CN105373687A - Multistage experiment-based heavy vehicle power system reliability evaluation method - Google Patents

Abstract

The invention discloses a multistage experiment-based heavy vehicle power system reliability evaluation method, and belongs to the technical field of heavy vehicle power system research. The method comprises the following steps: by utilizing the Weibull distribution of time between failures of the development stages of a heavy vehicle power system, obtaining reliability point estimation and lower confidence limit estimation of the stages under a rated task time, and then obtaining equivalent pass-fail type data of the stages; and from the first stage, carrying out Bayes data fusion under Beta distribution on the equivalent pass-fail type data of the stages in sequence, and carrying out reliability evaluation on the multistage experiment data. According to the method, the multistage experiment data is considered, and the Weibull distribution is adopted to describe the distribution of the time between failures, so that the defect that the present heavy vehicle power system reliability evaluation only considers single-stage experiment data and does not accord with the heavy vehicle power system reliability characteristics is overcome, and the confidence level of the reliability evaluation and the utilization rate of the experiment information are relatively high.

Description

A kind of heavy vehicle power system reliability estimation method based on dispersion

Technical field

The present invention relates to heavy vehicle power system studying technological domain, particularly relate to a kind of heavy vehicle power system reliability estimation method based on dispersion.

Background technology

Heavy vehicle all-up weight is generally more than 10 tons, and its power system bearing load is large, and design margin is little, and design difficulty is high, and therefore the development of heavy vehicle power system often will through multiple design phase.Because the experimentation cost of power system is very high, the sample size of each development stage fail-test is less.

At present in the development of heavy vehicle power system, the test figure of Main Basis current generation, adopts exponential distribution probabilistic method to carry out reliability assessment.Specific embodiments is:

(1) drop into the heavy vehicle power system that 2-4 platform is in current development stage state of the art and carry out fail-test;

(2) break down in process of the test, then fix a breakdown and continue test, fault correction time is not included within test period;

(3) record trouble interval time, think time between failures obeys index distribution, carry out reliability assessment according to exponential distribution probabilistic method.

There is following defect in such scheme:

(1) only can utilize the reliability test data of current generation, can not historical test data be utilized.Because the test sample amount of heavy vehicle power system each development stage is less, the confidence level of the reliability assessment result only utilizing single development stage testing data to obtain is lower.On the other hand, the design proposal of heavy vehicle power system each development stage has inheritance, and the reliability level of historical test data to current production has important references meaning, gives no thought to historical test data and reliability information will be caused to lose;

(2) exponential distribution probabilistic method is thought and time between failures obeys index distribution is mainly applicable to the product failure that random fault causes.And the key components and parts of heavy vehicle power system such as bent axle, piston ring, bearing, oil pump etc. all have significant consume type failure characteristics, this causes the time between failures of whole system closer to Weibull distribution.The mathematical principle of the reliability estimation method therefore adopted at present does not also meet the feature of heavy vehicle power system integrity problem.

Therefore, how designing one can comprehensive dispersion data, and embody the heavy vehicle power system reliability estimation method of consume type invalid characteristic, to improve confidence level and the information utilization of heavy vehicle power system reliability assessment, become technical matters urgently to be resolved hurrily.

Summary of the invention

(1) technical matters that will solve

The technical problem to be solved in the present invention is: for the defect of prior art, there is provided a kind of can fully utilize dispersion data and meet the heavy vehicle power system reliability estimation method of time between failures characteristic distributions, to improve confidence level and the test figure utilization factor of heavy vehicle power system reliability assessment.

(2) technical scheme

For solving the problems of the technologies described above, the invention provides a kind of heavy vehicle power system reliability estimation method based on dispersion, comprising the following steps:

S1, the time between failures data of collecting in each development stage testing of heavy vehicle power system;

S2, utilize each stage time between failures data to carry out the parameter estimation of Weibull distribution, obtain the Weibull distribution of each stage time between failures;

S3, Weibull distribution according to each stage time between failures obtained in S2, the fiduciary level of each stage heavy vehicle power system and Reliability confidence lower limit under calculating specified time between failures;

S4, calculated the equivalent success failure type data of each step-by-step test by the fiduciary level of each stage heavy vehicle power system obtained in S3 and Reliability confidence lower limit;

S5, the Beta building fiduciary level according to the equivalent success failure type data of first stage distribute Beta ₁;

S6, by Beta ₁as prior distribution, using the equivalent success failure type data of subordinate phase as field data, carry out bayesian data fusion, obtain the fiduciary level Beta distribution Beta of consideration first and second step-by-step test data _1,2;

S7, by Beta _1,2as prior distribution, using the equivalent success failure type data of phase III as field data, carry out bayesian data fusion, obtain the fiduciary level Beta distribution Beta of consideration first, second, and third step-by-step test data _1,2,3;

S8, method according to S5-S7, progressively merge the equivalent success failure type data of follow-up development stage, finally obtain the heavy vehicle power system fiduciary level Beta distribution function Beta considering all development stage testing data _all;

S9, utilize Beta _allcalculate the heavy vehicle power system fiduciary level based on dispersion data.

Preferably, in step S2, maximum likelihood function method is utilized to carry out the parameter estimation of Weibull distribution;

Preferably, in step S3, Reliability confidence lower limit is the one-sided confidence lower limit of degree of confidence 0.9;

Preferably, in step S3, utilize bootstrap to calculate Reliability confidence lower limit, Bootstrap sampling number of times is the integral multiple of 10, and is more than or equal to 1000 times;

Preferably, in step S4, the definition of moments method and Reliability confidence lower limit is utilized to be equivalent success or failure data by reliability assessment results conversion.

(3) beneficial effect

The present invention utilizes the Weibull distribution of each development stage time between failures of heavy vehicle power system, under obtaining specified time between failures, the point estimation of each stage heavy vehicle power system fiduciary level and confidence lower limit are estimated, obtain the equivalent success failure type data in each stage further.Then, from the first stage, successively Beta is carried out to the equivalent success failure type data in each stage and divide the bayesian data fusion planted, and carry out the reliability assessment based on dispersion data with this.Owing to considering dispersion data, and adopt Weibull distribution to describe the distribution of heavy vehicle power system time between failures, therefore the method compensate for current heavy vehicle power system reliability assessment and can only consider single step-by-step test data, and do not meet the shortcoming of consume type invalid characteristic, the confidence level of reliability assessment and the utilization factor of Test Information higher.

Accompanying drawing explanation

Accompanying drawing is method flow diagram of the present invention.

Embodiment

Below in conjunction with drawings and Examples, the specific embodiment of the present invention is described in further detail.Following examples for illustration of the present invention, but are not used for limiting the scope of the invention.

As shown in drawings, the invention provides a kind of heavy vehicle power system reliability estimation method based on dispersion, comprise the following steps:

S1, the time between failures data of collecting in each development stage testing of heavy vehicle power system;

S2, utilize each stage time between failures data to carry out the parameter estimation of Weibull distribution, obtain the Weibull distribution of each stage time between failures, the Weibull Function in the i-th stage is designated as F _i(t); In the present embodiment, maximum likelihood function method is utilized to carry out the parameter estimation of Weibull distribution;

S3, according to the F obtained in S2 _i(t), the fiduciary level R of each stage heavy vehicle power system under calculating specified time between failures T _iwith the one-sided confidence lower limit R of fiduciary level that degree of confidence is 0.9 _li; In the present embodiment, utilize relational expression R _i(T)=1-F _i(T) fiduciary level R is calculated _i; Bootstrap is utilized to calculate the one-sided confidence lower limit R of fiduciary level _li, Bootstrap sampling frequency n _ibe the multiple of 10, and be more than or equal to 1000 times, by the n that self-service sample calculates _iindividual reliability calculating result arranges from small to large, gets 0.1*n _iindividual reliability calculating result is the one-sided confidence lower limit R of fiduciary level of 0.9 as degree of confidence _li;

S4, obtain R by S3 _iwith R _licalculate the equivalent success failure type data (s of each step-by-step test _i, f _i); In the present embodiment, utilize the definition of moments method and confidence lower limit by R _iand R _litry to achieve (s _i, f _i), shown in (1), wherein B represents Beta function;

$\left\{\begin{array}{c}{R}_i=\frac{s_i}{s_i+f_i}\\ \frac{1}{B(s_i,f_i)}{\∫}_0^{R_{\mathrm{Li}}}{t}^{s_i-1}{(1-t)}^{f_i-1}\mathrm{dt}=0.1\end{array}\right.---\left(1\right)$

S5, the Beta building fiduciary level according to the equivalent success failure type data of first stage distribute Beta ₁, shown in (2);

Beta ₁＝Beta(s ₁，f ₁)(2)

S6, by Beta ₁as prior distribution, by the equivalent success failure type data (s of subordinate phase ₂, f ₂) as field data, carry out bayesian data fusion, obtain the fiduciary level Beta distribution Beta considering first and second step-by-step test data _1,2, shown in (3);

Beta _1，2＝Beta(s ₁+s ₂，f ₁+f ₂)(3)

S7, by Beta _1,2as prior distribution, by the equivalent success failure type data (s of phase III ₃, f ₃) as field data, carry out bayesian data fusion, obtain the fiduciary level Beta distribution Beta considering first, second and third step-by-step test data _1,2,3, shown in (4);

Beta _1，2，3＝Beta(s ₁+s ₂+s ₃，f ₁+f ₂+f ₃)(4)

S8, method according to S5-S7, progressively merge the equivalent success failure type data of follow-up development stage, finally obtain the fiduciary level Beta distribution function Beta of the heavy vehicle power system considering all development stage testing data _all, shown in (5);

Beta _all＝Beta(∑s _i，∑f _i)(5)

S9, utilize Beta _allcalculate the fiduciary level R based on the heavy vehicle power system of dispersion data, shown in (6).

$R=\frac{\mathrm{\Σ}{s}_i}{\mathrm{\Σ}{s}_i+\mathrm{\Σ}{f}_i}---\left(6\right)$

Below for certain type heavy vehicle power system, the solution of the present invention is further described.

Time between failures data in each step-by-step test are as shown in table 1-table 3.

The between-failures data of table 1 first stage test

The between-failures data of table 2 subordinate phase test

The between-failures data of table 3 phase III test

Utilize the time between failures data in maximum likelihood function method his-and-hers watches 1-table 3 to carry out Weibull distribution parameters matching, obtain the Weibull Function F of each stage time between failures _it () is such as formula shown in (7)-Shi (9).

$\left\{\begin{array}{c}{F}_1\left(t\right)={\∫}_0^t{m}_1\·{\mathrm{\η}}_1^{-m_1}\·x^{m_1-1}\·e^{-{\left(\frac{x}{{\mathrm{\η}}_1}\right)}^{m_1}}\mathrm{dx}\\ {\mathrm{\η}}_1=909.28\\ m_1=6.39\end{array}\right.---\left(7\right)$

$\left\{\begin{array}{c}{F}_2\left(t\right)={\∫}_0^t{m}_2\·{\mathrm{\η}}_2^{-m_2}\·x^{m_2-1}\·e^{-{\left(\frac{x}{{\mathrm{\η}}_2}\right)}^{m_2}}\mathrm{dx}\\ {\mathrm{\η}}_3=1263\\ m_2=3.2\end{array}\right.---\left(8\right)$

$\left\{\begin{array}{c}{F}_3\left(t\right)={\∫}_0^t{m}_3\·{\mathrm{\η}}_3^{-m_3}\·x^{m_3-1}\·e^{-{\left(\frac{x}{{\mathrm{\η}}_3}\right)}^{m_3}}\mathrm{dx}\\ {\mathrm{\η}}_3=1026.9\\ m_1=5.9\end{array}\right.---\left(9\right)$

The specified time between failures T=600 hour of this kind of power system, utilizes relational expression R _i(T)=1-F _i(T) each stage system fiduciary level R is calculated _i(600), as shown in table 4.

Table 4 each development stage power system fiduciary level

Development stage	1	2	3
				Fiduciary level	R1(600)＝0.9322	R2(600)＝0.9118	R3(600)＝0.9589

The data of his-and-hers watches 1-table 3 carry out 1000 Bootstrap samplings respectively, obtain 1000 groups of self-service samples of each development stage testing data.Calculate 1000 reliability calculating results corresponding to each development stage by self-service sample, and arrange from small to large.100th the reliability calculating result of getting each development stage is the one-sided confidence lower limit R of fiduciary level of 0.9 as its degree of confidence _li, as shown in table 5.

Table 5 each development stage power system Reliability confidence lower limit

Data in table 4 and table 5 are substituted into formula (1), calculates the equivalent success failure type data (s that each development stage testing of power system is corresponding _i, f _i), as shown in table 6.

The equivalent success failure type data of table 6 each development stage power system

The equivalent success failure type data corresponding to each development stage testing successively according to formula (2)-Shi (5) carries out Bayesian Fusion, and the fiduciary level posterior distribution obtaining power system is Beta _all=Beta (113.24,7.57).

Utilizing formula (6) to calculate this heavy vehicle power system Reliability assessment value is R=0.9373.

As can be seen from the above embodiments, the present invention utilizes the Weibull distribution of each development stage time between failures of heavy vehicle power system, under obtaining specified time between failures, the point estimation of each stage heavy vehicle power system fiduciary level and confidence lower limit are estimated, obtain the equivalent success failure type data in each stage further.Then, from the first stage, successively Beta is carried out to the equivalent success failure type data in each stage and divide the bayesian data fusion planted, and carry out the reliability assessment based on dispersion data with this.Owing to considering dispersion data, and adopt Weibull distribution to describe the distribution of heavy vehicle power system time between failures, therefore the method compensate for current heavy vehicle power system reliability assessment and can only consider single step-by-step test data, and do not meet the shortcoming of consume type invalid characteristic, the confidence level of reliability assessment and the utilization factor of Test Information higher.Utilize maximum likelihood function method to carry out estimation of distribution parameters, utilize the mathematical methods such as bootstrap calculating Reliability confidence lower limit more ripe, the method that therefore the present invention proposes also has good practicality.

The above is only the preferred embodiment of the present invention; it should be pointed out that for those skilled in the art, under the prerequisite not departing from the technology of the present invention principle; can also make some improvement and replacement, these improve and replace and also should be considered as protection scope of the present invention.

Claims (5)

1., based on a heavy vehicle power system reliability estimation method for dispersion, it is characterized in that, comprise the following steps:

S1, obtain each stage time between failures data by heavy vehicle power system each step-by-step test data fault-time;

S2, utilize each stage time between failures data to carry out the parameter estimation of Weibull distribution, obtain the Weibull distribution of each stage time between failures;

S3, Weibull distribution according to each stage time between failures obtained in S2, the fiduciary level of each stage heavy vehicle power system and Reliability confidence lower limit under calculating specified time between failures;

S4, obtained the equivalent success failure type data of each step-by-step test by the fiduciary level of each stage heavy vehicle power system obtained in S3 and Reliability confidence lower limit;

S5, the Beta building fiduciary level according to the equivalent success failure type data of first stage distribute Beta ₁;

S6, by Beta ₁as prior distribution, using the equivalent success failure type data of subordinate phase as field data, carry out bayesian data fusion, obtain the fiduciary level Beta distribution Beta of consideration first and second step-by-step test data _1,2;

S7, by Beta _1,2as prior distribution, using the equivalent success failure type data of phase III as field data, carry out bayesian data fusion, obtain the fiduciary level Beta distribution Beta of consideration first, second, and third step-by-step test data _1,2,3;

S8, method according to S5-S7, progressively merge the equivalent success failure type data of follow-up development stage, finally obtain the heavy vehicle power system fiduciary level Beta distribution function Beta considering all development stage testing data _all;

S9, utilize Beta _allcalculate the heavy vehicle power system fiduciary level based on dispersion data.

2., as claimed in claim 1 based on the heavy vehicle power system reliability estimation method of dispersion, it is characterized in that, in step S2, utilize maximum likelihood function method to carry out the parameter estimation of Weibull distribution.

3., as claimed in claim 1 based on the heavy vehicle power system reliability estimation method of dispersion, it is characterized in that, in step S3, Reliability confidence lower limit is the one-sided confidence lower limit of degree of confidence 0.9.

4. as claim 1 and the heavy vehicle power system reliability estimation method based on dispersion according to claim 3, it is characterized in that, in step S3, utilize bootstrap to calculate Reliability confidence lower limit, Bootstrap sampling number of times is the integral multiple of 10, and is more than or equal to 1000 times.

5. as claim 1 and the heavy vehicle power system reliability estimation method based on dispersion according to claim 3, it is characterized in that, in step S4, the definition of moments method and Reliability confidence lower limit is utilized to be equivalent success or failure data by reliability assessment results conversion.