用物理先验+机器学习，从噪声数据中自动发现铣削动力学方程。
A Cutting Mechanics-based Machine Learning Modeling Method to Discover Governing Equations of Machining Dynamics
- 融合切削力学物理规律与数据，构建可学习的微分代数方程框架。
- 在含噪声数据下成功复现含颤振抑制和刃口力的精确铣削模型。
- 适合需要高精度建模的智能制造与工艺优化场景。
本文提出一种基于切削力学的机器学习（CMML）建模方法，用于发现加工动态的控制方程。该方法将已知的切削力学物理规律与数据中未知的物理信息相结合，实现自动化模型发现。基于现有切削力学知识，CMML首先建立描述加工动态的一般模型结构，即一组未知的微分代数方程。通过基于切削力学的非线性学习函数空间设计与基于离散优化的学习算法，实现对这些未知方程的数据驱动发现。采用实验验证的时域铣削仿真进行测试，数值结果表明，即使在含噪声数据条件下，CMML仍能准确发现包含过程阻尼和刃口力的铣削动力学模型。这表明，随着精密测量系统的发展，该方法有望在实际加工建模中发挥重要作用。
原文摘要 · Abstract (English)
This paper proposes a cutting mechanics-based machine learning (CMML) modeling method to discover governing equations of machining dynamics. The main idea of CMML design is to integrate existing physics in cutting mechanics and unknown physics in data to achieve automated model discovery, with the potential to advance machining modeling. Based on existing physics in cutting mechanics, CMML first establishes a general modeling structure governing machining dynamics, that is represented by a set of unknown differential algebraic equations. CMML can therefore achieve data-driven discovery of these unknown equations through effective cutting mechanics-based nonlinear learning function space design and discrete optimization-based learning algorithm. Experimentally verified time domain simulation of milling is used to validate the proposed modeling method. Numerical results show CMML can discover the exact milling dynamics models with process damping and edge force from noisy data. This indicates that CMML has the potential to be used for advancing machining modeling in practice with the development of effective metrology systems.
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