Missile life prediction method under zero fault data condition

Abstract

The invention discloses a missile life prediction method under the condition of zero failure data, relates to the technical field of missile life prediction, and aims to solve the problem that life distribution fitting cannot be performed by using a traditional distribution method under the condition of zero failure in test data. The method comprises the following steps: collecting missile field detection data, arranging the missile field detection data into regular truncation data, and calculating Bayesian estimation of fault probability of each point in zero-fault truncation data by using a multilayer Bayesian method; selecting a Weibull distribution function as an empirical life distribution function of the missile, and calculating the Bayesian estimation of the fault probability of each point by using a weighted least square method to obtain shape parameter estimation and scale parameter estimation of the Weibull distribution function; and obtaining reliability estimation of the missile according to the shape parameter estimation and the scale parameter estimation of the Weibull distribution function. According to the method, the problem of zero failure existing in regular detection can be effectively solved, and product life distribution is obtained.

Description

Technical Field

[0001] This invention relates to the field of missile life prediction technology, and in particular to a method for predicting missile life under zero-failure data conditions. Background Technology

[0002] Failure data is a crucial source of information for missile product life assessment. This includes failure data from troop firing tests over various storage years, failure data from component, subsystem, and whole missile components obtained through specialized life test disassembly and inspection, failure data from accelerated life tests of components, and failure data from specialized flight tests. This data reflects the changes in reliability and lifespan of products at various levels over storage time. Especially when the collected failure data spans multiple storage periods, such as failure data from long-term service (1-13 years) or even extended service (over 13 years) products under actual storage conditions, relatively reliable and accurate life assessment predictions can be obtained based on this data. Therefore, research on life assessment and prediction methods based on failure data is of great significance for missile product life assessment and life extension management.

[0003] Field failure data, collected under actual product storage conditions, is extremely valuable. It reflects the changes in product reliability and lifespan under real storage conditions, and is more representative of product reliability performance than laboratory simulations or accelerated conditions. Field failure data for missile products includes failure data from troop use, failure data from disassembly and inspection of components, subsystems, and the entire missile, and failure data from accelerated life tests of components. This data, obtained from actual storage environments, is a crucial source for evaluating missile product reliability and lifespan and should be collected with special care. However, field failure data may show instances of "zero failures" in certain years due to limited troop test numbers (especially for longer storage years) or a limited number of disassembly and inspection samples. Therefore, traditional distribution methods cannot be directly used for lifespan distribution fitting. Summary of the Invention

[0004] The purpose of this invention is to provide a missile life prediction method under zero-failure data conditions, which is used to provide parameter estimates for the product when there are zero failures in the fault data.

[0005] To achieve the above objectives, the present invention provides the following technical solution: A method for predicting missile lifespan under zero-failure data conditions includes: The missile field detection data was collected and organized into periodic truncation data. The Bayesian estimate of the failure probability of each point in the zero-fault truncation data was calculated using the multi-level Bayesian method. The Weibull distribution function is selected as the empirical lifetime distribution function of the missile. The Bayesian estimate of the failure probability at each point is calculated using the weighted least squares method, and the shape parameter estimate and scale parameter estimate of the Weibull distribution function are obtained. Based on the shape parameter estimation and scale parameter estimation of the Weibull distribution function, the missile's lifetime distribution and reliability function are obtained.

[0006] More specifically, the Bayesian estimation of the failure probability at each time point in the zero-fault truncated data using the multi-level Bayesian method specifically includes: The beta distribution function is used as the prior distribution function of the failure probability; By combining the prior distribution function and the likelihood function of the fault probability, a Bayesian estimate of the fault probability is obtained.

[0007] Compared with existing technologies, the missile life prediction method under zero-fault data conditions provided by this invention has the following beneficial effects: This invention organizes missile periodic inspection data under zero-failure conditions into periodic truncated data, and uses hierarchical Bayesian method to obtain the failure probability estimate of each inspection point. Then, based on the failure probability estimate of each point, the weighted least squares method is used to obtain the lifetime distribution with the best fitting effect. Based on this, missile product lifetime prediction and analysis can be carried out, which can effectively deal with the "zero failure" problem in periodic inspection and obtain the product lifetime distribution. Attached Figure Description

[0008] The accompanying drawings, which are included to provide a further understanding of the invention and form part of this invention, illustrate exemplary embodiments of the invention and are used to explain the invention, but do not constitute an undue limitation of the invention. In the drawings: Figure 1 A flowchart of a method provided in an embodiment of the present invention; Figure 2 A Beta distribution density function curve is provided for an embodiment of the present invention; Figure 3 A Weibull distribution fitting result diagram provided in an embodiment of the present invention; Figure 4 A reliability curve is provided for an embodiment of the present invention. Detailed Implementation

[0009] To facilitate a clear description of the technical solutions in the embodiments of the present invention, the terms "exemplary" or "for example" are used to indicate that they are examples, illustrations, or descriptions. Any embodiment or design scheme described as "exemplary" or "for example" in the present invention should not be construed as being more preferred or advantageous than other embodiments or design schemes. Specifically, the use of terms such as "exemplary" or "for example" is intended to present the relevant concepts in a concrete manner.

[0010] In this invention, "at least one" means one or more, and "more than one" means two or more. "And / or" describes the relationship between related objects, indicating that there can be three relationships. For example, A and / or B can represent: A alone, A and B at the same time, or B alone, where A and B can be singular or plural.

[0011] To make the objectives, technical solutions, and advantages of the embodiments of the present invention clearer, the technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0012] The embodiments of the present invention will now be described in further detail with reference to the accompanying drawings.

[0013] This invention provides a method for predicting missile lifespan under zero-fault data conditions, such as... Figure 1 As shown, the main process of the method is described below.

[0014] Step S1: Collect missile field detection data and organize it into periodic tail data.

[0015] Missile product lifespan data, especially accelerated life tests of certain pyrotechnic components, sometimes show zero-failure data, and no performance data suitable for degradation modeling was collected during these tests. This type of test data can be represented as shown in Table 1, with time-truncated data. m Next, sort them in ascending order, τ1 < τ2 < ... < τ m , τ i For the first i Secondary truncation time n i For the corresponding number of test samples, the total number of test samples. , Indicates that among N samples s i The lifetime of each sample reached or exceeded τ i .

[0016] Table 1 Timed Truncation Data Table Serial Number <![CDATA[The i-th time-truncated τ i > <![CDATA[Number of tests n i > <![CDATA[Number of surviving samples s i > 1 <![CDATA[τ1]]> <![CDATA[n1]]> <![CDATA[s1]]> 2 <![CDATA[τ2]]> <![CDATA[n2]]> <![CDATA[s2]]> … … … … m <![CDATA[τ m ]]> <![CDATA[n m ]]> <![CDATA[s m ]]> Table 1 above requires at least three testing time points (time-cut-off time points), with at least five samples tested at each time point. The more testing time points and the larger the sample size at each time point, the more accurate and reliable the lifespan assessment and prediction results will be.

[0017] Step S2: Calculate the Bayesian estimate of the failure probability at each point in the zero-fault truncated data using the multilevel Bayesian method.

[0018] The traditional distribution curve method relies on the failure probability p at various points. i The estimated value The lifetime distribution that best fits the model is assigned. However, the failure probability p cannot be directly obtained in the zero-failure case. i The estimated value The failure probability p at each time point under zero-failure conditions can be obtained using the multi-level Bayesian method. i The Bayesian estimation includes the following steps.

[0019] Step S21: Use the beta distribution function as the prior distribution function of the failure probability.

[0020] Since no failures were observed during the test, the product failure probability within (0, τ1) is... p i The probability of a smaller value is high, while the probability of a larger value is low. Therefore, a uniform distribution on (0,1) is chosen as the basis for this distribution. p i The prior distribution is unreasonable, so we take the Beta distribution as the basis. p i The prior distribution is reasonable, and the probability density function of the Beta distribution is: (1) Where a > 0 and b > 0 are hyperparameters. B ( a,b ) is the Beta density function.

[0021] The next key question is how to determine the two hyperparameters. a,b Based on zero-fault data p i The smaller the probability, the greater the probability. p i The characteristic that a larger probability is small is used to determine hyperparameters. a,b The range of values ​​for is: 0 < a < 1, b > 1. Further determination is needed. a,b The exact value is difficult to determine, therefore... a,bBased on the range of values, a uniform distribution is defined as a hyperparameter for each. a,b The prior distribution of , i.e.: (2) (3) in, c It is a constant. a In the case of <1, b The larger the value, the thinner the right-hand tail of the Beta density function, such as... Figure 2 As shown, however, from the perspective of the robustness of Bayesian estimation, a prior distribution with a finer tail often leads to a worse robustness of Bayesian estimation. Therefore... b Not too large, tentatively. b The upper limit is c .generally c The value should be between (2, 8), and in this embodiment, the median value is preferred. c= 5.

[0022] exist a,b Under the independence assumption, using the multilevel prior method, we can obtain p i The prior distribution is: (4) Step S22: Combine the prior distribution function and the likelihood function of the fault probability to obtain the Bayesian estimate of the fault probability.

[0023] In the case of zero failures, the probability of failure p i The likelihood function is: (5) Combining equations (4) and (5), we can obtain the Bayes formula. p i The posterior distribution, under squared loss, p i The Bayesian estimate is the expectation of the posterior distribution, expressed by the following formula: (6) Substituting the zero-failure data from Table 1 into equation (6) above, the results at each time point can be calculated. p i , i =1,2,…, m It can be proven that the above method can be used to obtain... Satisfying the increasing relationship, that is .

[0024] Step S3: Select the Weibull distribution function as the empirical life distribution function of the missile product, and use the weighted least squares method to calculate the Bayesian estimate of the failure probability at each point to obtain the shape parameter estimate and scale parameter estimate of the Weibull distribution function.

[0025] Let t=τ i The failure probability of the product is p i ,but: (7) Taking the logarithm of equation (7) twice, we have: (8) use replace p i and order Then we have: (9) In the formula, ε i Because of the use replace p i The resulting error.

[0026] Since long-term zero-failure data is more important, it is more appropriate to use weighted least squares to determine the parameters m and η of the Weibull distribution.

[0027] The weights of the data at each detection time point are calculated as follows: (10) From this, the weighted least squares estimates of μ and σ can be obtained. and , making (11) Therefore, we can conclude that: (12) in: , Then by The parameter estimates of the Weibull distribution can be obtained. : (13) Step S4: Based on the shape parameter estimation and scale parameter estimation of the Weibull distribution function, the reliability estimate of the missile product is obtained. The product's lifetime distribution and reliability function can be obtained from equation (13).

[0028] The lifetime distribution function is: (14) The reliability function is: (15) The following examples will be used to verify this: Example of zero-failure data: A large amount of zero-failure data exists in the disassembly and inspection data of a certain product. The method of this invention is used to obtain truncated data and Bayesian estimates of the failure probability.

[0029] Choosing the Weibull distribution as the lifetime distribution, based on the failure probability p at each point... i The Bayesian estimate, through points The estimated values ​​of parameters m and η are obtained using the weighted least squares method: ; The fitting results are as follows Figure 3 As shown. The product reliability function is: ; Reliability curves and their B10 and B50 lifetimes are as follows: Figure 4 As shown.

[0030] In the above embodiments, implementation can be achieved entirely or partially through software, hardware, firmware, or any combination thereof. When implemented using software, it can be implemented entirely or partially in the form of a computer program product. The computer program product includes one or more computer programs or instructions. When the computer program or instructions are loaded and executed on a computer, the processes or functions described in the embodiments of the present invention are performed entirely or partially. The computer can be a general-purpose computer, a special-purpose computer, a computer network, a terminal, a user equipment, or other programmable device. The computer program or instructions can be stored in a computer-readable storage medium or transferred from one computer-readable storage medium to another. For example, the computer program or instructions can be transferred from one website, computer, server, or data center to another website, computer, server, or data center via wired or wireless means. The computer-readable storage medium can be any available medium that a computer can access or a data storage device such as a server or data center that integrates one or more available media. The available medium can be a magnetic medium, such as a floppy disk, hard disk, or magnetic tape; it can also be an optical medium, such as a digital video disc (DVD); or it can be a semiconductor medium, such as a solid-state drive (SSD).

[0031] Although the invention has been described herein in conjunction with various embodiments, those skilled in the art will understand and implement other variations of the disclosed embodiments by reviewing the accompanying drawings, the disclosure, and the appended claims in carrying out the claimed invention. In the claims, the word "comprising" does not exclude other components or steps, and "a" or "an" does not exclude a plurality. A single processor or other unit can implement several functions listed in the claims. While different dependent claims may recite certain measures, this does not mean that these measures cannot be combined to produce good results.

[0032] Although the invention has been described in conjunction with specific features and embodiments, it is obvious that various modifications and combinations can be made therein without departing from the spirit and scope of the invention. Accordingly, this specification and drawings are merely exemplary descriptions of the invention as defined by the appended claims, and are considered to cover any and all modifications, variations, combinations, or equivalents within the scope of the invention. Clearly, those skilled in the art can make various alterations and modifications to the invention without departing from its spirit and scope. Thus, if such modifications and modifications of the invention fall within the scope of the claims and their equivalents, the invention is also intended to include such modifications and modifications.

Claims

1. A method for predicting missile lifespan under zero-fault data conditions, characterized in that, include: The missile field detection data was collected and organized into periodic truncation data. The Bayesian estimate of the failure probability of each point in the zero-fault truncation data was calculated using the multi-level Bayesian method. The Weibull distribution function is selected as the empirical lifetime distribution function of the missile. The Bayesian estimate of the failure probability at each point is calculated using the weighted least squares method, and the shape parameter estimate and scale parameter estimate of the Weibull distribution function are obtained. Based on the shape parameter estimation and scale parameter estimation of the Weibull distribution function, the missile's lifetime distribution and reliability function are obtained.

2. The missile lifespan prediction method under zero-fault data conditions according to claim 1, characterized in that, The Bayesian estimation of the failure probability at each time point in the zero-fault truncated data using the multi-level Bayesian method specifically includes: The beta distribution function is used as the prior distribution function of the failure probability; By combining the prior distribution function and the likelihood function of the fault probability, a Bayesian estimate of the fault probability is obtained.

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