# Optimal Placement of Vibration Sensors for Industrial Robots Based on Bayesian Theory
## 3 Experiment
### Verification Method for Layout
According to the connection of the joint motion of the industrial robot, the sensor layout verification method of the industrial robot is first designed, and the probability of each joint is considered to be compared with the real moving joint to determine whether the maximum probability corresponds to the real moving joint, and joint 2 and joint 3 are determined as the judgment kinematic joints (two joints move in the same plane). For an industrial robot with a simulation model, its optimal layout is obtained, and the optimal layout, empirical layout, and uniform layout are used to verify the layout of the industrial robot sensors. It is calculated that the optimal layout has a probability increase of 0.0244 and a probability decrease of 0.0399 compared with the empirical layout, respectively. A relatively uniform layout has a probability increase of 0.1869 and 0.0339, respectively. For the model-free simulated industrial robot, its optimal layout is obtained. Compared with the empirical layout, the optimal layout has a probability increase of 0.2693 and 0.2630, respectively, and a probability increase of 0.0277 and 0.0255, respectively, compared to the uniform layout. Based on the above experimental conclusions, the effectiveness of the optimal layout method for industrial robot sensors can be proved, and the applicability of the method in the industrial field is proved. ## 4 Conclusions

This paper studies the optimal placement method of sensors to obtain better data sources for the health assessment and fault diagnosis of industrial robots. The work in this paper can be summarized as follows. Combining the 6-DOF industrial robot speed calculation formula with Bayesian optimization, taking redundancy as the constraint, and finally determining the layout method of the industrial robot acceleration sensor. Considering the importance of joint motion state information for the health assessment and fault diagnosis of industrial robots, we want this layout method to capture joint motion state information to the greatest extent. To obtain the initial sensor layout, we carry out the modal simulation of the industrial robot model. At the same time, considering the need to calculate the speed of specific points, the original speed transfer formula of the robot is rewritten, and the speed calculation formula of specific points is obtained. Considering that the evaluation function cannot give the number of sensors, the modal confidence matrix is improved by using the kinematic characteristics of the industrial robot, and the improved modal confidence matrix is used to constrain the evaluation function. Figure 5.8 Probabilistic verification of three layouts: (**a**) Probability verification of the second joint movement, (**b**) Probability verification of the third joint in motion. For different experimental objects, verification experiments with models and without models are carried out. Compared with the current common layout and uniform layout, the optimized layout obtained by this method can capture joint state information more effectively. The effectiveness of the optimal layout is verified by a model-based sensor optimal layout experiment, which verifies the effectiveness of the optimization method. The sensor optimal layout experiment realizes the extension of the layout method without a model. It is also proved that the optimal layout of the sensor depends on the structure of the industrial robot itself and the real signal collected by the sensor. The layout is evaluated by the error between the real signal collected by the sensor and the theoretical calculation value, and redundancy is taken as the constraint function of the layout by using part of the results of the modal simulation. Finally, the optimal layout objective function of the industrial robot acceleration sensor is obtained, which can provide better data sources for health assessment and fault diagnosis of industrial robots. Conceptualization, Q.H. and Y.Z. ; methodology, Q.H., Y.Z. and Y.L. ; software, Y.Z., X.X. and L.S. ; validation, Q.H., Y.Z. and X.X.