数控机床作为现代制造业的核心装备，其故障诊断能力直接影响生产效率和设备可靠性。针对现有故障可诊断性评价方法参数选择主观性强、特征提取不全面及传感器布置不合理等问题，本文提出一套面向元动作单元的故障可诊断性评价技术体系，从构成数控机床的最小独立且不可划分的元动作单元入手，开展故障可诊断性评价技术研究。

（1）由于数控机床结构复杂，本文采用“功能-运动-动作”的分解方法将数控机床映射至不可进一步分解的元动作单元，通过统计高频属性确定蜗杆转动元动作单元为本文的研究对象。并根据蜗杆元动作单元主要失效件提取主要故障模式，针对蜗杆元动作单元常见故障模式，利用振动加速度传感器采集不同状态下的振动信号。

（2）在对故障信号进行采集之后，本文提出了一种基于K-L散度的传感器优化布置方法。结合蜗杆转动元动作单元的有限元分析，运用二分K均值聚类算法和有效独立平均加速度幅值法筛选初选测点，并借助核密度估计和相关函数信息融合技术进一步优化传感器布置方案，通过模态置信准则、Fisher信息矩阵和K-L散度三个指标进行综合评价之后确定最优方案，以实现最优的故障特征区分性。

（3）在完成传感器布置优化之后，本文引入了一种融合黄金正弦的减法平均优化算法（GSABO）优化VMD参数，解决了传统VMD方法中参数选择的主观性和盲目性问题，显著提升了故障特征提取的准确性和鲁棒性。之后构建了基于余弦距离的故障可诊断性定量评价方法，将故障可诊断性评价转化为振动信号特征向量的相似性度量问题，实现了对故障可诊断性的精准量化评估。

（4）在传感器优化布置基础之上，通过使用四种不同的相似性度量方法对所提出的故障可诊断性评价方法的验证，并与未优化传感器布置的故障可诊断性评价结果比较，结果表明所提方法能够有效提升传感器布置的合理性，增强故障特征的区分性，显著提高故障可诊断性评价的精度和可靠性。与传统方法相比，余弦相似度使故障可检测性指标降低至3.971，分离性指标降至13.8864，较传统方法提升约40%。其中，GSABO-VMD方法在特征提取精度、抗噪性及计算效率上均展现出显著优势，为数控机床的故障诊断与健康管理提供了新的技术手段。

As a core equipment in modern manufacturing, the reliability and fault diagnosability of CNC machine tools directly impact production efficiency and operational stability. To address the limitations of existing fault diagnosability evaluation methods, such as subjective parameter selection, incomplete feature extraction, and suboptimal sensor placement, this study proposes a systematic fault diagnosability evaluation framework targeting the meta-action unit—the smallest independent and indivisible functional component of CNC machine tools.

(1) Fault Signal Acquisition and Feature Extraction: A "Function-Motion-Action" (FMA) decomposition method was employed to map CNC machine tools to meta-action units. The worm rotation meta-action unit was selected as the research object based on high-frequency attribute statistics. Common fault modes (e.g., coupling loosening, key wear) were identified, and vibration signals under different states were collected using acceleration sensors.

(2) Sensor Optimization Based on K-L Divergence: A sensor placement optimization method integrating finite element analysis, bisecting K-means clustering, and Effective Independence-Average Acceleration Amplitude (EI-AAA) was proposed. Initial measurement points were screened using kernel density estimation and correlation function information fusion. Comprehensive evaluation via Modal Assurance Criterion (MAC), Fisher Information Matrix (FIM), and K-L divergence identified the optimal configuration (nodes 775 and 1742). This reduced fault detectability and separability indices to 3.971 and 13.8864, respectively, achieving a 40% improvement over conventional methods.

(3) GSABO-Optimized VMD for Feature Enhancement: A Golden Sine-Subtraction Average-Based Optimization (GSABO) algorithm was developed to adaptively optimize Variational Mode Decomposition (VMD) parameters (modes K and penalty factor α), resolving modal aliasing and enhancing feature extraction robustness. Kurtosis-correlation coefficient criteria were applied to select intrinsic mode functions (IMFs), improving noise resistance and computational efficiency.

(4) Quantitative Diagnosability Evaluation: A cosine distance-based metric was established to transform fault diagnosability assessment into a similarity measurement problem of vibration signal feature vectors. Experimental validation using four similarity metrics confirmed the superiority of the proposed method. The GSABO-VMD framework demonstrated significant advantages in feature extraction accuracy (15% reduction in envelope entropy) and fault discrimination (20–30% increase in kurtosis values), providing a novel technical approach for CNC machine tool health management.

This study offers theoretical and practical advancements for intelligent fault diagnosis in CNC systems. Future work will focus on multi-sensor data fusion and lifecycle health management to further enhance manufacturing equipment reliability.