A reliability evaluation method for multi-engine synchronization of liquid rocket engines

Abstract

The present invention discloses a method for evaluating the reliability of multi-engine synchronization of a liquid rocket engine. Aiming at the reliability index requirements of multi-engine synchronization of a liquid rocket engine, by means of the Monte Carlo simulation algorithm, without restricting the distribution type of performance parameters under the condition of ensuring the calculation accuracy, it is applicable to the reliability evaluation of multi-engine synchronization with various distribution type parameters, which can expand the applicable scope of the method; at the same time, it can simplify the calculation process and improve the efficiency of multi-engine synchronization reliability evaluation. Starting from the principle of reliability interval estimation, no approximate algorithm is adopted in the whole calculation process, and the calculation accuracy requirements can be guaranteed under the condition of sufficient sampling simulation times.

Description

Technical Field

[0001] The present invention belongs to the technical field of aerospace quality and reliability, and particularly relates to a method for evaluating the reliability of multi-engine synchronization of liquid rocket engines. Background Technique

[0002] China's liquid launch vehicles generally consist of multiple engines in parallel. For example, the core first stage of the Long March 3 launch vehicle is composed of four engines in parallel. During the flight process, the 4 engines work simultaneously. Affected by factors such as production and processing deviations and engine combustion characteristics, the performance of each engine has certain differences. If the deviation values of each engine are too large, it will affect the flight mission of the launch vehicle and make it difficult to control the attitude of the launch vehicle.

[0003] To ensure the stable flight attitude of the launch vehicle, there are certain requirements for the performance deviation of the engine, such as a thrust of 500 kN ± 10 kN. Due to the certain uncertainty of the performance deviation of each engine, based on the performance deviation requirements, there are also requirements for the synchronization reliability of multiple engines working in parallel. For example, the multi-engine synchronization reliability of a certain type of launch vehicle engine is not less than 0.99 (evaluated at a 0.7 confidence level).

[0004] At present, for the multi-engine synchronization reliability index, the engine development unit has relevant standard methods. These standards were formulated in the 1990s. The standards use analytical methods for statistical inference. When conducting the evaluation of multi-engine synchronization reliability, it is necessary to calculate multiple intermediate variables, query multiple statistical data tables provided by the standards, and when there is no corresponding data in the tables, it is also necessary to use the interpolation method for linear interpolation, which affects the accuracy of the evaluation results, and the calculation efficiency of this method is low and the operation difficulty is large. In addition, this method is only applicable to the reliability evaluation where the performance parameters follow a normal distribution. If the corresponding performance parameters do not follow a normal distribution, this standard is no longer applicable. Summary of the Invention

[0005] In view of this, the purpose of the present invention is to provide a method for evaluating the reliability of multi-engine synchronization of liquid rocket engines, which is applicable to the reliability evaluation of multi-engine synchronization with various distribution type parameters under the condition of ensuring the calculation accuracy.

[0006] A method for evaluating the reliability of multi-engine synchronization of liquid rocket engines includes the following steps:

[0007] Step 1), according to the requirements of the multi-engine synchronization reliability index of the liquid rocket engine, collect the measured value data of the engine's performance parameters, and based on the measured value data of the performance parameters, conduct statistical inference to judge the probability distribution type of the data;

[0008] Step 2), based on the measured value data of the engine's performance parameters, calculate the distribution parameters of the probability distribution to obtain the probability density function of the key performance parameters of the engine;

[0009] Step 3), determine the number of cycles M1;

[0010] Step 4), determine the number of reliability evaluation simulations M2;

[0011] Step 5), for each simulation, generate a random number r consistent with the number N of multiple machines according to the probability density function j ; j = 1, 2, …, M2;

[0012] Step 6), for each simulation, calculate the maximum deviation:

[0013] Dev(j) = max(r j ) - min(r i )

[0014] where, max(r j ) and min(r j ) respectively represent the maximum and minimum values in r j ;

[0015] Step 7), determine whether the maximum deviation value Dev(j) is greater than the upper limit of the maximum deviation required for multi-machine synchronization. If it is greater, the result of the jth simulation is recorded as a failure, and the failure count fail is incremented by one; otherwise, it is recorded as a success, and the success count succ is incremented by one;

[0016] Step 8), repeat steps 5) to 7) M2 times, and calculate the success count succ and the failure count fail;

[0017] Step 9), based on the success count succ and the failure count fail, conduct a reliability estimation of multi-machine synchronization and calculate the reliability:

[0018]

[0019] In the formula, R i is the reliability calculated in the ith cycle;

[0020] Step 10), repeat steps 5) to 10) a total of M1 times, corresponding to obtaining M1 reliabilities. Sort the calculated M1 reliabilities in descending order, and take the reliability R K with the serial number K = M1 × γ as the reliability R L with a confidence lower limit of γ; γ is the set confidence lower limit;

[0021] Evaluate the multi-machine synchronization reliability of the liquid rocket engine according to the reliability R L .

[0022] Preferably, in step 1), the log-likelihood value is obtained for common probability distribution types based on the measured performance parameter data, and the probability distribution type with the minimum log-likelihood value is selected as the probability distribution type corresponding to the measured performance parameter data.

[0023] Preferably, in step 1), the log-likelihood value is obtained for common probability distribution types based on the measured performance parameter data, and the probability distribution type with the minimum log-likelihood value is selected for hypothesis testing. If the null hypothesis is accepted, the set of data follows the previously determined probability distribution type; if the null hypothesis is rejected, the probability distribution type with the second smallest log-likelihood value is selected and hypothesis testing is performed. If the hypothesis test is accepted, it belongs to the probability distribution type with the second smallest log-likelihood value; and so on until the belonging distribution type is found.

[0024] Preferably, in step 1), when the probability distribution type is a normal distribution, the Jarque-Bera method is used for hypothesis testing.

[0025] Preferably, in step 3), the method for determining the number of cycles M1 is as follows: ensure that the product of the set confidence lower limit γ and the number of cycles M1 is an integer and a multiple of 10. The M1 value that satisfies this condition is then expanded by 10 times, which is the final number of cycles M1.

[0026] Preferably, in step 5), the inverse function method is used to generate random numbers.

[0027] Preferably, the set confidence lower limit γ is selected as 70%.

[0028] The present invention has the following beneficial effects:

[0029] Aiming at the reliability index requirements of multi-engine synchronization of liquid rocket engines, the present invention proposes a reliability evaluation method for multi-engine synchronization of liquid rocket engines by means of the Monte Carlo simulation algorithm. Without restricting the distribution type of performance parameters, it is applicable to the reliability evaluation of multi-engine synchronization with various distribution type parameters, which can expand the applicable range of the method; at the same time, it can simplify the calculation process and improve the efficiency of multi-engine synchronization reliability evaluation. Starting from the principle of reliability interval estimation, no approximate algorithm is used in the whole calculation process, and the calculation accuracy requirements can be guaranteed under the condition of sufficient sampling simulation times. BRIEF DESCRIPTION OF THE DRAWINGS

[0030] Figure 1 It is a flowchart of the reliability evaluation method for multi-engine synchronization of liquid rocket engines of the present invention. DETAILED DESCRIPTION OF THE INVENTION

[0031] The following examples are given in conjunction with the drawings to describe the present invention in detail.

[0032] Aiming at the requirements of the multi-engine synchronization reliability of liquid rocket engines, a reliability evaluation method based on numerical simulation is proposed for the multi-engine synchronization reliability evaluation of liquid rocket engines.

[0033] The general form of the multi-engine synchronization reliability index is: when N engines work simultaneously, the probability that the maximum deviation of a certain key performance parameter (usually thrust) does not exceed K is not less than R.

[0034] To evaluate the multi-engine synchronization reliability, a reliability evaluation method is proposed. The implementation process of the multi-engine synchronization reliability evaluation is as Figure 1 shown, and the specific implementation process is as follows:

[0035] 1) Data collection and statistical inference

[0036] Aiming at the requirements of the multi-engine synchronization reliability index, collect the measured values of the performance parameters of each engine [x1, x2, …, x n , where n represents the number of samples.

[0037] For the collected data of the measured values of the performance parameters, conduct statistical inference. Through the goodness-of-fit test, judge the probability distribution type of the data. The commonly used probability distribution types include: normal distribution, lognormal distribution, inverse Gaussian distribution, Weibull distribution, exponential distribution, Beta distribution, Gamma distribution, Poisson distribution, extreme value distribution, generalized extreme value distribution, burr distribution, t-distribution, etc. According to the magnitude of the log-likelihood value, judge which probability distribution is more suitable for the engine performance data. The smaller the log-likelihood value, the higher the goodness of fit, and select the probability distribution type with the smallest log-likelihood value.

[0038] Taking the normal distribution as an example, use the Jarque-Bera method to test whether the data follows the normal distribution.

[0039]

[0040] In the formula, n represents the number of test samples; S represents the sample skewness; K represents the sample kurtosis.

[0041] JB ∼ χ 2 (2)

[0042] JB approximately follows the chi-square distribution with 2 degrees of freedom, and the significance level of the hypothesis test is usually taken as 0.05.

[0043] The null hypothesis is S = 0 and K = 3. Through hypothesis testing, if the null hypothesis is accepted, then this set of data follows a normal distribution; if the null hypothesis is rejected, then this set of data does not follow a normal distribution. Then select the probability distribution type with the second smallest log-likelihood value and conduct hypothesis testing, but the prerequisite is that if there is a corresponding hypothesis testing method for this distribution type, if the hypothesis test is accepted, then it belongs to the probability distribution type with the second smallest log-likelihood value; and so on until the belonging distribution type is found.

[0044] 2) Distribution parameter calculation

[0045] According to the classification type and the collected experimental data, methods such as maximum likelihood estimation and least squares method are used to calculate the distribution parameters of the probability distribution. As shown in Table 1, the probability density function f(·) of the key performance parameters of the engine is obtained.

[0046] Table 1 Probability distribution type and distribution parameter table

[0047] Serial number Probability distribution type Distribution parameter 1. Normal distribution Mean μ, standard deviation σ 2. Log-normal distribution Mean μ, standard deviation σ 3. Inverse Gaussian distribution Shape parameter m, scale parameter η 4. Weibull distribution Shape parameter m, scale parameter η 5. Exponential distribution Mean λ 6. Beta distribution Shape parameter m, scale parameter η 7. Gamma distribution Shape parameter m, scale parameter η 8. Poisson distribution Mean λ 9. Extreme value distribution Location parameter b, scale parameter η 10. Generalized extreme value distribution Shape parameter m, scale parameter η, location parameter b 11. Burr distribution First shape parameter m1, second shape parameter m2, scale parameter η 12. t-distribution Location parameter b, scale parameter η, degrees of freedom a

[0048] Taking the normal distribution as an example, when the data follows a normal distribution after passing the Jarque - Bera test, calculate the distribution parameters of the normal distribution, that is, the mean and standard deviation. The calculation method is:

[0049]

[0050]

[0051] where x i is the size of the performance parameter of the i-th sample; μ is the sample mean; σ is the sample standard deviation.

[0052] 3) Determine the number of cycles M1

[0053] To measure the uncertainty in reliability assessment, conduct reliability interval estimation and conduct reliability simulation assessment in cycles. For the determination of the number of simulation times, on the one hand, it should be ensured that the product of the confidence lower limit γ and the number of cycles M1 is an integer and a multiple of 10; on the other hand, to ensure the accuracy of the uncertainty measurement, under the condition that the product of the confidence lower limit γ and the number of cycles M1 is an integer, it should be one order of magnitude higher.

[0054] For example, if the confidence lower limit γ required for reliability assessment is 0.7, then the number of cycles is 10 times, that is, it satisfies that the product of the confidence lower limit γ and the number of cycles M1 is an integer and a multiple of 10. One order of magnitude higher is 100 times.

[0055] The more the number of cycles, the more accurate the uncertainty measurement in reliability assessment, but the longer the calculation time. To balance the calculation accuracy and calculation speed, the number of cycles is generally set to 100 times.

[0056] 4) Determine the number of simulation times M2 for reliability assessment

[0057] Determine the number of simulation times according to the requirements of the multi - machine synchronization reliability index. Generally, the requirements for the number of simulation times are as follows:

[0058]

[0059] Where M2 is the number of simulation times and R is the required reliability value.

[0060] For the convenience of subsequent statistics, the number of simulation times is generally set to an integer multiple of 10. For example, if the required value of the system reliability index is 0.99, the number of simulation times should be at least 10,000 times. The more simulation times, the more accurate the calculation result, but the longer the simulation calculation time.

[0061] 5) Generate random numbers

[0062] According to the number of multi - machines N in the requirements of the multi - machine synchronization reliability index, determine the number of random numbers N to be generated, and then according to the probability density function f(·) fitted by the performance parameter measurement values [x1, x2, …, x n , use the inverse function method to generate random numbers r j = [r j1 , r j2 , …, r jN . r j represents the random number generated in the i - th simulation.

[0063] 6) Calculate the maximum deviation of a single sampling

[0064] Dev(j) = max(r j ) - min(r j )

[0065] Where max(r j ) and min(r j ) represent the maximum value and the minimum value in r j respectively;

[0066] 7) Judge whether the maximum deviation of a single sampling exceeds the tolerance

[0067] Judge whether the maximum deviation value of the i - th sampling is greater than the upper limit of the maximum deviation required for multi - machine synchronization. If it is greater, the result of the i - th sampling is recorded as a failure, and the failure number fail is accumulated once; otherwise, it is recorded as a success, and the success number succ is accumulated once.

[0068] 8) Repeat sampling

[0069] Repeat steps 5) to 7) M2 times, and calculate the success number succ and the failure number fail.

[0070] 9) Reliability calculation for a single cycle

[0071] Based on the number of successes succ and the number of failures fail, perform multi-engine synchronous reliability estimation and calculate the reliability:

[0072]

[0073] where R i is the reliability calculated for the i-th cycle.

[0074] 10) Calculation of the lower confidence limit of reliability

[0075] Repeat steps 5) - 10) for a total of M1 times. Correspondingly, obtain M1 reliabilities. Sort the M1 calculated reliabilities in descending order. Denote the serial number of the sorted reliability as K, and take the R K value with the serial number K = M1×γ in the sorted order as the reliability R L with a confidence lower limit of γ (i.e., ensuring that 70% of the reliability calculation values are greater than R L , Pr(R≥R L ) = γ).

[0076] Example:

[0077] The rated thrust of a certain liquid rocket engine is 100N. A certain launch vehicle needs to install 4 liquid rocket engines of the same model. According to the flight attitude control requirements of the launch vehicle, the thrust synchronization reliability requirement for the 4 engines is proposed as follows: The probability that the thrust deviation of the 4 engines does not exceed 10% is not less than 0.98 (evaluated at a confidence level of 0.7).

[0078] According to the multi-engine synchronous reliability index requirements, collect the engine thrust data, and use the method of this patent to evaluate the multi-engine synchronous reliability of the engine and determine whether the reliability index requirements are met.

[0079] 1) Data collection and statistical inference

[0080] Collect the thrust measurement values of 20 engine samples, as shown in Table 2 respectively.

[0081] Table 2 Thrust measurement values of a certain type of engine

[0082]

[0083]

[0084] According to the above thrust test data, conduct a distribution test, as shown in Table 3.

[0085] Table 3 Selection results of the distribution type of engine thrust data

[0086] Serial number Probability distribution type Log-likelihood value 1. Normal distribution -44.70 2. Log-normal distribution -44.72 3. Inverse Gaussian distribution -44.71 4. Weibull distribution -45.02 5. Exponential distribution -112.19 6. Beta distribution — 7. Gamma distribution -44.70 8. Poisson distribution — 9. Extreme value distribution -45.10 10. Generalized extreme value distribution -44.16 11. Burr distribution — 12. t-distribution —

[0087] As can be seen from the above calculations, the thrust data of 20 engines are more compliant with the normal distribution and the Gamma distribution. In addition, through the Jarque-Bera method for hypothesis testing, it is calculated that: JB = 1.37, which is less than the statistic 3.80, so the original hypothesis is accepted, indicating that the above data follows the normal distribution.

[0088] 2) Calculation of distribution parameters

[0089] According to the calculation method of the distribution parameters of the normal distribution, the distribution parameters of the engine thrust distribution are calculated as follows:

[0090] μ = 100.43 N

[0091] σ = 2.32

[0092] 3) Determine the number of cycles M1

[0093] According to the reliability index requirement, γ = 0.7, and according to the requirement for setting the number of cycles, M1 = 100 is taken.

[0094] 4) Determine the number of simulation times M2 for reliability assessment

[0095] According to the requirement of the multi-machine synchronous reliability index of 0.98, it is determined that the number of simulation times is not less than 10,000 times. To make the calculation results more accurate, the number of simulation times is determined to be 1×10 6 times.

[0096] 5) Generate random numbers

[0097] According to the probability density function of the normal distribution, the inverse function method is used to generate random numbers. The specific method is as follows:

[0098] X' = μ + σX

[0099]

[0100] where Ui represents a random number in [0,1]; X represents a normal distribution N(0,1) with a mean of 0 and a standard deviation of 1; X' represents a normal distribution N(μ,σ) with a mean of μ and a standard deviation of σ.

[0101] 6) Simulation calculation

[0102] Among the 4 random numbers generated in each simulation, calculate the maximum thrust deviation, and then determine whether the single maximum deviation exceeds 10 N. If it exceeds, it is recorded as a failure subsample, fail + 1; if it is less than 10 N, it is recorded as a successful subsample, succ + 1.

[0103] 7) Calculation of the reliability of a single cycle

[0104] For example, in the 5th simulation calculation, through 1×10 6 samplings, the statistics show that fail = 12120 and succ = 987880.

[0105]

[0106] 8) Calculation of the lower confidence limit of reliability

[0107] After 100 cycles, 100 Rs are calculated, sorted in descending order, and the value at the 70th position in the sorting is taken as R L = 0.987953.

[0108] 9) Conclusion

[0109] Based on the test data of 20 engines, using the method of this patent, the multi-engine synchronization reliability of the engine is calculated to be 0.988 (0.7 confidence level), meeting the requirements of the multi-engine synchronization reliability index.

[0110] In summary, the above is only a preferred embodiment of the present invention and is not used to limit the protection scope of the present invention. Any modifications, equivalent replacements, improvements, etc. made within the spirit and principle of the present invention shall be included in the protection scope of the present invention.

Claims

1. A method for evaluating the reliability of multi-engine synchronization in a liquid rocket engine, characterized in that, It includes the following steps: Step 1): For the requirements of the multi-engine synchronization reliability index of a liquid rocket engine, collect the measured data of the engine's performance parameters. Based on the measured data of the performance parameters, conduct statistical inference to determine the probability distribution type of the data; Step 2): Based on the measured data of the engine's performance parameters, calculate the distribution parameters of the probability distribution to obtain the probability density function of the engine's key performance parameters; Step 3): Determine the number of cycles M1; Step 4): Determine the number of simulation times M2 for reliability assessment; Step 5): For each simulation, generate random numbers r with the same quantity as the number N of multiple machines according to the probability density function j ; j = 1, 2, …, M2; Step 6): For each simulation, calculate the maximum deviation: Dev(j) = max(r j ) - min(r i ) where max(r j ) and min(r j ) respectively represent the maximum value and the minimum value in r j ; Step 7): Determine whether the maximum deviation value Dev(j) is greater than the upper limit of the maximum deviation required for multi-engine synchronization. If it is greater, the result of the j-th simulation is recorded as a failure, and the failure number fail is accumulated once; otherwise, it is recorded as a success, and the success number succ is accumulated once; Step 8): Repeat steps 5) to 7) M2 times to calculate the success number succ and the failure number fail; Step 9): Based on the success number succ and the failure number fail, conduct multi-engine synchronization reliability estimation and calculate the reliability; where R i is the reliability calculated in the i-th cycle; Step 10): Repeat steps 5) to 10) for a total of M1 times, corresponding to obtaining M1 reliability values. Sort the calculated M1 reliability values in descending order, and take the reliability R with the serial number K = M1×γ in the sorted order. K The value is the reliability R with a confidence lower limit of γ. L ; γ is the set confidence lower limit. According to the reliability R L Perform reliability assessment on the multi-engine synchronization of liquid rocket engines.

2. The method for evaluating the reliability of multi-engine synchronization in a liquid rocket engine according to claim 1, characterized in that, In step 1), for the common probability distribution types, calculate the log-likelihood values based on the measured data of the performance parameters, and then select the probability distribution type with the smallest log-likelihood value as the probability distribution type corresponding to the measured data of the performance parameters.

3. The method for evaluating the reliability of multi-engine synchronization in a liquid rocket engine according to claim 1, characterized in that, In step 1), for the common probability distribution types, calculate the log-likelihood values based on the measured data of the performance parameters, and then select the probability distribution type with the smallest log-likelihood value for hypothesis testing. If the null hypothesis is accepted, the data set follows the previously determined probability distribution type; if the null hypothesis is rejected, select the probability distribution type with the second smallest log-likelihood value and conduct hypothesis testing. If the hypothesis test is accepted, it belongs to the probability distribution type with the second smallest log-likelihood value; and so on until the belonging distribution type is found.

4. The method for evaluating the reliability of multi-engine synchronization in a liquid rocket engine according to claim 3, characterized in that, In step 1), when the probability distribution type is the normal distribution, the Jarque-Bera method is used for hypothesis testing.

5. The method for evaluating the reliability of multi-engine synchronization in a liquid rocket engine according to claim 1, characterized in that, In step 3), the method for determining the number of cycles M1 is as follows: ensure that the product of the set confidence lower limit γ and the number of cycles M1 is an integer and a multiple of 10. The M1 value that meets this condition is then multiplied by 10, which is the final number of cycles M1.

6. The method for evaluating the reliability of multi-engine synchronization in a liquid rocket engine according to claim 1, characterized in that, In step 5), the inverse function method is used to generate random numbers.

7. The method for evaluating the reliability of multi-engine synchronization in a liquid rocket engine according to claim 1, characterized in that, The set confidence lower limit γ is selected as 70%.

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