CN112733281A - Machine tool reliability evaluation method considering truncation data deletion - Google Patents
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Abstract
The invention discloses a machine tool reliability evaluation method considering truncation data deletion, which is used for improving the precision of reliability evaluation parameters. Firstly, screening normal data based on an IQR method aiming at the data, secondly, reducing truncated data in the data by using a total fault time processing rule, expanding the sample size of failure data, secondly, preliminarily obtaining initial values of Weir parameters by using an average rank method, thirdly, completing new Weir parameter estimation by using a least square method according to a new empirical distribution function, and lastly, performing convergence inspection by using a K-S method.
Description
Technical Field
The invention relates to reliability assessment of a high-grade numerical control machine tool, and belongs to the field of reliability engineering of numerical control machine tools.
Background
The numerical control machine tool is the basis of the machine tool manufacturing industry and can show the comprehensive national strength of a country. With the development of the machine tool industry, many manufacturers and customers continuously pay attention to the reliability problem of the machine tool. However, the research of machine tools starts later in our country, most machine tool factories and users do not pay enough attention to reliability data, and do not collect enough data, so that how to improve the reliability of the machine tools becomes a problem which needs to be solved urgently by the industry.
Reliability is the ability of a product to complete the specified functions of the product under the specified time and conditions, wherein reliability evaluation is quantitative evaluation of the ability through reliability data, so that the reliability level of a machine tool is reflected, and experience is provided for future subsequent machine tool design improvement
The reliability evaluation method mainly evaluates the reliability from different angles according to the size of the sample quantity. Under the condition of small sample size, the prior distribution is completed by combining the opinions of experts and the previous data of the machine tool according to a Bayes method, and the posterior distribution is solved by using an MCMC method subsequently, so that the solving is complicated and the difficulty is high. In the case of a large sample size, there are mainly a moment estimation method, a maximum likelihood estimation method, a least square method, and the like. However, the screening research on the data itself is less, and it is worth exploring to improve the sample data precision and further improve the parameter estimation precision.
Disclosure of Invention
Aiming at the problem of insufficient reliability evaluation parameter precision caused by truncation data deletion, the invention provides a machine tool reliability evaluation method considering truncation data deletion so as to improve the precision of reliability evaluation parameters. Firstly, screening normal data based on an IQR method aiming at the data, secondly, reducing truncated data in the data by using a total fault time processing rule, expanding the sample size of failure data, secondly, preliminarily obtaining initial values of Weir parameters by using an average rank method, thirdly, completing new Weir parameter estimation by using a least square method according to a new empirical distribution function, and lastly, performing convergence inspection by using a K-S method.
A machine tool reliability assessment method considering truncation data deletion mainly comprises the following steps:
the method comprises the following steps: the data were screened using the IQR method. Dividing the data into four equal parts, wherein each interval of adjacent intervals contains 25% of data, and the three points are q1,q2,q3. The three critical values are corresponding regionsAverage value of (d) between. Calculating the highest and lowest critical values according to the following equations (1) and (2), if the data is not included in the interval (S)1,S2) It should be regarded as abnormal data and not selected.
S2＝q3+(1.5×(q3-q1)) (1)
S1＝q1-(1.5×(q3-q1)) (2)
Step two: and the screened data applies a fault time processing rule to the truncated data contained in the screened data, so that the amount of the truncated data is reduced, and the accuracy of an evaluation result is improved. Firstly, listing the fault occurrence time table of each model of numerical control machine tool according to the screened data. And secondly, calculating by using formulas (3) and (4) to obtain a fault data table concentrated on one machine tool.
The total time to failure processing rule is exemplified as follows. Assuming that three machine tools carry out truncation experiments simultaneously, the moment when the three machine tools respectively end is t1s,t2s,t3s. Sample t1sThe point of failure is t11Sample t2sThe point of failure is t21，t22Sample t3sThe point of failure is t31. Wherein t is11＜t21＜t22＜t1s＜t31＜t2s＜t3s. The time (t) when the equivalent fault of a machine tool occurs can be obtained by applying the following equations (3) and (4)1,t2,t3,t4) And time T at which the experiment was terminatedS。
t1＝3t11,t2＝3t21,t3＝3t22,t3＝2t31+t1s (3)
TS＝t1s+t2s+t3s (4)
Step three: and preprocessing the transformed middle fault data table, removing truncated data, and obtaining an empirical distribution function by using an average rank method. Firstly, integrating data into a fault interval time table, and calculating by using a formula (5) to obtain the increment of the rank as delta Ai. Second useEquation (6) can obtain the rank of the adjusted fault data as Ai. Finally, an approximate median rank formula (7) is utilized to obtain an empirical cumulative function Fi。
Ai＝Ai-1+ΔAi(6)
Wherein n is the total sample size; i is the sequence number of the failed data and k is the rank sequence number of all data.
And step four, fitting the obtained data by a least square method, wherein y is Bx + A, and preliminarily obtaining parameters of the Weir distribution model. First, x is calculated using equations (8) and (9)i,yiAnd (3) performing straight line fitting. Finally, the shape parameter beta of the Weir parameter is calculated by using the formulas (10) and (11)1And a size parameter alpha1
yi＝ln{-ln[1-F(ti)]} (8)
xi＝lnti (9)
β1＝B (10)
And step five, performing K-S inspection on the obtained cumulative distribution function and the empirical distribution function. Firstly, the maximum difference value calculation is completed by using a formula (12), the significance level in the table I is selected according to the sample size n, whether the distribution hypothesis is met is judged, and otherwise, the step four is recalculated.
D＝maxF(ti)-F′(ti)| (12)
table-K-S hypothesis testing rejection threshold table
Step six: and finishing a new distribution empirical formula considering the truncated data by taking the obtained parameters as initial values. And (4) taking the two parameter values obtained in the step four as initial values into the formulas (13) to (16), and repeating the step four again to obtain a new parameter estimation value.
Aii＝Aii-1+Ii+1 (15)
Wherein the truncation experimental data is tcThe probability of failure of the deleted data is Ic,i。
CiThe number of items deleted before i. I isiIs the increment of the rank of the failure data i.
Step seven: and (5) judging whether the obtained new parameters meet the formula (17), and if the new parameters do not meet the formula (17), repeating the step six until the conditions are met.
|βi-βi-1|＜0.01 (17)
Drawings
FIG. 1 is a flow chart of the method.
Detailed Description
The invention takes the data of a numerical control machine tool with a certain model as an example to complete the reliability evaluation.
The method comprises the following steps: and screening the normal data value interval to be (-380, 860) by using formulas (1) and (2) according to the fault interval data of the 10 numerical control machines in the second table. With the + number being truncated data.
Table two fault interval data
| Experiment machine tool | Failure data (h) | Experiment machine tool | Failure data (h) |
| 1 | 760，860，975，85+ | 6 | 760，1065，1575+ |
| 2 | 24，245，452+ | 7 | 560，200 |
| 3 | 780，80，320 | 8 | 685，782+ |
| 4 | 44，450+ | 9 | 750，120，365+ |
| 5 | 800，232，45+ | 10 | 1050，850，550+ |
Step two: and (3) sorting the screened data into a table three-fault time table, and calculating by using formulas (3) and (4) to obtain a fault data table four concentrated on one machine tool.
Table three fault time table
| Experiment machine tool | Failure data (h) | Experiment machine tool | Failure data (h) |
| 1 | 760，1620，1705+ | 6 | 760 |
| 2 | 25，270，722+ | 7 | 560，760 |
| 3 | 780，860，1180+ | 8 | 685，1467+ |
| 4 | 44，494+ | 9 | 750，870，1235+ |
| 5 | 800，1032，1077+ | 10 | 850，1400+ |
Table four-integrated machine tool fault time interval table
Step three: first, the truncated data is removed from the data in table four, and the rank is calculated by using equations (5) and (6). And finally, obtaining an empirical cumulative function by using an approximate median rank formula (7) to obtain a table five as follows.
Table five-integration machine tool fault time interval table
And step four, fitting the obtained data by a least square method, wherein y is Bx + A, and calculating by using formulas (8) and (9) to obtain a shape parameter beta11.245 and the size parameter α1＝2326.62。
And step five, performing K-S inspection on the obtained cumulative distribution function and the empirical distribution function. The maximum difference calculation is first performed using equation (12), and the significance level in table one is selected to be 0.01 and the threshold value is 0.352 according to the sample size 15. Wherein the difference is 0.124, and less than the threshold satisfies the condition, the next step can be performed.
Step six: and finishing a new distribution empirical formula considering the truncated data by taking the obtained parameters as initial values. Taking the two parameter values obtained in the step four as initial values into the formulas (13) to (16), and repeating the step four again to obtain a new shape parameter beta21.678 and the size parameter α2＝2136.95。
Step seven: whether the obtained new parameters meet the formula (17) or not can be obtained, the unsatisfied requirements can be obtained, the circular calculation is continued, and finally the final parameter obtained by the designed algorithm program is the shape parameter beta221.723 and a size parameter α2＝2026.46。
Claims (1)
1. A machine tool reliability assessment method considering truncation data deletion is characterized in that: the method comprises the following steps:
the method comprises the following steps: screening data by using an IQR method; dividing the data into four equal parts, wherein each interval of adjacent intervals contains 25% of data, and the three points are q1,q2,q3(ii) a Calculating the highest and lowest critical values according to the following equations (1) and (2), if the data is not included in the interval (S)1,S2) If so, the data is regarded as abnormal data and is not selected;
S2＝q3+(1.5×(q3-q1)) (1)
S1＝q1-(1.5×(q3-q1)) (2)
step two: the screened data is subjected to a fault time processing rule on the truncated data contained in the screened data, so that the amount of the truncated data is reduced, and the screened data is listed in a fault occurrence time table of each type of numerical control machine; calculating by using formulas (3) and (4) to obtain a fault data table concentrated on one machine tool;
assuming that three machine tools carry out truncation experiments simultaneously, the moment when the three machine tools respectively end is t1s,t2s,t3s(ii) a Sample t1sThe point of failure is t11Sample t2sThe point of failure is t21，t22Sample t3sThe point of failure is t31(ii) a Wherein t is11＜t21＜t22＜t1s＜t31＜t2s＜t3s(ii) a The time (t) of the equivalent fault of one machine tool is obtained by applying the formulas (3) and (4)1,t2,t3,t4) And time T at which the experiment was terminatedS；
t1＝3t11,t2＝3t21,t3＝3t22,t3＝2t31+t1s (3)
TS＝t1s+t2s+t3s (4)
Step three: preprocessing the transformed middle fault data table, removing truncated data, and obtaining an experience distribution function by using an average rank method; firstly, integrating data into a fault interval time table, and calculating by using a formula (5) to obtain the increment of the rank as delta Ai(ii) a Secondly, the adjusted fault data is obtained by using the formula (6) with the rank Ai(ii) a Finally, an approximate median rank formula (7) is utilized to obtain an empirical cumulative function Fi；
Ai＝Ai-1+ΔAi (6)
Wherein n is the total sample size; i is the sequence number of the fault, and k is the sequence number of all data;
performing least square fitting on the obtained data to obtain y-Bx + A, and preliminarily obtaining parameters of the Weir distribution model; first, x is calculated using equations (8) and (9)i,yiPerforming straight line fitting; finally, the shape parameter beta of the Weir parameter is calculated by using the formulas (10) and (11)1And a size parameter alpha1
yi＝ln{-ln[1-F(ti)]} (8)
xi＝lnti (9)
β1＝B (10)
Step five, performing K-S inspection on the obtained cumulative distribution function and the empirical distribution function; firstly, the maximum difference value calculation is completed by using a formula (12), the significance level in the table I is selected according to the sample size n, whether the distribution hypothesis is met is judged, and if not, the step four is recalculated;
D＝max|F(ti)-F′(ti)| (12)
step six: using the obtained parameters as initial values to complete a new distribution empirical formula considering the truncated data; taking the two parameter values obtained in the fourth step as initial values and bringing the initial values into formulas (13) to (16), and repeating the fourth step again to obtain a new parameter estimation value;
Aii＝Aii-1+Ii+1 (15)
wherein the truncation experimental data is tcThe probability of failure of the deleted data is Ic,i；
CiThe number of items deleted before i; i isiIncrement of rank for failure data i;
step seven: judging whether the obtained new parameters meet the formula (17), and if not, repeating the step six until the conditions are met;
|βi-βi-1|＜0.01 (17)。
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| CN111291486A (en) * | 2020-02-09 | 2020-06-16 | 吉林大学 | Reliability evaluation method for system component of numerical control machine tool |
| CN111291486B (en) * | 2020-02-09 | 2022-04-08 | 吉林大学 | Reliability evaluation method for system component of numerical control machine tool |
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