Method for modeling reliability of gun system based on copula and multi-performance degradation data

Abstract

The application provides a gun system reliability modeling method based on Copula and multi-performance degradation data, and the steps include: S1, determining the key performance parameters related to the failure of the gun system and the failure threshold value thereof through failure mechanism analysis; S2, obtaining initial values of the key performance parameters of the gun system; S3, carrying out a projectile test to obtain a numerical matrix of the degradation amount of the key performance parameters of the gun system; S4, identifying the edge distribution family and the statistical parameters thereof to which the degradation amount of the key performance parameters of the gun system is subjected according to the numerical matrix; S5, identifying the joint distribution family and the statistical parameters thereof to which the degradation amount of the key performance parameters of the gun system is subjected; and S6, constructing a gun system reliability model. The method of the application utilizes the multi-performance degradation data containing more information than the life data, and describes the correlation between the performances by means of the Copula function, does not depend on the complex hierarchical structure of the gun system, and can more accurately and efficiently realize the gun system reliability modeling.

Description

Technical Field

[0001] This invention belongs to the field of firearm system reliability modeling, and specifically relates to a firearm system reliability modeling method based on Copula and multiple performance degradation data. Background Technology

[0002] Firearm systems are complex systems with multiple levels and components. Reliability modeling of firearm systems has become an important issue for relevant designers and users, and it has important guiding significance for product development and use.

[0003] Traditional firearms system reliability modeling methods mainly revolve around the system's hierarchical structure framework and lifespan statistics. However, firearms systems generally have complex hierarchical structures and long lifespans, which leads to a dual dilemma for traditional firearms system reliability modeling methods: first, they cannot reflect the inherent coupling relationships between firearms system components through simple hierarchical diagrams; second, they cannot obtain sufficient lifespan data within a limited development cycle to fit or validate the key parameters of the established model.

[0004] Therefore, introducing a firearms system reliability modeling method based on multi-performance degradation data is of great significance. This type of method does not rely on the hierarchical structure and lifespan data of the firearms system, avoiding the difficulties faced by traditional methods. On the other hand, with the rapid development of system monitoring technologies such as sensors, we can obtain more comprehensive degradation data of various key performance parameters of firearms systems during operation. This data is easier to obtain than lifespan data and contains more information, improving the efficiency and accuracy of this type of method. However, there is currently no relevant technology, making the research on a firearms system reliability modeling method based on multi-performance degradation data particularly urgent. Summary of the Invention

[0005] To address the shortcomings of existing technologies, this invention proposes a firearm system reliability modeling method based on Copula and multi-performance degradation data. This method considers the joint degradation of multiple key performance parameters during the operation of the firearm system and uses the Copula function to characterize their correlation features, ultimately completing the firearm system reliability modeling. It fully utilizes the advantages of easily collected performance data and the presence of more firearm system degradation information, making the constructed firearm system reliability model more accurate and objective, ensuring the accuracy and reliability of the modeling.

[0006] Specifically, the present invention provides a method for reliability modeling of firearm systems based on Copula and multi-performance degradation data, which includes the following steps:

[0007] S1. Determine the key performance parameters Z1, Z2, ..., Z1, Z2, ..., Z3, which indicate whether the associated firearm system will fail, through failure mechanism analysis. m and its failure threshold Where Z is the key performance parameter, z th , where m is the failure threshold corresponding to the key performance parameter; among them, the key performance parameters related to the failure of the firearm system are the mechanical characteristic parameters of the elastic component, the morphological characteristic parameters of the impact component, or the material characteristic parameters of the ignition component of the firearm system.

[0008] S2. Obtain the initial values ​​of various key performance parameters of the firearm system at time t=0. (i = 1, 2, ..., m), where i is the i-th key performance parameter;

[0009] S3. Conduct projectile firing tests on the firearm system at the set time point t. j (j = 1, ..., n) Obtain the values ​​of its key performance parameters z. i (t j (i = 1, ..., m), forming multiple degenerate trajectories, and calculating the corresponding degeneracy amounts to obtain the numerical matrix Λ of the degenerate trajectories:

[0010]

[0011] in,

[0012] t0=0, Δz i (t j , t j-1 )=-Δz i (t j-1 , t j )=z i (t j-1 )-z i (t j (i = 1, ..., m; j = 1, ..., n) represents the firearm system at t j-1 to t j Key performance parameter Z during runtime i The amount of degradation;

[0013] S4. Based on the numerical matrix Λ of the degradation trajectory, using maximum likelihood estimation and the BIC criterion, identify the marginal distribution family and its statistical parameters that the degradation amount of various key performance parameters of the firearm system follows.

[0014] S41. Determine the candidate distribution family φ indexed by the time parameter. 1 , φ 2 , …, φ l ;

[0015] S42. Data of the i-th row (i = 1, 2, ..., m) of the numerical matrix Λ of any degenerate trajectory:

[0016] Λ i，： =[Δzi (t1, t0) Δz i (t2, t1) … Δz i (t n , t n-1 (2)

[0017] Suppose that the corresponding stochastic process follows a certain marginal distribution family, that is:

[0018] ΔZ i (t v , t u )~ψ i (t u , t v ;θ i )(t u <t v (3)

[0019] Where, ψ i Refers to the time parameter t u , t v , where is the distribution family of the index, containing the vector of statistical parameters to be estimated θ. i The subscripts u and v are used to distinguish between two time parameters with different values, and their probability density function is expressed as:

[0020]

[0021] Constructing the log-likelihood function

[0022]

[0023] Where j is the time index, representing the j-th time point;

[0024] S43. Randomly select the k-th (k = 1, 2, ..., l) distribution family φ from the candidate distribution families. k Its statistical parameter space is Θ, and the maximum likelihood function is used to estimate when ψ i =φ k The optimal statistical parameter vector at that time:

[0025]

[0026] And calculate the corresponding BIC value, where, The star in the upper right corner indicates that it is the optimal statistical parameter vector that maximizes the likelihood;

[0027] S44. Based on the BIC criterion, determine ΔZ from the candidate distribution families. i The optimal marginal distribution family it follows and its statistical parameters are:

[0028]

[0029] In the formula, The star in the upper right corner indicates that it is the optimal marginal distribution family that minimizes the BIC. Its corresponding optimal parameters;

[0030] S5. Based on the marginal distribution family and statistical parameters of the performance parameter degradation obtained in step S4, using the Copula function and maximum likelihood estimation, and based on the BIC criterion, identify the joint distribution family and statistical parameters of the degradation of each key performance parameter of the firearm system.

[0031] S6. Based on the joint distribution family and statistical parameters of the degradation of various key performance parameters of the firearm system obtained in step S5, the joint distribution of the values ​​of various key performance parameters of the firearm system at any time t is obtained:

[0032]

[0033] Construct a reliability model for the firearm system, characterized by a reliability function:

[0034]

[0035] Where Pr is a probability measure.

[0036] Preferably, step S5 specifically includes the following sub-steps:

[0037] S51. Determine multiple alternative Copula functions C 1 C 2 C w ;

[0038] S52. Assume that the degradation of key performance parameters of a firearm system follows a certain Copula function C∈{C 1 C 2 C w} represents a connected joint distribution family Right now:

[0039]

[0040] Where η is the vector of statistical parameters to be estimated contained in the Copula function, and the random vector ΔZ(t) v , t u The probability density function and probability distribution function of are expressed as:

[0041]

[0042] Suppose the distribution family The probability density function and probability distribution function are:

[0043]

[0044] In the formula, Yes A simplified representation; and let

[0045]

[0046] In the formula, To find the sign of the partial derivative, F i (i∈{1,…,m}) is the i-th representative element of function c, representing the value of a certain probability distribution function;

[0047] Then formula (10) can be written as:

[0048]

[0049] Let Δz i (t j , t j-1 ) for Λ i，j Construct the log-likelihood function:

[0050]

[0051] By removing the terms in formula (14) that are irrelevant to η, we obtain the simplified log-likelihood function:

[0052]

[0053] S53. Randomly select the k-th (k = 1, 2, ..., w) Copula function C from the candidate Copula functions. k Its statistical parameter space is Π, and the maximum likelihood estimation is used to determine when... The optimal statistical parameter vector at that time:

[0054]

[0055] And calculate the corresponding BIC value, where, The star in the upper right corner indicates that it is the optimal parameter vector that maximizes the likelihood;

[0056] S54. Based on the BIC criterion, determine the optimal function from the candidate Copula functions, that is:

[0057]

[0058] The optimal joint distribution family that ΔZ follows is In the formula, C * The star in the upper right corner indicates that it is the optimal Copula function that minimizes BIC, η * It is the corresponding optimal statistical parameter vector.

[0059] Preferably, the BIC value is calculated as follows:

[0060]

[0061] Where φ represents a statistical distribution with a statistical parameter vector θ, Data represents the data, which is a vector or matrix, and lnL φ (Data|θ) represents the log-likelihood function of the distribution φ with respect to the current parameters and data, λ(θ) represents the number of statistical parameters of θ, and n is the number of data samples in Data, which is equal to the number of elements contained in Data.

[0062] Preferably, the Copula function includes a multivariate normal Copula function and a multivariate Clayton Copula function.

[0063] Preferably, the multivariate normal Copula function and the multivariate Clayton Copula function have the following forms:

[0064] Multivariate normal Copula function:

[0065] C(u;ρ)=Φ(Φ inv (u1), ..., Φ inv (u n );ρ) (20)

[0066] Where Φ is the standard normal distribution function, Φ inv ρ is the inverse function of the standard normal distribution function, and ρ is the correlation coefficient matrix;

[0067] Multivariate Clayton Copula functions:

[0068]

[0069] Compared with existing methods, the advantages of the method of the present invention are:

[0070] (1) The reliability modeling method of the present invention does not rely on the hierarchical structure of the firearm system. When faced with the situation where the internal coupling relationship of components cannot be clarified due to the extreme complexity of the hierarchical structure of the firearm system, it directly takes the joint degradation characteristics of multiple key performances of the firearm system as the starting point and uses the Copula function to characterize its correlation as an aid. It concisely constructs the mapping relationship between the reliability model of the firearm system and the multi-performance degradation data, improves the accuracy of reliability modeling, and proposes a new modeling method for the reliability analysis of firearm systems, filling the gap in this part of the technology.

[0071] (2) Compared with traditional reliability analysis methods, the reliability modeling method of the present invention does not rely on life statistics data. Given that life data of firearm systems is becoming increasingly difficult to obtain and its information value is declining, the reliability prediction of firearm systems can be accurately modeled using degradation performance data. This overcomes the defect of difficulty in obtaining life data and can make full use of the advantages of easy collection of performance data and the fact that it contains more degradation information of firearm systems. This makes the constructed firearm system reliability model more accurate and objective, thereby enabling accurate prediction of the reliability of firearm systems. Attached Figure Description

[0072] Figure 1 This is a flowchart of the firearm system reliability modeling method based on Copula and multi-performance degradation data proposed in this invention;

[0073] Figure 2 This is a degradation trajectory diagram of multiple key performance parameters of the object involved in a specific implementation case of the present invention;

[0074] Figure 3 This is a reliability function diagram of the firearm system involved in a specific implementation case of the present invention. Detailed Implementation

[0075] The method of the present invention will now be described in detail with reference to the accompanying drawings and specific embodiments.

[0076] Specifically, this invention provides a method for reliability modeling of firearm systems based on Copula and multi-performance degradation data, such as... Figure 1 As shown, it includes the following steps:

[0077] S1. Determine the key performance parameters Z1, Z2, ..., Z1, Z2, ..., Z3, which indicate whether the associated firearm system will fail, through failure mechanism analysis. m and its failure threshold The failure threshold is set to the lower limit by default.

[0078] S2. Obtain the initial values ​​of various key performance parameters of the firearm system at time t=0.

[0079] S3. Put the firearm system into operation, i.e., conduct projectile firing tests, and complete the tests at a set time point, i.e., before the end of its service life. j (j = 1, ..., n) Obtain the values ​​of its key performance parameters z. i (t j (i = 1, ..., m), forming multiple degenerate trajectories, and calculating the corresponding degeneracy amounts to obtain a numerical matrix:

[0080]

[0081] in,

[0082] t0=0, Δz i (t j , t j-1 )=-Δz i (t j-1 , t j )=z i (t j-1 )-z i (t j (i = 1, ..., m; j = 1, ..., n) represents the firearm system at t j-1 to t j Key performance parameter Z during runtime i The amount of degradation.

[0083] S4. Based on the numerical matrix Λ, using maximum likelihood estimation and the BIC criterion, identify the marginal distribution family and statistical parameters that the degradation of various key performance parameters of the firearm system follows.

[0084] S41. Determine the candidate distribution family φ indexed by the time parameter, such as the Gamma process. 1 φ 2 , …, φ l That is, the family of alternative distributions for various stochastic processes.

[0085] S42. Randomly select the data from the i-th row of Λ (i = 1, 2, ..., m):

[0086] Λ i，： =[Δz i (t1, t0) Δz i (t2, t1) … Δz i (t n , t n-1 (2)

[0087] Suppose that the corresponding stochastic process follows a certain marginal distribution family, that is:

[0088] ΔZ i (t v , t u )~ψ i (t u , t v ;θ i )(t u <t v (3)

[0089] Where, ψ i Refers to the time parameter t u , t v The index is a distribution family containing the vector of statistical parameters to be estimated, θ. i Its probability density function is expressed as:

[0090]

[0091] Therefore, a log-likelihood function is constructed.

[0092]

[0093] In the formula, j is the time subscript, representing the j-th time point, which corresponds to t in S3. j They have the same meaning.

[0094] S43. Randomly select the k-th (k = 1, 2, ..., l) distribution family φ from the candidate distribution families. k Its statistical parameter space is Θ, and the maximum likelihood estimation is used to determine when ψ i =φ k The optimal statistical parameter vector at that time:

[0095]

[0096] And calculate the corresponding BIC value.

[0097]

[0098] in, express The dimension is the number of statistical parameters, where n is Λ i，： The dimension is the number of data samples.

[0099] S44. Based on the BIC criterion, determine ΔZ from the candidate distribution families. i The optimal marginal distribution family it follows and its statistical parameters are:

[0100]

[0101] S5. Based on the marginal distribution information of performance parameter degradation obtained in S4, using the Copula function and maximum likelihood estimation, and based on the BIC criterion, identify the joint distribution family and its statistical parameters that the degradation of various key performance parameters of the firearm system follows.

[0102] S51. Determine the alternative Copula functions C 1 C 2 C w .

[0103] S52. Assume that the degradation of key performance parameters of a firearm system follows a certain Copula function C∈{C 1 C 2 C w} represents a connected joint distribution family Right now:

[0104]

[0105] Where η is the vector of statistical parameters to be estimated contained in the Copula function, and the random vector ΔZ(t) v , t u The probability density function and probability distribution function of are expressed as:

[0106]

[0107] Suppose the distribution family The probability density function and probability distribution function are:

[0108]

[0109] Also set

[0110]

[0111] In the formula, To find the sign of the partial derivative, F i (i∈{1,…,m}) is the i-th representative element of function c, representing the value of a certain probability distribution function. Then formula (10) can be written as:

[0112]

[0113] Briefly denote Δz i (t j , t j-1 ) for Λ i，j Thus, the log-likelihood function is constructed.

[0114]

[0115] By removing the terms in (14) that are irrelevant to η, we obtain the simplified log-likelihood function:

[0116]

[0117] S53. Randomly select the k-th (k = 1, 2, ..., w) Copula function C from the candidate Copula functions. k Its statistical parameter space is Π, and the maximum likelihood estimation is used to determine when... The optimal statistical parameter vector at that time.

[0118]

[0119] And calculate the corresponding BIC value.

[0120]

[0121] in, express The dimension of Λ is the number of statistical parameters, and mn is the number of elements in Λ (i.e., the number of data samples).

[0122] S54. Based on the BIC criterion, determine the optimal function from the candidate Copula functions, that is:

[0123]

[0124] Wherein, the optimal joint distribution family that ΔZ follows is...

[0125] S6. Based on the joint distribution information of performance parameter degradation obtained in step S5, derive the joint distribution of the values ​​of various key performance parameters of the firearm system at any time t, that is:

[0126]

[0127] Therefore, a reliability model for the firearm system is constructed, characterized by a reliability function:

[0128]

[0129] Where Pr is a probability measure.

[0130] In practical applications, for upper limit thresholds or dual limit thresholds, simply change the corresponding event. Then, make the corresponding adjustments to the final form.

[0131] To describe in detail the specific implementation of the method of the present invention, a certain type of firearm system Q is taken as the research object, and the implementation steps are explained as follows. All data in this case have been converted into dimensionless data of the same order of magnitude:

[0132] S1. Perform a failure mechanism analysis on the firearm system Q to determine its key performance parameters Z = (Z1, Z2, Z3) and its failure threshold. Among them, (Z1, Z2, Z3) refer to the key performance parameters of the firearm system Q, namely the mechanical characteristic parameters of the elastic component, the morphological characteristic parameters of the impact component, and the material characteristic parameters of the ignition component.

[0133] S2. Obtain the initial values ​​of the key performance parameters of the firearm system Q.

[0134] S3. Put the firearm system Q into operation at the set time point t. i =1000i (i=1,2,…,10) to obtain the values ​​of its key performance parameters, forming multiple degradation trajectories as follows Figure 2 As shown, and in conjunction with the initial value information obtained in step S2, the compiled initial value information is shown in Table 1.

[0135] Table 1

[0136]

[0137] Based on the data in Table 1, the corresponding degradation amount was calculated, and the resulting 3×10 numerical matrix Λ was obtained:

[0138]

[0139] S4. Based on the numerical matrix Λ, using maximum likelihood estimation and the BIC criterion, identify the marginal distribution family and statistical parameters of the degradation of various key performance parameters of the firearm system:

[0140] The candidate distribution families (stochastic processes) are determined as shown in Table 2.

[0141] Table 2

[0142]

[0143] Taking any data from the i-th row of Λ (i = 1, 2, 3), the optimal distribution family is selected from the candidate distribution families based on maximum likelihood estimation and the BIC criterion, and its optimal statistical parameters are determined. The results are shown in Table 3. The numerical values ​​are expressed in scientific notation, and the suffix e-3 / e-4 / e-5 represents ×10. -3 / ×10 -4 / ×10 -5 .

[0144] Table 3

[0145]

[0146]

[0147] Final determination:

[0148]

[0149] S5. Based on the marginal distribution information of the performance parameter degradation obtained in step S4, and using the Copula function and maximum likelihood estimation, and based on the BIC criterion, identify the joint distribution family and statistical parameters of the degradation of each key performance parameter of the firearm system Q.

[0150] The alternative Copula functions are determined as shown in Table 4.

[0151] Table 4

[0152]

[0153] Based on the data of Λ, the optimal Copula function is selected from the candidate Copula functions according to the maximum likelihood estimation and the BIC criterion, and its optimal statistical parameters are determined. The results are shown in Table 5.

[0154] Table 5

[0155] <![CDATA[C 1 ]]> 7.2095 <![CDATA[(η1,η2,η3)=(ρ 12 ,r 13 ,r 23 )=(-0.0553,-0.0404,0.5471)]]> <![CDATA[C 2 ]]> 2.7437 η = 0.1817

[0156] The optimal Copula function was finally determined to be:

[0157]

[0158] S6. Based on the joint distribution information of performance parameter degradation obtained in step S5, derive the joint distribution of the key performance parameters of the firearm system Q at any time t, and construct a reliability model of the firearm system using the reliability function R. s (t) is characterized as:

[0159]

[0160] Its function graph is as follows Figure 3 As shown, the horizontal axis represents time, with the unit being the number of projectiles fired (Fa), and the vertical axis represents the system reliability.

[0161] The embodiments described above are merely preferred embodiments of the present invention and are not intended to limit the scope of the present invention. Various modifications and improvements made by those skilled in the art to the technical solutions of the present invention without departing from the spirit of the present invention should fall within the protection scope defined by the claims of the present invention.

Claims

1. A reliability modeling method for firearm systems based on Copula and multi-performance degradation data, characterized in that: It includes the following steps: S1. Determine the key performance parameters Z1, Z2, ..., Z1, Z2, ..., Z3, which indicate whether the associated firearm system will fail, through failure mechanism analysis. m and its failure threshold Where Z is the key performance parameter, Z th , where m is the failure threshold corresponding to the key performance parameter; among them, the key performance parameters related to the failure of the firearm system are the mechanical characteristic parameters of the elastic component, the morphological characteristic parameters of the impact component, or the material characteristic parameters of the ignition component of the firearm system. S2. Obtain the initial values ​​of various key performance parameters of the firearm system at time t=0. Where i is the i-th key performance parameter; S3. Conduct projectile firing tests on the firearm system at the set time point t. j (j = 1, ..., n) Obtain the values ​​of its key performance parameters z. i (t j (i = 1, ..., m), forming multiple degenerate trajectories, and calculating the corresponding degeneracy amounts to obtain the numerical matrix Λ of the degenerate trajectories: in, t0=0, Δz i (t j , t j-1 )=-Δz i (t j-1 , t j )=z i (t j-1 )-z i (t j (i = 1, ..., m; j = 1, ..., n) represents the firearm system at t j-1 to t j Key performance parameter Z during runtime i The amount of degradation; S4. Based on the numerical matrix Λ of the degradation trajectory, using maximum likelihood estimation and the BIC criterion, identify the marginal distribution family and statistical parameters of the degradation of various key performance parameters of the firearm system: S41. Determine the candidate distribution family φ indexed by the time parameter. 1 , φ 2 , …, φ l ; S42. Data of the i-th row (i = 1, 2, ..., m) of the numerical matrix Λ of any degenerate trajectory: Λ i，： =[Δz i (t1,t0) Δz i (t2,t1) … Δz i (t n ,t n-1 )] (2) Suppose that the corresponding stochastic process follows a certain marginal distribution family, that is: ΔZ i (t v ,t u )~ψ i (t u ,t v ;θ i )(t u <t v ) (3) Where, ψ i Generally refers to the time parameter t u , t v The index is a distribution family containing the vector of statistical parameters to be estimated, θ. i The subscripts u and v are used to distinguish between two time parameter values ​​that are not the same, and their probability density function is expressed as: Constructing the log-likelihood function Where j is the time index, representing the j-th time point; S43. Randomly select the k-th (k = 1, 2, ..., l) distribution family φ from the candidate distribution families. k Its statistical parameter space is Θ, and the maximum likelihood function is used to estimate when ψ i =φ k The optimal statistical parameter vector at that time: And calculate the corresponding BIC value; S44. Based on the BIC criterion, determine ΔZ from the candidate distribution families. i The optimal marginal distribution family it follows and its statistical parameters are: S5. Based on the marginal distribution family and statistical parameters of the performance parameter degradation obtained in step S4, using the Copula function and maximum likelihood estimation, and based on the BIC criterion, identify the joint distribution family and statistical parameters of the degradation of each key performance parameter of the firearm system. S6. Based on the joint distribution family and statistical parameters of the degradation of various key performance parameters of the firearm system obtained in step S5, the joint distribution of the values ​​of various key performance parameters of the firearm system at any time t is obtained: Construct a reliability model for the firearm system, using the reliability function R. s (t) is characterized as: Where Pr is a probability measure.

2. The firearm system reliability modeling method based on Copula and multi-performance degradation data according to claim 1, characterized in that: Step S5 specifically includes the following sub-steps: S51. Determine multiple alternative Copula functions C 1 C 2 C w ; S52. Assume that the degradation of key performance parameters of a firearm system follows a certain Copula function C∈{C 1 C 2 , ...C w } represents a connected joint distribution family Right now: Where η is the vector of statistical parameters to be estimated contained in the Copula function, and the random vector ΔZ(t) v , t u The probability density function and probability distribution function of are expressed as: Suppose the distribution family The probability density function and probability distribution function are: Also set in, To find the sign of the partial derivative, F i (i∈{1,…,m}) is the i-th representative element of function c, representing the value of a certain probability distribution function; Then formula (10) can be written as: Let Δz i (t j , t j-1 ) for Λ i，j Construct the log-likelihood function: By removing the terms in formula (14) that are irrelevant to η, we obtain the simplified log-likelihood function: S53. Randomly select the k-th (k = 1, 2, ..., w) Copula function C from the candidate Copula functions. k Its statistical parameter space is Π, and the maximum likelihood estimation is used to determine when... The optimal statistical parameter vector at that time: And calculate the corresponding BIC value; S54. Based on the BIC criterion, determine the optimal function from the candidate Copula functions, i.e.: The optimal joint distribution family that ΔZ follows is...

3. The firearm system reliability modeling method based on Copula and multi-performance degradation data according to claim 1, characterized in that: The specific calculation method for the BIC value is as follows: Where φ represents a statistical distribution with a statistical parameter vector θ, Data represents the data, which is a vector or matrix, and lnL φ (Data|θ) represents the log-likelihood function of the distribution φ with respect to the current parameters and data, λ(θ) represents the number of statistical parameters of θ, and n is the number of data samples in Data, which is equal to the number of elements contained in Data.

4. The firearm system reliability modeling method based on Copula and multi-performance degradation data according to claim 1, characterized in that: The Copula function includes the multivariate normal Copula function and the multivariate Clayton Copula function.

5. The firearm system reliability modeling method based on Copula and multi-performance degradation data according to claim 4, characterized in that: The multivariate normal Copula function and the multivariate Clayton Copula function have the following forms: Multivariate normal Copula function: C(u;ρ)=Φ(Φ inv (u1),…,Φ inv (u n );p) (20) Where Φ is the standard normal distribution function, Φ inv ρ is the inverse function of the standard normal distribution function, and ρ is the correlation coefficient matrix; Multivariate Clayton Copula functions:

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