The parameters of the rolling bearing friction torque with nonparametric analysis

Moment of the rolling bearing friction with only chromatography analysis with the parameters of fusion according to the total fusion evaluation of this chapter, the main evaluation and analysis to illustrate and friction performance evaluation method, and establish the number of estimates and the assessment system, parameter estimation about the number analysis rolling model; The characteristics of; Wiped moment white with parameters of the bearing and the participation method build bearing performance data of the static characteristics of the rolling bearing. 51 parameters and the fusion, the rolling bearing can evaluate problem, relying too much on the data, the existing research USES the parameters or the method and nonparametric method parameters roll data optical performance requirements for a variety of specific number ( Axis value of bearing torque more information based on the single nonparametric methods to analyze shaft to performance parameters and the parameters of friction torque tester is not desirable. Base level reflect the performance of bearing, the implementation of rolling bearing friction based on this, torque more accurate evaluation of fusion estimate method in flat rolling shaft, in this chapter, never tongfang for the selection of rolling bearing friction surface mining for reliable basis. 5. 1. 1 parameter estimation. Torque estimation in experiment and continuous measurement, according to the phase at the same time interval sampling, the experimental data obtained, a data time series X; :X,={ 。 ( n) } ，i=,2,. ,m; n = 1, 2,。 ,N ( 5 - 1) Type of x; Time series data, x ( n) For the first time I experiment of the NTH performance data, I for experimental sequence number, m for test times, n for data serial number, number n for the data. Moment estimates is the use of samples of moments or central moment as general moments or central moment estimation, is a kind of commonly used to estimate the parameter estimation. In the torque estimation, frequently used as well as overall torque estimation. Rolling bearing performance estimated parameter has the sample mean and variance, respectively (see type 5 - 2) Type ( 5) : n = xN - ( ) ,- ,,D2. 12,, type, x ( n) For the first time I experiment of the NTH performance data, I for experimental sequence number, m for test times, n for data serial number, number n for the data. Six (o Nx( m) - - - - - - The x ( ) , 1212. 。 。 = 2 - ,N ( 5 - 3) Type of x ( n) For the first set of bearings I n a performance data, I for experimental sequence number, m for test times, n for data serial number, number n for the data. For example, a small sample without failure data for ( Unit: h) : 40. 32, 48. 61, 56. 42, 56. Assuming the sample is normal distribution, 97 average estimate of 50. 58, the standard deviation is estimated at 7. 834. 2. Maximum likelihood estimation maximum likelihood estimation is based on the probability of the biggest events is most likely to happen to push the new principle to evaluate data, the estimation method is: first of all to estimate sample to establish the likelihood function, and then to take the natural logarithm likelihood function, the maximum likelihood estimator is obtained by extreme conditions. 5. 1. Two nonparametric estimation one. Symbol to estimate symbol estimation is - in modern statistics Important non-parametric estimation can be used to estimate the center of the single sample, can also be used to estimate the relationship between the two samples. Below to analyze relationship between the two samples as an example to illustrate the estimation method. ( 1) Z structure statistics; :( 1, x,( n) < x,( n) Z = { z( n} = < 0. 5, x,( n) =x,( n) ,我≠j∈( 1,m] ,i=,2,,m; n = 12日。 ,N ( 5 - 4) 0, x( n)> x; ( n) Type, Z; For two samples of comparative statistics, z ( n) And the first j a sample for the ith in the NTH interval compared as a result, the performance of x ( n) And x ( n) Respectively the ith a first j and a sample of the first n data, I for experimental sequence number, m for test times, n for data serial number, number n for the data. ( 2) Calculate statistics Z; Values of Z = Zz ( n) , n=,2,- ,N( 5 - 5) Type, z ( n) And the first j a sample for the ith in performance comparison result of the NTH interval, n for data serial number, number n for the data. ( 3) According to statistics Z; Numerical and under certain significance level a and a certain distribution of standard C the comparison result, it is concluded that the relationship between the two samples. J - generation of statistical analysis Kind of nonparametric estimation method and is 2. Rank and estimates rank and estimation is used to estimate whether there are differences of different samples performance to use the most - in the modern statistics Kind of method. 1) D structure statistics will be two different sample data in a block, according to the growing up of order statistic D order. 2) Data rank of r each rank of the location of the serial number for each data, according to the order statistics D, obtained the order of the each data r. 3) The sample rank and R will rank sum of all the data in each sample, the rank of each sample and R. 4) Sample relationship analysis according to the rank and the value of R and under certain significance level a and a certain distribution of standard comparison B as a result, it is concluded that the relationship between the two samples. The following two samples as an example to show symbol estimation and rank and estimation methods. For example, there are two samples as follows ( Unit: m) Y: X: 93, 86, 95:112, 90, a sample symbols is estimated to be 93 X 1, 0, the result of 2; Y samples shows that X sample data is less than Y sample data. X sample data of rank 3 respectively. 5, 1, 5, rank and 9. 5; Y sample data of rank and 11. 5; That X sample data is less than Y sample data, symbol estimates of 0, 1, the result is 1; Rank 6 respectively, 2, 3. 5, the main not no shield coarse estimation to estimate analysis often