1. Bibliographic Information

1.1. Title

Mass Finishing Process Elements Decision Based on Transfer Learning (Original: 基于迁移学习的滚磨光整加工工艺要素决策)

1.2. Authors

The authors of the paper are SHI Yuhao, TIAN Jianyan, YANG Yingbo, LI Wenhui, and YANG Shengqiang. They are affiliated with Taiyuan University of Technology, specifically the College of Electrical and Power Engineering, College of Mechanical and Vehicle Engineering, and College of Aeronautics and Astronautics.

1.3. Journal/Conference

The paper is slated for publication in Control Engineering (控制工程). The provided citation format is "Control Engineering, 2025, 32(3):481-491,552." Control Engineering is a well-regarded Chinese academic journal in the fields of control science, automation, and engineering applications. It is often listed as a "Chinese Core Journal," indicating its significant influence and peer-review standards within China.

1.4. Publication Year

2025 (according to the citation format, which suggests it is an accepted paper pending future publication).

1.5. Abstract

The paper addresses the issue of inaccurate decision-making in mass finishing process element selection when using traditional Case-Based Reasoning (CBR) and Expert Reasoning (ER) models, particularly when the feature information of new parts differs significantly from existing manufacturing experience. To solve this, the authors propose a Weighted Multi-domain Adaptation Transfer Learning (WMDA) algorithm and construct a decision-making model based on it. The methodology involves:

1. Characterizing the features of parts to be processed, processing requirements, and process elements.
2. Improving upon the multi-domain adaptation-manifold regularization (MDA-MR) algorithm by introducing an adaptation factor and Wasserstein Distance to enhance its applicability.
3. Designing a Process Element Similarity Matching (PESM) algorithm to solve the negative transfer problem that arises from having too many prediction categories.
4. Integrating these components to build the final decision model and designing a corresponding user interface. Simulation results indicate that the proposed model achieves higher decision accuracy and provides more valuable support for mass finishing processes.

1.6. Original Source Link

The provided link is /files/papers/6905d305d47c3f7df4650862/paper.pdf. This indicates a local file path. The paper has been accepted for official publication in the journal Control Engineering.

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2. Executive Summary

2.1. Background & Motivation

In advanced manufacturing, mass finishing (滚磨光整加工) is a critical process for improving the surface quality of mechanical parts. The success of this process heavily depends on selecting the correct process elements: the abrasive media (滚抛磨块), grinding fluid (磨液), and finishing equipment (光整设备). Traditionally, this selection is performed by human experts based on experience, a process that is subjective and difficult to scale.

To automate this, previous research by the same project team developed models based on Case-Based Reasoning (CBR) and Expert Reasoning (ER). However, these methods have a significant drawback: their accuracy drops when they encounter a new part whose characteristics (e.g., material, geometry, required finish) have a feature distribution that is very different from the historical cases stored in the database. This is a common challenge in data-driven manufacturing, as production demands constantly evolve.

The paper's innovative entry point is to apply Transfer Learning (TL) to overcome this problem. The core idea is that even if the new part's data distribution is different, there is still underlying knowledge in the historical data (source domains) that can be "transferred" to help make a decision for the new part (target domain).

2.2. Main Contributions / Findings

The paper makes several key contributions to intelligent manufacturing decision-making:

1. A Novel Transfer Learning Algorithm (WMDA): The authors propose the Weighted Multi-domain Adaptation (WMDA) algorithm, which is an enhancement of their previous MDA-MR algorithm. The improvements are:

   • Adaptation Factor ($α$): An adaptation factor is introduced to better balance the influence of distribution adaptation terms versus the manifold regularization term, improving single-domain adaptation efficiency.
   • Hybrid Distance Metric: WMDA incorporates Wasserstein Distance in addition to the standard Maximum Mean Discrepancy (MMD) to measure the similarity between source and target domains. This hybrid approach leads to more robust and accurate weighting of classifiers from multiple source domains.

2. A Multi-Step Decision Strategy (PESM): To address the negative transfer issue caused by an overly large number of discrete output classes (e.g., predicting one of dozens of specific machines), the authors designed the Process Element Similarity Matching (PESM) algorithm. Instead of directly predicting a final process element, the WMDA model predicts the ideal characteristics of the element. The PESM algorithm then matches these predicted characteristics against a library of available elements to find the best fit. This "predict-then-match" approach is a key innovation.

3. An Integrated Decision Model and System: The paper combines the WMDA and PESM algorithms into a comprehensive decision-making model for mass finishing. Furthermore, it details the design of a user-friendly decision interface integrated into a broader "Mass Finishing Process Intelligent Database Platform," making the research applicable in a real-world industrial setting.

4. Demonstrated Superiority: Experimental results on real-world data of shaft parts show that the proposed model significantly outperforms traditional CBR and ER methods, as well as previous transfer learning models like CDA-MR and MDA-MR, especially in scenarios with large distribution differences.

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3. Prerequisite Knowledge & Related Work

3.1. Foundational Concepts

• Mass Finishing (滚磨光整加工): A manufacturing process where parts are placed in a container (finishing equipment) with abrasive media and a grinding fluid. The relative motion between them causes micro-abrasion, rolling, and collision, which improves the surface quality of the parts by reducing roughness, removing burrs, and enhancing brightness. The choice of the three main process elements—media, fluid, and equipment—is critical for achieving the desired outcome.

• Case-Based Reasoning (CBR): A problem-solving method where solutions to new problems are found by retrieving and reusing solutions from similar past problems (cases) stored in a database. Its effectiveness relies heavily on the similarity between the new problem and the stored cases. When a new part is very different from any previous part, CBR struggles to find a relevant case to adapt.

• Expert Reasoning (ER): A branch of artificial intelligence that uses a knowledge base of "if-then" rules, facts, and logic derived from human experts to make decisions. Like CBR, ER systems are limited by their pre-programmed knowledge and cannot easily handle novel situations that fall outside their established rules.

• Transfer Learning (TL): A machine learning paradigm where a model trained on a source task is repurposed or fine-tuned for a related but different target task. This is particularly useful when the target task has limited labeled data.

  • Domain Adaptation: A subfield of TL, which is the focus of this paper. Here, the task remains the same (e.g., classification), but the data distribution of the source domain (historical manufacturing cases) differs from that of the target domain (the new part). The goal is to learn a model that performs well on the target domain by aligning the feature distributions of the source and target domains.

• Maximum Mean Discrepancy (MMD): A statistical metric used to measure the distance between two probability distributions. In domain adaptation, it is used to quantify how different the source and target domain data are. The core idea is to represent distributions as mean elements in a high-dimensional feature space called a Reproducing Kernel Hilbert Space (RKHS). If the mean elements are close in the RKHS, the distributions are considered similar. Minimizing MMD is a common objective in transfer learning to align the domains.

• Wasserstein Distance: Also known as Earth Mover's Distance, it is another metric for measuring the distance between two probability distributions. Intuitively, if each distribution is viewed as a pile of "earth" (probability mass), the Wasserstein Distance is the minimum "cost" (mass × distance) required to move the earth from one pile's shape to the other's. It is known to have better geometric properties than MMD in some contexts, especially when distributions are non-overlapping.

• Manifold Regularization (MR): A technique used in machine learning that leverages the underlying geometric structure of the data. It operates on the assumption that if two data points are close to each other on the data's intrinsic manifold (a low-dimensional surface embedded in a high-dimensional space), their corresponding labels should also be similar. In this paper, it is used as a regularization term to preserve the local data structure during the domain adaptation process, preventing the transformation from distorting the information within each domain.

3.2. Previous Works

The paper builds upon a series of prior research, mostly from the same project team, indicating a systematic and progressive research agenda.

• CBR [7] and ER [8] Models: These represent the initial attempts by the team to automate the decision-making process. The CBR model used fuzzy clustering to group similar cases, while the ER model was based on expert rules. The current paper identifies their limitations when facing new parts with different feature distributions as the primary motivation for exploring transfer learning.

• CDA-MR [16] (Conditional Distribution Adaptation-Manifold Regularization): This was the team's first foray into using transfer learning for this problem. CDA-MR aims to minimize the distance between source and target domains by adapting both the marginal distribution (the overall distribution of features) and the conditional distribution (the distribution of features given a specific class label). It also incorporates manifold regularization (MR) to preserve the data's internal structure. However, CDA-MR was designed for a single source domain and a single target domain.

• MDA-MR [18] (Multi-domain Adaptation-Manifold Regularization): This is the direct predecessor to the WMDA algorithm proposed in the current paper. MDA-MR extends CDA-MR to handle scenarios with multiple source domains. In the context of this paper, different types of historical parts (e.g., gear shafts, crankshafts) can be treated as separate source domains. MDA-MR works by training a separate classifier for each source domain and then weighting their predictions based on the MMD similarity between each source and the target domain. Sources more similar to the target are given higher weights.

3.3. Technological Evolution

The technological trajectory in this research area, as documented by the authors' work, shows a clear evolution:

1. Experience-Based Systems: Initial reliance on CBR and ER to digitize and automate existing human expertise.

2. Introduction of Basic Transfer Learning: Shift to CDA-MR to handle distribution gaps between a single historical data source and a new task.

3. Handling Multiple Data Sources: Advancement to MDA-MR to leverage knowledge from multiple, diverse historical datasets simultaneously.

4. Refinement and Robustness: The current paper introduces WMDA, which refines MDA-MR for better adaptation control and more robust domain similarity measurement.

5. Pragmatic Problem Decomposition: The introduction of PESM marks a shift from a purely theoretical model to a practical, two-step engineering solution that circumvents a common machine learning pitfall (high-cardinality classification).

   This paper's work sits at the cutting edge of this specific application, focusing on improving the robustness and practicality of multi-source transfer learning.

3.4. Differentiation Analysis

Compared to previous methods, this paper's approach is innovative in two key ways:

• Algorithmic Enhancement (WMDA vs. MDA-MR): While MDA-MR already handles multiple sources, WMDA refines it by:

  • Adding an adaptation factor ($α$) to the objective function, allowing for more flexible tuning of the trade-off between domain adaptation and manifold preservation.
  • Using a hybrid similarity metric (MMD + Wasserstein Distance) for weighting classifiers. This makes the model more robust, as one metric might be more suitable than the other depending on the specific data distributions.

• Structural Innovation (PESM): This is arguably the most significant contribution. Instead of treating the problem as a single, complex classification task (e.g., predict one of 20 specific abrasive media), the authors reframe it. The TL model (WMDA) predicts the ideal properties of the required process element (e.g., material: alumina, shape: spherical, type: fine-grinding). The PESM algorithm then performs a structured search in a database to find the real-world element that best matches these predicted properties. This decomposition simplifies the learning task and makes the system more modular and interpretable.

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4. Methodology

4.1. Principles

The core principle of the proposed model is to leverage historical manufacturing data (source domains) to make accurate decisions for new parts (target domain), even when their characteristics differ significantly. This is achieved through a two-stage process:

1. Knowledge Transfer with WMDA: The WMDA algorithm learns a transformation that projects data from all source domains and the target domain into a common subspace. In this subspace, the distributional differences are minimized. This alignment allows classifiers trained on the source data to be effectively applied to the target data. The algorithm is designed to handle multiple sources by weighting their contributions based on their similarity to the new part's data.

2. Decision Matching with PESM: Directly predicting a specific process element (e.g., "3号精磨磨块") is a difficult classification problem with many classes, which can lead to poor performance. The paper cleverly avoids this by having the WMDA model predict the underlying features of the optimal element (e.g., material, shape, type, size). The PESM algorithm then takes these predicted features and compares them against a database of all available process elements, selecting the one with the highest overall similarity. This makes the system more robust and scalable.

   The overall technical route is visualized in Figure 1 from the paper.

   该图像是图1，基于迁移学习的滚磨光整加工工艺要素决策模型的技术路线示意图，展示了从大量生产实例到特征参数分析，再到WMDA算法和PESM算法，最终输出加工工艺要素的流程。

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

4.2.1. Step 1: Process Feature Information Representation

Before any modeling, the data must be structured. The paper uses an Entity-Relationship (E-R) diagram to define the features for parts, requirements, and process elements. This provides a clear, structured representation of the problem space. The key features are:

• Part Information & Requirements:
  • Part dimensions: Length (F1), Diameter (F2)
  • Part material: Material (F3) (8 levels based on tensile strength)
  • Pre-processing features: Roughness (F4), Brightness (F5), Burr (F6), Hardness (F7)
  • Post-processing requirements: Roughness (F8), Brightness (F9), Burr (F10), Hardness (F11), Residual Stress Improvement (F12)
• Process Elements:

  • Abrasive Media: Material (M1), Shape (M2), Type (M3), Size (M4)

  • Grinding Fluid: Type (G)

  • Finishing Equipment: Type (T), Processable Length (L), Processable Diameter (D)

    The following E-R diagram (Figure 2 from the paper) illustrates these relationships.

    该图像是图2基于迁移学习的滚磨光整加工工艺E-R图，展示了待加工零件、加工要求和工艺要素之间的匹配关系及其细分属性。

4.2.2. Step 2: Weighted Multi-domain Adaptation Transfer Learning (WMDA)

The WMDA algorithm is an improved version of the MDA-MR algorithm. To understand WMDA, we must first understand its predecessor.

4.2.2.1. The Baseline: MDA-MR Algorithm

MDA-MR aims to find a transformation matrix $A$ that maps data into a common subspace where domain differences are minimized.

1. Data Adaptation: The core objective is to minimize the distribution distance between the source domain ($X^s$) and the target domain ($X^t$). This is done by minimizing both the marginal distribution distance (overall feature distribution) and the conditional distribution distance (feature distribution per class). A manifold regularization term is added to preserve the local geometry of the source data. The objective function to minimize is: $ \mu \mathrm{tr} ( \boldsymbol { A } ^ { \mathrm { T } } \boldsymbol { X } \boldsymbol { M } _ { 0 } \boldsymbol { X } ^ { \mathrm { T } } \boldsymbol { A } ) + ( 1 - \mu ) \sum _ { c = 1 } ^ { C } \mathrm{tr} ( \boldsymbol { A } ^ { \mathrm { T } } \boldsymbol { X } \boldsymbol { M } _ { c } \boldsymbol { X } ^ { \mathrm { T } } \boldsymbol { A } ) + \lambda \mathrm{tr} ( A ^ { \mathrm { T } } X ^ { \mathrm { s } } L ( X ^ { \mathrm { s } } ) ^ { \mathrm { T } } A ) $ Where:

• $A \in \mathbf { R } ^ { m \times k }$: The transformation matrix that maps data from an $m$-dimensional space to a $k$-dimensional subspace.

• $X$: The matrix containing all data samples from both source ($X^s$) and target ($X^t$) domains.

• $\mu \in [0, 1]$: A balance factor. When $\mu \to 1$, it prioritizes matching the marginal distributions. When $\mu \to 0$, it prioritizes matching the conditional distributions.

• $M_0$: The MMD matrix for the marginal distribution.

• $M_c$: The MMD matrix for the conditional distribution of class $c$.

• $\lambda$: The regularization coefficient that controls the importance of the manifold regularization term.

• $L$: The graph Laplacian matrix constructed from the source data, which captures its local geometry. tr(...) denotes the trace of a matrix.

  2. Optimization: To ensure the transformed data retains variance, a constraint to maximize the variance of the projected data is added. The optimization problem is solved using the Lagrange multiplier method, which results in a generalized eigenvalue problem: $ ( \mu X M _ { 0 } X ^ { \mathrm { { T } } } + ( 1 - \mu ) X \displaystyle \sum _ { c = 1 } ^ { C } M _ { c } X ^ { \mathrm { { T } } } ) + \lambda X ^ { \mathrm { s } } L ( X ^ { \mathrm { s } } ) ^ { \mathrm { { T } } } A = X H X ^ { \mathrm { { T } } } A \Phi $ Where:

• $H = I - \frac{1}{n}uu^T$ is a centering matrix.

• $\Phi$ is a diagonal matrix of Lagrange multipliers. The transformation matrix $A$ is formed by the eigenvectors corresponding to the smallest eigenvalues of this problem.

3. Classifier Weighting for Multiple Sources: When there are multiple source domains ($X_l^s, l=1,...,p$), MDA-MR trains a classifier for each source. Their predictions for a target sample are combined using weights. The weight for the $l$-th source is based on its MMD distance to the target domain in the learned subspace. $ d _ { l } ^ { 1 } = \frac { 1 } { M _ { \mathrm { MMD } } ( \mathbf { Z } _ { l } ^ { \mathrm { s } } , \mathbf { Z } ^ { \mathrm { t } } ) } $ Where $Z_l^s = A^T X_l^s$ and $Z^t = A^T X^t$ are the projected data. The similarity $d_l^1$ is inversely proportional to the MMD distance. The weights are then normalized: $ w _ { l } = \frac { d _ { l } ^ { 1 } } { \sum _ { l = 1 } ^ { p } d _ { l } ^ { 1 } } $ The final prediction is a weighted sum of the predictions from each classifier: $ \pmb { Y } = \sum _ { l = 1 } ^ { p } w _ { l } \pmb { M } ( \pmb { Z } _ { l } ^ { \mathrm { s } } , \pmb { Z } ^ { \mathrm { t } } , \pmb { Y } _ { l } ^ { \mathrm { s } } ) $

4.2.2.2. The WMDA Improvements

The paper introduces two key modifications to MDA-MR.

1. Improved Data Adaptation with Adaptation Factor: An adaptation factor $\alpha$ is introduced into the objective function to control the overall influence of the distribution adaptation terms relative to the manifold regularization term. The new objective function term is: $ \alpha ( \mu \mathrm{tr} ( \boldsymbol { A } ^ { \mathrm { T } } \boldsymbol { X } \boldsymbol { M } _ { 0 } \boldsymbol { X } ^ { \mathrm { T } } \boldsymbol { A } ) + ( 1 - \mu ) \sum _ { c = 1 } ^ { C } \mathrm{tr} ( \boldsymbol { A } ^ { \mathrm { T } } \boldsymbol { X } \boldsymbol { M } _ { c } \boldsymbol { X } ^ { \mathrm { T } } \boldsymbol { A } ) ) + \lambda \mathrm{tr} ( \boldsymbol { A } ^ { \mathrm { T } } \boldsymbol { X } ^ { \mathrm { s } } \boldsymbol { L } ( \boldsymbol { X } ^ { \mathrm { s } } ) ^ { \mathrm { T } } \boldsymbol { A } ) $ This leads to a modified generalized eigenvalue problem: $ ( \alpha ( \mu X M _ { 0 } X ^ { \mathrm { { T } } } + ( 1 - \mu ) X \sum _ { c = 1 } ^ { c } M _ { c } X ^ { \mathrm { { T } } } ) + \lambda X ^ { s } L ( X ^ { s } ) ^ { \mathrm { { T } } } A = X H X ^ { T } A \Phi $ This factor $\alpha$ provides an additional hyperparameter to fine-tune the model's behavior, potentially leading to better adaptation.

2. Improved Classifier Weighting with Wasserstein Distance: To make the weighting of source domain classifiers more robust, the paper proposes using both MMD and Wasserstein Distance. A second similarity score, $d_l^2$, is calculated based on the inverse of the Wasserstein Distance: $ d _ { l } ^ { 2 } = \frac { 1 } { W _ { \mathrm { Distance } } ( \pmb { Z } _ { l } ^ { \mathrm { s } } , \pmb { Z } ^ { \mathrm { t } } ) } $ The final weight $w_l'$ for each source domain is an average of the normalized similarities from both metrics: $ w _ { l } ^ { \prime } = 0.5 \times \frac { d _ { l } ^ { 1 } } { \sum _ { l = 1 } ^ { p } d _ { l } ^ { 1 } } + 0.5 \times \frac { d _ { l } ^ { 2 } } { \sum _ { l = 1 } ^ { p } d _ { l } ^ { 2 } } $ This hybrid approach aims to combine the strengths of both distance metrics, improving the robustness and applicability of the multi-source adaptation. The final prediction is then made using these improved weights: $ { \pmb Y } = \sum _ { l = 1 } ^ { p } w _ { l } ^ { \prime } M ( { \pmb Z } _ { l } ^ { \mathrm { s } } , { \pmb Z } ^ { \mathrm { t } } , { \pmb Y } _ { l } ^ { \mathrm { s } } ) $

4.2.3. Step 3: Process Element Similarity Matching (PESM)

After the WMDA model predicts the feature vector $Y_j$ for a new part, the PESM algorithm finds the best real-world process element from a pre-defined library.

1. Core Matching Logic: For each target sample $j$, the algorithm calculates a similarity score between its predicted feature vector $Y_j$ and the feature vector $T_q$ of every process element $q$ in the library. The element with the highest similarity is chosen as the final decision $R_j$. $ R _ { j } = \left{ T _ { \operatorname* { m a x } } : \operatorname* { m a x } _ { q = 1 , 2 , \cdots , M } \left{ \mathrm { SIM } ( T _ { q } , Y _ { j } ) \right} \right} $ Where:

• $R_j$: The final decision for the $j$-th target sample.

• $T_q$: The feature vector of the $q$-th process element in the library.

• $Y_j$: The predicted feature vector for the $j$-th target sample from WMDA.

• $M$: The total number of process elements in the library.

• SIM(...): The overall similarity function.

  2. Overall Similarity Calculation: The overall similarity is the average similarity across all $N$ features of the element. $ \mathrm { S I M } ( T _ { q } , Y _ { j } ) = \frac { 1 } { N } \sum _ { u = 1 } ^ { N } \mathrm { s i m } ( T _ { q u } , Y _ { j u } ) $ Where:

• $T_{qu}$ and $Y_{ju}$ are the $u$-th feature of the library element and the predicted vector, respectively.

• sim(...) is the individual feature similarity function, which varies by feature type.

  3. Feature-Specific Similarity Formulas: The paper defines three types of similarity calculations:

• Numerical Type (e.g., abrasive size): An exponential decay function where similarity is 1 if values are identical and decreases as they diverge. $ \sin ( T _ { _ { q u } } , Y _ { _ { j u } } ) = \exp \biggl [ - \frac { T _ { _ { q u } } - Y _ { _ { j u } } } { \sqrt { 2 } } \biggr ] $

• Binary Type (e.g., grinding fluid type): Similarity is 1 if the values match, and 0 otherwise. $ { \sin } ( { T _ { _ { q u } } } , { Y _ { _ { j u } } } ) = \left{ \begin{array} { l l } { { 1 , \ T _ { _ { q u } } = Y _ { _ { j u } } } } \ { { 0 , \ T _ { _ { q u } } \not = Y _ { _ { j u } } } } \end{array} \right. $

• Fuzzy Logic Type (e.g., abrasive type - coarse/medium/fine): Similarity is calculated as a normalized distance, where similarity is 1 for a perfect match and decreases linearly with the difference in category levels. $ \mathrm { s i m } ( T _ { q u } , Y _ { j u } ) = 1 - \frac { \left| T _ { q u } - Y _ { j u } \right| } { N _ { \mathrm { N U M } } } $ Where $N_{NUM}$ is the total number of categories for that feature.

4. Special Rule for Equipment: A crucial pre-filtering step is applied for finishing equipment. If the new part's dimensions (length or diameter) exceed the maximum processable dimensions of a piece of equipment, that equipment is excluded from the similarity matching process for that part. This prevents physically impossible recommendations.

4.2.4. Decision Interface

The paper also describes the design of a user interface built on their existing database platform. This interface allows technicians to input new part information and receive decision recommendations from the model. Importantly, it not only shows the top recommended element but also other highly similar alternatives, providing flexibility and supporting expert judgment. The interface also has modules for researchers to adjust feature representations and retrain models.

The figures below show the platform (Figure 3), the interface design concept (Figure 4), and the final implementation (Figure 5).

该图像是图3，面向全产业链应用的滚磨光整加工工艺数据库平台的界面示意图，展示了系统管理、基础信息、工艺案例、工艺分析和工艺决策等模块入口。

该图像是图4，基于迁移学习的滚光整加工工艺要素决策界面设计思路示意图，展示了特征表征模块、模型训练模块、迁移学习决策模块和模型说明模块的层次结构及其子模块。

该图像是图表，展示了基于迁移学习的滚磨光整加工工艺要素决策界面（图c），包括用户输入的工件信息、多维加工参数及决策结果，体现了模型的决策过程与界面设计。

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5. Experimental Setup

5.1. Datasets

The experiments were conducted using a real-world dataset from a mass finishing company. The data consists of processing cases for shaft-type parts (轴类零件), which are common and critical components in mechanical equipment. The dataset is divided into three sub-categories, treated as different domains in the experiments:

• Gear shafts (齿轮轴)

• Camshafts (凸轮轴)

• Crankshafts (曲轴)

  The paper provides an image (Figure 6) showing examples of these parts before and after mass finishing, which helps to visualize the application domain.

  该图像是图6，展示了常见轴类零件及滚磨光整前后的对比图，包括齿轮轴、凸轮轴和曲轴三种零件的加工前后状态，直观反映了滚磨光整工艺的表面加工效果。

The choice of these datasets is effective because they represent related but distinct product families. This creates a realistic multi-source domain adaptation scenario where knowledge from processing one type of shaft can be transferred to help with another, but their feature distributions are different enough to challenge traditional models.

5.2. Evaluation Metrics

The primary evaluation metric used in the paper is Decision Accuracy (A_Accuracy).

• Conceptual Definition: This metric measures the percentage of test cases for which the model's predicted process element (abrasive media, fluid, or equipment) exactly matches the one used in the actual, real-world manufacturing case. It is a straightforward and intuitive measure of the model's correctness.

• Mathematical Formula: The formula is given in the paper as Equation (19): $ A _ { \mathrm { A c c u r a c y } } = { \frac { n _ { \mathrm { c o } } } { n _ { \mathrm { t } } } } $

• Symbol Explanation:

  • $A_{Accuracy}$: The decision accuracy.
  • $n_{co}$: The number of cases in the target domain where the model's decision result matches the true result from the real case.
  • $n_t$: The total number of cases in the target domain set.

5.3. Baselines

The proposed WMDA model (combined with PESM) was compared against several baseline models to demonstrate its effectiveness. These baselines represent different technological approaches to the same problem:

• CBR (Case-Based Reasoning) [7]: A traditional AI method that retrieves similar past cases. This represents the non-machine learning, experience-based approach.

• ER (Expert Reasoning) [8]: A rule-based expert system. This also represents a traditional, knowledge-engineering approach.

• CDA-MR (Conditional Distribution Adaptation-Manifold Regularization) [16]: A single-source transfer learning method. This baseline helps to demonstrate the advantage of using a multi-source approach.

• MDA-MR (Multi-domain Adaptation-Manifold Regularization) [18]: The direct predecessor to WMDA. This comparison is crucial to validate the specific improvements (adaptation factor and Wasserstein distance) proposed in this paper.

  These baselines are well-chosen as they allow for a comprehensive evaluation of the paper's contributions, showing the benefit of (1) using transfer learning over traditional methods, (2) using a multi-source approach over a single-source one, and (3) using the proposed WMDA enhancements over the previous state-of-the-art MDA-MR.

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6. Results & Analysis

6.1. Core Results Analysis

The experimental results, primarily presented in Figure 7, comprehensively validate the superiority of the proposed WMDA+PESM model. The experiments were conducted using various combinations of the three shaft-part datasets (gear shaft, camshaft, crankshaft) as source and target domains.

该图像是图7，工艺要素决策对比实验的柱状图，展示了不同算法（CBR、CDA-MR、ER、MDA-MR、WMDA）在多种工艺要素组合下的决策准确率对比，反映了加权多源自适应迁移学习算法的优越性。

The key findings from the comparative experiments are:

1. Transfer Learning Models Outperform Traditional Methods: In all experimental settings (both single-source and multi-source), the transfer learning models (CDA-MR, MDA-MR, WMDA) consistently achieve significantly higher accuracy than CBR and ER. The paper states that the accuracy improvement can be up to 48.43%. This strongly confirms the initial hypothesis: transfer learning is necessary to handle the large distribution differences between new parts and historical experience.

2. Multi-Source Adaptation is Crucial: The CDA-MR model, which is designed for a single source, shows limited or even negative effects in multi-source scenarios. For instance, in the experiment "Gear shaft + Camshaft -> Crankshaft" (Figure 7(i)), the accuracy of CDA-MR is lower than in the single-source experiment "Camshaft -> Crankshaft" (Figure 7(c)), dropping by 10.34%. This demonstrates negative transfer—irrelevant source information harmed the model's performance. In contrast, MDA-MR and WMDA, which are designed to handle multiple sources by weighting their contributions, show consistent accuracy improvements. This validates the need for a proper multi-source adaptation mechanism.

3. WMDA is Superior to MDA-MR: Across all experiments, the proposed WMDA model achieves higher accuracy than its predecessor, MDA-MR. This validates the effectiveness of the two proposed improvements: the adaptation factor and the use of Wasserstein Distance for classifier weighting. For example, in the "Gear shaft + Crankshaft -> Camshaft" experiment (Figure 7(l)), WMDA shows a clear advantage over MDA-MR.

4. Final Achieved Accuracy: The model achieves the highest accuracy in the "Gear shaft + Crankshaft -> Camshaft" setting, with:

   • Abrasive Media Decision Accuracy: 75.00%
   • Grinding Fluid Decision Accuracy: 95.31%
   • Finishing Equipment Decision Accuracy: 65.63% The very high accuracy for grinding fluid suggests it is a simpler decision, while equipment selection remains the most challenging task.

6.2. Data Presentation (Tables)

The paper includes several tables to support its claims through transferability analysis, ablation studies, and interface validation.

6.2.1. Transferability Analysis

The following are the results from Table 4 of the original paper, which analyzes the distance between different datasets using MMD and Wasserstein Distance to assess their "transferability."

Analysis: This table shows that the distances (both MMD and Wasserstein) between the different types of shaft parts (e.g., gear shaft vs. camshaft) are significantly smaller than the distances between shaft parts and a non-shaft part (gear). For example, the MMD between shaft-types is ~0.001, while the MMD between a shaft-type and the gear-type is ~0.005 (up to 14 times larger). This quantitatively justifies the need for transferability analysis: using a highly dissimilar domain like "gear" as a source for a "shaft" target would likely lead to negative transfer.

6.2.2. Ablation Studies

The following are the results from Table 5 of the original paper, which presents an ablation study to verify the effectiveness of each component of the WMDA algorithm.

• MDA-MR: Baseline model.

• MDA-MR1: MDA-MR with only the data adaptation improvement (adaptation factor $α$).

• MDA-MR2: MDA-MR with only the classifier weighting improvement (Wasserstein distance).

• WMDA: Full proposed model.

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

  Tab.5 Accuracy(%) comparison of the decision model ablation experiment

  工艺要素 (Process Element)	MDA-MR	MDA-MR1	MDA-MR2	WMDA
  滚抛磨块 (Abrasive Media)	73.44	75.00	73.44	75.00
  磨液 (Grinding Fluid)	92.19	93.75	93.75	95.31
  光整设备 (Finishing Equipment)	59.38	62.50	60.93	65.63

  Analysis:

  • MDA-MR1 consistently outperforms MDA-MR, indicating that the adaptation factor ($α$) is effective in improving performance.
  • MDA-MR2 performs better than or equal to MDA-MR, demonstrating that incorporating Wasserstein Distance for classifier weighting is also beneficial.
  • WMDA, which combines both improvements, achieves the highest accuracy across all three decision tasks. This clearly demonstrates that both proposed modifications are valuable and contribute to the final model's superior performance.

  6.2.3. Decision Interface Validation

  The following are the results from Table 6 of the original paper, which shows 10 randomly selected results from the decision interface to verify its real-world functionality. Mismatched decisions are highlighted in bold in the original text.

  组号 (Group No.)	... (Input Features) ...	实际磨块 (Actual Media)	决策磨块 (Decision Media)	实际磨液 (Actual Fluid)	决策磨液 (Decision Fluid)	实际设备 (Actual Equipment)	决策设备 (Decision Equipment)
  1	...	2号三角磨块	**3号中磨磨块**	HYF	HYF	LL05	LL05
  2	...	3号精磨磨块	3号精磨磨块	HYF	HYF	W900	**W1300**
  3	...	3号精磨磨块	3号精磨磨块	HYF	**HYA**	W1300	**W1600**
  4	...	3号粗磨磨块	3号粗磨磨块	HYF	HYF	X400	X400
  5	...	3号精磨磨块	3号精磨磨块	HYA	HYA	W1300	W1300
  6	...	3号精磨磨块	3号精磨磨块	HYF	HYF	W1300	**W1600**
  7	...	3号精磨磨块	3号精磨磨块	HYF	HYF	W1300	W1300
  8	...	3号中磨磨块	3号中磨磨块	HYF	HYF	X600	X600
  9	...	3号精磨磨块	3号精磨磨块	HYF	HYF	W1600	W1600
  10	...	3号三角磨块	**3号粗磨磨块**	HYF	HYF	X400	**W1300**

  Analysis: This table shows the model's performance on individual cases. Out of 10 samples, there are 2 mismatches for abrasive media (80% accuracy), 1 for grinding fluid (90% accuracy), and 4 for equipment (60% accuracy). These sample accuracies are consistent with the overall model performance reported in the main experiments, validating that the implemented interface correctly uses the WMDA model and its performance is replicable.

  ---

  7. Conclusion & Reflections

  7.1. Conclusion Summary

  This paper successfully tackles a critical problem in intelligent manufacturing: the decision-making for mass finishing process elements when new parts have significantly different characteristics from historical data. The authors make the following key contributions:

  • They demonstrate that traditional CBR and ER models are inadequate for this task and that transfer learning is a highly effective alternative.

  • They propose the WMDA algorithm, an enhanced multi-source transfer learning method that improves upon MDA-MR by introducing an adaptation factor and a hybrid distance metric (MMD + Wasserstein Distance), leading to higher decision accuracy.

  • They design the innovative PESM algorithm, which reframes the decision problem from direct classification to a more robust "predict-then-match" process. This effectively mitigates the negative transfer caused by a large number of output classes.

  • The integrated WMDA+PESM model is validated on real-world industrial data, showing superior performance.

  • A practical decision-support interface is designed, bringing the research closer to industrial application and providing technicians with both optimal and alternative solutions.

    Overall, the research provides a precise and practical decision-support solution for the mass finishing domain and offers valuable technical guidance for its digital and intelligent transformation.

  7.2. Limitations & Future Work

  While the paper presents a robust model, some potential limitations and areas for future work can be identified:

  • Moderate Accuracy for Complex Decisions: The decision accuracy for finishing equipment (~65.6%) and abrasive media (~75.0%), while superior to baselines, still leaves room for improvement. This suggests that the feature representation or the model itself may not be capturing all the complexities of these choices. Future work could explore more advanced feature engineering or deep learning-based representation learning.
  • Arbitrary Weighting in WMDA: In the improved classifier weighting (Equation 11), the contributions of MMD-based similarity and Wasserstein-based similarity are equally weighted (0.5 each). This is a heuristic choice. A potential improvement would be to learn these weights dynamically, perhaps based on the characteristics of the domains, making the fusion more adaptive.
  • Dependency on the PESM Library: The effectiveness of the PESM algorithm is entirely dependent on the quality and completeness of the process element library. If a truly optimal element does not exist in the library, the model can only find the "best fit" among suboptimal choices. Future work could explore generative models that suggest novel combinations of features for new process elements.
  • Lack of Hyperparameter Details: The paper mentions "model parameter tuning" but does not provide the final values for key hyperparameters like $α$, $μ$, $λ$, and the kernel parameters for MMD. This omission makes it difficult for other researchers to reproduce the results exactly.

  7.3. Personal Insights & Critique

  This paper is an excellent example of applied academic research that directly addresses a real-world industrial problem.

  • Key Insight - Problem Decomposition: The most insightful aspect of this work is the PESM algorithm. It showcases a powerful principle: if an end-to-end prediction task is too complex or the output space is too large and structured, it's often better to decompose it. By changing the task from "predict the object" to "predict the object's properties" and then using a structured search, the authors made the learning problem more tractable and the system more modular. This "predict-then-match" paradigm is highly transferable to other domains like complex system configuration, personalized recommendation, and even drug discovery.

  • Critique and Areas for Reflection:

    • The paper's strength is its solid engineering and empirical results. However, the theoretical justification for some choices could be deeper. For example, a more thorough analysis of why and in which situations the combination of MMD and Wasserstein distance is better than either one alone would strengthen the contribution.

    • The similarity formulas in PESM are intuitive but somewhat ad-hoc. For instance, the exponential function for numerical features is one of many possible choices. A sensitivity analysis or comparison of different similarity functions would have added more rigor.

    • The work represents a significant step in applying "shallow" transfer learning models. A natural next step would be to explore deep transfer learning models, which could learn more powerful feature representations directly from raw or semi-structured data, potentially reducing the reliance on manual feature engineering.

      In conclusion, this paper provides a well-executed and practically relevant solution. Its main strength lies in the clever combination of a refined transfer learning algorithm with a pragmatic, structured matching process, demonstrating a clear path from theoretical machine learning to impactful industrial application.