CN110991059A - Runway failure rate analysis and calculation method based on Weili ring cutting method - Google Patents

Runway failure rate analysis and calculation method based on Weili ring cutting method Download PDF

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CN110991059A
CN110991059A CN201911257165.6A CN201911257165A CN110991059A CN 110991059 A CN110991059 A CN 110991059A CN 201911257165 A CN201911257165 A CN 201911257165A CN 110991059 A CN110991059 A CN 110991059A
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runway
bullet
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CN110991059B (en
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李新其
彭司萍
徐山林
张大巧
刘志钢
张戈
马毓宁
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Rocket Force University of Engineering of PLA
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Abstract

A runway failure rate analysis and calculation method based on a Weili ring cutting method belongs to the field of management efficiency analysis, and is characterized in that: cutting a runway by adopting an explosion-forming elastic power ring; dividing the whole runway into a plurality of single-section runways; cutting any one of the plurality of sections of the runway by adopting a single explosive bullet and a single aiming point, and calculating the failure rate of the single section of the runway by determining the geometric relationship between the explosive bullet parent bullet and the cut single section of the runway and the favorable impact area; and (3) successfully cutting the analytical model of the single-section runway through the explosive bomb power ring, and successfully cutting the analytical calculation model of the whole runway by a plurality of explosive bombs, and analyzing the calculation precision of the model. The established runway failure rate analysis, calculation and analysis model is strict in demonstration, rapid in calculation speed and feasible in result, and the accuracy can meet the requirements of operational efficiency analysis such as SEA.

Description

Runway failure rate analysis and calculation method based on Weili ring cutting method
Technical Field
The invention belongs to the field of management efficiency analysis, and relates to an application modeling technology for system combat efficiency analysis.
Background
The airport is blocked, and the taking off and landing of the fighter plane are prevented mainly by damaging the runway of the airport, so that favorable conditions are created for capturing the air control right. Limited by the guidance precision of missile weapons, at present, a master-slave type warhead is mainly used for explosion relief and large-scale bullet throwing on a runway to make up the defect of shooting precision. After the bullets hit and successfully penetrate the runway, craters are formed on the runway, and when the number of the craters on the runway surface is enough and a minimum landing window for taking off and landing of the airplane does not exist on the whole runway, the runway is considered to temporarily lose the function of guaranteeing the taking off and landing of the airplane.
On the calculation method of runway failure rate, there are two main categories of statistical test method and analytic method at present. At present, almost all the Monte Carlo method is adopted for modeling, but the Monte Carlo method is a statistical test method, is based on direct simulation, and has the advantages of strong universality, no principle error, predictable precision result and the like by carrying out statistical analysis on a system with random factor influence; but the needed samples are large and time-consuming, so that the requirement of military command assistant decision analysis with high requirements on real-time performance and rapidity is difficult to adapt.
The invention content is as follows:
in order to solve the problem of analytic algorithm of the damage effect index calculation of the airport runway blocked by the shrapnel, the invention provides a method for 'cutting' the runway by adopting a power ring, determining a favorable impact area by judging the geometric relationship between the falling point of the shrapnel and the 'cut' runway, and calculating the failure probability of the runway.
The runway failure rate analysis and calculation method based on the Weili ring cutting method adopts a detonation bomb Weili ring to cut the runway; dividing the whole runway into a plurality of single-section runways; cutting any one of the plurality of sections of the runway by adopting a single explosive bullet and a single aiming point, and calculating the failure rate of the single section of the runway by determining the geometric relationship between the explosive bullet parent bullet and the cut single section of the runway and the favorable impact area; calculating the failure probability of the whole runway under the conditions of multiple explosive bombs and multiple aiming points through multiple single explosive bombs, single aiming points and single-section failure rate of the single-section runway; and finally, carrying out precision analysis on the failure probability of the whole runway.
The invention relates to a runway failure rate analysis and calculation method based on a Weili ring cutting method, wherein the single explosive projectile and single aiming point cutting single-section runway comprises the following steps:
(1) according to the length requirement of the minimum take-off and landing window, dividing the runway into a plurality of sections by cutting;
(2) the bullets are uniformly distributed in the throwing circle and the radius of the bullets is RPThe average damage radius of the bullet to the runway is RhRadius of power ring RwIs the sum of the two, namely:
RW＝RP+Rh(1)
(3) and analyzing and judging the geometric relationship among the drop point of the parent projectile, the power ring and the runway to be cut, and when the power ring formed after the projectile throws the bullet enables the runway to have no minimum take-off and landing window for the take-off and landing of the airplane, determining that the runway is successfully cut.
The invention discloses a runway failure rate analysis and calculation method based on a power ring cutting method, wherein the successful cutting process of a single section of runway comprises the following steps: setting the i-th section of runway to be cut, the width of the runway is B meters, and the length of the runway is 2LdMeter, minimum take-off and landing window length LminRice, width BminThe aiming point of the missile is positioned in the center of the section of the runway; probability P of successful cutting of ith section of runway by one explosive bomb0The analytical formula (2) is:
Figure RE-GDA0002345454500000021
in the formula ：
Figure RE-GDA0002345454500000022
for simplicity of the processA function of the squre; wherein,
Figure RE-GDA0002345454500000023
wherein
Figure RE-GDA0002345454500000024
x0＝-ΔL
Figure RE-GDA0002345454500000025
When i is 1,2,3, …, n
Figure RE-GDA0002345454500000026
Figure RE-GDA0002345454500000027
1) Establishing a rectangular coordinate system by taking the center of the runway as an origin and the direction of the runway as the direction of an x axis; according to the aiming point selection method, the length to be cut is 2LdThis track, typically 2Ld≤2LminLet Δ L be Lnim-Ld。
2) Sequentially determining favorable impact areas according to the geometric relationship among the parent projectile falling points, the power rings and the 'cut' runway;
3) under the condition of a single aiming point and a single explosive bullet, the probability of successful cutting of a certain section of runway can be known according to the fire operating theory, and the probability of successful cutting of the certain section of runway is calculated, namely the probability of the bullet falling into the favorable impact area is calculated.
The invention discloses a runway failure rate analysis and calculation method based on a power ring cutting method, which comprises the following steps of sequentially determining favorable impact areas according to the geometrical relationship among a parent projectile falling point, a power ring and a cut runway:
(1) consider the scenario where the impact point of the parent projectile moves up and down
When the impact point of the mother bullet is positioned above,the width of the intact maximum channel formed at the point where the force ring "cuts" the runway should be less than the minimum take-off and landing window width BminSo that the impact point cannot be beyond the position above the runway
Figure RE-GDA0002345454500000031
Similarly, the impact point is located below the runway and cannot be beyond
Figure RE-GDA0002345454500000032
(2) The impact point of the mother bullet moves leftwards
The movement between the transverse directions (i.e. left and right directions) must not exceed-RW-ΔL；
(3) The impact point of the mother bullet moves to the upper left
When the impact point of the bullet moves to the upper left, the overlapping condition of the power ring and the right half runway is mainly examined. When the power ring always covers the lower left corner of the right half track, the right half track always has no minimum take-off and landing window at the moment; when the power ring continues to move towards the left upper side and cannot cover the lower left corner of the right half section of the runway, a minimum take-off and landing window begins to appear in the direction of the lower left corner of the right half section of the runway; for this purpose, let the coordinates of point H be
Figure RE-GDA0002345454500000033
Using the point H as the center of circle and R as the center of circleWA section of arc, AC or DC, is formed at the upper left part of the circle with a radius
Figure RE-GDA0002345454500000034
At point Q; coordinate of point Q of
Figure RE-GDA0002345454500000035
The intersection line y is 0 at the point S, and let the coordinate S be (x)s0), then:
Figure RE-GDA0002345454500000036
(4) the impact point of the mother bullet moves to other directions
Respectively drawing arcs when the power ring moves towards the left lower part, the right upper part and the right lower part according to an analysis method when a bullet impact point of a female bullet moves towards the left upper part, wherein the arcs are respectively called SP, TP and TQ; t and S are symmetric about the Y axis; p and Q are symmetric about the X axis; f and Q are symmetric about the Y axis; g and F are symmetric about the X axis.
The runway failure rate analysis and calculation method based on the Weili ring cutting method has the advantages that the probability that a certain section of runway is successfully cut, namely the probability that a bullet falls into a favorable bullet landing area is calculated according to the following steps: is provided with
(1) The missile aiming point is coincided with the center of the drop point, namely the system error is not considered;
(2) the bullet spread being a circular spread, i.e. sigmax＝σyσ, or Ex＝EyThe vertical and horizontal distribution density of the impact points is as follows:
Figure RE-GDA0002345454500000041
Figure RE-GDA0002345454500000042
the probability of landing in the favorable landing zone is:
Figure RE-GDA0002345454500000043
since the normal distribution density function is point symmetric to the distribution center (coinciding with the aiming point), and the region SQFTGP is also point symmetric to the aiming point, and the integrand is equal, then:
P{(x,y)∈D1}＝P{(x,y)∈D2}＝P{(x,y)∈D3}＝P{(x,y)∈D4} (6)
for D1Comprises the following steps:
Figure RE-GDA0002345454500000044
wherein
Figure RE-GDA0002345454500000045
To ensure the accuracy of the calculation of the integral, the region is defined as x0,x1,…,xnAre equally spaced apart, then
Figure RE-GDA0002345454500000051
Likewise, P can be obtained2,P3,P4The integral expression of (1);
after finishing, the method comprises the following steps:
Figure RE-GDA0002345454500000052
for D5It is known as a rectangular area,
Figure RE-GDA0002345454500000053
Figure RE-GDA0002345454500000054
the method is simplified as follows:
Figure RE-GDA0002345454500000055
therefore, the probability P that a certain section of runway is successfully cut under the condition that a single aiming point and a single bullet are formed into an explosive bullet0Comprises the following steps:
Figure RE-GDA0002345454500000056
the invention relates to a runway failure rate analysis and calculation method based on a Weili ring cutting method, which specifically comprises the following steps of calculating the failure probability of a whole runway under the conditions of a plurality of single explosive bombs, a plurality of single aiming points and single-section failure rates of the single section runway by the aid of a plurality of single explosive bombs, the single aiming points and the single-section failure rates of the single section runway: the relationship among the launching success probability, the penetration probability and the explosion-relief success probability of each missile corresponding to each aiming point is shown in the following table:
Figure RE-GDA0002345454500000061
then the calculation of runway failure rate is:
Figure RE-GDA0002345454500000062
wherein ,P0iThe probability of successfully "cutting" a certain section of runway for the ith completed bomb.
The runway failure rate analysis and calculation method based on the Weili ring cutting method has the accuracy estimation formula
Figure RE-GDA0002345454500000063
The invention relates to a runway failure rate analysis and calculation method based on a power ring cutting method, which comprises the following steps of: in the construction of the favorable impact area of the mother bullet, only the (-Delta L-R) taking the aiming point as the center is consideredW,ΔL+RW) An area; on the premise of assuming that the bullet drop points are normally distributed, the calculation accuracy of the analytical model is evaluated, and actually, the bullet drop points fall into (-Delta L-R) when the calculation is carried out left-right movementW,ΔL+RW) A probability of a region; the distribution density function of the impact point of the mother bullet is as follows:
Figure RE-GDA0002345454500000064
therefore, it is
PAccuracy of measurement＝P(-ΔL-RW≤x≤ΔL+RW) (28)。
The runway failure rate analysis and calculation method based on the Weili ring cutting method analyzes the model calculation precision through the analysis model of successfully cutting a single-section runway by the explosion-forming bomb power ring and the analysis and calculation model of successfully cutting the whole runway by a plurality of explosion-forming bombs. The established runway failure rate analysis, calculation and analysis model is strict in demonstration, rapid in calculation speed and feasible in result, and the accuracy can meet the requirements of operational efficiency analysis such as SEA.
Drawings
FIG. 1 is a schematic view of the favorable impact area of a Weili ring cutting runway bullet according to the present invention;
fig. 2 is a schematic view of the favorable impact zone division of the present invention.
Detailed Description
The runway failure rate analysis and calculation method based on the Weili ring cutting method is described in detail below with reference to the accompanying drawings and embodiments.
Example one
The specific steps of the explosive-forming elastic power ring for cutting the runway are as follows:
(1) according to the length requirement of the minimum take-off and landing window, dividing the runway into a plurality of sections by cutting;
(2) assuming that the bullet is uniformly distributed within the throwing circle, its radius is given by RPThe average damage radius of the bullet to the runway is RhThe power ring radius is the sum of the two, namely:
RW＝RP+Rh(1)
(3) checking the geometrical relationship among the falling point of the bullet, the power ring and the runway to be cut, and considering that the runway is successfully cut when the power ring formed after the bullet is thrown by the missile makes the runway have no minimum landing window for the take-off and landing of the airplane;
(4) and (4) integrating the successful cutting probability of each section of the runway to obtain the failure probability of the whole runway under the impact of a plurality of bullets.
According to the steps, the analytic expression of the probability that the runway is successfully cut under the condition that a single aiming point and a single explosive projectile are formed can be obtained.
The analytic expression of successfully cutting the single-section runway by the single explosion projectile is as follows:
suppose that the i-th runway to be cut has a width of B meters and a length of 2LdMeter, minimum take-off and landing window length LminRice, width BminAnd the aiming point of the missile is positioned in the center of the section of the runway. Probability P of successful cutting of ith section of runway by one explosive bomb0The analytical formula (2) is:
Figure RE-GDA0002345454500000081
in the formula ：
Figure RE-GDA0002345454500000082
for simplified Laplace function[6]. wherein ,
Figure RE-GDA0002345454500000083
wherein
Figure RE-GDA0002345454500000084
x0＝-ΔL
Figure RE-GDA0002345454500000085
When i is 1,2,3, …, n
Figure RE-GDA0002345454500000086
Figure RE-GDA0002345454500000087
And (3) proving that:
1) and establishing a rectangular coordinate system by taking the center of the runway as an original point and the direction of the runway as the direction of an x axis.
According to the aiming point selection method, the length to be cut is 2LdThis track, typically 2Ld≤2LminLet Δ L be Lmin-Ld。
2) Determining the favorable impact area according to the geometric relationship between the drop point of the bullet, the power ring and the cut runway
(1) Consider the scenario where the impact point of the parent projectile moves up and down
When the impact point of the mother bullet is positioned above, the width of a perfect maximum channel formed on the part of the power ring for cutting the runway should be less than the width B of the minimum lifting windowminSo that the impact point cannot be beyond the position above the runway
Figure RE-GDA0002345454500000088
Similarly, the impact point is located below the runway and cannot be beyond
Figure RE-GDA0002345454500000089
(2) The impact point of the mother bullet moves leftwards
It is apparent that the movement between the lateral (i.e. left-right) directions must not exceed-RW-ΔL。
(3) The impact point of the mother bullet moves to the upper left
When the impact point of the bullet moves to the upper left, the overlapping condition of the power ring and the right half runway is mainly examined.
When the power ring always covers the lower left corner of the right half track, the right half track always has no minimum take-off and landing window at the moment; when the power ring continues to move towards the upper left and cannot cover the lower left corner of the right half of the runway, the minimum take-off and landing window begins to appear in the direction of the lower left corner of the right half of the runway. For this purpose, let the coordinates of point H be
Figure RE-GDA0002345454500000091
Using the point H as the center of circle and R as the center of circleWA section of arc, AC or DC, is formed at the upper left part of the circle with a radius
Figure RE-GDA0002345454500000092
At point Q. It is apparent that the Q point coordinate is
Figure RE-GDA0002345454500000093
Line of intersection y0 at point S, let S coordinate be (x)s0), then:
Figure RE-GDA0002345454500000094
(4) the impact point of the mother bullet moves to other directions
And (3) respectively drawing arcs when the power ring moves towards the lower left, the lower right, the upper right and the lower right according to an analysis method when the impact point of the bullet moves towards the upper left, wherein the arcs are respectively represented as SP, TP and TQ. The favorable landing zone map shown in figure 1 is obtained. The coordinates of each point are:
t and S are symmetric about the Y axis; p and Q are symmetric about the X axis; f and Q are symmetric about the Y axis; g and F are symmetric about the X axis.
3) Probability of successful 'cutting' of a certain section of runway under the condition of single aiming point and single explosive projectile
According to the theory of firepower operation, the probability that a certain section of runway is successfully cut is obtained, namely the probability that the mother bullet falls into the favorable bullet zone is calculated. For this reason, the following assumptions are made:
(1) the missile aiming point is coincided with the center of the drop point, namely the system error is not considered;
(2) the bullet spread being a circular spread, i.e. sigmax＝σyσ, or Ex＝EyThe vertical and horizontal distribution density of the impact points is as follows:
Figure RE-GDA0002345454500000095
Figure RE-GDA0002345454500000101
for ease of calculation, the favorable impact region in fig. 1 is divided into 5 parts, as shown in fig. 2.
The probability of landing in the favorable landing zone is:
Figure RE-GDA0002345454500000102
since the normal distribution density function is point symmetric to the distribution center (coinciding with the aiming point), and the region SQFTGP is also point symmetric to the aiming point, and the integrand is equal, then:
P{(x,y)∈D1}＝P{(x,y)∈D2}＝P{(x,y)∈D3}＝P{(x,y)∈D4} (6)
for D1Comprises the following steps:
Figure RE-GDA0002345454500000103
wherein
Figure RE-GDA0002345454500000104
To ensure the accuracy of the calculation of the integral, the region is defined as x0,x1,…,xnAre equally spaced apart, then
Figure RE-GDA0002345454500000105
Likewise, P can be obtained2,P3,P4The integral expression of (1);
after finishing, the method comprises the following steps:
Figure RE-GDA0002345454500000106
for D5It is known as a rectangular area,
Figure RE-GDA0002345454500000111
Figure RE-GDA0002345454500000112
the method is simplified as follows:
Figure RE-GDA0002345454500000113
therefore, the probability P that a certain section of runway is successfully cut under the condition that a single aiming point and a single bullet are formed into an explosive bullet0Comprises the following steps:
Figure RE-GDA0002345454500000114
the analytic expression of successfully 'cutting' the whole runway by a plurality of explosive bombs is as follows:
on the basis, a calculation formula of runway failure probability under the conditions of multiple explosive bombs and multiple aiming points can be deduced. Setting m aiming points of a runway, and setting the conditions of launching, explosion prevention and explosion relief of each bullet corresponding to each aiming point as follows:
TABLE 1 relationship table of firing success probability, penetration probability and explosion-relief success probability of aiming point and each missile
Figure RE-GDA0002345454500000115
Then the calculation of runway failure rate is:
Figure RE-GDA0002345454500000121
wherein ,P0iThe probability of successfully "cutting" a certain section of runway for the ith completed bomb.
Example two
On the basis of the first embodiment, the failure probability of the whole runway is subjected to precision analysis; the damage of each section of the runway is not independent but related; the runway is artificially divided into a plurality of sections according to different aiming points, the damage probability of each section is calculated, then the probability that the whole runway is blocked is comprehensively solved, and some windows can be missed. In this model we only analyzed that a slug moves the impact point at twice the throw radius near the aiming point, which would cause the section of the runway to be successfully "cut", and in fact, in the presence of multiple aiming points, even if the slug impact point exceeds twice the throw radius near the aiming point, which would cause the section of the runway to fail to be successfully "cut", but as a whole, it is possible to cause the section of the runway to be successfully "cut" because slugs at other aiming points would also have impact points far from the aiming point. Therefore, the calculation result according to the model is slightly lower than the actual value, and the calculation accuracy is analyzed.
Here, we give an estimation formula of the calculation accuracy of the present model:
Figure RE-GDA0002345454500000122
the meaning of each symbol in the formula is as described above.
And (3) proving that: based on the foregoing analysis, the model considers only the (- Δ L-R) centered at the aiming point in constructing the favorable impact zone of the grenadeW,ΔL+RW) And (4) a region. On the premise of assuming that the bullet drop points are normally distributed, the calculation accuracy of the analytical model is evaluated, and actually, the bullet drop points fall into (-Delta L-R) when the calculation is carried out left-right movementW,ΔL+RW) Probability of a region. The distribution density function of the impact point of the mother bullet is as follows:
Figure RE-GDA0002345454500000123
therefore, it is
PAccuracy of measurement＝P(-ΔL-RW≤x≤ΔL+RW) (28)。
According to the precision estimation formula, the grenade throwing radius R can be calculatedPBullet damage radius R200h2, CEP 180, minimum take-off and landing length Lmin800, the actual aiming point interval L is selecteddDPR calculation accuracy at 700, its value is 0.9519; the accuracy of the model calculation is 0.9138 even though the actual selected aiming point spacing is 750 meters apart. Such calculation accuracy can meet the needs of battle.

Claims (8)

1. A runway failure rate analysis and calculation method based on a Weili ring cutting method is characterized by comprising the following steps: cutting a runway by adopting an explosion-forming elastic power ring; dividing the whole runway into a plurality of single-section runways; cutting any one of the plurality of sections of the runway by adopting a single explosive bullet and a single aiming point, and calculating the failure rate of the single section of the runway by determining the geometric relationship between the explosive bullet parent bullet and the cut single section of the runway and the favorable impact area; calculating the failure probability of the whole runway under the conditions of multiple explosive bombs and multiple aiming points through multiple single explosive bombs, single aiming points and single-section failure rate of the single-section runway; and finally, carrying out precision analysis on the failure probability of the whole runway.
2. The runway failure rate analysis and calculation method based on the Weili ring cutting method as claimed in claim 1, characterized in that: the single explosive bullet that becomes, single aiming point cutting single section runway include:
(1) according to the length requirement of the minimum take-off and landing window, dividing the runway into a plurality of sections by cutting;
(2) the bullets are uniformly distributed in the throwing circle and the radius of the bullets is RPThe average damage radius of the bullet to the runway is RhRadius of power ring RwIs the sum of the two, namely:
RW＝RP+Rh(1)
(3) and analyzing and judging the geometric relationship among the drop point of the parent projectile, the power ring and the runway to be cut, and when the power ring formed after the projectile throws the bullet enables the runway to have no minimum take-off and landing window for the take-off and landing of the airplane, determining that the runway is successfully cut.
3. The runway failure rate analysis and calculation method based on the Weili ring cutting method as claimed in claim 2, characterized in that: the process of successfully "cutting" the single track segment comprises the following steps: setting the i-th section of runway to be cut, the width of the runway is B meters, and the length of the runway is 2LdMeter, minimum take-off and landing window length LminRice, width BminThe aiming point of the missile is positioned in the center of the section of the runway; probability P of successful cutting of ith section of runway by one explosive bomb0The analytical formula (2) is:
Figure RE-FDA0002345454490000011
in the formula ：
Figure RE-FDA0002345454490000012
is a simplified Laplace function; wherein,
Figure RE-FDA0002345454490000013
wherein
Figure RE-FDA0002345454490000014
x0＝-ΔL
Figure RE-FDA0002345454490000021
When i is 1,2,3, …, n
Figure RE-FDA0002345454490000022
Figure RE-FDA0002345454490000023
1) Establishing a rectangular coordinate system by taking the center of the runway as an origin and the direction of the runway as the direction of an x axis; according to the aiming point selection method, the length to be cut is 2LdThis track, typically 2Ld≤2LminLet us order
Figure RE-FDA0002345454490000026
2) Sequentially determining favorable impact areas according to the geometric relationship among the parent projectile falling points, the power rings and the 'cut' runway;
3) under the condition of a single aiming point and a single explosive bullet, the probability of successful cutting of a certain section of runway can be known according to the fire operating theory, and the probability of successful cutting of the certain section of runway is calculated, namely the probability of the bullet falling into the favorable impact area is calculated.
4. The runway failure rate analytic calculation method based on the Weili ring cutting method according to claim 3, characterized in that: the steps of sequentially determining the favorable impact area according to the geometrical relationship among the parent bomb falling point, the power ring and the 'cut' runway are as follows:
(1) consider the scenario where the impact point of the parent projectile moves up and down
When the impact point of the mother bullet is positioned above, the width of a perfect maximum channel formed on the part of the power ring for cutting the runway should be less than the width B of the minimum lifting windowminSo that the impact point cannot be beyond the position above the runway
Figure RE-FDA0002345454490000024
Similarly, the impact point is located below the runway and cannot be beyond
Figure RE-FDA0002345454490000025
(2) The impact point of the mother bullet moves leftwards
The movement between the transverse directions (i.e. left and right directions) must not exceed-RW-ΔL；
(3) The impact point of the mother bullet moves to the upper left
When the bullet impact point of the bullet moves to the upper left, the overlapping condition of the power ring and the right half section of the runway is mainly examined; when the power ring always covers the lower left corner of the right half track, the right half track always has no minimum take-off and landing window at the moment; when the power ring continues to move towards the left upper side and cannot cover the lower left corner of the right half section of the runway, a minimum take-off and landing window begins to appear in the direction of the lower left corner of the right half section of the runway; for this purpose, let the coordinates of point H be
Figure RE-FDA0002345454490000031
Using the point H as the center of circle and R as the center of circleWA section of arc, AC or DC, is formed at the upper left part of the circle with a radius
Figure RE-FDA0002345454490000032
At point Q; coordinate of point Q of
Figure RE-FDA0002345454490000033
The intersection line y is 0 at the point S, and let the coordinate S be (x)s0), then:
Figure RE-FDA0002345454490000034
(4) the impact point of the mother bullet moves to other directions
Respectively drawing arcs when the power ring moves towards the left lower part, the right upper part and the right lower part according to an analysis method when a bullet impact point of a female bullet moves towards the left upper part, wherein the arcs are respectively called SP, TP and TQ; t and S are symmetric about the Y axis; p and Q are symmetric about the X axis; f and Q are symmetric about the Y axis; g and F are symmetric about the X axis.
5. The runway failure rate analysis and calculation method based on the Weili ring cutting method as claimed in claim 4, characterized in that: the probability that a certain runway is successfully cut, namely the probability that the mother bullet falls into the favorable impact area is calculated by the following steps: is provided with
(1) The missile aiming point is coincided with the center of the drop point, namely the system error is not considered;
(2) the bullet spread being a circular spread, i.e. sigmax＝σyσ, or Ex＝EyThe vertical and horizontal distribution density of the impact points is as follows:
Figure RE-RE-FDA0002345454490000035
the probability of landing in the favorable landing zone is:
Figure RE-RE-FDA0002345454490000041
since the normal distribution density function is point symmetric to the distribution center (coinciding with the aiming point), and the region SQFTGP is also point symmetric to the aiming point, and the integrand is equal, then:
P{(x,y)∈D1}＝P{(x,y)∈D2}＝P{(x,y)∈D3}＝P{(x,y)∈D4} (6)
for D1Comprises the following steps:
Figure RE-RE-FDA0002345454490000042
wherein
Figure RE-RE-FDA0002345454490000043
To ensure the accuracy of the calculation of the integral, the region is defined as x0,x1,…,xnAre equally spaced apart, then
Figure RE-RE-FDA0002345454490000044
Likewise, P can be obtained2,P3,P4The integral expression of (1);
after finishing, the method comprises the following steps:
Figure RE-RE-FDA0002345454490000045
for D5It is known as a rectangular area,
Figure RE-RE-FDA0002345454490000046
Figure RE-RE-FDA0002345454490000051
the method is simplified as follows:
Figure RE-RE-FDA0002345454490000052
therefore, the probability P that a certain section of runway is successfully cut under the condition that a single aiming point and a single bullet are formed into an explosive bullet0Comprises the following steps:
Figure RE-RE-FDA0002345454490000053
6. the runway failure rate analysis and calculation method based on the Weili ring cutting method of claim 5, wherein: the specific steps of calculating the failure probability of the whole runway under the conditions of a plurality of single explosive bombs and a plurality of aiming points through a plurality of single explosive bombs and single aiming points and the single-section failure rate of the single runway are as follows: the relationship among the launching success probability, the penetration probability and the explosion-relief success probability of each missile corresponding to each aiming point is shown in the following table:
Figure RE-FDA0002345454490000054
then the calculation of runway failure rate is:
Figure RE-FDA0002345454490000055
wherein ,P0iThe probability of successfully "cutting" a certain section of runway for the ith completed bomb.
7. The runway failure rate analysis and calculation method based on the Weili ring cutting method of claim 6, wherein: the accuracy is estimated by the formula
Figure RE-FDA0002345454490000061
8. The runway failure rate analysis and calculation method based on the Weili ring cutting method of claim 7, wherein: the pair of wholeThe steps of carrying out precision analysis on the runway failure probability are as follows: in the construction of the favorable impact area of the mother bullet, only the (-Delta L-R) taking the aiming point as the center is consideredW,ΔL+RW) An area; on the premise of assuming that the bullet drop points are normally distributed, the calculation accuracy of the analytical model is evaluated, and actually, the bullet drop points fall into (-Delta L-R) when the calculation is carried out left-right movementW,ΔL+RW) A probability of a region; the distribution density function of the impact point of the mother bullet is as follows:
Figure RE-FDA0002345454490000062
therefore, it is
PAccuracy of measurement＝P(-ΔL-RW≤x≤ΔL+RW) (28)。
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