CN110263419A - A kind of loading machine drive axle extreme small sample reliability estimation method based on support vector machines - Google Patents
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Abstract
A kind of loading machine drive axle extreme small sample reliability estimation method based on support vector machines provided by the invention, the following steps are included: step 1, carries out fatigue life test to n loading machine drive axle exemplar respectively, obtains n data of fatigue life value, wherein, n=1~3；Step 2, supporting vector machine model is established according to the resulting n data of fatigue life value of step 1, then the resulting n data of fatigue life of step 1 is extended to by m+n sample data by support vector machines, obtain sample data X；Step 3, the service life average value u of sample data X obtained in step 2 is calculatedY' and standard deviation sigma '；Step 4, according to the service life average value u of the resulting sample data X of step 3Y' with standard deviation sigma ' acquires the service life average value u of the corresponding sample data of 75% confidence levelY' lower limit value uY'min；Step 5, the lower limit value u according to obtained in step 4Y'minThe reliability index of loading machine drive axle is calculated；Loading machine drive axle reliability estimation method of the invention is also applied for other fail-safe analyses for being not easy to obtain the engineering goods of great amount of samples.
Description
Technical field
The invention belongs to Mechanical Product Reliability assessment technology fields, and in particular to a kind of loading based on support vector machines
Machine drive axle extreme small sample reliability estimation method.
Background technique
Loading machine belongs to earth moving machinery class, is a kind of engineering machinery that purposes is very extensive, can be used for loading and unloading, remove
Fortune, smooth material and slight spading operation, are widely used in building, mine, highway, railway, water power, defence engineering and city
In infrastructure.
When loading machine operation: the torque that drive axle transmits transmission output shaft further increases, and revolving speed further decreases,
To overcome the resistance of wheel, while 90 ° of directions of the power of input change are transmitted to wheel；Drive axle solves left and right by differential mechanism
The differential problem of wheel, with the abrasion of convenient steering and reduction tire；Suffered various load pass to vehicle by drive axle
On wheel, while tractive resistance suffered by wheel, brake drag and lateral resistance are also transmitted to rack by drive axle.Therefore loading machine
The fatigue durability of drive axle is directly related to the working performance and working efficiency of loading machine, to the intensity and reliability of drive axle
Research also has very important significance.
But due to the limitation of time and funds, the fatigue life test of loading machine drive axle cannot take a large amount of test specimens to carry out
Test.And Small Sample Database is unable to satisfy the reliability analysis research requirement of mechanical structure, therefore for structure mechanical under System in Small Sample Situation
The fail-safe analysis domestic and international researcher of part has done related work: " Gao Zhentong fatigue reliability [M] the Beijing Aviation boat of document 1
Its university press, 2000 " study fatigue reliability using life scatter factor method." the Madsen H of document 2
O.Bayesian Fatigue Life Prediction [J] .1985. " Bayes's linear regression analysis and similar priori
Then information carries out fatigue life prediction with the Posterior distrbutionp of regression parameter using single order and Second Order Reliability.
But life scatter factor method is generally used for the assessment of group of planes safe life, the under test preceding average life span estimation of Bayes method
Value is affected.Bootstrap method avoids semiempirical Evaluation Method and Bayes method is needed to overall logarithm service life distribution of mean value
It is assumed that put back to simulation resampling by enough, reduce the influence of human factor.Bootstrap method is usually suitable
Small-Sample Test Circumstances for sample size n >=10 are assessed, and the extreme small sample for n=1~3 is simultaneously not suitable for；And loading machine drive axle
As engineering machinery key components and parts, progress Full-scale Fatigue Experiments are at high cost and sample number is few, generally 1~3 part.
Summary of the invention
The purpose of the present invention is to provide a kind of, and the loading machine drive axle extreme small sample reliability based on support vector machines is commented
Estimate method, solves the existing fatigue life test that cannot be loaded machine drive axle using Small Sample Database.
In order to achieve the above object, the technical solution adopted by the present invention is that:
A kind of loading machine drive axle extreme small sample reliability estimation method based on support vector machines provided by the invention, packet
Include following steps:
Step 1, fatigue life test is carried out to n loading machine drive axle exemplar respectively, obtains n fatigue life test number
According to value, wherein n=1~3；
Step 2, supporting vector machine model is established according to the resulting n data of fatigue life value of step 1, then passes through branch
It holds vector machine and the resulting n data of fatigue life of step 1 is extended into m+n sample data, obtain sample data X；
Step 3, the service life average value u of sample data X obtained in step 2 is calculatedY' and standard deviation sigma '；
Step 4, according to the service life average value u of the resulting sample data X of step 3Y' and standard deviation sigma ' acquire 75% confidence level
The service life average value u of corresponding sample dataY' lower limit value uY'min；
Step 5, the lower limit value u according to obtained in step 4Y'minThe reliability index of loading machine drive axle is calculated.
Preferably, in step 2, the specific method of supporting vector machine model is established according to the resulting n test data of step 1
It is:
S1 forms original series t by the resulting n data of fatigue life value of step 11,t2,...tn, and utilizing can
It is calculated by degree formula (1), obtains reliability R (t1),R(t2),...R(tn), as the defeated of Training Support Vector Machines
Enter:
Wherein, uYFor the service life average value of loading machine drive axle fatigue test exemplar；σ is the mark of loading machine drive axle exemplar
Quasi- poor, value is σ=0.17；
N data of fatigue life value is formed original series t by S21,t2,...tnAs Training Support Vector Machines
Output；
S3, the reliability R (t that will be calculated1),R(t2),...R(tn) and n data of fatigue life t1,t2,
...tnIt respectively as outputting and inputting for Training Support Vector Machines, imported into supporting vector machine model and it is trained, together
When using data of fatigue life value as the test data of assessment models training precision, when supporting vector machine model output and phase
The percent error of output is hoped to be less than or equal to 10-3When, then it is assumed that model training success.
Preferably, in step 2, the resulting n data of fatigue life value of step 1 is extended to by support vector machines
M+n sample data, specific method are:
S1, in [R (t1),R(tn)] m RANDOM RELIABILITY is taken at random in range, it is entered into trained supporting vector
Machine model obtains m output valve, the sample as expanded:
S2 will expand obtained m data and merge with n original test data, obtains m+n sample data X, i.e.,
Preferably, in step 3, the service life for calculating sample data X obtained in step 2 using Bootstrap method is average
Value uY' and standard deviation sigma '.
Preferably, in step 5, the reliability index of loading machine drive axle includes the function between reliability and fatigue life
It is relationship, failure probability density and functional relation between fatigue life, crash rate and functional relation between fatigue life, reliable
Service life and average life span.
Preferably, the functional relation expression formula between reliability and fatigue life:
Preferably, failure probability density and the functional relation expression formula between fatigue life:
Preferably, the functional relation expression formula between crash rate and fatigue life:
Wherein, t is fatigue life value,
Preferably, the Q-percentile life calculation formula of drive axle:
Preferably, average life span calculation formula:
Compared with prior art, the beneficial effects of the present invention are:
A kind of loading machine drive axle extreme small sample reliability estimation method based on support vector machines provided by the invention, it is first
Expand first with Minimum Sample of the supporting vector machine model to loading machine drive axle, these expanding datas can admirably after
Hold the characteristic of initial data, the result credibility for carrying out fail-safe analysis using it in this way is higher, will for project planner and
User provides relatively reliable data reference；Average life span value and standard deviation are solved using Bootstrap later, it is right on this basis
Probability density function is estimated solve the problems, such as the loading machine drive axle fail-safe analysis with Minimum Sample characteristic, together
When, loading machine drive axle reliability estimation method of the invention is also applied for other and is not easy to obtain the engineering goods of great amount of samples
Fail-safe analysis.
Detailed description of the invention
Fig. 1 is the work flow diagram of the embodiment of the present invention.
Fig. 2 is support vector machines system assumption diagram in the embodiment of the present invention.
Fig. 3 is supporting vector machine model prediction result and original value comparison diagram in the embodiment of the present invention.
Fig. 4 is obtained after carrying out 1000 sampling to exptended sample using Bootstrap method in the embodiment of the present invention
Sample average histogram and normal distribution matched curve；
Fig. 5 is obtained after carrying out 1000 sampling to exptended sample using Bootstrap method in the embodiment of the present invention
Sample variance histogram and normal distribution matched curve；
Fig. 6 is obtained after carrying out 10000 sampling to exptended sample using Bootstrap method in the embodiment of the present invention
Sample average histogram and normal distribution matched curve；
Fig. 7 is obtained after carrying out 10000 sampling to exptended sample using Bootstrap method in the embodiment of the present invention
Sample variance histogram and normal distribution matched curve；
Fig. 8 is obtained after carrying out 100000 sampling to exptended sample using Bootstrap method in the embodiment of the present invention
Sample average histogram and normal distribution matched curve；
Fig. 9 is obtained after carrying out 100000 sampling to exptended sample using Bootstrap method in the embodiment of the present invention
Sample variance histogram and normal distribution matched curve；
Figure 10 is the reliability of drive axle and between fatigue life in the embodiment of the present invention in confidence level γ=75%
Relational graph；
Figure 11 is the failure probability density of drive axle and tired longevity in the embodiment of the present invention in confidence level γ=75%
Relational graph between life；
Figure 12 is the crash rate of drive axle and between fatigue life in the embodiment of the present invention in confidence level γ=75%
Relational graph.
Specific embodiment
With reference to the accompanying drawing, the present invention is described in more detail.
As shown in Figure 1, a kind of loading machine drive axle extreme small sample reliability based on support vector machines provided by the invention
Appraisal procedure, comprising the following steps:
Step 1, fatigue life test is carried out to n loading machine drive axle exemplar respectively, obtains n fatigue life test number
According to value, wherein n=1~3；
Step 2, supporting vector machine model is established according to the resulting n data of fatigue life value of step 1, then passes through branch
It holds vector machine and the resulting n data of fatigue life of step 1 is extended into m+n sample data, obtain sample data X；
As shown in Fig. 2, being according to the specific method that the resulting n test data of step 1 establishes supporting vector machine model:
S1 forms original series t by the resulting n data of fatigue life value of step 11,t2,...tn, and utilizing can
It is calculated by degree formula (1), obtains reliability R (t1),R(t2),...R(tn), as the defeated of Training Support Vector Machines
Enter:
Wherein, uYFor the service life average value of loading machine drive axle fatigue test exemplar；σ is the mark of loading machine drive axle exemplar
Quasi- poor, value is σ=0.17；
N data of fatigue life value is formed original series t by S21,t2,...tnAs Training Support Vector Machines
Output；
S3, the reliability R (t that will be calculated1),R(t2),...R(tn) and n data of fatigue life t1,t2,
...tnIt respectively as outputting and inputting for Training Support Vector Machines, imported into supporting vector machine model and it is trained, together
When using data of fatigue life value as the test data of assessment models training precision, when supporting vector machine model output and phase
Hope the percent error of output 10-3Within when, then it is assumed that model training success, that is, can be used this model carry out data prediction.
The resulting n data of fatigue life value of step 1 is extended into m+n sample data by support vector machines,
Specific method is:
S1, in [R (t1),R(tn)] m RANDOM RELIABILITY is taken at random in range, it is entered into trained supporting vector
Machine model obtains m output valve, the sample as expanded:
S2 will expand obtained m data and merge with n original test data, obtains m+n sample data X, i.e.,
Step 3: the service life average value u of sample data X obtained in step 2 is found out using Bootstrap methodY' and mark
Quasi- difference σ '；
Step 4: according to the service life average value u of the resulting sample data X of step 3Y' and standard deviation sigma ' acquire 75% confidence level
The service life average value u of corresponding sample dataY' lower limit value uY'min；
Step 5: the lower limit value u according to obtained in step 4Y'minThe reliability index of loading machine drive axle is calculated.
Wherein, the reliability index of loading machine drive axle includes functional relation between reliability and fatigue life, failure
Functional relation, crash rate between probability density and fatigue life and the functional relation between fatigue life, Q-percentile life peace
The equal service life, in which:
Functional relation expression formula between reliability and fatigue life:
Failure probability density and the functional relation expression formula between fatigue life:
Functional relation expression formula between crash rate and fatigue life:
Wherein, t is fatigue life value,
The Q-percentile life calculation formula of drive axle:
Average life span calculation formula:
A kind of loading machine drive axle extreme small sample reliability assessment side based on supporting vector machine model provided by the invention
Method, this method are based on supporting vector machine model and Bootstrap principle, effectively can carry out sample with a small amount of sample obtained
Expand, probability density function is estimated on this basis, solving the loading machine drive axle with Minimum Sample characteristic can
By the problem of property analysis, meanwhile, loading machine drive axle reliability estimation method of the invention is also applied for other and is not easy to obtain greatly
Measure the fail-safe analysis of the engineering goods of sample.
Embodiment 1
Loading machine drive axle reliability estimation method under a kind of extreme small sample based on support vector machines, including following step
It is rapid:
1) it is measured 3 fatigue lives of loading machine drive axle respectively by testing and is respectively as follows: t1=39476.16h, t2=
42275.04h t3=41181.92h；
2) supporting vector machine model is established；
Original experiment data { 39476.16,41181.92,42275.04 } are substituted into formula of reliability (1), are acquired
Reliability is { 0.54,0.49,0.46 }, as the input of Training Support Vector Machines.
Reliability R (the t that will be calculated1),R(t2),...R(tn) and n data of fatigue life t1,t2,...tn
It respectively as outputting and inputting for Training Support Vector Machines, imported into supporting vector machine model and it is trained, simultaneously will
Test data of the data of fatigue life value as assessment models training precision, when supporting vector machine model output and expectation are defeated
Percent error out is 10-3Within when, then it is assumed that model training success, that is, can be used this model carry out data prediction.Take σ=
0.17.It is as shown in table 1 that the corresponding reliability value of 3 original fatigue life sample datas is calculated according to formula (1):
1. reliability of table
Its training result is as shown in table 2:
2. training result of table
As can be seen from Table 2, predicted value can preferably inherit the characteristic of initial data, the percentage of network output and desired value
Error is 10-3Within when, therefore this supporting vector machine model can be used to the fatigue life of loading machine drive axle under extreme small sample
Expanded, as shown in Figure 3.
3) 3 test datas are extended to 10 by trained support vector machines；
It is at least 10 requirement to reach the fail-safe analysis of Bootstrap method for sample size, needs to obtain 7 expansions
The sample data filled.By 7 random numbers of 0~1 range by sequence arrangement from small to large, trained support vector machines is inputted
It is emulated to obtain 7 prediction result data in model, combines the data as reliability assessment with original measured data.
7 prediction data are obtained by trained supporting vector machine model: 38086.41,40324.69,41880.63,
43441.74,43695.03,44651.33,49443.22 }.
10 are obtained after original 3 test datas are added 7 fatigue lives predicted by supporting vector machine model
A data 39476.16,41181.92,42275.04,38086.41,40324.69,41880.63,43441.74,
43695.03,44651.33,49443.22 }, obtained after this data being taken logarithm:
X=4.5963,4.6147,4.6261,4.5808,4.6056,4.6220,4.6379,4.6404,4.6498,
4.6941 }, the sample data as the processing of Bootstrap method.
4) will 3) obtain sample data X=4.5963,4.6147,4.6261,4.5808,4.6056,4.6220,
4.6379,4.6404,4.6498,4.6941 }, sample data is handled using Bootstrap method, finds out the estimation of sample average
Value.Random sampling with replacement, the average value of 1000,10000,100000 data of frequency in sampling and side are carried out to above-mentioned sample X
The fit solution of difference and normal curve is as shown in figures 4-9.
It can be seen that result all Normal Distributions after sampling by Fig. 4-9, with increasing for frequency in sampling, normal distribution
The fitting precision of curve and histogram is higher.By Fig. 8, Fig. 9 can be seen that sampling 100000 times when its result obey N (4.625,
0.1302) normal distribution and original sample average value (4.6125) it is almost the same, illustrate support vector machines-herein
Bootstrap combined method can effectively inherit the basic statistics feature of initial data.
α=0.25 is taken to meet the confidence level of bilateral 75%, it is [4.5777,4.6723] that μ, which corresponds to confidence interval,.
The correlation function expression formula that the confidence lower limit 4.5777 of confidence level γ=0.75 is substituted into logarithm normal distribution, can obtain
The reliability index of loading machine drive axle is as follows:
Functional relation expression formula between reliability and fatigue life:
Failure probability density and the functional relation expression formula between fatigue life:
Functional relation expression formula between crash rate and fatigue life:
Wherein, t is fatigue life value,
The Q-percentile life of drive axle:
Average life span are as follows:
In conclusion the Reliability Function of loading machine drive axle under 75% confidence level can be drawn by formula (2), (4), (5)
Curve, failure probability density function curve and failure rate estimation curve are as shown in Figure 10-Figure 12.
Content described in this specification embodiment is only enumerating to the way of realization of inventive concept, protection of the invention
Range should not be construed as being limited to the specific forms stated in the embodiments, and protection scope of the present invention also includes art technology
Personnel conceive according to the present invention it is conceivable that equivalent technologies mean.
Claims (10)
1. a kind of loading machine drive axle extreme small sample reliability estimation method based on support vector machines, which is characterized in that including
Following steps:
Step 1, fatigue life test is carried out to n loading machine drive axle exemplar respectively, obtains n data of fatigue life
Value, wherein n=1~3；
Step 2, supporting vector machine model is established according to the resulting n data of fatigue life value of step 1, then by support to
The resulting n data of fatigue life of step 1 is extended to m+n sample data by amount machine, obtains sample data X；
Step 3, the service life average value u of sample data X obtained in step 2 is calculatedY' and standard deviation sigma '；
Step 4, according to the service life average value u of the resulting sample data X of step 3YIt is corresponding that ' with standard deviation sigma ' acquires 75% confidence level
Sample data service life average value uY' lower limit value
Step 5, the lower limit value according to obtained in step 4The reliability index of loading machine drive axle is calculated.
2. a kind of loading machine drive axle extreme small sample reliability assessment side based on support vector machines according to claim 1
Method, which is characterized in that in step 2, the specific method of supporting vector machine model is established according to the resulting n test data of step 1
It is:
S1 forms original series t by the resulting n data of fatigue life value of step 11,t2,...tn, and utilize reliability
Formula (1) is calculated, and reliability R (t is obtained1),R(t2),...R(tn), as the input of Training Support Vector Machines:
Wherein, uYFor the service life average value of loading machine drive axle fatigue test exemplar；σ is the standard deviation of loading machine drive axle exemplar,
Its value is σ=0.17；
N data of fatigue life value is formed original series t by S21,t2,...tnOutput as Training Support Vector Machines；
S3, the reliability R (t that will be calculated1),R(t2),...R(tn) and n data of fatigue life t1,t2,...tnPoint
Not outputting and inputting as Training Support Vector Machines, imported into supporting vector machine model and is trained to it, while will be tired
Test data of the labor testing data of life-span value as assessment models training precision, when supporting vector machine model output and desired output
Percent error be less than or equal to 10-3When, then it is assumed that model training success.
3. a kind of loading machine drive axle extreme small sample reliability assessment side based on support vector machines according to claim 1
Method, which is characterized in that in step 2, the resulting n data of fatigue life value of step 1 is extended to by m by support vector machines
+ n sample datas, specific method is:
S1, in [R (t1),R(tn)] m RANDOM RELIABILITY is taken at random in range, it is entered into trained support vector machines mould
Type obtains m output valve, the sample as expanded:
S2 will expand obtained m data and merge with n original test data, obtains m+n sample data X, i.e.,
4. a kind of loading machine drive axle extreme small sample reliability assessment side based on support vector machines according to claim 1
Method, which is characterized in that in step 3, the service life average value of sample data X obtained in step 2 is calculated using Bootstrap method
uY' and standard deviation sigma '.
5. a kind of loading machine drive axle extreme small sample reliability assessment side based on support vector machines according to claim 1
Method, which is characterized in that in step 5, the reliability index of loading machine drive axle includes the function between reliability and fatigue life
It is relationship, failure probability density and functional relation between fatigue life, crash rate and functional relation between fatigue life, reliable
Service life and average life span.
6. a kind of loading machine drive axle extreme small sample reliability assessment side based on support vector machines according to claim 5
Method, which is characterized in that the functional relation expression formula between reliability and fatigue life:
7. a kind of loading machine drive axle extreme small sample reliability assessment side based on support vector machines according to claim 5
Method, which is characterized in that failure probability density and the functional relation expression formula between fatigue life:
8. a kind of loading machine drive axle extreme small sample reliability assessment side based on support vector machines according to claim 5
Method, which is characterized in that the functional relation expression formula between crash rate and fatigue life:
Wherein, t is fatigue life value,
9. a kind of loading machine drive axle extreme small sample reliability assessment side based on support vector machines according to claim 5
Method, which is characterized in that the Q-percentile life calculation formula of drive axle:
10. a kind of loading machine drive axle extreme small sample reliability assessment based on support vector machines according to claim 5
Method, which is characterized in that average life span calculation formula:
Priority Applications (1)
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| CN201910523542.XA CN110263419B (en) | 2019-06-17 | 2019-06-17 | Loader drive axle minimum subsample reliability assessment method based on support vector machine |
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| CN201910523542.XA CN110263419B (en) | 2019-06-17 | 2019-06-17 | Loader drive axle minimum subsample reliability assessment method based on support vector machine |
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