Satellite random failure type single-machine fault probability calculation method

Abstract

The invention relates to a satellite random failure type single-machine fault probability calculation method. The method comprises a recoverable fault probability calculation step and a resident fault probability calculation step. The recoverable fault probability calculation step is as follows: for each single machine in each sample, the recoverable fault probability of the single machine is calculated respectively; when more than one single machine in the same sample has a recoverable fault, correcting the recoverable fault probability of the single machine by using the common cause factor; and when the single machine is reconstructed, calculating the self-recoverable fault probability of the reconstructed single machine so as to update the self-recoverable fault probability of the single machine. According to the step of calculating the probability of the resident faults, different calculation methods for the probability of the resident faults are selected according to the total number of times of the resident faults occurring in the samples.

Description

Technical Field

[0001] The invention belongs to the technical field of satellite stand-alone risk quantitative assessment, and relates to a method for calculating the probability of satellite-borne random failure stand-alone failure. Background Art

[0002] At present, due to the small sample size of satellite units and the complexity of failure modes, there are still few studies on the failure probability of random failure units in China. In the existing single-unit failure probability assessment methods, on the one hand, no separate calculations are performed according to the single-unit failure type, and on the other hand, the concept of samples is not considered, and different methods need to be selected based on the characteristics of different samples to calculate the failure probability. Summary of the invention

[0003] The technical problem solved by the present invention is: to overcome the shortcomings of the prior art and propose a method for calculating the probability of single-machine failure of satellite random failures. Based on the suppliers and on-orbit baseline data of all single-machine satellites, the probability of single-machine failure is calculated in a quantitative manner.

[0004] The technical solution of the present invention is: a method for calculating the probability of a single-machine failure of a satellite random failure, the method comprising the steps of calculating the probability of a recoverable failure:

[0005] A random failure type single machine refers to a single machine whose life follows a random failure distribution. It may soon experience an on-track fault and fail permanently, or it may operate normally for a long time and far exceed its design life.

[0006] The machines with the same batch, model and supplier are divided into the same sample. On this basis, the existing samples are divided again. As of the current calculation time, the machines that have been worked in the existing samples are divided into the same sample, and the machines that have not been worked are divided into another sample.

[0007] For each single machine in each sample, calculate the probability of single machine recoverable failure;

[0008] When more than one machine in the same sample has experienced recoverable failures up to the current calculation time, the probability of recoverable failures of the machine itself is corrected using the common cause factor;

[0009] When a single machine has been reconstructed up to the current calculation time, the self-recoverable failure probability of the single machine after the reconstruction is calculated to update the self-recoverable failure probability of the single machine.

[0010] Preferably, the method for correcting the probability of recoverable failure of a single machine itself by using the common cause factor is:

[0011] Corrected single machine recoverable failure probability =

[0012] The probability of a single machine's own recoverable failure before correction + β*the sum of the probabilities of other single machines' recoverable failures in the sample to which the single machine belongs

[0013] Among them, β is the common cause factor.

[0014] Preferably, the common cause factor β may have a value between 0.001 and 0.10.

[0015] Preferably, the calculation formula for the probability of a single machine's own recoverable failure is:

[0016]

[0017] In the formula, MTBF is the mean time between failures, and MTTR is the mean time to repair.

[0018] Preferably, the calculation formula for the probability of a single machine's own recoverable failure after reconstruction is:

[0019]

[0020] Where, MTBF 重构后 MTTR is the average trouble-free working time of a single machine after reconstruction 重构后 is the average repair time of a single machine after reconstruction.

[0021] Preferably, the above-mentioned method for calculating the probability of a single-machine failure of a satellite random failure further includes a step of calculating the probability of a resident failure:

[0022] The machines with the same batch, model and supplier are divided into the same sample. On this basis, the existing samples are divided again. As of the current calculation time, the machines that have been worked in the existing samples are divided into the same sample, and the machines that have not been worked are divided into another sample.

[0023] According to the total number of resident faults that occurred in the sample up to the current calculation time, different resident fault probability calculation methods are selected to calculate the reliability distribution R(t) of the single machine in the sample;

[0024] Substitute the running time t0 of each single machine up to the current calculation time into the reliability distribution R(t) of the single machine, and calculate the reliability R(t0) of each single machine up to the current calculation time;

[0025] According to the reliability R(t0) of each single machine as of the current calculation time, the resident failure probability of the single machine as of the current calculation time is calculated.

[0026] Preferably, when the total number of resident faults that have occurred in all single machines in the sample up to the current calculation time is 0, the single machine reliability distribution R(t) is calculated using a zero-failure small sample analysis model;

[0027] When the total number of resident faults that have occurred in all single machines in the sample up to the current calculation time is 1-2, the timed truncation model is used to calculate the single machine reliability distribution R(t);

[0028] When the cumulative number of permanent failures of all single machines in the sample as of the current calculation time is greater than or equal to 3, the non-parametric estimation model is used to calculate the single machine reliability distribution R(t);

[0029] Preferably, the resident failure probability of a single machine as of the current calculation time is:

[0030] 1-R(t0).

[0031] Considering the impact of reconstruction on a single machine, after calculating the resident failure probability of a single machine, the resident failure probability of a single machine is corrected using the correction coefficient λ1. The corrected resident failure probability of a single machine is:

[0032] λ1(1-R(t0))

[0033] Among them, λ1 is the correction coefficient.

[0034] When no reconstruction occurs on a single machine, λ1=1; when reconstruction can effectively solve or improve the working condition of the single machine on orbit, the correction coefficient λ1 is 0.5~1; when the reconstruction scheme worsens the working condition of the specified single machine or increases the load, the correction coefficient λ1 takes a value of 1~1.5.

[0035] The beneficial effects of the present invention compared with the prior art are:

[0036] (1) The present invention comprehensively utilizes the supplier of a single machine and the on-orbit baseline data to classify samples, which can comprehensively consider the impact of different single machines on the samples, express the risk impact surface in a quantitative manner, and realize data fusion.

[0037] (2) The present invention selects different methods to calculate the failure probability according to the characteristics of different samples, thereby avoiding the problem that some special samples cannot be calculated and solving the problem that the reliability of products cannot be evaluated under very little failure data or no failure data. BRIEF DESCRIPTION OF THE DRAWINGS

[0038] Figure 1 This is the calculation process of the probability of single-machine failure due to random failure.

[0039] Figure 2 The non-parametric estimation of the sample single machine reliability changes over time in the embodiment of the present invention;

[0040] Figure 3 This is a non-parametric estimation of the single-machine reliability fitting curve in an embodiment of the present invention. DETAILED DESCRIPTION

[0041] The present invention will be further described below in conjunction with the embodiments.

[0042] Random failure type single machine refers to a single machine whose life follows the random failure distribution. It may soon fail on track and fail permanently, or it may operate normally for a long time and far exceed the design life. The failure probability of random failure type single machine is divided into recoverable failure probability and permanent failure probability.

[0043] 1. Single Machine Sample Classification

[0044] According to the failure mechanism of a single machine, after completing the classification of a single machine, it is necessary to divide the sample range of the single machine of the same failure type. The specific division steps are as follows:

[0045] 1) According to the machine name, machines with the same name are divided into the same sample;

[0046] 2) Based on the above samples, according to the supplier data, the single machines with the same name and the same supplier name are divided into the same sample;

[0047] 3) Based on the samples divided in the first two steps, the existing samples are divided again. As of the current calculation time, the single machines that have worked in the existing samples are divided into the same sample, and the single machines that have not worked are divided into another sample.

[0048] 2. Calculation Method of Recoverable Failure Probability

[0049] like Figure 1 As shown, for each single machine in each sample, the probability of single machine recoverable failure is calculated separately; when more than one single machine in the same sample has experienced recoverable failures up to the current calculation time, the common cause factor is used to correct the probability of single machine recoverable failure; when a single machine has been reconstructed up to the current calculation time, the probability of self-recoverable failure of the reconstructed single machine is calculated to update the probability of self-recoverable failure of the single machine. The specific calculation method is as follows:

[0050] 1) According to the recoverable fault data of random failure units, the availability of each unit during on-orbit operation is calculated and used as the probability of recoverable failure of the unit itself. Therefore, the calculation formula for the probability of recoverable failure of the unit itself is:

[0051]

[0052] In the formula, MTBF is the mean time between failures, and MTTR is the mean time to repair.

[0053] 2) Correction of single-machine recoverable failure probability considering reconstruction

[0054] If a single machine has a recoverable failure again after reconstruction as of the current calculation time, the probability of recoverable failure of the single machine itself needs to be corrected. The calculation formula is as follows:

[0055]

[0056] Where, MTBF 重构后 MTTR is the average trouble-free working time after the single machine is rebuilt 重构后 It is the average repair time after a single machine is rebuilt.

[0057] If no quality problems occur on a single machine after reconstruction up to the current calculation time, the probability of recoverable failure of the single machine is corrected to 0 (MTTR 重构后 is 0).

[0058] 3) Probability of single machine recoverable failure considering common causes

[0059] In the same sample, single machines with the same structure and working environment often have common cause failures. Therefore, for the probability of recoverable failure of a single machine, the common cause failure part must be comprehensively considered, and the common cause factor must be used to make corrections based on the divided sample results.

[0060] The method of using common cause factors to correct the probability of recoverable failure of a single machine is as follows:

[0061] Corrected single machine recoverable failure probability =

[0062] The probability of a single machine's own recoverable failure before correction + β*the sum of the probabilities of other single machines' recoverable failures in the sample to which the single machine belongs. β is the common cause factor, which is 0.001-0.01 based on expert experience.

[0063] Preferably, the single machine type and sample situation can be further considered, and the β value is as follows.

[0064]

[0065] Similarly, taking into account the common cause failures, the probability of a single machine's own recoverable failure after reconstruction can be substituted into the probability of a single machine's own recoverable failure before correction to calculate the probability of a single machine's own recoverable failure considering common causes.

[0066] 3. Calculation method of resident failure probability

[0067] The probability of resident failure is mainly calculated based on the resident failures in the quality problem combined with the on-orbit baseline and supplier data. Based on the division of samples according to supplier information and working status, the actual number of resident failures in different samples is different, so the analysis methods used are different. The on-orbit baseline refers to the current on-orbit operation status of the satellite at the time of calculation.

[0068] The machines with the same batch, model and supplier are divided into the same sample. On this basis, the existing samples are divided again. As of the current calculation time, the machines that have been worked in the existing samples are divided into the same sample, and the machines that have not been worked are divided into another sample.

[0069] According to the total number of resident faults that occurred in the sample up to the current calculation time, different resident fault probability calculation methods are selected:

[0070] When the total number of resident faults that have occurred in all single machines in the sample up to the current calculation time is 0, the reliability distribution R(t) is calculated using the zero-failure small sample analysis model;

[0071] When the total number of resident faults that have occurred in all single machines in the sample up to the current calculation time is 1-2, the timed truncation model is used to calculate the single machine reliability distribution R(t);

[0072] When the cumulative number of resident failures of all single machines in the sample as of the current calculation time is greater than or equal to 3, the non-parametric estimation model is used to calculate the single machine reliability distribution R(t).

[0073] According to the reliability R(t0) of each single machine up to the current calculation time, the resident failure probability of the single machine up to the current calculation time is calculated.

[0074] 1) Calculate the probability of permanent failure using the zero-failure data analysis model

[0075] If no permanent faults have occurred in all the single machines in the sample up to the current calculation time, it can be regarded as a small sample with no failure. The structure of the no-failure data is shown in the following table.

[0076] Table 1. Data structure of small sample without failure

[0077] Group number i Truncation time T The number of samples in the i-th group n Number of unfailed 1 <![CDATA[T1]]> <![CDATA[n1]]> <![CDATA[S1]]> 2 <![CDATA[T2]]> <![CDATA[n2]]> <![CDATA[S2]]> 3 … … … 4 T n S

[0078] According to the definition of the multi-layer Bayes method and the Bayes theorem, under square loss, the failure probability p of a single machine in the i-th group of samples is ihB The calculation of is as follows:

[0079]

[0080] In the formula, S i is the number of non-failures in the i-th group of samples, c is the hyperparameter engineering recommended value of 5, and the failure probability p of a single machine in the i-th group of samples can be obtained according to the above formula ihB Estimated value.

[0081] According to the weighted least squares estimation method, the Weibull double parameter estimation values ​​of shape parameter β and life parameter η are obtained as follows:

[0082]

[0083] η=expμ

[0084] Where:

[0085]

[0086] Where:

[0087]

[0088] Where ω i is the weight value, T i is the censoring time of the i-th group, k is the number of samples, n i is the number of single machines in the i-th group of samples.

[0089] x i and i The formula is as follows:

[0090]

[0091] Where p ihB is the failure probability of a single machine in the i-th group of samples, T i is the censoring time of group i.

[0092] Substituting the obtained Weibull parameter point estimate into the reliability formula, we can get the reliability R of the original sample that obeys the Weibull sampling function. 无失效 (t), as follows:

[0093]

[0094] Substituting the running time t0 of the single machine up to the current calculation time, we can get the resident failure probability of the single machine under this sample as 1-R 无失效 (t0).

[0095] 2) Calculation of resident fault probability using the time-truncation model

[0096] For single machine samples that have experienced less than three times and more than zero resident faults up to the current calculation time, the timed truncation test method can be used to calculate the reliability distribution parameters and further obtain the resident fault probability.

[0097] According to the reliability index model R = e -λt , parameter θ is the mean failure time, which is the inverse of the failure rate λ, and the formula is as follows:

[0098]

[0099] Where, T ris the sum of the running time of all the machines in the sample, and r is the sum of the number of resident faults that occur in the sample.

[0100] Combined with the reliability function, it is as follows:

[0101]

[0102] Substituting the running time t0 of a single machine up to the current calculation time into the above formula, we can obtain the probability of a single machine with no resident faults in the sample as 1-R 定时截尾 (t0).

[0103] 3) Non-parametric estimation model to calculate the probability of permanent failure

[0104] For single machine samples that have experienced more than three resident faults up to the current calculation time, the reliability distribution parameters can be calculated using non-parametric estimation methods, and the resident fault probability can be further obtained.

[0105] The total number of samples is N, the number of failed (abnormal) samples is n, and the number of truncated test samples is Nn. Using the failure / abnormal information of the single machine sample, calculate the reliability of 1, 2, ..., n failed (abnormal) machines.

[0106] The reliability of one failed unit is:

[0107] The reliability of failed 2 units is:

[0108] …

[0109] The reliability of n failed units is:

[0110] The nonparametric estimated single machine reliability probability is expressed in terms of operating time (days), and the curve is fitted using Weibull distribution to calculate the shape parameter β′ and life parameter η′ of the nonparametric estimated Weibull distribution. The results of the nonparametric analysis of the sample single machine are logarithmized twice and the minimum variance fitting is performed.

[0111] Through fitting, the slope of the straight line is a and the intercept is b, so the shape parameter β′ and life parameter η′ of the Weibull distribution of non-parametric estimation can be obtained:

[0112] β′=a

[0113]

[0114] The reliability calculation formula is as follows:

[0115]

[0116] Substituting the running time t0 of a single machine up to the current calculation time into the above formula, we can obtain the probability of a single machine with no resident faults in the sample as 1-R 非参数估计 (t0).

[0117] Considering the impact of reconstruction on a single machine, a correction factor is added to the calculation result of the resident fault probability. The calculation formula for the resident fault of a single machine with random failure is as follows:

[0118] λ1(1-R(t0))

[0119] When the reconstruction scheme can effectively solve or improve the working condition of a single machine on orbit, the correction coefficient λ1 takes a value of 0.5 to 1; when the reconstruction scheme is irrelevant to the single machine, λ1=1; when the reconstruction scheme worsens the working condition of the specified single machine or increases the load, the correction coefficient λ1 takes a value of 1 to 1.5.

[0120] Example

[0121] (1) Calculation of small sample analysis model without failure

[0122] Assume that there are 10 stand-alone machines in a sample, with the machine codes 1-10. No permanent faults have occurred in all of them so far. They can be regarded as a small sample with no failures. The structure of the no-failure data is shown in the following table.

[0123] Table 1 Data structure

[0124] Group number i Censorship time Ti The number of samples in the i-th group ni Number of unfailed 1 1000 2 10 2 1050 2 8 3 1200 2 6 4 1400 2 4 5 1500 2 2

[0125] According to the definition of the multi-layer Bayes method and the Bayes theorem, the multi-layer failure probability p of a single machine in the i-th group of samples can be obtained under square loss: ihB , as shown in Table 3. The hyperparameter c is set to the engineering recommended value of 5.

[0126]

[0127] Table 2 Failure probability calculation results

[0128] Group number i <![CDATA[p ihB ]]> 1 0.070068967 2 0.081696981 3 0.098087158 4 0.123104617 5 0.166932032

[0129] Table 4 Calculation results of weight values ​​and other intermediate values

[0130] Group number i <![CDATA[ω i ]]> <![CDATA[x i ]]> <![CDATA[y i ]]> 1 0.162601626 -2.622172724 6.907755279 2 0.170731707 -2.462426946 6.956545443 3 0.195121951 -2.270724177 7.090076836 4 0.227642276 -2.029755904 7.244227516 5 0.243902439 -1.700238025 7.313220387

[0131] According to the above results, the values ​​of A, B, C, and D are as follows:

[0132]

[0133] From this we can get

[0134]

[0135] The Weibull double parameter estimates β and η are obtained as follows:

[0136]

[0137] η=expμ=3421.53434

[0138] Substituting the obtained Weibull parameter estimate into the reliability formula, we can get the reliability R of the original sample that obeys the Weibull sampling function. 无失效 (t), as follows:

[0139]

[0140] Substituting the running time t0 of the single machine up to the current calculation time, the resident failure probability of the single machine under this sample can be obtained.

[0141] (2) Timed truncation model calculation

[0142] Assume that there are 20 stand-alone machines in a sample, with machine codes 1-20. Only stand-alone machine 2 has a permanent fault after running for 1020 hours. The rest of the stand-alone machines are still running normally. The data information is shown in the following table:

[0143] Table 5. Data structure of timed censored samples

[0144]

[0145]

[0146] The value of θ is obtained as follows:

[0147]

[0148] Combined with the reliability function, it is as follows:

[0149]

[0150] Substituting the running time t0 of the single machine up to the current calculation time into the above formula, the resident failure probability of the other single machines in the sample except single machine 2 can be obtained.

[0151] (3) Nonparametric estimation calculation

[0152] Assume that a sample contains 60 stand-alone machines, 5 of which have permanent faults. The fault information is shown in the following table.

[0153] Table 6 Reliability calculation of failed single machine

[0154] Machine name Running time when resident fault occurs Single machine 1 416 Standalone 2 428 Standalone 3 435 Standalone 4 440 Standalone 5 469

[0155] Using the failure / abnormal information of individual machines in the sample, calculate the reliability of 1, 2, 3, 4, and 5 failures (abnormalities) of individual machines.

[0156] Table 7 Reliability calculation of failed single machine

[0157]

[0158]

[0159] The probability of a single machine estimated by nonparametric estimation is expressed by the running time (days), such as Figure 2 shown.

[0160] The above curve is fitted using Weibull, and the shape and life parameters of the Weibull distribution are calculated. The results of the nonparametric analysis of the two-floating gyro are logarithmic twice and fitted with the minimum variance. The fitting results are shown in Figure 3 shown.

[0161] By calculation, the slope of the straight line of the nonparametric estimation sample single machine fitting is 13.051, and the intercept is -82.466, so the shape parameter β′ and life parameter η′ of the nonparametric estimation Weibull distribution can be obtained:

[0162] β′=13.051, η′=554.88

[0163] The reliability calculation formula of this nonparametric estimation sample is as follows:

[0164]

[0165] Substituting the running time t0 of a single machine up to the current calculation time into the above formula, the resident failure probability of a single machine in which no resident failure occurs in the sample can be obtained.

[0166] Although the present invention has been disclosed as above in the form of a preferred embodiment, it is not intended to limit the present invention. Any person skilled in the art may make possible changes and modifications to the technical solution of the present invention by using the methods and technical contents disclosed above without departing from the spirit and scope of the present invention. Therefore, any simple modifications, equivalent changes and modifications made to the above embodiments based on the technical essence of the present invention without departing from the content of the technical solution of the present invention shall fall within the protection scope of the technical solution of the present invention.

Claims

1. A method for calculating the probability of a single satellite failure due to random failure, characterized in that The calculation steps of recoverable failure probability are as follows: The machines with the same batch, model and supplier are divided into the same sample. On this basis, the existing samples are divided again. As of the current calculation time, the machines that have been worked in the existing samples are divided into the same sample, and the machines that have not been worked are divided into another sample. For each single machine in each sample, calculate the probability of single machine recoverable failure; When more than one machine in the same sample has experienced recoverable failures up to the current calculation time, the probability of recoverable failures of the machine itself is corrected using the common cause factor; When a single machine has been reconstructed up to the current calculation time, the self-recoverable failure probability of the single machine after the reconstruction is calculated to update the self-recoverable failure probability of the single machine.

2. The method for calculating the probability of a single satellite random failure according to claim 1 is characterized in that: The method of using common cause factors to correct the probability of recoverable failure of a single machine is as follows: Corrected single machine recoverable failure probability = The probability of a single machine's own recoverable failure before correction + β*the sum of the probabilities of other single machines' recoverable failures in the sample to which the single machine belongs Among them, β is the common cause factor.

3. The method for calculating the probability of a single satellite random failure according to claim 2 is characterized in that: The value of the common cause factor β is between 0.001 and 0.

10.

4. The method for calculating the probability of a single satellite random failure according to claim 1 is characterized in that: The calculation formula for the probability of a single machine's self-recoverable failure is: In the formula, MTBF is the mean time between failures, and MTTR is the mean time to repair.

5. The method for calculating the probability of a single satellite random failure according to claim 1 is characterized in that: The calculation formula for the probability of a single machine's own recoverable failure after reconstruction is: Where, MTBF 重构后 MTTR is the average trouble-free working time of a single machine after reconstruction 重构后 is the average repair time of a single machine after reconstruction.

6. The method for calculating the probability of a single satellite failure due to random failure according to claim 1 is characterized in that It also includes the steps for calculating the probability of resident failure: The machines with the same batch, model and supplier are divided into the same sample. On this basis, the existing samples are divided again. As of the current calculation time, the machines that have been worked in the existing samples are divided into the same sample, and the machines that have not been worked are divided into another sample. According to the total number of resident faults that occurred in the sample up to the current calculation time, different resident fault probability calculation methods are selected to calculate the reliability distribution of the machines in the sample; Substitute the running time t0 of each single machine up to the current calculation time into the reliability distribution R(t) of the single machine, and calculate the reliability R(t0) of each single machine up to the current calculation time.

7. The method for calculating the probability of a single satellite random failure according to claim 6 is characterized in that: The probability of resident failure of a single machine as of the current calculation time is: 1-R(t0).

8. The method for calculating the probability of a single satellite random failure according to claim 6 is characterized by: Considering the impact of single-machine reconstruction, the corrected resident failure probability of a single machine is: λ1(1-R(t0)) Among them, λ1 is the correction coefficient.

9. The method for calculating the probability of a single satellite random failure according to claim 6 is characterized by: When no reconstruction occurs on a single machine, λ1=1; when reconstruction can effectively solve or improve the working condition of the single machine on orbit, the correction coefficient λ1 is 0.5~1; when the reconstruction scheme worsens the working condition of the specified single machine or increases the load, the correction coefficient λ1 takes a value of 1~1.

5.

10. A method for calculating the probability of a single satellite random failure according to any one of claims 6 to 9, characterized in that: When the total number of resident faults that have occurred in all single machines in the sample up to the current calculation time is 0, the single machine reliability distribution R(t) is calculated using the zero-failure small sample analysis model; When the total number of resident faults that have occurred in all single machines in the sample up to the current calculation time is 1-2, the timed truncation model is used to calculate the single machine reliability distribution R(t); When the cumulative number of resident failures of all single machines in the sample as of the current calculation time is greater than or equal to 3, the non-parametric estimation model is used to calculate the single machine reliability distribution R(t).

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