## 1 Introduction  
The prospect of applications of manipulators draws attention to robot training, in which technicians learn to control the robotic arms and fulfill tasks through programming. By analyzing the performance of robots automatically, the evaluation system for robot training may help reduce manual participation, improve training efficiency and minimize the cost. Performance evaluation of robotic arms is an important research topic in industrial manufacturing with the wide application of manipulators [1]. The motion stability of robotic arms may affect their working accuracy, energy consumption, and service life. However, few studies have paid enough attention to the stability evaluation of robotic arms at work. Therefore, it is meaningful to establish an evaluation system to assess the degree of stability of robotic arms for robot training. Stability issues manifest as the apparent vibration of the manipulator tool center point (TCP), which is closely related to the operations and set parameters by the technicians in robot training. The paper aims to develop a stability evaluation scheme for robot training based on the analysis of vibration signals of manipulators. Presently, most research related to industrial manipulators focuses on mathematical modeling, control theory optimization, and trajectory planning. [PERSON] and [PERSON] proposed the classical D-H parameter method to describe the transmission relationship between the joints and the arm of the serial manipulator [2]. Through the solution of forward and inverse kinematics, the mutual conversion between the angles of each joint and the motion of the end of the manipulator can be realized. The dynamic analysis method of the manipulator is employed to calculate the force and torque applied to the robot. The commonly used methods include the Newton-Euler method [3], Lagrange method [4], and Kane method [5], which explore the relationship between the driving force on the robot and the set of dynamic parameters. Efficiency, smoothness, and energy consumption are common issues considered in the trajectory planning of the manipulator [6]. Dynamics-based planning also takes into account the constraints of the manipulator's drive capability, which is closer to the physical model [7]. When it comes to research about the stability of the manipulator, the related work mainly analyzed and optimized the vibration characteristics of the robots from the aspects of mathematical modeling, trajectory algorithm, and controlling optimization [8; 9]. Ref. [10] proposed dividing the continuous time sequence of vibration signals into pieces of states and realized abnormal detection by analyzing information extracted from each state. As for the measurement of vibration signals, ref. [11] put forward a performance evaluation method for industrial robots based on camera-mirror binocular vision, which improved the positioning accuracy of the end of the robotic arm. Research [12] implemented a multi-scale entropy method to extract features and applied it to fault diagnosing of robots. [PERSON] et al. [13] obtained features from vibration signals through fast Fourier transform and continuous wavelet transform, and they combined SVM to achieve the joint health assessment of industrial manipulators. The article [14] analyzed the vibration-free working conditions of the manipulator through the frequency response of vibration signals at the end of the manipulator and managed to compensate for the influence of the acceleration sensor's weight that collects signals. [PERSON] et al. designed an experiment to explore the relationship between the motion parameters of the manipulator and the stability performance [15]. In addition, [PERSON] et al. [16] explored the structural vibration of the manipulator and proposed an optimization method regarding structure designing. These and other unmentioned works have made remarkable contributions to the advancement of understanding and improvement of robotic stability.