A Prediction Method for the Demand of Aviation Materials during War Based on Monte Carlo and Grey System

Abstract

The present invention relates to a method for predicting the demand of aviation materials during war based on Monte Carlo and grey system, comprising the following steps: constructing a non-combat loss demand prediction model based on Monte Carlo simulation; constructing a combat loss demand prediction model based on Monte Carlo simulation; respectively using the non-combat loss demand prediction model, the combat loss demand prediction model and the grey dynamic GM(1,1) model to predict the demand of aviation materials during war, adding the demand of aviation materials predicted by the non-combat loss demand prediction model to the demand of aviation materials of the combat loss demand prediction model, and making a mutual comparison and verification with the demand predicted by the grey dynamic GM(1,1) model. The present invention conducts a comparative analysis on the prediction results of Monte Carlo simulation prediction and grey system prediction, checks each other, reduces errors, has high prediction accuracy, does not require a large amount of reserve of the required aviation materials, and reduces resource waste.

Description

Technical Field

[0001] The invention belongs to the technical field of aviation equipment support, and relates to a method for predicting the demand of aviation materials during war based on Monte Carlo and grey system. Background Technique

[0002] In modern high-tech wars, aviation troops are one of the important factors determining the outcome of the war. Combat aircraft are highly dependent on aviation materials, so it is of great military and economic significance to do a good job in predicting the demand for aviation materials. Modern wars have strong variability, complexity and diversity. Coupled with the frequent use of combat aircraft and the harsh battlefield environment, the combat damage of aircraft is inevitable, and the consumption of aviation materials during war will show many different characteristics and laws compared with peacetime. However, due to the extremely small sample size during war, it is very difficult to use general prediction methods for demand prediction, and the prediction accuracy is low, which brings great difficulties to support personnel in aviation material support.

[0003] Various large-scale military exercises and missile firing tests are the main means for our army to obtain the demand data of aviation materials for combat aircraft during war. However, the drills simulating actual combat have large investment and poor repeatability. At the same time, it is easy to cause damage to equipment and environmental pollution, and even cause accidental casualties of personnel participating in the exercises. At the same time, some countries impose strict technical blockades and arms embargoes on our country in order to restrict the development of our national defense industry. It is extremely difficult to obtain data through live ammunition attack tests on our combat aircraft using enemy weapons, but certain performance parameters of enemy equipment can be obtained through some channels. Based on these limited data and computer simulations, actual combat simulations can be carried out better.

[0004] In order to ensure sufficient supply of aviation materials during war, the traditional demand prediction model for aviation materials during war often stores a large amount of required aviation materials, resulting in overstocking of aviation materials, wasting a large amount of resources, and having low prediction accuracy and large errors. Summary of the Invention

[0005] Aiming at the above problems existing in the prior art, the invention provides a method for predicting the demand of aviation materials during war based on Monte Carlo and grey system, which has high prediction accuracy, does not require a large amount of storage of required aviation materials, and reduces resource waste.

[0006] In order to achieve the above object, the invention provides a method for predicting the demand of aviation materials during war based on Monte Carlo and grey system. S1. Construct a non-combat loss demand prediction model;

[0007] Hypotheses: (1) Only one failure rate curve is considered during the period when the aviation materials fail; (2) After the aviation materials cannot work properly, the reserved aviation materials are used for replacement, and the reuse after repair is not considered; (3) Once the aviation materials fail, they are immediately replaced with reserved parts, and the replacement time is ignored; (4) The demand for aviation materials is mainly affected by one of the factors, and the mixed influence of multiple factors is not considered; (5) According to the reliability of the aviation materials, in the natural situation of failure, it is assumed that the service life of the aviation materials follows a Weibull distribution with two undetermined parameters, the scale parameter α and the shape parameter β; (6) It is assumed that the demand for aviation materials generated by battlefield environmental factors follows an exponential distribution with parameter θ; (7) It is assumed that the demand for aviation materials generated by improper human operation follows a normal distribution with parameters μ and σ.

[0008] Suppose there are M aviation materials of a specific type, and each aviation material has been used for a different duration.

[0009] Determine the step size Δt of each simulation advance according to the duration of the battle. Let n represent the number of Δt, and S k represents the result of the set number of simulations for the k-th (1 ≤ k ≤ M) aviation material. t0 represents the duration that the aviation material has been working, and p represents the probability that the aviation material cannot be used during the duration of the war. And there is:

[0010] p = 1 - (1 - p λ ) × (1 - p h ) × (1 - p r )

[0011]

[0012] In the formula, p λ is the probability density of the Weibull distribution, p h is the probability density of the exponential distribution, p r is the probability density of the normal distribution. λ(t) represents the probability density function of the Weibull distribution, f h (t) represents the probability density function of the exponential distribution, f r (t) represents the probability density function of the normal distribution, and t is the duration of the war.

[0013] After computer simulation of each aviation material for a total of 1000 × M times, the demand S corresponding to the M aviation materials during the duration of the war is obtained n as:

[0014]

[0015] Repeat another group of simulations with 1000 × M times of computer simulation for each group. Suppose the demand for aviation materials obtained from another group of computer simulations is S n (l), where \(l = 1, 2, \cdots, L\), \(L\) is the number of simulation runs, and \(L\lt1000\times M\), then the predicted value \(S\) of the demand for this type of aviation materials w is:

[0016]

[0017] Use the rounding function to round the predicted value \(S\) of the demand for aviation materials w After rounding, the final demand \(S'\) of aviation materials is obtained: w ' is:

[0018]

[0019] The calculation formula for the final demand \(S'\) of aviation materials shown in formula (4) is the constructed prediction model for non-combat loss demand; w

[0020] S2. Construct a prediction model for combat loss demand;

[0021] Let events \(K\), \(D\), \(H\), and \(F\) represent the attacks of combat aircraft by air-to-air missiles, surface-to-air missiles, aircraft cannons, and anti-aircraft guns during a single combat sortie, respectively. Let \(M\) represent the event that a certain aviation material of the fighter is battle-damaged. The combat damage probability \(P\) of a certain component of a combat aircraft during a single sortie is expressed as: \(P = P(\text{aircraft survival}\cap\text{damage of a certain aviation material})\);

[0022] By analyzing the minimum kinetic energy \(E\) required to damage a certain aviation material k , according to the relationship between speed and energy, the minimum attack speed \(v\) for damaging the aviation material is obtained as:

[0023]

[0024] where \(m\) d is the mass of the explosive fragment;

[0025] According to the motion equation of the explosive fragment Solve to get where \(d\) t is the infinitesimal change in time \(t\), \(C\) x represents the windward resistance coefficient of the explosive fragment, \(\rho\) represents the air density under the set temperature and pressure conditions, and \(S\) represents the windward area of the explosive fragment;

[0026] Then, based on the initial velocity \(v_0\) of the fragment after the projectile explodes and the mass \(m\) of the explosive fragment d , the effective damage radius \(r\) of the explosive fragment is obtained as:

[0027]

[0028] ​Let the three-dimensional coordinates of the impact point be (x0, y0, z0), consider the target to be attacked as a cuboid, the three-dimensional coordinates of the center of the target be (x1, y1, z1), and the length, width, and height of the cuboid be set as g, d, and h in sequence. Then the area occupied by the target is:

[0029]

[0030] The area where damage may occur is:

[0031]

[0032] In the formula, x g is the projected coordinate of the length g of the cuboid on the x-axis, y g is the projected coordinate of the length g of the cuboid on the y-axis, z g is the projected coordinate of the length g of the cuboid on the z-axis;

[0033] When the area where damage may occur is an empty set, the explosion fragments do not cause damage to the aircraft materials.

[0034] According to the random number R uniformly distributed between (0, 1), determine the attack mode by the method of random simulation, and randomly determine the attack position (x, y, z) according to the probability distribution of the effective impact points;

[0035] Calculate the effective damage radius r according to formula (6), and then according to the three-dimensional coordinates of the impact point (x0, y0, z0) and the center positions (x1, y1, z1) of each aircraft material, calculate whether the aircraft material is within the effective damage radius r. If the aircraft material can work normally, the damage times of this aircraft material remain unchanged, and record the initial damage times I = 0. If the aircraft material is within the area where damage may occur, determine whether the aircraft material is blocked by other components according to the three-dimensional view of the fighter. If there is no blocking situation and the initial velocity of the explosion fragments of the projectile is greater than the minimum necessary strike velocity of this aircraft material, then determine that this aircraft material is damaged, and the damage times of this aircraft material increase by one, and count the total damage times;

[0036] Conduct N computer simulations on the attacks of the enemy's weapons, divide the number of times of aircraft material damage accumulated by random simulation by the total number of simulations, and obtain the battle damage probability of a certain aircraft material in one combat operation

[0037] According to the central limit theorem, we get:

[0038]

[0039] In the formula, X i is a random variable, representing the number of damaged aircraft equipped with this aircraft material in W combat sorties. The possible values of the random variable are 0, 1, 2,..., W; is the mean value of the random variable X i , a' and b' are arbitrary constants in any finite interval, satisfying a' < b';

[0040] Assume that the maximum acceptable error is ε, and the required number of computer simulations n through probability calculation is at least

[0041] In each combat operation, the event of damage to this aviation material is independent of the damage events in other combat operations. Given the random variable X i follows a binomial distribution with parameters W and P s , then:

[0042]

[0043] where p(X i = j) is the probability that the fighter equipped with this aviation material is damaged j times in W combat sorties;

[0044] Then the calculation formula for the combat loss demand of aviation materials is:

[0045]

[0046] where P M is the satisfaction rate of the wartime aviation material reserve;

[0047] Solve for the demand S z , use the rounding function to round the predicted value S of the aviation material demand z , and the quantity of aviation materials required for combat loss reserve after processing is expressed as:

[0048]

[0049] The calculation formula for the final demand S z ' of the aviation material shown in formula (12) is the constructed combat loss demand prediction model;

[0050] S3. Respectively use the non-combat loss demand prediction model, the combat loss demand prediction model and the grey dynamic GM(1,1) model to predict the wartime aviation material demand, add the predicted aviation material demand of the non-combat loss demand prediction model and the combat loss demand prediction model of aviation materials, and compare and verify with the demand predicted by the grey dynamic GM(1,1) model.

[0051] Preferably, in step S1, the probability density function and distribution function of the Weibull distribution are expressed as:

[0052]

[0053] where F(t) represents the distribution function of the Weibull distribution.

[0054] Preferably, in step S1, the probability density function and distribution function of the exponential distribution are expressed as:

[0055]

[0056] In the formula, F h (t) represents the distribution function of the exponential distribution.

[0057] Preferably, in step S1, the probability density function and distribution function of the normal distribution are expressed as:

[0058]

[0059] In the formula, F r (t) represents the distribution function of the normal distribution.

[0060] Preferably, in step S2, according to the random number R uniformly distributed between (0, 1), the method for determining the attack mode by random simulation is as follows: when 0 < R < 0.25, it means the aircraft is attacked by an air defense missile; when 0.25 ≤ R < 0.5, it means the aircraft is attacked by an air defense gun; when 0.5 ≤ R < 0.75, it means the aircraft is attacked by an air-to-air missile; when 0.75 ≤ R < 1, it means the aircraft is attacked by an aircraft cannon.

[0061] Compared with the prior art, the beneficial effects of the present invention are as follows:

[0062] The present invention comprehensively considers various factors affecting the demand for wartime aviation materials, constructs a non-war loss demand prediction model and a combat loss demand prediction model based on Monte Carlo simulation, uses the constructed non-war loss demand prediction model, combat loss demand prediction model and grey system to predict the demand for wartime aviation materials, and then conducts a comparative analysis of the prediction results of Monte Carlo simulation prediction and grey system prediction, comparing and contrasting with each other to reduce errors and achieve high prediction accuracy. In the traditional wartime aviation material demand prediction mode, in order to ensure sufficient supply of wartime aviation materials, a large amount of required aviation materials are often stockpiled, resulting in overstocking of aviation materials and wasting a large amount of resources. Compared with the traditional wartime aviation material demand prediction mode, the prediction method of the present invention does not require a large amount of stockpiling of required aviation materials, reducing resource waste. BRIEF DESCRIPTION OF THE DRAWINGS

[0063] Figure 1 It is a schematic diagram of the aviation material demand structure in the wartime aviation material demand prediction method based on Monte Carlo and grey system according to an embodiment of the present invention;

[0064] Figure 2 It is a simulation flowchart of the non-combat loss demand in the wartime aviation material demand prediction method based on Monte Carlo and grey system according to an embodiment of the present invention;

[0065] Figure 3 This is the flowchart of the simulation of the combat loss demand quantity in the wartime aviation material demand prediction method based on Monte Carlo and grey system according to the embodiments of the present invention;

[0066] Figure 4 This is the comparison chart of the aviation material demand quantities predicted by using the non-combat loss demand prediction model and the combat loss demand prediction model according to the embodiments of the present invention and the aviation material demand quantities predicted by the grey dynamic GM(1,1) model. Specific embodiments

[0067] Next, the present invention will be specifically described by way of exemplary embodiments. However, it should be understood that, without further elaboration, the elements, structures, and features in one embodiment can also be beneficially incorporated into other embodiments.

[0068] There are many factors affecting the wartime aviation material requirements, which can generally be divided into two aspects: non-combat damage and combat damage. Non-combat damage includes the natural failures and damages of aviation materials caused by the normal use of aviation materials and random factors, and its consumption mainly depends on the reliability of aviation materials, the losses of aviation materials caused by harsh battlefield environments (such as high temperature, high humidity, high salinity, etc.) and complex geographical conditions, and the damages of aviation materials caused by improper human operations. Combat damage includes the damages caused by the attacks of aircraft against air defense missiles (including ground-fixed unit air defense missiles, shipborne air defense missiles, submarine-launched air defense missiles, vehicle-mounted air defense missiles, etc.) and anti-aircraft guns from the ground or sea during combat, and the damages caused by the attacks of air-to-air missiles and aircraft guns from enemy aircraft. The present invention provides a wartime aviation material demand prediction method based on Monte Carlo and grey system, which simultaneously considers non-combat damage (including damages caused by natural losses, environmental factors, and human factors) and combat damage (including damages caused by the attacks of air-to-air missiles (i.e., air-to-air missiles), air defense missiles (i.e., surface-to-air missiles), aircraft guns (i.e., aircraft guns), and anti-aircraft guns) (see Figure 1 ), and constructs a non-combat loss demand prediction model and a combat loss demand prediction model based on Monte Carlo simulation, adds the results predicted by the two models to obtain the wartime aviation material demand quantity, and conducts mutual comparison and verification with the wartime aviation material demand quantity predicted by the grey system to reduce errors and achieve high prediction accuracy. The wartime aviation material demand prediction method based on Monte Carlo and grey system will be described in detail below with reference to the accompanying drawings.

[0069] The present invention provides a wartime aviation material demand prediction method based on Monte Carlo and grey system, which comprises the following steps:

[0070] S1. Construct a non-combat loss demand prediction model.

[0071] Assume:

[0072] (1) Only consider one failure rate curve during the period when the aviation materials fail.

[0073] (2) After the aviation materials cannot work properly, use the reserved aviation materials for replacement, and do not consider reusing them after repair.

[0074] (3) Once the aviation materials fail, immediately replace them with the reserved parts, and the replacement time is ignored.

[0075] (4) The demand for aviation materials is mainly affected by one of the factors, and the mixed influence of multiple factors is not considered.

[0076] (5) Based on the reliability of the aviation materials, assuming that they fail under natural conditions, assume that the service life of the aviation materials follows a Weibull distribution with two undetermined parameters, the scale parameter α and the shape parameter β; the probability density function and distribution function of the Weibull distribution are expressed as:

[0077]

[0078] In the formula, F(t) represents the distribution function of the Weibull distribution.

[0079] (6) Assume that the demand for aviation materials generated by battlefield environmental factors follows an exponential distribution with parameter θ; the probability density function and distribution function of the exponential distribution are expressed as:

[0080]

[0081] In the formula, F h (t) represents the distribution function of the exponential distribution.

[0082] (7) Assume that the demand for aviation materials generated by improper human operation follows a normal distribution with parameters μ and σ; the probability density function and distribution function of the normal distribution are expressed as:

[0083]

[0084] In the formula, F r (t) represents the distribution function of the normal distribution.

[0085] Assume that there are M specific types of aviation materials, and each aviation material has been used for different durations;

[0086] Determine the step size Δt for each simulation advance according to the duration of the battle. Let n represent the number of Δt, and S k represents the result of setting the number of simulations for the kth aviation material, where 1 ≤ k ≤ M, t0 represents the duration that the aviation material has been working, and p represents the probability that the aviation material cannot be used during the duration of the war; and there is:

[0087] p = 1 - (1 - p λ ) × (1 - p h)×(1 - p r )

[0088]

[0089] where p λ is the probability density of the Weibull distribution, p h is the probability density of the exponential distribution, p r is the probability density of the normal distribution, λ(t) represents the probability density function of the Weibull distribution, f h (t) represents the probability density function of the exponential distribution, f r (t) represents the probability density function of the normal distribution;

[0090] After 1000×M computer simulations for each aviation material, the demand S corresponding to M aviation materials during the war duration is obtained n as follows:

[0091]

[0092] Another set of simulations is repeated with 1000×M computer simulations for each group. Assume that the demand for aviation materials obtained from another set of computer simulations is S n (l) , l = 1, 2,..., L, where L is the number of simulation runs and L is less than 1000×M. Then the predicted value S w of the demand for this type of aviation material is as follows:

[0093]

[0094] The predicted value S w of the demand for aviation materials is rounded using the rounding function. After processing, the final demand S w ' is as follows:

[0095]

[0096] The calculation formula for the final demand S w ' shown in formula (4) is the constructed non-combat loss demand prediction model.

[0097] It should be noted that referring to Figure 2, during the computer simulation process, the duration of the battle is divided into several small time periods according to a specific time step. Using the probability density curve of the failure and consumption of aviation materials caused by influencing factors, the cumulative probability of corresponding inability to work properly is obtained by integration. For each small time period divided, MATLAB is used to generate a random number r that conforms to the corresponding distribution, and whether the event of the aviation material being unable to be used occurs is simulated for each small time segment, and compared with the obtained cumulative probability p. If it is less than the corresponding cumulative probability p, it means that the aviation material will fail within this time, and the corresponding demand needs to be increased by one. Finally, the total cumulative number of times is counted to obtain the total demand. For each aviation material, at least 1000 computer simulations need to be carried out.

[0098] S2. Construct a prediction model for combat loss requirements.

[0099] The reserve of aviation materials for aircraft combat damage mainly depends on the combat damage law of aircraft aviation materials. Scientifically and accurately predicting the combat damage law of aircraft aviation materials is the key to determining the reserve quantity of aviation materials. The main reasons for aircraft to be damaged in combat are projectile damage and explosion fragment damage, mainly from air defense missiles and anti-aircraft guns launched by the enemy, and aircraft guns and air-to-air missiles launched by enemy aircraft. Therefore, the present invention calculates the combat damage distribution probability models when different weapons attack the aircraft from four aspects: air-to-air missile, surface-to-air missile, aircraft gun, and anti-aircraft gun attacks.

[0100] According to the infrared radiation characteristics of fighter jets, infrared radiation is mainly generated by the engine nozzle, exhaust wake, and skin of the fighter jet. The expected value of the attack position of air-to-air missiles is near the rear of the engine. Assuming that general air-to-air missiles track aircraft through infrared radiation, the approximate range where the bomb fragments generated after detonation hit the aircraft is that within a range of ±4m along the tail direction of the aircraft with a 90% probability, and within a range of ±2.5m along the wing direction with a 90% probability. Therefore, for the sake of simplicity in calculation, the impact point of the air-to-air missile is taken as a one-dimensional Gaussian distribution along the nose direction of the aircraft, and there is:

[0101]

[0102] Where:

[0103] M0 represents the mathematical expectation of the probability distribution of the missile explosion point;

[0104] R x represents the radius of the hit accuracy range of the missile along the length of the aircraft, R x = 2m;

[0105] x represents the establishment of the x-axis along the length direction of the aircraft, and the coordinate of the x-axis;

[0106] There are many types of launch carriers for air defense missiles, and the technical characteristics of air defense missiles are complex. It is relatively complicated to determine the damage range of a close - range explosion on a fighter jet. Generally speaking, the scattering range of explosion fragments is taken as within a range of 6m along the nose direction of the aircraft with an 80% probability. Therefore, assuming the length of the aircraft fuselage is 17m, we can solve for σ = 4.1. That is, the hit probability distribution of air - to - air missile explosion fragments is as follows:

[0107]

[0108] There are many types of launch carriers for air defense missiles, and the technical characteristics of air defense missiles are complex. It is relatively complicated to determine the damage range of a close - range explosion on a fighter jet. Therefore, the scattering range of explosion fragments of the air defense missile is taken as within a range of ±6m along the nose direction of the aircraft with an 80% probability. Given that the length of the aircraft fuselage is 17m, we can solve for σ = 6.82. The hit probability distribution of air defense missile explosion fragments is as follows:

[0109]

[0110] The probability distribution of the hit points of anti - aircraft guns is on both sides of the wings and both sides of the fuselage. Assuming that the hitting accuracy of the anti - aircraft gun is 30% concentrated within a range of ±7m in the wing direction, and the length of the aircraft fuselage is 17m, we can solve for σ = 1.18. The hit probability distribution of anti - aircraft gun explosion fragments is as follows:

[0111]

[0112] For aircraft cannons, for the convenience of calculation, assume that the probability distribution of the hit points follows a uniform distribution, and the direction of the hit points is along the length of the aircraft. Then the hit probability distribution of the aircraft cannon is as follows:

[0113]

[0114] Let events K, D, H, and F represent the attacks on a combat aircraft by air - to - air missiles, surface - to - air missiles, aircraft cannons, and anti - aircraft guns respectively during a single sortie. Let event M represent the event that a certain aviation material on the fighter jet is battle - damaged. The probability P of a combat damage to a certain component of a combat aircraft during a single sortie is expressed as: P = P(aircraft survival ∩ a certain aviation material is damaged); it should be noted that the probability that a certain aviation material needs to be stocked due to combat damage during a single sortie of the aircraft is the probability that the aircraft for this sortie survives in a high - intensity confrontation battle (i.e., can return to the airport) and this component is damaged in the battle. Calculation through this formula can avoid including the parts of aircraft that have been damaged on the battlefield in the battle - stocked aviation materials, improving the accuracy of aviation material demand prediction.

[0115] It should be noted that the damage modes of general air defense shells and various types of missiles to aviation materials are similar. After the projectile explodes, a fragment field and shock wave with high energy are formed, causing irreversible damage to aviation materials. The damage of broken fragments to aviation materials is not only related to the shape and size of the fragments generated by the explosion, but also greatly related to the flying speed and scattering direction of the fragments.

[0116] By obtaining the minimum kinetic energy E required to damage a certain aviation material k , the minimum attack speed v for damaging the aviation material is obtained according to the relationship between speed and energy as follows:

[0117]

[0118] In the formula, m d is the mass of the explosion fragment;

[0119] According to the motion equation of the explosion fragment The solution is Among them, d t is the infinitesimal change of time t, C x represents the windward resistance coefficient of the explosion fragment, ρ represents the air density under the set temperature and pressure conditions, and S represents the windward area of the explosion fragment;

[0120] Based on the initial velocity v0 of the fragment after the projectile explodes and the mass m of the explosion fragment d , the effective damage radius r of the explosion fragment is obtained as:

[0121]

[0122] Let the three-dimensional coordinates of the impact point be (x0, y0, z0), regard the attack target as a cuboid, the three-dimensional coordinates of the center of the target are (x1, y1, z1), and the length, width, and height of the cuboid are set as g, d, and h in sequence. Then the area occupied by the target is:

[0123]

[0124] The area where damage may occur is:

[0125]

[0126] In the formula, x g is the projection coordinate of the length g of the cuboid on the x-axis, y g is the projection coordinate of the length g of the cuboid on the y-axis, and z g is the projection coordinate of the length g of the cuboid on the z-axis;

[0127] When the area where damage may occur is an empty set, the explosion fragment does not cause damage to the aviation material.

[0128] According to the random number R uniformly distributed between (0, 1), the attack mode is determined by the method of random simulation, and the attack position (x, y, z) is randomly determined according to the probability distribution of the effective impact points; the method of determining the attack mode by the random simulation according to the random number R uniformly distributed between (0, 1) is as follows: when 0 < R < 0.25, it means that the aircraft is attacked by air defense missiles, when 0.25 ≤ R < 0.5, it means that the aircraft is attacked by anti-aircraft guns, when 0.5 ≤ R < 0.75, it means that the aircraft is attacked by air-to-air missiles, and when 0.75 ≤ R < 1, it means that the aircraft is attacked by aircraft cannons.

[0129] Calculate the effective damage radius r according to formula (6), and then calculate whether the aviation material is within the effective damage radius r according to the three-dimensional coordinates of the impact point (x0, y0, z0) and the center position (x1, y1, z1) of each aviation material. If the aviation material can work normally, the damage times of this aviation material remain unchanged. Record the initial damage times I = 0. If the aviation material is within the area where damage may occur, determine whether the aviation material is blocked by other components according to the three-dimensional view of the fighter. If there is no blocking situation and the initial velocity of the flying fragments of the warhead explosion is greater than the minimum necessary strike velocity of the aviation material, it is determined that the aviation material is damaged, and the damage times of this aviation material increase by one, and the total damage times are counted;

[0130] Conduct N computer simulations on the attacks of enemy weapons, and divide the number of times of aviation material damage accumulated by random simulation by the total number of simulations to obtain the battle damage probability of a certain aviation material in one combat operation

[0131] According to the central limit theorem, it is obtained that:

[0132]

[0133] In the formula, X i is a random variable, representing the number of damaged aircraft equipped with this aviation material in W combat sorties. The possible values of the random variable are 0, 1, 2,..., W; is the random variable X i 's average value, and a' and b' are arbitrary constants in any finite interval, satisfying a' < b';

[0134] Assume that the maximum acceptable error is ε. The required number of computer simulations n is at least

[0135] The event of damage to this aviation material in each combat operation is independent of the damage events in other combat sorties. Given that the random variable X i obeys the binomial distribution with parameters W and P s , then:

[0136]

[0137] Wherein, p(X i =j) is the probability that the fighter equipped with this aviation material is damaged j times in W combat sorties;

[0138] Then the calculation formula for the demand of combat losses of aviation materials is:

[0139]

[0140] Wherein, P M is the satisfaction rate of wartime aviation material reserves;

[0141] Take P M =0.9, solve for the demand S z , use the rounding function to round the predicted value S of the demand for aviation materials z After processing, the quantity of aviation materials required for combat losses is expressed as:

[0142]

[0143] The calculation formula for the final demand S z ' of the aviation materials shown in formula (12) is the constructed prediction model for combat loss demand.

[0144] S3. Respectively use the non-combat loss demand prediction model, the combat loss demand prediction model and the grey dynamic GM(1,1) model to predict the wartime demand for aviation materials, add the demand for aviation materials predicted by the non-combat loss demand prediction model and the demand for aviation materials of the combat loss demand prediction model, and conduct mutual comparison and verification with the demand predicted by the grey dynamic GM(1,1) model.

[0145] It should be noted that when the information in a system is completely clear and transparent, it is called a "white system". Similarly, when the information in a system is completely unknown, it is called a "black system". When we know part of the information of the system but cannot master all of its information, the system is called a "grey system". The grey system prediction model originated from ordinary differential theory. It has certain advantages over other prediction methods in predicting samples with small quantities and unclear rules, and the prediction results are relatively accurate and reliable. Its notation is GM(M',N'), where N' represents the number of input quantities, and M' represents the order of the ordinary differential equation used for model operation. Among them, the most widely used is the grey dynamic GM(1,1) model. The present invention uses the grey dynamic GM(1,1) model for prediction. The grey dynamic GM(1,1) model represents the differential function of the variable with respect to time, and the corresponding equation is:

[0146]

[0147] Where t represents time, a and u are parameters to be estimated, a is called the development grey number, and u is called the grey action.

[0148] The specific method of using the grey dynamic GM (11,) model to predict the demand for wartime aviation materials is as follows:

[0149] (1) Calculate the level ratio between data, When the calculated value is between When the original data is not passed the level ratio test, it means that the original data is suitable for grey prediction. If the original sequence fails to pass the level ratio test, just add a constant C to each original value (the determination of constant C can be done by searching for suitable values one by one through MATLAB programming) to make the new sequence pass the level ratio test. After that, the new sequence is used in all calculations, and the constant C is subtracted at the same time when the predicted value is obtained.

[0150] (2) Accumulation of aviation material demand data. The aviation material data we have is often interfered by many factors. By accumulating the data, we can reduce the interference and make it easier to mine the data rules. Assume that the original non-negative number column is:

[0151] X (0) =(X (0) (1), X (0) (2), ..., X (0) (n))

[0152] The original sequence is accumulated by the following formula to obtain X (0) 1-AGO data column X (1) .

[0153]

[0154] X (1) =(X (1) (1), X (1) (2), …, X (1) (n))

[0155] (3) Calculate the estimated values of a and u parameters, and set the matrix

[0156]

[0157] y n =[x (0) (2),x (0) (3),...,x (0) (n)] T

[0158]

[0159] (4) Whitening GM(1,1) model:

[0160]

[0161] (5) After the GM(1,1) model is established, before using the model, it is also necessary to use the variance ratio to test the accuracy and stability of the model. First, calculate the mean square deviation S0 of the original data series:

[0162]

[0163] Then calculate the mean square deviation S1 of the residual data series :

[0164]

[0165] The ratio of the two mean square deviations is Substitute each data to calculate the small error probability:

[0166]

[0167] Finally, according to the model accuracy test classification table, as shown in Table 1, test the accuracy of the GM(1,1) model.

[0168] Table 1

[0169]

[0170]

[0171] If the prediction accuracy level is less than level Ⅳ, then the grey dynamic GM(1,1) prediction can be used. That is, use …… as the data x (0) (n + 1), x (0) (n + 2),...... of the grey prediction value.

[0172] The following takes the aircraft of a certain flight regiment as an example to illustrate the above prediction method.

[0173] Suppose a certain flight regiment has 24 new fighter jets in total. The weekly fighter jet sortie situation during combat missions is shown in Table 2, and the aviation material demand data for a certain type of aviation material in the past 6 months is shown in Table 3. The aviation material has been used for 231 hours on the fighter jets. The aviation material demand rate curves affected by natural wear and tear, environmental factors, human factors, and resulting in the abnormal operation of the aviation material are respectively:

[0174]

[0175] f h (t) = 0.2e -0.2t (t ≥ 0)

[0176]

[0177] It is now necessary to predict the demand for such aviation materials of this flight group during the three-month combat operation.

[0178] Table 2

[0179]

[0180]

[0181] Table 3

[0182] Month 1 2 3 4 5 6 Demand Quantity 8 7 9 13 12 15

[0183] Specifically, using the non-combat loss demand prediction model and combat loss demand prediction model in the present invention to conduct computer simulation on this problem, taking the Monte Carlo simulation time step Δt as 0.02, it can be obtained through calculation that the non-combat loss demands for this aviation material in the future three-month combat are 6, 10, and 13, and the combat loss demands are 11, 9, and 8. Adding them up, the demands for the three months are 17, 19, and 21 respectively.

[0184] Using the grey dynamic GM(1,1) model for prediction, where the ratio of March to April is 0.6923, which fails to pass the ratio test. Adding 15 to each original value to make the new sequence pass the test and using it for prediction. Substituting into the aforementioned formula, a is -0.0716 and b is 20.1375. The variance ratio 0.1047 < 0.35, and the model prediction accuracy is good. Using it for prediction, the demands for the future three months are 17.299, 19.696, and 22.270 respectively. The results are shown in Figure 4 As shown, it can be seen that the grey system prediction values and the computer simulation values do not differ much, and both can relatively truly reflect the actual demand for aviation materials during the war. At the same time, using the grey system prediction values and computer simulation, comparing the two prediction results with each other for verification helps to reduce the accidental errors in single-method prediction and more comprehensively and reliably predict the demand quantity of aviation materials during the war.

[0185] The above embodiments are used to explain the present invention, rather than limiting the present invention. Any modifications and changes made to the present invention within the spirit and protection scope of the claims of the present invention fall within the protection scope of the present invention.

Claims

1. A wartime aviation material demand forecasting method based on Monte Carlo and grey system, characterized in that It includes the following steps: S1. Construct a non-combat loss demand prediction model; Assumptions: (1) Only one failure rate curve is considered during the period when the aviation materials fail; (2) After the aviation materials cannot work properly, the reserved aviation materials are used for replacement, and the reuse after maintenance is not considered; (3) Once the aviation materials fail, they are immediately replaced with spare parts, and the replacement time is ignored; (4) The demand for aviation materials is mainly affected by one of the factors, and the mixed influence of multiple factors is not considered; (5) According to the reliability of the aviation materials, when they fail under natural conditions, it is assumed that the service life of the aviation materials follows a Weibull distribution with two undetermined parameters, namely scale parameter α and shape parameter β; (6) It is assumed that the demand for aviation materials caused by battlefield environmental factors follows an exponential distribution with parameter θ; (7) It is assumed that the demand for aviation materials caused by improper human operation follows a normal distribution with parameters μ and σ. It is assumed that there are M specific types of aviation materials, and each aviation material has been used for different durations. Determine the step size Δt advanced in each simulation according to the duration of the battle. Let n represent the number of Δt, and S k represents the result of setting the number of simulations for the k-th aviation material, where 1 ≤ k ≤ M, t0 represents the duration for which the aviation material has been in operation, and p represents the probability that the aviation material cannot be used during the duration of the war; and there is: p = 1 - (1 - p λ ) × (1 - p h ) × (1 - p r ) where p λ is the probability density of the Weibull distribution, p h is the probability density of the exponential distribution, p r is the probability density of the normal distribution, λ(t) represents the probability density function of the Weibull distribution, f h (t) represents the probability density function of the exponential distribution, f r (t) represents the probability density function of the normal distribution, and t is the duration of the war; After performing computer simulations on each aviation material for a total of 1000×M times, the demand S corresponding to M aviation materials during the duration of the war is obtained n as follows: Another set of simulations is carried out with 1000×M repetitions for each computer simulation. Assume that the demand for aviation materials obtained from another set of computer simulations is S n (l) , l = 1, 2,..., L, where L is the number of times the simulation is carried out and L is less than 1000×M. Then the predicted value S of the demand for this type of aviation materials w is: Use the rounding function to round the predicted value S of the demand for aviation materials w After rounding, the final demand S for aviation materials is obtained w ' as follows: The final demand S of aviation materials shown in formula (4) w The calculation formula of 'is the constructed prediction model for non-combat loss demand; S2. Construct a combat loss demand prediction model; Let events K, D, H, and F represent the attacks on combat aircraft by air-to-air missiles, surface-to-air missiles, aircraft cannons, and anti-aircraft guns during a single combat sortie respectively. Let M represent the event that a certain aviation material of the fighter aircraft is damaged in combat. The combat damage probability P of a certain component of the combat aircraft during a single sortie is expressed as: P = P(aircraft survival ∩ damage of a certain aviation material). By determining the minimum kinetic energy E required to damage a certain aircraft component k and based on the relationship between velocity and energy, the minimum attack velocity v for damaging the aircraft component is obtained as follows: where m d is the mass of the explosion fragment; According to the motion equation of the explosion fragments The solution is where d t is the infinitesimal change in time t, C x represents the windward resistance coefficient of the explosion fragments, ρ represents the air density under the set temperature and pressure conditions, and S represents the windward area of the explosion fragments; According to the initial velocity v0 of the fragments after the projectile explodes and the mass m of the explosion fragments d , the effective damage radius r of the explosion fragments is obtained as follows: Let the three-dimensional coordinates of the impact point be (x0, y0, z0), regard the attack target as a cuboid, the three-dimensional coordinates of the center of the target be (x1, y1, z1), and the length, width, and height of the cuboid be set as g, d, and h in sequence. Then the area occupied by the target is: The area where damage may occur is: where x g is the projected coordinate of the length g of the cuboid on the x-axis, y g is the projected coordinate of the length g of the cuboid on the y-axis, z g is the projected coordinate of the length g of the cuboid on the z-axis; When the area where damage may occur is an empty set, the explosion fragments do not cause damage to the aviation materials. According to the random number R uniformly distributed between (0, 1), the attack mode is determined by the method of random simulation, and the attack position (x, y, z) is randomly determined according to the probability distribution of the effective impact points. Calculate the effective damage radius r according to formula (6). Then, according to the three-dimensional coordinates of the impact point (x0, y0, z0) and the center position (x1, y1, z1) of each aviation material, calculate whether the aviation material is within the effective damage radius r. If the aviation material can work properly, the number of damage times of this aviation material remains unchanged, and record the initial number of damage times I = 0. If the aviation material is within the area where damage may occur, determine whether the aviation material is blocked by other components according to the three-dimensional view of the fighter aircraft. If there is no blocking situation and the initial velocity of the explosion fragments of the warhead is greater than the minimum necessary impact velocity of this aviation material, it is determined that this aviation material is damaged, and the number of damage times of this aviation material increases by one, and the total number of damage times is counted. Conduct N computer simulations of attacks on enemy weapons. Divide the number of times of damage to aviation materials obtained by cumulative random simulation by the total number of simulations to obtain the battle damage probability of a certain aviation material in a combat operation. According to the central limit theorem, it can be obtained that: In the formula, X i is a random variable representing the number of damaged aircraft equipped with this aviation material during W combat sorties. The possible values of the random variable are 0, 1, 2,..., W; is the average value of the random variable X i , a' and b' are arbitrary constants in any finite interval, satisfying a' < b'; assuming the maximum acceptable error is ε, the minimum number of computer simulation runs n required through probability calculation is at least The event of damage to this aviation material in each combat operation is independent of the damage events in other sorties. Given that the random variable X i follows a binomial distribution with parameters W and P s , then: where p(X i = j) is the probability that the fighter equipped with this aviation material is damaged j times in W combat sorties; Then the calculation formula for the combat loss demand of the aviation materials is: where P M is the satisfaction rate of wartime aviation material reserves; Solve for the demand quantity S z , use the rounding function to round the predicted value of the aviation material demand quantity S z . After processing, the quantity of aviation materials required for combat losses is expressed as: The final demand S of aviation materials shown in formula (12) z The calculation formula of 'is the constructed prediction model for combat loss demand S3. Respectively use the non-combat loss demand prediction model, the combat loss demand prediction model, and the grey dynamic GM(1,1) model to predict the demand for wartime aviation materials. Add the demand for aviation materials predicted by the non-combat loss demand prediction model to the demand for aviation materials predicted by the combat loss demand prediction model, and conduct mutual comparison and verification with the demand predicted by the grey dynamic GM(1,1) model.

2. The wartime aviation material demand prediction method based on Monte Carlo and grey system according to claim 1, wherein In step S1, the probability density function and distribution function of the Weibull distribution are expressed as: In the formula, F(t) represents the distribution function of the Weibull distribution.

3. The wartime aviation material demand prediction method based on Monte Carlo and grey system according to claim 1, characterized in that In step S1, the probability density function and distribution function of the exponential distribution are expressed as: where F h (t) represents the distribution function of the exponential distribution.

4. The wartime aviation material demand prediction method based on Monte Carlo and grey system according to claim 1, wherein In step S1, the probability density function and distribution function of the normal distribution are expressed as: where F r (t) represents the distribution function of the normal distribution.

5. The wartime aviation material demand prediction method based on Monte Carlo and grey system according to claim 1, wherein In step S2, according to the random number R uniformly distributed between (0, 1), the method for determining the attack mode by random simulation is as follows: when 0 < R < 0.25, it means the aircraft is attacked by an air defense missile; when 0.25 ≤ R < 0.5, it means the aircraft is attacked by an air defense gun; when 0.5 ≤ R < 0.75, it means the aircraft is attacked by an air-to-air missile; when 0.75 ≤ R < 1, it means the aircraft is attacked by an aircraft cannon.

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