A Bearing Life Prediction Method of Improving Smooth Degree and the Background Value

Bearings, as a component in many complex weapons, can be used to reduce friction to improve the efficiency of equipment. Bearing CV value can quantify the working performance of bearings, which can act as a reference standard for staff to evaluate the working condition of bearings. According to the known data, the real CV value of the bearing is calculated in this paper. In order to improve the smoothing ratio, the data is processed by the idea of data transformation and the background value is optimized by the new formula. The two improve the GM (1,1) model and simulate the predicted bearing CV and calculate the moment of failure by this model, which is compared with the traditional GM (1,1) and the improved GM (1,1) by cumulative method in terms of error and accuracy. It is verified that the average relative error and the model prediction accuracy of the model prediction life are 0.0185 and 98.15% respectively after the improvement of the stability and background value. Therefore, this method has certain practical value in engineering, and is more effective than the cumulative GM (1,1) model.


Introduction
Bearings are present in most weaponry, for example, the trunnion section of the launcher arm of a missile launcher requires bearings to rotate, and many small and medium sized motors use bearings [1]. One disadvantage, however, is that these bearings often fail, causing damage and eventual failure [2].
Reference 3 takes the rolling bearing as an example. It is mentioned that the defects of the inner and outer rings will make the metal in contact surface flake off and form pits on the bearing surface, and the impact of the rolling body on the racetrack on one or both sides will cause various pollutants such as external viscosity and particles to enter between the rolling body and the racetrack, leading to wear or scratch, etc. [3].Using the maximum likelihood estimation method, the CV values of the bearings are calculated to quantify their operating conditions, and an algorithm is designed based on the original GM (1,1) method to predict the CV values by reducing the smoothing ratio of the original data series and optimizing the background value calculation method. In addition, in terms of relative error and prediction accuracy, this paper accordingly compares the former with the improved GM (1,1) model based on the cumulative method.

Calculation method of bearing's real confidential value
In fact, the CV value, also known as the performance evaluation index [4], can be seen as a dichotomous probability, so you can generally use the CV (Confidential Value) as a measure of rolling bearing failure. CV value can quantify the rolling bearing failure degree, its value range between 0 and 1, where 0 is the rolling bearing complete failure state, 1 is the best working performance state (where less than or equal to 0.05 is taken to mean that the rolling bearing is no longer capable of operating), then the CV value is expressed as follows [5]:

CV = P (cv = | x ) = (1) + e
Where, x is the k-dimensional column vector, 0 E is the regression intercept, and i E is the regression coefficient.
In this paper, bearing data from the University of Cincinnati was chosen to test the accuracy of the performance of three prediction methods [6]. First, the CV is calculated for the entire operating cycle of the rolling bearing, which has 984 moments of sampling for this bearing type, with a 10-min interval between each of the sampling moments, and the rolling bearing CV is then calculated according to the method of maximum likelihood estimation.

Prediction method of bearing's real confidential value
So far, the most extensive and direct method to predict the data sequence is to use the grey GM (1,1) model for calculation. The GM (1,1) modified models commonly used include the GM (1,1) model with improved metabolism, GM (1,1) model with optimized combination of intelligent functions, GM (1,1) model with coupled trigonometric function transformation, etc. However, after comparison with the real value, the average relative error of these models is still some way from the ideal value. In view of this, the GM (1,1) model with improved smoothness and optimized background value is compared with the original GM (1,1) model and the GM (1,1) model with improved accumulation method, and the relative error and multiple indexes of prediction accuracy are analyzed.

Principle of improved GM (1,1) prediction model with cumulative method
When predicting CV values, it adopts the model of GM (1,1) based on cumulative method, the cumulative method is a method of fitting, it combines with the original GM (1,1) model can improve the performance of the prediction model [7].

x (i -1)+ x (i) z (i) = (5) 2
The equation set consists of first-order operator and second-order operator can solve the prediction parameters a and u:

7)
Substitute a and u in grey equation of GM (1,1) model, it can get the CV value prediction formula:

Improvement of smoothness
It can be assumed that there are data sequences, then the ratio between the sum of the KTH data x(k) and the first k-1 data in the whole sequence is called the data smoothness ratio [8], which can reflect the smoothness of the change of the whole data sequence, which is
To reduce the value of ( ) k U , this paper proposes an improved data processing method of  (ln ) (ln ) Therefore, Equation (18) proves that i c x (ln i ) transformation can optimize the smoothness of the whole data sequence.

Background value optimization
The background value of grey prediction model is one of the important factors that affect the prediction precision [9]. By bearing the CV value of actual change trend is hard to predict, in order to further reduce the error, in the prediction of model bearing CV value using the following formula instead of the general model of the background value.

Comparison of simulation results of three prediction models
In the first stage (time 1-700), bearing failure data at time 1-20 were used for training. The second stage (701-900 moments) was trained with data from 701-720 moments. And the third stage (901-984 moments) was trained with data from 901-910 moments. The accuracy test methods of general gray prediction model include residual error, posterior error or correlation degree, etc. Here, the residual test method is used to compare the relative error, average relative error and model prediction accuracy index between the improved model  It can be seen from Figure. 2that, when CV value is equal to 0.05, the X-axis coordinate (failure time) corresponding to the traditional GM (1,1) model is about 945 time, while the X-axis coordinate corresponding to the GM (1,1) model improved by the accumulation method is about 953 time. The predicted data and residual curves are shown in Figure 2 and Figure 3. The X-axis coordinate corresponding to the GM ( value are the closest to the reality.

Conclusion
In this paper, bearing failure data from the university of Cincinnati, USA were used to test the accuracy of the new prediction model with improved stability and background values, and the results were compared with those of the traditional GM (1,1) model and the GM (1,1) model based on the cumulative method. On this basis, the relative errors and model prediction accuracy for each stage of the three models are calculated. Finally, the conclusion is drawn as follows: the relative error value of the new prediction model is much lower than the latter two and the prediction accuracy is greatly improved, so it is more practical for the maintenance of weapons and equipment, especially rotating machinery. The value of this improved forecasting method lies in its ability to facilitate the actual operation of the staff.