Optimization method of equivalent accelerated life test for gun system based on maintenance behavior modeling

Abstract

The application provides an equivalent optimization method for in-field accelerated life test of a gun system considering maintenance behavior modeling, which comprises the following steps: constructing a system reliability model considering maintenance behavior modeling, determining to-be-optimized parameters of equivalent in-field test, obtaining a system log-likelihood function of in-field and out-field test, estimating to-be-determined parameters in the constructed system reliability model considering maintenance behavior modeling, calculating an asymptotic variance of in-field and out-field test, constructing an asymptotic variance constraint condition, constructing an optimization model and obtaining an optimal solution of the to-be-optimized parameters. The application introduces maintenance behavior modeling in reliability modeling and considers the asymptotic variance constraint, so that the in-field test design of the repairable system is more reasonable and effective, the life prediction is more accurate, and the actual problem that the existing in-field test cannot effectively reflect the complex out-field use environment is overcome.

Description

Technical Field

[0001] This invention belongs to the field of reliability design technology, specifically a method for equivalent optimization of accelerated life testing in a firearm system considering maintenance behavior modeling during in-field testing. Background Technology

[0002] Accelerated life testing is widely used in product design and manufacturing processes, serving as a crucial means of verifying whether products meet design requirements. Over decades of development, accelerated life testing has evolved from the initial constant stress accelerated life testing to sequential stress accelerated life testing, step stress accelerated life testing, and time-varying stress accelerated life testing, among others. The choice of different types of accelerated life testing often has a significant impact on the expected results; therefore, selecting the appropriate accelerated life test type and developing a suitable accelerated life test plan is essential for obtaining ideal accelerated life test data.

[0003] The environmental stresses faced by products in actual use are highly complex. However, laboratory field tests can only provide a limited range of environmental stress types and intensities. Therefore, laboratory field tests cannot accurately reflect the complex environmental loads encountered by products during actual use. Furthermore, repairable products are common in production and daily life, but related research often fails to consider the impact of product maintenance on test results when proposing equivalent design methods. Simply treating faulty products as failures in test design significantly underestimates the product's lifespan, thereby reducing the rationality and accuracy of the designed test scheme and failing to reflect the product's true operating conditions.

[0004] Therefore, to address this issue, it is urgent and necessary to seek an equivalent optimization method for accelerated life testing of firearm systems that considers maintenance behavior modeling by introducing a maintenance behavior model and considering asymptotic variance constraints. This aims to design an equivalent indoor test scheme for repairable systems under their actual use environment and achieve more realistic and accurate life prediction. Summary of the Invention

[0005] This invention addresses the shortcomings of existing technologies by proposing an equivalent optimization method for accelerated life testing of firearm systems in an indoor field, incorporating maintenance behavior modeling. This method includes constructing a system reliability model considering maintenance behavior modeling, determining the parameters to be optimized in the equivalent indoor field test, obtaining the system's log-maximum likelihood function for both indoor and outdoor field tests, estimating the undetermined parameters in the constructed system reliability model considering maintenance behavior modeling, calculating the asymptotic variance of the indoor and outdoor field tests, constructing asymptotic variance constraints, building an optimization model, and obtaining the optimal solution for the parameters to be optimized. By introducing maintenance behavior modeling into reliability modeling and considering asymptotic variance constraints, this invention makes the design of indoor field tests for repairable systems more reasonable and effective, resulting in more realistic and accurate life predictions. It overcomes the problem that existing indoor field tests cannot effectively reflect the actual conditions of complex outdoor operating environments.

[0006] This invention provides an equivalent optimization method for accelerated life testing of a firearm system considering maintenance behavior modeling, comprising the following steps:

[0007] S1. Construct a system reliability model that considers maintenance behavior modeling: Determine the system's sensitive stresses through mechanism analysis, determine the maintenance behavior model based on historical system data, and comprehensively establish a system reliability model that considers maintenance behavior modeling.

[0008] S2. Determine the parameters to be optimized for the equivalent indoor field test: Based on the system's historical data, determine the types of indoor field test profiles, form an equivalent indoor field test model, and determine the parameters to be optimized for the equivalent indoor field test.

[0009] S3. Obtain the maximum log-likelihood function L of the system in the internal and external field tests and estimate the undetermined parameters in the constructed system reliability model considering maintenance behavior modeling: Based on the system reliability model considering maintenance behavior modeling constructed in step S1, obtain the maximum log-likelihood function L of the system in the internal and external field tests, substitute the historical environmental data and failure data in the corresponding historical environment in the historical data of the system, and estimate the undetermined parameters in the constructed system reliability model considering maintenance behavior modeling by using the maximum likelihood estimation method.

[0010] S4. Calculate the asymptotic variance Avar of the internal and external field tests: Based on the system log-maximal likelihood function L obtained in step S3, construct the Fisher information matrix I for the internal and external field tests. n =[I nY I nX ], calculate the asymptotic variance Avar of the indoor and outdoor field tests = [Avar Y Avar X ], where I nY Indicates the Fischer information matrix for the indoor field test; I nX Represents the Fischer information matrix for field testing; Avar YAvar represents the asymptotic variance of the indoor test. x Indicates the asymptotic variance of the field test;

[0011] S5. Constructing asymptotic variance constraints The equivalent criterion function Q(Θ) is determined based on the statistical optimization criterion, where Θ represents the parameter to be determined; and the asymptotic variance constraint conditions are constructed based on the asymptotic variance Avar of the internal and external field experiments obtained in step S4.

[0012] S6. Construct an optimization model and obtain the optimal solution for the parameter Λ to be optimized: based on the asymptotic variance constraint conditions obtained in step S5. An optimization constraint is constructed, and the optimization parameter Λ of the equivalent indoor field test obtained in step S2 is used as the optimization objective. An optimization model is established, and optimization design is performed to obtain the optimal solution for the optimization parameter Λ under the optimization constraint. The optimization model is as follows:

[0013]

[0014] Among them, Λ min Λ max These represent the maximum and minimum value vectors of the parameter Λ to be optimized, respectively.

[0015] Furthermore, step S4 specifically includes the following steps:

[0016] S41. Based on the system's logarithmic maximum likelihood function L obtained in step S3, construct the Fisher information matrix I for the internal and external field experiments. n :

[0017]

[0018] Where n represents the number of elements in the undetermined parameter Θ; θ i Represents the i-th element in the undetermined parameter Θ and T represents matrix transpose; E represents expectation; the Fischer information matrix I of the indoor field experiment nY The results are obtained by substituting the indoor field data into equation (3); the Fischer information matrix I of the outdoor field test is obtained. nX The result is obtained by substituting the field data into equation (3);

[0019] S42. Calculate the asymptotic variance Avar of the indoor and outdoor field tests:

[0020]

[0021] Among them, a Θ Describes the gradient vector and R(Θ) represents the system reliability function; Represents the Fischer information matrix I for indoor and outdoor field tests n The inverse matrix; the asymptotic variance Avar of the indoor field test. Y By using the Fischer information array I of the indoor field test nY Substituting into equation (4), we obtain the asymptotic variance Avar of the field test. X By using the Fischer information array I of the field test nX Substituting into equation (4) yields the result.

[0022] Preferably, obtaining the system's log-maximum likelihood function L in step S3 specifically includes the following steps:

[0023] S31. Determine whether there are any fault time records in the historical data of the system, including the internal and external field test data. If the specific fault time of the system is recorded, the log maximum likelihood function is obtained directly. If the fault observation time is recorded but the specific fault time of the system is unknown, proceed to step S32. If there are no fault records, proceed to step S33.

[0024] S32. Considering the censored case, we obtain the log-maximum likelihood function under the censored case.

[0025] S33. Based on the system reliability model considering maintenance behavior modeling constructed in step S1, and taking into account the test time and test environment parameters, calculate the theoretical number of system failures under test conditions. Based on step S32, obtain the log-maximum likelihood function under censoring conditions, which is the system log-maximum likelihood function L of the internal and external field tests.

[0026] Preferably, the system reliability model considering maintenance behavior modeling in step S1 is constructed using an equivalent virtual service time or an equivalent failure intensity function. If constructed using an equivalent failure intensity function, then step S1 specifically includes the following steps:

[0027] S11. Based on the system's historical data, establish a system reliability model R(t|Θ), where t represents the system's lifetime;

[0028] S12. Calculate the failure strength function λ(t) of the first system:

[0029]

[0030] S13. Establish the equivalent system failure strength function λ that considers maintenance behavior. t :

[0031] λ t =λ(t)-Δλ (2)

[0032] Wherein, Δλ represents the reduction in system failure strength considering maintenance behavior;

[0033] S14, λ t Substituting the second system failure intensity function into the system reliability model, we obtain the system reliability model R that considers maintenance behavior modeling. M .

[0034] Preferably, the asymptotic variance constraint condition in step S5 It is established based on the similarity of evaluating asymptotic variance, assuming If the constraint function is defined, then the asymptotic variance constraint condition is... satisfy:

[0035]

[0036] Where q represents the numerical value of similarity, and its value ranges from [0, 1). The smaller the value, the stricter the constraint.

[0037] Preferably, the system reliability model considering maintenance behavior modeling in step S1 is a new system reliability model that integrates system reliability modeling and maintenance behavior modeling. It reflects the impact of maintenance behavior on system reliability by introducing maintenance parameters that affect the values ​​of system reliability parameters.

[0038] Preferably, in step S6, it is determined whether there are integer constraints in the optimization design solution process. If there are, the integer constraints are separated first, and the optimal solution of the parameter to be optimized Λ under the optimization constraint is obtained under each integer constraint. Then, the optimal solution of the parameter to be optimized Λ under the optimization constraint is obtained by comparison. If there are no integer constraints, the optimal solution of the parameter to be optimized Λ under the optimization constraint is directly solved.

[0039] Preferably, in step S6, the stress magnitude in the optimization constraint is normalized based on the highest and lowest loaded stresses, and the normalized stress values ​​are between 0 and 1.

[0040] Preferably, the statistical optimization criteria in step S5 include A-optimal design, C-optimal design, D-optimal design, E-optimal design and T-optimal design.

[0041] Compared with the prior art, the technical effects of the present invention are as follows:

[0042] 1. The present invention provides an equivalent optimization method for accelerated life testing of firearm systems in the field, which takes into account maintenance behavior modeling. It has significant advantages. For accelerated life testing schemes of repairable systems, it introduces maintenance behavior modeling into reliability modeling and considers asymptotic variance constraints to optimize and obtain an equivalent accelerated life testing scheme for the real use environment in the field. This provides an equivalent design criterion for the design of field tests of repairable systems.

[0043] 2. The present invention provides an equivalent optimization method for accelerated life testing of firearm systems in the field, which considers maintenance behavior modeling. This design method, which considers maintenance behavior modeling, ensures that the estimation accuracy of the in-field test is close to that of the actual use in the field, making the design of in-field tests for repairable systems more reasonable and effective, and facilitating more realistic and accurate life prediction. In addition, this method is general and overcomes the problem that existing in-field tests cannot effectively reflect the actual situation of complex field use environments. It can provide a design method for in-field test schemes for repairable systems under different use environments. Attached Figure Description

[0044] Other features, objects, and advantages of this application will become more apparent from the following detailed description of non-limiting embodiments with reference to the accompanying drawings.

[0045] Figure 1 This is a flowchart of the equivalent optimization method for accelerated life testing of a firearm system considering maintenance behavior modeling in this invention. Detailed Implementation

[0046] The present application will now be described in further detail with reference to the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are merely illustrative of the invention and not intended to limit it. Furthermore, it should be noted that, for ease of description, only the parts relevant to the invention are shown in the accompanying drawings.

[0047] It should be noted that, unless otherwise specified, the embodiments and features described in this application can be combined with each other. This application will now be described in detail with reference to the accompanying drawings and embodiments.

[0048] Figure 1 This invention illustrates an equivalent optimization method for accelerated life testing of firearm systems in the field, considering maintenance behavior modeling. The method includes the following steps:

[0049] S1. Construct a system reliability model that considers maintenance behavior modeling: Determine the system's sensitive stresses through mechanism analysis, determine the maintenance behavior model based on the system's historical data, and comprehensively establish a system reliability model that considers maintenance behavior modeling.

[0050] The system reliability model considering maintenance behavior modeling is constructed using equivalent virtual service time or equivalent failure intensity function. If constructed using equivalent failure intensity function, step S1 specifically includes the following steps:

[0051] S11. Based on the system's historical data, establish a system reliability model R(t|Θ), where t represents the system lifetime and Θ represents undetermined parameters.

[0052] S12. Calculate the failure strength function λ(t) of the first system:

[0053]

[0054] S13. Establish the equivalent system failure strength function λ that considers maintenance behavior. t :

[0055] λ t =λ(t)-Δλ (2)

[0056] Where Δλ represents the reduction in system failure intensity considering maintenance behavior.

[0057] S14, λ t Substituting the second system failure intensity function into the system reliability model, we obtain the system reliability model R that considers maintenance behavior modeling. M .

[0058] The system reliability model that considers maintenance behavior modeling is a new system reliability model that integrates system reliability modeling and maintenance behavior modeling. It reflects the impact of maintenance behavior on system reliability by introducing maintenance parameters that affect the values ​​of system reliability parameters.

[0059] S2. Determine the optimization parameters Λ for the equivalent indoor field test: Based on the system's historical data, determine the types of indoor field test profiles, form an equivalent indoor field test model, and determine the optimization parameters Λ for the equivalent indoor field test.

[0060] S3. Obtain the maximum likelihood function L of the system logarithmic model for indoor and outdoor field tests and estimate the undetermined parameters in the constructed system reliability model considering maintenance behavior modeling: Based on the system reliability model considering maintenance behavior modeling constructed in step S1, obtain the maximum likelihood function L of the system logarithmic model for indoor and outdoor field tests, substitute the historical environmental data and failure data in the corresponding historical environment from the system historical data, and estimate the undetermined parameters in the constructed system reliability model considering maintenance behavior modeling by using the maximum likelihood estimation method.

[0061] The specific steps to obtain the system's log-maximum likelihood function L are as follows:

[0062] S31. Determine whether there are any fault time records in the system's historical data of internal and external field test data. If the specific fault time of the system is recorded, the logarithmic maximum likelihood function is obtained directly. If the fault observation time is recorded but the specific fault time of the system is unknown, proceed to step S32. If there are no fault records, proceed to step S33.

[0063] S32. Considering the censored case, we obtain the log-maximum likelihood function under the censored case.

[0064] S33. Based on the system reliability model considering maintenance behavior modeling constructed in step S1, and taking into account the test time and test environment parameters, calculate the theoretical number of system failures under test conditions. Based on step S32, obtain the log-maximum likelihood function under censoring conditions, which is the system log-maximum likelihood function L for internal and external field tests.

[0065] S4. Calculate the asymptotic variance Avar of the internal and external field tests: Based on the system log-maximal likelihood function L obtained in step S3, construct the Fischer information matrix I for the internal and external field tests. n =[I nY I nX ], calculate the asymptotic variance Avar of the indoor and outdoor field tests = [Avar Y Avar X ], where I nY Indicates the Fischer information matrix for the indoor field test; I nX Represents the Fischer information matrix for field testing; Avar Y Avar represents the asymptotic variance of the indoor test. X This represents the asymptotic variance of the field test.

[0066] S41. Based on the system logarithmic maximum likelihood function L obtained in step S3, construct the Fisher information matrix I for the internal and external field experiments. n :

[0067]

[0068] Where n represents the number of elements in the undetermined parameter Θ; θ i Represents the i-th element in the undetermined parameter Θ and T represents matrix transpose; E represents expectation; Fischer information matrix I for indoor experiments nY The results are obtained by substituting the indoor field data into equation (3); the Fischer information matrix I for the outdoor field experiment is obtained. nX The result is obtained by substituting the field data into equation (3).

[0069] S42. Calculate the asymptotic variance Avar of the indoor and outdoor field tests:

[0070]

[0071] Among them, a Θ Describes the gradient vector and R(Θ) represents the system reliability function; Represents the Fischer information matrix I for indoor and outdoor field tests n Inverse matrix; AvarY of the in-field test asymptotic variance is obtained by using the Fischer information matrix of the in-field test. nY Substituting into equation (4), we obtain the asymptotic variance Avar of the field experiment. X By using the Fischer information array I in the field experimentnX Substituting into equation (4) yields the result.

[0072] The gradient vector is the gradient vector a under specified conditions. Θ Furthermore, the same gradient vector is used in both the equivalent and non-equivalent models.

[0073] S5. Constructing asymptotic variance constraints Based on the statistical optimization criteria, the equivalent criterion function Q(Θ) is determined. Then, based on the asymptotic variance Avar of the internal and external field experiments obtained in step S4, asymptotic variance constraints are constructed.

[0074] Statistical optimization criteria include A-optimal design, C-optimal design, D-optimal design, E-optimal design, and T-optimal design. Among these, A-optimal design refers to selecting a specific experimental design that maximizes the Fischer information matrix I. n The trace of the inverse matrix reaches a minimum; C-optimal design refers to selecting a specific experimental design that minimizes the trace of the Fischer information matrix I. n The calculated asymptotic variance value reaches a minimum; D-optimal design refers to selecting a specific experimental design that minimizes the Fischer information matrix I. n The determinant of the inverse matrix reaches a minimum; E-optimal design refers to selecting a specific experimental design that minimizes the Fischer information matrix I. n The maximum eigenvalue is minimized; T-optimal design refers to selecting a specific experimental design that minimizes the Fischer information matrix I. n The reciprocal of the trace of the inverse matrix reaches a minimum.

[0075] Based on different statistical optimization criteria, the corresponding equivalent criterion functions Q(Θ) are obtained, as shown in Table 1.

[0076]

[0077] Table 1

[0078] asymptotic variance constraints It is established based on the similarity of evaluating asymptotic variance, assuming If is a constraint function, then the asymptotic variance constraint condition is... satisfy:

[0079]

[0080] Where q represents the numerical value of similarity, and its value ranges from [0, 1). The smaller the value, the stricter the constraint.

[0081] S6. Construct an optimization model and obtain the optimal solution for the parameter to be optimized, Λ: based on the asymptotic variance constraints obtained in step S5. Optimization constraints are constructed, and the optimization parameter Λ obtained from the equivalent indoor field test in step S2 is used as the optimization objective. An optimization model is established, and optimization design is performed to obtain the optimal solution for the optimization parameter Λ under the optimization constraints. The optimization model is as follows:

[0082]

[0083] Among them, Λ min Λ max These represent the maximum and minimum value vectors of the parameter Λ to be optimized, respectively.

[0084] In step S6, it is determined whether there are integer constraints in the optimization design solution process. If there are, the integer constraints are separated first, and the optimal solution of the parameter to be optimized Λ under the optimization constraint is obtained under each integer constraint. Then, the optimal solution of the parameter to be optimized Λ under the optimization constraint is obtained by comparison. If there are no integer constraints, the optimal solution of the parameter to be optimized Λ under the optimization constraint is directly solved.

[0085] The stress magnitudes in the optimization constraints are normalized based on the highest and lowest loaded stresses, and the normalized stress values ​​are between 0 and 1.

[0086] The present invention will be further described in detail below with reference to the equivalent design process of an indoor accelerated life test of a rifle.

[0087] S1. For the selected rifle, use historical system data to determine the system's sensitive stresses through mechanistic analysis, and then combine existing empirical models to obtain a rifle system reliability model that takes into account maintenance behavior modeling.

[0088] Based on historical test data of a certain type of rifle and test results of similar models, assuming that the mechanism of temperature-induced failure conforms to the Arrhenius model and the mechanism of humidity-induced failure conforms to the Eyring model, the coupling effect of sand and wind speed on the rifle is regarded as mechanical stress, and an inverse power-law model is used for modeling. By integrating various stress models, the system failure probability function F(t) is established as follows:

[0089]

[0090] Where A, φ, b, c, and n represent the first, second, third, fourth, and fifth coefficients, respectively; T represents temperature stress; RH represents humidity stress; ω represents salt spray stress; P represents wind speed stress; and D represents dust stress.

[0091] After normalizing the stresses, a more general failure probability model is obtained, namely, the rifle system reliability model:

[0092]

[0093] Where f(t) represents the failure probability density function of the system; F(t) represents the failure distribution function of the system; Λ represents the parameters to be optimized in the equivalent indoor field test, and we have:

[0094] Λ=exp(θ0+θ1Z1+θ2Z2+θ3Z3+θ4Z4)=exp(Θ·Z) (9)

[0095] Where Z represents the normalized stress vector after normalization of temperature stress, humidity stress, salt spray stress, wind speed stress, and dust stress, and satisfies Z = [1, Z1, Z2, Z3, Z4]. T ; Θ represents an undetermined parameter, and satisfies Θ = [θ0, θ1, θ2, θ3, θ4].

[0096] Considering the nature of the repairable system, an appropriate maintenance behavior modeling method should be selected for maintenance behavior modeling. For this type of rifle, ARI (Automatic Repair Technology) is considered. m Modeling:

[0097]

[0098] Where λt represents the equivalent system failure strength function considering maintenance behavior; λ(t) represents the first system failure strength function; N t This represents the number of maintenance cycles the system has undergone at the current moment; m represents the impact of the previous m maintenance cycles on the current system failure rate; ρ represents the maintainability parameter.

[0099] Let m = 1, then λ t =Λ(1-ρ).

[0100] Substituting Λ(1-ρ) into equation (8) and replacing Λ, we obtain the system reliability model that considers maintenance behavior modeling.

[0101] S2. Based on the actual use of the rifle, select appropriate types of indoor test profiles as the objects to be optimized in this method.

[0102] Four test profiles were selected here, and the optimized schemes for the indoor test are shown in Table 2. In the table, the parameter A to be optimized is indicated by X(i).

[0103]

[0104] Table 2S3. Based on the test conditions and failure scenarios, the log-likelihood function L of the rifle is obtained:

[0105]

[0106] Based on historical rifle data, parameter estimation was performed for the given parameter Θ and maintainability parameter ρ. Table 3 provides an overview of the environmental profile and total failures from field tests in the historical rifle data, while Table 4 shows the failure times of the field test samples.

[0107]

[0108] Table 3

[0109]

[0110] Table 4

[0111] By substituting historical data into the log-likelihood function and taking partial derivatives with respect to the parameters, a likelihood equation is established to obtain the value of the undetermined parameter Θ.

[0112] Specifically, substituting the system reliability model that considers maintenance behavior modeling into the log-likelihood function, we get:

[0113]

[0114] For stress parameter θ i Establish the likelihood equation:

[0115]

[0116] Substituting the data from Tables 3 and 4, we solve the likelihood equation and obtain Θ = [-6.10, 1.93, -0.04, -0.73, -0.41]. T .

[0117] Similarly, a likelihood equation is established for the maintainability parameter ρ:

[0118]

[0119] Substituting the data from Tables 3 and 4, we solve the likelihood equation and get ρ = -3.7682.

[0120] S4. Substituting the undetermined parameter Θ into the system reliability model considering maintenance behavior modeling and the logarithmic maximum likelihood function, and based on the field test data in Tables 3 and 4, the field test Fischer information matrix I is calculated. nX :

[0121]

[0122] Based on the field test data, the gradient vector a is obtained. Θ :

[0123]

[0124] Obtain the asymptotic variance Avar of the field experiment X

[0125]

[0126] Similarly, during the optimization iteration process, the asymptotic variance Avar of the indoor field experiment was calculated. Y The temporary value.

[0127] S5. Consider constructing an equivalent criterion function Q(Θ) using D-optimal design, then Meanwhile, we consider establishing asymptotic variance constraints based on general criteria.

[0128]

[0129] S6. Numerical optimization is performed using the interior point method to obtain the optimal solution X for the parameter Λ to be optimized, which meets the conditions. The optimization model is as follows:

[0130]

[0131] Among them, T A This indicates the temperature value to be optimized for the high-temperature test; T B This indicates the temperature value to be optimized for the low-temperature test; T C This indicates the temperature value to be optimized in the dust emission test; T D This indicates the temperature value to be optimized for the salt spray test; RH A This indicates the humidity value to be optimized for high-temperature testing; W D This indicates the salt spray concentration value to be optimized in the salt spray test; P C D C These represent the wind speed and dust concentration values ​​to be optimized in the dust storm test profile, respectively; n g Indicates the sample size to be optimized for each profile; t g This indicates the time required for optimization testing of each profile.

[0132] The optimized scheme for the indoor field test is shown in Table 5 after solving the problem.

[0133]

[0134] Table 5

[0135] Based on the information in Table 5, the asymptotic variance of the optimized indoor test profile is calculated as follows:

[0136] Avar Y =3.087×10 -24 (20).

[0137] The existing indoor test schemes are shown in Table 6.

[0138]

[0139] Table 6

[0140] Based on the information in Table 6, the asymptotic variance of the existing indoor test profile is obtained as follows:

[0141] Avar0 = 1.488 × 10 -23 (twenty one).

[0142] The criteria for measuring the similarity of experimental schemes used in the examples are as follows:

[0143]

[0144] Where p represents similarity.

[0145] By calculating the similarity between the optimized indoor test scheme and the existing indoor test scheme and the outdoor test, we can obtain the following results:

[0146] p Y =99.77%, p0=59.06% (23).

[0147] Where, p Y p0 represents the similarity between the optimized indoor test scheme and the outdoor test; p0 represents the similarity between the existing indoor test scheme and the outdoor test. Clearly, the method of the present invention is superior in the embodiments.

[0148] This invention presents an equivalent optimization method for accelerated life testing of firearm systems in the field, incorporating maintenance behavior modeling. This method offers significant advantages. For accelerated life testing schemes of repairable systems, it introduces maintenance behavior modeling into reliability modeling and considers asymptotic variance constraints to optimize and obtain an equivalent accelerated life testing scheme for real-world field use environments. This provides an equivalent design criterion for the design of field tests for repairable systems. The design method considering maintenance behavior modeling ensures that the estimation accuracy of field tests closely approximates actual field usage conditions, making the design of field tests for repairable systems more reasonable and effective, and facilitating more realistic and accurate life prediction. Furthermore, this method is general, overcoming the problem that existing field tests cannot effectively reflect the actual conditions of complex field use environments, and can provide a design method for field test schemes of repairable systems under different usage environments.

[0149] Finally, it should be noted that the above embodiments are for illustration only and not for limiting the technical solutions of the present invention. Although the present invention has been described in detail with reference to the above embodiments, those skilled in the art should understand that modifications or equivalent substitutions can still be made to the present invention without departing from the spirit and scope of the present invention. Any modifications or partial substitutions should be covered within the scope of the claims of the present invention.

Claims

1. An equivalent optimization method for accelerated life testing of a firearm system considering maintenance behavior modeling, characterized in that, It includes the following steps: S1. Construct a system reliability model that considers maintenance behavior modeling: Determine the system's sensitive stresses through mechanism analysis, and determine the maintenance behavior model based on historical system data to establish a system reliability model that considers maintenance behavior modeling. The system reliability model considering maintenance behavior modeling is constructed using an equivalent virtual service time or an equivalent failure intensity function. If constructed using an equivalent failure intensity function, then step S1 specifically includes the following steps: S11. Establish a system reliability model based on historical system data. , where t represents the system lifetime; S12. Calculate the failure strength function of the first system. : ； S13. Establish an equivalent system failure strength function that considers maintenance behavior. : ； in, This represents the reduction in system failure strength after considering maintenance actions; S14, will Substituting the second system failure intensity function into the system reliability model, we obtain the system reliability model that considers maintenance behavior modeling. ; S2. Determine the parameters to be optimized for the equivalent interior field test. Based on historical system data, the types of indoor test profiles are determined, an equivalent indoor test model is formed, and the parameters to be optimized for the equivalent indoor test are determined. ; S3. Obtain the system log-maximal likelihood function of the indoor and outdoor field tests. And estimate the undetermined parameters in the constructed system reliability model considering maintenance behavior modeling: Based on the system reliability model considering maintenance behavior modeling constructed in step S1, obtain the system log-maximum likelihood function of the indoor and outdoor field tests. Substitute the historical environmental data and failure data under the corresponding historical environment into the historical data of the system, and estimate the undetermined parameters in the system reliability model that considers maintenance behavior modeling by using the maximum likelihood estimation method. S4. Calculate the asymptotic variance of the indoor and outdoor field tests. The system's log-maximum likelihood function obtained in step S3 Constructing the Fischer information array for indoor and outdoor field experiments Calculate the asymptotic variance of indoor and outdoor field tests. ,in, This represents the Fischer information array used in the indoor field test; This represents the Fischer information array used in field experiments. This represents the asymptotic variance of the indoor field test; Indicates the asymptotic variance of the field test; S5. Constructing asymptotic variance constraints Determining the equivalent criterion function based on statistical optimization criteria ,in, Indicate the parameters to be determined; and based on the asymptotic variance of the internal and external field tests obtained in step S4. Construct asymptotic variance constraints ; S6. Construct an optimization model and obtain the parameters to be optimized. The optimal solution is based on the asymptotic variance constraint obtained in step S5. Construct optimization constraints, and use the parameters to be optimized from the equivalent interior field test obtained in step S2. As the optimization objective, an optimization model is established, and optimization design and solution are performed to obtain the parameters to be optimized under the aforementioned optimization constraints. The optimal solution; the optimization model is: （5）； in, , They respectively represent the parameters to be optimized. The maximum and minimum value vectors.

2. The equivalent optimization method for accelerated life testing of a firearm system considering maintenance behavior modeling as described in claim 1, characterized in that, Step S4 specifically includes the following steps: S41. Based on the system's log-maximum likelihood function obtained in step S3. Constructing the Fischer information array for indoor and outdoor field experiments : ； Where n represents the parameter to be determined. The number of elements in the middle; Indicates parameters to be determined The i-th element in ; Represents matrix transpose; E represents expectation; the Fischer information matrix of the indoor test The Fischer information matrix of the external field test is obtained by substituting the indoor field data into equation (3). The result is obtained by substituting the field data into equation (3); S42. Calculate the asymptotic variance of the indoor and outdoor field tests. : ； in, Describes the gradient vector and ; A function representing system reliability; Fischer information array representing indoor and outdoor field tests The inverse matrix; the asymptotic variance of the indoor field test. By using the Fischer information array of the indoor test Substituting into equation (4), we obtain the asymptotic variance of the field test. By using the Fischer information array of the field test Substitute into equation (4) to obtain the result.

3. The equivalent optimization method for accelerated life testing of a firearm system considering maintenance behavior modeling as described in claim 1, characterized in that, The system log-maximum likelihood function in step S3 The specific steps to obtain it are as follows: S31. Determine whether there are any fault time records in the historical data of the system, including the internal and external field test data. If the specific fault time of the system is recorded, the log maximum likelihood function is obtained directly. If the fault observation time is recorded but the specific fault time of the system is unknown, proceed to step S32. If there are no fault records, proceed to step S33. S32. Considering the censored case, we obtain the log-maximum likelihood function under the censored case. S33. Based on the system reliability model considering maintenance behavior modeling constructed in step S1, and taking into account the test time and test environment parameters, calculate the theoretical number of system failures under the test conditions. Obtain the log-maximum likelihood function under censoring conditions according to step S32; this is the system log-maximum likelihood function for the internal and external field tests. .

4. The equivalent optimization method for accelerated life testing of a firearm system considering maintenance behavior modeling as described in claim 1, characterized in that, The asymptotic variance constraint condition in step S5 It is established based on the similarity of evaluating asymptotic variance, assuming If the constraint function is defined, then the asymptotic variance constraint condition is... satisfy: ； in, This represents a numerical value used to measure similarity, with a range of values. The smaller the value, the stricter the constraint.

5. The equivalent optimization method for accelerated life testing of a firearm system considering maintenance behavior modeling as described in claim 1, characterized in that, The system reliability model that considers maintenance behavior modeling in step S1 is a new system reliability model that integrates system reliability modeling and maintenance behavior modeling. It reflects the impact of maintenance behavior on system reliability by introducing maintenance parameters that affect the values ​​of system reliability parameters.

6. The equivalent optimization method for accelerated life testing of a firearm system considering maintenance behavior modeling as described in claim 1, characterized in that, In step S6, it is determined whether there are integer constraints in the optimization design solution process. If so, the integer constraints are separated first, and the parameters to be optimized under the optimization constraints are calculated for each integer constraint. The optimal solution is then compared to obtain the parameters to be optimized under the aforementioned optimization constraints. The optimal solution is found; if no optimal solution is found, the parameters to be optimized under the aforementioned optimization constraints are directly solved. The optimal solution.

7. The equivalent optimization method for accelerated life testing of a firearm system considering maintenance behavior modeling as described in claim 1, characterized in that, In step S6, the stress magnitude in the optimization constraint is normalized based on the highest and lowest loaded stresses, and the normalized stress values ​​are between 0 and 1.

8. The equivalent optimization method for accelerated life testing of a firearm system considering maintenance behavior modeling as described in claim 1, characterized in that, The statistical optimization criteria in step S5 include A-optimal design, C-optimal design, D-optimal design, E-optimal design and T-optimal design.

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