CN110717253B - Ballistic consistency testing method for two types of ammunition - Google Patents
Ballistic consistency testing method for two types of ammunition Download PDFInfo
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Abstract
The invention relates to a method for testing the trajectory consistency of two types of ammunition, belonging to the technical field of trajectory testing. The method comprises the following steps: obtaining the minimum test sample size according to the specified significance level and the false storage probability of the test; determining the quantity of the two types of ammunition to be fired according to the minimum test sample size, comparing and firing the two types of ammunition one by one under the same firing condition, and acquiring the landing point coordinates of the two types of ammunition one by one; respectively obtaining the average shooting distance and the variance of the two types of ammunition after the standardization of shooting conditions, and obtaining a distance variance weighted average value according to the distance variance of the two types of ammunition; and (3) judging whether the two types of ammunition are scattered in a consistent manner or not by adopting an F test according to the distance variance of the two types of ammunition, and judging the average trajectory consistency of the two types of ammunition by adopting a t test according to the weighted average value of the distance variance if the two types of ammunition are scattered in a consistent manner. The invention can test the ballistic consistency of two types of ammunition belonging to different parent bodies, overcomes the limitation of testing the ballistic consistency in the prior art and has wider engineering use characteristics.
Description
Technical Field
The invention relates to the technical field of ballistic trajectory inspection, in particular to a ballistic trajectory consistency inspection method for two types of ammunition.
Background
The ballistic consistency is the premise of sharing shooters, and is an outer ballistic problem which is often encountered when a ammunition design, model technical index demonstration and a test identification base are carried out to carry out shaping and examination on products. Ballistic conformance tests are typically used for many types of ammunition intended for the same gun, all of which do not have a firing plan, and require ballistic tests in planning decisions for the firing plan of that type of gun. The firing table is specially programmed for specific launching devices such as guns, cannons, rockets and the like and matched bullet types, carries the corresponding relation between a firing angle and a range and the corresponding relation between the firing angle and other trajectory elements, and is the basis for implementing accurate shooting and manufacturing a sighting device. The formulation of the shooter depends on the shooting test data, and the acquisition of the shooter needs to consume a large amount of ammunition and invest high test cost, and the cost is high. In practical application, multiple types of ammunition matched with the same gun usually only has one shooter, and both subsequently developed or improved ammunition are based on the first developed ammunition and are required to share the same shooter with the first developed ammunition, so that the requirement of trajectory consistency is particularly important as the technical basis of sharing the shooter.
Aiming at the problem of ballistic consistency assessment, the ballistic firing chart is widely researched, relevant standards are established, the method introduced in the American army test and identification commander background document, namely artillery range and ballistic consistency test (MTP3-1-004) is taken as a typical example internationally, and China also has the relevant ballistic consistency assessment standards (GJB 349.17-89). These criteria, all using the t-test method, are only suitable for assessing the average ballistic consistency of two ammunition types with a zero difference between the average values.
On the one hand, the ballistic characteristics of different types of projectiles matched with the same artillery are different. Because different types of bullets have different use purposes, the warheads are inevitably required to be designed differently, and in order to achieve the same trajectory, the center of mass position has to be adjusted under the condition that the appearance is basically the same, the total weight is the same, and the initial speed is the same. The difference of aerodynamic moment and rotational inertia of different projectile types is inevitably caused, so that the dynamic change rule of the flight attitude angle of the projectile in the flight process is different, and the difference of the external ballistic characteristics is caused. Therefore, test samples of different bullet types matched with the same artillery in a ballistic contrast shooting test belong to different parent bodies, and the conventional ballistic consistency evaluation method has great inapplicability in practical use and is mainly reflected in the following three aspects: firstly, the standard of 'consistency' requires that the average drop point difference value is zero, which is too harsh compared with the actual requirement; secondly, the threshold value in the consistency evaluation criterion is completely determined by a mathematical statistics method, and the difference of the use purposes among different ammunitions cannot be reflected; thirdly, the average ballistic consistency test in the standard has an increasing tendency to be judged unacceptable as the sample size increases, and for this reason, there is no constraint condition of the sample size.
On the other hand, in various trajectory consistency test methods, the charge number (initial speed of the projectile) and the firing angle are not clearly tested, so that the test randomness is high, and the test quality cannot be guaranteed.
Disclosure of Invention
In view of the above analysis, the present invention aims to provide a method for testing the ballistic consistency of two types of ammunition, so as to solve the problem that the existing method for evaluating the average ballistic consistency is not suitable for testing the ballistic consistency of a plurality of ammunition matched with the same gun, so as to perfect a method for determining the limit value and the sample size.
The purpose of the invention is mainly realized by the following technical scheme:
the invention provides a ballistic conformance testing method for two types of ammunition, which comprises the following steps:
s1, before ammunition is launched, obtaining the minimum test sample size according to the specified significance level and the false storage probability of the test;
s2, determining the number of the two types of ammunition to be fired according to the minimum test sample size, comparing and firing the two types of ammunition one by one under the same firing condition, and acquiring the firing ranges of the two types of ammunition one by one;
s3, obtaining the respective average shooting distance and distance variance of the two types of ammunition after the shooting conditions are standardized according to the shooting ranges of the two types of ammunition which are obtained one by one, and obtaining the weighted average value of the distance variance according to the distance variance of the two types of ammunition;
and S4, judging whether the two types of ammunition are uniformly distributed by adopting an F test according to the distance variance of the two types of ammunition, and judging the uniformity of the average trajectory of the two types of ammunition by adopting a t test according to the weighted average value of the distance variance if the two types of ammunition are uniformly distributed.
Further, the calculation formula for obtaining the minimum test sample size according to the significance level and the false-positive probability of the specified test is as follows:
wherein α is the significance level of the test, the abandonment probability of truth, β is the false probability of existence, z1-αAnd z1-βObtained by referring to a standard normal distribution integral function table,
allowable deviation value for center of ellipse of dispersion of two-type ammunition and dispersion variance thereof
The ratio of (a) to (b).
Further, the shooting conditions comprise ballistic conditions, topographic conditions and meteorological conditions, and the test efficacy of judging the ballistic consistency by the F test and the t test in the step S4 is according to α, n,
Or
From the corresponding OC curve, 1- β was identified.
Further, the two types of ammunition comprise type a ammunition and type B ammunition; the step S4 of determining whether the two types of ammunition are spread uniformly by using the F-test based on the distance variance of the two types of ammunition includes:
when F is satisfied1-α/2(nA-1,nB-1)≤F≤Fα/2(nA-1,nB-1), then the two types of ammunition are judged to be spread uniformly; otherwise, judging that the two types of ammunition are not uniformly scattered;
wherein the content of the first and second substances,
is the distance variance of the type a ammunition,
distance variance for type B ammunition, α significance level for test, probability of abandonment, nATest sample size of type A ammunition, nBTest specimen size for type B ammunition, F1-α/2And Fα/2Obtained by consulting a distribution table of F1-α/2Is the lower limit of the F test, Fα/2Is the upper limit value of the F test, and
further, the
In order to function the statistics of the data,
wherein n isATest sample size of type A ammunition, nBTest specimen size for type B ammunition, RAAt each throw of type A ammunition, RBIs the range of each round of type B ammunition.
Further, if the two types of ammunition are uniformly scattered, the step of judging the uniformity of the average trajectory of the two types of ammunition by adopting a t test according to the weighted average of the distance variance comprises the following steps:
when it is satisfied with
If so, judging that the average trajectories of the two types of ammunition are consistent; otherwise, judging that the average trajectories of the two types of ammunition are inconsistent;
wherein the content of the first and second substances,
is the average firing distance of the type a ammunition,
mean firing distance of B-type ammunition, deviation value of center of ellipse allowed to spread of two-type ammunition when mean trajectory of two-type ammunition is consistent, nATest sample size of type A ammunition, nBTest sample size, t, for type B ammunitionαBy consulting a t-distribution table, SPThe weighted average of the distance variances of the two types of ammunition is used.
Further, when the average trajectories of the two types of ammunition are consistent, the deviation value of the center of the ellipse allowing the dispersion of the two types of ammunition is determined by the falling probability K of the overlapping area:
when K is equal to 0.95, σ ═ SP；
When K is equal toAt 0.8, ═ 1.75 σ ═ 1.75SP；
When K is equal to 0.7, 2 σ 2SP；
Wherein, the value of K is determined according to the type of ammunition.
Further, the distance variance weighted average of the two types of ammunition is calculated as follows:
wherein the content of the first and second substances,
is the distance variance of the type a ammunition,
distance variance of B-type ammunition, nATest sample size of type A ammunition, nBThe test sample size for type B ammunition.
Further, the calculation formulas of the average shooting distances of the A-type ammunition and the B-type ammunition are respectively as follows:
wherein R isAAt each throw of type A ammunition, nATest specimen size for type A ammunition, RBFor each shot of B-ammunition, nBThe test sample size for type B ammunition.
Further, test sample quantities n for type A and type B ammunitionAAnd nBDetermined by the minimum test sample size N of type A ammunition and type B ammunition respectively plus the corresponding additional value 1 or 2, where NA＝nB。
The invention has the beneficial effects that the invention discloses a method for testing the ballistic consistency of two types of ammunition, which is required by the ballistic consistency test of different ammunition according to the tested significance level α and the storage false probability β
And obtaining the minimum test sample size, measuring after the two types of ammunition are launched to obtain each launching stroke of the two types of ammunition, standardizing the range, and constructing a statistic function. The method comprises the steps of firstly carrying out F test, carrying out t test after the original hypothesis is established, and judging that the trajectories of the two types of ammunition have consistency, so that the requirement of testing the trajectory consistency of the two types of ammunition belonging to different matrixes is met, the limitation that the two types of ammunition need to be tested by the same matrix in the process of evaluating the trajectory consistency in the prior art is overcome, namely the method is not suitable for the trajectory consistency test of multiple types of ammunition matched with the same gun, and the method for determining the threshold value and the sample amount is perfected.
Additional features and advantages of the invention will be set forth in the description which follows, and in part will be obvious from the description, or may be learned by the practice of the invention. The objectives and other advantages of the invention will be realized and attained by the structure particularly pointed out in the written description and claims hereof as well as the appended drawings.
Drawings
The drawings are only for purposes of illustrating particular embodiments and are not to be construed as limiting the invention, wherein like reference numerals are used to designate like parts throughout.
FIG. 1 is a flow chart of a method for ballistic conformance testing of two types of ammunition in accordance with an embodiment of the present invention;
fig. 2 is a bilateral F-test OC plot (α ═ 0.05) of an embodiment of the present invention;
fig. 3 is a one-sided t-test OC plot (α ═ 0.05) of an embodiment of the present invention;
fig. 4 is a bilateral F-test OC plot (α ═ 0.01) of an embodiment of the present invention;
fig. 5 is a one-sided t-test OC plot (α ═ 0.01) of an embodiment of the present invention;
FIG. 6 is a schematic view of the intersection of the dispersion ellipses of two types of ammunition drops of an embodiment of the present invention;
fig. 7 is a schematic view showing a positional relationship of spreading ellipses of two types of ammunition according to an embodiment of the present invention;
figure 8 is a schematic diagram of the maximum allowable deviation of the center of the dispersion ellipse when the average trajectories of the grenades are consistent according to an embodiment of the invention;
FIG. 9 is a schematic view of the coincidence of the centers of the ellipse of the dispersal of the two types of ammunition according to the embodiment of the present invention;
FIG. 10 is a schematic diagram of a probability density function of a normal distribution according to an embodiment of the invention;
FIG. 11 is a graph showing the variation of the detonation-killing resistance coefficient with the Mach number according to the embodiment of the present invention;
fig. 12 is a graph of dynamic equilibrium angle of a detonation-killing bomb according to the embodiment of the invention, as a function of firing angle and altitude.
Detailed Description
The accompanying drawings, which are incorporated in and constitute a part of this application, illustrate preferred embodiments of the invention and together with the description, serve to explain the principles of the invention and not to limit the scope of the invention.
The technical idea of the invention is as follows: under the same shooting condition, if the difference between the average impact points of the two types of ammunition systems is small as shown in the shooting test result, the two types of ammunition can be considered to meet the ballistic consistency, so that a firing table can be shared on the same artillery system, and a certain degree of equivalence of the shooting effect is ensured. If the same series of ammunition can share the shooter, then only need compile a shooter or one set of fire control trajectory and solve the software, this high cost that not only can save and compile many shooters can simplify same series of ammunition transmission command flow moreover, improves shooting command efficiency: firstly, the same artillery continuously launches different types of ammunition to the same target area, and only needs to calculate the trajectory once, turn the artillery firing angle and shoot once, so that the time is greatly saved; secondly, under the same shooting condition, different types of ammunition can be corrected according to the shooting error of one type by only mastering the shooting error of the other type, so that the use convenience is greatly improved. Therefore, the scientific ballistic consistency inspection method is determined, and the method has great economic benefit and great military benefit. The invention uses the premise that certain difference exists between the two types of ammunition, constructs a corresponding test statistic function, derives the limit value of the ballistic consistency test according to the requirement of the probability of the projectile falling into the elliptical overlapping area of the two types of ammunition dispersion, and determines the test sample amount according to the requirement of the tested false probability.
One embodiment of the present invention, as shown in fig. 1, discloses a method for testing the ballistic conformance of two types of ammunition, comprising the following steps:
s1, before ammunition is launched, obtaining the minimum test sample size according to the specified significance level and the false storage probability of the test;
s2, determining the number of the two types of ammunition to be fired according to the minimum test sample size, comparing and firing the two types of ammunition one by one under the same firing condition, and acquiring the firing ranges of the two types of ammunition one by one;
s3, obtaining the respective average shooting distance and distance variance of the two types of ammunition after the shooting conditions are standardized according to the shooting ranges of the two types of ammunition which are obtained one by one, and obtaining the weighted average value of the distance variance according to the distance variance of the two types of ammunition;
and S4, judging whether the two types of ammunition are uniformly distributed by adopting an F test according to the distance variance of the two types of ammunition, and judging the uniformity of the average trajectory of the two types of ammunition by adopting a t test according to the weighted average value of the distance variance if the two types of ammunition are uniformly distributed.
Compared with the prior art, the method can test the ballistic consistency of the two types of ammunition belonging to different parents and scientifically determine the test sample size.
It should be noted that the distribution of the landing points of the projectile is generally regarded as a normal distribution, and the landing point distribution refers to the percentage of the number of projectiles reaching each distance (height or direction) in the mean square difference region to the total number of projectiles when a large number of projectiles are fired under the same conditions. If two normal parents
Satisfies the following characteristic quantities:
|μA-μB|≤；
The mathematical description of ballistic consistency is as follows, under the same shooting conditions, if satisfied:
distance: | uxA-uxB|≤x 
The direction is as follows: | uzA-uzB|≤z 
In the formula:x，x，z，zthe trajectory of the two types of ammunition is consistent when the amount is small.
Thus, it can be seen that | μ is solvedA-μB|≤；
And (3) constructing a problem by using a tested statistic function, determining a limit value, and scientifically solving the core problem of ballistic consistency test by using the sample capacity n.
In one embodiment of the present invention, the calculation formula for obtaining the minimum test sample size according to the significance level and the false probability of the specified test is as follows:
wherein α is the significance level of the test, the abandonment probability of truth, β is the false probability of existence, z1-αAnd z1-βObtained by referring to a standard normal distribution integral function table,
allowable deviation value for center of ellipse of dispersion of two-type ammunition and dispersion variance thereof
The ratio of (a) to (b). Here, the scattering means the degree of deviation of the drop points of the multiple projectiles from their average drop point. The significance level refers to the probability that the overall parameters are estimated to fall in a certain interval to possibly make errors, and the false probability refers to the probability that the overall parameters are actually false and are judged to be possible to make errors.
In particular, since the rules are based on samples, there is always a possibility of making erroneous decisions, at hypothesis H0If true, a rejection H may be made0Such errors are called "leave true" errors, and when H0In the case of actual unreal, it is also possible to accept H0Such errors are referred to as "false" errors. In other words, if the hypothesis test is a logical judgment on the rationality of the test and not a judgment on the correctness of the result, and if the fact is true, the judgment on the test result is negative, the error made is called a false positive error, and the possibility or chance size of the false positive error is called a false negative probability. The false rejection probability in the embodiment of the invention is the significance level of the test; if the actual result of the verification process is false and the result of the verification determines that the result is positive, the error made is referred to as a false error, and the probability or chance magnitude of the false error made is referred to as a false probability.
When hypothesis testing H0Is | muA-μBWhen | ≦ is based on the "leave true" probability α (significance level of the test), "false" probability β, and
the minimum test sample size can be determined.
It should be noted that, when the sample size increases, the more difficult the discriminant of the t-test becomes, and therefore, it is necessary to determine the minimum test sample size that satisfies the test efficacy requirement. Along with the increase of the sample size, the statistical characteristic information is richer and more accurate, and the judgment is more and more accurate. The sample amount is small, the efficacy of the judgment conclusion is not high, the sample amount is too large, the judgment quality can be improved, but the test cost is too high, so that the sample amount n can be determined according to the efficacy requirement of the test.
According to a specific embodiment of the invention, the shooting conditions comprise ballistic conditions, topographic conditions and meteorological conditions, and the test efficacy of judging the ballistic consistency by the F test and the t test in the step S4 is according to α, n,
Or
The curve is determined to be 1- β by the corresponding OC (operating Characteristics curve).
Specifically, in order to accurately judge the bullet trajectory consistency of the two types of weapons, objective basis is provided, accurate technical preparation needs to be carried out on artillery, ammunition, geodetic survey and meteorological detection, the four technical parameters are accurately measured during the test, and the shooting test conditions are ensured to be the same:
(1) the same charge and the same charge number;
(2) the same altitude;
(3) the same shooting angle and the same shooting direction;
(4) the same pellet mass;
(5) the same initial speed;
(6) the same meteorological conditions;
(7) adjusted to the same reference in range and time of flight.
In the ballistic consistency test, α is generally taken as 5%, fig. 2 and 3 are OC curves commonly used in the ballistic consistency test, and when α is taken as 1%, the amount of samples required for the test is higher than 50% of the samples required for the test, α is taken as 5%, as shown in fig. 4 and 5
Or
The relationship of variation between the sample size n is according to the normalThe method is widely applied to quality control in the inspection process, is used for measuring the inspection effect, and defines the inspection efficacy as 1- β, namely the false probability.
In a specific embodiment of the invention, the two types of ammunition comprise type a ammunition and type B ammunition; the step S4 of determining whether the two types of ammunition are spread uniformly by using the F-test based on the distance variance of the two types of ammunition includes:
when F is satisfied1-α/2(nA-1,nB-1)≤F≤Fα/2(nA-1,nB-1), then the two types of ammunition are judged to be spread uniformly; otherwise, judging that the two types of ammunition are not uniformly scattered;
wherein the content of the first and second substances,
is the distance variance of the type a ammunition,
distance variance for type B ammunition, α significance level for test, probability of abandonment, nATest sample size of type A ammunition, nBTest specimen size for type B ammunition, F1-α/2And Fα/2Obtained by consulting a distribution table of F1-α/2Is the lower limit of the F test, Fα/2Is the upper limit value of the F test, and
the type a ammunition and the type B ammunition are two different types of ammunition among multiple types of ammunition for the same gun, and they have the same diameter, generally similar shape, the same or similar weight, and the same initial velocity, but have different purposes. Whether the two types of ammunition are spread uniformly or not is checked by using an F check, which is a check problem (mu)A,μBUnknown) are:
H0：σA＝σB，H1：σA≠σB；
the function of the statistics is
Given a significant level of α, when F > Fα/2(nA-1,nB-1) or F < F1-α/2(nA-1,nB-1) rejecting hypothesis H0Otherwise, accept H0。
I.e. F1-α/2(nA-1,nB-1)≤F≤Fα/2(nA-1,nB-1) if satisfied, then the scatter is judged to be consistent.
The F-test is a mathematical statistical test for comparing the sizes of two random variances, and the F-test in the embodiment of the present invention is used to test the relationship between the sizes of the radii of two scattered ellipses.
According to a specific embodiment of the present invention
In order to function the statistics of the data,
wherein n isATest sample size of type A ammunition, nBTest specimen size for type B ammunition, RAAt each throw of type A ammunition, RBIs the range of each round of type B ammunition.
Preferably, the operating characteristics of the test (operating characteristics of the test) for the dispersion consistency test are typically α -0.05, and H may be accepted0Probability β of as
For a particular value of λ, n, β can be read from the OC curve of fig. 2 or fig. 4, corresponding to test efficacy of 1- β.
In one embodiment of the present invention, if it is determined that the two types of ammunition are scattered in a consistent manner, the determining the consistency of the average trajectory of the two types of ammunition by using the t-test according to the weighted average of the distance variance comprises:
when it is satisfied with
If so, judging that the average trajectories of the two types of ammunition are consistent; otherwise, judging that the average trajectories of the two types of ammunition are inconsistent;
wherein the content of the first and second substances,
is the average firing distance of the type a ammunition,
mean firing distance of B-type ammunition, deviation value of center of ellipse allowed to spread of two-type ammunition when mean trajectory of two-type ammunition is consistent, nATest sample size of type A ammunition, nBTest sample size, t, for type B ammunitionαBy consulting a t-distribution table, SPThe weighted average of the distance variances of the two types of ammunition is used.
When comparing the average trajectories of the type a ammunition and the type B ammunition to determine whether they are consistent, a pair-wise observation is usually performed using a t-test.
The ballistic mean test problem to be considered for the group determination is:
H0：|μA-μB|≤，H1：|μA-μB|>；
make statistics
Given significance level α of the test, when t > tα(nA+nB-2) rejecting hypothesis H0Otherwise, accept H0. Namely, it is
And if so, judging that the average trajectory is consistent.
the t-test is a test performed on the average value of the random variable measurement values when the variance is unknown, and is used for testing the average flight distance and the average flight direction in the embodiment of the present invention.
In the concrete application, the grenade range is tested by taking:
＝1.0σ≈SP，
Specifically, the operating characteristics of the test, for the average ballistic consistency test, are typically taken to be α ═ 0.05, numbered α, d*、n＝nA+nB-1, referring to FIG. 3 or FIG. 5, the hypothesis H in the actual test can be obtained0The false probability of existence β of the test and the efficacy of the test 1- β.
In one embodiment of the invention, the deviation value of the center of the ellipse of dispersion of the two types of ammunition, when the average trajectories of the two types of ammunition are consistent, is determined by the falling probability K of the projectile in the overlapping area:
when K is equal to 0.95, σ ═ SP；
When K is equal to 0.8, 1.75 σ is 1.75SP；
When K is equal to 0.7, 2 σ 2SP；
The falling probability K is determined by the kind of ammunition. It should be noted that the ammunition is a general name of a bullet, a shell, a grenade, a rocket shell, a missile and the like, and the ammunition is particularly a shell in the embodiment of the invention, the shell comprises a grenade, a armor-breaking shell, a lighting shell, a smoke shell and the like, and the blasting shell, the killing shell and the blasting shell are collectively called the grenade.
That is, as shown in fig. 6, the intersection of the dispersion ellipses of the two types of ammunition drops is schematically indicated, and the region of the dispersion ellipse of the a type ammunition is represented by ΩAThe probability of falling into a certain region is PAThe elliptical region of B-type ammunition dispersion is omegaBThe probability of falling into a certain region is PBThen P isA(ΩA)≈1.0，PB(ΩB) 1.0, ballistic consistency, expressed by the falling probability K, is defined as:
PA(ΩA∩ΩB)≥K；
PB(ΩA∩ΩB)≥K；
in the formula: k is more than 0.5 and less than or equal to 1.0.
Specifically, with respect to the two-dimensional plane of the projectile landing point, the positional relationship of the dispersion ellipses of the two types of ammunition in the longitudinal and transverse directions is as shown in fig. 7, in which the mean square deviations are the same, the ellipse centers are different, and the left diagram is that the ellipse centers are shifted by one σ left and rightzThe right graph is the ellipse center shifted forward and backward by one sigmax，
In summary, as shown in the schematic diagram of fig. 8, the maximum allowable deviation of the center of the dispersion ellipse when the average trajectories of the grenades are consistent is obtained as | μ |A-μBAnd | ≦ σ as the maximum allowable deviation of the center of the grenade two-type ammunition spreading ellipse. The values K for the illuminating bomb and the smoke bomb were 0.8 and 0.7, respectively, and 1.75 σ and 2.0 σ, respectively.
Regarding the test of mean square error, for the purpose of determination, it is assumed that the centers of the drop point spread ellipses of the A, B two-type ammunition coincide, i.e., μA＝μB；
Let K equal to 0.95, muAx-μBx＝0,μAz-μ Bz0, i.e. the two interspersed ellipse centers coincide, as shown in fig. 9.
When the hit probability is reduced by 5%, assuming that the effect of causing the probability of the type B ammunition falling into the type A ammunition is reduced in the distance and direction is equivalent, then
According to the standard normal distribution table and FIG. 9, it can be calculated and derived:
similarly, when K is 0.8, it can be deduced that
When K is 0.7, it can be deduced that
Therefore, the temperature of the molten metal is controlled,
this confirms what has been said above.
From the above analysis, it can be seen that the dispersion variance σ coincides with the A, B two-model ammunition center of dispersionA、σBIs insensitive to the influence of its overlap region falling into the probability, i.e. the falling probability is reduced by 5%, allowing sigma toA、σBThere was a 1.34 fold difference.
However, any two types of ammunition which ballistic consistency needs to be compared are designed by ballistic consistency during development, particularly, the projectile density design technology level is high at present, the two types of ammunition are easy to approach, the value range cannot be obtained in practice, and only a small number near zero can be obtained in practice, so that sigma is pursued during designA＝σBIt is this proposition that is examined.
In one embodiment of the present invention, the distance variance weighted average of the two types of ammunition is calculated as follows:
wherein the content of the first and second substances,
is the distance variance of the type a ammunition,
distance variance of B-type ammunition, nATest sample size of type A ammunition, nBThe test sample size for type B ammunition.
In a specific embodiment of the present invention, the calculation formula of the average firing distance of the type a ammunition and the type B ammunition is as follows:
wherein R isAAt each throw of type A ammunition, nATest specimen size for type A ammunition, RBFor each shot of B-ammunition, nBThe test sample size for type B ammunition.
In practical application, the average shooting distances of the two types of ammunition can be obtained by calculating the average value of the measured average shooting ranges of a plurality of groups of the two types of ammunition, and the group number is set in groups according to the number of the two types of ammunition.
Test sample size n for type A and type B ammunition, a specific embodiment of the inventionAAnd nBDetermined by the minimum test sample size N of type A ammunition and type B ammunition respectively plus the corresponding additional value 1 or 2, where NA＝nB。
Specifically, the sample amount N in the case of different combinations of α, β, and d can be calculated according to the formula of the minimum test sample amount, which is detailed in tables 1 and 2. The sample quantities determined by using the graph 3 and the graph 5 and the graph 1 and the graph 2 are consistent, and the sample quantity N is consulted by using the graph 3 and the graph 5, so that the regularity is intuitive and clear at a glance; using table 1, table 2 to look up N, is accurate in magnitude, without interpolation. In actual use, the two can be combined for verification.
Table 1 α ═ 0.05
Table 2 α ═ 0.01
Note that z in the formula of the minimum test sample size1-αAnd z1-βThe normal distribution density function is obtained by looking up a standard normal distribution integral function table and is as follows:
the one-dimensional normal distribution probability density here is, as shown in fig. 10, according to the "3 σ rule", although the range of the normal variable X is (— ∞, + ∞), the probability that its value falls within (μ -3 σ, μ +3 σ) is as high as 99.73%, and therefore, the range of the range X can be considered approximately as (μ -3 σ, μ +3 σ). Thus, under the same coordinate system, XATake the value of (mu)A-3σx,μA+3σx)，XBIs taken as (mu)B-3σx,μB+3σx). As can be seen from fig. 10, when the scattering center of the two-type ammunition is shifted by | mu |A-μBNormal distribution density function intersection f (x) of two types of ammunition when | ═ σA)∩f(xB) 97.59%, this is in accordance with
Close to this, it was determined that grenade pickup was 1.0 σ.
In practice, for a multi-charge gun, firing should be carried out with a specific number of charges, typically 3 charges:
(1) subsonic (generally the entire trajectory is subsonic);
(2) transonic (initial velocity slightly higher than sonic, excessive to subsonic speed in the initial segment of trajectory);
(3) supersonic (initial velocity is much higher than sonic, transition to subsonic velocity in the later stages of trajectory).
The selection of the charge is based on different change laws of aerodynamic characteristics of the projectile in different flight speed intervals, as shown in fig. 11: if the outer trajectory agreement is judged in two charges of the same type, then the outer trajectory agreement between those two types of charges is also assumed.
For artillery with both high and low ranges, the fire should be at a specific few fire angles, typically 3 angles are required:
(1)20 ° (low range);
(2)42 ° (near the maximum range angle);
(3)62 ° (high range).
If a finer inspection is to be performed at 5 firing angles, 18 °, 33 °, 42 °, 53 ° and 64 ° may be chosen. For cannons with only low range, this is typically 18 °, 42 °; only mortars with high calibers, typically 53 deg., 75 deg..
The selection of the shooting angle is based on that the flying postures of the rocket are different under the conditions of different shooting angles and flying heights, so that the stress characteristics of the rocket are different, as shown in fig. 12: if the outer ballistic coincidence is judged in two firing angles of the same charge, then the outer ballistic coincidence between those two firing angles is also identified.
Only when both types A, B were judged to have trajectory coincidence at all charge numbers and all firing angles, it was judged that both types A, B of ammunition had trajectory coincidence.
Specific application example 1
The full-size explosive charging of the grenade gun explosion-killing (A) bomb and the powerful (B) bomb is shot and compared under the condition of a 220-mil firing angle, the true abandoning probability of the detection of the average range difference of the two types of bombs is required to be not more than 5%, the false storage probability is not more than 5%, the test sample size is planned, the drop point ranges after the test are compared, and whether the average ballistic trajectories are consistent or not is judged.
When the average ballistic trajectory consistency of the grenades is tested, taking 1.0 sigma as the corresponding value
From the table 1, the sample size satisfying the test requirement is N + 1-22 + 1-23, and N-23 can also be obtained from fig. 3.
In order to compare the average ballistic consistency of the ammunition types A and B, 24 ammunitions are respectively taken for the two types A and B, divided into 3 groups and 8 ammunitions in each group, and shot by comparing one by one, and the landing points and the range are standardized as follows:
test data 1:
Group 2
According to the inspection, three groups of data in the test data 1 have no abnormal result, and the following data are calculated according to the data:
the average range and the comprehensive spread of the three groups are as follows:
firstly, whether the scatter of the two types of bullet drop points is the same or not is judged, and then the judgment and comparison are respectively carried out by the existing method and the method established by the invention.
Giving significance level α ═ 0.05, look up F distribution table and obtain F0.05/2(21,21)＝2.408，
The type A ammunition and the type B ammunition have consistent landing point dispersion, namely the dispersion ellipses have the same size, and the difference of the average landing point values can be judged by using a t test.
a. The first test method of the prior art (MTP3-1-004 in USA) is:
giving significance level α equal to 0.05, looking up a distribution table of t to obtain t0.05/2(21+21)＝2.0181，
The ballistic trajectories of the type A ammunition and the type B ammunition are inconsistent, namely the ballistic trajectories of the killing blasting bomb and the powerful bomb are inconsistent.
b. The second test method (China GJB349.17-89) in the prior art comprises the following steps:
giving significance level α equal to 0.05, looking up a distribution table of t to obtain t0.05/2(21)＝2.0796，
The ballistic trajectories of the type A ammunition and the type B ammunition are inconsistent, namely the ballistic trajectories of the killing blasting bomb and the powerful bomb are inconsistent.
c. The judgment method established according to the scheme of the invention comprises the following steps:
giving significance level α equal to 0.05, looking up a distribution table of t to obtain t0.05(42)＝1.6820；
Grenade taking 1.0 sigma ≈ 1.0SP，
The type A ammunition and the type B ammunition have the same ballistic trajectory, namely, the killing blasting bomb and the high power bomb have the same ballistic trajectory.
The operating characteristics examined, according to a 0.05,
Specific application example two
The full-size charges of the grenade explosion-killing (A) bomb and the smoke-generating bomb (B) bomb are shot under the condition of a 590-density firing angle, the firing ranges of the grenade explosion-killing (A) bomb and the smoke-generating bomb are standardized and are shown as test data 2, whether the average firing ranges of the grenade explosion-killing (A) bomb and the smoke-generating bomb are consistent or not is judged in a trial mode, and whether the requirement that the significance level alpha is 0.05 and the storage probability beta is less than or.
Test data 2:
from experimental data 2, it can be calculated that:
giving significance level α ═ 0.05, look up F distribution table and obtain F0.05/2(6,6)＝5.82，
The landing points of the A-type ammunition and the B-type ammunition are scattered in a consistent mode, namely the scattering ellipses are the same in size, and the difference of the average landing points of the A-type ammunition and the B-type ammunition can be judged by using a t test.
a. The first test method of the prior art (MTP3-1-004 in USA) is:
giving significance level α equal to 0.05, looking up a distribution table of t to obtain t0.05/2(7+7-2)＝2.1788，
The ballistic trajectories of the type A bullet and the type B bullet are inconsistent, namely the ballistic trajectories of the killing blasting bullet and the smoke bomb are inconsistent. b. The second test method (China GJB349.17-89) in the prior art comprises the following steps:
giving significance level α equal to 0.05, looking up a distribution table of t to obtain t0.05/2(7-1)＝2.4469，
The ballistic trajectories of the type A bullet and the type B bullet are inconsistent, namely the ballistic trajectories of the killing blasting bullet and the smoke bomb are inconsistent. c. The judgment method established according to the scheme of the invention comprises the following steps:
giving significance level α equal to 0.05, looking up a distribution table of t to obtain t0.05(7+7-2)＝1.7823，
2 sigma ≈ 2S for smoke bombP，
The type A ammunition and the type B ammunition have the same ballistic trajectory, namely the average ballistic range of the killing blasting bomb and the smoke bomb is consistent.
The operating characteristics tested, according to α -0.05,
referring to fig. 3, when n is 13, β is 0.08, and the efficacy of the test is 1- β is 0.92.
From the two examples above, it can be seen that: the first and second inspection methods in the prior art judge that the trajectories of the A-type ammunition and the B-type ammunition with similar landing point shooting effects are inconsistent, and the method established by the invention can judge that the trajectories of the A-type ammunition and the B-type ammunition with similar landing point shooting effects are consistent according to the hit requirements of different ammunition types, so that the method has universality of practical use.
Comparing example one with example two, it can also be seen that the required sample amount n is different, increasing and decreasing for different required ammunition trajectory conformance tests at the same significance level α and false negative probability β.
In particular, it is noted that: when 0 is taken, the method established by the invention is the same as the existing method, and can be used for checking whether two types of ammunition belonging to the same parent body are required to have consistent ballistic trajectories.
The ballistic consistency determination in the shooting direction is exactly the same as the ballistic consistency determination in the range.
For the two types of ammunition, the judgment is carried out by using the method established by the technical scheme of the invention only under the conditions of the determined charge number and firing angle, and the bullet tracks of the A, B two types of ammunition can be judged to be consistent when all the bullet tracks are judged to be consistent.
In summary, the invention discloses a ballistic consistency testing method for two types of ammunition, which comprises the following steps: s1, before ammunition is launched, obtaining the minimum test sample size according to the specified significance level and the false storage probability of the test; s2, determining the number of the two types of ammunition to be fired according to the minimum test sample size, comparing and firing the two types of ammunition one by one under the same firing condition, and acquiring the firing ranges of the two types of ammunition one by one; s3, obtaining the respective average shooting distance and distance variance of the two types of ammunition after the shooting conditions are standardized according to the shooting ranges of the two types of ammunition which are obtained one by one, and obtaining the weighted average value of the distance variance according to the distance variance of the two types of ammunition; and S4, judging whether the two types of ammunition are uniformly distributed by adopting an F test according to the distance variance of the two types of ammunition, and judging the uniformity of the average trajectory of the two types of ammunition by adopting a t test according to the weighted average value of the distance variance if the two types of ammunition are uniformly distributed. The invention establishes a systematic and complete average ballistic trajectory consistency test method, can meet the requirement of testing the ballistic trajectory consistency of two types of ammunition belonging to different parent bodies, overcomes the limitation in testing and evaluating the ballistic trajectory consistency in the prior art, and has wider engineering use characteristics; an OC (operating Characteristics curve) curve is introduced into the testing method, so that the relation between testing efficiency alpha and beta and the allowable difference value of average ballistic performance and the sample amount n is clearly embodied, the problem that the relation between testing efficiency and sample amount cannot be embodied in the original method is solved, the ballistic consistency testing test condition, the charge number and the firing angle are determined, and the ballistic Characteristics are objectively and fully tested in a full speed domain and a full firing boundary.
Those skilled in the art will appreciate that all or part of the processes for implementing the methods in the above embodiments may be implemented by a computer program, which is stored in a computer-readable storage medium, to instruct associated hardware. The computer readable storage medium is a magnetic disk, an optical disk, a read-only memory or a random access memory.
The above description is only for the preferred embodiment of the present invention, but the scope of the present invention is not limited thereto, and any changes or substitutions that can be easily conceived by those skilled in the art within the technical scope of the present invention are included in the scope of the present invention.
Claims (8)
1. A ballistic conformance testing method for two types of ammunition is characterized by comprising the following steps:
s1, before ammunition is launched, obtaining the minimum test sample size according to the specified significance level and the false storage probability of the test;
s2, determining the number of the two types of ammunition to be fired according to the minimum test sample size, comparing and firing the two types of ammunition one by one under the same firing condition, and acquiring the firing ranges of the two types of ammunition one by one;
s3, obtaining the respective average shooting distance and distance variance of the two types of ammunition after the shooting conditions are standardized according to the shooting ranges of the two types of ammunition which are obtained one by one, and obtaining the weighted average value of the distance variance according to the distance variance of the two types of ammunition;
s4, according to the distance variance of the two types of ammunition, adopting an F test to judge whether the two types of ammunition are uniformly scattered, if so, adopting a t test to judge the uniformity of the average trajectory of the two types of ammunition according to the weighted average value of the distance variance;
if the dispersion of the two types of ammunition is consistent, the step of judging the consistency of the average trajectory of the two types of ammunition by adopting a t test according to the weighted average of the distance variance comprises the following steps:
when it is satisfied with
If so, judging that the average trajectories of the two types of ammunition are consistent; otherwise, judging that the average trajectories of the two types of ammunition are inconsistent;
wherein the content of the first and second substances,
is the average firing distance of the type a ammunition,
mean firing distance of B-type ammunition, deviation value of center of ellipse allowed to spread of two-type ammunition when mean trajectory of two-type ammunition is consistent, nATest sample size of type A ammunition, nBTest sample size, t, for type B ammunitionαBy consulting a t-distribution table, SPWeighted average of the distance variances of the two types of ammunition;
when the average trajectories of the two types of ammunition are consistent, the deviation value of the center of the dispersion ellipse of the two types of ammunition is allowed to be determined by the probability K that the projectile in the overlapped area of the two types of ammunition falls into the overlapping area:
when K is equal to 0.95, σ ═ SP；
When K is equal to 0.8, 1.75 σ is 1.75SP；
When K is equal to 0.7, 2 σ 2SP；
Wherein, the value of K is determined according to the type of ammunition;
artillery of multiple charge sizes was tested with specific charges including: 3 charges corresponding to subsonic, transonic and supersonic speeds;
for artillery with high and low ranges, shooting at specific angles, including 20 degrees at low range, 42 degrees near the maximum range angle, and 62 degrees at high range; 18 ° for cannons with only low range, 42 °; for mortars with only high fire boundaries, 53 degrees and 75 degrees;
when both types of A, B ammunition were judged to have trajectory coincidence under all charge numbers and all firing angles, it was judged that both types of A, B ammunition had trajectory coincidence.
2. The method of claim 1, wherein the minimum test sample size is calculated from the significance level and the false positive probability of a given test as follows:
wherein α is the significance level of the test, the abandonment probability of truth, β is the false probability of existence, z1-αAnd z1-βObtained by referring to a standard normal distribution integral function table,
allowable deviation value for center of ellipse of dispersion of two-type ammunition and dispersion variance thereof
The ratio of (a) to (b).
3. The method as claimed in claim 1, wherein the shooting conditions include ballistic conditions, topographic conditions, and meteorological conditions, and the test efficacy of the F-test and the t-test in the step S4 for judging the ballistic consistency is according to α, n,
Or
From the corresponding OC curve, 1- β was identified.
4. The method of claim 1, wherein the two types of ammunition comprise type a ammunition and type B ammunition; the step S4 of determining whether the two types of ammunition are spread uniformly by using the F-test based on the distance variance of the two types of ammunition includes:
when F is satisfied1-α/2(nA-1,nB-1)≤F≤Fα/2(nA-1,nB-1), then the two types of ammunition are judged to be spread uniformly; otherwise, judging that the two types of ammunition are not uniformly scattered;
wherein the content of the first and second substances,
is the distance variance of the type a ammunition,
distance variance for type B ammunition, α significance level for test, probability of abandonment, nATest sample size of type A ammunition, nBTest specimen size for type B ammunition, F1-α/2And Fα/2Obtained by consulting a distribution table of F1-α/2Is the lower limit of the F test, Fα/2Is the upper limit value of the F test, and
5. the method of claim 4, wherein the step of determining the target position is performed by a computer
In order to function the statistics of the data,
wherein n isATest sample size of type A ammunition, nBTest specimen size for type B ammunition, RAAt each throw of type A ammunition, RBIs the range of each round of type B ammunition.
6. The method according to claim 1, characterized in that the calculation formula of the distance variance weighted average of the two types of ammunition is as follows:
wherein the content of the first and second substances,
is the distance variance of the type a ammunition,
distance variance of B-type ammunition, nATest sample size of type A ammunition, nBThe test sample size for type B ammunition.
7. The method according to claim 1, characterized in that the calculation formula of the mean firing distance of the type a ammunition and the type B ammunition is respectively as follows:
wherein R isAAt each throw of type A ammunition, nATest specimen size for type A ammunition, RBFor each shot of B-ammunition, nBThe test sample size for type B ammunition.
8. Method according to any of claims 1 or 4-7, characterized in that the test sample quantities n for ammunition types A and BAAnd nBDetermined by the minimum test sample size N of type A ammunition and type B ammunition respectively plus the corresponding additional value 1 or 2, where NA＝nB。
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