mathrm{e}\mathrm{s}\mathrm{s}& T_l\\ & \mathrm{F}\mathrm{r}\mathrm{i}\mathrm{c}\mathrm{t}\mathrm{i}\mathrm{o}\mathrm{n}\mathrm{c}\mathrm{o}\mathrm{e}\mathrm{f}\mathrm{f}\mathrm{i}\mathrm{c}\mathrm{i}\mathrm{e}\mathrm{n}\mathrm{t}& f_l\\ & \mathrm{T}\mathrm{h}\mathrm{i}\mathrm{c}\mathrm{k}\mathrm{n}\mathrm{e}\mathrm{s}\mathrm{s}& d_l\end{array}\right]\end{array}$$

(7)

In the formula, $H_1$ represents the hardness of high-hardness ceramic coating, which enhances wear resistance; $f_1$ represents the low friction coefficient of the ceramic coating, which helps reduce wear; $T_2$ represents the impact resistance of high-toughness materials; $R_2$ represents crack resistance; $H_l$, $T_l$, $f_l$, and $d_l$ represent the coating material and its process parameters. Under condition $l$, if a ceramic coating is selected to improve wear resistance ($g_1$), it may reduce impact resistance ($g_2$); whereas if a more ductile metal coating is used, it may fail to meet the wear resistance requirement. Therefore, this problem is a case of mutation contradiction and requires further analysis. Optimization solutions can be sought through extenics transformation or TRIZ methods, such as applying a gradient coating (high toughness in the inner layer and wear resistance in the outer layer) or using nanocomposite coatings.

3.3. Mutation Conflict Resolution Method Based on Transforming Bridge–TRIZ

3.3.1. Mapping Relationship Between $G_{RMPart}$ Mutation Conflict Parameters and TRIZ Engineering Parameters

The process of solving $G_{RMPart}$ mutation conflict problems can be regarded as the search for and construction of connections and transformation paths between different systems. The transforming bridge method builds a link between conflicting elements by expanding thinking and introducing third-party elements. Its construction usually relies on specific industry resources, such as technologies, platforms, or design standards. However, traditional transforming bridge methods lack support from a systematic and generalized principle library, often relying on human expertise during application. TRIZ (Theory of Inventive Problem Solving), with its systematic mechanism for solving engineering problems, has been widely applied in product design [23,24,25]. Its core lies in abstracting engineering parameters and using the contradiction matrix to match inventive principles, thereby providing directions for problem solving. However, the inventive principles of TRIZ are highly abstract and lack concrete implementation details, which results in solutions with weak operability. Therefore, this paper proposes a mutation conflict resolution method based on the transforming bridge–TRIZ approach. By leveraging TRIZ tools to assist in constructing transforming bridges, the method overcomes the limitations of traditional transforming bridge techniques and supports engineers in thinking from multiple perspectives to improve bridge design. This method is mainly divided into two parts:

(1)

Extraction of conflict parameters: Establishes a knowledge-based association between $G_{RMPart}$ mutation conflict parameters and TRIZ engineering parameters, enabling fast and effective parameter retrieval and extraction.

(2)

Generation of resolution strategies: Links TRIZ inventive principles with the transforming bridge method, providing a knowledge base for resolving $G_{RMPart}$ mutation conflicts.

When applying TRIZ to the conflict resolution of $G_{RMPart}$ mutations, it is necessary to first map the characteristics of the conflicting objectives to TRIZ engineering parameters and then identify the corresponding inventive principles through the TRIZ contradiction matrix. However, traditional TRIZ engineering parameter terminology is often vague in classification, making it difficult to directly apply to $G_{RMPart}$ mutation conflicts. Therefore, the 39 engineering parameters are deconstructed and restructured. The goal of $G_{RMPart}$ mutation is to eliminate failure features of parts, enabling repair or the embedding of new modules, ultimately reflected in changes to the part’s material, structure, function, and performance. Conflicts also predominantly occur among these four types of genes. By extracting commonly used engineering parameters related to these conflicting genes in the remanufacturing domain, a dedicated set of $G_{RMPart}$ mutation conflict parameters can be constructed. Using feature analysis and classification, the characteristics of conflict parameters and TRIZ engineering parameters can be categorized and generalized to establish direct correspondence between $G_{RMPart}$ mutation conflict parameters and TRIZ engineering parameters. Certain engineering parameters in TRIZ are irrelevant to $G_{RMPart}$ mutations and can be filtered or optimized in the early stages. For example, illumination has limited impact in most remanufacturing scenarios, as modern remanufacturing technologies typically rely on high-precision detection tools such as built-in sensors, infrared imaging, and laser rangefinders, which are independent of external lighting conditions. Parameters like degree of automation and productivity mainly target manufacturing efficiency, whereas key concerns in remanufacturing lie in flexibility and process adaptability, making productivity and automation less critical. Parameters such as speed, power, and energy of a moving object are difficult to intuitively reflect the causes of conflicts in part remanufacturing; instead, they can be transformed into requirements for the part’s material, structure, and performance. The conflict parameter mappings are established, as shown in

Table 1. Mapping of $G_{RMPart}$ mutation conflict parameters to TRIZ engineering parameters.

Gene Bases	Number	Conflict Parameters	Number	TRIZ Engineering Parameters
material	1	hardness	14	strength
	2	strength	14	strength
	3	heat-resistance	17	temperature
	4	resilience	11	stress or pressure
	5	corrosion resistance	15	durability
	6	conductivity	34	maintainability
	7	solderability	32	manufacturable
structure	8	shape	12	shape
	9	precision of fit	29	manufacturing precision
	10	connection method	27	dependability
	11	thicknesses	4	length of an object at rest
	12	geometric complexity	32	manufacturable
			36	complexity of installations
function	13	load-carrying capacity	14	strength
			11	stress or pressure
	14	durability	15	durability
			27	dependability
	15	operational precision	28	test accuracy
			33	operability
	16	scope of work	35	adaptability and versatility
performance	17	dependability	27	dependability
	18	durability	15	durability
	19	load capacity	14	strength
			11	stress or pressure
	20	fatigue resistance	11	stress or pressure
	21	stability	13	structural stability

.

3.3.2. Mapping Relationship Between Invention Principles and Transforming Bridges

The core of the transforming bridge method lies in expanding the solution space of the problem. By adjusting or reconstructing the relationships and conditions within the conflict, feasible solution paths can be found. It mainly includes four bridge-building ideas as shown in Figure 4.

(1)

Establish a connecting bridge: Introduce a third-party element to construct a turning point, Z, connecting the conflicting objectives so that they can coexist. For example, if a part needs to be used in two different types of equipment, with differing requirements for the part, a modular design can be applied to the part so that different functions coexist on the same part.

(2)

Establish a separating bridge: Introduce a third-party element to construct a turning point, Z, separating the conflicting objectives to reduce the overlap of contradictions and ease the conflict. For example, if a part’s main failure mode is wear and the part material is expensive, requiring cost control for replacements, the easily worn parts of the component can be designed as detachable structures, so that only the worn parts need to be replaced when wear occurs.

(3)

Establish a goal transforming bridge: Implement a transformation, $T_g,$ for the goal, $g$, and under the constraints of the conditions achieved by the $G_{RMPart}$ mutation, look for cases in actual production that meet these conditions. From these, find the feasible transformation path for the goal to achieve compatibility.

(4)

Establish a condition transforming bridge: Implement a transformation, $T_l,$ for the condition, $l$. For the conflicting constraint conditions, $l$, resolve the conflict through methods such as parameter optimization, assembly adjustments, or process changes, thereby transforming the conditions to eliminate the conflict.

After describing the problem in terms of engineering parameters, TRIZ solves it by identifying relevant inventive principles from the contradiction matrix. However, most of these principles only offer macro-level solutions, lacking detailed guidance for developing practical resolutions. As a result, engineers often find it difficult to translate theoretical principles into actionable solutions. Establishing a mapping relationship between TRIZ inventive principles and the transforming bridge method can help provide concrete construction strategies for solution development, avoiding reliance on singular or suboptimal paths. The Word2Vec algorithm can extract semantic associations from text corpora, enabling rapid computation of many-to-many mapping relationships, and its results can continuously improve as the corpus expands. By applying the Word2Vec algorithm to build a mapping between TRIZ inventive principles and the transforming bridge method, a knowledge base foundation can be established for resolving $G_{RMPart}$ mutation conflicts. The specific implementation steps are as follows:

Step 1. Create the corpus. Establish the corpus for TRIZ invention principles, denoted as id, TRIZ−principles, description, where id and TRIZ-principles represent the fixed number and name of each TRIZ inventive principle, and description refers to the detailed explanation of the corresponding principle, as shown in

Table 2. TRIZ invention principles corpus (partial).

ID	TRIZ Principles	Description
1	Segmentation	Splitting an object into distinct parts that are independent of each other and can be easily and quickly combined and integrated to enhance the functionality of the object or to reduce (or eliminate) the negatives inherent in working with the object as a whole.
2	Extract	To spatially or temporally dissociate the parts (or attributes) of the system that can have a negative impact from the subject, or to extract only those parts (or attributes) of the system that are of use and utilize them.
3	Local quality	Reducing the degree of homogeneity of an object, environment, or external action, so that different parts have different functions, or so that different parts are in an optimal state to fulfill their respective functions.
4	Asymmetric	Increasing the asymmetry of an object in terms of structure, geometry, etc., for the purpose of enhancing functionality, eliminating or reducing negative factors (error-proofing, dork-proofing), etc.
5	Combinatorial	Combining (merging) physical or non-physical objects in space or time to achieve enhanced functionality and efficiency, or combining (merging) different (or opposite) functional objects to produce new functionality.
6	Versatility	It refers to making things or parts of things realize multiple functions, increasing the value of a product by making it have multiple functions, making it more competitive. Or combining multiple functions of relevance in one product can reduce the overall cost and ease of use.
7	Nested	Combine more than one thing, increase in size, put one object in a second object, put a second object in a third object.
8	Weight Compensation	Also known as “counterweight”, it refers to compensating, balancing, and creating a uniform distribution of equal weights (quantities). Determining the current situation of the system and looking for an opposite effect, or an effect that can be counteracted in order to minimize the problems caused by weight.
9	Backfire	In order for something to function in a way that removes a certain action, a counteraction is applied in advance.
—	——	——

. Similarly, establish the corpus for transforming bridge methods, denoted as id, bridges−methods, description, where id is the identifier for the transforming bridge method, bridges–methods include the four types—connecting bridge, separating bridge, goal transforming bridge, and condition transforming bridge; and description provides the corresponding explanation of each method, as shown in

Table 3. Transforming bridge corpus.

ID	Bridge Methods	Description
1	Connecting bridge	Improvement of overall performance through enhanced coupling between materials and structures
2	Separating bridge	Reduce performance or functionality conflicts through physical isolation
3	Goal transforming bridge	For conflict problems that cannot be solved by combining or separating attributes, material, structural, functional, and performance characteristics of objects are replaced, inserted, deleted, and scaled to reduce conflicts.
4	Conditional transforming bridge	For conflict problems that cannot be solved by combining or separating attributes, replace, insert, delete, expand, and contract transformations to reduce the conflict with respect to external factors such as the environment, process conditions, and work status of the object.

.

Step 2. Text preprocessing. The purpose of text preprocessing is to remove noise and ensure corpus quality. In this step, stop words, special symbols, and other meaningless information are removed from the corpus. Secondly, since the actual corpus used in this study consists of Chinese texts, and Chinese expressions are continuous without natural word boundaries—unlike English, where words are separated by spaces—it is necessary to employ the Jieba segmentation system. By converting continuous sequences of Chinese characters into semantically independent word units, this ensures that the subsequent Word2Vec-based semantic mapping is built upon accurate linguistic components.

Step 3. Model selection and training. The Word2Vec model offers two training modes: CBOW and Skip-Gram. The Skip-Gram model generally provides higher accuracy in training word-level semantic relationships, making it suitable for finding word similarities. The CBOW model, on the other hand, offers more stable vector representations for sentences or short texts and has faster training speed. Since this section mainly focuses on computing semantic similarity of descriptive texts and emphasizes the overall meaning, the CBOW model is chosen for training the corpus and generating vectorized text representations. Key parameter settings for the model include the following: vector dimension: 200; context window size: 10; minimum word frequency: 2; model type: 0 (CBOW); number of iterations: 30.

Step 4. Similarity calculation and mapping rule establishment. Cosine similarity is used to measure the similarity between word vectors. A mapping association matrix is then established to link each transforming bridge method with relevant TRIZ principles.

Step 5. Result visualization. The mapping results are exported into an Excel table, displaying multiple matching TRIZ principles for each transforming bridge method along with their similarity scores. A similarity heatmap is also generated (as shown in Figure 5) to visually represent the degree of similarity between transforming bridge methods and TRIZ principles.

Step 6. Conflict resolution strategy generation. Based on the mapping association matrix, the transforming bridge method with the highest similarity to a TRIZ principle can be selected. The extensible transformations contained within the selected bridge method are then extracted, and by applying these transformations to relevant elements, concrete conflict resolution strategies can be generated.

To further validate the effectiveness of the Word2Vec-based semantic mapping method proposed in this study for aligning TRIZ inventive principles with transforming bridge methods, the bidirectional encoder representations from transformers (BERT) semantic model was introduced as a comparative algorithm. A performance evaluation experiment was conducted, and the similarity results between TRIZ principles and transforming bridge methods generated by the BERT model are shown in Figure 6.

An artificial semantic matching annotation set between TRIZ inventive principles and transforming bridge methods was constructed as the evaluation benchmark for algorithmic accuracy. The annotated samples comprehensively cover the entire semantic combination space between TRIZ principles and transforming bridges. A systematic annotation process and terminology control mechanism were employed, along with expert review, to ensure the consistency and reliability of the annotations. Based on the manually annotated semantic matching reference set, the accuracy of the Word2Vec and BERT algorithms in the TRIZ–transforming bridge semantic mapping task was calculated as 0.88 and 0.80. This indicates that Word2Vec demonstrates better adaptability under the characteristics of the current corpus and task. The superior performance of the Word2Vec algorithm can be attributed to the inherent characteristics of the textual descriptions associated with TRIZ principles and transforming bridge methods. These descriptions are generally concise, rich in domain-specific terminology, and exhibit a stable syntactic structure with concentrated semantic content. Such features align well with the modeling assumptions of word vector–based approaches, making Word2Vec particularly effective in capturing the semantic similarity between terms. In contrast, although BERT demonstrates strong contextual representation capabilities, its advantages are more pronounced in tasks involving longer texts with abundant contextual dependencies. Given the short-text nature and limited contextual cues in the present dataset, Word2Vec proves to be more suitable for the semantic mapping task in this study.

To further validate the robustness of the proposed Word2Vec-based semantic mapping model between TRIZ principles and transforming bridge methods, this study conducted a multi-source corpus evaluation experiment. Three additional representative corpora were constructed, namely: a patent corpus, an academic corpus, and an encyclopedia corpus. Each corpus was used to separately construct semantic representations of 40 TRIZ principles and four types of transforming bridge methods, structured in three columns: ID, name, and description. The patent corpus was built from technical abstracts and specification paragraphs related to mechanical innovation design, extracted from the China National Intellectual Property Administration and Google Patents. The academic corpus was derived from term definitions and case analyses found in TRIZ- and Extenics-related literature indexed by databases such as CNKI and Web of Science. The encyclopedia corpus was compiled from authoritative explanatory content on relevant concepts obtained from platforms such as Baidu Baike and Wikipedia. In each type of corpus, the Word2Vec algorithm was applied to compute the semantic similarity between each pair of TRIZ principles and transforming bridge methods, resulting in a semantic similarity matrix. By comparing these computed similarities with a manually annotated reference set, the model’s matching accuracy under different corpus conditions was calculated, enabling a systematic evaluation of the stability and robustness of the semantic mapping method. In the manually annotated reference set, the value ‘1’ indicates that a semantic association exists between a given TRIZ principle and a transforming bridge method, while ‘0’ indicates no such association. Since the Word2Vec algorithm computes similarity scores between every TRIZ principle and each transforming bridge method, the bridge method with the highest similarity score for each TRIZ principle is identified as semantically associated, while the others are considered unassociated. The manually annotated reference set, the mapping results based on the primary corpus used in this study, and the results based on the patent corpus, academic corpus, and encyclopedia corpus are shown in Figure 7.

The experimental results show that the semantic mapping accuracy of the Word2Vec-based algorithm across the four corpora is 0.88, 0.89, 0.88, and 0.89, respectively, with a fluctuation range of less than ±0.01. This indicates that the proposed method exhibits strong adaptability to different corpus styles and expression patterns. These results demonstrate that the semantic mapping approach maintains good robustness and generalization ability across diverse corpus scenarios, effectively capturing the semantic associations between TRIZ principles and transforming bridge methods, thus showcasing its high practical application value.

3.3.3. Evaluation of Mutation Conflict Resolution

Traditional transforming bridge methods often lack standardized quantitative indicators or evaluation functions for assessing the effectiveness of conflict resolution. The coexistence degree function of the transforming bridge enables a quantitative evaluation and comparison of the coexistence level among multiple design objectives under specific component attributes and parameter conditions. It also serves as a tool to classify product components into different sets. Based on the concept of coexistence degree for contradictory problems in extenics, resolving a contradiction essentially means converting it into a coexistence relationship—that is, turning the coexistence degree of a contradiction from less than or equal to zero to greater than zero. The specific definition is described as follows:

Definition 3.

Let $U$ be the universe representing all product components, and let $u$ be any element in $U$. Let $K$ be a mapping from $U$ to the real domain $I$, and let $E\left(T\right)=\left\{\right(u,w\left)\right|u\in TuU,w=K\left(u\right)\in I\}$ be the extension set over domain $U$. Then, $w=K\left(u\right)$) is defined as the coexistence degree function of the transforming bridge for the extension set $E\left(T\right)$. It is specifically expressed as follows:

$$\begin{array}{c}K\left(u\right)=K\left(x\right)^K\left(y\right)\end{array}$$

(8)

Here, x, y—two design features of the element $u$ in the domain $U$ . K(x), K(y)—the associated degrees of the design features x and y, respectively.

$$\begin{array}{c}K\left(x\right)=\left\{\begin{array}{cc}\hfill {\displaystyle \frac{\rho \left(x, x_0, X\right)}{D\left(x, X_0, X\right)}},& D\left(x, X_0, X\right)\ne 0,x\in X\hfill \\ \hfill -\rho \left(x, x_0, X_0\right)+1,& D\left(x, X_0, X\right)=0,x\in X_0\hfill \\ \hfill 0,& D\left(x, X_0, X\right)=0,x\notin X_0,x\in X\hfill \end{array}\right.\end{array}$$

(9)

$$\begin{array}{c}K\left(y\right)=\left\{\begin{array}{cc}\hfill {\displaystyle \frac{\rho \left(y, y_0, Y\right)}{D\left(y, Y_0, Y\right)}},& D\left(y, Y_0, Y\right)\ne 0,y\in Y\hfill \\ \hfill -\rho \left(y, y_0, Y_0\right)+1,& D\left(y, Y_0, Y\right)=0,y\in Y_0\hfill \\ \hfill 0,& D\left(y, Y_0, Y\right)=0,y\notin Y_0,x\in Y\hfill \end{array}\right.\end{array}$$

(10)

• $X,X_0,Y,Y_0$—Four value intervals for two parameters of element $u$ in the domain $U$.
• $\rho (x,x_0,X_0)$—The degree to which the feature $x$ of element $u$ satisfies the target mutation interval $X_0$, where $x_0$ represents the optimal mutation value.
• $\rho \left(y,y_0,Y_0\right)$—The degree to which the feature $y$ of element $u$ satisfies the target mutation interval $Y_0$, where $y_0$ represents the optimal mutation value.
• $D\left(x,X_0,X\right)$—The degree to which the mutation parameter $x$ of element $u$ satisfies the entire mutation interval.
• $D\left(y,Y_0,Y\right)$—The degree to which the mutation parameter $y$ of element $u$ satisfies the entire mutation interval.
• $^$—The extenics and operation, indicating the minimum value is taken.

4. Case Study

The gear shaft is a critical component in gear transmission systems, responsible for supporting rotating parts and transmitting motion, torque, or bending moments. However, during operation, continuous contact with components such as sleeves, bearings, and bushings leads to relative surface motion, which causes friction and wear. Over time, this wear alters the shaft’s dimensions and compromises its original geometry, machining accuracy, and positional precision, ultimately reducing its operational efficiency and service life. We focus on a failed input shaft component from a gearbox, with its structural schematic illustrated in Figure 8. The gear shaft is composed of 40Cr steel and features a cylindrical main body. The shaft end is composed of both a spur gear and a helical gear, which engage with external components for power transmission. Threads and splines are machined onto the main body to facilitate mechanical connections with external parts. The observed failure was attributed to thread deformation, which subsequently resulted in relative motion between the shaft and connected components, leading to wear.

We collected a corpus composed of text excerpts from publicly available Chinese online sources, including patents, academic papers, and datasets in the field of mechanical manufacturing and remanufacturing. A total of 145 text segments related to part remanufacturing were compiled and used as training data for the knowledge extraction model. Using knowledge extraction techniques, remanufacturing entities and their relationships were identified from the text and subsequently imported into a Neo4j graph database to construct the $G_{RMPart}$ mutation graph model, as illustrated in Figure 9. The orange circles in Figure 9 represent retired mechanical parts, the green circles represent parts under Generalized Remanufacturing, the blue circles represent base features, and the pink circles represent failure features.

The historical data were retrieved in order to establish the gene mutation description set Q for the gear shaft part, as presented in

Table 4. Description set Q for gene mutation of gear shaft part.

ID	Mutation Description
$Q_1$	Overlay repair. Surface material change to improve localized wear resistance, possibly introducing residual stresses.
$Q_2$	Laser cladding repair. The change in the composition of the surface material significantly improves wear resistance and fatigue strength, but due to the difference in the coefficient of thermal expansion of the coating/substrate, residual stresses may be generated resulting in a reduction of the bond strength and fatigue life of the repaired area.
$Q_3$	Turning and press-fitting/bonding of high-precision sleeves on worn shaft segments. Replacement of partial material by sleeve material, addition of new structural elements, restoration of coaxiality, wear resistance depending on sleeve material.
$Q_4$	A metal (often chromium or nickel) is plated over the wear area to restore dimensions. The surface material is changed to improve surface hardness and finish, but the plating has limited bonding strength and may wear out and lead to reduced wear resistance and surface degradation.
$Q_5$	Thermal spray repair. Surface material changes to improve localized wear resistance and possible introduction of residual stresses.
$Q_6$	Turning of shaft body sections to change geometry to match new application scenarios. Changes in dimensions, contours, shorter or thinner shaft bodies, possible reduction in strength and rigidity, adaptation to new load conditions, simplification or transformation of functions (e.g., transmission of light load torques only).
$Q_7$	Roughing removes non-critical areas and retains high quality areas as new part blanks. The structure is completely reconstructed, information is reset, and the design is based on new functional objectives.
$Q_8$	New connection structure on the shaft body to adapt to the new assembly system. Local structural changes to transform the functional mode, performance adaptation to the new system and no more contact friction on worn shaft segments.
$Q_9$	Sub-component extraction for reuse. Precise separation of the large gear section from the main shaft body by wire or lathe cutting, assembly of the extracted large gear with a newly machined or standardized shaft body by means of keying + gluing + hot assembly, etc., and partial performance restoration.

.

Using the keyword extraction, rule-based classification rules, word segmentation, and other NLP toolkits in PyCharm 2023.3.2 (Community Edition), the mutation description set is evaluated through the discriminant set D, resulting in the discriminant outcomes shown in

Table 5. Classification of conflict types in mutation descriptions.

ID	Conflict Type
$Q_1$	No apparent conflict
$Q_2$	Material–Performance Conflict
$Q_3$	No apparent conflict
$Q_4$	Material–Performance Conflict
$Q_5$	No apparent conflict
$Q_6$	Structure–Performance/Structure–Function conflicts
$Q_7$	No apparent conflict
$Q_8$	No apparent conflict
$Q_9$	No apparent conflict

.

In accordance with the aforementioned results, it can be concluded that method $Q_6$ entails the modification of the geometric dimensions of the shaft. However, due to constraints imposed by the original material and structural design, the newly manufactured component often fails to meet essential functional or performance requirements, such as enhanced load-bearing capacity or corrosion resistance under specific conditions. Consequently, the component is not immediately suitable for direct application. One representative variant scheme involves machining the gear section, worn journal, and spline area, followed by redesign and remanufacturing into a mandrel. In light of the shaft’s loading conditions and mechanical strength theory, the load-bearing capacity of a mandrel is generally determined by bending stress (${\sigma }_b$), as defined in Equation (10).

$$\begin{array}{c}{\sigma }_b={\displaystyle \frac{M}{W_b}}\end{array}$$

(11)

• $M$ denotes the bending moment, determined by the applied load $F$ and the lever arm $L$ (i.e., $M=F\times L$). Under the assumption of identical working conditions, the bending moment is considered constant.
• $W_b$ represents the section modulus, which characterizes the shaft’s resistance to bending, $W_b={\displaystyle \frac{\pi d^3}{32}}$, $d$ denotes the diameter of the shaft.

It can thus be concluded that the bending stress is inversely proportional to the cube of the shaft diameter. As the diameter, d, decreases, the load-bearing capacity of the shaft rapidly declines. The original diameter of the gear shaft (root circle diameter) is insufficient to meet the design strength requirements of the new shaft. However, increasing the diameter is limited by the blank size and existing structural constraints. This creates a conflict between the redesign remanufacturing process and maintaining the shaft’s load-bearing capacity. Let G₁ = (structure, shaft diameter, d) represent the goal of modifying the shaft, and G₂ = (performance, load-bearing capacity, v) represent the goal of maintaining the shaft’s operational performance. L = (L₁, L₂, L₃) represents the conditions that must be met to achieve both goals G₁ and G₂, as detailed in

Table 6. Element representation of remanufacturing conditions for gear shaft parts.

Condition Name	Element Representation
$L_1$	$\left[\begin{array}{ccc}\mathrm{D}\mathrm{i}\mathrm{m}\mathrm{e}\mathrm{n}\mathrm{s}\mathrm{i}\mathrm{o}\mathrm{n}& \mathrm{D}\mathrm{i}\mathrm{a}\mathrm{m}\mathrm{e}\mathrm{t}\mathrm{e}\mathrm{r}\mathrm{o}\mathrm{f}\mathrm{s}\mathrm{h}\mathrm{a}\mathrm{f}\mathrm{t}& \mathrm{d}\\ & \mathrm{L}\mathrm{e}\mathrm{n}\mathrm{g}\mathrm{t}\mathrm{h}\mathrm{o}\mathrm{f}\mathrm{s}\mathrm{h}\mathrm{a}\mathrm{f}\mathrm{t}& \mathrm{L}\\ & \mathrm{S}\mathrm{u}\mathrm{p}\mathrm{p}\mathrm{o}\mathrm{r}\mathrm{t}\mathrm{s}\mathrm{p}\mathrm{a}\mathrm{c}\mathrm{i}\mathrm{n}\mathrm{g}& {\mathrm{L}}_{\mathrm{s}}\end{array}\right]$
$L_2$	$\left[\begin{array}{ccc}\mathrm{M}\mathrm{a}\mathrm{t}\mathrm{e}\mathrm{r}\mathrm{i}\mathrm{a}\mathrm{l}& \mathrm{Y}\mathrm{i}\mathrm{e}\mathrm{l}\mathrm{d}\mathrm{i}\mathrm{n}\mathrm{g}\mathrm{s}\mathrm{t}\mathrm{r}\mathrm{e}\mathrm{n}\mathrm{g}\mathrm{t}\mathrm{h}& {\mathsf{\sigma }}_{\mathrm{s}}\\ & \mathrm{M}\mathrm{o}\mathrm{d}\mathrm{u}\mathrm{l}\mathrm{u}\mathrm{s}\mathrm{o}\mathrm{f}\mathrm{e}\mathrm{l}\mathrm{a}\mathrm{s}\mathrm{t}\mathrm{i}\mathrm{c}\mathrm{i}\mathrm{t}\mathrm{y}& \mathrm{E}\end{array}\right]$
$L_3$	$\left[\begin{array}{ccc}\mathrm{L}\mathrm{o}\mathrm{a}\mathrm{d}\mathrm{i}\mathrm{n}\mathrm{g}& \mathrm{L}\mathrm{o}\mathrm{a}\mathrm{d}\mathrm{i}\mathrm{n}\mathrm{g}\mathrm{s}\mathrm{i}\mathrm{z}\mathrm{e}& \mathrm{F}\\ & \mathrm{L}\mathrm{o}\mathrm{a}\mathrm{d}\mathrm{i}\mathrm{n}\mathrm{g}\mathrm{d}\mathrm{i}\mathrm{s}\mathrm{t}\mathrm{r}\mathrm{i}\mathrm{b}\mathrm{u}\mathrm{t}\mathrm{i}\mathrm{o}\mathrm{n}& \mathrm{C}\mathrm{o}\mathrm{n}\mathrm{c}\mathrm{e}\mathrm{n}\mathrm{t}\mathrm{r}\mathrm{a}\mathrm{t}\mathrm{e}\mathrm{d}\mathrm{l}\mathrm{o}\mathrm{a}\mathrm{d}/\mathrm{d}\mathrm{i}\mathrm{s}\mathrm{t}\mathrm{r}\mathrm{i}\mathrm{b}\mathrm{u}\mathrm{t}\mathrm{e}\mathrm{d}\mathrm{l}\mathrm{o}\mathrm{a}\mathrm{d}\\ & \mathrm{L}\mathrm{o}\mathrm{a}\mathrm{d}\mathrm{i}\mathrm{n}\mathrm{g}\mathrm{p}\mathrm{o}\mathrm{s}\mathrm{i}\mathrm{t}\mathrm{i}\mathrm{o}\mathrm{n}& \mathrm{A}\mathrm{w}\mathrm{a}\mathrm{i}\mathrm{t}\mathrm{a}\mathrm{d}\mathrm{e}\mathrm{c}\mathrm{i}\mathrm{s}\mathrm{i}\mathrm{o}\mathrm{n}\end{array}\right]$

.

The goals, G₁ and G₂, are determined by the characteristics and values of the primitives in the conditions L. Therefore, the conflict can be expressed as (G₁, G₂) ↑ (L₁, L₂, L₃).

By substituting G₁ = (structure, shaft diameter, d) and G₂ = (performance, load-bearing capacity, v) into the $G_{RMPart}$ mutant conflict parameters-TRIZ engineering parameter mapping table, the mapping relationship between the conflicting objectives and TRIZ engineering parameters is obtained, as shown in

Table 7. Mapping relationship between conflict targets and TRIZ engineering parameters.

Conflict Objective	Goal Features	Corresponding to TRIZ Engineering Parameters	Parameter Type
$G_1$	Shaft diameter	4. Length of stationary object	Improvement parameters
$G_2$	Load-carrying capacity	11. Stress	Anti-deterioration parameters

. Among them, the engineering parameter to be improved is parameter 4, the length of the stationary object, and the engineering parameter to be protected from deterioration is parameter 11, stress. Upon querying the conflict matrix for engineering parameters 4 and 11, three inventive principles are identified: Principle 1, segmentation; Principle 14, curvature; and Principle 35, change of physical or chemical parameters. Descriptions of the corresponding inventive principles are provided in

Table 8. The invention principle used.

Number	Name	Description of the Invention Principle
1	Segmentation	Splitting an object into distinct parts that are independent of each other and can be quickly combined and integrated to enhance the functionality of the object or to reduce the negatives inherent in working with the object as a whole.
14	Curvature	Use of curved parts instead of straight parts, including curved motion instead of straight motion
35	Change of physical or chemical parameters	Changing the concentration, density, flexibility, temperature, etc., of aggregates (states of matter) to simplify the process or to improve product properties.

.

By querying the mapping correlation similarity table between inventive principles and transforming bridge methods, the semantic similarity between the three inventive principles and the four transforming bridge methods can be obtained, as illustrated in

Table 9. Semantic similarity between TRIZ inventive principles and transforming bridges.

Similarity	Divider	Visualize	Change of Physical or Chemical Parameters
Connecting bridge	0.878	0.826	0.849
Separating bridge	0.981	0.906	0.960
Goal transformation bridge	0.946	0.956	0.937
Conditional transformation bridge	0.961	0.924	0.988

.

For each inventive principle, the transforming bridge method with the highest similarity is selected for implementation. The extenics transformations contained in the transforming bridge method are extracted, and the relevant elements are transformed to generate specific conflict resolution solutions.

Solution 1: Segmentation principle—separating bridge. The segmentation principle can be understood as decomposing the modified and remanufactured shaft structure into a core part (existing shaft) and an external reinforcement part. The construction method of the separating bridge involves interrupting the force transmission path of local shaft segments through structural reinforcement components (such as reinforcement sleeves), thereby enhancing the bending stiffness and overall load-bearing capacity of the shaft. It is assumed that the modified shaft part is used to manufacture a positioning mandrel, with a clearance fit positioning method and a four-step stepped shaft structure. The diameters of each shaft segment after size reduction are as follows:

$$\begin{array}{c}{Gb}_{RMPart}^S=\left[\begin{array}{ccc}ShaftSegment1& d_1& 28\mathrm{m}\mathrm{m}\\ ShaftSegment2& d_2& 40\mathrm{m}\mathrm{m}\\ ShaftSegment3& d_3& 30\mathrm{m}\mathrm{m}\\ ShaftSegment4& d_4& 17\mathrm{m}\mathrm{m}\end{array}\right]\end{array}$$

(12)

Since Shaft Segment 3 of the mandrel is the assembly section and comes into direct contact with the mating component, its relatively long length and small diameter may lead to insufficient load-bearing capacity, making it prone to bending, instability, or fatigue failure. By adding a reinforcing sleeve to Shaft Segment 3, the diameter of the section is increased, thereby enhancing the moment of inertia $W_b$. As a result, ${\sigma }_{new}<{\sigma }_{original}$, meaning the bending stress on the segment is reduced, thus improving the shaft’s bending resistance.

Solution 2: Curvature principle—goal transforming bridge. The curvature principle emphasizes alleviating conflict problems through geometric transition forms. The construction method of the goal transforming bridge can be understood as a transformation of the target, ${\mathrm{G}}_1$, i.e., introducing a geometric transition into the mandrel structure. After modification, the diameter difference between Shaft Segment 1 and Shaft Segment 2 of the mandrel is 12 mm. Due to insufficient load-bearing capacity during use, fatigue fracture is likely to occur at the diameter transition between the two shaft segments. Based on the analysis of the curvature principle, a filet transition instead of a right-angle transition is applied at the diameter change of the shaft. By introducing a filet radius R, the stress concentration factor of the shaft can be reduced.

Solution 3: Change of physical or chemical parameters principle—conditional transforming bridge. Analyzing this principle, the primary approach to modifying the physical and chemical parameters of mechanical parts lies in treating the part material to alter its surface hardness or material properties. Specific techniques include surface carburizing or surface quenching, as well as applying high-strength or high-hardness coatings such as nickel-based alloy coatings or ceramic coatings, aiming to enhance surface hardness and wear resistance, thereby improving load-bearing capacity. Accordingly, a conditional transforming bridge can be constructed by transforming the material characteristics in condition $L_2$. For the original 40Cr shaft part, its tensile strength is approximately 600–750 MPa, and its yield strength is about 350–500 MPa. After material treatment, these values can be increased to 810–980 MPa and 785–800 MPa, respectively, effectively improving the part’s dynamic load-bearing capacity and reducing crack initiation and propagation caused by cyclic loading.

After proposing a conflict resolution scheme for part mutation, the transforming bridge coexistence degree function should be used to determine whether the proposed scheme successfully resolves the conflict. Taking solution 1 as an example, in practical application, the reinforcement component is a shaft sleeve added to Shaft Section 3, increasing its diameter from 30 mm to 40 mm. According to test data provided by the enterprise, the bending stress on the original mandrel part is 260 MPa, while after adding the reinforcement, the bending stress is reduced to 110 MPa. In engineering applications, the diameter range of mandrels is usually determined by specific application scenarios, load requirements, material properties, and manufacturing standards. Generally, for light machinery and general industrial equipment, the typical diameter range is [10, 80] mm. Thus, the qualitative mutation domain for the mandrel’s diameter characteristic can be defined as X = [10, 80] mm. For the retired shaft part selected in this section, the maximum diameter of the shaft section after being reduced to a blank is 60 mm, which determines the target quantitative mutation domain for the mandrel diameter as X₀ = [10, 60] mm. During the part mutation process, the more material is retained, the higher the value of the mutated part; therefore, X₀ = 60 is taken as the optimal point.

In engineering applications, the bending stress of a mandrel is typically determined based on the allowable stress of the material and specific working conditions. Generally, the bending stress range of a mandrel depends on the yield strength, fatigue strength, and safety factor of the material. For alloy steel, the allowable bending stress generally does not exceed 320 MPa. Therefore, the qualitative mutation domain for the mandrel’s load-bearing capacity characteristic can be defined as Y = [0, 320] MPa. After reinforcement, the bending stress of the mandrel part should be controlled within 260 MPa. Thus, the target quantitative mutation domain for the mandrel’s load-bearing capacity characteristic is Y₀ = [0, 260] MPa. Since the smaller the bending stress the mandrel bears, the better its stability, the optimal value is taken as y₀ = 0. Once all parameters are determined, they can be substituted into Equations (8) and (9) to obtain the following:

$$\begin{array}{c}K\left(x\right)={\displaystyle \frac{\rho \left(x, x_0, X\right)}{D\left(x, X_0, X\right)}}={\displaystyle \frac{10-x}{\left|x-45\right|-\left|x-35\right|-10}}=3\end{array}$$

(13)

$$\begin{array}{c}K\left(y\right)=-\rho \left(y, y_0, Y_0\right)+1=-\left(x-260\right)+1=51\end{array}$$

(14)

The calculation yields the coexistence function $K(x,y)=\left(51\right)^\left(3\right)$. In the transforming bridge coexistence function, if any target yields a negative value, it indicates a contradiction between the two related objectives. The absolute value represents the degree of opposition or conflict between the two objectives. Since the two conflicting objectives in the modified remanufacturing of the gear shaft do not yield a negative value under the current conditions, it indicates that there is no contradiction. Therefore, this scheme is capable of achieving effective conflict resolution.

5. Discussion

We propose a novel conflict resolution strategy for $G_{RMPart}$ mutation. The proposed strategy integrates the fusion transforming bridge method and the TRIZ invention principle. The strategy constructs four types of bridges: a connecting bridge, a separating bridge, a goal transforming bridge, and a conditional transforming bridge. The strategy realizes a semantic mapping between the TRIZ invention principle and the transforming bridge method through the Word2Vec algorithm. Additionally, a coexistence degree function is introduced to quantitatively evaluate the effectiveness of conflict resolution, thereby enabling systematic identification and intelligent resolution of technical conflicts during the $G_{RMPart}$ mutation process.

From a methodological perspective, the strategy boasts several advantages. First, it integrates the TRIZ theory and the transformation bridge method, providing multiple solution paths for conflict resolution from multiple dimensions. This enhances the breadth and innovativeness of the solutions. Second, it realizes an intelligent matching between TRIZ invention principles and the transformation bridge strategy through the semantic mapping mechanism, improving the relevance and effectiveness of the solution recommendation. Third, it introduces the coexistence function to quantitatively evaluate solution effects, helping to optimize the screening and decision support among multiple conflict resolution paths.

From a theoretical perspective, the conflict resolution mechanism is extended to the modeling and mutation analysis of mechanical part genes. And a generalized model for conflict transformation and solution generation is established. It provides systematic methodological support for conflict identification, transformation, and innovation in the remanufacturing process, enriching the cross-disciplinary integration and application pathways of TRIZ theory and extenics in the engineering domain.

From an application perspective, this strategy holds significant value in enhancing the systematic, intelligent, and sustainable development of remanufacturing processes for retired mechanical parts. By identifying and resolving gene-level conflicts, it effectively supports functional reconstruction and performance improvement during repair, optimization, and redesign. Moreover, it provides methodological support for intelligent decision-making in remanufacturing service systems, thereby improving resource utilization efficiency.

However, the proposed method in this study still faces certain limitations in practical applications.

(1)

Due to limitations in experimental equipment and data collection conditions, the data used in this study are all from Chinese corpora, and the semantic processing techniques applied have been specifically adapted to the characteristics of the Chinese language. If the proposed method is to be extended to an international context, targeted modifications will be required. In addition, the robustness of the proposed knowledge graph model has not yet been validated in large-scale or more complex scenarios involving sparse or low-quality data. However, the graph modeling method developed in this study, based on semantic relation extraction and node structure optimization, provides a certain degree of scalability and adaptability. Future studies may further explore and address this issue by optimizing the technical framework and data acquisition mechanisms, thereby enhancing the model’s applicability in more complex environments.

(2)

This research primarily focuses on the technical feasibility of the remanufacturing process. The current coexistence degree function does not fully incorporate the multidimensional impacts of technical, economic, and environmental factors. Nevertheless, the proposed method lays a solid theoretical and modeling foundation for future studies on trade-offs between performance and cost. It could be further extended by integrating economic and environmental evaluation indicators, enabling multi-objective conflict assessment and optimization in terms of performance-cost or resource efficiency. This would offer a more comprehensive reflection of the synergy between economic and sustainability goals in remanufacturing.

(3)

The applicability and feasibility of the method in complex engineering environments require further enhancement. The gear shaft used in the case study represents a typical rotating mechanical component, exhibiting representative failure modes (e.g., fatigue fracture and surface degradation) and performance evolution characteristics, thus partially demonstrating the practical value of the proposed method. However, the method still shows limitations in addressing integrated conflicts in complex systems involving multi-level, multi-scale, and multi-objective coupling. Even so, this research provides an exploratory approach that bridges theory and practice for remanufacturing conflicts of complex components, with potential for further refinement and cross-industry application. Future work may expand the gene modeling framework to the “product” level and explore optimization methods for coordinated multi-conflict resolution, thereby meeting the demands of complex systems.

In summary, the conflict resolution strategy proposed in this paper exhibits significant innovation and applicability in both theoretical research and engineering practice. However, further research is necessary to enhance model intelligence, semantic precision, and multi-objective trade-offs. This will provide more comprehensive support for intelligent decision-making of remanufacturing under complex systems in the future.

6. Conclusions

This paper focuses on the conflict identification and resolution issues of retired mechanical part genes during the mutation process and constructs a systematic theoretical and methodological framework. First, a mutation graph model is proposed to achieve the integrated representation of material, structure, function, performance, failure information, and remanufacturing process information of the parts. A conflict identification method based on rules is designed to recognize four types of attribute conflicts, and a formalized conflict problem model is constructed using the element representation method, enhancing the formalization and solvability of conflict modeling. Secondly, a conflict resolution strategy that integrates TRIZ and the transforming bridge method is proposed. TRIZ engineering parameters are reconstructed to address the mutation conflict issues of retired mechanical part genes. Semantic mapping between TRIZ inventive principles and the transforming bridge method is achieved using Word2Vec. Four methods—connecting bridge, separating bridge, goal transforming bridge, and condition transforming bridge—are designed to generate resolution schemes, and a coexistence degree function is introduced to quantitatively evaluate the resolution effects, enhancing the systematization of conflict transformation and the diversity of scheme generation. Finally, taking retired shaft parts as an example, three resolution schemes are constructed, and their feasibility is verified, confirming the effectiveness and practical value of the proposed method. The research results provide new methodological insights for conflict identification and modeling of multi-source heterogeneous data, laying the theoretical foundation and data support for generalized remanufacturing scheme design, and contributing to the development of intelligent remanufacturing.