Models that predict the Frequency Response Function (FRF) of six degree-of-freedom (6-dof) industrial robots used for machining operations such as milling are usually built using Experimental Modal Analysis (EMA) of vibration data obtained from modal impact hammer tests performed at a finite number of points in the robot's workspace corresponding to specific arm configurations. While modal impact hammer tests are not constrained by the operating conditions of the robot, such as specific arm configurations allowed by part fixturing, they are limited by the number of workspace points that can be practically sampled and the associated robot downtime. Alternatively, the process of determining robot FRFs from on-line machining process data (e.g., forces and vibration) through Operational Modal Analysis (OMA) enables a denser sampling of the robot's workspace without requiring robot downtime. However, OMA may require several long tool paths and one or more complex part setups to enable sampling of a sufficiently large number of locations/arm configurations. This paper presents an efficient hybrid statistical modelling methodology that combines the two approaches, thus enabling possible optimization of sampling density and robot downtime, to efficiently determine the robot FRFs as a function arm configuration. The approach consists of first calibrating a Gaussian Process Regression (GPR) model with FRF data derived from EMA conducted at a small number of discrete locations in the robot's workspace. Then, FRFs calculated from OMA of milling forces and tool tip vibration data derived from robotic milling tests are used to update the initial GPR model using Bayesian inference and efficient hyperparameter updating. The proposed hybrid robot FRF modelling method is experimentally validated and shown to yield accurate predictions of the robot FRF while being computationally efficient.

通常使用对模态冲击锤测试获得的振动数据的实验模态分析（EMA）建立预测用于铣削等机械加工的六个自由度（6-dof）工业机器人的频率响应函数（FRF）的模型在机器人工作空间中与特定手臂配置相对应的有限数量的点上执行。虽然模态冲击锤测试不受机器人操作条件的限制，例如零件固定所允许的特定手臂配置，但它们受到可实际采样的工作空间点数以及相关的机器人停机时间的限制。或者，根据在线加工过程数据确定机器人FRF的过程（例如，力和振动）通过操作模态分析（OMA）可以对机器人工作区进行更密集的采样，而无需停机。但是，OMA可能需要几个较长的刀具路径和一个或多个复杂的零件设置，才能对足够多的位置/臂配置进行采样。本文提出了一种有效的混合统计建模方法，该方法结合了这两种方法，从而可以优化采样密度和减少机器人停机时间，从而有效地将机器人FRF确定为功能臂配置。该方法包括首先用机器人工作空间中少量离散位置上的EMA得出的FRF数据校准高斯过程回归（GPR）模型。然后，从铣削力的OMA计算得出的FRF和从机器人铣削测试得出的刀尖振动数据被用于通过贝叶斯推断和有效的超参数更新来更新初始GPR模型。提出的混合机器人FRF建模方法已通过实验验证，并显示出对机器人FRF的准确预测，同时计算效率很高。