Method and system for predicting health staff reduction based on Lanchester equation

Abstract

The present invention discloses a method and system for predicting health attrition based on the Lanchester equation, wherein the method includes introducing a time lag function and random white noise into the Lanchester equation to obtain a health attrition prediction model, wherein the time lag function is used to represent the time delay of troop reinforcement, and the random white noise is used to represent the uncontrollable factors affecting the development trend of the war; setting initial simulation parameters; performing numerical simulation on the health attrition prediction model based on the initial simulation parameters by simulation software, and obtaining a distribution curve of attrition of both sides of the war. The present invention can more effectively simulate the war process and show the evolution of the battlefield situation. The predicted results of attrition can reflect the uncertainty of the war to a certain extent, thereby effectively improving the accuracy of health attrition prediction.

Description

Technical Field

[0001] The present invention relates to the technical field of data processing, and in particular to a method and system for predicting health attrition based on the Lanchester equation. Background Art

[0002] The prediction of health attrition is the starting point and premise of health resource planning and guarantee, and its role is crucial. In the past records of health attrition, the distribution of attrition usually follows a pattern, which can be predicted by methods based on empirical data, mathematical models, and simulations. However, the existing health attrition prediction methods lack effective means for process simulation and process deduction, and mostly rely on historical data, which has the problem of overfitting, resulting in low accuracy of health attrition prediction. In addition, the style of modern warfare has undergone tremendous changes, and the classic health attrition law has begun to be broken. The basic process and methods of health attrition prediction also need to be adjusted in a targeted manner to meet the needs of future health attrition prediction.

[0003] Therefore, how to more effectively simulate the war process and better reflect the uncertainty of war, so as to improve the accuracy of health attrition prediction, is an urgent problem to be solved by technical personnel in this field. Summary of the invention

[0004] The present invention aims to solve the technical problems existing in the prior art, and particularly innovatively proposes a health attrition prediction method and system based on the Lanchester equation, which can more effectively simulate the war process and show the evolution of the battlefield situation. The predicted attrition results can reflect the uncertainty of the war to a certain extent, thereby effectively improving the accuracy of the health attrition prediction.

[0005] In order to achieve the above-mentioned object of the present invention, according to a first aspect of the present invention, the present invention provides a method for predicting health attrition based on the Lanchester equation, the method comprising the following steps:

[0006] A health attrition prediction model is obtained by introducing a time lag function and random white noise into the Lanchester equation, wherein the time lag function is used to represent the time delay of troop reinforcement, and the random white noise is used to represent the uncontrollable factors that affect the development trend of the war;

[0007] Set the initial parameters of the simulation;

[0008] The health attrition prediction model is numerically simulated by simulation software based on the initial simulation parameters to obtain a distribution curve of attrition of both combatants.

[0009] Preferably, the health attrition prediction model obtained by introducing the time lag function and random white noise into the Lanchester equation is as follows:

[0010]

[0011] Among them, t represents the time of war, r 1 represents the force reinforcement function of the first combatant, r 2 represents the force reinforcement function of the second combatant, τ 1 represents the delay time of the reinforcement of the first combatant, τ 2 represents the delay time of the reinforcement of the second combatant, α represents the combat effectiveness coefficient of the first combatant, β represents the combat effectiveness coefficient of the second combatant, x(t) is the combat capability of the first combatant over time, y(t) represents the combat capability of the second combatant over time, σ 1 represents the size of the white noise of the first combatant, σ 2 Indicates the size of the white noise of the second combatant, B 1 (t), B 2 (t) is a standard Brownian motion defined on the complete probability space.

[0012] Preferably, before setting the initial simulation parameters, the method further comprises:

[0013] The combat effectiveness coefficients of the two combatants in the health attrition prediction model are revised using a pre-constructed multi-factor combat effectiveness coefficient model.

[0014] Preferably, the method further comprises:

[0015] The multi-factor combat effectiveness coefficient model is constructed based on multiple factors affecting the war through the Dupai index method, wherein the multi-factor combat effectiveness coefficient model is as follows:

[0016] Q α / β =S·m·l e ·p·o·b·u s ·r u ·h u ·z u ·v

[0017] Among them, Q α / β represents the combat effectiveness coefficient, m represents the mobility factor of the combat force, l e represents the command factor, p represents the training factor, o represents the morale factor, b represents the logistics factor, and u s represents the situation factor related to strength, r u represents the terrain factor related to the situation, h u represents the meteorological factors related to the situation, z u represents the seasonal factor related to the situation, v represents the vulnerability factor, and S represents the combat strength.

[0018] Preferably, the setting of the initial simulation parameters includes:

[0019] The reinforcement function, the reinforcement delay time value of the combatants and the random white noise value are set, and the initial number of troops of the combatants and the specific values ​​of multiple influencing factors related to the combat effectiveness coefficient are input into the simulation software as initial parameters.

[0020] According to a second aspect of the present invention, the present invention also provides a health attrition prediction system based on the Lanchester equation, the system comprising:

[0021] A prediction model building module, used to introduce a time lag function and random white noise into the Lanchester equation to obtain a health attrition prediction model, wherein the time lag function is used to represent the time delay of troop reinforcement, and the random white noise is used to represent uncontrollable factors that affect the development trend of the war;

[0022] A simulation parameter setting module is used to set the initial parameters of the simulation;

[0023] The attrition prediction simulation module is used to perform numerical simulation on the health attrition prediction model based on the initial simulation parameters through simulation software to obtain the attrition distribution curve of the two combatants.

[0024] Preferably, the health attrition prediction model obtained by introducing the time lag function and random white noise into the Lanchester equation is as follows:

[0025]

[0026] Among them, t represents the time of war, r 1 represents the force reinforcement function of the first combatant, r 2 represents the force reinforcement function of the second combatant, τ 1 represents the delay time of the reinforcement of the first combatant, τ 2 represents the delay time of the reinforcement of the second combatant, α represents the combat effectiveness coefficient of the first combatant, β represents the combat effectiveness coefficient of the second combatant, x(t) is the combat capability of the first combatant over time, y(t) represents the combat capability of the second combatant over time, σ 1 represents the size of the white noise of the first combatant, σ 2 Indicates the size of the white noise of the second combatant, B 1 (t), B 2 (t) is a standard Brownian motion defined on the complete probability space.

[0027] Preferably, the system further comprises:

[0028] The combat effectiveness coefficient revision module is used to revise the combat effectiveness coefficients of the two combatants in the health attrition prediction model using a pre-built multi-factor combat effectiveness coefficient model before setting the initial simulation parameters.

[0029] Preferably, the system further comprises:

[0030] The combat effectiveness coefficient model construction module is used to construct the multi-factor combat effectiveness coefficient model based on multiple factors affecting the war through the Dupai index method, wherein the multi-factor combat effectiveness coefficient model is as follows:

[0031] Q α / β =S·m·l e ·p·o·b·u s ·r u ·h u ·z u ·v

[0032] Among them, Q α / β represents the combat effectiveness coefficient, m represents the mobility factor of the combat force, l e represents the command factor, p represents the training factor, o represents the morale factor, b represents the logistics factor, and u s represents the situation factor related to strength, r u represents the terrain factor related to the situation, h u represents the meteorological factors related to the situation, z u represents the seasonal factor related to the situation, v represents the vulnerability factor, and S represents the combat strength.

[0033] Preferably, the simulation parameter setting module is specifically used for:

[0034] The reinforcement function, the reinforcement delay time value of the combatants and the random white noise value are set, and the initial number of troops of the combatants and the specific values ​​of multiple influencing factors related to the combat effectiveness coefficient are input into the simulation software as initial parameters.

[0035] It can be seen from the above scheme that the present invention provides a method and system for predicting health attrition based on the Lanchester equation. A health attrition prediction model is obtained by introducing a time lag function and random white noise into the Lanchester equation, wherein the time lag function is used to represent the time delay of troop reinforcement, and the random white noise is used to represent the uncontrollable factors that affect the development trend of the war; the initial parameters of the simulation are set; the health attrition prediction model is numerically simulated based on the initial parameters of the simulation by the simulation software to obtain the attrition distribution curve of the combatants. When the present invention uses the Lanchester equation to predict health attrition, the time lag function is taken into account, and random white noise is added, which can more effectively simulate the war process and show the evolution of the battlefield situation. The predicted results of attrition can reflect the uncertainty of the war to a certain extent, thereby effectively improving the accuracy of the health attrition prediction.

[0036] Additional aspects and advantages of the present invention will be given in part in the following description and in part will be obvious from the following description, or will be learned through practice of the present invention. BRIEF DESCRIPTION OF THE DRAWINGS

[0037] The above and / or additional aspects and advantages of the present invention will become apparent and easily understood from the description of the embodiments in conjunction with the following drawings, in which:

[0038] Figure 1 It is a flow chart of a method for predicting health attrition based on the Lanchester equation in a preferred embodiment of the present invention;

[0039] Figure 2 It is a structural schematic diagram of a health attrition prediction system based on the Lanchester equation in a preferred embodiment of the present invention. DETAILED DESCRIPTION

[0040] The exemplary embodiments of the present disclosure will be described in more detail below with reference to the accompanying drawings. Although the exemplary embodiments of the present disclosure are shown in the accompanying drawings, it should be understood that the present disclosure can be implemented in various forms and should not be limited by the embodiments set forth herein. On the contrary, these embodiments are provided in order to enable a more thorough understanding of the present disclosure and to fully convey the scope of the present disclosure to those skilled in the art.

[0041] Those skilled in the art will appreciate that, unless otherwise defined, all terms (including technical and scientific terms) used herein have the same meaning as those generally understood by those skilled in the art in the art to which the present invention belongs. It should also be understood that terms such as those defined in general dictionaries should be understood to have meanings consistent with the meanings in the context of the prior art, and will not be interpreted with idealized or overly formal meanings unless specifically defined.

[0042] The Lanchester equation is a set of differential equations that describes the relationship between the forces of both sides in the battle process. It is also called the Lanchester battle theory or the battle dynamics theory. It is a branch of operations research that uses mathematical methods to study the process of weapons and forces elimination of the hostile parties in battle. The various forms and scales of combat models formed by combining the Lanchester equation with computer combat simulation have been widely used in various related fields of military decision-making.

[0043] The Lanchester equation-based health attrition prediction method and system of the present invention combines the Lanchester equation with computer simulation to achieve the prediction of health attrition during war.

[0044] like Figure 1 As shown, it is a flowchart of a method for predicting health attrition based on the Lanchester equation in a preferred embodiment of the present invention, and the method may include the following steps:

[0045] S101, introducing time lag function and random white noise into the Lanchester equation to obtain the health attrition prediction model;

[0046] When it is necessary to predict the health attrition of both sides in a war, the classic Lanchester equation needs to be improved first, that is, the time lag function and random white noise are introduced into the Lanchester equation to obtain the health attrition prediction model (that is, the improved Lanchester equation).

[0047] Specifically, the time lag function is used to represent the time delay of troop reinforcement, and the random white noise is used to represent the uncontrollable factors that affect the development trend of the war.

[0048] It can be understood that the two combatants are the two warring parties participating in the war. For the sake of convenience, the present invention uses the first combatant and the second combatant to represent, that is, the first combatant and the second combatant are hostile combatants. Specifically, the two combatants can also be represented by our side and the enemy, or by the red side and the blue side.

[0049] Specifically, the classic Lanchester equation can be expressed as follows:

[0050]

[0051] Among them, t represents the time of war, α represents the combat effectiveness coefficient of the first combatant, β represents the combat effectiveness coefficient of the second combatant, x(t) represents the combat capability of the first combatant over time, and y(t) represents the combat capability of the second combatant over time.

[0052] Modern warfare is complex and changeable. Commanders may decide whether to send reinforcements at any time based on battlefield dynamics. However, there is a certain time delay from the time the reinforcements receive the order to the time they arrive at the scene. Therefore, the present invention introduces a time lag function into the Lanchester equation to reflect this factor.

[0053] In addition, since there are many uncontrollable factors on the battlefield, such as changes in weather and temperature, which can affect the development trend of the war to a certain extent, in view of this, the present invention introduces random white noise into the model to simulate this random phenomenon, making the model more in line with the actual situation, and can effectively avoid the overfitting problem caused by the existing health attrition prediction method due to reliance on historical data.

[0054] Specifically, in this embodiment, the health attrition prediction model obtained by introducing the time lag function and random white noise into the Lanchester equation is as follows:

[0055]

[0056] Among them, t represents the time of war, r 1 represents the force reinforcement function of the first combatant, r 2 represents the force reinforcement function of the second combatant, τ 1 represents the delay time of the reinforcement of the first combatant, τ 2 represents the delay time of the reinforcement of the second combatant, α represents the combat effectiveness coefficient of the first combatant, β represents the combat effectiveness coefficient of the second combatant, x(t) is the combat capability of the first combatant over time, y(t) represents the combat capability of the second combatant over time, σ 1 represents the size of the white noise of the first combatant, σ 2 Indicates the size of the white noise of the second combatant, B 1 (t), B 2 (t) is a standard Brownian motion defined on the complete probability space.

[0057] Specifically, the above force reinforcement function r 1 、r 2 and the delay time τ of reinforcement 1 , τ 2 They are all empirical values, which can be selected from the expert database according to needs and set in advance according to needs before numerical simulation. The white noise size σ 1 , σ 2 It is randomly generated by the simulation software during the simulation process.

[0058] S102, setting initial simulation parameters;

[0059] After the health attrition prediction model is constructed, the model can be used to predict health attrition through numerical simulation. Specifically, the constructed model can be injected into the simulation software first, and then the initial simulation parameters can be set through the human-computer interaction interface of the simulation software.

[0060] Specifically, the setting of the initial simulation parameters includes:

[0061] The reinforcement function, the reinforcement delay time value of the combatants and the random white noise value are set, and the initial number of troops of the combatants and the specific values ​​of multiple influencing factors related to the combat effectiveness coefficient are input into the simulation software as initial parameters.

[0062] S103, performing numerical simulation on the health attrition prediction model based on the initial simulation parameters by means of simulation software, and obtaining a distribution curve of attrition of both combatants.

[0063] After the initial simulation parameters are set, the simulation function of the simulation software can be started to perform numerical simulation on the health attrition prediction model based on the initial simulation parameters, and then after the simulation is completed, the attrition distribution curve of the two combatants can be obtained. Through the attrition distribution curve, users can intuitively and clearly conduct prediction analysis and research related to health attrition, such as the health attrition situation of the two combatants at a certain moment, the health attrition situation of the two combatants in a certain period of time, etc.

[0064] Specifically, in this embodiment, Matlab simulation software is used to perform numerical simulation on the health attrition prediction model.

[0065] In summary, this embodiment provides a method for predicting health attrition based on the Lanchester equation. First, a health attrition prediction model is obtained by introducing a time lag function and random white noise into the Lanchester equation, wherein the time lag function is used to represent the time delay of troop reinforcement, and the random white noise is used to represent the uncontrollable factors affecting the development trend of the war; then the initial parameters of the simulation are set; finally, the health attrition prediction model is numerically simulated based on the initial parameters of the simulation by the simulation software to obtain the attrition distribution curve of the combatants. This embodiment takes into account the time lag function and adds random white noise when predicting health attrition through the Lanchester equation, which can more effectively simulate the war process and show the evolution of the battlefield situation. The predicted results of attrition can reflect the uncertainty of the war to a certain extent, thereby effectively improving the accuracy of the health attrition prediction.

[0066] Since there are many factors that affect war, the combat effectiveness coefficients α and β of the first and second combatants cannot directly reflect the impact of these factors on the war, so this application considers revising the parameters α and β in combination with the Dupai index. In some other embodiments of the present invention, based on the above embodiments, before setting the initial parameters of the simulation, the method further includes:

[0067] The combat effectiveness coefficients of the two combatants in the health attrition prediction model are revised using a pre-constructed multi-factor combat effectiveness coefficient model.

[0068] Specifically, the method further includes the step of constructing a multi-factor combat effectiveness coefficient model, that is, constructing the multi-factor combat effectiveness coefficient model based on multiple factors affecting the war through the Dupai index method, wherein the multi-factor combat effectiveness coefficient model is as follows:

[0069] Q α / β =S·m·l e ·p·o·b·u s ·r u ·h u ·z u ·v

[0070] Among them, Q α / β represents the combat effectiveness coefficient, m represents the mobility factor of the combat force, l e represents the command factor, p represents the training factor, o represents the morale factor, b represents the logistics factor, and u s represents the situation factor related to strength, r u represents the terrain factor related to the situation, h u represents the meteorological factors related to the situation, z u represents the seasonal factor related to the situation, v represents the vulnerability factor, and S represents the combat strength.

[0071] Specifically, the combat effectiveness coefficients of the combatants in the health attrition prediction model are revised by using the pre-constructed multi-factor combat effectiveness coefficient model, that is, by converting Q α / β To replace the combat effectiveness coefficients α and β of the first and second combatants in the health attrition prediction model, so that when the health attrition prediction model is used for health attrition prediction simulation, multiple factors affecting the war will be taken into account, making the simulation process more realistic and improving the accuracy of the prediction results.

[0072] Specifically, in this embodiment, the combat strength S can be expressed as follows:

[0073]

[0074] Where n represents the number of weapon types, i represents the i-th weapon, TLI represents the theoretical lethality index of the weapon, and M represents the battlefield mobility factor. V is the maneuvering speed, r is the active radius, PF is the penalty factor, which is related to the weapon weight, RFE is the firing rate effect, FCE is the fire control effect, which is generally 0.8-0.9, ASE is the ammunition supply effect, SX is the aircraft ceiling, K Srepresents the evacuation factor.

[0075] Specifically, the values ​​of each factor in the multi-factor combat effectiveness coefficient model in this embodiment all adopt the reference values ​​provided by the expert database.

[0076] like Figure 2 As shown, it is a structural schematic diagram of a health attrition prediction system based on the Lanchester equation in a preferred embodiment of the present invention, and the system may include:

[0077] A prediction model building module 201 is used to introduce a time lag function and random white noise into the Lanchester equation to obtain a health attrition prediction model, wherein the time lag function is used to represent the time delay of troop reinforcement, and the random white noise is used to represent uncontrollable factors that affect the development trend of the war;

[0078] When it is necessary to predict the health attrition of both sides in a war, the classic Lanchester equation needs to be improved first, that is, the time lag function and random white noise are introduced into the Lanchester equation to obtain the health attrition prediction model (that is, the improved Lanchester equation).

[0079] Specifically, the time lag function is used to represent the time delay of troop reinforcement, and the random white noise is used to represent the uncontrollable factors that affect the development trend of the war.

[0080] It can be understood that the two combatants are the two warring parties participating in the war. For the sake of convenience, the present invention uses the first combatant and the second combatant to represent, that is, the first combatant and the second combatant are hostile combatants. Specifically, the two combatants can also be represented by our side and the enemy, or by the red side and the blue side.

[0081] Specifically, the classic Lanchester equation can be expressed as follows:

[0082]

[0083] Among them, t represents the time of war, α represents the combat effectiveness coefficient of the first combatant, β represents the combat effectiveness coefficient of the second combatant, x(t) represents the combat capability of the first combatant over time, and y(t) represents the combat capability of the second combatant over time.

[0084] Modern warfare is complex and changeable. Commanders may decide whether to send reinforcements at any time based on battlefield dynamics. However, there is a certain time delay from the time the reinforcements receive the order to the time they arrive at the scene. Therefore, the present invention introduces a time lag function into the Lanchester equation to reflect this factor.

[0085] In addition, since there are many uncontrollable factors on the battlefield, such as changes in weather and temperature, which can affect the development trend of the war to a certain extent, in view of this, the present invention introduces random white noise into the model to simulate this random phenomenon, making the model more in line with the actual situation, and can effectively avoid the overfitting problem caused by the existing health attrition prediction method due to reliance on historical data.

[0086] Specifically, in this embodiment, the health attrition prediction model obtained by introducing the time lag function and random white noise into the Lanchester equation is as follows:

[0087]

[0088] Among them, t represents the time of war, r 1 represents the force reinforcement function of the first combatant, r 2 represents the force reinforcement function of the second combatant, τ 1 represents the delay time of the reinforcement of the first combatant, τ 2 represents the delay time of the reinforcement of the second combatant, α represents the combat effectiveness coefficient of the first combatant, β represents the combat effectiveness coefficient of the second combatant, x(t) is the combat capability of the first combatant over time, y(t) represents the combat capability of the second combatant over time, σ 1 represents the size of the white noise of the first combatant, σ 2 Indicates the size of the white noise of the second combatant, B 1 (t), B 2 (t) is a standard Brownian motion defined on the complete probability space.

[0089] Specifically, the above force reinforcement function r 1 、r 2 and the delay time τ of reinforcement 1 , τ 2 They are all empirical values, which can be selected from the expert database according to needs and set in advance according to needs before numerical simulation. The white noise size σ 1 , σ 2 It is randomly generated by the simulation software during the simulation process.

[0090] The simulation parameter setting module 202 is used to set the initial parameters of the simulation;

[0091] After the health attrition prediction model is constructed, the model can be used to predict health attrition through numerical simulation. Specifically, the constructed model can be injected into the simulation software first, and then the initial simulation parameters can be set through the human-computer interaction interface of the simulation software.

[0092] In this embodiment, setting the initial simulation parameters specifically includes:

[0093] The reinforcement function, the reinforcement delay time value of the combatants and the random white noise value are set, and the initial number of troops of the combatants and the specific values ​​of multiple influencing factors related to the combat effectiveness coefficient are input into the simulation software as initial parameters.

[0094] The attrition prediction simulation module 203 is used to perform numerical simulation on the health attrition prediction model based on the initial simulation parameters through simulation software to obtain the attrition distribution curve of the two combatants.

[0095] After the initial simulation parameters are set, the simulation function of the simulation software can be started to perform numerical simulation on the health attrition prediction model based on the initial simulation parameters, and then after the simulation is completed, the attrition distribution curve of the two combatants can be obtained. Through the attrition distribution curve, users can intuitively and clearly conduct prediction analysis and research related to health attrition, such as the health attrition situation of the two combatants at a certain moment, the health attrition situation of the two combatants in a certain period of time, etc.

[0096] Specifically, in this embodiment, Matlab simulation software is used to perform numerical simulation on the health attrition prediction model.

[0097] In summary, the present embodiment provides a health attrition prediction system based on the Lanchester equation. First, the prediction model building module 201 introduces a time lag function and random white noise into the Lanchester equation to obtain a health attrition prediction model, wherein the time lag function is used to represent the time delay of troop reinforcement, and the random white noise is used to represent the uncontrollable factors affecting the development trend of the war; then the simulation parameter setting module 202 sets the initial parameters of the simulation; finally, the attrition prediction simulation module 203 uses the simulation software to perform numerical simulation on the health attrition prediction model based on the initial parameters of the simulation, and obtains the attrition distribution curve of the combatants. When the present embodiment predicts health attrition through the Lanchester equation, the time lag function is taken into account, and random white noise is added, which can more effectively simulate the war process and show the evolution of the battlefield situation. The predicted results of attrition can reflect the uncertainty of the war to a certain extent, thereby effectively improving the accuracy of the health attrition prediction.

[0098] Since there are many factors that affect war, the combat effectiveness coefficients α and β of the first and second combatants cannot directly reflect the impact of these factors on the war, so this application considers revising the parameters α and β in combination with the Dupai index. In some other embodiments of the present invention, based on the above embodiments, the system also includes:

[0099] The combat effectiveness coefficient revision module is used to revise the combat effectiveness coefficients of the two combatants in the health attrition prediction model using a pre-built multi-factor combat effectiveness coefficient model before setting the initial simulation parameters.

[0100] Specifically, in this embodiment, the system further includes:

[0101] The combat effectiveness coefficient model construction module is used to construct the multi-factor combat effectiveness coefficient model based on multiple factors affecting the war through the Dupai index method, wherein the multi-factor combat effectiveness coefficient model is as follows:

[0102] Q α / β =S·m·l e ·p·o·b·u s ·r u ·h u ·z u ·v

[0103] Among them, Q α / β represents the combat effectiveness coefficient, m represents the mobility factor of the combat force, l e represents the command factor, p represents the training factor, o represents the morale factor, b represents the logistics factor, and u s represents the situation factor related to strength, r u represents the terrain factor related to the situation, h u represents the meteorological factors related to the situation, z u represents the seasonal factor related to the situation, v represents the vulnerability factor, and S represents the combat strength.

[0104] Specifically, the combat effectiveness coefficients of the combatants in the health attrition prediction model are revised by using the pre-constructed multi-factor combat effectiveness coefficient model, that is, by converting Q α / β To replace the combat effectiveness coefficients α and β of the first and second combatants in the health attrition prediction model, so that when the health attrition prediction model is used for health attrition prediction simulation, multiple factors affecting the war will be taken into account, making the simulation process more realistic and improving the accuracy of the prediction results.

[0105] Specifically, in this embodiment, the combat strength S can be expressed as follows:

[0106]

[0107] Where n represents the number of weapon types, i represents the i-th weapon, TLI represents the theoretical lethality index of the weapon, and M represents the battlefield mobility factor. V is the maneuvering speed, r is the active radius, PF is the penalty factor, which is related to the weapon weight, RFE is the firing rate effect, FCE is the fire control effect, which is generally 0.8-0.9, ASE is the ammunition supply effect, SX is the aircraft ceiling, K S represents the evacuation factor.

[0108] Specifically, the values ​​of each factor in the multi-factor combat effectiveness coefficient model in this embodiment all adopt the reference values ​​provided by the expert database.

[0109] In this specification, each embodiment is described in a progressive manner, and each embodiment focuses on the differences from other embodiments. The same or similar parts between the embodiments can be referred to each other. For the system disclosed in the embodiment, since it corresponds to the method disclosed in the embodiment, the description is relatively simple, and the relevant parts can be referred to the method part.

[0110] Professionals may further appreciate that the units and algorithm steps of each example described in conjunction with the embodiments disclosed herein can be implemented in electronic hardware, computer software, or a combination of the two. In order to clearly illustrate the interchangeability of hardware and software, the composition and steps of each example have been generally described in the above description according to function. Whether these functions are performed in hardware or software depends on the specific application and design constraints of the technical solution. Professionals and technicians may use different methods to implement the described functions for each specific application, but such implementation should not be considered to be beyond the scope of the present invention.

[0111] The steps of the method or algorithm described in conjunction with the embodiments disclosed herein may be implemented directly using hardware, a software module executed by a processor, or a combination of the two. The software module may be placed in a random access memory (RAM), a memory, a read-only memory (ROM), an electrically programmable ROM, an electrically erasable programmable ROM, a register, a hard disk, a removable disk, a CD-ROM, or any other form of storage medium known in the art.

[0112] The above description of the disclosed embodiments enables one skilled in the art to implement or use the present invention. Various modifications to these embodiments will be apparent to one skilled in the art, and the general principles defined herein may be implemented in other embodiments without departing from the spirit or scope of the present invention. Therefore, the present invention will not be limited to the embodiments shown herein, but rather to the widest scope consistent with the principles and novel features disclosed herein.

Claims

1. A method for predicting health attrition based on the Lanchester equation. It is characterized in that include: A health attrition prediction model is obtained by introducing a time lag function and random white noise into the Lanchester equation, wherein the time lag function is used to represent the time delay of troop reinforcement, and the random white noise is used to represent the uncontrollable factors that affect the development trend of the war; Set the initial parameters of the simulation; Performing numerical simulation on the health attrition prediction model based on the initial simulation parameters by simulation software to obtain a distribution curve of attrition of both combatants; The health reduction prediction model is as follows: Among them, t represents the time of war, r 1 represents the force reinforcement function of the first combatant, r 2 represents the force reinforcement function of the second combatant, τ 1 represents the delay time of the reinforcement of the first combatant, τ 2 represents the delay time of the reinforcement of the second combatant, α represents the combat effectiveness coefficient of the first combatant, β represents the combat effectiveness coefficient of the second combatant, x(t) is the combat capability of the first combatant over time, y(t) represents the combat capability of the second combatant over time, σ 1 represents the size of the white noise of the first combatant, σ 2 Indicates the size of the white noise of the second combatant, B 1 (t), B 2 (t) is a standard Brownian motion defined on the complete probability space.

2. The method for predicting health attrition based on the Lanchester equation according to claim 1, It is characterized in that Before setting the initial simulation parameters, the method further includes: Using a pre-constructed multi-factor combat effectiveness coefficient model, the combat effectiveness coefficients of the combatants in the health attrition prediction model are revised; and The multi-factor combat effectiveness coefficient model is constructed based on multiple factors affecting the war through the Dupai index method, wherein the multi-factor combat effectiveness coefficient model is as follows: Q α / β =S·m·l e ·p·o·b·u s ·r u ·h u ·z u ·v Among them, Q α / β represents the combat effectiveness coefficient, m represents the mobility factor of the combat force, l e represents the command factor, p represents the training factor, o represents the morale factor, b represents the logistics factor, and u s represents the situation factor related to strength, r u represents the terrain factor related to the situation, h u represents the meteorological factors related to the situation, z u represents the seasonal factor related to the situation, v represents the vulnerability factor, and S represents the combat strength.

3. The method for predicting health attrition based on the Lanchester equation according to claim 2, It is characterized in that The setting of the initial simulation parameters includes: The reinforcement function, the reinforcement delay time value of the combatants and the random white noise value are set, and the initial number of troops of the combatants and the specific values ​​of multiple influencing factors related to the combat effectiveness coefficient are input into the simulation software as initial parameters.

4. A health attrition prediction system based on the Lanchester equation, It is characterized in that include: A prediction model building module, used to introduce a time lag function and random white noise into the Lanchester equation to obtain a health attrition prediction model, wherein the time lag function is used to represent the time delay of troop reinforcement, and the random white noise is used to represent uncontrollable factors that affect the development trend of the war; A simulation parameter setting module is used to set the initial parameters of the simulation; A reduction in personnel prediction simulation module is used to perform numerical simulation on the health reduction in personnel prediction model based on the initial simulation parameters through simulation software to obtain a reduction in personnel distribution curve of both combatants; The health reduction prediction model is as follows: Among them, t represents the time of war, r 1 represents the force reinforcement function of the first combatant, r 2 represents the force reinforcement function of the second combatant, τ 1 represents the delay time of the reinforcement of the first combatant, τ 2 represents the delay time of the reinforcement of the second combatant, ɑ represents the combat effectiveness coefficient of the first combatant, β represents the combat effectiveness coefficient of the second combatant, x(t) is the combat capability of the first combatant over time, y(t) represents the combat capability of the second combatant over time, σ 1 represents the size of the white noise of the first combatant, σ 2 Indicates the size of the white noise of the second combatant, B 1 (t), B 2 (t) is a standard Brownian motion defined on the complete probability space.

5. The health attrition prediction system based on the Lanchester equation according to claim 4, It is characterized in that The system further comprises: A combat effectiveness coefficient revision module is used to revise the combat effectiveness coefficients of the combatants in the health attrition prediction model by using a pre-built multi-factor combat effectiveness coefficient model before setting the initial parameters of the simulation; and The combat effectiveness coefficient model construction module is used to construct the multi-factor combat effectiveness coefficient model based on multiple factors affecting the war through the Dupai index method, wherein the multi-factor combat effectiveness coefficient model is as follows: Q α / β =S·m·l e ·p·o·b·u s ·r u ·h u ·z u ·v Among them, Q α / β represents the combat effectiveness coefficient, m represents the mobility factor of the combat force, l e represents the command factor, p represents the training factor, o represents the morale factor, b represents the logistics factor, and u s represents the situation factor related to strength, r u represents the terrain factor related to the situation, h u represents the meteorological factors related to the situation, z u represents the seasonal factor related to the situation, v represents the vulnerability factor, and S represents the combat strength.

6. The health attrition prediction system based on the Lanchester equation according to claim 5, It is characterized in that The simulation parameter setting module is specifically used for: The reinforcement function, the reinforcement delay time value of the combatants and the random white noise value are set, and the initial number of troops of the combatants and the specific values ​​of multiple influencing factors related to the combat effectiveness coefficient are input into the simulation software as initial parameters.

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