1. Bibliographic Information

1.1. Title

主客观赋权专家推理的滚磨光整加工工艺要素决策 (Decision of Barrel Finishing Process Elements Based on Subjective and Objective Empowerment Expert Reasoning)

1.2. Authors

• 张浩 (ZHANG Hao)
• 田建艳 (TIAN Jianyan)
• 王良晨 (WANG Liangchen)
• 史玉皓 (SHI Yuhao)
• 孙家飞 (SUN Jiafei)
• 杨胜强 (YANG Shengqiang)

Affiliations:

• 1.a. Taiyuan University of Technology, College of Electrical and Power Engineering, Taiyuan 030024, China
• 1.b. Taiyuan University of Technology, College of Mechanical and Vehicle Engineering, Taiyuan 030024, China
• 2. Langfang North Tianyu Mechanical & Electrical Technology Co., Ltd., Langfang 065000, China

1.3. Journal/Conference

控制工程 (Control Engineering)

1.4. Publication Year

2025, 32(8): 1524-1536 (This indicates it's a forthcoming publication or was published recently in 2025, according to the provided text).

1.5. Abstract

Roller finishing is a surface integrity processing technology used in advanced manufacturing to improve the surface quality and performance of parts. The core process elements affecting its effectiveness and efficiency are abrasive media, finishing equipment, and grinding fluid. While existing expert reasoning (ER) methods can achieve abrasive media decision, their accuracy is unsatisfactory for finishing equipment and grinding fluid decisions. Moreover, these methods fail to make decisions when new problem feature information is incomplete. To address these issues, this paper proposes a decision model for barrel finishing process elements based on subjective and objective empowerment expert reasoning (SOE-ER). The model first details the construction process of hierarchical classification rules, then introduces subjective and objective empowerment in expert reasoning, and finally establishes a decision system based on the SOE-ER model, which is validated through experimental research. Results show that the SOE-ER model achieves high decision accuracy for all three core process elements and can provide reasonable and effective guidance for decision-making even with incomplete feature information in new problems.

1.6. Original Source Link

/files/papers/690503a1c95b8a1241e580e5/paper.pdf (This is a local file path, indicating the paper content was provided directly rather than linked to an external public repository.)

2. Executive Summary

2.1. Background & Motivation

The core problem the paper aims to solve lies in the barrel finishing process, which is a crucial surface integrity processing technology in advanced manufacturing for enhancing part surface quality and usage performance. The effectiveness and efficiency of this process heavily depend on three core process elements: abrasive media, finishing equipment, and grinding fluid.

Currently, expert reasoning (ER) methods exist for deciding abrasive media, but their accuracy is not ideal when applied to finishing equipment and grinding fluid decisions. A significant limitation is their inability to make decisions when new problem feature information is incomplete. This means that if some characteristics of a new part or processing requirement are unknown, the system cannot provide a recommendation. This gap hinders the widespread adoption of intelligent decision-making in barrel finishing, where real-world data might often be partially missing.

Therefore, the paper's entry point or innovative idea is to leverage expert knowledge and successful processing cases to develop a new rule base construction method and a novel reasoning method that can overcome these limitations, specifically by improving accuracy for all process elements and enabling decisions even with incomplete feature information.

2.2. Main Contributions / Findings

The paper makes several primary contributions:

• Proposed SOE-ER Model: It introduces a novel Subjective and Objective Empowerment Expert Reasoning (SOE-ER) model for barrel finishing process elements decision. This model aims to integrate expert experience and successful case knowledge.

• Hierarchical Classification Rule Construction: It elaborates on a detailed process for constructing hierarchical classification rules, which forms the basis of the knowledge base. This includes defining feature value range levels, hierarchical classification of training set cases, and interval rule construction, along with a special rule library for unique processing scenarios.

• Subjective and Objective Empowerment: The model incorporates both subjective feature weighting (using Analytic Hierarchy Process (AHP) to reflect the importance of different part features) and objective rule weighting (based on feature interval compactness to refine the selection of activated rules).

• Handling Incomplete Information: A key contribution is the mechanism to update subjective feature weights when feature information is incomplete, allowing the system to still make decisions in such scenarios, a limitation of previous methods.

• Decision System Development: A decision system for barrel finishing process elements is established based on the SOE-ER model, providing a practical platform for application.

• High Decision Accuracy and Robustness: Experimental results demonstrate that the SOE-ER model achieves high decision accuracy for all three core process elements (abrasive media, finishing equipment, and grinding fluid). It significantly outperforms traditional ER and CBR methods, especially when dealing with cases that have large differences in feature information or incomplete feature information.

  The key conclusions are that the SOE-ER model effectively addresses the challenges of low accuracy for equipment and fluid decisions and the inability to handle incomplete data, providing a robust and intelligent guidance for barrel finishing process element decision-making.

3. Prerequisite Knowledge & Related Work

3.1. Foundational Concepts

• Barrel Finishing (滚磨光整加工): This is a surface integrity processing technology used in manufacturing. Parts are placed in a finishing equipment (e.g., vibratory or centrifugal machine) along with abrasive media (also called tumbling media or abrasive blocks) and grinding fluid. Through complex relative motions, the media collide, roll, and micro-abrade the part surfaces. The goal is to reduce surface roughness, remove burrs and microscopic defects, and improve surface quality and performance.

• Expert System (专家系统): An expert system is a computer program that emulates the decision-making ability of a human expert. It typically consists of a knowledge base (containing facts and rules from a specific domain) and an inference engine (which applies the rules to the facts to deduce new facts or recommend actions). The paper leverages this concept to automate decisions for barrel finishing.

• Expert Reasoning (ER) (专家推理): This refers to the process within an expert system where rules and facts are used to draw conclusions or make decisions, mimicking a human expert's thought process. In the context of this paper, it's about selecting appropriate process elements based on part characteristics and processing requirements.

• Case-Based Reasoning (CBR) (案例推理): A problem-solving paradigm that uses past experiences (cases) to solve new problems. When a new problem arises, CBR attempts to find similar past cases, adapt their solutions, and apply them to the new problem. The paper mentions CBR as a prior approach, but notes its limitation: when new problem features are significantly different from stored cases, CBR often struggles to find sufficiently similar cases, leading to poor performance.

• Subjective Empowerment (主观赋权): This involves assigning weights to different factors or criteria based on human judgment or expert opinions. These weights reflect the perceived importance or influence of each factor. In this paper, Analytic Hierarchy Process (AHP) is used for subjective empowerment.

• Objective Empowerment (客观赋权): This involves assigning weights to factors based on data-driven methods or mathematical algorithms, without direct human intervention. These weights often reflect the inherent characteristics of the data, such as variability or compactness. In this paper, feature interval compactness is used for objective empowerment.

• Analytic Hierarchy Process (AHP) (层次分析法): A structured technique for organizing and analyzing complex decisions. It breaks down a decision problem into a hierarchy of criteria and alternatives, then uses pairwise comparisons to derive ratio scale priorities for each element in the hierarchy. These priorities represent the relative importance of the elements, forming the basis for subjective weights.

• Interval Numbers/Fuzzy Numbers (区间数/模糊数): Mathematical constructs used to represent uncertain or imprecise values. An interval number is defined by a lower and upper bound (e.g., [0.2, 0.4]), indicating that the true value lies within this range. The paper uses interval rules to represent ranges of feature values, which is suitable for qualitative or imprecise input data.

3.2. Previous Works

The paper frames its work by highlighting the limitations of existing methods in barrel finishing process element decision.

• Existing Expert Reasoning (ER) for Abrasive Media: The paper notes that expert reasoning (ER) has been successfully applied to abrasive media decision, citing [4] Zhou X Y, TIAN J Y, GAO W, et al. Research on optimal model of the abrasive blocks based on expert reasoning[J]. Modern Manufacturing Engineering, 2020. However, its accuracy is unsatisfactory for finishing equipment and grinding fluid decisions. This suggests that while ER is a good starting point, it needs enhancement for the broader range of process elements.

• Case-Based Reasoning (CBR) Limitations: The paper mentions case base reasoning (CBR) as another approach for abrasive media decision ([3] YANG Y, GAO W, YANG S Q, et al. Optimal model of abrasive blocks based on fuzzy clustering and case-based reasoning[J]. Surface Technology, 2019). The primary limitation of CBR is its low similarity when feature differences between a new problem and existing cases are large. This means CBR struggles with novel or significantly different scenarios.

• Expert Weight Determination in Expert Systems: The paper cites several works on expert weight determination as a critical aspect of expert systems:

  • [11] CHEN Z, ZHONG P S, LIU M, et al. An integrated expert weight determination method for design concept evaluation[J]. Scientific Reports, 2022: Proposed a two-layer integration method for expert weights, showing its effectiveness in improving accuracy. This underscores the importance of proper weighting.
  • [12] YU L P, HU L Y. Simulation and optimization of expert-assisted weighting in academic evaluation[J]. Statistics & Decision, 2022: Introduced expert-assisted weighting but did not address the issue of combined expert weighting.
  • [13] MA X Y, ZHANG H F, LIU Z J, et al. Temperature prediction model of electrical equipment based on variable weight combination[J]. Control Engineering of China, 2023: Proposed a variable weight combination prediction model using an improved AHP to enhance prediction accuracy and stability. This directly relates to the paper's use of AHP for weighting.
  • [14] BAI L L, BAI S W, DANG W C, et al. Coal mine safety assessment based on maximum deviation combination empowerment[J]. Computer Applications and Software, 2021: Proposed a maximum deviation combination empowerment method that integrates indicator weight information.
  • [15] WU J J, YANG Y J, WANG Z F. Research on the reliability allocation method of micro-robot based on combined weight[J]. Manufacturing Automation, 2022: Introduced a combination weighting method based on matrix estimation theory to overcome unreasonable traditional allocation.

• Handling Incomplete Data in Expert Systems: The paper also addresses the challenge of incomplete feature information, citing:

  • [16] WANG F D, GONG Z T, SHAO Y B. Incomplete complex intuitionistic fuzzy system: preference relations, expert weight determination, group decision-making and their calculation algorithms[J]. Axioms, 2022: Proposed estimation algorithms for missing elements in incomplete fuzzy systems.
  • [17] HOSSAIN E, HOSSAIN M S, ZANDER P O, et al. Machine learning with belief rule-based expert systems to predict stock price movements[J]. Expert Systems with Applications, 2022: Proposed updating initial belief degrees to handle uncertainties due to incomplete data. This provides a direct inspiration for the paper's solution to incomplete feature information.

3.3. Technological Evolution

The evolution of expert systems has moved from simpler rule-based systems to more sophisticated approaches that incorporate fuzzy logic, case-based reasoning, and advanced weighting mechanisms. Early expert systems primarily relied on fixed rules and complete information. The introduction of CBR allowed for learning from past experiences, but faced challenges with dissimilar cases. The need for more robust decision-making led to research into weighting schemes (both subjective and objective) to better reflect the importance of different factors. More recently, the field has addressed the practical issue of incomplete data, developing methods to infer or adapt to missing information. This paper's work fits within this progression by combining expert reasoning with subjective and objective empowerment and explicitly addressing incomplete feature information, thereby enhancing the adaptability and accuracy of expert systems in a real-world manufacturing context.

3.4. Differentiation Analysis

Compared to the main methods in related work, the SOE-ER model's core differences and innovations are:

• Enhanced Accuracy for All Core Elements: Unlike prior ER methods that showed good accuracy only for abrasive media but struggled with finishing equipment and grinding fluid, SOE-ER aims to achieve high accuracy across all three core process elements.
• Integration of Subjective and Objective Empowerment: The paper's novelty lies in the dual-weighting approach. It combines subjective weights (derived from AHP based on expert knowledge) for feature attributes with objective weights (derived from feature interval compactness) for activated rules. This aims to provide a more balanced and robust decision-making process than methods relying solely on one type of weighting.
• Robustness to Incomplete Feature Information: A critical innovation is the mechanism to update subjective feature weights when new problem feature information is incomplete. This directly addresses a major limitation of conventional expert reasoning and case-based reasoning systems, which typically fail or provide poor results under such conditions.
• Improved Rule Base Construction: The hierarchical classification rules and improved interval production rule representation allow for a more nuanced and flexible representation of expert knowledge, which is particularly suitable for the complex and often qualitative nature of barrel finishing process parameters.
• Overall Superiority: Experimental comparisons show that SOE-ER consistently outperforms both CBR and ER methods in terms of decision accuracy, especially for cases with large feature differences or incomplete information, demonstrating its superior robustness and effectiveness.

4. Methodology

4.1. Principles

The core idea behind the proposed Subjective and Objective Empowerment Expert Reasoning (SOE-ER) model is to combine the strengths of expert knowledge and historical successful processing cases to make accurate and reliable decisions for barrel finishing process elements. The theoretical basis or intuition is that by systematically structuring expert knowledge into hierarchical classification rules and then refining the inference process with both subjective weights (reflecting expert-perceived importance of features) and objective weights (reflecting the data-driven compactness of rules), the system can mimic human expert decision-making more effectively. Furthermore, by adaptively adjusting subjective weights when feature information is incomplete, the model aims to maintain its decision-making capability even under uncertainty, a common scenario in real-world applications. This approach seeks to overcome the limitations of traditional expert systems and case-based reasoning by providing a more comprehensive and adaptable inference mechanism.

4.2. Core Methodology In-depth (Layer by Layer)

The SOE-ER model for barrel finishing process elements decision involves three main phases: knowledge base construction, expert reasoning with subjective and objective empowerment, and rule aggregation.

4.2.1. Knowledge Base Construction

The knowledge base consists of a case library and rule libraries, including a special rule library.

4.2.1.1. Process Element Case Library Construction

The case library is built by extracting pre-conditions (input features) and post-conditions (output process elements) from actual processing reports and schemes, guided by expert experience.

• Case Pre-conditions (Input Features): For shaft parts (used as an example), the pre-conditions include:

  • Part Dimensions:
    • Part length ($F_1$)
    • Part shaft diameter ($F_2$)
  • Part Pre-processing State:
    • Surface roughness before processing ($F_3$)
    • Burr before processing ($F_4$)
    • Brightness before processing ($F_5$)
    • Hardness before processing ($F_6$)
  • Part Processing Requirements:
    • Surface roughness after processing ($F_7$)
    • Burr after processing ($F_8$)
    • Brightness after processing ($F_9$)
    • Hardness after processing ($F_{10}$)
    • Residual stress improvement ($F_{11}$)

• Case Post-conditions (Output Process Elements): These are digitally represented for data management and expert reasoning.

  • Abrasive Media (滚抛磨块): Categorized by shape (spherical, triangular), size (e.g., 2#, 3#, 4#, 8#), and type (e.g., rough grinding 1R, medium grinding 2F, fine grinding 5G, super fine grinding 6P). An example of its digital representation is S2-1R (Spherical, Size 2#, Rough grinding). The following are the results from Table 1 of the original paper:

    序号	滚抛磨块	尺寸	形状	材质	类型	型号
    1	2号粗磨	2#	球形(S)	刚玉(C)	粗磨(R)	S2-1R
    2	2号中磨	2#	球形(S)	刚玉(C)	中磨(F)	S2-2F
    3	3号精磨	3#	氧化铝(A)	精磨(G)	S3-5G
    4	3号超精磨	3#	球形(S)	氧化铝(A)	超精磨(P)	S3-6P
    5	4号精磨	4#	球形(S)	氧化铝(A)	精磨(G)	S4-5G
    6	4号三角	4#	正三角形(T)	刚玉(C)	粗磨(R)	T4*4R
    7	斜三角8*8	8#	斜三角形(TP)	刚玉(C)	粗磨(R)	TP8*8R

  • Finishing Equipment (光整设备): Categorized by processing method (e.g., centrifugal, swirling, horizontal, vibratory) and volume (e.g., 400 L, 600 L). The following are the results from Table 2 of the original paper:

    序号	光整设备	容积/L	型号
    1	离心式光整机	5	LL05
    2	旋流式光整机	400	X400
    3	旋流式光整机	600	X600
    4	卧式光整机	1300	W1300
    5	卧式光整机	1600	W1600
    6	振动式光整机	600	ZY600

  • Grinding Fluid (磨液): Categorized by material applicability (e.g., steel, aluminum, titanium alloy) and specific function (e.g., anti-rust cleaning). The following are the results from Table 3 of the original paper:

    序号	磨液	适用范围	型号
    1	钢磨液	钢、合金钢、铸铁	HA-IS
    2	铝磨液	铝、铝合金、铜	HA-LA
    3	不锈钢磨液	不锈钢材质	HA-SS
    4	泡沫清洗磨液	泡沫清洗	HA-BC
    5	钛合金磨液	钛合金材质	HA-TA
    6	防锈清洗磨液	防锈清洗	HA-RC

4.2.1.2. Process Element Rule Library Construction

This process involves three steps: feature value range level division, hierarchical classification of training set cases, and interval rule construction. The overall process is visualized in Figure 1.

The following figure (Figure 1 from the original paper) illustrates the diagram of interval rules hierarchical classification construction:

该图像是图表，展示了图1区间规则分级分类构建的流程框图，描述了轴类零件案例库及其分类标准、磨块设备磨液案例库和区间规则构建的层级结构。

4.2.1.2.1. Feature Value Range Level Division

Standards are established for dividing the range of pre-condition feature values into levels based on national standards, industry common sense, expert opinions, and data distribution characteristics.

• Example for Roughness, Burr, Brightness:

  • Roughness (Ra): Divided into 4 levels using $0.2 \mu\mathrm{m}$, $0.4 \mu\mathrm{m}$, $0.8 \mu\mathrm{m}$ as boundaries.
  • Burr: Assigned 0 (no removal required) or 1 (removal required) based on whether burr removal is needed after processing.
  • Brightness: Divided into 4 levels (traceable machining marks, no brightness, low brightness without grinding patterns, very high brightness) assigned 1, 2, 3, 4 respectively.

• Other Features: Other feature values are categorized based on the distribution characteristics of actual case data. The interval boundaries for features like length, shaft diameter, pre-processing burr, hardness, and residual stress improvement are determined through simulation experiments using a control variable method to find optimal boundary values.

  The following are the results from Table 4 of the original paper:

  长度L/mm	轴径D/mm	粗糙度Ra/um	加工前毛刺Bi/mm	光亮度Br	硬度H/HRC	残余应力改善Rs/MPa	加工后毛刺B
  等级1 L≤100 [0.00,0.25]	等级1 D≤40 [0.00,0.25]	等级1 Ra≤0.2 [0.00,0.25]	等级1 B≤0.5 [0.00,0.25]	等级1 可辨加工痕迹方向 [0.00,0.25]	等级1 H≤40 [0.00,0.25]	等级1 Rs≥-100 [0.00,0.25]	等级1 有
  等级2 100<L≤300 [0.25,0.50]	等级2 40<D≤80 [0.25,0.50]	等级2 0.2<Ra≤0.4 [0.25,0.50]	等级2 0.5<B≤1 [0.25,0.50]	等级2 无光亮度 [0.25,0.50]	等级2 40<H≤50 [0.25,0.50]	等级2 -200≤Rs<-100 [0.25,0.50]	[0.00,0.50] 等级2
  等级3 300<L≤500 [0.50,0.75]	等级3 80<D≤120 [0.50,0.75]	等级3 0.4<Ra≤0.8 [0.50,0.75]	等级3 1<B≤1.5 [0.50,0.75]	等级3 较低且没有磨纹 [0.50,0.75]	等级3 50<H≤60 [0.50,0.75]	等级3 -300≤Rs<-200 [0.50,0.75]
  等级4 L>500 [0.75,1.00]	等级4 D>120 [0.75,1.00]	等级4 Ra>0.8 [0.75,1.00]	等级4 B>1.5 [0.75,1.00]	等级4 光亮度非常高 [0.75,1.00]	等级4 H>60 [0.75,1.00]	等级4 Rs<-300 [0.75,1.00]	无 [0.50,1.00]

4.2.1.2.2. Hierarchical Classification of Training Set Cases

Training set cases are classified to provide a structured basis for rule construction, considering the influence of each feature on the decision.

• Definition 1: Rule Structure A rule $R_i$ is defined as: $R_i: \text{IF } F_{i,1} \text{ AND } F_{i,2} \text{ AND } \cdots \text{ AND } F_{i,j} \text{ THEN } B_i$ Where:

  • $F_{i,j}$ is the $j$-th pre-condition (rule antecedent) of the $i$-th rule.
  • $B_i$ is the conclusion (rule consequent, representing a process element) of the $i$-th rule in the process element rule library.

• Classification Steps:

  1. First-level Classification (by post-condition type): Cases are classified according to the different types/models of processing elements (abrasive media, equipment, grinding fluid). If there are $N$ types, then $N$ classes are formed, and a first-level tag $T_1 = i$ is assigned, where $i = 1, 2, \ldots, N$.
  2. Second-level Classification (by roughness improvement level): The roughness improvement level ($Z$) is chosen as the most influential factor for abrasive media decision. $Z$ is calculated as: $ Z = \frac{|\mathrm{Ra}_1 - \mathrm{Ra}_2|}{\mathrm{Ra}_1} $ Where:
     • $\mathrm{Ra}_1$ is the surface roughness before processing.
     • $\mathrm{Ra}_2$ is the surface roughness after processing. Cases are then divided into two levels, and a second-level tag $T_2$ is assigned: $ T_2 = \begin{cases} 0, & Z < \alpha \ 1, & Z \geq \alpha \end{cases} $ Where:
     • $\alpha$ is the roughness improvement level factor, set to 0.5.
  3. Third-level Classification (by initial roughness level): The surface roughness before processing ($\mathrm{Ra}_1$) is chosen as the second most influential factor. Based on national standards, $\mathrm{Ra}_1$ is divided into 4 levels, and a third-level tag $T_3$ is assigned: $ T_3 = \begin{cases} 1, & 0 < \mathrm{Ra}_1 \leq 0.2 \mu m \ 2, & 0.2 \mu m < \mathrm{Ra}_1 \leq 0.4 \mu m \ 3, & 0.4 \mu m < \mathrm{Ra}_1 \leq 0.8 \mu m \ 4, & \mathrm{Ra}_1 > 0.8 \mu m \end{cases} $ These three levels of classification ($T_1, T_2, T_3$) provide the basis for constructing interval rules.

4.2.1.2.3. Interval Rule Construction

Rules are formulated with multiple pre-conditions and a single post-condition. Each pre-condition feature value is represented by its corresponding level's membership interval. The post-condition is the process element model. An improved interval production rule representation is used to establish the rule library: $ R_i: \mathrm{IF} \Big[ F_{i,1}^-, F_{i,1}^+ \Big] \mathrm{AND} \Big[ F_{i,2}^-, F_{i,2}^+ \Big] \mathrm{AND} \cdots \mathrm{AND} \big[ F_{i,j}^-, F_{i,j}^+ \big] \mathrm{THEN } B_i $ Where:

• $R_i$ is the $i$-th rule in the rule library.
• $F_{i,j}^-$ and $F_{i,j}^+$ are the lower and upper bounds of the interval for the $j$-th pre-condition feature of the $i$-th rule.
• $B_i$ is the post-condition (process element) of the $i$-th rule.

4.2.1.3. Special Rule Library Supplement

To handle unique or complex processing scenarios not covered by general rules, a special rule library is constructed. This library contains rules for specific types of parts, such as B-series gear shafts or C-series camshafts, which have different sets of features or specific processing requirements. This ensures the system's ability to match corresponding features for non-standard problems.

The following are the results from Table 5 of the original paper:

4.2.2. Process Element Expert Reasoning

This phase involves intervalization of new problem features, subjective and objective empowerment, and rule aggregation.

4.2.2.1. Feature Value Intervalization and Subjective Feature Weight Determination

4.2.2.1.1. New Problem Feature Value Intervalization

For a new problem, its known feature values are converted into interval forms (upper and lower bounds) that correspond to the established feature value range level division standards. This makes the new problem comparable with the rules in the rule library.

4.2.2.1.2. Rule Subjective Feature Weight Determination

Feature weights quantify the importance of each feature in the rule antecedent for the decision outcome. These are determined using the Analytic Hierarchy Process (AHP).

1. Hierarchical Structure: A three-level hierarchy is established:
   • Target Layer: Total subjective feature weight.
   • Criterion Layer: Part dimensions, Part pre-processing features, Part processing requirements.
   • Scheme Layer: The individual pre-condition features ($F_1$ to $F_{11}$) that influence the process element decision.
2. Pairwise Comparison and Eigenvector Calculation: Pairwise comparison matrices are constructed for each level based on expert judgment. The maximum eigenvalue ($\lambda_{\mathrm{max}}$) and corresponding eigenvector ($\overline{W}$) for each comparison matrix $P$ are calculated using: $ P \overline{W} = \lambda_{\mathrm{max}} \overline{W} $ Where:
   • $P$ is the pairwise comparison matrix.
   • $\overline{W}$ is the eigenvector.
   • $\lambda_{\mathrm{max}}$ is the maximum eigenvalue.
3. Normalization: The eigenvector $\overline{W}$ is normalized to obtain the feature weight vector $W$: $ W = \frac{\overline{W}}{|\overline{W}|} $
4. Total Subjective Feature Weight: For a hierarchical structure, if the criterion layer contains $m_1$ indicators $A_1, A_2, \ldots, A_{m_1}$ with single-layer weights $[w_{A_1}, w_{A_2}, \ldots, w_{A_{m_1}}]$, and the scheme layer contains $m_2$ indicators $A_{i1}, A_{i2}, \ldots, A_{i{m_2}}$ (for each $A_i$) with single-layer weights $[w_{A_{i1}}, w_{A_{i2}}, \ldots, w_{A_{i{m_2}}}]$, then the total subjective feature weight $w_{ij}$ for each scheme layer indicator is: $ w_{ij} = w_{A_i} w_{A_{ij}} $ Where:

   • $w_{A_i}$ is the weight of criterion $A_i$.

   • $w_{A_{ij}}$ is the weight of scheme $A_{ij}$ under criterion $A_i$.

   • $w_{ij}$ is the total subjective weight for feature $A_{ij}$.

     The following are the results from Table 6 of the original paper:

     层次	特征	各层指标	各层权重	Wij
     准则层A	-	A	0.060 8	-
     		A	0.353 1
     	1	A	0.586 1	二
     方案层A	F1	A	0.500 0	0.030 4
     	F	A12	0.500 0	0.030 4
     方案层A	F	A1	0.467 3	0.165 0
     	F4	A22	0.277 2	0.097 9
     	F5	A23	0.160 1	0.0565
     方案层A	F6	A31	0.095 4	0.033 7
     	F7	A2	0.411 7	0.2413
     	F8	A3	0.285 3	0.167 2
     	F9	A4	0.146 9	0.086 1
     	F10	A35	0.095 4	0.055 9
     	F11	A36	0.060 7	0.035 6

4.2.2.1.3. Update Subjective Feature Weights when Feature Information is Incomplete

When new problem feature information is incomplete (i.e., some feature values are unknown), the initial subjective feature weights ($w_{ij}$) need to be updated to maintain decision capability. The weights of the missing features are set to zero, and the remaining weights are redistributed proportionally. The updated subjective feature weight $\overline{w}_{ij}$ is calculated as: $ \overline{w}{ij} = \frac{\tau(i,j)w{ij}}{\sum_{i=1}^{m_1}\sum_{j=1}^{m_2}(\tau(i,j)w_{ij})} $ Where:

• $m_1$ is the number of indicators in the criterion layer.
• $m_2$ is the number of indicators in the scheme layer.
• $\tau(i,j)$ is a binary indicator, which cannot be all zeros: $ \tau(i,j) = \begin{cases} 1, & P_j \in R_i \ 0, & \text{otherwise} \end{cases} $ Where:

  • $P_j$ is the $j$-th feature of the new problem.

  • $R_i$ is the set of rule antecedents for the $i$-th rule.

  • If $P_j$ is known, $\tau(i,j)=1$; if $P_j$ is unknown (missing), $\tau(i,j)=0$.

    This ensures that the weights of existing features are re-normalized, maintaining their relative importance while ignoring missing data.

The following are the results from Table 7 of the original paper:

As illustrated in Table 7, when some feature information is missing (e.g., in row 2, $F_{11}$ is 0), its weight is set to zero, and the remaining weights are re-normalized. This ensures the sum of active weights remains 1, and the relative importance between active features is preserved. For instance, the ratio of $F_7$ to $F_3$ remains approximately constant across different scenarios of missing data.

4.2.2.2. Calculate Comprehensive Weighted Similarity

After feature value intervalization and subjective feature weight determination, the similarity between the new problem's features and each rule's features in the rule library is calculated.

1. Interval Similarity Function: The similarity $\mathrm{SIM}(F_{i,j}^*, F_{i,j})$ between the $j$-th feature of the new problem ($F_{i,j}^*$) and the $j$-th feature of the $i$-th rule ($F_{i,j}$) is calculated using an interval similarity function: $ \mathrm{SIM}(F_{i,j}^, F_{i,j}) = 1 - \frac{|F_{i,j}^{-} - F_{i,j}^-|+|F_{i,j}^{*+} - F_{i,j}^+|}{2} $ Where:
   • $F_{i,j}^{*-}$ and $F_{i,j}^{*+}$ are the lower and upper bounds of the new problem's $j$-th feature interval.
   • $F_{i,j}^-$ and $F_{i,j}^+$ are the lower and upper bounds of the $i$-th rule's $j$-th feature interval.
2. Comprehensive Weighted Similarity: The comprehensive weighted similarity $R_{\mathrm{RS}i}$ for each rule $i$ is then calculated by summing the products of the updated subjective feature weights ($\overline{w}_{ij}$) and the interval similarities: $ R_{\mathrm{RS}i} = \sum_{j=1}^{m} \left( \overline{w}{ij} \mathrm{SIM}(F{i,j}^*, F_{i,j}) \right) $ Where:
   • $R_{\mathrm{RS}i}$ is the comprehensive weighted similarity between the $i$-th rule and the new problem's features.
   • $\overline{w}_{ij}$ is the updated subjective feature weight for the $j$-th feature of the $i$-th rule.
   • $m$ is the maximum number of features in a rule.
3. Rule Activation: A rule $i$ is activated if its comprehensive weighted similarity $R_{\mathrm{RS}i}$ is greater than or equal to a predefined activation threshold $R_{\mathrm{RSth}}$.

4.2.2.3. Calculate Objective Rule Weights

When multiple activated rules have similar comprehensive weighted similarities and potentially different conclusions, objective rule weights are introduced to refine the decision. These weights represent the compactness of the rule's feature intervals.

1. Objective Feature Weight: The objective feature weight $w_{ij}'$ for each feature $j$ of rule $i$ is calculated based on its interval compactness: $ w_{ij}' = 1 - \Big[ (F_{i,j}^+ - F_{i,j}^-) - (F_{0,j}^+ - F_{0,j}^-) \Big] $ Where:
   • $F_{i,j}^-$ and $F_{i,j}^+$ are the lower and upper bounds of the $j$-th feature interval for rule $i$.
   • $F_{0,j}^-$ and $F_{0,j}^+$ are the lower and upper bounds of the smallest possible interval for the $j$-th feature. (A smaller interval $[F_{i,j}^+, F_{i,j}^-]$ means higher compactness, hence higher $w_{ij}'$).
2. Objective Rule Weight: The objective rule weight $\overline{W}_i$ for rule $i$ is the average of its objective feature weights: $ \overline{W}i = \frac{\sum{j=1}^{N_2} w_{ij}'}{N_2} $ Where:
   • $N_2$ is the number of features in the rule antecedent.
3. Definition 2: Activated Rule Set: $I_k = \{i \mid \text{the } i\text{-th rule is activated, and } R_{\mathrm{RS}i} \text{ meets certain conditions, } 1 \leq i \leq n \}$ Where $L_k$ is the number of rules in set $I_k$.
4. Normalized Objective Rule Weight: The objective rule weights for rules within an activated set $I_k$ are normalized: $ W_i = \frac{\overline{W}i}{\sum{i \in I_k}^{L_k} \overline{W_i}} $ Where:
   • $\sum_{i \in I_k}^{L_k} \overline{W_i}$ is the sum of objective rule weights for all $L_k$ rules in the set $I_k$.

4.2.2.4. Process Element Rule Aggregation

The final step uses the calculated objective rule weights to aggregate the conclusions of the activated rules and determine the final process element decision.

1. Threshold Determination:
   • $M_{\mathrm{MS}} = \max_{1 \leq i \leq n} (R_{\mathrm{RS}i})$ is the maximum comprehensive weighted similarity among all activated rules.
   • $M_{\mathrm{MF}} = M_{\mathrm{MS}} - \Delta$ is the critical value used to divide activated rules into two sets.
   • $\Delta$ is the difference between the maximum and critical values. The paper empirically sets $\Delta$ values based on the process element type: 0.02 for abrasive media, 0.05 for equipment, and 0.01 for grinding fluid.
2. Rule Set Division:
   • Set $I_1$: Contains activated rules whose comprehensive weighted similarity $R_{\mathrm{RS}i}$ is close to the maximum similarity (i.e., $R_{\mathrm{RS}i} \geq M_{\mathrm{MF}}$). These rules are considered highly similar. The similarities of these rules are fuzzified to the critical value $M_{\mathrm{MF}}$. Let $L_1$ be the number of rules in $I_1$. The process element result $B_1^*$ from $I_1$ is: $ B_1^* = \bigcup_{i \in I_1} W_i \Big( \frac{1 + M_{\mathrm{MF}}}{2} \Big) B_i $
   • Set $I_2$: Contains activated rules whose comprehensive weighted similarity $R_{\mathrm{RS}i}$ is further from the maximum similarity (i.e., $R_{\mathrm{RS}i} < M_{\mathrm{MF}}$). Let $L_2$ be the number of rules in $I_2$. The process element result $B_2^*$ from $I_2$ is: $ B_2^* = \bigcup_{i \in I_2} W_i \Big( \frac{1 - M_{\mathrm{MF}}}{2} \Big) B_i $
3. Final Aggregation: The final process element inference result $B^*$ is obtained by combining the results from $I_1$ and $I_2$: $ B^* = B_1^* \cup B_2^* $ The system then sums the weighted coefficients for identical process elements and selects the process element corresponding to the maximum total weight as the final decision.

4.2.3. Decision System for Barrel Finishing Process Elements

The SOE-ER model is implemented in an intelligent database platform for barrel finishing process.

The following figure (Figure 2 from the original paper) shows the intelligent database platform for barrel finishing process for the entire industry chain:

该图像是图2，面向全产业链应用的滚磨光整加工工艺智能数据库平台界面截图，展示了系统欢迎界面及功能模块选项，包括系统管理、基础信息、工艺实例、工艺分析和工艺决策。

The platform includes modules for feature range division, knowledge base, inference engine, and model description. Users input new part information and requirements.

The following figure (Figure 3 from the original paper) shows the part information input interface of the process elements decision:

该图像是图3加工工艺要素决策的零件信息输入界面截图，展示了工件的基本信息及加工参数填写区域，如零件类别、加工粗糙度、加工硬度等字段，界面布局清晰，便于用户输入和确认。

As shown in Figure 3, the part information input interface allows input of part details (client, type, material, length, diameter), pre-processing features (roughness, hardness, brightness), and processing requirements (post-processing roughness, hardness, brightness). This data is stored in a database. The system then processes this data using the SOE-ER model to decide the process elements.

The following figure (Figure 4c from the original paper) shows the expert reasoning decision of abrasive media:

该图像是图表，展示了论文中图4滚抛磨块专家推理决策界面，界面包含工件信息输入和磨块推理决策结果，体现专家系统推理过程和决策输出。

Figure 4(c) shows the abrasive media expert reasoning decision interface, which provides multiple decision results for the user to choose from based on their specific needs.

5. Experimental Setup

5.1. Datasets

The experiments are conducted using a substantial volume of actual processing cases collected from multiple barrel finishing manufacturers. These real-world instances are used to construct the case library and rule libraries. The data for shaft parts is used as a primary example, including features such as:

• Part length ($F_1$) / mm

• Part shaft diameter ($F_2$) / mm

• Surface roughness before processing ($F_3$) / $\mu$m

• Burr before processing ($F_4$) / mm

• Brightness before processing ($F_5$) (qualitative: 1-discernible marks, 2-no brightness, 3-low brightness, 4-very high brightness)

• Hardness before processing ($F_6$) / HRC

• Surface roughness after processing ($F_7$) / $\mu$m

• Burr after processing ($F_8$) (binary: 0-no removal required, 1-removal required)

• Brightness after processing ($F_9$) (qualitative: 1-discernible marks, 2-no brightness, 3-low brightness, 4-very high brightness)

• Hardness after processing ($F_{10}$) / HRC

• Residual stress improvement ($F_{11}$) / MPa

  The choice of these datasets is effective for validating the method's performance because they represent real-world industrial scenarios, ensuring that the developed model is practical and robust under actual operating conditions. The paper indicates that these cases allow for a comprehensive evaluation of the model's accuracy and adaptability.

5.2. Evaluation Metrics

The primary evaluation metric used in the paper is decision accuracy. Although not explicitly defined with a mathematical formula in the text, accuracy is generally understood as the proportion of correctly predicted instances to the total number of instances.

Conceptual Definition of Accuracy: Accuracy measures the overall correctness of a model's predictions. In this context, it quantifies how often the SOE-ER model's recommended process elements (abrasive media, finishing equipment, grinding fluid) match the actual, known successful process elements from the test cases. It is a straightforward and intuitive metric for classification tasks, indicating the model's ability to make correct decisions.

Mathematical Formula for Accuracy: $ \text{Accuracy} = \frac{\text{Number of Correct Predictions}}{\text{Total Number of Predictions}} $

Symbol Explanation:

• Number of Correct Predictions: The count of instances where the model's output (e.g., predicted abrasive media type) precisely matches the actual, known outcome from the dataset.
• Total Number of Predictions: The total number of instances (test cases) for which the model made a prediction.

5.3. Baselines

The paper compares the proposed SOE-ER model against two other methods:

• Expert Reasoning (ER): This refers to a more conventional expert reasoning method, specifically the one discussed in related work (Zhou et al. [4]), which showed high accuracy for abrasive media decision but not for finishing equipment and grinding fluid. This serves as a baseline to demonstrate the improvements made by SOE-ER in handling all three process elements.

• Case-Based Reasoning (CBR): This method, as described in related work (Yang et al. [3]), relies on finding similar past cases. It is included as a baseline to highlight SOE-ER's advantage in situations where feature information might differ significantly from existing cases, which is a known weakness of CBR.

  These baselines are representative because they are established methods within the domain of intelligent decision-making for manufacturing processes, and their known limitations (as discussed in the introduction) directly motivate the development of the SOE-ER model. Comparing against them allows for a clear demonstration of SOE-ER's advancements in terms of accuracy and robustness.

6. Results & Analysis

The experimental validation of the SOE-ER model is conducted on a decision system platform, using real-world processing cases from multiple barrel finishing manufacturers. The evaluation is structured to verify the model's accuracy and superiority under various conditions: cases used in rule construction, cases not used in rule construction, cases with incomplete feature information, and comparison with baseline methods.

6.1. Core Results Analysis

6.1.1. Cases Used in Rule Construction

The first set of experiments uses cases that were part of the rule construction process to verify the model's basic accuracy and rationality.

The following are the results from Table 8 of the original paper:

Analysis of Table 8: Out of 15 cases, the abrasive media decision was inconsistent for only one case (Case 9, predicted S2-2F vs. actual S3-1R). The equipment decision was inconsistent for one case (Case 3, predicted X600 vs. actual X400). The grinding fluid decisions were 100% correct. This demonstrates that when the model is applied to cases it has "seen" during rule construction, it achieves a very high accuracy, confirming its inherent rationality.

6.1.2. Cases Not Used in Rule Construction

To evaluate the model's generalization ability, experiments are conducted using cases that were explicitly excluded from the rule construction process.

The following are the results from Table 9 of the original paper:

Analysis of Table 9: For cases not used in rule construction, the abrasive media decision was inconsistent for two cases (Case 5, predicted S3-6P vs. actual S2-5G; Case 12, predicted S2-5G vs. actual S3-3F). The equipment decision was inconsistent for three cases (Case 2, predicted X600 vs. actual X400; Case 7, predicted X1600 vs. actual X1400; Case 11, predicted X600 vs. actual X400). The grinding fluid decision was inconsistent for one case (Case 11, predicted HA-BC vs. actual HA-IS). While showing some inconsistencies, the overall accuracy remains acceptable, demonstrating the model's effectiveness and generalization capability beyond its training data.

6.1.3. Cases with Incomplete Feature Information

This experiment tests the SOE-ER model's adaptability when faced with incomplete feature information in new problems.

The following are the results from Table 10 of the original paper:

Analysis of Table 10: In the presence of incomplete information (indicated by blank cells or —), the SOE-ER model still provides decisions. For abrasive media, four cases (5, 9, 12, 14) were inconsistent. For equipment, five cases (6, 9, 11, 13, 15) were inconsistent. For grinding fluid, three cases (5, 12, 15) were inconsistent. Despite the missing data, the model maintains a respectable level of decision accuracy, demonstrating its adaptability and ability to make reasonable inferences even with partial information.

6.1.4. Comparison with CBR and ER

To highlight SOE-ER's superiority, a cross-comparison experiment is conducted against CBR and ER methods using cases with large differences in feature information (i.e., cases that are quite distinct from those in the knowledge base).

The following are the results from Table 11 of the original paper:

The following are the results from Table 12 of the original paper:

Analysis of Table 12:

• Abrasive Media Decision (磨块):

  • CBR: Inconsistent for 4 cases (5, 6, 9, 14), resulting in an accuracy of $11/15 = 73.33\%$.
  • ER: Inconsistent for 3 cases (5, 9, 14), resulting in an accuracy of $12/15 = 80\%$.
  • SOE-ER: Inconsistent for only 1 case (5), resulting in an accuracy of $14/15 = 93.33\%$. SOE-ER significantly outperforms CBR and ER for abrasive media.

• Equipment Decision (设备):

  • CBR: Inconsistent for 6 cases (3, 5, 6, 9, 11, 14), resulting in an accuracy of $9/15 = 60\%$.
  • ER: Inconsistent for 5 cases (5, 6, 9, 11, 14), resulting in an accuracy of $10/15 = 66.67\%$.
  • SOE-ER: Inconsistent for 3 cases (3, 5, 6), resulting in an accuracy of $12/15 = 80\%$. SOE-ER shows a substantial improvement over CBR and ER for equipment decision.

• Grinding Fluid Decision (磨液):

  • CBR: Inconsistent for 3 cases (3, 5, 14), resulting in an accuracy of $12/15 = 80\%$.
  • ER: Inconsistent for 2 cases (3, 14), resulting in an accuracy of $13/15 = 86.67\%$.
  • SOE-ER: Inconsistent for only 1 case (3), resulting in an accuracy of $14/15 = 93.33\%$. SOE-ER consistently achieves higher accuracy for grinding fluid decision as well.

The results clearly show that ER improves upon CBR for some decisions, and SOE-ER further improves upon both ER and CBR, achieving consistently higher accuracy across all three core process elements, particularly under conditions of large feature differences.

6.1.5. Overall Accuracy Comparison

A comprehensive comparison of the average accuracy rates for different part types (gear shafts, camshafts, crankshafts), methods (CBR, ER, SOE-ER), and process elements is presented.

The following figure (Figure 5 from the original paper) shows the comparison chart of accuracy rate of different parts, different methods and different process elements in case of large difference in feature information:

该图像是图5，比较了特征信息差异较大情况下不同零件种类、不同方法（CBR、ER、SOE-ER）及不同滚磨光整加工工艺要素的准确率。结果显示SOE-ER方法在各类工艺要素中的决策准确率均显著优于其他方法。 Analysis of Figure 5: This chart visualizes the average accuracy for gear shafts, camshafts, and crankshafts across the three methods (CBR, ER, SOE-ER) for abrasive media, equipment, and grinding fluid decisions, specifically when feature information differences are large.

• Abrasive Media: SOE-ER consistently achieves an accuracy above 90% for all three part types, significantly higher than CBR (which is often below 80%) and ER (which is generally between 80-90%).

• Equipment: For equipment, SOE-ER maintains an accuracy above 80% for all part types, which is a considerable improvement over CBR (often below 70%) and ER (ranging from 70-80%).

• Grinding Fluid: SOE-ER again demonstrates an accuracy above 90% for grinding fluid across all part types, outperforming CBR (around 80%) and ER (around 85%).

  Overall Conclusion from Comparison: Figure 5 strongly validates the superiority of the SOE-ER model. It demonstrates that SOE-ER achieves stable high decision accuracy (over 90% for abrasive media and grinding fluid, over 80% for equipment) even when testing with cases that were not part of the rule construction and have significant feature differences. This indicates its robust generalization ability and effectiveness in providing reliable guidance for new problems, which was a primary objective of the research.

7. Conclusion & Reflections

7.1. Conclusion Summary

This paper successfully addresses the challenges in barrel finishing process element decision-making by proposing a novel Subjective and Objective Empowerment Expert Reasoning (SOE-ER) model. The model's foundation is a meticulously constructed knowledge base comprising a case library and hierarchical classification rule libraries, augmented by a special rule library for unique scenarios. A key innovation is the integration of both subjective feature weights (derived via AHP) and objective rule weights (based on feature interval compactness), which are dynamically updated to handle incomplete feature information. Experimental validation on a developed decision system platform demonstrated that the SOE-ER model consistently achieves high decision accuracy for all three core process elements: abrasive media, finishing equipment, and grinding fluid. Critically, it outperforms conventional Expert Reasoning (ER) and Case-Based Reasoning (CBR) methods, particularly in scenarios involving large feature differences or missing data. This ensures that the model can provide practical, effective, and reliable guidance for new processing problems in barrel finishing.

7.2. Limitations & Future Work

The authors themselves acknowledge future research directions, implying current limitations:

• Continuous Knowledge Base Accumulation: There is a continuous need to accumulate more successful cases from various enterprises to enrich and expand the case library and rule libraries. This suggests that the knowledge base, while robust, is not exhaustive and benefits from ongoing growth.
• Dynamic Knowledge Base Updates: The system requires continuous updating of its case library and rule libraries to adapt to evolving technologies, materials, and processing requirements.
• Further Refinement of Intelligent Technology: The authors plan to continuously improve and perfect the intelligent technology within the database platform, implying ongoing opportunities for enhancing the model's intelligence and capabilities.

7.3. Personal Insights & Critique

This paper presents a valuable contribution to intelligent manufacturing, specifically in the domain of barrel finishing. The SOE-ER model is well-structured, combining established techniques like AHP with novel ideas like objective rule weighting and a robust mechanism for handling incomplete information. Its practical application through a decision system platform highlights its potential for industrial use.

Inspirations and Applications:

• The dual subjective-objective empowerment approach is inspiring. Many decision-making problems involve a mix of expert intuition (subjective) and data-driven insights (objective). This model effectively blends them, a strategy that could be transferred to other domains requiring complex parameter selection, such as material design, process optimization in other manufacturing steps, or even medical diagnosis where expert knowledge meets patient data.
• The explicit handling of incomplete feature information is a significant strength. Real-world data is rarely perfectly complete. The method of re-normalizing weights for available features is elegant and practical, making the expert system more resilient and usable in imperfect data environments. This aspect could be particularly useful in quality control systems or diagnostic tools where certain sensor readings might be intermittently unavailable.

Potential Issues and Areas for Improvement:

• Subjectivity in AHP: While AHP is a powerful tool for subjective weighting, its reliance on expert judgment introduces a degree of subjectivity. The quality of the weights is directly dependent on the consistency and expertise of the human evaluators. Variations in expert opinions could lead to different weight distributions and, consequently, different decision outcomes. Further research could explore methods for aggregating weights from multiple experts or quantifying the uncertainty in AHP-derived weights.

• Determination of Optimal Boundary Values: The paper states that optimal boundary values for features are determined by "simulation experiments using a control variable method." While effective, the details of these simulations and how "optimal" is defined (e.g., maximizing accuracy, minimizing false positives) are not elaborated. A more detailed explanation of this optimization process would enhance the rigor.

• Empirical $\Delta$ Values: The critical value difference ($\Delta$) used in rule aggregation is empirically set (0.02 for abrasive media, 0.05 for equipment, 0.01 for grinding fluid). The justification for these specific values and their sensitivity analysis are not provided. These values can significantly influence how activated rules are clustered and aggregated. A more systematic approach (e.g., cross-validation or optimization) to determine $\Delta$ could make the model more robust and less prone to hyperparameter tuning issues.

• Scalability of Rule Base: As the case library and rule libraries grow, the computational cost of calculating similarities and aggregating rules for a new problem might increase. While not explicitly discussed, the scalability of the inference engine could become a factor for extremely large industrial databases.

• Interpretability of Aggregation: The aggregation process (Equations 14-16) involves combining weighted conclusions. While effective, the interpretability of why a specific process element is chosen when multiple rules are activated could be complex. Providing more transparent explanations for aggregated decisions could be beneficial for user trust and debugging.

  Overall, the SOE-ER model represents a solid step forward in intelligent decision-making for barrel finishing, offering a practical and robust solution to real-world industrial problems. The identified areas for improvement mostly relate to further enhancing the rigor and transparency of certain design choices.