# Optimal Placement of Vibration Sensors for Industrial Robots Based on Bayesian Theory
## 3 Experiment  
### Verification Method for Layout  
Because the sensor layout of an industrial robot has not formed a complete theoretical system, the judgment basis of the sensor layout should be given according to the above probabilistic method. The flow chart of the layout verification method is shown in Figure 4.  
1. According to the given initial position, sensors are arranged in the corresponding position of the real industrial robot;
2. Set the joint speed of the industrial robot as a fixed speed, make the industrial robot move accordingly, and collect the acceleration of sensor distribution in the process of motion;
3. The acceleration signal is processed to get the velocity of each point, and the probability of motion from each joint is calculated by using the probability model;
4. Compare the probability of each joint with the real motion joint to determine whether the maximum probability corresponds to the real motion joint. If so, it is considered that the sensor layout can obtain the whole machine state. In this paper, two types of experiments are conducted for industrial robots with and without models, and each type of experiment acquires a series of measured experimental data through multi-channel sensors and calculates the data pre-processing and sensor optimization layout through MATLAB for the measured experimental data. Algorithm 1 is the pseudo code for the sensor-optimized layout algorithm. ``` Input: the measured velocity \(V_{t}\) and the predicted velocity \(V^{\prime}(r;s)\) of the sensor. Output: optimal sensor placement s_best. 1 rn = 3;
2 ifsn = 1 do
3 for i = 1 to rm do
4 for j = 1 to le do
5 compute p(i,j).//according to Equation (16). 6 end if
7
8 for i = 1 to rm do
9 for j = 1 to le do
10 compute U(i,j).//according to Equation (19)
11 end if
12
13 for i = 1 to rm do
14 compute Us(i).//sum U(i,j)
15 end for
16 s_best = s(max(Us));
17 else
18 sn = sn + 1;
19 for i = 1 to rm do
20 for j = 1 to le do
21 compute p(i,j).//according to Equation (16)
22 end if
23
24 for i = 1 to rm do
25 for j = 1 to le do
26 compute U(i,j).//according to Equation (19)
27 end if
28
29 for i = 1 to rm do
30 compute Us(i).//sum U(i,j)
31 end if
32 s_best = snew(max(Us));
33 for i = 1 to rm do
34 compute n_best;//according to Equation (21)
35 end for
36 s_best = s_best(n_best).//optimal sensor placement
37 end for
38//rm--number of joints;
39//s--initial Sensor placement;
40//sn--number of sensors currently optimized;
41//le--number of sensors in the initial layout;
42//p(i)--the likelihood function;
43//U(i,j)--the sensor placement evaluation function according to Equation (19);
44//Us(i)--sum of regression values of each sensor coordinate;
45//snew--the new sensor placement based on heuristic sequential sensor placement;
46//n_best--the optimal number of sensors according to the change of the objective function;

### Verification of Optimal Sensor Placement for Industrial Robots Based on the Simulation Model

To verify the effectiveness of the sensor placement method proposed in this paper, we carry out a single joint motion verification experiment for a six-axis industrial robot. The experimental scene is shown in Figure 5.

To obtain the real speed, we combined the measured acceleration with the theoretical speed as noise. Moreover, because the frequency of the real collected signal is generally high, it is not advisable to reduce all acceleration points to one dimension. At the same time, bringing all acceleration points into the calculation will lead to too much calculation. Therefore, an appropriate dimension reduction method is needed to process the original signal. Considering the signal preprocessing method of the vibration signal, we select the typical time-domain characteristics of the vibration signal. The time-domain characteristics

Figure 4: Flow chart of the layout verification method. Figure 5: Industrial robot with the simulation model. of the input vibration signal are taken as the input of the probability model for calculation.