CN112395805B - EBSM cathode life assessment method - Google Patents

EBSM cathode life assessment method Download PDF

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CN112395805B
CN112395805B CN202011164426.2A CN202011164426A CN112395805B CN 112395805 B CN112395805 B CN 112395805B CN 202011164426 A CN202011164426 A CN 202011164426A CN 112395805 B CN112395805 B CN 112395805B
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CN112395805A (en
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叶志鹏
李亚球
梁佩博
李骞
雷柏茂
时钟
王春辉
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China Electronic Product Reliability and Environmental Testing Research Institute
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    • G06F30/00—Computer-aided design [CAD]
    • G06F30/20—Design optimisation, verification or simulation
    • G06F30/27—Design optimisation, verification or simulation using machine learning, e.g. artificial intelligence, neural networks, support vector machines [SVM] or training a model
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    • G06F—ELECTRIC DIGITAL DATA PROCESSING
    • G06F2113/00—Details relating to the application field
    • G06F2113/10—Additive manufacturing, e.g. 3D printing
    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06F—ELECTRIC DIGITAL DATA PROCESSING
    • G06F2119/00—Details relating to the type or aim of the analysis or the optimisation
    • G06F2119/04—Ageing analysis or optimisation against ageing

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Abstract

The application relates to the technical field of electron beam selective melting additive manufacturing, and discloses an EBSM cathode service life assessment method. Firstly, designing a corresponding test scheme for an EBSM printing process, and developing an EBSM printing test according to the test scheme to obtain test data of a test group. Modeling the test data, and establishing a mapping model for representing the mapping relation between the process parameters and the distribution parameters of the acquisition time. And acquiring actual process parameters and the used time of the cathode in the EBSM actual printing process, and evaluating the service life of the cathode according to the actual process parameters and the used time of the cathode by combining the mapping model so as to acquire the residual service life of the cathode, wherein a confidence interval and a confidence coefficient for acquiring the service life of the cathode can be calculated. The EBSM cathode life assessment method provided by the application can accurately predict the residual life of the cathode according to the process parameters of the EBSM actual printing process and the used time of the cathode.

Description

EBSM cathode life assessment method
Technical Field
The application relates to the technical field of electron beam selective melting additive manufacturing, in particular to an EBSM cathode service life assessment method.
Background
Electron beam selective melting (EBSM, electronic Beam Selective Melting) additive manufacturing technology is one of the powder-laid additive manufacturing technologies, and EBSM heats powder metal by using an electron beam as an energy source, causes it to melt, solidify rapidly, and prints layer by layer to manufacture parts. The energy density of the electron beam is far higher than that of the laser beam, so that the electron beam has great application advantages in the aspects of a plurality of high-reflection materials and high-melting-point materials. However, the life of the cathode or filament, a core part of the EBSM, almost determines the maintenance cycle of the EBSM equipment, and the cathode or filament itself is expensive, so it is particularly critical to predict the life of the cathode or filament.
Disclosure of Invention
Based on this, it is necessary to provide an EBSM cathode lifetime assessment method for the problem of how to accurately predict the cathode lifetime.
An EBSM cathode service life assessment method designs a test scheme for an EBSM printing process, and develops an EBSM printing test according to the test scheme to obtain test data; the test data comprise process parameters and acquisition time during an EBSM printing test; modeling according to the test data, and obtaining a mapping model between the process parameters and the distribution parameters of the acquisition time; and acquiring actual process parameters and the used time of the cathode in the EBSM actual printing process, evaluating the service life of the cathode by combining the mapping model, acquiring the residual service life of the cathode, and acquiring a confidence interval and a confidence coefficient of the service life of the cathode.
According to the EBSM cathode life assessment method, a corresponding test scheme is designed for an EBSM printing process, and an EBSM printing test is carried out according to the test scheme to obtain test data of a test group. The test data comprise process parameters and acquisition time of the EBSM printing test. Modeling the test data, and establishing a mapping model for representing the mapping relation between the process parameters and the distribution parameters of the acquisition time. And acquiring actual process parameters and the used time of the cathode in the EBSM actual printing process, and evaluating the service life of the cathode according to the actual process parameters and the used time of the cathode by combining the mapping model so as to acquire the residual service life of the cathode, wherein a confidence interval and a confidence coefficient for acquiring the service life of the cathode can be calculated. The EBSM cathode life assessment method provided by the application can accurately predict the residual life of the cathode according to the process parameters of the EBSM actual printing process and the used time of the cathode. In addition, the accuracy of the cathode life prediction can also be expressed by acquiring the confidence interval and the confidence of the cathode life.
In one embodiment, the process parameters include cathode current, cathode temperature, gas pressure in the electron gun, gas pressure in the forming chamber, and cathode beam current.
In one embodiment, the acquisition time is the time that the cathode beam current needs to drop to a preset threshold.
In one embodiment, each of the process parameters has a corresponding range of operating values, and the designing a test plan for the EBSM printing process includes selecting a plurality of values from the range of operating values for each of the process parameters; wherein the plurality of values includes an upper limit value, a lower limit value, and at least one value located between the upper limit value and the lower limit value; and combining a plurality of values selected by the process parameters to be used as test conditions to design a plurality of test groups, and screening out part of the test groups to be used as test schemes.
In one embodiment, the test panel is screened using an orthogonal test design method.
In one embodiment, a support vector regression method is used to build a mapping model between the process parameters and the distribution parameters of the acquisition time.
In one embodiment, when the support vector regression method is used to build a mapping model between the process parameters and the distribution parameters of the service life, a gaussian kernel function is selected for fitting.
In one embodiment, the evaluating the cathode lifetime in combination with the actual process parameter, the used time of the cathode, and the mapping model includes obtaining a distribution parameter of the cathode lifetime according to the actual process parameter in the EBSM actual printing process and the mapping model; acquiring a life estimated value of the cathode according to the distribution parameters of the life of the cathode, and acquiring the residual life of the cathode according to the life estimated value of the cathode and the used time of the cathode; and evaluating the distribution parameters of the cathode service life by using an interval estimation method to obtain the confidence interval and the confidence of the cathode service life.
In one embodiment, the distribution parameter of the cathode lifetime includes two feature quantities of a lognormal distribution, and the EBSM cathode lifetime assessment method further includes: and obtaining a density function of the cathode beam according to the distribution parameters of the cathode service life.
In one embodiment, the density function is
Wherein p (t) is a density function, t is acquisition time, x is the number of experimental groups after screening, mu is the average value of the acquisition time, and sigma is the variance of the acquisition time.
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In order to more clearly illustrate the technical solutions of the embodiments or the conventional techniques of the present application, the drawings required for the descriptions of the embodiments or the conventional techniques will be briefly described below, and it is apparent that the drawings in the following description are only some embodiments of the present application, and other drawings may be obtained according to the drawings without inventive effort for those skilled in the art.
FIG. 1 is a flow chart of a method for EBSM cathode life assessment in accordance with one embodiment of the present application;
FIG. 2 is a flow chart of a method of designing a test plan for an EBSM printing process in accordance with one embodiment of the present application;
FIG. 3 is a flow chart of a method for evaluating the lifetime of the cathode in one embodiment of the application.
Detailed Description
In order that the application may be readily understood, a more complete description of the application will be rendered by reference to the appended drawings. The drawings illustrate preferred embodiments of the application. This application may, however, be embodied in many different forms and should not be construed as limited to the embodiments set forth herein. Rather, these embodiments are provided so that this disclosure will be thorough and complete.
It will be understood that when an element is referred to as being "fixed to" another element, it can be directly on the other element or intervening elements may also be present. When an element is referred to as being "connected" to another element, it can be directly connected to the other element or intervening elements may also be present. The terms "vertical," "horizontal," "left," "right," "upper," "lower," "front," "rear," "circumferential," and the like as used herein are based on the orientation or positional relationship shown in the drawings and are merely for convenience of description and to simplify the description, rather than to indicate or imply that the devices or elements referred to must have a particular orientation, be constructed and operated in a particular orientation, and thus are not to be construed as limiting the application.
Unless defined otherwise, all technical and scientific terms used herein have the same meaning as commonly understood by one of ordinary skill in the art to which this application belongs. The terminology used herein in the description of the application is for the purpose of describing particular embodiments only and is not intended to be limiting of the application. The term "and/or" as used herein includes any and all combinations of one or more of the associated listed items.
The application provides a method for calculating the cathode life distribution characteristic parameters by a machine learning method, and further provides a method for estimating the EBSM cathode life score by statistical estimation, which can estimate the life distribution and the estimated value of the EBSM special cathode. Fig. 1 is a flowchart of a method for evaluating the lifetime of an EBSM cathode according to an embodiment of the present application, wherein the method for evaluating the lifetime of an EBSM cathode includes the following steps S100 to S300.
S100: designing a test scheme for an EBSM printing process, developing an EBSM printing test according to the test scheme, and acquiring test data; the test data comprise process parameters and acquisition time during the EBSM printing test.
S200: modeling is carried out according to the test data, and a mapping model between the process parameters and the distribution parameters of the acquisition time is obtained.
S300: and acquiring actual process parameters and the used time of the cathode in the EBSM actual printing process, evaluating the service life of the cathode by combining the mapping model, acquiring the residual service life of the cathode, and acquiring a confidence interval and a confidence coefficient of the service life of the cathode.
According to the EBSM cathode life assessment method, firstly, a test scheme is designed for an EBSM printing process, and a corresponding EBSM printing test is carried out according to the designed test scheme so as to obtain test data of a test group. The test data comprise process parameters and acquisition time acquired in an EBSM printing test. Modeling is carried out according to the test data, and a mapping model for representing a mapping piping between the process parameters and the distribution parameters of the acquisition time is established. When the EBSM printing is carried out in the practical application, the process parameters and the used time of the cathode in the practical printing process are acquired and recorded. And according to the process parameters and the used time of the cathode, which are acquired in the actual printing process, evaluating the service life of the cathode by combining the mapping model so as to acquire the residual service life of the cathode, and calculating a confidence interval and a confidence coefficient for acquiring the service life of the cathode. The method for evaluating the service life of the EBSM cathode provided by the application can accurately predict the residual service life of the cathode according to the process parameters of the EBSM actual printing process and the service time of the cathode, and provides a reliable cathode service life evaluating method for the application of the EBSM and other electron beam processing fields. By predicting the life of the cathode, the occurrence of defective workpieces can be avoided, and further, the direct or indirect economic loss caused by the failure of the workpieces in the application process is avoided. In addition, the confidence interval and the confidence coefficient of the cathode life are obtained, so that the accuracy of cathode life prediction can be expressed, and a reference is provided for research and development of the anti-poisoning cathode.
In one embodiment, the process parameters include cathode current, cathode temperature, gas pressure in the electron gun, gas pressure in the forming chamber, and cathode beam current. In designing a test plan for an EBSM printing process, it is necessary to design a test plan for some of the process parameters associated with the lifetime of the cathode during the EBSM process. In this embodiment, the process parameters include, but are not limited to, cathode current i, cathode temperature T, gas pressure P in the electron gun 1 Air pressure P in forming cavity 2 And a cathode beam I. Test data P (X, (mu, sigma)) of a plurality of different test groups are obtained by developing an EBSM test scheme, wherein P represents the number of each test group, X is a process parameter during EBSM processing, mu and sigma are distribution functions of the acquisition time, mu is an average value of the acquisition time of each test group, and sigma is a variance of the acquisition time of each test group.
In one embodiment, the acquisition time is the time that the cathode beam current needs to drop to a preset threshold. And when the beam current I of the cathode drops to a preset threshold value, the device performance of the cathode is reduced to failure. Therefore, the time that the cathode takes from the start of EBSM printing to the cathode beam falling to the preset threshold is the service life of the cathode. In this embodiment, the preset threshold is 90% of the original threshold, that is, the cathode failure is determined as the time t taken for the cathode beam I to drop to 90% of the original cathode beam I is the lifetime of the cathode.
Fig. 2 is a flowchart of a method for designing a test plan for an EBSM printing process according to an embodiment of the present application, wherein in one embodiment, each of the process parameters has a corresponding working numerical range, and the test plan for an EBSM printing process includes the following steps S110 to S120.
S110: selecting a plurality of values in a range of operating values for each of the process parameters; wherein the plurality of values includes an upper limit value, a lower limit value, and at least one value located between the upper limit value and the lower limit value.
S120: and combining a plurality of values selected by the process parameters to be used as test conditions to design a plurality of test groups, and screening out part of the test groups to be used as test schemes.
When the test scheme is designed for the EBSM printing process, except for the fact that the cathode beam I is unknown and needs to be measured and obtained in the test process, other parameters of the test group are designed according to the upper limit and the lower limit of the EBSM processing window during design, and the maximum value, the minimum value, the intermediate value and the like in the working range are respectively selected as reference values according to the respective working ranges. For example, the upper and lower limits of the cathode current i are i respectively max And i min The reference value of the cathode current i in the test group should at least comprise i max And i min And should be within interval (i) min ，i max ) Taking at least one cathode current value as a reference value. And selecting different reference values for each process parameter to be combined, and then respectively designing a plurality of groups of test groups as test conditions. Because the process parameters are multiple, at least three reference values are selected for each process parameter, the number of the reference values for each process parameter after being arranged and combined is large, and therefore, part of test groups need to be randomly screened out as test schemes, and generally, not less than 5 test groups are screened out and EBSM printing tests are respectively carried out.
In one embodiment, the test panel is screened using an orthogonal test design method. Orthogonal test design refers to a test design method for researching multiple factors and multiple levels. And selecting partial representative points from the comprehensive test according to the orthogonality to test, wherein the representative points have the characteristics of uniform dispersion and uniformity and comparability. When the factors involved in the test are 3 or more and there is a possibility of interaction between the factors, the test workload becomes large or even difficult to implement. The problem of large test workload can be solved by using an orthogonal test design to screen out part of the test groups as test schemes. The main tool of the orthogonal test design is an orthogonal table, which can be searched according to the requirements of the factor number, the level number of factors, interaction and the likeAccording to the corresponding orthogonal table, a part of representative points are selected from the comprehensive test for test according to the orthogonality of the orthogonal table, and the equivalent result of a large number of comprehensive tests can be achieved with the minimum test times, so that the test design can be efficiently, quickly and economically completed by using the orthogonal table design test. In this example, a total of 27 test groups were designed using the orthogonal test design method. Respectively carrying out EBSM printing tests on 27 groups of test groups, collecting the beam current I of the cathode under 27 groups of test conditions, and recording the time spent by the beam current I in the 27 groups of test groups to be reduced to 90% as t respectively 1 ～t 27 According to t 1 ～t 27 Calculating a distribution function (mu, sigma) for acquiring the acquisition time.
In one embodiment, a support vector regression method is used to build a mapping model between the process parameters and the distribution parameters of the acquisition time. In modeling, as a preferred scheme, a support vector machine is used to establish a relationship between the process parameter X and the distribution function (μ, σ) of the acquisition time, and a plurality of kernel functions can be used for fitting. The support vector machine (Support Vector Machine, SVM) is a two-class classification model whose basic model is defined as the most-spaced linear classifier in feature space, and whose learning strategy is interval maximization, which can ultimately be translated into a solution to a convex quadratic programming problem. The support vector machine method is based on the VC dimension theory of statistical learning theory and the minimum structural risk theory, and the best compromise is sought between the complexity and learning capacity of the model according to limited sample information so as to obtain the best popularization capacity. A true model of the relationship between the process parameter X and the distribution function (μ, σ) of the acquisition time can be approximated by machine learning. Modeling is carried out by using a relation between the process parameter X and the distribution function (mu, sigma) of the acquisition time by using a support vector regression method, and popularization is carried out by using the established mapping model, so that the residual life of the EBSM cathode in the actual use condition can be effectively predicted.
In one embodiment, when the support vector regression method is used to build a mapping model between the process parameters and the distribution parameters of the service life, a gaussian kernel function is selected for fitting. In modeling the relationship between the process parameter X and the distribution function (μ, σ) of the acquisition time using a support vector machine, a kernel function is required to fit the data to build a classifier. In this embodiment, a gaussian kernel function is selected to construct a classifier, so as to establish a mapping relationship between the process parameter X and the distribution parameter (μ, σ) of the acquisition time t.
FIG. 3 is a flowchart of a method for estimating the lifetime of the cathode according to one embodiment of the present application, wherein the estimating the lifetime of the cathode by combining the actual process parameter, the used time of the cathode and the mapping model includes the following steps S310 to S330.
S310: and acquiring the distribution parameters of the cathode service life according to the actual process parameters in the EBSM actual printing process and the mapping model.
S320: and acquiring a life estimated value of the cathode according to the distribution parameters of the life of the cathode, and acquiring the residual life of the cathode according to the life estimated value of the cathode and the used time of the cathode.
S330: and evaluating the distribution parameters of the cathode service life by using an interval estimation method to obtain the confidence interval and the confidence of the cathode service life.
In predicting life of an EBSM cathode in actual use, a time t is used for the cathode 0 Recording and collecting actual process parameters of an EBSM actual machining process, wherein the actual process parameters comprise the cathode beam I. And calculating cathode life distribution parameters (mu, sigma) of the EBSM cathode to be predicted by using the mapping model between the process parameters and the service life distribution parameters established in the steps, wherein mu is the point estimation value of the cathode life. Based on the estimated lifetime value mu of the cathode and the used time t of the cathode 0 Obtaining the residual life of the cathode, wherein the residual life of the cathode is the estimated life value mu of the cathode and the used time t of the cathode 0 The difference between the residual life of the cathode, i.e. μ -t 0 。
And after the life prediction of the EBSM cathode is completed, obtaining a confidence interval and a confidence degree of the life prediction by using an interval estimation method. The interval estimation (Interval Estimate) is an interval range that gives an overall parameter estimate on the basis of a point estimate, which interval is typically derived from the sample statistic plus or minus the estimation error. Unlike point estimation, interval estimation can give a probability measure for the closeness of the sample statistic to the overall parameter according to the sampling distribution of the sample statistic. First, t in the distribution function is converted to lnt, lnt, which follows the normal distribution, and the normal distribution is converted to the standard normal distribution, i.e., (lnt- μ)/σ -N (0, 1). And calculating confidence intervals of mu and sigma by using the obtained lognormal distribution, setting single-side or double-side confidence degrees alpha and beta for the function, and finally obtaining the single-side or double-side confidence interval of the cathode life prediction under a certain confidence degree by table lookup or formula calculation. The confidence coefficient calculation for the service life of the cathode can respectively set the single-side confidence coefficient alpha and the double-side confidence coefficient beta or set the single-side confidence coefficient alpha and the double-side confidence coefficient beta according to specific requirements, and the values of the single-side confidence coefficient alpha and the double-side confidence coefficient beta can be set to corresponding values according to the requirements of operators.
It should be understood that, although the steps in the flowcharts of fig. 1-3 are shown in order as indicated by the arrows, these steps are not necessarily performed in order as indicated by the arrows. The steps are not strictly limited to the order of execution unless explicitly recited herein, and the steps may be executed in other orders. Moreover, at least a portion of the steps of fig. 1-3 may include multiple steps or stages that are not necessarily performed at the same time, but may be performed at different times, nor does the order in which the steps or stages are performed necessarily occur sequentially, but may be performed alternately or alternately with other steps or at least a portion of the steps or stages in other steps.
In one embodiment, the distribution parameters of the cathode life include two characteristic quantities of lognormal distribution, the two characteristic quantities remaining for the EBSMThe estimating step of lifetime prediction further includes obtaining a density function of the cathode beam I according to the distribution parameter of the cathode lifetime. After the distribution parameters (mu, sigma) of the cathode life are obtained according to the mapping model calculation, t in the function is converted into lnt, and then the cathode life distribution functions lnt-N (mu, sigma) can be obtained 2 ) The distribution parameters (mu, sigma) of the cathode life are two characteristic quantities of lognormal distribution respectively, so that a density function of the cathode beam I is obtained.
In one embodiment, the density function is:
wherein p (t) is a density function, t is acquisition time, x is the number of experimental groups after screening, mu is the average value of the acquisition time, and sigma is the variance of the acquisition time. And setting single-side or double-side confidence degrees alpha and beta for the function according to the density function of the cathode beam I, and obtaining a single-side or double-side confidence interval of the cathode life prediction under a certain confidence degree through table lookup or formula calculation.
According to the EBSM cathode life assessment method provided by the application, firstly, an appropriate test group is selected according to the working numerical value of each process parameter in the printing process of the EBSM, and the EBSM printing test is respectively carried out on each test group to obtain test data P (X, (mu, sigma)). Then selecting a proper kernel function to construct a classifier, establishing a mapping relation between the process parameter X and the distribution parameters (mu, sigma) of the acquisition time t by adopting a support vector regression method, and establishing a reliable mapping model by a machine learning mode. Secondly, in the EBSM actual processing printing process, the actual process parameter X and the cathode processed time t 0 Collecting, and calculating distribution parameters (mu, sigma) of the cathode life by using the established mapping model, wherein mu is the point estimated value of the cathode life. Obtaining the residual life of the cathode according to the estimated life value of the cathode and the used time of the cathode, namely the residual life of the cathode isμ-t 0 Meanwhile, a confidence interval and a confidence degree of cathode life prediction can be obtained by using an interval estimation method. The EBSM cathode life assessment method provided by the application can accurately predict the residual life of the cathode according to the process parameters of the EBSM actual printing process and the used time of the cathode, and provides more accurate and dependable results for the detection process of the additive manufacturing parts. In addition, the confidence interval and the confidence degree of the cathode service life are obtained to represent the accuracy of the cathode service life prediction.
In the description of the present specification, reference to the terms "some embodiments," "other embodiments," "desired embodiments," and the like, means that a particular feature, structure, material, or characteristic described in connection with the embodiment or example is included in at least one embodiment or example of the application. In this specification, schematic descriptions of the above terms do not necessarily refer to the same embodiment or example.
The technical features of the above-described embodiments may be arbitrarily combined, and all possible combinations of the technical features in the above-described embodiments are not described for brevity of description, however, as long as there is no contradiction between the combinations of the technical features, they should be considered as the scope of the description.
The above examples illustrate only a few embodiments of the application, which are described in detail and are not to be construed as limiting the scope of the application. It should be noted that it will be apparent to those skilled in the art that several variations and modifications can be made without departing from the spirit of the application, which are all within the scope of the application. Accordingly, the scope of protection of the present application is to be determined by the appended claims.

Claims (8)

1. An EBSM cathode life assessment method, comprising:
designing a test scheme for an EBSM printing process, developing an EBSM printing test according to the test scheme, and acquiring test data; the test data comprise process parameters and acquisition time during an EBSM printing test;
modeling according to the test data, and obtaining a mapping model between the process parameters and the distribution parameters of the acquisition time;
collecting actual process parameters and the used time of a cathode in the EBSM actual printing process, evaluating the service life of the cathode by combining the mapping model, obtaining the residual service life of the cathode, and obtaining a confidence interval and a confidence coefficient of the service life of the cathode;
the process parameters comprise cathode current, cathode temperature, air pressure in an electron gun, air pressure in a forming cavity and cathode beam current;
the acquisition time is the time required by the cathode beam current to drop to a preset threshold value.
2. The EBSM cathode lifetime assessment method of claim 1, wherein each of the process parameters has a corresponding range of operating values, the programming test scheme for the EBSM printing process comprising:
selecting a plurality of values in a range of operating values for each of the process parameters; wherein the plurality of values includes an upper limit value, a lower limit value, and at least one value located between the upper limit value and the lower limit value;
and combining a plurality of values selected by the process parameters to be used as test conditions to design a plurality of test groups, and screening out part of the test groups to be used as test schemes.
3. The EBSM cathode life assessment method of claim 2, wherein the test groups are screened using an orthogonal test design method.
4. The EBSM cathode lifetime assessment method of claim 1, wherein a support vector regression method is used to build a mapping model between the process parameters and the distribution parameters of the acquisition time.
5. The EBSM cathode lifetime assessment method of claim 4, wherein a gaussian kernel function is selected for fitting when a mapping model between process parameters and lifetime distribution parameters is established using a support vector regression method.
6. The EBSM cathode life assessment method of claim 1, wherein assessing the cathode life in combination with the actual process parameters, the time of use of the cathode, and the mapping model comprises:
acquiring the distribution parameters of the cathode service life according to the actual process parameters in the EBSM actual printing process and the mapping model;
acquiring a life estimated value of the cathode according to the distribution parameters of the life of the cathode, and acquiring the residual life of the cathode according to the life estimated value of the cathode and the used time of the cathode;
and evaluating the distribution parameters of the cathode service life by using an interval estimation method to obtain the confidence interval and the confidence of the cathode service life.
7. The EBSM cathode lifetime assessment method according to claim 1, wherein the distribution parameter of the cathode lifetime includes two feature amounts of a lognormal distribution, the EBSM cathode lifetime assessment method further comprising:
and obtaining a density function of the cathode beam according to the distribution parameters of the cathode service life.
8. The EBSM cathode lifetime assessment method of claim 7, wherein the density function is:
wherein p (t) is a density function, t is acquisition time, x is the number of experimental groups after screening, mu is the average value of the acquisition time, and sigma is the variance of the acquisition time.
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