# Optimal Placement of Vibration Sensors for Industrial Robots Based on Bayesian Theory
## 1 Introduction
### Related Work  
Juri [11] proposed a greedy frame sense algorithm to select the optimal sensor location when estimating parameters from the measured data of sensors. This algorithm is the first one that is close to optimal in the mean square error. In the last 10 years, the optimal placement of sensors in mechanical systems and structures has become a hot research topic. Applications include modeling, identification, fault detection, and active control of systems, such as bridges [12]. To ensure safety and functionality, more and more structures are equipped with various types of sensors, such as accelerometers, displacement sensors, strain gauges, and fiber optic sensors for monitoring [13]. The modal confidence matrix is an excellent tool for evaluating the correlation of modal shape vector space. The calculated scalar value is between 0-1 or expressed as a percentage. For industrial robots, the redundancy of sensor placement can be evaluated using a modal confidence matrix. [PERSON] [14] proposed a hybrid optimization method to optimize sensor placement when constructing an effective structural health detection system. In this method, the modal confidence matrix is introduced, and dual structure coding based on a generalized genetic algorithm is used to determine the sensor position. [PERSON] [15] argued that sensor configurations should also minimize unnecessary high-mode spillovers in addition to the classic EFI approach. [PERSON] [16] used four classical sensor location methods: two based on the Fisher information matrix and two based on the rank optimization of the energy matrix. Methods based on information theory have been developed to provide reasonable solutions to the problem of selecting the optimal sensor configuration in modal identification and structural parameter estimation [17; 18]. [PERSON] [19] considered that, in the sensor placement of the structural health monitoring system, the structural array and natural frequency should be considered, along with the degree of participation in the structural response. Therefore, a sensor placement method considering both the dynamic characteristics of the structure and the actual load conditions is proposed, and it is verified that the method has a better modal identification effect. [PERSON] [20] focused on the problem of determining the optimal reference sensor position under random excitation in a weakly stationary process, combined with the set design variables of the sensor location, and the genetic algorithm was used to avoid evaluating all possible combinations of reference sensor positions. The proposed method was verified by a numerical benchmark study of a supported beam and a practical sample. [PERSON] used a theoretical estimation framework to calculate the optimal geometric sensor formations that would yield the best achievable performance in terms of target positioning accuracy by maximizing the determinant of the appropriately defined Fisher Information Matrix (FIM) [21]. [PERSON] [22] considered the optimal sensor placement problem in structural health inspections. Based on the general Bayes formula, optimal placement was established as a process of minimizing the expectation of specific errors. Finally, the optimal solution generated by the algorithm was discussed. Using the influence of spatial correlation prediction error on optimal placement, [PERSON] [23] used information entropy as the performance measure of sensor configuration, and he expressed the optimal position of sensors as the optimization problem of discrete variables, which solved the problem of modal identification and parameter estimation of the structure-related model. [PERSON] [24] transformed the optimization problem into an integer optimization problem and then proposed a discrete optimization scheme based on an artificial bee colony algorithm to solve the optimization problem. Health monitoring and fault diagnosis of industrial robots are essential for safe and reliable operation, and a practical sensor layout is essential for fault diagnosis and other work.