# Optimal Placement of Vibration Sensors for Industrial Robots Based on Bayesian Theory
## 3 Experiment
### Verification Method for Layout
The selected features should reflect the amplitude and fluctuation characteristics of the signal. Therefore, the selected time-domain characteristics include mean value, root mean square value, absolute mean value, skewness, kurtosis, and variance. Divide the above-mentioned original signals into two groups, take 40,000 sampling points for each group of original signals, calculate the time domain signal characteristics of the two groups of signals, respectively, and combine the real speed with the time domain characteristics' overall input. The input is shown in Figure 6.

The signal features of the three joints in motion are input into the probability model program. The optimal layout evaluation is calculated circularly, and the corresponding redundancy is calculated. The optimal layout order is [0.7, 1.47, 0.7, 0.8, 1.18, 0.8, 1.56, 1.47, 1.37, 1.37, 1.18, 0.8, 0.5, 0.5, 0.2, 0.2]. By observing the distribution of objective function values, as shown in Figure 7, and considering the problem of the degree of freedom of the industrial robot, ten sensors are selected to be arranged. The optimal sensor layout is [0.7, 1.47, 0.7, 0.8, 1.18, 0.8, 1.56, 1.47, 1.37, 1.37]. The corresponding objective function value is 2.4. The empirical layout and uniform layout are shown in Figure 8.

Figure 6: Data characteristics of motion data: (a) data characteristics of the first joint, (b) data characteristics of the second joint, and (c) data characteristics of the third joint. Figure 8: Three kinds of layouts for Industrial robot with the simulation model: (**a**) optimal layout, (**b**) empirical layout, and (**c**) uniform layout. Figure 7: Objective function value for Industrial robot with the simulation model. According to the process shown in Section 3.1, the second and third joint motions are judged by probability, respectively, and the optimal layout, empirical layout, and uniform layout are selected for comparison. According to the results in Figure 9, in the layout verification experiment with the simulation model, the empirical layout and the optimal layout have a higher discrimination effect. In the judgment results of the third joint motion, the empirical layout shows a better discrimination effect than the optimal layout. In general, both empirical layout and optimal layout have good performance in the layout verification experiment with the model. However, due to the complex process of model simulation and kinematic analysis, this method cannot be applied to large-scale industrial scenes. ### Optimal Sensor Placement Method and Verification of Industrial Robots without Simulation Models

In the implementation process of the sensor layout optimization method, first, the kinematics and dynamics simulation analyses are carried out based on the simulation model and DH parameters, and the theoretical speed is taken as the theoretical value of the probability model. The subsequent optimization is carried out through the error distribution. However, in the actual scene, in some cases, the simulation model of the industrial robot is not easy to obtain, and the calculation process based on simulation analysis is more complex, which is not suitable for the scene that needs to conclude sensor placement quickly. Therefore, based on the defects of the above placement method, a sensor-optimal placement method that discards the simulation model is considered. Considering that the calculation of theoretical velocity is due to the quantization of the error distribution in the new layout method, the acceleration signal collected by the sensor is directly taken as the real value. Because of the uniform motion of each joint, the theoretical acceleration value of each layout point is 0, so the error of the two is the real acceleration signal collected by the sensor.