CN111597663A - Momentum wheel residual life prediction method fusing residual life empirical data - Google Patents

Momentum wheel residual life prediction method fusing residual life empirical data Download PDF

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CN111597663A
CN111597663A CN202010727427.7A CN202010727427A CN111597663A CN 111597663 A CN111597663 A CN 111597663A CN 202010727427 A CN202010727427 A CN 202010727427A CN 111597663 A CN111597663 A CN 111597663A
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life
momentum wheel
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empirical data
residual life
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CN111597663B (en
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贾祥
程志君
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National University of Defense Technology
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Abstract

The invention belongs to the field of residual life prediction, and discloses a momentum wheel residual life prediction method fusing residual life empirical data. The method well solves the problem of predicting the residual life by fusing the empirical data of the residual life of the momentum wheel, fills the blank of the existing research, and has clear steps, easy operation and convenient application.

Description

Momentum wheel residual life prediction method fusing residual life empirical data
Technical Field
The invention belongs to the field of residual life prediction, and particularly relates to a momentum wheel residual life prediction method aiming at fusion of residual life empirical data.
Background
The reliability refers to the capability of a product to complete a specified function under a specified condition and within a specified time, is an inherent attribute of the product, and is an important index for measuring the quality of the product, so that the reliability problem of the product is very important. The reliability evaluation problem is an important content of reliability research, and the reliability evaluation indexes include reliability, service life, residual service life and the like, wherein the residual service life represents the remaining normal working time of the product after the current time.
The momentum wheel is an important component in space equipment such as a satellite, and the reliability level of the momentum wheel is important for the reliability of the whole space equipment, so that a residual life prediction method of the momentum wheel needs to be researched. Since the momentum wheel is an electromechanical component in nature, its lifetime is generally considered to follow the weibull distribution. The probability density function of the Weibull distribution is
Figure 533968DEST_PATH_IMAGE001
Wherein
Figure 587637DEST_PATH_IMAGE002
In order to be able to maintain the life of the product,
Figure 445872DEST_PATH_IMAGE003
and
Figure 261381DEST_PATH_IMAGE004
the shape parameters and the scale parameters of the weibull distribution are respectively.
For predicting the residual life of the momentum wheel, according to the traditional prediction method based on large sample failure data, firstly, sample data of a momentum wheel life test is utilized to estimate the life distribution parameters of the momentum wheel
Figure 205066DEST_PATH_IMAGE005
And
Figure 701906DEST_PATH_IMAGE006
then, the remaining life distribution is derived from the life distribution of the momentum wheel
Figure 680227DEST_PATH_IMAGE007
The probability density function of the remaining life at the time is
Figure 666637DEST_PATH_IMAGE008
Wherein
Figure 97619DEST_PATH_IMAGE009
For the remaining life of the product, further processingNumber of
Figure 398150DEST_PATH_IMAGE010
And
Figure 965398DEST_PATH_IMAGE011
substituting the estimated value of (A) into the expectation of remaining life
Figure 889753DEST_PATH_IMAGE012
As a predicted value of the remaining life, wherein
Figure 808031DEST_PATH_IMAGE013
Is a gamma function;
Figure 443412DEST_PATH_IMAGE014
is an incomplete gamma function. However, since the momentum wheel is typically a highly reliable, long-life product, limited by the cost and time of the life test, it is difficult to collect a large amount of failure time. When the life test data is few failure data or even no failure data, the traditional residual life prediction method based on the large sample failure data is poor in precision and difficult to meet the actual requirement.
On the other hand, according to other types of reliability data of the momentum wheel, such as scrapped data of the same type of momentum wheel, running data of similar momentum wheels, performance degradation data of the momentum wheel or development requirement data of the momentum wheel, and the like, the residual life of the momentum wheel can be predicted, and the prediction is called as empirical data. By fusing the residual life experience data and the life test data of the momentum wheel, the information source can be expanded, thereby improving the precision of residual life prediction. In the existing research, the residual life prediction research of the product is carried out by fusing other types of reliability information, such as product reliability data given by experts, life data and performance degradation data of similar products, and the like, relatively fully. However, for the problem of predicting the residual life of the momentum wheel by fusing the empirical data of the residual life, the existing research is deficient, and no related public technology exists at present.
Disclosure of Invention
Aiming at the problem of predicting the residual life of the momentum wheel, the invention provides a momentum wheel residual life prediction method fusing residual life empirical data.
In order to solve the technical problems, the invention adopts the technical scheme that:
the momentum wheel residual life prediction method fusing the residual life empirical data comprises the following steps:
s1, determining the residual life empirical data type of the momentum wheel, and setting the life distribution parameters of the momentum wheel
Figure 130745DEST_PATH_IMAGE015
And
Figure 193379DEST_PATH_IMAGE016
determining the pre-test distribution parameters based on the collected residual life empirical data of the momentum wheel and the fitting of the pre-test moment of the momentum wheel;
s2 extraction
Figure 333373DEST_PATH_IMAGE017
The momentum wheel is used as a test sample to carry out a life test, life test sample data of each test sample is collected, and a likelihood function of the life test sample data is given;
and S3, predicting the residual life of the momentum wheel based on a random sampling method.
Preferably, the empirical data of the remaining life of the momentum wheel in step S1 of the present invention is that the momentum wheel is in
Figure 38024DEST_PATH_IMAGE018
Remaining life point estimation of time of day
Figure 845443DEST_PATH_IMAGE019
Or/and momentum wheel at confidence level
Figure 840163DEST_PATH_IMAGE020
Remaining life confidence interval
Figure 670716DEST_PATH_IMAGE021
。
Preferably, in step S1 of the present invention, a life distribution parameter of the momentum wheel is set
Figure 647899DEST_PATH_IMAGE022
And
Figure 575404DEST_PATH_IMAGE023
the pre-test distribution form is
Figure 448682DEST_PATH_IMAGE024
Wherein
Figure 563268DEST_PATH_IMAGE025
Figure 609722DEST_PATH_IMAGE026
I.e. distribution parameter
Figure 126154DEST_PATH_IMAGE027
And
Figure 170333DEST_PATH_IMAGE028
are independent of each other, and
Figure 772216DEST_PATH_IMAGE029
prior distribution of
Figure 622360DEST_PATH_IMAGE030
In order to be evenly distributed, the water is mixed,
Figure 494763DEST_PATH_IMAGE031
prior distribution of
Figure 709844DEST_PATH_IMAGE032
Is a gamma distribution in which
Figure 799023DEST_PATH_IMAGE033
In order to be a parameter of the shape,
Figure 187279DEST_PATH_IMAGE034
is a scale parameter.
Figure 615986DEST_PATH_IMAGE035
Is generally in the range of
Figure 798706DEST_PATH_IMAGE036
Can be determined according to actual conditions
Figure 640760DEST_PATH_IMAGE037
。
Preferably, step S1 of the present invention includes determining a pre-test moment of the empirical data of the remaining life of the momentum wheel based on the collected empirical data of the remaining life of the momentum wheel;
if the rest life empirical data of the momentum wheel is that the momentum wheel is in
Figure 567127DEST_PATH_IMAGE038
Remaining life point estimation of time of day
Figure 850341DEST_PATH_IMAGE039
Then the pre-test moment thereof
Figure 735121DEST_PATH_IMAGE040
Is composed of
Figure 533312DEST_PATH_IMAGE041
If the residual life empirical data of the momentum wheel is
Figure 201054DEST_PATH_IMAGE042
Moment at confidence level
Figure 902556DEST_PATH_IMAGE043
Remaining life confidence interval
Figure 958237DEST_PATH_IMAGE044
Then the pre-test moments are respectively
Figure 978145DEST_PATH_IMAGE045
Wherein
Figure 715157DEST_PATH_IMAGE046
In order to be a function of the beta function,
Figure 769701DEST_PATH_IMAGE047
in order to be a super-geometric function,
Figure 730704DEST_PATH_IMAGE048
，kis a subscript of the power series expansion,
Figure 503488DEST_PATH_IMAGE049
to be distributed uniformly
Figure 778611DEST_PATH_IMAGE050
Extracted by
Figure 687661DEST_PATH_IMAGE051
In a sampleiThe number of the samples is one,
Figure 85145DEST_PATH_IMAGE052
。
preferably, the method for determining the distribution parameters before the test in step S1 of the present invention includes:
is provided to collect
Figure 282908DEST_PATH_IMAGE053
Empirical data of the residual life of the individual momentum wheel, wherein
Figure 659925DEST_PATH_IMAGE054
Is marked as a momentum wheel
Figure 954640DEST_PATH_IMAGE055
Remaining life point estimation of time of day
Figure 991866DEST_PATH_IMAGE056
Or confidence level
Figure 942504DEST_PATH_IMAGE057
Remaining life confidence interval
Figure 356168DEST_PATH_IMAGE058
Wherein
Figure 505390DEST_PATH_IMAGE059
；
By fitting empirical data of residual life
Figure 916780DEST_PATH_IMAGE060
Or
Figure 885873DEST_PATH_IMAGE061
And the pre-test moment of the empirical data of the residual life of the momentum wheel, and simultaneously introducing a new variable
Figure 368807DEST_PATH_IMAGE062
And
Figure 106955DEST_PATH_IMAGE063
wherein
Figure 954826DEST_PATH_IMAGE064
And
Figure 906820DEST_PATH_IMAGE065
，
Figure 927866DEST_PATH_IMAGE066
and
Figure 786101DEST_PATH_IMAGE067
for any real number, the following unconstrained optimization problem model is constructed:
Figure 601610DEST_PATH_IMAGE068
solving the unconstrained optimization problem model to obtain variables
Figure 279716DEST_PATH_IMAGE069
And
Figure 838873DEST_PATH_IMAGE070
the distribution parameters before test can be determined
Figure 551614DEST_PATH_IMAGE071
And
Figure 741287DEST_PATH_IMAGE072
wherein
Figure 172268DEST_PATH_IMAGE073
The empirical data representative of the remaining life of the momentum wheel is in the form of a point estimate,
Figure 36582DEST_PATH_IMAGE074
the empirical data representative of the remaining life of the momentum wheel is in the form of a confidence interval.
Preferably, step S2 of the present invention includes:
random decimation
Figure 807091DEST_PATH_IMAGE075
The momentum wheel is used as a sample to carry out a life test, and the working state of each test sample is observed in the life test; before the observation is stopped, if the test sample cannot work continuously at a certain moment, the moment is the failure time of the test sample; if the observation time is reached, if the test sample can still work, the time is the truncation time of the test sample; the failure time and the tail-cutting time are collectively called as life test sample data and are recorded as
Figure 964403DEST_PATH_IMAGE076
Wherein
Figure 882681DEST_PATH_IMAGE077
，
Figure 783641DEST_PATH_IMAGE078
The representative life test sample data is the failure time,
Figure 674236DEST_PATH_IMAGE079
representing the life test sample data as the tail-cutting time; sample data based on life test
Figure 268029DEST_PATH_IMAGE080
Giving it a likelihood function of
Figure 408023DEST_PATH_IMAGE081
Wherein
Figure 50357DEST_PATH_IMAGE082
And
Figure 592197DEST_PATH_IMAGE083
is a parameter of the distribution of the service life of the momentum wheel,
Figure 356890DEST_PATH_IMAGE084
in order to be a parameter of the shape,
Figure 485646DEST_PATH_IMAGE085
is a scale parameter.
Preferably, S3 of the present invention includes:
s3.1 utilization of
Figure 931670DEST_PATH_IMAGE086
Is located at
Figure 593596DEST_PATH_IMAGE087
Random number of
Figure 529191DEST_PATH_IMAGE088
Wherein
Figure 581461DEST_PATH_IMAGE089
Are respectively based on
Figure 627914DEST_PATH_IMAGE090
And
Figure 409925DEST_PATH_IMAGE091
give a sample
Figure 250842DEST_PATH_IMAGE092
And
Figure 790408DEST_PATH_IMAGE093
is regarded as being from
Figure 640552DEST_PATH_IMAGE094
And
Figure 11491DEST_PATH_IMAGE095
the pre-test sample extracted is distributed, wherein
Figure 226571DEST_PATH_IMAGE096
；
S3.2 comparing the pre-test samples based on the likelihood function given in S2
Figure 817215DEST_PATH_IMAGE097
And
Figure 205471DEST_PATH_IMAGE098
updating to generate a post-test sample
Figure 899758DEST_PATH_IMAGE099
And
Figure 82477DEST_PATH_IMAGE100
instant command
Figure 658952DEST_PATH_IMAGE101
And is
Figure 585320DEST_PATH_IMAGE102
Wherein
Figure 134113DEST_PATH_IMAGE103
Is composed of
Figure 284471DEST_PATH_IMAGE104
The random number of (2) is greater than,
Figure 285925DEST_PATH_IMAGE105
，
Figure 15984DEST_PATH_IMAGE106
，
Figure 643DEST_PATH_IMAGE107
；
s3.3 post-test samples based on post-update
Figure 525166DEST_PATH_IMAGE108
And
Figure 13916DEST_PATH_IMAGE109
prediction of
Figure 547665DEST_PATH_IMAGE110
The residual life of the momentum wheel at the moment after the momentum wheel is fused with the residual life empirical data is as follows:
Figure 867788DEST_PATH_IMAGE111
。
the invention provides computer equipment which comprises a memory and a processor, wherein the memory stores a computer program, and the processor realizes the steps of any one of the momentum wheel residual life prediction methods fusing residual life empirical data when executing the computer program.
The present invention also provides a computer readable storage medium having stored thereon a computer program which, when executed by a processor, performs the steps of any of the above-described momentum wheel remaining life prediction methods incorporating empirical data of remaining life.
The invention has the following beneficial technical effects:
aiming at the problem of predicting the residual life by fusing the empirical data of the residual life of the momentum wheel, the invention firstly gives the distribution form before the test of the distribution parameters of the life of the momentum wheel, and respectively considers the empirical data of the residual life as the different forms of point estimation and confidence interval, and gives the moment before the test of the empirical data of the residual life of the momentum wheel. And further determining parameters of pre-test distribution by fitting empirical data and pre-test moments thereof, collecting service life test data of the momentum wheel and giving a corresponding likelihood function, and finally predicting the residual service life of the momentum wheel after the empirical data is fused by a random sampling method. The method well solves the problem of predicting the residual life by fusing the empirical data of the residual life of the momentum wheel through the steps, fills the blank of the existing research, and has clear steps, easy operation and convenient application.
Detailed Description
In order to make the objects, technical solutions and advantages of the present invention more apparent, the present invention is further described in detail with reference to specific embodiments. It should be noted that, in the description, the undescribed contents and parts of english are abbreviated as well known to those skilled in the art. Some specific parameters given in the present embodiment are only exemplary, and the values may be changed to appropriate values accordingly in different real-time manners.
Example 1:
the embodiment provides a momentum wheel residual life prediction method fusing residual life empirical data, which comprises the following steps:
s1, determining the residual life empirical data type of the momentum wheel, and setting the life distribution parameters of the momentum wheel
Figure 563212DEST_PATH_IMAGE112
And
Figure 539258DEST_PATH_IMAGE113
determining the pre-test distribution parameters based on the collected residual life empirical data of the momentum wheel and the pre-test moment thereof;
s1.1 empirical data on the remaining life of a momentum wheel
Figure 876698DEST_PATH_IMAGE114
Remaining life point estimation of time of day
Figure 785749DEST_PATH_IMAGE115
Or/and momentum wheel at confidence level
Figure 917653DEST_PATH_IMAGE116
Remaining life confidence interval
Figure 413618DEST_PATH_IMAGE117
。
S1.2 setting a service life distribution parameter of the momentum wheel
Figure 492433DEST_PATH_IMAGE118
And
Figure 255989DEST_PATH_IMAGE119
the pre-test distribution form is
Figure 824374DEST_PATH_IMAGE120
Wherein
Figure 306171DEST_PATH_IMAGE121
Figure 923097DEST_PATH_IMAGE122
I.e. distribution parameter
Figure 806740DEST_PATH_IMAGE123
And
Figure 546025DEST_PATH_IMAGE124
are independent of each other, and
Figure 515118DEST_PATH_IMAGE125
prior distribution of
Figure 935735DEST_PATH_IMAGE126
In order to be evenly distributed, the water is mixed,
Figure 939464DEST_PATH_IMAGE127
prior distribution of
Figure 85536DEST_PATH_IMAGE128
Is a gamma distribution.
S1.3, determining the moment before the test of the empirical data of the residual life of the momentum wheel based on the collected empirical data of the residual life of the momentum wheel.
a. If the rest life empirical data of the momentum wheel is that the momentum wheel is in
Figure 541925DEST_PATH_IMAGE129
Remaining life point estimation of time of day
Figure 297392DEST_PATH_IMAGE130
Then the pre-test moment is obtained by the following steps:
based on the expected residual life (given in the background and not described further herein), it can be seen that
Figure 155626DEST_PATH_IMAGE131
Empirical data due to remaining life
Figure 908819DEST_PATH_IMAGE132
Containing distribution parameters
Figure 852504DEST_PATH_IMAGE133
And
Figure 411661DEST_PATH_IMAGE134
and is and
Figure 124402DEST_PATH_IMAGE135
and
Figure 376392DEST_PATH_IMAGE136
obeying to the pre-test distribution in S1.2
Figure 745057DEST_PATH_IMAGE137
Thus, the empirical data of the remaining life can be known
Figure 343791DEST_PATH_IMAGE138
Is also a random variable, based on a pre-test distribution
Figure 442197DEST_PATH_IMAGE139
Can obtain the product
Figure 599508DEST_PATH_IMAGE138
The specific derivation process of the prior moment is as follows:
Figure 252207DEST_PATH_IMAGE140
due to the fact that
Figure 153167DEST_PATH_IMAGE141
And
Figure 840500DEST_PATH_IMAGE142
wherein
Figure 371975DEST_PATH_IMAGE143
In order to be a function of the beta function,
Figure 511970DEST_PATH_IMAGE144
in order to be a super-geometric function,
Figure 951041DEST_PATH_IMAGE145
。
this can be achieved
Figure 254066DEST_PATH_IMAGE146
Taking into account that the analytical expressions for the integrals cannot be derived further, numerical approximation is used by changing from a uniform distribution
Figure 753180DEST_PATH_IMAGE147
Extraction of
Figure 380471DEST_PATH_IMAGE148
A sample
Figure 826495DEST_PATH_IMAGE149
Wherein
Figure 222842DEST_PATH_IMAGE150
Then the pre-test moment thereof
Figure 158437DEST_PATH_IMAGE151
Is composed of
Figure 273023DEST_PATH_IMAGE152
b. If the residual life empirical data of the momentum wheel is
Figure 319477DEST_PATH_IMAGE153
Moment at confidence level
Figure 773592DEST_PATH_IMAGE154
Remaining life confidence interval
Figure 614509DEST_PATH_IMAGE155
Then the pre-test moment is obtained by the following steps:
based on the remaining lifetime probability density function (given in the background, and not described further herein), the remaining lifetime probability density function can be obtained
Figure 983435DEST_PATH_IMAGE156
With respect to the above formula, introduce
Figure 568001DEST_PATH_IMAGE157
And deducing the prior moment thereof as follows:
Figure 142201DEST_PATH_IMAGE158
according to the generalized theorem of two terms, it can be known
Figure 419599DEST_PATH_IMAGE159
Thus, it is possible to obtain
Figure 508778DEST_PATH_IMAGE160
Determining the pre-test moment
Figure 631454DEST_PATH_IMAGE161
Is composed of
Figure 60162DEST_PATH_IMAGE162
By numerical approximation algorithm, can obtain
Figure 508461DEST_PATH_IMAGE163
So that a remaining life confidence interval can be obtained
Figure 819356DEST_PATH_IMAGE164
Respectively of prior moments
Figure 745724DEST_PATH_IMAGE165
S1.4 determining Pre-test distribution parameters
Figure 592719DEST_PATH_IMAGE166
And
Figure 211920DEST_PATH_IMAGE167
is provided to collect
Figure 10111DEST_PATH_IMAGE168
Empirical data of the residual life of the individual momentum wheel, wherein
Figure 943432DEST_PATH_IMAGE169
Is marked as a momentum wheel
Figure 409049DEST_PATH_IMAGE170
Remaining life point estimation of time of day
Figure 933571DEST_PATH_IMAGE171
Or confidence level
Figure 422321DEST_PATH_IMAGE172
Remaining life confidence interval
Figure 690491DEST_PATH_IMAGE173
Wherein
Figure 10614DEST_PATH_IMAGE174
. By fitting empirical data of residual life
Figure 174879DEST_PATH_IMAGE175
Or
Figure 947663DEST_PATH_IMAGE176
And the pre-test moment of the empirical data of the residual life of the momentum wheel in S1.3 can determine the pre-test distribution parameters in S1.2
Figure 520989DEST_PATH_IMAGE177
And
Figure 695619DEST_PATH_IMAGE178
i.e. when fitting the error function
Figure 765206DEST_PATH_IMAGE179
At the minimumThe distribution parameters before test can be obtained
Figure 290865DEST_PATH_IMAGE180
And
Figure 900838DEST_PATH_IMAGE181
wherein, in
Figure 133236DEST_PATH_IMAGE182
The empirical data representative of the remaining life of the momentum wheel is in the form of a point estimate,
Figure 436042DEST_PATH_IMAGE183
the empirical data representative of the remaining life of the momentum wheel is in the form of a confidence interval. For this purpose, the following constrained optimization problem model is constructed
Figure 917839DEST_PATH_IMAGE184
Further by introducing new variables
Figure 597082DEST_PATH_IMAGE185
And
Figure 683986DEST_PATH_IMAGE186
wherein
Figure 157693DEST_PATH_IMAGE187
And
Figure 887971DEST_PATH_IMAGE188
，
Figure 43009DEST_PATH_IMAGE189
and
Figure 46737DEST_PATH_IMAGE190
for any real number, converting the constrained optimization problem model into an unconstrained optimization problem model
Figure 956924DEST_PATH_IMAGE191
Solving an unconstrained optimization problem model to obtain variables
Figure 413313DEST_PATH_IMAGE192
And
Figure 372042DEST_PATH_IMAGE193
the distribution parameters before test can be determined
Figure 964697DEST_PATH_IMAGE194
And
Figure 45786DEST_PATH_IMAGE195
。
s2 extraction
Figure 989471DEST_PATH_IMAGE196
The momentum wheel is used as a test sample to carry out a life test, life test sample data of each test sample is collected, and a likelihood function of the life test sample data is given.
Random decimation
Figure 751890DEST_PATH_IMAGE196
The momentum wheel is used as a sample to carry out a life test, and the working state of each test sample is observed in the life test. Before the observation is terminated, if the test sample cannot continue to work at a certain moment, the moment is the failure time of the test sample. If the observation time is reached, if the test sample can still work, the time is the truncation time of the test sample. The failure time and the tail-cutting time are collectively called as life test sample data and are recorded as
Figure 730211DEST_PATH_IMAGE197
Wherein
Figure 952507DEST_PATH_IMAGE198
，
Figure 586751DEST_PATH_IMAGE199
The representative life test sample data is the failure time,
Figure 684020DEST_PATH_IMAGE200
the representative life test sample data is the tail-off time. Sample data based on life test
Figure 782426DEST_PATH_IMAGE201
Giving it a likelihood function of
Figure 674158DEST_PATH_IMAGE202
S3 predicts the remaining life of the momentum wheel based on a random sampling method.
S3.1 utilization of
Figure 795698DEST_PATH_IMAGE203
Is located at
Figure 962237DEST_PATH_IMAGE204
Random number of
Figure 587254DEST_PATH_IMAGE205
Wherein
Figure 915467DEST_PATH_IMAGE206
Are respectively based on
Figure 321040DEST_PATH_IMAGE207
And
Figure 228953DEST_PATH_IMAGE208
give a sample
Figure 770793DEST_PATH_IMAGE209
And
Figure 771372DEST_PATH_IMAGE210
is regarded as being from
Figure 398663DEST_PATH_IMAGE211
And
Figure 907005DEST_PATH_IMAGE212
the pre-test sample extracted is distributed, wherein
Figure 506613DEST_PATH_IMAGE213
。
S3.2 comparing the pre-test samples based on the likelihood function given in S2
Figure 176629DEST_PATH_IMAGE214
And
Figure 556795DEST_PATH_IMAGE215
updating to generate a post-test sample
Figure 337669DEST_PATH_IMAGE216
And
Figure 57363DEST_PATH_IMAGE217
instant command
Figure 163859DEST_PATH_IMAGE218
And is
Figure 765742DEST_PATH_IMAGE219
Wherein
Figure 553570DEST_PATH_IMAGE220
Is composed of
Figure 691552DEST_PATH_IMAGE221
The random number of (2) is greater than,
Figure 703370DEST_PATH_IMAGE222
，
Figure 730232DEST_PATH_IMAGE223
，
Figure 118488DEST_PATH_IMAGE224
。
s3.3 post-update based postObtained post-test sample
Figure 343933DEST_PATH_IMAGE225
And
Figure 792232DEST_PATH_IMAGE226
prediction of
Figure 368707DEST_PATH_IMAGE227
The residual life of the momentum wheel at the moment after the momentum wheel is fused with the residual life empirical data is as follows:
Figure 498337DEST_PATH_IMAGE228
example 2:
based on the method given in embodiment 1, a specific application example of the present invention is given below, and this example predicts the remaining life of a certain type of momentum wheel product by collecting empirical data and experimental data of the remaining life, and the specific method of this embodiment is as follows:
in a first step, from historical product reliability data of the momentum wheel, 2 empirical data of remaining life are given, wherein 1 data is a point estimated to be 114144 hours at 1000 hours of remaining life, and another data is a confidence interval [76035, 138473 ] of 5000 hours of remaining life at a confidence level of 0.9]And (4) hours. The service life distribution parameter of the momentum wheel is set according to S1.2
Figure 843868DEST_PATH_IMAGE229
And
Figure 666330DEST_PATH_IMAGE230
after the distribution form before examination, get
Figure 464522DEST_PATH_IMAGE231
Estimating the residual life of the momentum wheel by using the empirical data of the residual life of the momentum wheel and the residual life point
Figure 690186DEST_PATH_IMAGE232
A moment before experiment
Figure 890223DEST_PATH_IMAGE233
And remaining life confidence interval
Figure 883587DEST_PATH_IMAGE234
A moment before experiment
Figure 434654DEST_PATH_IMAGE235
、
Figure 702824DEST_PATH_IMAGE236
Fitting, and obtaining the distribution parameters before the test according to the unconstrained optimization problem model constructed in S1.4
Figure 960630DEST_PATH_IMAGE237
And
Figure 921633DEST_PATH_IMAGE238
。
secondly, collecting the life test sample data of the momentum wheel according to the method in S2, and determining whether each sample data is failure data or truncated data, as shown in table 1, the likelihood function in S2 can be given.
Watch (A)
Figure 694417DEST_PATH_IMAGE239
Life test sample data (unit: hour) of momentum wheel
Figure 766278DEST_PATH_IMAGE240
Thirdly, utilizing the service life distribution parameters of the momentum wheel set in the S1.2
Figure 144170DEST_PATH_IMAGE241
And
Figure 10495DEST_PATH_IMAGE242
pre-test distribution form generation
Figure 37619DEST_PATH_IMAGE243
And
Figure 647592DEST_PATH_IMAGE244
the pre-test sample of (1). The post-test samples are obtained by further updating the pre-test samples with the likelihood function given in S2. And predicting the residual life of the momentum wheel after the empirical data are fused by using the method in S.3.3. Such as taking
Figure 879990DEST_PATH_IMAGE245
The remaining life point of the momentum wheel at 1000 hours may be estimated to be 131189 hours. Compared with the empirical data in the first step, the residual life of the momentum wheel obtained by fusing the empirical data is more accurate, and the effectiveness of the method provided by the invention is demonstrated. In conclusion, the momentum wheel residual life prediction method fusing the residual life empirical data is easy to operate and accurate in result.
Example 3:
a computer device comprising a memory storing a computer program and a processor implementing the steps of the momentum wheel remaining life prediction method fusing remaining life empirical data as provided in embodiment 1 above when the computer program is executed.
Example 4:
the present invention also provides a computer-readable storage medium, on which a computer program is stored, the computer program, when being executed by a processor, implementing the steps of the method for predicting the remaining life of the momentum wheel by fusing empirical data of the remaining life provided in the above embodiment 1.
The foregoing description of the preferred embodiments of the present invention has been included to describe the features of the invention in detail, and is not intended to limit the inventive concepts to the particular forms of the embodiments described, as other modifications and variations within the spirit of the inventive concepts will be protected by this patent. The subject matter of the present disclosure is defined by the claims, not by the detailed description of the embodiments.

Claims (2)

1. The momentum wheel residual life prediction method fused with the residual life empirical data is characterized by comprising the following steps:
s1, determining the residual life empirical data type of the momentum wheel, and setting the life distribution parameters of the momentum wheel
Figure 191387DEST_PATH_IMAGE001
And
Figure 639686DEST_PATH_IMAGE002
determining the pre-test distribution parameters based on the collected residual life empirical data of the momentum wheel and the fitting of the pre-test moment of the momentum wheel;
s1.1 empirical data on the remaining life of a momentum wheel
Figure 685003DEST_PATH_IMAGE003
Remaining life point estimation of time of day
Figure 345791DEST_PATH_IMAGE004
Or/and momentum wheel at confidence level
Figure 691322DEST_PATH_IMAGE005
Remaining life confidence interval
Figure 779364DEST_PATH_IMAGE006
；
S1.2 setting a service life distribution parameter of the momentum wheel
Figure 577555DEST_PATH_IMAGE007
And
Figure 42035DEST_PATH_IMAGE008
the pre-test distribution form is
Figure 976493DEST_PATH_IMAGE009
Wherein
Figure 501015DEST_PATH_IMAGE010
Figure 520923DEST_PATH_IMAGE011
I.e. distribution parameter
Figure 290559DEST_PATH_IMAGE012
And
Figure 79523DEST_PATH_IMAGE013
are independent of each other, and
Figure 774947DEST_PATH_IMAGE014
prior distribution of
Figure 547731DEST_PATH_IMAGE015
In order to be evenly distributed, the water is mixed,
Figure 88433DEST_PATH_IMAGE016
prior distribution of
Figure 997483DEST_PATH_IMAGE017
Is a gamma distribution;
s1.3, determining the moment before the test of the empirical data of the residual life of the momentum wheel based on the collected empirical data of the residual life of the momentum wheel;
if the rest life empirical data of the momentum wheel is that the momentum wheel is in
Figure 863808DEST_PATH_IMAGE018
Remaining life point estimation of time of day
Figure 858309DEST_PATH_IMAGE019
Then the pre-test moment thereof
Figure 202703DEST_PATH_IMAGE020
Is composed of
Figure 231839DEST_PATH_IMAGE021
If the residual life empirical data of the momentum wheel is
Figure 269065DEST_PATH_IMAGE022
Moment momentum wheel at confidence level
Figure 485282DEST_PATH_IMAGE023
Residual life confidence interval of
Figure 400411DEST_PATH_IMAGE024
Then the pre-test moments are respectively
Figure 18474DEST_PATH_IMAGE025
Wherein
Figure 492181DEST_PATH_IMAGE026
In order to be a function of the beta function,
Figure 195695DEST_PATH_IMAGE027
in order to be a super-geometric function,
Figure 881891DEST_PATH_IMAGE028
，
Figure 885619DEST_PATH_IMAGE029
to be distributed uniformly
Figure 264648DEST_PATH_IMAGE030
Extracted by
Figure 455458DEST_PATH_IMAGE031
In a sampleiThe number of the samples is one,
Figure 210924DEST_PATH_IMAGE032
；
s1.4 determining Pre-test distribution parameters
Figure 538000DEST_PATH_IMAGE033
And
Figure 87930DEST_PATH_IMAGE034
；
is provided to collect
Figure 31616DEST_PATH_IMAGE035
Empirical data of the residual life of each momentum wheel is recorded as the momentum wheel
Figure 922316DEST_PATH_IMAGE036
Remaining life point estimation of time of day
Figure 369478DEST_PATH_IMAGE037
Or confidence level
Figure 90309DEST_PATH_IMAGE038
Remaining life confidence interval
Figure 255711DEST_PATH_IMAGE039
Wherein
Figure 352980DEST_PATH_IMAGE040
；
By fitting empirical data of residual life
Figure 920228DEST_PATH_IMAGE041
Or
Figure 546381DEST_PATH_IMAGE042
And the pre-test moment of the empirical data of the residual life of the momentum wheel, and simultaneously introducing a new variable
Figure 199079DEST_PATH_IMAGE043
And
Figure 100039DEST_PATH_IMAGE044
wherein
Figure 256214DEST_PATH_IMAGE045
And
Figure 318848DEST_PATH_IMAGE046
，
Figure 960307DEST_PATH_IMAGE047
and
Figure 399379DEST_PATH_IMAGE048
for any real number, the following unconstrained optimization problem model is constructed:
Figure 675639DEST_PATH_IMAGE049
solving the unconstrained optimization problem model to obtain variables
Figure 174754DEST_PATH_IMAGE050
And
Figure 536465DEST_PATH_IMAGE051
the distribution parameters before test can be determined
Figure 779227DEST_PATH_IMAGE052
And
Figure 909995DEST_PATH_IMAGE053
wherein
Figure 580010DEST_PATH_IMAGE054
The empirical data representative of the remaining life of the momentum wheel is in the form of a point estimate,
Figure 429018DEST_PATH_IMAGE055
the empirical data representing the residual life of the momentum wheel is in the form of a confidence interval;
s2 extraction
Figure 944313DEST_PATH_IMAGE056
The momentum wheel is used as a test sample to carry out a life test, life test sample data of each test sample is collected, and a likelihood function of the life test sample data is given;
random decimation
Figure 195165DEST_PATH_IMAGE056
The momentum wheel is used as a sample to carry out a life test, and the working state of each test sample is observed in the life test; before the observation is stopped, if the test sample cannot work continuously at a certain moment, the moment is the failure time of the test sample; if the observation time is reached, if the test sample can still work, the time is the truncation time of the test sample; the failure time and the tail-cutting time are collectively called as life test sample data and are recorded as
Figure 36082DEST_PATH_IMAGE057
Wherein
Figure 873851DEST_PATH_IMAGE058
，
Figure 458416DEST_PATH_IMAGE059
The representative life test sample data is the failure time,
Figure 563775DEST_PATH_IMAGE060
representing the life test sample data as the tail-cutting time; sample data based on life test
Figure 310014DEST_PATH_IMAGE061
Giving it a likelihood function of
Figure 133614DEST_PATH_IMAGE062
Wherein
Figure 256290DEST_PATH_IMAGE063
And
Figure 216156DEST_PATH_IMAGE064
is a parameter of the distribution of the service life of the momentum wheel,
Figure 398876DEST_PATH_IMAGE065
in order to be a parameter of the shape,
Figure 709771DEST_PATH_IMAGE066
is a scale parameter;
s3, predicting the residual life of the momentum wheel based on a random sampling method;
s3.1 utilization of
Figure 370560DEST_PATH_IMAGE067
Is located at
Figure 450511DEST_PATH_IMAGE068
Random number of
Figure 804132DEST_PATH_IMAGE069
Wherein
Figure 103789DEST_PATH_IMAGE070
Are respectively based on
Figure 568268DEST_PATH_IMAGE071
And
Figure 502726DEST_PATH_IMAGE072
give a sample
Figure 27249DEST_PATH_IMAGE073
And
Figure 312736DEST_PATH_IMAGE074
is regarded as being from
Figure 315327DEST_PATH_IMAGE075
And
Figure 104292DEST_PATH_IMAGE076
the pre-test sample extracted is distributed, wherein
Figure 65295DEST_PATH_IMAGE077
；
S3.2 comparing the pre-test samples based on the likelihood function given in S2
Figure 306920DEST_PATH_IMAGE078
And
Figure 113202DEST_PATH_IMAGE079
updating to generate a post-test sample
Figure 287831DEST_PATH_IMAGE080
And
Figure 384183DEST_PATH_IMAGE081
instant command
Figure 644263DEST_PATH_IMAGE082
And is
Figure 988656DEST_PATH_IMAGE083
Wherein
Figure 17792DEST_PATH_IMAGE084
Is composed of
Figure 789439DEST_PATH_IMAGE085
The random number of (2) is greater than,
Figure 536815DEST_PATH_IMAGE086
，
Figure 950479DEST_PATH_IMAGE087
，
Figure 568542DEST_PATH_IMAGE088
；
s3.3 post-test samples based on post-update
Figure 42249DEST_PATH_IMAGE089
And
Figure 745763DEST_PATH_IMAGE090
prediction of
Figure 431959DEST_PATH_IMAGE091
The residual life of the momentum wheel at the moment after the momentum wheel is fused with the residual life empirical data is as follows:
Figure 937152DEST_PATH_IMAGE092
。
2. the method for predicting the remaining life of a momentum wheel by fusing the empirical data of the remaining life according to claim 1, wherein the collected empirical data of the remaining life of the momentum wheel is in a number
Figure 50601DEST_PATH_IMAGE093
。
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