A method for predicting residual velocity of penetration based on acceleration signal

Abstract

The application provides a penetration residual velocity prediction method based on acceleration signals, which divides the projectile penetration process into three penetration states of a projectile head partially entering a target, the projectile head completely entering the target and the projectile head partially leaving the target, determines the projectile overload expression of each penetration state, and then constructs the motion equation of the projectile penetration process; for a specified type of projectile, the motion equations of the projectile penetration process in the three penetration states are comprehensively utilized to generate the overload time history data of various working conditions; the overload time history data is divided into three intervals by using the acceleration peak value; for each interval, the residual velocity prediction formula with the initial velocity and the penetration time as the independent variables is constructed by data fitting; when the residual velocity is actually predicted, the corresponding prediction formula is selected for residual velocity prediction according to the acceleration peak value in the penetration process. The application can be directly carried on the fuze and realizes real-time prediction only by using the initial velocity, the penetration time and the acceleration of the three sensor sensing signals in the penetration process.

Description

Technical Field

[0001] This invention belongs to the field of penetration fuse detonation point identification technology, specifically relating to a method for predicting the remaining penetration velocity based on acceleration signals. Background Technology

[0002] For projectiles that penetrate hard targets, cavitation is the core control mode. It requires that after the fuse identifies the projectile's penetration of the target (out of the target), it can control the warhead to detonate precisely within a preset distance behind the target according to the projectile's motion state, so as to achieve maximum destructive power.

[0003] To achieve this goal, the fuze system must acquire and process two key parameters in real time: the ejection point and the remaining velocity. However, the actual penetration environment is extremely complex, with high-frequency oscillations and various interferences often superimposed on the impact overload signal, making it extremely challenging to accurately identify the ejection state and determine the remaining velocity. Therefore, researching high-precision methods for determining the remaining velocity is currently a hot topic in the field of penetration fuze detonation point identification technology.

[0004] Currently, there are three main representative patented technologies and implementation methods for predicting the residual velocity of projectiles during the penetration of concrete strength targets:

[0005] (a) A method for predicting the failure behavior of a projectile penetrating a reinforced concrete target plate (Application No.: 201911010512.5). This method divides the projectile penetration process into three physical stages: penetration cratering, tunneling, and back-target impingement. During implementation, the energy consumption of each stage is calculated separately—including energy consumption for cratering, tunneling, concrete shear impingement, and steel reinforcement tensile failure. Based on the law of conservation of energy, the initial kinetic energy of the projectile is subtracted from the total energy consumption to determine the remaining velocity after penetration. This method theoretically solves for the remaining velocity, and the predicted results may differ significantly from the actual situation.

[0006] (b) A method for state estimation and adaptive detonation point control for penetrating complex thick targets (Application No.: 202410593718.X). This scheme utilizes finite element analysis (FEM) technology to establish a dynamic model of the projectile and complex media (such as concrete, rock, and steel plates with different reinforcement ratios). By setting up a concrete plastic damage model (CDP) and an erosion contact algorithm, the simulated velocity-time and acceleration-time curves are extracted in batches. This method, by establishing a simulation database covering multiple parameters, can quickly assess the impact of different target variables (such as thickness and strength) on residual velocity loss, providing a basis for the design and improvement of weapon systems. However, this scheme relies on finite element analysis software, requires mesh generation and finite element calculation, resulting in a large computational load, making it unsuitable for direct deployment onto projectiles.

[0007] (c) A method for state estimation and adaptive detonation point control for penetrating complex thick targets (202410593718.X). This scheme constructs an "expert knowledge system" based on dynamic simulation and range test data, covering prior behavioral information under different working conditions (such as entry / exit thresholds, locking time, etc.). During fuze operation, dynamic identification is performed by combining the envelope characteristics of the overload signal acquired in real time, and the fourth-order Runge-Kutta method is used to calculate the acceleration signal in real time to obtain the projectile's residual velocity. Finally, by fusing the prior residual velocity range with the real-time calculation results, the target residual velocity is finely identified and the detonation delay is adaptively determined. This scheme requires real-time calculation using the Runge-Kutta algorithm, which is complex and not suitable for direct deployment to projectiles.

[0008] It is evident that the existing technology using finite element software can obtain the remaining velocity prediction results relatively accurately. However, this method not only takes a long time to obtain the results, but also requires known parameters such as the target plate strength and thickness, and cannot be directly deployed into the projectile's fuse for calculation during the penetration process. Summary of the Invention

[0009] In view of this, the present invention provides a method for predicting the remaining penetration velocity based on acceleration signals. It only requires three sensor signals during the penetration process: initial velocity, penetration time, and maximum overload value. It can be directly mounted in the fuze to achieve real-time prediction.

[0010] To solve the above-mentioned technical problems, the present invention is implemented as follows.

[0011] A method for predicting residual penetration velocity based on acceleration signals, comprising: Step 1: Divide the projectile penetration process into three penetration states: partial projectile entry into the target, complete projectile entry into the target, and projectile separation from the target. Determine the projectile overload expression for each penetration state. Then, the equations of motion for the projectile penetration process are constructed; Step 2: For a specified projectile type, comprehensively utilize the projectile penetration process motion equations under three penetration states to generate overload time history data for various operating conditions, including penetration time. Remaining speed And peak acceleration; using peak acceleration as the segmentation criterion, the overload time history data is divided into three data intervals; Step 3: Within each data interval, perform regression fitting using a nonlinear mapping model to establish a model based on the initial velocity. With penetration time The formula for predicting residual velocity is given by the independent variable. Step 4: When actually predicting the remaining velocity, extract the peak acceleration during the penetration process, select the corresponding remaining velocity prediction formula based on the data range where the peak acceleration is located, and substitute it into the measured initial velocity and penetration time to obtain the predicted remaining velocity. .

[0012] Preferably, in step 1, the projectile penetration process is divided into three penetration states: partial projectile entry into the target, complete projectile entry into the target, and projectile separation from the target, and a projectile overload expression is determined for each penetration state. Specifically, it includes: Axial stress on the arc surface of the warhead By integrating along the projectile's axis, an expression for the projectile's axial penetration resistance is constructed, which is the overall expression for projectile overload. Based on the different lengths of the projectile's arc within the target plate under three penetration conditions, the upper and lower limits of the integral of the overall projectile overload expression are adjusted to obtain sub-expressions for projectile overload under the three penetration conditions, thus obtaining the projectile overload expression for each penetration condition. .

[0013] Preferably, the projectile overload expression for each penetration state is... for: Let the angle between the line connecting the centers of curvature of the projectile and the projectile axis be... ; to reduce the axial stress on the arc surface of the warhead The integral is converted into Angle integral; With the warhead partially impacting the target, the projectile overload expression is derived by integrating the portion of the warhead surface from the tip to the frontal boundary of the target plate:

[0014] in, This refers to the warhead coefficient. The diameter of the bullet, For the normal stress on the warhead surface, It is the coefficient of sliding friction at the interface; For the bullet tip horn, The front boundary of the target plate horn, , , Indicates the projectile's penetration displacement; With all warheads in target position, integrating over the entire warhead surface, the projectile overload expression is:

[0015] In the projectile-target separation state, integrating over the portion of the projectile surface from the target plate's back boundary to the projectile's final position, the projectile overload expression is:

[0016] in The boundary of the back of the target plate horn:

[0017] in, The thickness is the target plate thickness.

[0018] Preferably, in step 1, the equation of motion for the projectile penetration process is: based on the projectile overload expression Based on Newton's second law, construct the equation of motion of the projectile during the penetration of the target plate: (I) in, For the mass of the projectile, This refers to the acceleration during the projectile's penetration process.

[0019] Preferably, in step 2, the step of generating overload time history data for various working conditions by comprehensively utilizing the projectile penetration process motion equations under three penetration states for a specified projectile type specifically includes: Step 21: Determine the normal stress on the warhead surface based on the cavity expansion theory. The expression: (II) in, A , B The constant is a dimensionless target material. Y and These represent the yield strength and density of the target plate material, respectively. It is the expansion velocity of the cavity interface; determined by the projectile penetration velocity. The expansion velocity of the cavity interface can be derived as the velocity of the particle particles at the projectile-target interface. ; Axial stress on the surface of the warhead If we decompose the structure and assume that the tangential stress on the warhead surface is determined by the interfacial sliding friction, then we have: (III) in, The angle between the line connecting the centers of curvature of the projectile and the projectile axis; It is the coefficient of sliding friction at the interface; Step 22: Combine equations (I), (II), and (III) and simplify to obtain the differential equation: (IV) Among them, coefficient and They are respectively: , , in, Projectile penetration velocity , This refers to the warhead coefficient. The diameter of the bullet, For the mass of the projectile; Step 23: Use the fourth-order Runge-Kutta algorithm to solve the differential equation of formula (IV) to generate a large amount of overload time history data for various operating conditions.

[0020] Preferably, the operating condition is configured as follows: For different target plate strengths, target plate thicknesses, and initial penetration velocities By combining these methods, different operating conditions can be obtained.

[0021] Preferably, in step 3, the nonlinear mapping model is a quadratic polynomial model or a nonlinear hybrid model; The nonlinear hybrid model is as follows:

[0022] in, These are the model parameters for the nonlinear hybrid model.

[0023] Preferably, in step 2, the segmented intervals for constructing the three acceleration peaks are: [0, 1w g ], [1w g 1.5w g ], [1.5w g 4w g ];w g It represents the acceleration due to gravity.

[0024] Beneficial effects: (1) The input parameters required for the remaining velocity prediction of the present invention are only the initial velocity, penetration time and maximum overload value that the sensor can directly collect during the penetration process. There is no need to know the target plate strength, thickness, reinforcement ratio and other working condition information that cannot be determined in advance in the actual penetration scenario. It can be used directly in the fuze system in real time, which greatly improves the feasibility and practicality in the real penetration environment.

[0025] (2) Existing technologies rely on finite element simulation, which requires complex modeling, mesh generation and long-term iterative calculation, and cannot be used in projectile fuses. This method only requires a preliminary dataset construction and formula fitting for a specific type of projectile. Subsequent predictions are calculated quickly by fitting the formula. There are no complex models or high computing power requirements. The computational resources are extremely low, which fully meets the requirements of lightweight fuses and real-time solution.

[0026] (3) This invention innovatively introduces overload peak value as the basis for interval division, splits the originally overlapping multi-value mapping data into non-overlapping intervals, and then fits the prediction formula in intervals, effectively eliminating the many-to-many mapping ambiguity of initial velocity, penetration time and remaining velocity, realizing interval-based accurate prediction, and meeting the accuracy requirements of accurate detonation of penetration fuse.

[0027] (4) The patents (a) and (b) in the background technology require known working parameters and can only be calculated individually, which is time-consuming; however, the working parameters cannot be predicted during the actual penetration of the projectile, and the fuze cannot be loaded with a system that can be used for finite element simulation. This method avoids this approach, using the widely accepted cavity expansion theory and the projectile surface penetration stress formula, and the fourth-order Runge-Kutta algorithm to numerically obtain a large amount of working condition data, and to perform quadratic polynomial formula fitting and nonlinear hybrid formula fitting. The fitted formula only requires the three parameters that are directly known from the sensors: penetration time, initial velocity, and overload peak value.

[0028] (5) The patent (c) in the background technology requires the construction of an expert knowledge system for multi-condition penetration datasets, but it cannot cover all possible conditions. The theoretical model of this method is applicable to various conditions, including target plate thickness, target plate strength, initial velocity and other possibilities can be arbitrarily selected, and its fitting formula has a wide range of applicability. Attached Figure Description

[0029] Figure 1 This is a flowchart of the penetration residual velocity prediction method based on acceleration signals according to an embodiment of the present invention; Figure 2 A schematic diagram of the process of a projectile penetrating a concrete target plate; Figure 3 This is a schematic diagram illustrating the solution process of the Runge-Kutta algorithm. Figure 4 The following are data distribution plots for an example where initial velocity and penetration time are independent variables and remaining velocity is the dependent variable: (a) is a data distribution plot where initial velocity is the independent variable and remaining velocity is the dependent variable; (b) is a data distribution plot where penetration time is the independent variable and remaining velocity is the dependent variable. Figure 5 A three-dimensional image of penetration time and initial velocity versus remaining velocity; Figure 6 To introduce a four-dimensional image of the peak acceleration region, penetration time, initial velocity, and remaining velocity; Figure 7 The data fitting effect of the quadratic polynomial model; (a) comparison of the original data and the fitted surface; (b) comparison of the predicted value and the actual value; Figure 8The data fitting effect of the nonlinear hybrid model; (a) comparison of the original data and the fitted surface; (b) comparison of the predicted value and the actual value; Figure 9 To compare the fitting effects and residual distributions of regression fitting using a quadratic polynomial model and a nonlinear hybrid model in three data intervals. Detailed Implementation

[0030] This invention provides a method for predicting the remaining penetration velocity based on acceleration signals. The basic idea is as follows: Step 1: Divide the projectile penetration process into three penetration states: partial projectile entry into the target, complete projectile entry into the target, and projectile separation from the target. Determine the projectile overload expression for each penetration state. Then, the equations of motion for the projectile penetration process are constructed; Step 2: For a specified projectile type, comprehensively utilize the projectile penetration process motion equations under three penetration states to generate overload time history data for various operating conditions, including penetration time. Remaining speed And the peak acceleration (also known as the peak overload); using the peak acceleration as the segmentation criterion, the overload time history data is divided into three data intervals; Step 3: Within each data interval, perform regression fitting using a nonlinear mapping model to establish a model based on the initial velocity. With penetration time The formula for predicting residual velocity is given by the independent variable. Step 4: When actually predicting the remaining velocity, extract the peak acceleration during the penetration process, select the corresponding remaining velocity prediction formula based on the data range where the peak acceleration is located, and substitute it into the measured initial velocity and penetration time to obtain the predicted remaining velocity. .

[0031] As can be seen, this invention focuses on the practical constraint of "unknown target conditions". It does not require prior knowledge of target material, thickness and other prior information. It can achieve rapid and autonomous estimation of the remaining velocity based solely on the real-time acquisition signal of the fuze. It can be used directly in the fuze system in real time and has wide applicability. It provides reliable support for the adaptive delay detonation control of intelligent penetration fuzes.

[0032] Furthermore, this invention innovatively introduces the acceleration overload peak value as a segmentation criterion, dividing the data into three intervals. Within each interval, a nonlinear mapping model is used for regression fitting to establish a formula for predicting the remaining velocity with the initial velocity and penetration time as independent variables. The introduction of the acceleration peak value effectively solves the problem of overlapping multi-value mappings, achieving accurate interval-based prediction of the remaining velocity and meeting the real-time requirements for precise fuse detonation.

[0033] The present invention will now be described in detail with reference to the accompanying drawings and embodiments.

[0034] Figure 1 A flowchart of a penetration residual velocity prediction method based on acceleration signals according to an embodiment of the present invention is shown. As shown in the figure, it includes the following steps: Step 1: Constructing the normal stress on the warhead surface based on the cavity expansion theory It is decomposed into axial stress on the surface of the warhead. .

[0035] In ballistics, the cavity expansion theory is a widely accepted model for penetration resistance. For the process of a projectile penetrating a concrete target, such as... Figure 2 As shown, the diameter of the projectile is D The radius of curvature of the warhead is R The mass of the projectile is m The line connecting the centers of warhead curvature and the penetration velocity The angle between the directions is Because the warhead penetrates axially, therefore It is also the angle between the line connecting the centers of curvature of the warhead and the warhead axis. Regardless of how the model is improved, the final normal stress on the warhead surface... All can be represented as: (1) in, A , B The constant is a dimensionless target material. Y and These represent the yield strength and compaction density of the target plate material, respectively. It is the expansion velocity of the cavity interface. It is determined by the projectile penetration velocity. The expansion velocity of the cavity interface can be derived as the velocity of the particle particles at the projectile-target interface. : (2) For concrete, the dimensionless target constant is determined by equation (3): (3) in, The initial density of the concrete material. For the initial penetration velocity, This refers to the projectile head coefficient; Tangential stress on the warhead surface It is believed to be determined by the sliding friction of the interface: (4) in, It is the coefficient of friction of the interface sliding. Normal stress on the surface of the warhead.

[0036] Therefore, the axial stress on the warhead surface The expression is: (5) It can be seen that, through the expression of formula (5), It is the coefficient of interfacial sliding friction, therefore the axial stress on the arc surface of the warhead. Only with and normal stress Related, while normal stress It can be obtained through formula (1).

[0037] Step 2: Apply axial stress to the arc surface of the projectile. Integrating along the projectile's axis, we construct the expression for the projectile's axial penetration resistance. This refers to projectile overload. The projectile penetration process is divided into three penetration states: partial projectile entry into the target, complete projectile entry into the target, and projectile separation from the target. The projectile overload expression for each penetration state is determined.

[0038] Since the warhead is a pointed oval shape with the positive penetration velocity direction as its axis of rotation, considering a circular arc element on the warhead surface, we have: (6) Introducing the warhead coefficient Equation (6) becomes: (7) For micro-element surfaces Axial stress Integrating along the projectile's axis yields the projectile's axial penetration resistance. That is, projectile overload: (8) in The initial angle for integration, i.e., the angle corresponding to the tip of the bullet. Angle; the terminating angle of the integral Corresponding to the end position of the corresponding warhead horn.

[0039] Combination Figure 2 The projectile penetration process is divided into three penetration states: partial target entry, complete target entry, and target separation. Based on the different lengths of the projectile's arc within the target plate under these three penetration states, the upper and lower limits of the integral of the overall projectile overload expression are adjusted to obtain sub-expressions for projectile overload under each of the three penetration states, thus obtaining the projectile overload expression for each penetration state: (1) Under the condition that the projectile partially enters the target, the integral over the partial projectile surface from the projectile tip to the front boundary of the target plate is given by the following expression for the projectile overload: (9) in, This refers to the warhead coefficient. The diameter of the bullet, For the normal stress on the warhead surface, It is the coefficient of sliding friction at the interface; For the bullet tip horn, The front boundary of the target plate horn, , , Indicates the projectile's penetration displacement; (2) With all warheads in the target state, integrating over the entire warhead surface, the projectile overload expression is: (10) (3) In the case of the projectile separation from the target, the integral over the portion of the projectile surface from the back boundary of the target plate to the end position of the projectile is given by the projectile overload expression: (11) in The boundary of the back of the target plate horn: (12) in, The thickness is the target plate thickness.

[0040] Step 3: Based on the projectile overload expression, construct the equation of motion for the projectile penetration process.

[0041] Based on the axial penetration resistance of the projectile and Newton's second law, the equation of motion of the projectile during the penetration of the target plate can be obtained: (13) in, For the mass of the projectile, Let v be the projectile penetration velocity. This represents the total acceleration during the projectile's penetration process.

[0042] Step 4: For a specified projectile model, generate overload time history data for various working conditions by comprehensively utilizing the projectile penetration process motion equations under three penetration states.

[0043] For a specific type of projectile, with its projectile geometry and mass remaining constant, the projectile's performance varies depending on the target plate strength, target plate thickness, and initial penetration velocity. By combining these parameters, different working conditions are obtained. Using the parameters of each working condition as input, and employing the motion equations of the projectile penetration process, the output of the projectile's motion state under each working condition is generated, including the penetration time. and remaining speed This invention also includes a maximum overload value.

[0044] In one preferred embodiment, the fourth-order Runge-Kutta algorithm is used to calculate the overload time history of a specific projectile type, generating overload time history data for various operating conditions. Specifically: Combining equations (13), (11), and (5) and simplifying them, we get: (14) Among them, coefficient and They are respectively: ; .

[0045] The differential equation in equation (14) is solved using the high-precision fourth-order fixed-step Runge-Kutta algorithm. The standard first-order explicit differential equation is: (15) Assume the initial value of the system state vector is Define the computation time step h According to the definition of the derivative, equation (16) can be rewritten as: (16) in: (17) Since equation (14) is a higher-order ordinary differential equation, let Then it can be transformed into a system of first-order explicit differential equations: (18) in Indicates the displacement of the projectile. This indicates the velocity of the projectile.

[0046] Combining the integral expressions for the warhead in three typical cases given by equations (9), (10), and (11), state vectors are used to solve the problem using the Runge-Kutta algorithm. Represents the displacement of the projectile, corresponding to equation (18) State vector Represents the projectile velocity, corresponding to equation (18) ; H Let be the thickness of the target plate. Then, under three typical conditions, the process of an ovoid projectile penetrating a single-layer concrete strength target plate is as follows: Phase 1: Part of the warhead enters the target plate. , Let this represent the length of the warhead. Integrating this portion of the warhead surface yields: (19) in , .

[0047] Phase 2, all warheads enter the target plate. At this point, integrating over the entire surface of the warhead yields: (20) Phase 3, some warheads leave the target plate. At this point, the integral over the surface of this portion of the warhead is: (twenty one) in .

[0048] like Figure 3 As shown, the Runge-Kutta algorithm can be programmed and solved using the above integral formula. Each run of the algorithm first requires inputting projectile parameters (projectile diameter, projectile length, projectile radius of curvature, projectile mass, etc.), target parameters (target thickness, material constitutive model, etc.), and the projectile-target interface friction coefficient, among other projectile-target system parameter types. Then, the initial position variable of the projectile is defined. and initial velocity variable A while loop is used, starting when the projectile tip coincides with the target plate interface, and then the loop continues as the projectile displacement... When the projectile's length is less than the sum of the target plate thickness and the projectile's length, the drag function is integrated and the position and velocity are updated; otherwise, the loop is exited, and the projectile's acceleration history curve is plotted and stored. The process of the projectile penetrating the target plate is divided into three stages: the projectile partially enters the target plate, the projectile completely enters the target plate, and the projectile partially leaves the target plate. The integration range can be obtained from the above. In a single time step, the projectile's penetration of the target plate belongs to only one stage. Therefore, the integration range is updated in real time according to the corresponding formula to obtain the axial drag value for each time step. Combining Newton's second law and the fourth-order Runge-Kutta algorithm, the changes in displacement and velocity are calculated and updated until the projectile completely leaves the target. After this, according to theory, the projectile will not experience drag, therefore the projectile velocity... Remains unchanged, displacement It increases at a constant rate.

[0049] Using the Runge-Kutta algorithm, for a specific projectile model with constant parameters such as projectile geometry and mass, four different target plate strengths (C40, C60, C80, C100), different target plate thicknesses (1m, 2m, 3m, 4m, 5m, 6m), and different initial penetration velocities (800m / s, 1000m / s, 1200m / s, 1500m / s) were combined to obtain 96 working conditions. The parameters for each working condition were used as input to the calculation model to obtain the output of the projectile's motion state under each condition. Data distribution plots with initial velocity and penetration time as independent variables and residual velocity as dependent variable are shown below. Figure 4 As shown.

[0050] like Figure 4 As shown in subgraph (a), the initial velocity and the remaining velocity exhibit a positive correlation, and the distribution range of each velocity is basically the same; as Figure 4 As shown in subplot (b), the penetration time and residual velocity exhibit an exponential decay, with a longer penetration time implying a lower residual velocity. Therefore, we can establish a system with initial velocity and penetration time as independent variables. With penetration time The formula for predicting the residual velocity is given by the independent variable.

[0051] In the 96 sets of data obtained, the values ​​of the independent variables, namely target plate strength, target plate thickness, and initial velocity, had large intervals. Therefore, to further ensure the predictive ability of the formula, the intervals of the independent variables were reduced: the initial velocity was taken at intervals of 10 m / s, the target plate strength at intervals of 5 MPa, and the target plate thickness at intervals of 0.25 m. The resulting three-dimensional images of penetration time, initial velocity, and residual velocity are shown below. Figure 5 As shown.

[0052] Depend on Figure 5 It is known that given the penetration time and initial velocity, a maximum of three residual velocities can be obtained, resulting in a three-layered surface in the image. According to mathematical definition, the residual velocity cannot be predicted using only two independent variables—penetration time and initial velocity—through a single function formula. Since the fuze generates an acceleration peak during penetration, this peak is introduced for interval determination (i.e., the maximum overload value added in this invention above, used to distinguish different operating conditions), ensuring no overlap between layers and allowing for fitting different surfaces based on the intervals. A preferred interval division is [0, 1w]. g ], [1w g 1.5w g ], [1.5w g 4w g ];w g This represents gravitational acceleration. Each surface exhibits a high initial velocity and a high residual velocity at a low penetration time, which aligns with practical experience. A four-dimensional relationship mapping diagram is drawn based on different intervals, as shown below. Figure 6 As shown, after introducing the acceleration peak value for region division, the original overlapping three-layer surface is transformed into a non-overlapping three-layer surface, so formula fitting can be performed separately.

[0053] Therefore, the overload time history data for various operating conditions generated in this step include penetration time. Remaining speed And the maximum overload value. Using the peak acceleration overload as the segmentation criterion, the overload time history data is divided into three data intervals.

[0054] Step 5: Within each data interval, perform regression fitting using a nonlinear mapping model to establish a model based on the initial velocity. With penetration time The formula for predicting the residual velocity is given by the independent variable.

[0055] Nonlinear mapping models can employ conventional linear regression models—quadratic polynomial models, the specific expression of which is: (twenty two) for Figure 4 The dataset, the fitting effect of the quadratic polynomial model is as follows Figure 7 As shown, the predicted values ​​are evenly and densely distributed on both sides of the actual values, and the fitted surface matches the actual data points well.

[0056] In a preferred embodiment, by Figure 4 It can be seen that the residual velocity and the initial velocity exhibit a certain positive linear correlation, while the residual velocity and the penetration time show a clear exponential decay relationship. Furthermore, since the initial velocity and penetration time also show a correlation in the qualitative analysis, a nonlinear hybrid model is attempted to be constructed to explain this relationship: (twenty three) for Figure 4 The dataset, the fitting effect of the nonlinear mixture model is as follows Figure 8 As shown, the distribution is also relatively uniform and dense on both sides of the actual value.

[0057] Therefore, this step can use the model of formula (22) or (23) to perform regression fitting in the three data intervals respectively, such as Figure 9 As shown, the intervals are established with an initial velocity. With penetration time The formula for predicting residual velocity is given by the independent variable. (10,000) g In the following intervals, the fitted lines of both model formulas are close to the baseline; 10,000-15,000 g The quadratic polynomial model within the interval exhibits warping at low residual velocities, while the nonlinear model shows a higher degree of agreement; 15,000-40,000 g The quadratic polynomial model within the interval still exhibits warping when there is low residual velocity, while the nonlinear hybrid model is basically near the baseline.

[0058] Step Six: When actually predicting the remaining velocity, extract the maximum overload value during the penetration process. Based on the data range containing the maximum overload value, select the corresponding remaining velocity prediction formula, substitute it into the measured initial velocity and penetration time, and obtain the predicted remaining velocity. .

[0059] Here are the fitting formulas for the residual velocity of a certain type of projectile and a comparison of its actual test results at the test range, as shown in Tables 1, 2 and 3 respectively.

[0060] Table 1. Fit coefficients for the quadratic polynomial formula

[0061] Table 2 Fitting coefficients for nonlinear hybrid formulas

[0062] Table 3. Validation of Formula Fitting Effect

[0063] In summary, the above are merely preferred embodiments of the present invention and are not intended to limit the scope of protection of the present invention. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of the present invention should be included within the scope of protection of the present invention.

Claims

1. A method for predicting residual penetration velocity based on acceleration signals, characterized in that, include: Step 1: Divide the projectile penetration process into three penetration states: partial projectile entry into the target, complete projectile entry into the target, and projectile separation from the target. Determine the projectile overload expression for each penetration state. Then, the equations of motion for the projectile penetration process are constructed; Step 2: For a specified projectile type, comprehensively utilize the projectile penetration process motion equations under three penetration states to generate overload time history data for various operating conditions, including penetration time. Remaining speed And peak acceleration; using peak acceleration as the segmentation criterion, the overload time history data is divided into three data intervals; Step 3: Within each data interval, perform regression fitting using a nonlinear mapping model to establish a model based on the initial velocity. With penetration time The formula for predicting residual velocity is given by the independent variable. Step 4: When actually predicting the remaining velocity, extract the peak acceleration during the penetration process, select the corresponding remaining velocity prediction formula based on the data range where the peak acceleration is located, and substitute it into the measured initial velocity and penetration time to obtain the predicted remaining velocity. .

2. The method as described in claim 1, characterized in that, In step 1, the projectile penetration process is divided into three penetration states: partial target entry, complete target entry, and target separation. The projectile overload expression for each penetration state is then determined. Specifically, it includes: Axial stress on the arc surface of the warhead By integrating along the projectile's axis, an expression for the projectile's axial penetration resistance is constructed, which is the overall expression for projectile overload. Based on the different lengths of the projectile's arc within the target plate under three penetration conditions, the upper and lower limits of the integral of the overall projectile overload expression are adjusted to obtain sub-expressions for projectile overload under the three penetration conditions, thus obtaining the projectile overload expression for each penetration condition. .

3. The method as described in claim 2, characterized in that, The projectile overload expression for each penetration state for: Let the angle between the line connecting the centers of curvature of the projectile and the projectile axis be... ; to reduce the axial stress on the arc surface of the warhead The integral is converted into Angle integral; With the warhead partially impacting the target, the projectile overload expression is derived by integrating the portion of the warhead surface from the tip to the frontal boundary of the target plate: in, This refers to the warhead coefficient. The diameter of the bullet, For the normal stress on the warhead surface, It is the coefficient of sliding friction at the interface; For the bullet tip horn, The front boundary of the target plate horn, , , Indicates the projectile's penetration displacement; With all warheads in target position, integrating over the entire warhead surface, the projectile overload expression is: In the projectile-target separation state, integrating over the portion of the projectile surface from the target plate's back boundary to the projectile's final position, the projectile overload expression is: in The boundary of the back of the target plate horn: in, The thickness is the target plate thickness.

4. The method as described in claim 1, characterized in that, In step 1, the equation of motion for the projectile penetration process is: based on the projectile overload expression Based on Newton's second law, construct the equation of motion of the projectile during the penetration of the target plate: （I） in, For the mass of the projectile, This refers to the acceleration during the projectile's penetration process.

5. The method as described in claim 4, characterized in that, Step 2, specifically, involves generating overload time history data for various working conditions by comprehensively utilizing the projectile penetration process motion equations under three penetration states for a specified projectile type. Step 21: Determine the normal stress on the warhead surface based on the cavity expansion theory. The expression: (II) in, A , B The constant is a dimensionless target material. Y and These represent the yield strength and density of the target plate material, respectively. It is the expansion velocity of the cavity interface; determined by the projectile penetration velocity. The expansion velocity of the cavity interface can be derived as the velocity of the particle particles at the projectile-target interface. ; Axial stress on the surface of the warhead If we decompose the structure and assume that the tangential stress on the warhead surface is determined by the interfacial sliding friction, then we have: (III) in, The angle between the line connecting the centers of curvature of the projectile and the projectile axis; It is the coefficient of sliding friction at the interface; Step 22: Combine equations (I), (II), and (III) and simplify to obtain the differential equation: (IV) Among them, coefficient and They are respectively: ， ， in, Projectile penetration velocity , This refers to the warhead coefficient. The diameter of the bullet, For the mass of the projectile; Step 23: Use the fourth-order Runge-Kutta algorithm to solve the differential equation of formula (IV) to generate a large amount of overload time history data for various operating conditions.

6. The method as described in claim 1 or 5, characterized in that, The working condition is constructed as follows: For different target plate strengths, target plate thicknesses, and initial penetration velocities By combining these methods, different operating conditions can be obtained.

7. The method as described in claim 1, characterized in that, In step 3, the nonlinear mapping model is a quadratic polynomial model or a nonlinear hybrid model; The nonlinear hybrid model is as follows: in, These are the model parameters for the nonlinear hybrid model.

8. The method as described in claim 1, characterized in that, In step 2, the segmented intervals for the three acceleration peaks are constructed as follows: [0, 1w g ], [1w g 1.5w g ], [1.5w g 4w g ];w g It represents the acceleration due to gravity.

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