Non-parametric reliability analysis method for high-speed driving roller

Abstract

The invention relates to the technical field of reliability design analysis of mechanical products, in particular to a non-parametric reliability analysis method for a high-speed driving roller, which comprises the following steps of: S1, acquiring fault data of the high-speed driving roller, and combining the same fault time in the fault data into a fault time point ti; s2, calculating a risk value of each fault time point ti according to a Nelson-Aalen estimation method, and performing continuous accumulation to obtain an accumulation risk function # imgabs0 #; S3, calculating a reliability function # imgabs2 # according to the accumulation risk function # imgabs1 # to obtain reliability; s4, non-parametric reliability degree confidence evaluation based on Nelson-Aalen estimation is carried out; the problem of reliability calculation when the theoretical distribution of the fault time of the high-speed driving roller is uncertain in engineering practice can be solved.

Description

Technical Field

[0001] The invention relates to the technical field of mechanical product reliability design and analysis, and more specifically to a non-parametric reliability analysis method for a high-speed driving roller. Background Art

[0002] Reliability analysis can identify potential failure modes and predict the failure risk of systems or components in advance, so as to take preventive measures during the design and operation process. At present, the design and processing of transmission systems are developing in the direction of fast, long-distance, and large load. As a key component of such systems, the structure, size, and speed of the drive roller are also increasing. The high-speed operation of the drive roller will greatly increase the probability of various failures. Therefore, it is very necessary to conduct reliability analysis on high-speed drive rollers. However, at present, almost all performance reliability calculations for high-speed drive rollers require the assumption of a cumulative failure probability model, which may lead to model setting errors. In addition, in engineering practice, the theoretical distribution of product failure time is usually unclear, and it is also difficult to accurately select parameter distribution. Therefore, there is an urgent need for a non-parametric reliability analysis method for high-speed drive rollers to meet the reliability assessment needs when the theoretical distribution of high-speed drive roller failure time is uncertain in engineering practice. Summary of the invention

[0003] The purpose of the present invention is to provide a non-parametric reliability analysis method for a high-speed drive roller, so as to solve the reliability calculation problem when the theoretical distribution of the failure time of the high-speed drive roller is uncertain in engineering practice.

[0004] The purpose of the present invention is achieved through the following technical solutions:

[0005] A non-parametric reliability analysis method for a high-speed drive roller, the method comprising the following steps:

[0006] S1: Obtain the fault data of the high-speed drive roller and merge the same fault time in the fault data into one fault time point t i ;

[0007] S2: Calculate each failure time point t according to the Nelson-Aalen estimation method i The risk value is accumulated continuously to obtain the cumulative risk function

[0008] S3: Based on the cumulative risk function Calculate the reliability function Get reliability;

[0009] S4: Nonparametric reliability confidence assessment based on Nelson-Aalen estimation;

[0010] The fault data are actual fault data of high-speed drive rollers in engineering practice, and the fault data include serial number, main fault mode and fault time;

[0011] Sort the observed failure time data sets of high-speed drive rollers from small to large and label them as t 1 ,t 2 ,t 3 ,…,t n , then t 1 ≤t 2 ≤t 3 ≤…≤t n , where n is the total number of data in the data set;

[0012] Combine the same failure times into one failure time point t i , denoted as t 1 ,t 2 ,t 3 ,…,t k (k≤n), and record each failure time point t i The number of failures that occurred on i ;

[0013] For each failure time point t i , calculate the risk set size at that moment, the risk set is the failure time point t i The number of individuals that have not yet failed i ;

[0014] At each failure time t i The risk value is d i / n i , the cumulative risk function The calculation formula is:

[0015]

[0016] The reliability function The calculation method is:

[0017] Clarify the relationship between the cumulative risk function Λ(t) and the cumulative failure probability function F(t):

[0018]

[0019] Then we have:

[0020] R(t)=1-F(t)=e -Λ(t) ;

[0021] In the above formula, R(t) is the reliability function, then

[0022] The non-parametric reliability confidence assessment method based on Nelson-Aalen estimation is:

[0023] According to the central limit theorem constructor, it is made to conform to the standard normal distribution. Then, combined with the confidence level 1-α and the α / 2 quantile of the standard normal distribution, the confidence interval of the reliability of the high-speed drive roller can be solved without knowing the overall distribution.

[0024] The method of constructing the function according to the central limit theorem is:

[0025] Let the random variable X represent the failure time of the high-speed drive roller, and for n samples from the population, their failure times satisfy independent and identical distribution, then I {X>t} A two-point distribution with parameter R(t);

[0026] It can be seen that E(I {X>t} )=R(t),D(I {X>t} ) = R(t)[1-R(t)];

[0027] The confidence level 1-α is a given confidence level; the α / 2 quantile of the standard normal distribution is Z α / 2 ;

[0028] According to the central limit theorem, the asymptotic distribution of the sample mean is normal distribution, and the normal distribution standardization method is

[0029] Based on the above preconditions, we can get:

[0030]

[0031] Then we have:

[0032]

[0033] The upper confidence limit of the reliability of the high-speed driving roller at time t can be derived as:

[0034]

[0035] The lower limit is:

[0036]

[0037] When the sample size is large, the confidence interval of reliability can be further simplified as:

[0038]

[0039] The beneficial effects of the present invention are:

[0040] By using the cumulative risk function The reliability function is obtained by calculating Then, the non-parametric reliability confidence assessment of the high-speed drive roller is completed, which can solve the reliability calculation problem when the theoretical distribution of the failure time of the high-speed drive roller in engineering practice is uncertain, and can avoid the model setting error caused by assuming a cumulative failure probability model. Compared with the reliability analysis process of traditional complex distribution parameters, it is more concise and direct, and can provide a more accurate and reliable basis for engineering decision-making. BRIEF DESCRIPTION OF THE DRAWINGS

[0041] The present invention is further described in detail below with reference to the accompanying drawings and specific implementation methods.

[0042] Figure 1 It is a schematic flow chart of the non-parametric reliability analysis method for the high-speed drive roller of the present invention. DETAILED DESCRIPTION

[0043] The present invention is further described in detail below with reference to the accompanying drawings.

[0044] like Figure 1 As shown, in order to solve the reliability calculation problem when the theoretical distribution of the failure time of the high-speed drive roller is uncertain in engineering practice, the steps and functions of a non-parametric reliability analysis method for the high-speed drive roller are described in detail below;

[0045] A non-parametric reliability analysis method for a high-speed drive roller comprises the following steps:

[0046] S1: Obtain the fault data of the high-speed drive roller, obtain the fault data of the high-speed drive roller, and merge the same fault time in the fault data into one fault time point t i The fault data comes from the actual fault data of the high-speed drive roller in engineering practice. The fault data set of the high-speed drive roller is formed according to the fault data of the high-speed drive roller. The data set includes the sequence number, the main fault mode and the fault time.

[0047] Assume that there are the following failure time data of 30 high-speed drive rollers (unit: hours):

[0048] {18,2,13,28,6,24,12,30,9,7,20,20,4,21,25,16,4,18,32,8,23,10,13,8,26,17,14,20,19,8}

[0049] Sort the observed failure time data set of high-speed drive rollers from small to large to form an ascending order of life data; then

[0050] {2,4,4,6,7,8,8,8,9,10,12,13,13,14,16,17,18,18,19,20,20,20,21,23,24,25,26,28,30,32}

[0051] and are marked as t 1 ,t 2 ,t 3 ,…,t 30 , then t 1 ≤t 2 ≤t 3 ≤…≤t n ;

[0052] The same fault time points are merged into one fault time point, denoted as t 1 ,t 2 ,t 3 ,…,t 23 , and record each failure time point t i The number of failures that occurred on i ;

[0053] For each failure time point t i , calculate the risk set size at that moment; the risk set is the failure time point t i The number of individuals that have not yet failed i ; As shown in Table 1 below;

[0054]

[0055]

[0056] Table 1

[0057] S2: Calculate each failure time point t according to the Nelson-Aalen estimation method i The risk value is accumulated continuously to obtain the cumulative risk function

[0058] Each failure time point t i The risk value is d i / n i ; The cumulative risk function The calculation formula is:

[0059]

[0060] Then there is

[0061]

[0062] S3: Based on the cumulative risk function Calculate the reliability function Get reliability;

[0063] Clarify the relationship between the cumulative risk function Λ(t) and the cumulative failure probability function F(t):

[0064]

[0065] Then there is

[0066] R(t)=1-F(t)=e -Λ(t)

[0067] In the above formula, R(t) is the reliability function, Then there is

[0068]

[0069] The specific failure time, cumulative risk function and reliability correspond to the following Table 2;

[0070]

[0071]

[0072] Table 2

[0073] S4: Nonparametric reliability confidence assessment based on Nelson-Aalen estimation;

[0074] The function is constructed according to the central limit theorem to conform to the standard normal distribution. Combined with the confidence level 1-α and the α / 2 quantile of the standard normal distribution, the confidence interval of the reliability of the high-speed drive roller can be solved without knowing the overall distribution. The confidence level in this embodiment is 0.98.

[0075] Furthermore, the method of constructing the function according to the central limit theorem is:

[0076] Let the random variable X represent the failure time of the high-speed drive roller, and for 30 samples from the population, the failure time satisfies independent and identical distribution, then I {X>t} A two-point distribution with parameter R(t).

[0077] Furthermore, we know that E(I {X>t} )=R(t),D(I {X>t} )=R(t)[1-R(t)].

[0078] Furthermore, the confidence level 1-α=0.98 is a given confidence level; the α / 2 quantile of the standard normal distribution is Z 0.01 =-2.326.

[0079] According to the central limit theorem, the asymptotic distribution of the sample mean is normal distribution, and the normal distribution standardization method is

[0080] Based on the above preconditions, we can get:

[0081]

[0082] Then there is

[0083]

[0084] Since the sample size is relatively large, the confidence interval of reliability can be simplified to:

[0085]

[0086] The confidence interval calculation results are shown in Table 3 below:

[0087]

[0088] Table 3

[0089] The principles and implementation methods of the present invention are described in this article using specific examples. The description of the above embodiments is only used to help understand the method and core idea of ​​the present invention. At the same time, for those skilled in the art, according to the idea of ​​the present invention, there will be changes in the specific implementation methods and application scope. In summary, the content of this specification should not be understood as limiting the present invention.

Claims

1. A non-parametric reliability analysis method for a high-speed drive roller, characterized in that: The method comprises the following steps: S1: Obtain the fault data of the high-speed drive roller and merge the same fault time in the fault data into one fault time point t i ; S2: Calculate each failure time point t according to the Nelson-Aalen estimation method i The risk value is accumulated continuously to obtain the cumulative risk function S3: Based on the cumulative risk function Calculate the reliability function Get reliability; S4: Non-parametric reliability confidence assessment based on Nelson-Aalen estimation.

2. The non-parametric reliability analysis method of a high-speed drive roller according to claim 1, characterized in that: The fault data are from actual fault data of high-speed drive rollers in engineering practice, and the fault data include sequence number, main fault mode and fault time.

3. The non-parametric reliability analysis method of a high-speed drive roller according to claim 2 is characterized in that: The observed failure time data set of high-speed drive rollers is sorted from small to large and marked as t1, t2, t3, …, t n , then t1≤t2≤t3≤…≤t n , where n is the total number of data in the dataset.

4. The non-parametric reliability analysis method of a high-speed driving roller according to claim 3 is characterized in that: Combine the same failure times into one failure time point t i , denoted as t1, t2, t3, …, t k (k≤n), and record each failure time point t i The number of failures that occurred on i .

5. The non-parametric reliability analysis method of a high-speed driving roller according to claim 4 is characterized in that: For each failure time point t i , calculate the risk set size at that moment, the risk set is the failure time point t i The number of individuals that have not yet failed i .

6. The non-parametric reliability analysis method of a high-speed drive roller according to claim 5, characterized in that: At each failure time t i The risk value is d i / n i , the cumulative risk function The calculation formula is:

7. The non-parametric reliability analysis method of a high-speed driving roller according to claim 6 is characterized in that: The reliability function The calculation method is: Clarify the relationship between the cumulative risk function Λ(t) and the cumulative failure probability function F(t): Then we have: R(t)=1-F(t)=e -Λ(t) ; In the above formula, R(t) is the reliability function, then 8. The non-parametric reliability analysis method of a high-speed driving roller according to claim 7, characterized in that: The non-parametric reliability confidence assessment method based on Nelson-Aalen estimation is: The function is constructed according to the central limit theorem to conform to the standard normal distribution. Combined with the confidence level 1-α and the α / 2 quantile of the standard normal distribution, the confidence interval of the reliability of the high-speed drive roller can be solved without knowing the overall distribution.

9. The non-parametric reliability analysis method of a high-speed driving roller according to claim 8, characterized in that: The method of constructing the function according to the central limit theorem is: Let the random variable X represent the failure time of the high-speed drive roller, and for n samples from the population, their failure times satisfy independent and identical distribution, then I {X>t} A two-point distribution with parameter R(t); It can be seen that E(I {X>t} )=R(t),D(I {X>t} ) = R(t)[1-R(t)]; The confidence level 1-α is a given confidence level; the α / 2 quantile of the standard normal distribution is Z α / 2 ; According to the central limit theorem, the asymptotic distribution of the sample mean is normal distribution, and the normal distribution standardization method is 10. The non-parametric reliability analysis method of a high-speed driving roller according to claim 9, characterized in that: Based on the above preconditions, we can get: Then we have: The upper confidence limit of the reliability of the high-speed driving roller at time t can be derived as: The lower limit is: When the sample size is large, the confidence interval of reliability can be further simplified as:

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