Reliability Evaluation and Prediction Method and System for Shipborne Missiles in Combat Duty Status

Abstract

The present invention relates to a method and system for reliability evaluation and prediction of shipborne missiles in the combat duty state, belonging to the field of fault prediction. The method includes: obtaining the interval fault data and right censored data of shipborne missiles and constructing a sudden fault model; obtaining the test data of shipborne missiles and constructing a degradation fault model; constructing a competing failure model according to the sudden fault model and the degradation fault model; evaluating the reliability of shipborne missiles at the current moment according to the competing failure model; determining the probability of sudden fault at the next moment according to the sudden fault model; determining the probability of degradation fault at the next moment according to the degradation fault model and the GA-BP neural network; predicting the reliability of shipborne missiles at the next moment according to the probability of sudden fault at the next moment, the probability of degradation fault at the next moment and the competing failure model. The present invention can evaluate and predict the reliability of shipborne missiles in the combat duty state, and judge the types and probabilities of faults occurring.

Description

Technical Field

[0001] The present invention relates to the field of fault prediction, and particularly to a method and system for reliability evaluation and prediction of shipborne missiles in the combat duty state. Background Art

[0002] With the movement of China's aircraft carriers or large ship formations from inshore waters to deep sea areas, higher requirements are put forward for the reliability, storage conditions, combat capabilities, etc. of shipborne missiles. Different from the shore-based storage environment, the shipborne storage environment features high temperature, high humidity, and high salt fog. At the same time, the missiles are also affected by wave slamming and landing impact. Currently, there are few relevant studies on the collection, processing of reliability data for shipboard duty and the reliability analysis of shipborne environment missiles. In view of the problem of reliability analysis of a certain type of shipborne missile in the shipboard duty state, the present invention establishes a missile reliability evaluation and prediction model, conducts application verification and analysis, and provides a basis for the reliability analysis of shipborne missiles in the shipboard duty state. Summary of the Invention

[0003] The purpose of the present invention is to provide a method and system for reliability evaluation and prediction of shipborne missiles in the combat duty state, which can evaluate and predict the reliability of shipborne missiles in the combat duty state, and judge the types and probabilities of faults occurring.

[0004] To achieve the above object, the present invention provides the following solutions:

[0005] A method for reliability evaluation and prediction of shipborne missiles in the combat duty state, comprising:

[0006] Obtaining interval fault data and right censored data of shipborne missiles;

[0007] Constructing a sudden fault model according to the interval fault data and the right censored data;

[0008] Obtaining test data of shipborne missiles;

[0009] Constructing a degradation fault model according to the test data;

[0010] Constructing a competing failure model according to the sudden fault model and the degradation fault model;

[0011] Evaluating the reliability of shipborne missiles at the current moment according to the competing failure model;

[0012] Determining the probability of sudden faults at the next moment according to the sudden fault model;

[0013] Determining the probability of degradation faults at the next moment according to the degradation fault model and the GA-BP neural network;

[0014] Predict the reliability of shipborne missiles at the next moment based on the probability of sudden failure, the probability of degradation failure, and the competing failure model at the next moment.

[0015] Optionally, after the step of "obtaining the interval failure data and right censored data of shipborne missiles" and before the step of "constructing a sudden failure model based on the interval failure data and right censored data", it further includes:

[0016] Process the right censored data using the residual ratio method.

[0017] Optionally, the sudden failure model satisfies the Weibull distribution, and the sudden failure model is:

[0018]

[0019] where, F s (t) is the probability of sudden failure of shipborne missiles at time t, T h is the sudden failure threshold, R s (t) is the reliability of shipborne missiles at time t, respectively represent the estimated values of the scale parameter and shape parameter of the Weibull distribution.

[0020] Optionally, the degradation failure model is:

[0021]

[0022] where, F id (t) is the probability of degradation failure of the i-th test data at time t, x i is the i-th test data, x si is the standard value of the i-th test data, δ i is the half-interval length of the i-th test data, R id (t) is the reliability of the i-th test data at time t, D is the degradation amount distribution function, x iu , x il are the maximum threshold and minimum threshold of the i-th test data respectively, where i = 1, 2,..., n.

[0023] Optionally, the competing failure model is:

[0024] F(t) = P(t ≥ T h ∪|x1 - x s1 | ≥ δ1 ∪ |x2 - x s2 | ≥ δ2 ∪... ∪ |x n - x sn | ≥ δ n )

[0025] = 1 - P(t ≤ Th ∩ |x1 - x s1 | ≤ δ1 ∩ |x2 - x s2 | ≤ δ2 ∩ … ∩ |x n - x sn | ≤ δ n )

[0026] Wherein, T h is the sudden - failure threshold, x i is the i - th test data, x si is the standard value of the i - th test data, δ i is the half - interval length of the i - th test data, where i = 1, 2, …, n.

[0027] Optionally, the competing - failure model is constructed based on the hybrid Copula function.

[0028] Optionally, determining the probability of the degradation failure at the next moment according to the degradation failure model and the GA - BP neural network specifically includes:

[0029] Determining the time - varying distribution parameters according to the degradation failure model;

[0030] Determining the mean and variance of the time - varying distribution parameters;

[0031] Constructing a training set according to the mean and variance;

[0032] Training the GA - BP neural network according to the training set to obtain the trained GA - BP neural network;

[0033] Using the trained GA - BP neural network to determine the probability of the degradation failure at the next moment.

[0034] A reliability evaluation and prediction system for ship - borne missiles in the combat duty state, comprising:

[0035] A first data acquisition module, configured to acquire the interval - failure data and right - censored data of the ship - borne missile;

[0036] A sudden - failure model construction module, configured to construct a sudden - failure model according to the interval - failure data and right - censored data;

[0037] A second data acquisition module, configured to acquire the test data of the ship - borne missile;

[0038] A degradation - failure model construction module, configured to construct a degradation - failure model according to the test data;

[0039] A competing - failure model construction module, configured to construct a competing - failure model according to the sudden - failure model and the degradation - failure model;

[0040] A reliability evaluation module for evaluating the reliability of a shipborne missile at the current moment according to the competing failure model;

[0041] A first probability determination module for determining the probability of a sudden failure at the next moment according to the sudden failure model;

[0042] A second probability determination module for determining the probability of a degradation failure at the next moment according to the degradation failure model and the GA-BP neural network;

[0043] A reliability prediction module for predicting the reliability of the shipborne missile at the next moment according to the probability of the sudden failure at the next moment, the probability of the degradation failure at the next moment, and the competing failure model.

[0044] An electronic device includes a memory and a processor. The memory is used to store a computer program, and the processor runs the computer program to enable the electronic device to execute the reliability evaluation and prediction method of the shipborne missile in the combat duty state.

[0045] A computer-readable storage medium stores a computer program, and when the computer program is executed by a processor, it implements the reliability evaluation and prediction method of the shipborne missile in the combat duty state.

[0046] According to the specific embodiments provided by the present invention, the following technical effects are disclosed by the present invention:

[0047] The present invention aims at the reliability analysis problem of shipborne missiles in the shipboard duty state, establishes a missile reliability evaluation and prediction model, conducts application verification and analysis, and provides a basis for the reliability analysis of shipborne missiles in the shipboard duty state. BRIEF DESCRIPTION OF THE DRAWINGS

[0048] In order to more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the following will briefly introduce the drawings required in the embodiments. Obviously, the drawings in the following description are only some embodiments of the present invention, and those of ordinary skill in the art can also obtain other drawings based on these drawings without creative efforts.

[0049] Figure 1 It is a flowchart of the reliability evaluation and prediction method of the shipborne missile in the combat duty state of the present invention;

[0050] Figure 2 It is a flowchart of the reliability evaluation of the shipborne missile of the present invention;

[0051] Figure 3 It is a flowchart of the state prediction of the shipborne missile of the present invention;

[0052] Figure 4This is the flowchart of the GA-BP neural network of the present invention;

[0053] Figure 5 This is the schematic diagram of the actual value and Copula fitting value of the fault probability of the present invention;

[0054] Figure 6 This is the schematic diagram of the mean prediction result of the present invention;

[0055] Figure 7 This is the schematic diagram of the mean prediction error of the present invention. Specific embodiments

[0056] Next, the technical solutions in the embodiments of the present invention will be clearly and completely described in conjunction with the accompanying drawings in the embodiments of the present invention. Obviously, the described embodiments are only a part of the embodiments of the present invention, rather than all the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those of ordinary skill in the art without creative efforts shall fall within the protection scope of the present invention.

[0057] The purpose of the present invention is to provide a method and system for reliability evaluation and prediction of shipborne missiles in the combat duty state, which can evaluate and predict the reliability of shipborne missiles in the combat duty state, judge the types and probabilities of faults, and further provide guidance for missile service.

[0058] To make the above objects, features, and advantages of the present invention more obvious and understandable, the present invention will be further described in detail below in conjunction with the accompanying drawings and specific embodiments.

[0059] The missile reliability evaluation method proposed by the present invention is based on a competing failure model. First, the distribution type of sudden failure data is determined through mathematical statistics methods, and parameter estimation and fitting distribution tests are carried out to establish a sudden failure model; then, statistical analysis is performed on performance degradation data from the perspective of degradation quantity distribution to establish a degradation failure model; finally, a mixed Copula function is introduced to establish the correlation between sudden failures and degradation failures, and the competing failure probability is evaluated to achieve the evaluation of reliability. The missile reliability prediction method proposed by the present invention is based on a genetic algorithm-BP neural network (GA-BP) model parameter prediction method. Specifically, Figure 1 This is the flowchart of the method for reliability evaluation and prediction of shipborne missiles in the combat duty state of the present invention, as Figure 1 shown, a method for reliability evaluation and prediction of shipborne missiles in the combat duty state specifically includes:

[0060] Step 1: Obtain the interval failure data and right-censored data of the shipborne missile.

[0061] Step 2: Construct a sudden failure model according to the interval failure data and right-censored data.

[0062] Step 3: Obtain the test data of shipborne missiles.

[0063] Step 4: Construct a degradation fault model based on the test data.

[0064] Step 5: Construct a competing failure model based on the sudden fault model and the degradation fault model.

[0065] Step 6: Evaluate the reliability of the shipborne missile at the current moment according to the competing failure model.

[0066] Among them, Steps 1-6 are the process of evaluating the reliability of the shipborne missile at the current or previous moment. As Figure 2 shown, the specific implementation solution is:

[0067] The missile has two fault modes: sudden faults and degradation faults. Its final fault manifestation is the first-occurring fault mode, which is the result of the competition between the two fault modes. A sudden fault of a missile refers to a sudden loss of function such as component damage, huge impact, and illegal operation during the missile's on-ship duty, which is random and unpredictable; a degradation fault of a missile refers to a fault caused by the degradation of the missile over the years of use. There is a correlation between different degradation fault modes of the missile and between degradation faults and sudden faults. By analyzing and establishing the competing failure model of the missile, the reliability assessment of the missile can be realized.

[0068] A. Sudden fault modeling:

[0069] During the on-ship duty of the missile, it will inevitably bear corresponding working loads. Some larger working loads such as landing impact, wave slamming, and component damage caused by sudden changes in temperature and humidity will cause unpredictable faults in the missile. Usually, functions such as exponential distribution, Weibull distribution, and lognormal distribution are used to describe sudden faults. Due to the randomness of the missile's on-ship duty task, its data shows the characteristics of random censoring, and the residual ratio method needs to be used for data processing to obtain the actual reliability distribution curve of sudden faults. And through the empirical distribution function for fitting and goodness-of-fit test, the parameters of the empirical distribution function are estimated. Finally, the empirical distribution with the best fitting effect is determined as the sudden fault model.

[0070] The data required for modeling and the data processing method are as follows:

[0071] (1) Interval data

[0072] Fault data is usually determined by regular inspections. An overly short regular inspection interval will result in waste of manpower, material resources, and financial resources, and at the same time induce missile failures; an overly long regular inspection interval will affect the analysis of missile reliability. Therefore, it is necessary to formulate an appropriate regular inspection period. If a missile fails, the failure time is between two adjacent inspections. To improve the accuracy of determining the failure time, assume that r missile failures are found between two adjacent inspections, and the time length between the two inspections is T. Divide T into r + 1 equal parts, and assume that the missile fails at the right endpoint of each time interval. The fault data obtained after processing can be regarded as non-replacement test data.

[0073] (2) Right censored data

[0074] For right censored data, the residual ratio method is used for processing. Let N be the total number of missile samples in the warehouse storage or on combat readiness duty, t i be the inspection time, and R(t i ) be the reliability at time t i . Then

[0075] R(t i ) = R(t i-1 ) · S(t i ) (1)

[0076] In the formula, S(t i ) is the residual probability of the missile sample in the interval (t i-1 , t i ), indicating the probability that the non-failed samples at time t i-1 continue to maintain the available state until time t i . The calculation formula is

[0077]

[0078] In the formula, n(t i-1 ) is the number of samples continuing to be tested at time t i-1 , and Δr(t i ) is the number of failures in the interval (t i-1 , t i ). n(t i ) can be obtained from the following formula

[0079]

[0080] In the formula, Δm(t j ) is the number of deleted samples in the interval (t i - 1, t i ). F(t i ) is the cumulative failure probability at time t i , and is obtained from F(t i ) = 1 - R(t i)The cumulative failure probability θ at each detection time can be obtained as θ = [F(t1), F(t2), …, F(t i ),]. Then, different distribution functions are used to fit θ, and a better-fitting distribution function type can be obtained for further statistical analysis.

[0081] In this invention, a sudden failure model is constructed with the Weibull function as an example, and the Kolmogorov test method is used for goodness-of-fit test. The corresponding parameters of the Weibull function are obtained through estimation.

[0082] When it comes to the Weibull distribution, its distribution function and mean time to failure are as follows

[0083]

[0084] In the formula, F w (t) is the distribution function, η is the scale parameter, and m is the shape parameter. After fitting with the standard distribution function, it is necessary to test the fitting effect. Commonly used goodness-of-fit test parameters include the correlation coefficient, sum of squared residuals, and root mean square error. The correlation coefficient is closer to 1, and the sum of squared residuals and the root mean square error are smaller, indicating a better fitting effect.

[0085] Assume that the sudden failure satisfies the Weibull distribution. Then the probability of the missile having a sudden failure at time t is

[0086]

[0087] In the formula, respectively represent the estimated values of the scale parameter and shape parameter of the Weibull distribution.

[0088] B. Degradation failure modeling

[0089] Degradation failure refers to the failure mode in which the performance of the missile gradually deteriorates over time during use (such as circuit aging, metal corrosion, rubber melting, etc.) until it can no longer meet the usage requirements. The degradation failure probability increases with time and is predictable, generally characterized by test parameters. The type of distribution function of the test parameters generally remains unchanged. The degradation amounts at different times follow the same family of distribution forms, but the distribution parameters of this distribution family change with time and can be expressed as D(x, d(t)), where D represents the type of distribution function and d(t) represents the time-varying distribution parameter.

[0090] According to engineering experience, the distribution function of the test parameters generally conforms to the normal distribution. Since the sample of the missile is small, the research uses the Shapiro-Wilk test, a normal distribution test method specifically for small samples, for distribution test.

[0091] The test steps of the Shapiro-Wilk test are as follows:

[0092] a. Arrange the samples in ascending order (x1 ≤ x2 ≤ … ≤ x n ) to form order statistics.

[0093] b. Look up the table to obtain the α k,n value corresponding to the n value.

[0094] c. Calculate the statistic

[0095]

[0096] where α i,n is the Shapiro-Wilk test coefficient, x i is the i-th test data, is the average of n test data.

[0097] d. Look up the critical value Z of Z according to the significance level α .

[0098] e. If Z ≤ Z α then reject the hypothesis, otherwise accept the hypothesis.

[0099] Determine the degradation failure model according to the test results. The probability that the i-th test data has a degradation failure at time t is:[[]]

[0100]

[0101] where are the maximum threshold and minimum threshold of the i-th test data respectively.

[0102] C. Competing failure model based on the mixed Copula function

[0103] There is a correlation in the degradation between missile test parameters, which is manifested as the degradation of one test parameter will lead to the degradation of other parameters; and there is a correlation between sudden failures and degradation failures, which is manifested as degradation failures will increase the probability of sudden failures. The final failure of the missile is the result of the competition between sudden failures and degradation failures. According to the sudden failure model and the degradation failure model, establish the missile competing failure model at time t as follows:

[0104]

[0105] In the formula, T h is the sudden failure threshold, x i (i = 1, 2, …, n) is the i-th test data, x si is the standard value of the i-th test data, δi is the half - interval length of the i - th test data.

[0106] For the situation where the above - mentioned life data and test data exist simultaneously, the core of analyzing the missile reliability lies in establishing the joint distribution function (CDF) of various failure modes, that is, F(t). However, due to the complex correlation relationship between sudden failures and degradation failures, it is difficult to construct the CDF. The Copula function can well describe the variable correlation. The present invention adopts a mixed Copula function to establish the correlation relationship between sudden failures and degradation failures, calculate the competing failure probability, and realize the evaluation of reliability.

[0107] The n - dimensional Copula function can be expressed as: C(u1,u2,…,u n ) = P(U1≤u1,U2≤u2,…,U2≤u2,), where U i is a uniform variable, that is, U1~N(0,1), and has the following properties: (1) C = I N = [0,1] N , the domain of the Copula function is on the n - dimensional space of; (2) The Copula function is a monotonically increasing function in each dimension; (3) Assume that any m∈(0,1), the marginal distribution C n (·) of the Copula function satisfies C n (1,…,m n ,…,1) = m, n∈[1,N].

[0108] According to Sklar's theorem, there exists an n - dimensional Copula function C such that for all n - dimensional random variables (x1,x2,…,x n )∈(-∞,+∞) n the joint distribution function F1(x1,x2,…,x n ) and the marginal distribution functions F1(x1),F2(x2),…,F n (x n ) satisfy

[0109] F1(x1,x2,…,x n ) = C(F1(x1),F2(x2),…,F n (x n )) (9)

[0110] If the marginal distributions F1(x1),F2(x2),…,F n (x n ) are all continuous functions, then there exists a unique Copula function C that satisfies

[0111]

[0112] where \(u\) i = F i (x i ).

[0113] Therefore, Equation (8) can be written as

[0114]

[0115] where is the cumulative distribution function of the \(i\)-th test data at time \(t\).

[0116] Copula functions are divided into elliptical type, Archimedean type and quadratic type. Archimedean Copula functions have the characteristics of simple calculation and accurate results, and are the most widely used. Typical Archimedean Copula functions include Clayton Copula function, Frank Copula function and Gumbel Copula function.

[0117] The Clayton Copula function is suitable for correlation modeling with obvious lower-tail thick-tail characteristics and not obvious upper-tail thick-tail characteristics, and is expressed as follows:

[0118] \(C(u, v)=\max([u -θ + v -θ - 1] -1 / θ , 0)\ (12)

[0119] The Frank Copula function is suitable for correlation modeling with symmetric thick-tail, and is expressed as follows:

[0120] \(C(u, v)=-\theta -1 \ln[1 + (e -θu - 1)(e -θv - 1) / (e -θ - 1)]\ (13)

[0121] The Gumbel Copula function is suitable for correlation modeling with obvious upper-tail thick-tail characteristics and not obvious lower-tail thick-tail characteristics, and is expressed as follows:

[0122] \(C(u, v)=\exp[-((-\ln u) θ + (-\ln v) θ ) 1 / θ \ (14)

[0123] Affected by the shipborne environment and the randomness of mission duty, the tail characteristics of the missile's test data sequence and life data sequence cannot meet the tail characteristics of a single Copula function. Using a mixed Copula function to establish a correlation model can better reflect the reliability of the missile.

[0124] Since the missile failure probability usually has the characteristic of non - decreasing monotonicity, the Frank Copula function is not applicable to the modeling of competing failures. Therefore, the research uses the Clayton Copula function and the Gumbel Copula function to establish a mixed Copula function for modeling competing failures. The mixed Copula model is established as follows:

[0125] C = ω c C c + ω g C g ,(ω c + ω g = 1)(15)

[0126] In the formula, C c , C g represent the Clayton Copula function and the Gumbel Copula function respectively, and ω c , ω g represent the weights of the corresponding Copula functions.

[0127] After using multiple Copula functions for joint distribution fitting, a goodness - of - fit test is required to determine the optimal - fitting Copula function. The commonly used goodness - of - fit test method for Copula functions is the AIC information criterion method. AIC is expressed as

[0128] AIC = nln(MSE)+2m(16)

[0129]

[0130] In the formula, n is the number of predictions, m is the number of parameters (1 for a single Copula function and 2 for a mixed Copula function), y pi is the predicted value of the failure probability, and y i is the actual value of the failure probability. The smaller the AIC value, the better the fitting effect of the corresponding Copula function.

[0131] According to the AIC information criterion, the global search method is used to determine the combination of weights of the mixed Copula function that minimizes the AIC value. By calculating the missile competing - failure probability using the test data and the failure data, the curve of missile reliability changing with time R(t)=1 - F(t) is obtained to realize missile reliability assessment.

[0132] Step 7: Determine the probability of the sudden failure at the next moment according to the sudden - failure model.

[0133] Step 8: Determine the probability of the degradation failure at the next moment according to the degradation - failure model and the GA - BP neural network.

[0134] Step 9: Predict the reliability of the shipborne missile at the next moment according to the probability of sudden failure, the probability of degradation failure at the next moment, and the competing failure model.

[0135] Steps 7-9 are the process of predicting the reliability of the shipborne missile at the next moment. As Figure 3 shown, the specific implementation solution is as follows:

[0136] In order to analyze the reliability of the missile after being on duty for a certain duration of the mission profile and estimate the on-ship service life of the missile, it is necessary to predict the missile reliability. The prediction of missile reliability can be divided into sudden failure prediction and degradation failure prediction. The sudden failure is analyzed using the fitted empirical distribution function. The probability of degradation failure increases with time and is predictable. The prediction of degradation failure can be achieved through the method of predicting model parameters. The present invention adopts the GA-BP neural network to predict the distribution parameters of the degradation data.

[0137] According to the sudden failure model established in Step 2 above, the probability of sudden failure F i+1 at the t s th moment is obtained. Taking the Weibull distribution as an example. i+1

[0138]

[0139] According to the degradation failure model established in Step 4, the time-varying distribution parameter d(t) is calculated. Taking the test parameters satisfying the normal distribution as an example, the distribution parameter d(t) (including the mean and variance σ (i)2 ) sequence of the test data is calculated.

[0140]

[0141]

[0142] The mean and variance sequences of the test data are divided into a training set and a validation set. The GA-BP neural network is trained using the training set to achieve the prediction of the mean and variance, and the validation set is used for validation.

[0143] The training process of the GA-BP neural network is as Figure 4 shown and specifically includes:

[0144] a. Population initialization. The individual coding method is real number coding. Each individual is a real number string, which consists of 4 parts: the connection weights between the input layer and the hidden layer, the hidden layer threshold, the connection weights between the hidden layer and the output layer, and the output layer threshold. The individual contains all the weights and thresholds of the neural network. Given a known network structure, a neural network with a determined structure, weights, and thresholds can be formed.

[0145] b. Fitness function. According to the initial weights and thresholds of the BP neural network obtained by an individual, the BP neural network is trained with training data to predict the system output. The sum of the absolute values of the errors E between the predicted output and the expected output is used as the individual fitness value F. The calculation formula is

[0146]

[0147] where n is the number of network output nodes, y i is the expected output of the i-th node of the BP neural network, o i is the predicted output of the i-th node, and k is a coefficient.

[0148] c. Selection operation. There are various methods for the selection operation of genetic algorithms, such as roulette wheel method, tournament method, etc. In this study, the roulette wheel method is selected, that is, the selection strategy based on fitness proportion. The selection probability of each individual i is

[0149] f i = k / F i (22)

[0150]

[0151] where F i is the fitness value of individual i. Since the smaller the fitness value, the better, the reciprocal of the fitness value is taken before individual selection. k is a coefficient, and N is the number of population individuals.

[0152] d. Crossover operation. Since the individuals adopt real number coding, the real number crossover method is used for the crossover operation. The crossover operation of the k-th chromosome a k and the l-th chromosome a l at the j-th position is as follows:

[0153]

[0154] where b is a random number between [0, 1].[[]END]]

[0155] e. Mutation operation. Select the j-th gene of the i-th individual for mutation. The mutation operation method is as follows:

[0156]

[0157] where a max is the upper bound of gene a ij , a min is the lower bound of gene a ij , f(g) = r2(1 - g / G max ), r2 is a random number, g is the current iteration number, G 2 , and G maxis the maximum number of evolutions, and r is a random number between [0, 1].

[0158] f. BP neural network prediction. The BP neural network uses the mean square error MSE between the predicted value and the true value as the loss function.

[0159]

[0160] As the number of iterations increases, the loss function gradually converges to the minimum. If the loss function MSE does not reach the set value, the model needs to be adjusted and continue iterative training until the set value is reached. Save the weights and thresholds that minimize the loss function of the learning samples to obtain the final variance and mean prediction values.

[0161] According to Equation (8), calculate the failure probability of the missile, and the missile reliability prediction value can be obtained.

[0162] Based on the above method, the present invention provides Embodiment 1:

[0163] This time, the method proposed by the present invention is verified by simulating the missile data.

[0164] Step 1. Reliability assessment.

[0165] Refer to the evaluation test data of the same type of missile on ship duty as the failure data of the two types of missiles. During the ship duty of this type of missile, it was installed on the ship for 2 years, and regular inspections were carried out during this period. After 18 months of ship duty, 2 failures were found, and after 2 years, 3 failures were found. Calculate the fitting evaluation parameters as shown in Table 1.

[0166] Table 1 Fitting evaluation parameter values

[0167]

[0168] As can be seen from the above table, the lognormal distribution has a better fitting effect on the actual failure probability curve in the ship duty state. The lognormal distribution is used for fitting to obtain the missile failure probability distribution curve as follows:

[0169]

[0170] 1. Sudden failure modeling

[0171] Usually, functions such as exponential distribution, Weibull distribution, and lognormal distribution are used to describe sudden failures. Due to the randomness of the missile ship duty mission, its data shows the characteristics of random censoring. The residual ratio method needs to be used for data processing to obtain the actual sudden failure reliability distribution curve. And through the empirical distribution function for fitting and goodness-of-fit test, estimate the parameters of the empirical distribution function. Finally, the empirical distribution with the best fitting effect is determined as the sudden failure model.

[0172] Assume that all the failure types discovered at 18 months are sudden failures, and among the failure types discovered at 2 years, 2 are sudden failures. Then the sudden failure failure rate of the missile is shown in Table 2.

[0173] Table 2 Missile sudden failure failure rate

[0174]

[0175] Exponential distribution, Weibull distribution, and lognormal distribution are used for curve fitting. By comparing the fitting evaluation parameters, it is concluded that the fitting effect of the lognormal distribution is the best. Point estimation and interval estimation are performed on the log mean and log variance of the lognormal distribution. The point estimate of μ is 3.726, and the confidence interval at the 95% confidence level is (3.424, 4.028); the point estimate of σ is 0.5747, and the confidence interval at the 95% confidence level is (0.3046, 0.8448). The missile sudden failure probability distribution curve represented by the lognormal distribution is as follows:

[0176]

[0177] 2. Degradation failure modeling

[0178] The test parameters of the missile from 0 to 24 months are obtained through simulation. Taking the test item data of the main channel self-check parameters (0.6 - 2.9V) of 10 missiles at the start of the test as an example, the simulation test data is established as: 1.491, 1.859, 2.001, 1.985, 1.496, 1.633, 1.749, 1.743, 1.507, 1.996.

[0179] According to engineering experience, the distribution function of test parameters generally conforms to the normal distribution. Since the sample of the missile is small, the research uses the Shapiro-Wilk test, a normal distribution test method specifically for small samples, for distribution test. The test steps of the Shapiro-Wilk test are as follows:

[0180] a. Arrange the samples in ascending order as the order statistic x1 ≤ x2 ≤ … ≤ x n :

[0181] That is, 1.291 < 1.496 < 1.507 < 1.633 < 1.743 < 1.749 < 1.859 < 1.985 < 1.996 < 2.201.

[0182] b. Look up the α k,n value corresponding to the n value in the table.

[0183] α 1,n = 0.5739, α 2,n = 0.3291, α3,n = 0.2141, α 4,n = 0.1244, α 5,n = 0.0399

[0184] c. Calculate the statistic

[0185] d. Take α = 0.05 and look up the table to get Z α = 0.842, then Z = 0.9027 > Z α = 0.842.

[0186] e. Therefore, accept the hypothesis and consider that the test data follows a normal distribution.

[0187] The research hypothesis is that the test data all conform to a normal distribution. The mean and variance sequences of the main channel self - test parameters of 10 missiles in 0 - 24 months obtained by simulation are shown in Table 3 as follows:

[0188] Table 3 Simulation data of main channel self - test parameters

[0189]

[0190] According to Equation (13), establish a degradation failure model, and the probability of the test data having a degradation failure at time t is

[0191]

[0192] 3. Competing failure model based on the mixed Copula function

[0193] The present invention adopts a mixed Copula function to establish the correlation between sudden failures and degradation failures, calculate the competing failure probability, and realize the evaluation of reliability.

[0194] The Clayton Copula function is suitable for correlation modeling with obvious lower - tail heavy - tail characteristics and non - obvious upper - tail heavy - tail characteristics, and is expressed as follows:

[0195] C(u, v) = max([u -θ + v -θ - 1] -1 / θ , 0) (30)

[0196] The Gumbel Copula function is suitable for correlation modeling with obvious upper - tail heavy - tail characteristics and non - obvious lower - tail heavy - tail characteristics, and is expressed as follows:

[0197] C(u, v) = exp[-((-lnu) θ + (-lnv) θ ) 1 / θ (31)

[0198] Affected by the shipboard environment and the randomness of mission duty, the tail characteristics of the missile's test data sequence and life data sequence cannot meet the tail characteristics of a single Copula function. Using a mixed Copula function to establish a correlation model can better reflect the reliability of the missile.

[0199] Since the missile failure probability usually has the characteristic of non-decreasing monotonically, the Frank Copula function is not applicable to the modeling of competing failures. Therefore, the study uses the Clayton Copula function and the Gumbel Copula function to establish a mixed Copula function for modeling competing failures. The mixed Copula model is established as follows:

[0200] C = ω c C c + ω g C g , (ω c + ω g = 1) (32)

[0201] In the formula, C c , C g represent the Clayton Copula function and the Gumbel Copula function respectively, and ω c , ω g represent the weights of the corresponding Copula functions.

[0202] After using multiple Copula functions for joint distribution fitting, a goodness-of-fit test is required to determine the optimal-fitting Copula function. The commonly used Copula function goodness-of-fit test method is the AIC information criterion method, and AIC is expressed as

[0203] AIC = nln(MSE)+2m (33)

[0204]

[0205] In the formula, n is the number of predictions, m is the number of parameters (1 for a single Copula function and 2 for a mixed Copula function), y pi is the predicted value of the failure probability, and y i is the actual value of the failure probability. The smaller the AIC value, the better the fitting effect of the corresponding Copula function.

[0206] According to the AIC information criterion, the global search method is used to determine the combination of weights of the mixed Copula function that minimizes the AIC value. The competing failure probability of the missile is calculated through the test data and the failure data, and the curve of the missile reliability changing with time R(t)=1 - F(t) is obtained to realize the reliability assessment of the missile.

[0207] Considering the correlation between different failure modes, the Clayton Copula function, the Gumbel Copula function, and a hybrid Copula function combining the two are respectively used to establish a competing failure model. Among them, the weight of the hybrid Copula model is obtained through global search, and the Copula function parameters and the corresponding AIC results are shown in Table 4

[0208] Table 4 Copula Function Parameters and AIC Results

[0209]

[0210] As can be seen from Table 4, according to the AIC information criterion, the fitting effect of the hybrid Copula function is the best, followed by the Gumbel Copula function, but it is better than the Clayton Copula function.

[0211] The actual missile failure values and the failure fitting values of the three Copula functions are plotted as Figure 5 shown. As can be seen from the figure, the Clayton Copula function has a better fitting effect in the second half of the failure probability curve; while the Gumbel Copula function has a better fitting effect in the first half of the failure probability curve. The hybrid Copula function combines the modeling characteristics of the Clayton Copula function and the Gumbel Copula function, and has a better correlation modeling effect.

[0212] Using the sudden failure model and the main channel self-checking degradation failure model, the competing failure probabilities at the 21st month and the 24th month are 0.1253 and 0.1776 respectively. The same data processing method is adopted for the other 12-dimensional test parameters, and the final competing failure probability is calculated and compared with the actual missile failure probabilities of 0.1374 and 0.2097 at the corresponding moments to test the accuracy of the proposed hybrid Copula function method.

[0213] Step 2: Reliability prediction.

[0214] (a) According to the sudden failure model established in Step 1, the sudden failure probability F i+1 (t s ) at time t i+1 ) is obtained.

[0215]

[0216] (b) According to the degradation failure model established in Step 1, the time-varying distribution parameter d(t) is calculated. Taking the test parameters satisfying the normal distribution as an example, the mean value and variance σ (i)2 of the test data are calculated. The sequences are shown in Table 5.

[0217]

[0218] Table 5 Mean and Variance Sequences of Test Data

[0219]

[0220] (c) Divide the mean and variance sequences of the test data into a training set and a validation set. Use the training set to train the GA-BP neural network to achieve the prediction of the mean and variance, and use the validation set for verification.

[0221] Divide the mean and variance sequences of the test data into a training set and a validation set. Use the training set to train the GA-BP neural network to achieve the prediction of the mean and variance, and use the validation set for verification.

[0222] The mean input vector is x im = [1.746, 1.673, 1.604, 1.517, 1.433, 1.326, 1.259], and the output vector is x om = [1.673, 1.604, 1.517, 1.433, 1.326, 1.259, 1.184].

[0223] The variance input vector is x iv = [0.068, 0.143, 0.218, 0.341, 0.374, 0.405, 0.483], and the output vector is x iv = [0.143, 0.218, 0.341, 0.374, 0.405, 0.483, 0.432].

[0224] The parameter settings of the GA-BP neural network are shown in Table 6:

[0225] Table 6 GA-BP Neural Network Parameter Settings

[0226]

[0227] If the prediction error is within the acceptable range, proceed to the next step; if the prediction error is large, repeat step d and retrain the model. The mean prediction results and mean prediction errors of the GA-BP neural network and the BP neural network are plotted as shown in Figure 5 、 Figure 6 respectively.

[0228] From Figure 5 、 Figure 6It can be seen that compared with the BP neural network, the prediction result of the GA-BP neural network is closer to the actual value, the absolute value of the prediction error is smaller, and the prediction result is more accurate. Using the GA-BP neural network to predict the mean and variance of the test data in the 24th month are 1.102 and 0.521 respectively. Substituting them into Equation (36), the degradation failure probability of this parameter is calculated to be 0.1679. From Equation (35), the sudden failure probability of the missile at the 24th month is 0.1702. Using the mixed Copula function to calculate the competing failure probability between this test item and the sudden failure is 0.198.

[0229] Corresponding to the above method, the present invention also discloses a reliability evaluation and prediction system for shipborne missiles in the combat duty state, including:

[0230] The first data acquisition module is used to acquire the interval failure data and right censored data of the shipborne missile.

[0231] The sudden failure model construction module is used to construct a sudden failure model according to the interval failure data and right censored data.

[0232] The second data acquisition module is used to acquire the test data of the shipborne missile.

[0233] The degradation failure model construction module is used to construct a degradation failure model according to the test data.

[0234] The competing failure model construction module is used to construct a competing failure model according to the sudden failure model and the degradation failure model.

[0235] The reliability evaluation module is used to evaluate the reliability of the shipborne missile at the current moment according to the competing failure model.

[0236] The first probability determination module is used to determine the probability of sudden failure at the next moment according to the sudden failure model.

[0237] The second probability determination module is used to determine the probability of degradation failure at the next moment according to the degradation failure model and the GA-BP neural network.

[0238] The reliability prediction module is used to predict the reliability of the shipborne missile at the next moment according to the probability of sudden failure at the next moment, the probability of degradation failure at the next moment and the competing failure model.

[0239] The beneficial effects and advantages of the present invention are as follows:

[0240] The present invention establishes a competing failure model for missiles to evaluate the reliability of missiles. The mixed Copula function is used to model the correlation between sudden failure and degradation failure, and to determine the change law of missile reliability over time.

[0241] The present invention proposes a method for predicting the reliability of a missile. The GA-BP neural network is used to realize the prediction of the distribution parameters of test data, so as to realize the reliability prediction of the missile.

[0242] In this specification, each embodiment is described in a progressive manner. The key point of each embodiment is to illustrate the differences from other embodiments. For the same or similar parts among the embodiments, reference can be made to each other. For the system disclosed in the embodiments, since it corresponds to the method disclosed in the embodiments, the description is relatively simple. For the relevant parts, reference can be made to the description in the method part.

[0243] In this article, specific examples are used to elaborate on the principle and implementation manner of the present invention. The description of the above embodiments is only used to help understand the method of the present invention and its core idea. At the same time, for those of ordinary skill in the art, based on the idea of the present invention, there will be changes in the specific implementation manner and application scope. In summary, the content of this specification should not be construed as a limitation to the present invention.

Claims

1. A reliability evaluation and prediction method for shipborne missiles in the combat duty state, characterized in that Including: Obtain the interval fault data and right censored data of shipborne missiles; Construct a sudden fault model based on the interval fault data and right censored data; Obtain the test data of shipborne missiles; Construct a degradation fault model based on the test data; Construct a competing failure model based on the sudden fault model and degradation fault model; Evaluate the reliability of shipborne missiles at the current moment according to the competing failure model; Determine the probability of sudden faults at the next moment according to the sudden fault model; Determine the probability of degradation faults at the next moment according to the degradation fault model and GA-BP neural network; Predict the reliability of shipborne missiles at the next moment according to the probability of sudden faults at the next moment, the probability of degradation faults at the next moment, and the competing failure model; The sudden fault model satisfies the Weibull distribution, and the sudden fault model is: Among them, F s (t) is the probability that the shipborne missile has a sudden failure at time t, and T h is the sudden failure threshold, and R s (t) is the reliability of the shipborne missile at time t, respectively represent the estimated values of the scale parameter and shape parameter of the Weibull distribution; The degradation fault model is: Among them, F id (t) is the probability that the i-th test data has a degradation failure at time t, x i is the i-th test data, x si is the standard value of the i-th test data, δ i is the half-interval length of the i-th test data, R id (t) is the reliability of the i-th test data at time t, D is the degradation amount distribution function, x iu and x il are the maximum threshold and the minimum threshold of the i-th test data respectively, where i = 1, 2, …, n; The competing failure model is: F(t) = P(t ≥ T h ∪ |x1 - x s1 | ≥ δ1 ∪ |x2 - x s2 | ≥ δ2 ∪ … ∪ |x n - x sn | ≥ δ n ) = 1 - P(t ≤ T h ∩ |x1 - x s1 | ≤ δ1 ∩ |x2 - x s2 | ≤ δ2 ∩ … ∩ |x n - x sn | ≤ δ n ) Among them, T h is the sudden failure threshold, x i is the i-th test data, x si is the standard value of the i-th test data, δ i is the half-interval length of the i-th test data, where i = 1, 2, …, n.

2. The reliability evaluation and prediction method of shipborne missiles in the combat duty state according to claim 1, characterized in that After the step of "obtaining the interval fault data and right censored data of shipborne missiles" and before the step of "constructing a sudden fault model based on the interval fault data and right censored data", it also includes: Process the right censored data using the residual ratio method.

3. The reliability evaluation and prediction method of shipborne missiles in the combat duty state according to claim 1, characterized in that Construct the competing failure model based on the hybrid Copula function.

4. The reliability evaluation and prediction method of shipborne missiles in the combat duty state according to claim 1, characterized in that, The specific process of determining the probability of degradation faults at the next moment according to the degradation fault model and GA-BP neural network includes: Determine the time-varying distribution parameters according to the degradation fault model; Determine the mean and variance of the time-varying distribution parameters; Construct a training set according to the mean and variance; Train the GA-BP neural network according to the training set to obtain the trained GA-BP neural network; Use the trained GA-BP neural network to determine the probability of degradation faults at the next moment.

5. A reliability evaluation and prediction system for shipborne missiles in the combat duty state, characterized in that, Including: The first data acquisition module is used to obtain the interval fault data and right censored data of shipborne missiles; The sudden fault model construction module is used to construct a sudden fault model based on the interval fault data and right censored data; The sudden fault model satisfies the Weibull distribution, and the sudden fault model is: Among them, F s (t) is the probability that a shipborne missile has a sudden failure at time t, and T h is the sudden failure threshold, and R s (t) is the reliability of the shipborne missile at time t, respectively represent the estimated values of the scale parameter and the shape parameter of the Weibull distribution; The second data acquisition module is used to obtain the test data of shipborne missiles; The degradation fault model construction module is used to construct a degradation fault model based on the test data; The degradation fault model is: Among them, F id (t) is the probability that the i-th test data has a degradation failure at time t, x i is the i-th test data, x si is the standard value of the i-th test data, δ i is the half-interval length of the i-th test data, R id (t) is the reliability of the i-th test data at time t, D is the degradation amount distribution function, x iu and x il are the maximum threshold and the minimum threshold of the i-th test data respectively, where i = 1, 2, …, n; The competing failure model construction module is used to construct a competing failure model based on the sudden fault model and degradation fault model; The competing failure model is: F(t) = P(t ≥ T h ∪ |x1 - x s1 | ≥ δ1 ∪ |x2 - x s2 | ≥ δ2 ∪ … ∪ |x n - x sn | ≥ δ n ) = 1 - P(t ≤ T h ∩ |x1 - x s1 | ≤ δ1 ∩ |x2 - x s2 | ≤ δ2 ∩ … ∩ |x n - x sn | ≤ δ n ) Among them, T h is the sudden failure threshold, x i is the i-th test data, x si is the standard value of the i-th test data, δ i is the half-interval length of the i-th test data, where i = 1, 2, …, n; The reliability evaluation module is used to evaluate the reliability of shipborne missiles at the current moment according to the competing failure model; The first probability determination module is used to determine the probability of sudden faults at the next moment according to the sudden fault model; The second probability determination module is used to determine the probability of degradation faults at the next moment according to the degradation fault model and GA-BP neural network; The reliability prediction module is used to predict the reliability of shipborne missiles at the next moment according to the probability of sudden faults at the next moment, the probability of degradation faults at the next moment, and the competing failure model.

6. An electronic device, characterized in that, It includes a memory and a processor. The memory is used to store a computer program, and the processor runs the computer program to enable the electronic device to execute the reliability evaluation and prediction method of shipborne missiles in the combat duty state as described in any one of claims 1-4.

7. A computer-readable storage medium, characterized in that, It stores a computer program, and when the computer program is executed by a processor, it realizes the reliability evaluation and prediction method of shipborne missiles in the combat duty state as described in any one of claims 1-4.

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