System and method for controlling firing of an artillery gun

Abstract

Disclosed herein is a system (100) and a method (300) for controlling firing of an artillery gun. The method includes receiving (302) one or more input parameters inputted by a user through a graphical user interface and estimating (304) a reduced order model of a projectile including one or more aerodynamic coefficients of the projectile of the artillery gun. Further, the method includes optimizing (306), using one or more scientific machine learning models, values of the one or more aerodynamic coefficients. Furthermore, the method includes predicting (308), based on the optimized values of the one or more aerodynamic coefficients, one or more output parameters and a trajectory of the projectile using the one or more scientific machine learning models. Thereafter, the method includes controlling (310) firing of the artillery gun based on the one or more output parameters.

Description

SYSTEM AND METHOD FOR CONTROLLING FIRING OF AN ARTILLERY GUN TECHNICAL FIELD

[0001] The embodiments of the present disclosure generally relate to the field of aerodynamics and battlefield management systems. More particularly, the present disclosure relates to a system and method for controlling firing of an artillery gun in battlefield.BACKGROUND OF THE INVENTION

[0002] The subject matter disclosed in the background section should not be assumed or construed to be prior art merely because of its mention in the background section. Similarly, any problem statement mentioned in the background section or its association with the subject matter of the background section should not be assumed or construed to have been previously recognized in the prior art.

[0003] Fire control systems help artillery gun to point in direction of targets and to select the right quantity of propellant, which is an integral part of battlefield management. However, the army of a country will have a range of the artillery gun of varied capacities suiting different applications. Currently, every artillery gun has a separate fire control system that helps the artillery fire the projectile at the target, and each artillery gun will also be supplied with a range table for each projectile. This makes the entire battlefield complicated to manage and requires intense and long hours of training for the artillery gun crew to master the entire process, which adds to the cost and is also prone to human errors, which can increase the causalities due to collateral damage.

[0004] The development of a conventional fire control system involves two stages. The first stage is preparing the range table or firing data collection. The range table is a data handbook for the artillery gun and ammunition combination, and a specific projectile with a firing zone and elevations for various target locations, the projectile's mass, and metrological conditions like headwind, tailwind wind, andcrosswind. The interpolation of these data will give the artillery gun conditions for the new target location, done manually or by a system. The preparation of the range table for a single projectile involves almost 1400 firings, incorporating all possible variations in projectile mass, propellant temperature, and propellant mass.

[0005] The conventional range table preparation typically takes about one year to complete, requires highly skilled personnel to collect data, and is prone to errors. However, rectifying the errors requires the whole process to be repeated and incurs huge amounts of money in millions of dollars. The second stage involves the fire control system with three main parts: a “ballistic computer”, “sensor fusion” of sensors like laser range finder, barrel distortion meter, inertial measurement unit, and radar, and a “director” which calculates the moving target location.

[0006] The ballistic computer simulates the trajectory of the projectile using the data from the first stage, i.e., the range table; sensor fusion helps to correct the artillery gun parameters to increase the accuracy of the projectile target, and the director helps to strike a moving target. The difficulties in the preparation and analysis of the range table for the ballistic computer simulation and the logistics problems arising due to networking issues may be removed if a single fire control system which requires less data to predict the zone of firing and the elevation of barrel to hit the target is available.

[0007] Therefore, there is a need for improved system and method for efficiently controlling firing of the artillery gun in battlefield.SUMMARY

[0008] The following embodiments present a simplified summary to provide a basic understanding of some aspects of the disclosed invention. This summary is not an extensive overview, and it is not intended to identify key / critical elements or to delineate the scope thereof. Its sole purpose is to present some concepts in a simplified form as a prelude to the more detailed description that is presented later.

[0009] In an embodiment of the present disclosure, a method for controlling firing of an artillery gun is disclosed. The method includes receiving, by a reception module, one or more input parameters inputted by a user through a graphical user interface. The method further includes estimating, by an estimation module based on the one or more input parameters, a reduced order model of a projectile including one or more aerodynamic coefficients of the projectile of the artillery gun. Further, the method includes optimizing, by an optimization module using one or more scientific machine learning models, values of one or more aerodynamic coefficients. Furthermore, the method includes predicting, by a prediction module based on the optimized values of one or more aerodynamic coefficients, one or more output parameters, and a trajectory of the projectile using one or more scientific machine learning models. Thereafter, the method includes controlling, by a firing control module, the firing of the artillery gun based on one or more output parameters.

[0010] In some aspects of the present disclosure, the method includes estimating, by the estimation module based on one or more scientific machine learning models, the one or more aerodynamic coefficients of the artillery gun using one or more attributes of the trajectory of the projectile.

[0011] In some aspects of the present disclosure, one or more attributes of the trajectory of the projectile comprise at least one of location, velocity, acceleration, or orientation of the projectile in one whole trajectory with the highest range.

[0012] In some aspects of the present disclosure, the one or more input parameters comprise at least one of a target location, a location of the artillery gun, sensor fusion data, or the type of the projectile.

[0013] In some aspects of the present disclosure, the one or more output parameters comprise at least one of muzzle velocity, elevation, time of flight, appropriate artillery gun, zone of firing, quantity of propellant, maximum pressure, maximum acceleration, or maximum spin.

[0014] In some aspects of the present disclosure, the one or more aerodynamic coefficients comprise at least one of drag, lift, Magnus force, spin damping moment, or overturning moment.

[0015] In some aspects of the present disclosure, the sensor fusion data comprises at least one of wear and distortion of a barrel, laser range finder, inertial measurements, aerodynamic model of the projectile, current location of the artillery gun, or metrological conditions, including crosswind, tailwind, and headwind.

[0016] In some aspects of the present disclosure, the method includes predicting, by the prediction module based on one or more aerodynamic coefficients, an optimum trajectory of the projectile with minimum muzzle velocity and appropriate elevation that utilizes less amount of propellant.

[0017] In some aspects of the present disclosure, the reduced order model of the projectile comprises the one or more aerodynamic coefficients and the one or more output parameters of the artillery gun.

[0018] In another embodiment of the present disclosure, a system for controlling firing of an artillery gun is disclosed. The system includes an edge device with Graphical Processing Unit (GPU), an interactive display unit, and a communication device. The edge device includes a reception module configured to receive, one or more input parameters inputted by a user through a graphical user interface and an estimation module configured to estimate, based on the one or more input parameters, a reduced order model of a projectile including one or more aerodynamic coefficients the projectile of the artillery gun. The edge device further includes an optimization module configured to optimize, using one or more scientific machine learning models, values of the one or more aerodynamic coefficients. Further, the edge device includes a prediction module configured to predict, based on the optimized values of the one or more aerodynamic coefficients, one or more output parameters and a trajectory of a projectile using the one or more scientific machine learning models, and a firing control module configured to control firing of the artillery gun based on the one or more output parameters. The interactive display unitconfigured to accept the one or more input parameters from the user and display the one or more output parameters. The communication device configured to communicate the one or more output parameters with the user.BRIEF DESCRIPTION OF DRAWINGS

[0019] Various embodiments disclosed herein will become better understood from the following detailed description when read with the accompanying drawings. The accompanying drawings constitute a part of the present disclosure and illustrate certain non-limiting embodiments of inventive concepts. Further, components and elements shown in the drawings are not necessarily to scale, emphasis instead being placed upon clearly illustrating the principles of the present disclosure. For consistency and ease of understanding, similar components and elements are annotated by reference numerals in the exemplary drawings.

[0020] FIG. 1 illustrates a system for controlling the firing of an artillery gun, in accordance with an embodiment of the present disclosure.

[0021] FIG. 2 illustrates a system architecture of an edge device with Graphical Processing Unit (GPU), in accordance with an embodiment of the present disclosure.

[0022] FIG. 3 illustrates a method for controlling the firing of the artillery gun, in accordance with an embodiment of the present disclosure.

[0023] FIG. 4 illustrates a schematic diagram of a Universal Fire Control System (FCS), in accordance with an embodiment of the present disclosure.

[0024] FIG. 5 illustrates a schematic diagram displaying one or more output parameters and a trajectory of a projectile, in accordance with an embodiment of the present disclosure.

[0025] FIG.6A illustrates an architecture for predicting the trajectory and estimating the one or more aerodynamic coefficients, in accordance with an embodiment of the present disclosure.

[0026] FIG. 6B illustrates an architecture for optimizing values of one or more aerodynamic coefficients, in accordance with an embodiment of the present disclosure.

[0027] FIGS.7A-7D illustrates graphs depicting comparison of predicted and actual values of the one or more aerodynamic coefficients, in accordance with an embodiment of the present disclosure.

[0028] FIGS.8A-8D illustrates graphs depicting comparison of predicted and actual trajectories of the projectile, in accordance with an embodiment of the present disclosure.DETAILED DESCRIPTION

[0029] Inventive concepts of the present disclosure will now be described more fully hereinafter with reference to the accompanying drawings, plots, and photographs in which examples of one or more embodiments of inventive concepts are shown. Inventive concepts may, however, be embodied in different forms and should not be construed as limited to the embodiments set forth herein. Further, the one or more embodiments disclosed herein are provided to describe the inventive concept thoroughly and completely, and to fully convey the scope of each of the present inventive concepts to those skilled in the art. Furthermore, it should be noted that the embodiments disclosed herein are not mutually exclusive concepts. Accordingly, one or more components from one embodiment may be tacitly assumed to be present or used in any other embodiment.

[0030] The following description presents various embodiments of the present disclosure. The embodiments disclosed herein are presented as teaching examples and are not to be construed as limiting the scope of the present disclosure. The present disclosure should in no way be limited to the illustrative implementations, drawings, and techniques illustrated below, including the exemplary design and implementation illustrated and described herein, but may be modified, omitted, or expanded upon without departing from the scope of the present disclosure.

[0031] The following description contains specific information pertaining to embodiments in the present disclosure. The detailed description uses the phrases “in some embodiments” or “some implementations” which may each refer to one or more or all of the same or different embodiments or implementations. The term “some” as used herein is defined as “one, or more than one, or all.” Accordingly, the terms “one,” “more than one,” “more than one, but not all” or “all” would all fall under the definition of “some.” In view of the same, the terms, for example, “in an embodiment” or “in an implementation” refers to one embodiment or one implementation and the term, for example, “in one or more embodiments” refers to “at least one embodiment, or more than one embodiment, or all embodiments ”. Further, the term, for example, “in one or more implementations” refers to “at least one implementation, or more than one implementation, or all implementations.

[0032] The term “comprising,” when utilized, means “including, but not necessarily limited to;” it specifically indicates open-ended inclusion in the so-described one or more listed features, elements in a combination, unless otherwise stated with limiting language. Furthermore, to the extent that the terms “includes,” “has,” “have,” “contains,” and other similar words are used in either the detailed description, such terms are intended to be inclusive in a manner similar to the term “comprising.”

[0033] In the following description, for the purposes of explanation, various specific details are set forth in order to provide a thorough understanding of embodiments of the present disclosure. It will be apparent, however, that embodiments of the present disclosure may be practiced without these specific details. Several features described hereafter can each be used independently of one another or with any combination of other features.

[0034] The description provided herein discloses exemplary embodiments only and is not intended to limit the scope, applicability, or configuration of the present disclosure. Rather, the foregoing description of the exemplary embodiments will provide those skilled in the art with an enabling description for implementing any of the exemplary embodiments. Specific details are given in the following descriptionto provide a thorough understanding of the embodiments. However, it may be understood by one of the ordinary skilled in the art that the embodiments disclosed herein may be practiced without these specific details.

[0035] The terminology used herein is for the purpose of describing particular embodiments only and is not intended to be limiting of the disclosure. As used herein the description, the singular forms "a", "an", and "the" include plural forms unless the context of the invention indicates otherwise.

[0036] The terminology and structure employed herein are for describing, teaching, and illuminating some embodiments and their specific features and elements and do not limit, restrict, or reduce the scope of the present disclosure. Accordingly, unless otherwise defined, all terms, and especially any technical and / or scientific terms, used herein may be taken to have the same meaning as commonly understood by one having ordinary skill in the art.

[0037] Embodiments of the present disclosure will be described below in detail with reference to the accompanying figures. FIG. 1 to FIG. 8, discussed below, and the one or more embodiments used to describe the principles of the present disclosure are by way of illustration only and should not be construed in any way to limit the scope of the present disclosure. Those skilled in the art will understand that the principles of the present disclosure may be implemented in any suitably arranged system or device.

[0038] Further, a few of the figures in the accompanying drawings are represented in color for accurate illustration of results. The color drawings illustrate one or more results which cannot be adequately represented in black and white or gray scale. The color drawings are, therefore necessary to ensure proper interpretation of the disclosed invention.

[0039] Various aspects of the present disclosure provide a system and a method for controlling firing of an artillery gun in a battlefield.

[0040] Another aspect of the present disclosure provides an optimized fire control system for battlefield management.

[0041] Yet another aspect of the present disclosure provides an Artificial Intelligence (Al)-based portable edge device with Graphical Processing Unit (GPU) and method for predicting an appropriate artillery gun and a firing zone to hit a target.

[0042] Yet another aspect of the present disclosure acquires fast and inexpensive firing data using minimum firing.

[0043] FIG. 1 illustrates a system 100 for controlling firing of an artillery gun, in accordance with an embodiment of the present disclosure.

[0044] In one embodiment, the system 100 may be configured as a universal Fire Control System (FCS). The system 100 may be an edge Al-based system with sensor fusion. The system 100 may be intended to eliminate the need for a separate system that depends on the artillery gun and artillery shells for firing ammunition at targets.

[0045] The system 100 may comprise an edge device with Graphical Processing Unit (GPU) 102, an interactive display unit 104, and a communication device 106. The edge device 102 may be capable of housing and executing all core algorithms, including scientific machine learning models and sensor fusion algorithms. The edge device 102 may be configured to execute ballistics simulations for controlling the firing of the artillery gun. The edge device 102 with scientific machine learning models and sensor fusion may be integrated with one or more sensors and the interactive display unit 104 for interactive and accurate ballistics simulation for battlefield management. The interactive display unit 104 may be configured to accept one or more input parameters from user, namely an artillery gun crew, and may display one or more output parameters after simulation execution. The one or more output parameters may include trajectory details and gun orientation parameters required to achieve the desired target location.

[0046] The communication device 106 may be configured to communicate the one or more output parameters with the user. The communication device 106 may beconfigured to communicate target location of the artillery gun to the edge device 102 for ballistic simulation. The communication device 106 may be configured to receive projectile information from the edge device 102 and transfer the target location and the effectiveness of the projectile hit to the edge device 102 for further corrections.

[0047] In some aspects of the present disclosure, the communication device 106 may be configured to securely communicate through voice, data, and video.

[0048] FIG. 2 illustrates a system architecture 200 of the edge device 102, in accordance with an embodiment of the present disclosure. The edge device 102 may include a processor 202, a memory 204 coupled to the processor 202, an Input / Output (I / O) interface 206, a communication interface 208, one or more modules 210 (hereinafter also referred to as the “modules 210”), and a database 212. The processor 202 may control the operation of the edge device 102. The processor 202 may also be referred to as a Central Processing Unit (CPU). The memory 204 may provide instructions and data to the processor 202 for performing functions of the edge device 102. The memory 204 may include a Random Access Memory (RAM), a Read-Only Memory (ROM) and a portion of the memory 204 may also include Non-Volatile Random Access Memory (NVRAM). The processor 202 may perform logical and arithmetic operations based on instructions stored within the memory 204. The communication interface 208 may allow transmission and reception of data between the edge device 102 and the communication device 106. The communication interface 208 may include a transmitter, a receiver, and a single or multiple transmit antennas electrically coupled to the transmitter and the receiver of the communication interface 208.

[0049] The I / O interface 206 may include suitable logic, circuitry, interfaces, and / or codes that may be configured to receive input(s) and present (or display) output(s) on the edge device 102. For example, the I / O interface 206 may have an input interface and an output interface. The input interface may be configured to enable a user to provide input(s) to trigger (or configure) the edge device 102 to perform various operations such as but not limited to, providing input(s) to initiate fetchingof input data from the user, configure the edge device 102 to fetch the input data periodically, etc. Examples of the input interface may include, but are not limited to, a touch interface, a mouse, a keyboard, a motion recognition unit, a gesture recognition unit, a voice recognition unit, or the like. Aspects of the present disclosure are intended to include or otherwise cover any type of the input interface including known, related art, and / or later developed technologies without deviating from the scope of the present disclosure. The output interface may be configured to display (or present) output(s) by the edge device 102. In some aspects of the present disclosure, the output interface may provide the output(s) based on an instruction provided via a graphical user interface. Examples of the output interface of the I / O interface 206 may include, but are not limited to, a digital display, an analog display, a touch screen display, an appearance of a desktop, and / or illuminated characters.

[0050] The communication interface 208 may be configured to enable the edge device 102 to communicate with various entities of the system 200. Examples of the communication interface 208 may include, but are not limited to, a modem, a network interface such as an Ethernet card, a communication port, and / or a Personal Computer Memory Card International Association (PCMCIA) slot and card, an antenna, a radio frequency (RF) transceiver, a subscriber identity module (SIM) card, and a local buffer circuit. It will be apparent to a person of ordinary skill in the art that the communication interface 208 may include any device and / or apparatus capable of providing wireless or wired communications between the edge device 102 and various other entities of the system 200.

[0051] In one or more embodiments, the edge device 102 may be coupled to the database 212 that provides data storage space to the edge device 102. The database 212 may store information related to configuration parameters and other relevant information needed for the operation of the edge device 102. The database 212 may be accessed and updated by the edge device 102 for accessing the records stored in the database 212. The database 212 may correspond to a centralized database system configured to store and manage structured data. The database 212 may be large databases of same type or combination of different type such as structured databases,non-structured databases, or distributed databases. The database 212 may be a relational database organizing related data such as in a table, or a non-relational database organizing graphical and time series data. The database 212 may be implemented as a centralized database, Relational Database Management System (RDBMS), Non-Relational Database Management System, and Hierarchical Database Management System, and Network Database Management System. The edge device 102 may be connected to a storage medium for storing and managing the data. The storage medium may generally be one or more of, without limitation, disk drives, hard-disk arrays, solid state storage devices, Network Attached Storage (NAS) devices, tape libraries or other magnetic, non-tape storage devices, and optical media storage devices.

[0052] In some aspects of the present disclosure, the database 212 may be configured to store training data from one or more scientific machine learning models. The one or more scientific machine learning models may correspond to the Al-based models. The edge device 102 may utilize Al-based models for prediction and estimation of various parameters for controlling firing of the artillery gun.

[0053] The processor 202 may include one or more general purpose processors and / or one or more special purpose processors, a microprocessor, a digital signal processor, an application specific integrated circuit, a microcontroller, a state machine, or any type of programmable logic array. The processor 202 may include may include an intelligent hardware device including a general-purpose processor, such as, for example, and without limitation, a Central Processing Unit (CPU), an Application Processor (AP), a dedicated processor, or the like, a graphics-only processing unit such as a Graphics Processing Unit (GPU), a microcontroller, a Field-Programmable Gate Array (FPGA), a programmable logic device, a discrete hardware component, or any combination thereof.

[0054] The memory 204 may further include, but not limited to, non-transitory machine-readable storage devices such as hard drives, magnetic tape, floppy diskettes, optical disks, compact disc read-Only Memories (CD-ROMs), andmagneto-optical disks, semiconductor memories, such as ROMs, RAMS, programmable read-only memories PROMs), erasable PROMs (EPROMs), electrically erasable PROMs (EEPROMs), flash memory, magnetic or optical cards, or other type of media / machine-readable medium suitable for storing electronic instructions.

[0055] The modules 210 may include a reception module 214, an estimation module 216, an optimization module 218, a prediction module 220, a firing control module 222, and a transmission module 224. In an embodiment, the modules 210 may be combined to a single module, or each module of the modules 210 may be further subdivided into different modules with divided responsibilities.

[0056] The modules 210 may be implemented as a combination of hardware and programming (for example, programmable instructions) to implement one or more functionalities of the edge device 102. In non-limiting examples, described herein, such combinations of hardware and programming may be implemented in several different ways. For example, the programming for the modules 210 may be processor-executable instructions stored on a non-transitory machine-readable storage medium and the hardware for the processor 202 may comprise a processing resource (for example, one or more processors), to execute such instructions. In the present examples, the machine-readable storage medium may store instructions that, when executed by the processing resource, implement the modules 210. In such examples, the edge device 102 may also comprise the machine-readable storage medium storing the instructions and the processing resource to execute the instructions, or the machine-readable storage medium may be separate but accessible to the edge device 102 and the processing resource. In other examples, the modules 210 may be implemented using an electronic circuitry.

[0057] Although FIG. 1 and FIG. 2 illustrate one example of the system 100 and the system 200, various changes may be made to FIG. 1 and FIG. 2. For example, the system 200 may include any number of modules in any suitable arrangement. Further, in another example, the edge device 102 may include any number ofcomponents in addition to the components shown in FIG. 2. Further, various components in FIG. 1 and FIG. 2 may be combined, further subdivided, or omitted and additional components may be added according to particular needs.

[0058] FIG. 3 illustrates a method 300 for controlling firing of the artillery gun, in accordance with an embodiment of the present disclosure. The method 300 comprises a series of operation steps indicated by blocks 302 through 310. The processor 202 of the edge device 102 may perform the method 300 using the one or more modules 210 of the edge device 102.

[0059] At block 302, the reception module 214 of the edge device 102 may be configured to receive, one or more input parameters inputted by a user through the graphical user interface. The one or more input parameters may comprise at least one of a target location, a location of the artillery gun, sensor fusion data, or type of the projectile.

[0060] In some aspects of the present disclosure, the sensor fusion data may comprise at least one of wear and distortion of a barrel, laser range finder, inertial measurements, aerodynamic model of the projectile, current location of the artillery gun, or metrological conditions including crosswind, tailwind, and headwind. The edge device 102 with scientific machine learning models and sensor fusion 102 may be configured to estimate accurate measurements from multiple sensors and sense the sensor fusion data. The interactive display unit 104 may be configured to receive the one or more input parameters related to the sensor fusion data and transmit the one or more input parameters to the edge device 102.

[0061] At block 304, the estimation module 216 of the edge device 102 may be configured to estimate, based on the one or more input parameters, a reduced order model of the projectile including one or more aerodynamic coefficients of the projectile of the artillery gun. The one or more aerodynamic coefficients may comprise at least one of drag, lift, Magnus force, spin damping moment, or overturning moment.

[0062] At block 306, the optimization module 218 of the edge device 102 may be configured to optimize, using the one or more scientific machine learning models, values of the one or more aerodynamic coefficients. In a non-limiting example, optimization module 218 may use Physics-Informed Neural Network (PINN) as the one or more scientific machine learning model to estimate and optimize the values of the one or more aerodynamic coefficients.

[0063] In some aspects of the present disclosure, the edge device 102 may perform the method 300 as described in blocks 304 and 306 as an offline process. The estimation and the optimization of the one or more aerodynamic coefficients may be executed offline. The estimation and the optimization may be performed during non-real-time conditions (before deployment), i.e., during peacetime or before a war scenario, and not during active operation.

[0064] At block 308, the prediction module 220 of the edge device 102 may be configured to predict, based on the optimized values of the one or more aerodynamic coefficients, one or more output parameters and a trajectory of the projectile using the one or more scientific machine learning models. The prediction module 220 may use a modified point mass model as a loss function to predict the one or more output parameters and the trajectory.

[0065] The one or more output parameters may comprise at least one of muzzle velocity, elevation, time of flight, appropriate artillery gun, zone of firing, quantity of propellant, maximum pressure, maximum acceleration, or maximum spin. The reduced order model of the projectile may comprise the one or more aerodynamic coefficients and the one or more output parameters of the projectile of the artillery gun.

[0066] At block 310, the firing control module 222 of the edge device 102 may be configured to control firing of the artillery gun based on the one or more output parameters.

[0067] In some aspects of the present disclosure, the estimation module 216 may estimate, by the one or more scientific machine learning models, the one or more aerodynamic coefficients of the artillery gun using one or more attributes of the trajectory of the projectile. The one or more attributes of the trajectory of the projectile may comprise at least one of location, velocity, acceleration, or orientation of the projectile in one whole trajectory with a highest range.

[0068] In some aspects of the present disclosure, the prediction module 220 may predict, based on the one or more aerodynamic coefficients, an optimum trajectory of the projectile with minimum muzzle velocity and appropriate elevation that utilizes less amount of propellant.

[0069] FIG. 4 illustrates a schematic diagram 400 of the universal FCS, in accordance with an embodiment of the present disclosure. The development of the FCS may be performed in two phases, namely first phase 402 and second phase 404, as illustrated in FIG. 4.

[0070] The edge device 102 may prepare the reduced order model of the projectile based on mathematical model of ammunition in the first phase 402. The first phase 402 may be utilized to prepare the mathematical model of ammunition during non-real-time conditions. The mathematical model of ammunition may involve the estimation of the one or more aerodynamic coefficients of the projectile, such as (not limited to) drag (Cd) (Force equivalent term: Fdrag), lift (Cia) (Force equivalent term: Fiift), Magnus force (CNpa) (Force equivalent term: FMagnus), spin moment ((spin moment coefficient) Cis or (spin damping moment coefficient) Cip), overturning moment (Cma), Magnus moment (Cmpa) and pitch damping moment (Cmq) of the projectile as a function of Mach number. The Mach number (M) may be a dimensionless value representing ratio of speed of the projectile to speed of sound in the surrounding medium. The edge device 102 may use the one or more scientific machine learning models for estimating the one or more aerodynamic coefficients and may require only the location of the projectile, velocity, acceleration and orientation in one whole trajectory with the highest range.

[0071] If firing data in the form of a range table exists for the existing projectile, then the first phase 402 may be skipped entirely by providing the firing data to the second phase 404. In the second phase 404, the edge device 102 may receive, through the graphical user interface, one or more input parameters such as the target location, location of the artillery gun, sensor fusion data, and the type of the projectile to be fired. The one or more output parameters such as the muzzle velocity and the elevation may be predicted by optimizing the values of the one or more aerodynamic coefficients by directly taking the one or more aerodynamic coefficients from the first phase 402 or the existing range table. The existing firing data from all the artillery gun may be used to estimate the optimum artillery gun and the firing zone using an Al-based classification algorithm to achieve the desired target. Since the estimation is data-intensive, which is ideal only for the existing artillery gun, for new artillery gun, a reduced order model may be planned to estimate based on a minimum number of firing data leveraging the optimization of the PINN.

[0072] FIG. 5 illustrates a schematic diagram 500 displaying one or more output parameters and a trajectory of a projectile, in accordance with an embodiment of the present disclosure.

[0073] The edge device 102 may utilize the one or more input parameters from the graphical user interface developed using an open-source platform, for instance, Tkinter / custom Tkinter, coupled with a programming language, for instance Python, as illustrated in FIG. 5. The edge device 102 may run the one or more scientific machine learning models, for instance the machine learning models, with the sensor fusion data in the background. The edge device 102 may utilize the one or more input parameters to predict the one or more output parameters. In a non-limiting example, coordinates of the target location may be fed provided as the one or more input parameters. The edge device 102 may predict the one or more output parameters such as the muzzle velocity, the elevation, the time of flight, the type of the artillery gun and the amount of propellant denoted as zone in the FIG. 5. The edge device 102 may predict the trajectory of the projectile along with range, height, drift, gyro index, time of flight, and spin using the one or more aerodynamic coefficients.

[0074] In some aspects of the present disclosure, the edge device 102 may require only the target location as the input parameter. The edge device 102 may utilize the one or more scientific machine learning models to predict the artillery gun, firing zone, elevation, time of flight by incorporating the sensor fusion data such as the wear and distortion of the barrel measured by the barrel distortion meter, metrological conditions like crosswind, tailwind, and headwind, laser range finder, aerodynamic model of the projectile from the first phase 402 and current locations from Inertial Measurement Unit (IMU) with a Global Positioning System (GPS). This makes the edge device 102 operatable by personnel with minimum experience.

[0075] FIG. 6A illustrates an architecture 600-1 for predicting the trajectory and estimating the one or more aerodynamic coefficients, in accordance with an embodiment of the present disclosure.

[0076] As illustrated in FIG. 6A, the edge device 102 may predict the trajectory of the projectile and the one or more aerodynamic coefficients using the PINN machine learning techniques. In conventional Fire Control System (FCS), the one or more output parameters of the artillery gun from the firing data recorded in the range table may be prepared separately for every ammunition round. The range table preparation may take roughly 1400 firings while accounting for the variation of the mass of the projectile, different zones of firing, elevations and bearings of the artillery gun, the propellant temperature and the erosion of the artillery gun barrel. Making the range table is cumbersome and expensive, and utmost care should be taken while measuring and recording the parameters and the location of the artillery gun. The accuracy of predicting the parameters of the artillery gun to achieve the target depends on the type and nonlinearity of the interpolation scheme used in the FCS. This usually results in a significant drift from the intended target location and is corrected in subsequent trials.

[0077] In conventional FCS, the trajectory calculation may be done by integrating Newtons law of motion as given in Equation (1) and Equation (2):dV nm — = F (1)dtv’ly^ = T (2)where, m is the mass of the projectile, V is the velocity vector, co is the angular velocity vector, Iyis the moment of inertia of the projectile about any transverse axis, F is the force vector, and T is the torque vector.

[0078] Since solving the equations requires complete information on the forces and the moments acting on the body in the trajectory, the similarity parameters like drag coefficient (Cd), lift coefficient (Clα), Magnus force coefficient (CNP«), spin damping coefficient (Cip ), overturning moment coefficient (CM«), Magnus moment coefficient (CMpa), and pitch damping moment coefficient ((CMQ + CM«)) are determined experimentally or computationally. The assumption is that the parameters depend only on the flow Mach number and can completely define the forces and moments as given in Equation (3)- Equation (12):F Fdrag T T F Magnus T Fcorrions+ Fgravif;y(3)F TSpin+ T Magnus T ^overturning T Tpdch.-dampi.ng (4)Fdrag ~Cd.qinfSV (5)Flift=~ClaqinfS(V X X X 7) (6)Fuagnus ~ ~CNpa<linfS v %) s')Fcorriolis 2m i X V) (8)_ ClpqinfSdz(anx)xspin — |j_ CMpaqinfSd2(oj-x)(xxf'x£) ' Magnus ~ ](^)T1overturning = CMaqinfSd\v\(y x x) (H)(^Mq +CMa)clinfSd2(xxT (12pitch-damping Fi )qinf, S, d, x, V, andQ are dynamic pressure, frontal area, nominal diameter of the projectile, unit vector in the direction of the projectile, unit velocity vector, and angular velocity of the earth (rad / s), respectively.

[0079] The model that incorporates all these forces and moments is called the six degrees of freedom (6-DoF) model. Since solving this system requires elaborate calculation, three other models exist with different degrees of complexity: the vacuum trajectory model, the point mass model and the modified point mass model. The vacuum trajectory model assumes no air resistance and the only significant forces acting are gravitational force and Coriolis force. However, the vacuum model estimates and overpredicts the range and height of the trajectory. The point mass model reduces the error in calculating the trajectory by adding drag due to air in the model. This model also fails to capture the drift due to several factors, such as yaw and yaw rate at the barrel exit produced because of the barrel distortion, erosion and the in-bore balloting of the shot.

[0080] To overcome these issues, the present disclosure uses the modified point mass model. The modified point mass model relaxed the assumptions in the point mass model by taking lift force, Magnus force, and overturning moment using yaw of repose while calculating the net force acting on the projectile. In this model, the spindamping moment is decoupled from other moments. Calculating the trajectory of the projectile may be framed as an optimization problem, leveraging the vast data in range tables. By harnessing the capabilities of neural networks, a functional representation of the trajectory parameters may be effectively learned, enabling accurate predictions and efficient optimization. A neural network is a composite of interconnected neurons, where inputs are linearly combined with weights and biases and then transformed through a nonlinear activation function. However, optimizing the network weights and biases may typically require vast data, encompassingdiverse parametric variations such as projectile mass, elevation, bearing, and firing zones. Incorporating governing differential equations as regularization terms may significantly reduce the required training data and may enable efficient neural network training, leveraging physical laws to augment data-driven learning.

[0081] In some aspects of the present disclosure, the edge device 102 may estimate the range tables by leveraging trajectory information to calculate the one or more aerodynamic coefficients within a modified point mass model. Specifically, the edge device 102 may use the Physics-Informed Neural Network (PINN) to estimate key aerodynamic coefficients, including drag, lift, Magnus moment, spin, and overturning moment, from x, y, z, and spin data obtained from a single ammunition firing. The estimated coefficients may be utilized within the modified point mass model to predict the parameters of the artillery gun, such as elevation, bearing, and muzzle velocity, based on the target location, further demonstrating the capabilities of the PINN in solving inverse problems.

[0082] In some embodiments of the present disclosure, Computational Fluid Dynamics (CFD) simulations are conducted to investigate the flow field around an axisymmetric 155 mm projectile (modified M107 shell for the short-range test) with a mass of 42.7 kg, Ix= 0.1452 kg·m2(Moment of inertia about the rotational axis), Iy= 1.1861 kg·m2(Moment of inertia about any transverse axis) operating at Mach numbers ranging from 0.6 to 2.5. The yaw and yaw rate are assumed to be zero. The tailwind / headwind / crosswind is also neglected. Ansys Fluent is employed, utilizing a Shear Stress Transport (SST) k-co turbulence model to estimate the variation of the aerodynamic coefficients with the Mach number. Due to logistical constraints, a six-degree-of-freedom (6-DoF) model is used to predict the trajectory of the projectile, with aerodynamic coefficients estimated from CFD simulations. The projectile is simulated to be fired at an elevation of 5 degrees with a muzzle velocity of 805.8 m / s. In a non-limiting example, the International Civil Aviation Organization (ICAO) atmospheric model is adopted to account for atmospheric density, pressure, and temperature variations with altitude. Furthermore, the neural network incorporating the modified point mass model is utilized by the edge device 102 to estimate the oneor more aerodynamic coefficients, achieving prediction accuracy comparable to the 6-DoF model.

[0083] In some aspects of the present disclosure, a network is designed with time as the only input and x,y,z, spin rate, drag coefficient (Cd), lift coefficient (Clα), Magnus force coefficient (CNP«), spin damping coefficient (Cip), overturning moment coefficient (CM) as output. The physics-informed neural network (PINN) may be trained using a multi-task loss function, combining data loss and physics loss terms. The data loss terms may be constructed from the x, y, and z location data and spin rate data generated by a 6-DoF model of the projectile. The network architecture consists of 8 hidden layers, each with 20 neurons. Additionally, the differential equations of the modified point mass model may be incorporated as a regularization term (physics loss), enforcing adherence to fundamental physical principles. The data loss and physics loss terms calculated using the mean square error may be weighted such that the physics loss is always two orders of magnitude less than the data loss.

[0084] The neural network is optimized using the Adam algorithm with a learning rate of 1e-3 and a weight decay of 1e-3, and the tanh activation function may be employed. The predicted aerodynamic coefficients may be subsequently integrated into the modified point mass model to estimate the elevation, bearing, and muzzle velocity based on the target location by an inverse method using a second physics-informed neural network with the network parameters, the same as the first. The training iterations may be stopped while achieving an error of 1e-6 for data loss and 1e-2 for physics loss in both networks.

[0085] FIG. 6B illustrates an architecture 600-2 for optimizing values of the one or more aerodynamic coefficients, in accordance with an embodiment of the present disclosure. The edge device 102 may use the one or more scientific machine learning models for estimating the one or more aerodynamic coefficients and optimizing the values of the one or more aerodynamic coefficients. In a non-limiting example, the edge device 102 may utilize the PINN based scientific machine learning models to estimate and optimize the one or more aerodynamic coefficients.

[0086] In some aspects of the present disclosure, the estimation of the one or more output parameters may be achieved by optimizing the values of the one or more aerodynamic coefficients using a Force-moment equations, represented using Equations (13) and (14):dv / dt = Fdrag(Cd) + Flift(Clα) + FMagnus(CNpα) + FCoriolis / mdω / dt = (Toverturning(CMα) + TMagnus(CMpα) + TPitch-damping(CMq) + Tspin) / Iwherein v represents velocity vector in the Equation (13) and h represents angular velocity vector in the Equation (14). The edge device 102 may use the PINN with a tuned hyperparameter for accurate ballistics simulation and the prediction. The Fcomoiis in the Equation (13) may take care of the deflection of the projectile due to earth rotation.

[0087] In some aspects of the present disclosure, the system 100 (FCS) may be tested by synthetically creating the first phase firing data using six-degree-of-freedom trajectory estimator and estimating the one or more aerodynamic coefficients like drag, lift, Magnus force, Magnus moment, pitch damping moment, overturning moment, and spin damping moment using the PINN machine learning techniques. The International Civil Aviation Organization (ICAO) model has modelled the metrological variations. The muzzle velocity, elevation, and flight time may be predicted by optimizing the Equations (13) and (14) using the inverse technique in the PINN machine learning technique, and then this may be mapped to available artillery gun and the firing zone (mass / amount of the propellant). The system 100 in the present disclosure may also predict the minimum velocity and appropriate elevation from the available combinations, which require the least amount of propellant.

[0088] FIGS. 7A-7D illustrates graphs 700-1 to 700-4 depicting comparison of predicted and actual values of the one or more aerodynamic coefficients, in accordance with an embodiment of the present disclosure.

[0089] In some embodiments, the physics-informed neural network is successful in predicting the one or more aerodynamic coefficients such as drag coefficient (Cd), lift coefficient (Clα), Magnus force coefficient (CNP«), spin damping coefficient (Cip), overturning moment coefficient (CM«) while matching the range, height and drift with a mean square error of 1e-06 from a single fire. The drag coefficient variation with the Mach number predicted by the PINN is compared with the exact one, as illustrated in FIG. 7A.

[0090] It may be inferred from the FIG. 7 A that the drag divergence profile, a crucial metric in exterior ballistics matches the predicted and exact drag coefficient. The difference between the predicted and exact drag coefficient may indicate that the modified point mass model adapts to the six degrees of freedom model results. A similar trend may be observed in the lift coefficient (Clα), Magnus force coefficient (CNpa), spin damping coefficient (Cip), overturning moment coefficient (CM«) as illustrated in FIGS. 7B-7D respectively. This innovative proof of concept showcases a realistic trajectory model that streamlines operations by removing the necessity for range table preparation, ultimately saving billions of dollars and countless work hours.

[0091] In a non-limiting example, the edge device 102 may use parameters and corresponding values mentioned in Table 1 for predicting the range table. Table 1 illustrates trajectory data and PINN parameters for predicting the range table:Table 1: Trajectory Data and PINN Parameters for Range TableParameter ValueNetwork size 1 - 9 -8 - 20Activation Function tanhOptimizer AdamNumber of Iterations 40,000Learning Rate 0.001Loss Function Mean Square ErrorWeight Initialization XavierBatch Size Full-batchFramework PyTorchMuzzle velocity 805.8 m / sDiameter 155 mmMass 42.7 kg

[0092] In a non-limiting example, the edge device 102 may use parameters and corresponding values mentioned in the Table 2 for the FCS to predict the one or more output parameters. The Table 2 illustrates trajectory data and PINN parameters for the FCS:Table 2: Trajectory Data and PINN Parameters for the FCSNetwork ParametersParameter ValueNetwork size 1 - 4- 8 - 20Activation Function tanhOptimizer AdamNumber of Iterations 40,000Learning Rate 0.001Loss Function Mean Square Error Weight Initialization XavierBatch Size Full-batchFramework PyTorchTraining DataX 4367.65y 0z 19.2

[0093] FIGS. 8A-8D illustrates graphs 800-1 to 800-4 depicting comparison of predicted and actual trajectories of the projectile, in accordance with an embodiment of the present disclosure.

[0094] In some aspects of the present disclosure, the modified point mass model, enhanced with PINN-predicted aerodynamic coefficients along the trajectory, is subsequently integrated into a second Physics-Informed Neural Network (PINN) with the same network parameters as the first PINN. By leveraging the target location as the only known data, the PINN optimizes critical parameters, including flight time, muzzle velocity, elevation, and bearing of the artillery gun. The predicted results are verified by comparing exact values illustrated in Table 3:Table 3: Comparison of PINN prediction with exact values for one or more output parametersMuzzle Elevation Bearing Time of flight velocity (degree) (degree) (s)(m / s)PINN 801.73 5.02 0.04 10.35Exact 805.8 5.0 0.0 10.4

[0095] The prediction error of the parameters of the artillery gun is only 0.5%. Along with the parameters, the network successfully predicts the complete trajectory without additional computations. The predicted trajectory details, such as range versus height, drift, and spin rate, are verified through a comparison with exact values, as illustrated in FIGS. 8A-8D, respectively. The results demonstrate that the network accurately predicts the trajectory from the target location alone.

[0096] The unique feature of the present disclosure is that the FCS may predict the minimum velocity and appropriate elevation from the available combinations, which require the least propellant amount, as shown in FIG. 8B. As illustrated in FIG. 8B, the trajectory predicted by the FCS is represented in dotted red and another trajectory with a high muzzle velocity in a blue solid line (or high propellant mass) to reach the same target location of (13875.35 m, 0 m, 0 m), which is calculated using the conventional solver (six degrees of freedom solver). So, the FCS is a versatile tool for technical and tactical fire control and battlefield management. The FCS may keep the cost of operation significantly low by selecting the least propellant to achieve the target. It is clear from the FIG. 8B that the PINN based solver is successful in predicting the trajectory operating cost of the artillery gun. The network size of the PINN needed is only 1 hidden layer with four neurons with tanh activation function to predict the trajectory details and artillery gun conditions such as muzzle velocity and elevation which makes the implementation computationally inexpensive.

[0097] Referring to the technical abilities and advantageous effect of the present disclosure, operational advantages that may be provided by one or more embodiments may include predicting the appropriate artillery gun, the firing zone,the trajectory and the aerodynamic coefficients based on the physics inspired neural networks and Artificial Intelligence based techniques. The present disclosure may acquire fast and inexpensive firing data using minimum firing. The FCS may be operatable by personnel with minimum experience. The present disclosure predicts the minimum velocity and appropriate elevation with least amount of propellant

[0098] Those skilled in the art will appreciate that the methodology described herein in the present disclosure may be carried out in other specific ways than those set forth herein in the above disclosed embodiments without departing from essential characteristics and features of the present invention. The above-described embodiments are therefore to be construed in all aspects as illustrative and not restrictive.

[0099] The drawings and the forgoing description give examples of embodiments. Those skilled in the art will appreciate that one or more of the described elements may well be combined into a single functional element. Alternatively, certain elements may be split into multiple functional elements. Elements from one embodiment may be added to another embodiment. For example, orders of processes described herein may be changed and are not limited to the manner described herein. Any combination of the above features and functionalities may be used in accordance with one or more embodiments.

[0100] In the present disclosure, each of the embodiments has been described with reference to numerous specific details which may vary from embodiment to embodiment. The foregoing description of the specific embodiments disclosed herein may reveal the general nature of the embodiments herein that others may, by applying current knowledge, readily modify and / or adapt for various applications such specific embodiments without departing from the generic concept, and, therefore, such adaptations and modifications are intended to be comprehended within the meaning of the disclosed embodiments. It is to be understood that the phraseology or terminology employed herein is for the purpose of description and is not limited in scope.

Claims

I / We claim:

1. A method (300) for controlling firing of an artillery gun, the method (300) comprising:receiving (302), by a reception module (214), one or more input parameters inputted by a user through a graphical user interface;estimating (304), by an estimation module (216) based on the one or more input parameters, a reduced order model of a projectile including one or more aerodynamic coefficients of the projectile of the artillery gun;optimizing (306), by an optimization module (218) using one or more scientific machine learning models, values of the one or more aerodynamic coefficients;predicting (308), by a prediction module (220) based on the optimized values of the one or more aerodynamic coefficients, one or more output parameters and a trajectory of the projectile using the one or more scientific machine learning models; andcontrolling (310), by a firing control module (222), firing of the artillery gun based on the one or more output parameters.

2. The method (300) as claimed in claim 1, the method (300) comprises:estimating, by the estimation module (216) based on the one or more scientific machine learning models, the one or more aerodynamic coefficients of the artillery gun using one or more attributes of the trajectory of the projectile.

3. The method (300) as claimed in claim 2, wherein the one or more attributes of the trajectory of the projectile comprise at least one of location, velocity, acceleration, or orientation of the projectile in one whole trajectory with a highest range.

4. The method (300) as claimed in claim 1, wherein the one or more input parameters comprise at least one of a target location, a location of the artillery gun, sensor fusion data, or type of the projectile.

5. The method (300) as claimed in claim 1, wherein the one or more output parameters comprise at least one of muzzle velocity, elevation, time of flight, appropriate artillery gun, zone of firing, quantity of propellant, maximum pressure, maximum acceleration, or maximum spin.

6. The method (300) as claimed in claim 1, wherein the one or more aerodynamic coefficients comprise at least one of drag, lift, magnus force, spin damping moment, or overturning moment.

7. The method (300) as claimed in claim 4, wherein the sensor fusion data comprise at least one of wear and distortion of a barrel, laser range finder, inertial measurements, aerodynamic model of the projectile, current location of the artillery gun, or metrological conditions including crosswind, tailwind, and headwind.

8. The method (300) as claimed in claim 1, the method (300) comprises:predicting, by the prediction module (220) based on the one or more aerodynamic coefficients, an optimum trajectory of the projectile with minimum muzzle velocity and appropriate elevation that utilizes less amount of propellant.

9. The method (300) as claimed in claim 1, wherein the reduced order model of the projectile comprises the one or more aerodynamic coefficients and the one or more output parameters of the projectile of the artillery gun.

10. A system (100) for controlling firing of an artillery gun, the system comprising:an edge device with Graphical Processing Unit (GPU) (102) comprising:a reception module (214) configured to receive, one or more input parameters inputted by a user through a graphical user interface;an estimation module (216) configured to estimate, based on the one or more input parameters, a reduced order model of a projectile including one or more aerodynamic coefficients of the projectile of the artillery gun;an optimization module (218) configured to optimize, using one or more scientific machine learning models, values of the one or more aerodynamic coefficients;a prediction module (220) configured to predict, based on the optimized values of the one or more aerodynamic coefficients, one or more output parameters and a trajectory of the projectile using the one or more scientific machine learning models; anda firing control module (222) configured to control firing of the artillery gun based on the one or more output parameters;an interactive display unit (104) configured to accept the one or more input parameters from the user and display the one or more output parameters; anda communication device (106) configured to communicate the one or more output parameters with the user.

Images