CN109344472B - Method for estimating reliability parameters of mechanical and electrical components - Google Patents

Method for estimating reliability parameters of mechanical and electrical components Download PDF

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CN109344472B
CN109344472B CN201811083898.8A CN201811083898A CN109344472B CN 109344472 B CN109344472 B CN 109344472B CN 201811083898 A CN201811083898 A CN 201811083898A CN 109344472 B CN109344472 B CN 109344472B
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徐立
张宁
李华
蒋涛
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Naval University of Engineering PLA
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Abstract

The invention discloses a method for estimating reliability parameters of an electromechanical part, which comprises the following steps: the method comprises the following steps: determining candidate service life distribution parameters, and determining the upper limit alpha of the scale parameter of Weibull distribution of the service life of the electric element to be estimated according to the distribution rule of the existing reliability data max And a lower limit of alpha min And upper limit of its shape parameter b max And a lower limit of b min Respectively determining the step length d1 of the scale parameter and the step length d2 of the shape parameter according to the upper limit value and the lower limit value, and calculating alpha 1 j1 And b1 j2 Then to alpha 1 j1 And b1 j2 Traversing and combining; step two: traversing the life scale parameter alpha j And a shape parameter b j And calculating likelihood values, and finding the maximum likelihood value and recording as L M Then the maximum value corresponds to alpha M As an estimate of a life scale parameter, b M Is an estimate of the life shape parameter. The invention estimates the distribution rule of the product life by using a small amount of reliability test data and a large amount of data generated in the stages of product development, production, use and the like.

Description

Method for estimating reliability parameters of electromechanical parts
Technical Field
The invention relates to the technical field of reliability tests, in particular to a method for estimating reliability parameters of an electromechanical part.
Background
Reliability is a core attribute for describing product quality, and is usually quantitatively described by using a distribution rule (distribution type and parameters) of the service life. Theoretically, a large number of reliability tests are conducted on the product, a sufficient number of product life data can be obtained, and then a mature mathematical statistical method can be adopted to estimate the distribution type and parameters of the product life. However, in actual work, a large number of reliability tests are carried out on products, which often means high economic cost and long test time, so that the more common method is to estimate the distribution rule of the product life by using a small amount of reliability test data and a large amount of data generated in stages of product development, production, use and the like. In a reliability test of a product, a special online detection device is generally arranged for monitoring the integrity state of the product in real time and recording the fault time of the product in time, so that the service life of the product can be obtained. However, in the non-reliability test scenes such as product development, production, use and the like, a special online detection device is not necessarily equipped, and the integrity of the product can only be checked regularly or irregularly, so that the fault time of the product cannot be accurately known, and the numerical information of the service life cannot be obtained.
Disclosure of Invention
In order to overcome the defects in the background art, the invention provides a method for estimating reliability parameters of an electromechanical part.
In order to achieve the purpose, the invention adopts the technical scheme that: a method of estimating a reliability parameter of an electromechanical component, comprising the steps of:
the method comprises the following steps: determining candidate service life distribution parameters, and preliminarily determining the upper limit alpha of the scale parameter of Weibull distribution of the service life of the electric element to be estimated according to the distribution rule of the reliability data of the existing electric element max And lower limit of scale parameter alpha min And the upper limit b of the shape parameter of the Weibull distribution of the service life of the electric element to be estimated max And a lower shape parameter limit b min ；
At a determined Weibull cell life Weibull scale parameter upper limit alpha max And lower limit of scale parameter alpha min Within the interval, n1 candidate scale parameters are generated at equal intervals, the step length between each adjacent parameter in the candidate parameters is equal to d1, and the scale parameters alpha 1 of n1 Weibull distributions are sequentially calculated according to the step length d1 of the Weibull distribution scale parameters j1 Wherein j1 is more than or equal to 1 and less than or equal to n1;
at a determined Weibull cell life Weibull shape parameter upper limit b max And a lower shape parameter limit b min Within the interval, n2 candidate shape parameters are generated at equal intervals, the step length between each adjacent parameter in the candidate parameters is equal to d2, and n2 Weibull distribution shape parameters b1 are sequentially calculated according to the step length d2 of the Weibull distribution shape parameters j2 Wherein j2 is more than or equal to 1 and less than or equal to n2;
let n = n1 × n2, from α 1 j1 And b1 j2 Traversing and combining to obtain n groups of candidate distribution parameters (alpha) j ,b j ),1≤j≤n；
Step two: the ergodic life scale parameter is alpha j The shape parameter is b j For each of the candidates, calculating a likelihood valueSelecting parameter combination, aiming at a group of data groups containing m pieces of detection information of the electromechanical parts, and according to the position T contained in the ith detection information i Unit state information F of time i Determining a calculation coefficient W i Continuously iteratively updating the likelihood value L according to the m detection data j Setting the initial value of the likelihood value corresponding to each candidate parameter combination to be 0 at the beginning of iteration, and searching the maximum value L in the likelihood value after the iteration corresponding to each candidate parameter combination is finished M Then the maximum value corresponds to alpha M As an estimate of a Weibull-type cell Weibull scale parameter, b M Is an estimate of the weibull-type unit weibull shape parameter.
In the above solution, the candidate lifetime distribution parameter calculation process in the first step is as follows:
1) Determining a scale parameter alpha 1 of a Weir distribution j1 And step d1 is calculated as follows:
Figure GDA0001837777110000031
wherein alpha is max Representing the upper limit of the scale parameter, alpha, of the Weibull distribution min Represents the lower limit of the scale parameter of the Weibull distribution, n1 is a positive integer, and n1 is more than or equal to 2;
2) Determining the shape parameter b1 of a Weibull distribution j2 And step d2 is calculated as follows:
Figure GDA0001837777110000032
wherein, b max Upper limit of shape parameter representing Weibull distribution, b min Represents the lower limit of the shape parameter of the Weibull distribution, n2 is a positive integer, and n2 is more than or equal to 2;
3)α1 j1 and b1 j2 The calculation mode of the traversal combination is as follows:
let j =1, traverse j1=1 in the first tier loop, traverse j2=1 in the second tier loop; let alpha j ＝α1 j1 ，b j ＝b1 j2 J = j +1; wherein alpha is max ≥α1 j1 ≥α min ，b max ≥b1 j2 ≥b min 。
In the above scheme, the second step calculates the coefficient W i And likelihood value L j The calculation formula of (a) is as follows:
Figure GDA0001837777110000041
Figure GDA0001837777110000042
wherein log (. Alpha.) is a natural logarithmic function j Is a scale parameter of a Weibull distribution, b j Is the shape parameter of the Weibull distribution, T i Is the detection time of the ith product.
In the above scheme, the likelihood value L in the second step j The traversal calculation process is as follows:
1) Let j =1;
2) Let i =1,L j ＝0；
3) Calculating coefficients
Figure GDA0001837777110000043
Wherein log (. Alpha.) is a natural logarithmic function j Is a scale parameter of a Weibull distribution, b j Is the shape parameter of the Weibull distribution, T i The detection time of the ith product;
4) Updating i = i +1, if i is less than or equal to m, turning to 3), and otherwise, turning to 5);
5) Update j = j +1, go 2 if j ≦ n), otherwise 6);
6) At L j (j is more than or equal to 1 and less than or equal to n) and recording the maximum value as L M Then α is M As an estimate of a parameter of the size of the life distribution of the electromechanical component, b M The method is an estimated value of the service life distribution shape parameter of the electromechanical part.
Compared with the prior art, the invention has the beneficial effects that: the distribution rule of the service life of the product is estimated by using a small amount of reliability test data and a large amount of data generated in the stages of product development, production, use and the like, so that the consumption of manpower, physics and financial resources caused by developing a large amount of reliability tests on the product is avoided.
Detailed Description
The present invention will be described in further detail below with reference to an electromechanical device.
The invention discloses a method for estimating reliability parameters of an electromechanical part, which comprises the following steps:
the method comprises the following steps: determining candidate service life distribution parameters, and preliminarily determining the upper limit alpha of the scale parameter of Weibull distribution of the service life of the electric element to be estimated according to the distribution rule of the reliability data of the existing electric element max And lower limit of scale parameter alpha min And the upper limit b of the shape parameter of the Weibull distribution of the service life of the electric element to be estimated max And a lower shape parameter limit b min ；
At a determined Weibull cell life Weibull scale parameter upper limit alpha max And lower limit of scale parameter alpha min Within the interval, n1 candidate scale parameters are generated at equal intervals, the step length between each adjacent parameter in the candidate parameters is equal to d1, and the scale parameters alpha 1 of n1 Weibull distributions are sequentially calculated according to the step length d1 of the Weibull distribution scale parameters j1 Wherein j1 is more than or equal to 1 and less than or equal to n1;
at a determined Weibull cell life Weibull shape parameter upper limit b max And a lower shape parameter limit b min Within the interval, n2 candidate shape parameters are generated at equal intervals, the step length between each adjacent parameter in the candidate parameters is equal to d2, and n2 Weibull distribution shape parameters b1 are sequentially calculated according to the step length d2 of the Weibull distribution shape parameters j2 Wherein j2 is more than or equal to 1 and less than or equal to n2;
let n = n1 × n2, from α 1 j1 And b1 j2 Traversing and combining to obtain n groups of candidate distribution parameters (alpha) j ,b j ),1≤j≤n；
Wherein, the scale parameter alpha 1 of the Weir distribution j1 And step d1 is calculated as follows:
Figure GDA0001837777110000061
in the formula, alpha max Representing the upper limit of the scale parameter, alpha, of the Weibull distribution min Represents the lower limit of the scale parameter of Weibull distribution, n1 is a positive integer, and n1 is more than or equal to 2;
wherein the shape parameter b1 of the Weibull distribution j2 And step d2 is calculated as follows:
Figure GDA0001837777110000062
in the formula, b max Upper limit of shape parameter representing Weibull distribution, b min Represents the lower limit of the shape parameter of the Weibull distribution, n2 is a positive integer, and n2 is more than or equal to 2;
wherein, alpha 1 j1 And b1 j2 The calculation way for performing traversal combination is as follows:
let j =1, traverse j1=1 in the first tier loop, traverse j2=1 in the second tier loop; let alpha be j ＝α1 j1 ，b j ＝b1 j2 J = j +1; wherein alpha is max ≥α1 j1 ≥α min ，b max ≥b1 j2 ≥b min 。
Step two: the ergodic life scale parameter is alpha j The shape parameter is b j For each candidate parameter combination, for a group of data sets containing m pieces of detection information of the electromechanical element, calculating a likelihood value according to the value T contained in the ith detection information i Unit state information F of time i Determining a calculation coefficient W i Continuously iteratively updating likelihood value L according to m detection data j Setting the initial value of the likelihood value corresponding to each candidate parameter combination to be 0 at the beginning of iteration, and searching the maximum value in the likelihood values after the iteration corresponding to each candidate parameter combination is finished and recording the maximum value as L M Then the maximum value corresponds to alpha M As an estimate of a Weibull-type cell Weibull scale parameter, b M Is an estimate of the weibull-type cell weibull shape parameter.
Wherein the coefficient W is calculated i Likelihood value L j The calculation formula of (c) is as follows:
Figure GDA0001837777110000071
Figure GDA0001837777110000072
in the formula, log (. Alpha.) is a natural logarithmic function j Is a scale parameter of a Weibull distribution, b j Is the shape parameter of the Weibull distribution, L j As likelihood value, T i The detection time of the ith product.
Wherein the likelihood value L j The traversal calculation process of (1) is as follows:
1) Let j =1;
2) Let i =1,L j ＝0；
3) Calculating coefficients
Figure GDA0001837777110000073
In the formula, log (. Alpha.) is a natural logarithmic function j Is a scale parameter of a Weibull distribution, b j Is the shape parameter of the Weibull distribution, L j As likelihood value, T i The detection time of the ith product;
4) Updating i = i +1, if i is less than or equal to m, turning to 3), and otherwise, turning to 5);
5) Updating j = j +1, if j is less than or equal to n, turning to 2), otherwise 6);
6) At L j (j is more than or equal to 1 and less than or equal to n) and recording the maximum value as L M Then α is M As an estimate of a parameter of the lifetime distribution of the electromechanical component, b M The method is an estimated value of the service life distribution shape parameter of the electromechanical part.
In the following table, the reliability data of type ft of an electromechanical device is obtained by trying to estimate the dimension and shape parameters of the lifetime distribution of the electromechanical device according to weibull distribution.
Figure GDA0001837777110000081
From past experience, the dimension parameter of the service life distribution of the electromechanical part is in the range of 500-3000, and 500 is taken as a step length; the shape parameters are in the range of 1.1-3.8, and the step length is 0.3, and 60 candidate distribution parameters (alpha) are formed j ,b j ) J is more than or equal to 1 and less than or equal to 60, and the calculation result is shown in the following table:
Figure GDA0001837777110000082
Figure GDA0001837777110000083
Figure GDA0001837777110000084
Figure GDA0001837777110000091
Figure GDA0001837777110000092
Figure GDA0001837777110000093
Figure GDA0001837777110000094
as can be seen from the table, at L j The maximum value of (1. Ltoreq. J. Ltoreq.64) is L 35 Then α is 35 ＝2000，b 35 And =2.3 is an estimated value of the service life distribution parameter of the electromechanical part.
In order to further verify the feasibility of the method, the following simulation model is established:
it is assumed that the lifetime of a certain electromechanical part follows a weibull distribution W (α, b).
(1) Generating k 1 A random number simT i (1≤i≤k1)，simT i Obeying a Weibull distribution W (alpha, b) for simulating the life value of the electromechanical part. Let F i ＝0,T i ＝simT i To obtain k1 group [ F ] i T i ],1≤i≤k1。
(2) Generating k2 random numbers simT i (k1+1≤i≤k1+k2)，simT i Obeying a Weibull distribution W (alpha, b) for simulating the life value of the electromechanical part.
(3) Generating k2 uniform random numbers simTc i And (k 1+1 is not less than i not less than k1+ k 2) for simulating the checking time.
(4) In the range of k1+1 is more than or equal to i and less than or equal to k1+ k2, the
Figure GDA0001837777110000101
K1+ k2 sets of lifetime data [ F ] obtained by the above simulation i T i ]Thereafter, estimates of the distribution parameters can be obtained by applying the methods herein. Taking α =2000, b =2.3, k1=5, k2=15 as an example, the mean value of the statistical results of the lifetime distribution scale parameter of the electrical component obtained by the method in this document after a large number of simulations is 1995.0, the root variance is 286.2, and the mean value of the statistical results of the shape parameter is 2.72, and the root variance is 0.78. If the k1+ k2 group life data simT is used i If the mean value of the statistical results of the scale parameters calculated by adopting a theoretical method is 1972.2, the root variance is 195.8, the mean value of the statistical results of the shape parameters is 2.46, the root variance is 0.47, and the difference between the two is within the engineering allowable range.
The above description is only an embodiment of the present invention, and not intended to limit the scope of the present invention, and all modifications of equivalent structures and equivalent processes, or direct or indirect applications in other related fields, which are made by the contents of the present specification, are included in the scope of the present invention.

Claims (4)

1. A method of estimating reliability parameters of an electromechanical component, characterized in that the reliability parameter estimation is developed for electromechanical components whose lifetime is subject to a weibull distribution, comprising the steps of:
the method comprises the following steps: determining candidate service life distribution parameters, and preliminarily determining the upper limit alpha of the scale parameter of Weibull distribution of the service life of the electric element to be estimated according to the distribution rule of the reliability data of the existing electric element max And lower limit of scale parameter alpha min And the upper limit b of the shape parameter of the Weibull distribution of the service life of the electric element to be estimated max And a lower shape parameter limit b min ；
At a determined Weibull-type cell life Weibull scale parameter upper limit alpha max And lower limit of scale parameter alpha min Within the interval, n1 candidate scale parameters are generated at equal intervals, the step length between each adjacent parameter in the candidate parameters is equal to d1, and the scale parameters alpha 1 of n1 Weibull distributions are sequentially calculated according to the step length d1 of the Weibull distribution scale parameters j1 Wherein j1 is more than or equal to 1 and less than or equal to n1;
at a determined Weibull cell life Weibull shape parameter upper limit b max And a lower shape parameter limit b min Within the interval, n2 candidate shape parameters are generated at equal intervals, the step length between each adjacent parameter in the candidate parameters is equal to d2, and n2 Weibull distribution shape parameters b1 are sequentially calculated according to the step length d2 of the Weibull distribution shape parameters j2 Wherein j2 is more than or equal to 1 and less than or equal to n2;
let n = n1 × n2, from α 1 j1 And b1 j2 Traversing and combining to obtain n groups of candidate distribution parameters (alpha) j ,b j ),1≤j≤n；
Step two: the ergodic life scale parameter is alpha j The shape parameter is b j For each candidate parameter combination, for a group of data sets containing m pieces of detection information of the electromechanical component, calculating likelihood values based on the value at T contained in the ith piece of detection information i Unit state information F of time i Determining a calculation coefficient W i Continuously iteratively updating the likelihood value L according to the m detection data j At the beginning of iteration, setting the initial value of likelihood value corresponding to each candidate parameter combination as 0Finding the maximum value L in the likelihood values after the iteration corresponding to the parameter combination is finished M Then the maximum value corresponds to alpha M As an estimate of a Weibull-type cell Weibull scale parameter, b M Is an estimate of the weibull-type cell weibull shape parameter.
2. A method of estimating reliability parameters of electromechanical devices according to claim 1, characterized by: the calculation process of the candidate life distribution parameters in the first step is as follows:
1) Determining a scale parameter alpha 1 of a Weir distribution j1 And step d1 is calculated as follows:
Figure FDA0001802610960000021
wherein alpha is max Upper limit of the scale parameter, α, representing the Weibull distribution min Represents the lower limit of the scale parameter of Weibull distribution, n1 is a positive integer, and n1 is more than or equal to 2;
2) Determining the shape parameter b1 of a Weibull distribution j2 And step d2 is calculated as follows:
Figure FDA0001802610960000022
wherein, b max Representing the upper limit of the shape parameter of the Weibull distribution, b min Represents the lower limit of the shape parameter of the Weibull distribution, n2 is a positive integer, and n2 is more than or equal to 2;
3)α1 j1 and b1 j2 The calculation mode of the traversal combination is as follows:
let j =1, traverse j1=1 in the first tier loop, traverse j2=1 in the second tier loop; let alpha j ＝α1 j1 ，b j ＝b1 j2 J = j +1; wherein alpha is max ≥α1 j1 ≥α min ，b max ≥b1 j2 ≥b min 。
3. A method of estimating reliability parameters of electromechanical devices according to claim 1, characterized by: calculating the coefficient W in the second step i And likelihood value L j The calculation formula of (c) is as follows:
Figure FDA0001802610960000031
Figure FDA0001802610960000032
wherein log (. Alpha.) is a natural logarithm function j Is a scale parameter of a Weibull distribution, b j Is the shape parameter of the Weibull distribution, T i Is the detection time of the ith product.
4. A method of estimating reliability parameters of an electromechanical component according to claim 1 or 3, characterized by: likelihood value L in the second step j The traversal calculation process is as follows:
1) Let j =1;
2) Let i =1,L j ＝0；
3) Calculating coefficients
Figure FDA0001802610960000033
Wherein log (. Alpha.) is a natural logarithmic function j Is a scale parameter of a Weibull distribution, b j Is the shape parameter of the Weibull distribution, T i The detection time of the ith product;
4) Updating i = i +1, if i is less than or equal to m, turning to 3), and otherwise, turning to 5);
5) Update j = j +1, go 2 if j ≦ n), otherwise 6);
6) At L j (j is more than or equal to 1 and less than or equal to n) and recording the maximum value as L M Then α is M As an estimate of a parameter of the size of the life distribution of the electromechanical component, b M The method is an estimated value of the service life distribution shape parameter of the electromechanical part.
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