1. A wartime aviation material demand prediction method is characterized by comprising the following steps:

s1, constructing a Markov prediction model, and solving the state probability of the flight material demand;

s11, dividing the time t into stages, taking the consumption condition of a certain navigation material in a certain past time period as a state quantity, taking the monthly demand quantity of the navigation material as X, and then taking the navigation material in the state t₁，t₂，...，t_nAre each x₁，x₂，...，x_nThe maximum value X in the flight material demand of the flight material_maxMinimum value is denoted X_minIf the required quantity of the navigation material is an integer, the navigation material has n ═ X_max-X_min+1 state;

s12, when the number of samples is large enough, the probability is replaced by the approximate frequency, and Y is set_iTo be in a state E_iNumber of samples of (2), Y_ij(k) Is in a state E_iTransitioning to State E through k Steps_jNumber of data of (1), P_ij(k) The k-step transition probability is expressed as follows:

the corresponding k-step state transition probability matrix p (k) is then expressed as:

s13, establishing a Markov prediction model according to the k-step state transition probability matrix P (k) and expressing as follows:

C(t)＝C(t-k)×P(k) (1)

in the formula, C (t) represents a predicted value of the state probability of the aviation material demand amount of k months in the future, and C (t-k) represents the state probability value of the aviation material demand amount at the time t-k stage;

and S2, simulating random simulation by adopting a Monte Carlo algorithm based on the Markov prediction model to obtain the random simulation sailing stock demand, comparing the random simulation sailing stock demand with the historical sailing stock demand, and performing error analysis.

2. The method for predicting demand for flight materials in wartime according to claim 1, wherein in step S2, the specific steps of obtaining the demand for random simulation flight materials by using monte carlo algorithm simulation random simulation and performing error analysis are as follows:

s21, inputting historical flight material demand in an MATLAB form by taking the MATLAB as a platform, finding out the maximum value and the minimum value, calculating the possible existing state of the flight material demand, making t equal to 0, and recording the number k of k months in the future which needs to be predicted;

s22, counting the quantity of the required quantity states of each type of navigation materials and the quantity of the next transition states of the type of the states, calculating a state transition probability matrix P (1) in the 1 st step, and calculating state transition matrixes in the 2 nd, 3 rd, … th and k th steps in the same way;

s23, calculating probability prediction values of the corresponding navigation material demand of each state by the Markov prediction model according to the sample value of the last state;

s24, making t equal to t +1, and generating k random numbers obeying uniform distribution on [0,1] by using a unifrnd function built in MATLAB;

s25, converting the probability fitting of the aviation material demand into a specific aviation material demand, wherein if the generated random number is greater than 0 and less than or equal to the probability of being in the first state, the aviation material demand is 0, and if the generated random number is greater than the probability of being in the first state and less than or equal to the sum of the probabilities of being in the first two states, the aviation material demand is 1, and the aviation material demands in months 2, 3, … and k are obtained by analogy;

s26, when t is less than N, N is the set simulation times, when the simulation is not finished, the step is switched to S22, when t is more than or equal to N, the simulation is finished, and the step is switched to S27;

s27, generating a random sequence value obeying exponential distribution by using an exprand function built in MATLAB, selecting random simulation flight material demand quantity by taking the variance of the historical flight material demand quantity as a judgment standard, comparing the selected random simulation flight material demand quantity with the historical flight material demand quantity, and carrying out error analysis.

3. The method as claimed in claim 2, wherein the step S27 of obtaining the demand of the random simulation flight material comprises the following steps:

generating random numbers which are subject to exponential distribution by using an exprand function built in MATLAB;

calculating the mean value and the variance of the historical aviation material demand;

generating a random sequence value according to the average value of the historical aviation material demand by using an exprand function built in the MATLAB;

and selecting a group of random sequence values with the minimum variance with the historical navigation material demand as the random simulation navigation material demand by taking the variance of the historical navigation material demand as a judgment standard.

Background

In modern high-tech wars, the role of aviation soldiers is more and more remarkable, and the air strength becomes the dominant factor for determining the victory or defeat of the wars. In order to improve the usability of the fighter in war and enhance the continuous moving capability of the fighter, good wartime flight material guarantee plays a vital role. Because modern wars have strong variability, complexity and diversity, and the frequent use of combat airplanes and the severe battlefield environment, and combat damages are inevitable, the consumption of flight materials in wartime varies greatly and presents many different characteristics and laws. The dependence of the combat aircraft on the aeronautical materials is extremely high, so that the prediction work of the aeronautical material demand has important military and economic significance. However, the demand prediction is difficult to be carried out by using a general prediction method due to the extremely small quantity of the wartime samples, and the prediction precision is very low, which brings great difficulty to wartime aviation material support personnel during aviation material support. Meanwhile, due to the fact that the war flight material demand prediction is a complex system, an accurate mathematical model is difficult to establish for accurate prediction.

Disclosure of Invention

Aiming at the problems in the prior art, the invention provides a method for predicting the demand of wartime aviation materials, which combines a Markov model and Monte Carlo simulation, and has high prediction reliability by carrying out simulation processing and error analysis on limited historical data.

In order to achieve the aim, the invention provides a method for predicting the demand of a wartime aviation material, which comprises the following steps:

s1, constructing a Markov prediction model, and solving the state probability of the flight material demand;

s11, dividing the time t into stages, taking the consumption condition of a certain navigation material in a certain past time period as a state quantity, taking the monthly demand quantity of the navigation material as X, and then taking the navigation material in the state t₁，t₂，...，t_nAre each x₁，x₂，...，x_nThe maximum value X in the flight material demand of the flight material_maxMinimum value is denoted X_minIf the required quantity of the navigation material is an integer, the navigation material has n ═ X_max-X_min+1 states；

S12, when the number of samples is large enough, the probability is replaced by the approximate frequency, and Y is set_iTo be in a state E_iNumber of samples of (2), Y_ij(k) Is in a state E_iTransitioning to State E through k Steps_jNumber of data of (1), P_ij(k) The k-step transition probability is expressed as follows:

the corresponding k-step state transition probability matrix p (k) is then expressed as:

s13, establishing a Markov prediction model according to the k-step state transition probability matrix P (k) and expressing as follows:

C(t)＝C(t-k)×P(k) (1)

in the formula, C (t) represents a predicted value of the state probability of the aviation material demand amount of k months in the future, and C (t-k) represents the state probability value of the aviation material demand amount at the time t-k stage;

and S2, simulating random simulation by adopting a Monte Carlo algorithm based on the Markov prediction model to obtain the required amount of the flight material, comparing the randomly simulated required amount of the flight material with the historical required amount of the flight material, and performing error analysis.

Preferably, in step S2, the specific steps of obtaining the demand of the random simulation marine material by using the monte carlo algorithm to simulate the random simulation and performing the error analysis include:

s21, inputting historical flight material demand in an MATLAB form by taking the MATLAB as a platform, finding out the maximum value and the minimum value, calculating the possible existing state of the flight material demand, making t equal to 0, and recording the number k of k months in the future which needs to be predicted;

s22, counting the quantity of the required quantity states of each type of navigation materials and the quantity of the next transition states of the type of the states, calculating a state transition probability matrix P (1) in the 1 st step, and calculating state transition matrixes in the 2 nd, 3 rd, … th and k th steps in the same way;

s23, calculating probability prediction values of the corresponding navigation material demand of each state by the Markov prediction model according to the sample value of the last state;

s24, making t equal to t +1, and generating k random numbers obeying uniform distribution on [0,1] by using a unifrnd function built in MATLAB;

s25, converting the probability fitting of the aviation material demand into a specific aviation material demand, wherein if the generated random number is greater than 0 and less than or equal to the probability of being in the first state, the aviation material demand is 0, and if the generated random number is greater than the probability of being in the first state and less than or equal to the sum of the probabilities of being in the first two states, the aviation material demand is 1, and the aviation material demands in months 2, 3, … and k are obtained by analogy;

s26, when t is less than N, N is the set simulation times, when the simulation is not finished, the step is switched to S22, when t is more than or equal to N, the simulation is finished, and the step is switched to S27;

s27, generating a random sequence value obeying exponential distribution by using an exprand function built in MATLAB, selecting random simulation flight material demand quantity by taking the variance of the historical flight material demand quantity as a judgment standard, comparing the selected random simulation flight material demand quantity with the historical flight material demand quantity, and carrying out error analysis.

Preferably, in step S27, the specific step of acquiring the random simulated flight material demand includes:

generating random numbers which are subject to exponential distribution by using an exprand function built in MATLAB;

calculating the mean value and the variance of the historical aviation material demand;

generating a random sequence value according to the average value of the historical aviation material demand by using an exprand function built in the MATLAB;

and selecting a group of random sequence values with the minimum variance with the historical navigation material demand as the random simulation navigation material demand by taking the variance of the historical navigation material demand as a judgment standard.

Compared with the prior art, the invention has the beneficial effects that:

according to the method, a Markov prediction model is built based on Markov property of flight material demand, the Markov prediction model and Monte Carlo algorithm simulation are combined, limited historical flight material demand data are subjected to simulation processing based on the built Markov prediction model by taking MATLAB as a platform, the flight material demand prediction is realized, error analysis is carried out, and the reliability of the flight material demand prediction is improved. Meanwhile, the prediction method is simple and practical, can be processed in batch through computer software, has higher reliability, can be popularized to the prediction of other similar fields, and has wide application range.

Drawings

FIG. 1 is a flow chart of Monte Carlo algorithm simulation based on a Markov prediction model according to an embodiment of the present invention;

FIG. 2 is a diagram illustrating the relationship between the number of flight materials and the satisfaction rate of the flight materials according to an embodiment of the present invention;

FIG. 3 is a graph showing the change of raw data (i.e., historical flight material demand) and simulated data (i.e., simulated flight material demand) of the accumulator with months according to the embodiment of the present invention.

Detailed Description

The invention is described in detail below by way of exemplary embodiments. It should be understood, however, that elements, structures and features of one embodiment may be beneficially incorporated in other embodiments without further recitation.

In a traditional wartime aviation material demand forecasting mode, in order to ensure sufficient supply of wartime aviation materials, a large amount of aviation materials are usually reserved, so that aviation material backlog is caused, and a large amount of resources are consumed. In the outbreak of war, there are a considerable number of flight materials, the monthly demand of which is a small integer, the consumption of the low-demand flight materials is a random variable which shows random fluctuation in a certain range, and neither the time series prediction method nor the grey system prediction method can effectively predict the demand. The past war data and the ordinary training data can only be used as a reference, the evolution speed of the war is high, the demands for materials during the war are changed day by day, and the past data information has little value to the present. In the present invention, the future demand of such a material is assumed to be the same as the past "The situation of (1) is irrelevant and only relevant to the current state, namely the type of the navigation material demand has Markov property, and the Markov property is also called non-aftereffect. From the markov property of the type of the flight material demand, the probability that the process still leaves the state i in the following t units of time under the condition that the process is in the state i at the time s is the unconditional probability that the process is in i at least t units. If remember h_iFor the time that the process stays in state i before moving to another state, then for everything s, t ≧ 0 there is:

P{h_i>s+t|h_i>s}＝P{h_i>t}

it follows that the random variable h_iA continuous time markov chain with no memory, whenever it enters state i, follows an exponential distribution at the time of state i before transitioning to another state.

If the demand for the current month is known, the probability of the occurrence of various demand states for the next several months can be derived by solving a transition probability matrix. For example: summing the probabilities of the various states of the flight profile demand for the 3 months into the future can result in a probability distribution of the flight profile demand for a quarter of the future (i.e., assuming the duration of the war is one quarter).

The invention provides a wartime aviation material demand forecasting method which comprises the steps of establishing a Markov forecasting model according to Markov of aviation material demand, simulating random simulation by adopting a Monte Carlo algorithm based on the Markov forecasting model to obtain random simulation aviation material demand, comparing the random simulation aviation material demand with historical aviation material demand, carrying out error analysis and improving forecasting accuracy. The method for predicting demand of flight materials in wartime according to the invention is explained in detail below.

The invention provides a method for predicting demand of war-hour flight materials, which comprises the following steps:

s1, constructing a Markov prediction model, and solving the state probability of the flight material demand;

s11, dividing the time t into stages, taking the consumption condition of a certain navigation material in a certain past time period as a state quantity, taking the monthly demand quantity of the navigation material as X, and then taking the navigation material in the state t₁，t₂，...，t_nAre each x₁，x₂，...，x_nThe maximum value X in the flight material demand of the flight material_maxMinimum value is denoted X_minIf the required quantity of the navigation material is an integer, the navigation material has n ═ X_max-X_min+1 state;

s12, when the number of samples is large enough, the probability is replaced by the approximate frequency, and Y is set_iTo be in a state E_iNumber of samples of (2), Y_ij(k) Is in a state E_iTransitioning to State E through k Steps_jNumber of data of (1), P_ij(k) The k-step transition probability is expressed as follows:

the corresponding k-step state transition probability matrix p (k) is then expressed as:

s13, establishing a Markov prediction model according to the k-step state transition probability matrix P (k) and expressing as follows:

C(t)＝C(t-k)×P(k) (1)

in the formula, C (t) represents the predicted value of the state probability of the flight material demand amount in the future k months, and C (t-k) represents the state probability value of the flight material demand amount in the time t-k stage.

And S2, simulating random simulation by adopting a Monte Carlo algorithm based on the Markov prediction model to obtain the required amount of the flight material, comparing the randomly simulated required amount of the flight material with the data index of the original required amount of the flight material, and performing error analysis.

Specifically, the specific steps of obtaining the random simulation aviation material demand by adopting the Monte Carlo algorithm to simulate the random simulation and carrying out error analysis are as follows:

s21, taking MATLAB as a platform, inputting aviation material demand historical data in the MATLAB in a matrix form, finding out the maximum value and the minimum value, calculating the possible existing state of aviation material demand, making t equal to 0, and recording the number k of future k months to be predicted;

s22, counting the quantity of the required quantity states of each type of navigation materials and the quantity of the next transition states of the type of the states, calculating a state transition probability matrix P (1) in the 1 st step, and calculating state transition matrixes in the 2 nd, 3 rd, … th and k th steps in the same way;

s23, calculating probability prediction values of the corresponding navigation material demand of each state by the Markov prediction model according to the sample value of the last state;

s24, making t equal to t +1, and generating k random numbers obeying uniform distribution on [0,1] by using a unifrnd function built in MATLAB;

s25, converting the probability fitting of the aviation material demand into a specific aviation material demand, wherein if the generated random number is greater than 0 and less than or equal to the probability of being in the first state, the aviation material demand is 0, and if the generated random number is greater than the probability of being in the first state and less than or equal to the sum of the probabilities of being in the first two states, the aviation material demand is 1, and the aviation material demand in months 2, 3, … and k is obtained by analogy;

s26, when t is less than N, N is the set simulation times, when the simulation is not finished, the step is switched to S22, when t is more than or equal to N, the simulation is finished, and the step is switched to S27;

s27, generating a random sequence value obeying exponential distribution by using an exprand function built in MATLAB, selecting random simulation flight material demand quantity by taking the variance of the historical flight material demand quantity as a judgment standard, comparing the selected random simulation flight material demand quantity with the historical flight material demand quantity, and carrying out error analysis.

Specifically, the specific steps for acquiring the demand of the random simulation aviation material are as follows:

(1) generating random numbers with the average value of n multiplied by n order being MU and complying with exponential distribution by using exprand (MU, n) function built in MATLAB;

(2) calculating the mean value and the variance of the historical aviation material demand;

(3) generating a random sequence value according to the average value of the historical aviation material demand by using an exprand function built in the MATLAB;

(4) and selecting a group of random sequence values with the minimum variance with the historical navigation material demand as the random simulation navigation material demand by taking the variance of the historical navigation material demand as a judgment standard.

The Monte Carlo algorithm is a method for carrying out experiments and distribution probability simulation on random variables based on probability theory and mathematical statistics, so as to approximately solve to obtain a predicted value, and when the simulation times reach a certain number, the more the characteristics of the simulation data approach the real situation. According to the invention, the Monte Carlo algorithm is adopted to carry out random simulation on the aviation material demand, so that the reliability of prediction can be effectively improved, and the random sequence value complying with exponential distribution is generated by using the exprend function built in the MATLAB, so that the reliability of the Monte Carlo simulation random simulation effect is higher.

The method for predicting the demand of the wartime aviation materials is described by taking a certain device of a certain type of airplane as an example.

The statistical time limit of the demand data samples of the certain type of the pressure accumulator loaded on the airplane is from 2019 to 2020 and 7, and the demand data samples are shown in the following table 1.

TABLE 1

Month of the year	1	2	3	4	5	6	7	8
									Number of demands	1	0	2	1	1	0	1	2
Month of the year	9	10	11	12	13	14	15	16
									Number of demands	0	0	1	0	2	0	0	1

From the above table, it can be seen that the maximum value is 2 and the minimum value is 0, the required number of the accumulator is three states, the time series is counted, the frequency is used to approximate the one-step transition probability, and from the above data, the number of samples in the state 0 is 7, and the number of samples in the state 0 which is one-step transition to the state 0 is 2, then the maximum value is 2 and the minimum value is 0

Similarly, a one-step probability transition matrix P (1) can be calculated:

by analogy, P (2) and P (3) are calculated by using MATLAB as follows:

according to the demand time sequence, the monthly demand of the current aviation material is 1, the aviation material demand state probability distribution of 1 st, 2 nd and 3 rd months in the future can be calculated according to the probability transfer matrixes P (1), P (2) and P (3), in order to obtain the probability distribution of the total demand of the aviation material in three months, Matlab is used for 10000 times of simulation calculation, and the obtained result is shown in a table 2.

TABLE 2

According to the corresponding relationship between the flight material demand and the cumulative probability, the meeting rate of the flight material demand in wartime corresponding to the quantity of the flight material in three months of continuous battle can be drawn, as shown in fig. 2, it can be known from the figure that when the demand of the flight material in three months of wartime is 7, the corresponding demand meeting rate reaches more than 96%. It should be noted that, the invention does not need to require one hundred percent of satisfaction rate to reserve 10 accumulators in advance, and needs to invest huge manpower cost and economic cost for improving the small satisfaction rate, although the military benefit is the first place compared with the economic cost, 7 accumulators can be reserved firstly when the war starts, and then the replenishment is flexibly carried out according to the change of the battlefield situation, thereby ensuring the military benefit on the basis of saving the economic cost.

The lack of real battlefield requirement data as the basis for error analysis adds a lot of difficulties to the error analysis. In order to test the reliability of the simulation prediction, the prediction method calculates the mean value of the simulation prediction to be 0.75 and the variance of the simulation prediction to be 0.60 according to the existing aviation material demand. Using the MATLAB built-in exprand function, an exponential distribution-compliant random number with a mean of 0.75 of order 1000 x 1000 was generated. And selecting a group with the smallest sum of squares of the errors with the historical navigation material demand as a result of the random simulation navigation material demand by taking the sum of squares of the errors with the historical navigation material demand (namely the variance) as a judgment standard, and comparing and analyzing the result with the historical navigation material demand.

It can be seen from fig. 3 that in the aircraft material demand sequence randomly simulated according to the exponential distribution, the overall fluctuation is reduced, but most of the maximum points are better fitted with the original demand sequence in the time trend change. The mean value and the variance indexes simulated by the exponential distribution have little difference with the historical data of the aeronautical material demand. According to the new flight material demand, the demand quantities of 1.6910, 2.2587 and 0.9347 in the 1 st, 2 nd and 3 rd months in the future are simulated, and the total flight material demand quantity of 4.8844 in the three months in the future, so that the result of reserving 7 pressure accumulators before the beginning of a war, which is calculated based on the method, is reasonable, and the supply of the pressure accumulator in the wartime can be guaranteed at a high probability. If the duration of the war exceeds three months, the transition probability matrix can be continuously used for demand prediction, but the change of the transition probability matrix is increased along with the increase of the prediction time, so that the error is increased, and the error is required to be corrected subsequently. The method has good simulation effect, and the prediction result has high reliability although some errors exist.

The above-described embodiments are intended to illustrate rather than to limit the invention, and any modifications and variations of the present invention are possible within the spirit and scope of the claims.