Detonation wave propagation multifunctional calculation method fusing data and physical information

Abstract

The invention relates to the field of detonation wave simulation calculation, in particular to a detonation wave propagation multifunctional calculation method fusing data and physical information, and is suitable for solving various detonation wave propagation scenes. According to the method, a full-connection neural network is constructed by obtaining position coordinates of sample points and known physical information. Wherein the physical information comprises a detonation time control equation, a boundary condition and a propagation direction rule. And establishing a total residual error according to the known physical information and other known conditions provided by different scenes. The problem of the minimum value of the total residual error is iteratively solved through the optimization algorithm, solving of different scenes is achieved, and the solving precision meets the application requirement.

Description

Technical Field

[0001] The invention relates to the field of detonation wave simulation calculation, and in particular to a multifunctional calculation method for detonation wave propagation integrating data and physical information. Background Art

[0002] The existing method is to combine the Detonation Shock Dynamics (DSD) theory with the level-set method to simulate the propagation of detonation waves. The level-set method is an effective method to describe the movement of material interfaces or phase interfaces, and can describe the numerical calculation of crystallization surfaces, combustion fronts, and detonation wave front propagation. By converting continuous time and space (x, t) into discrete spatial points x i and time step t n , using an appropriate numerical format to transform the differential equation into a difference equation. Then gradually solve it in time steps, that is, calculate the next time step based on the results of the previous time step to achieve the simulation of detonation wave propagation. However, the above method can only solve specific scenario problems, that is, the wavefront position at a certain initial moment must be provided to calculate the subsequent propagation process; in addition, the traditional numerical solution method has great limitations, mainly manifested in the difficulty of mesh generation in complex geometric areas, high computational consumption and complex algorithms.

[0003] In order to solve various detonation wave scenario problems and meet the computational requirements of high-precision and fast detonation wave propagation simulation, a multifunctional calculation method for detonation wave propagation that integrates data and physical information is proposed. Summary of the invention

[0004] The purpose of the present invention is to provide a multifunctional calculation method for detonation wave propagation that integrates data and physical information to solve various detonation wave scenario problems.

[0005] An embodiment of the present invention provides a multifunctional calculation method for detonation wave propagation integrating data and physical information, the method comprising the following steps:

[0006] Acquire the sample point position coordinates and known physical information, wherein the known physical information includes a detonation time control equation, boundary conditions, and propagation direction law;

[0007] Constructing a fully connected neural network, the fully connected neural network comprising an input layer, an output layer and a hidden layer; the input data of the input layer is the coordinates, and the output data of the output layer is the predicted detonation time;

[0008] Establishing a total residual according to the known physical information and the predicted detonation time corresponding to the position coordinates of the sample points;

[0009] The determined parameters are iteratively optimized according to the total residual until a preset convergence condition is met.

[0010] Optionally, the known physical information also includes an initial wavefront;

[0011] The step of establishing a total residual according to the known physical information and the predicted detonation time corresponding to the position coordinates of the sample points includes:

[0012] loss(θ)=A1loss pde (θ)+A2loss idf (θ)+A3loss bc (θ)+Δ4loss dr (θ),

[0013] Wherein, loss(θ) is the total residual; θ is the weight and bias parameter in the fully connected neural network, and is the undetermined parameter; loss pde (θ) is the corresponding residual component of the detonation time control equation; loss idf (θ) is the corresponding residual component of the initial wavefront; loss bc (θ) is the residual component corresponding to the boundary condition; loss dr (θ) is the residual component corresponding to the propagation direction law; A1-A4 are preset weight values ​​and A4 is greater than A1, A2, and A3.

[0014] Optionally, the known physical information also includes the detonation time of the measuring point;

[0015] The step of establishing a total residual according to the known physical information and the predicted detonation time corresponding to the position coordinates of the sample points includes:

[0016] loss(θ)=B1loss pde (θ)+B2loss exp (θ)+B3loss bc (θ)+B4loss dr (θ),

[0017] Wherein, loss(θ) is the total residual; θ is the weight and bias parameter in the fully connected neural network, and is the undetermined parameter; loss pde (θ) is the corresponding residual component of the detonation time control equation; loss exp (θ) is the corresponding residual component of the detonation time of the measuring point; loss bc (θ) is the residual component corresponding to the boundary condition; loss dr(θ) is the residual component corresponding to the propagation direction law; B1-B4 are preset weight values ​​and B4 is greater than B1, B2, and B3.

[0018] Optionally, the known physical information also includes the initial wavefront and the detonation time of the measuring point;

[0019] The step of establishing a total residual according to the known physical information and the predicted detonation time corresponding to the position coordinates of the sample points includes:

[0020] loss(θ,α)=C1loss pde (θ, α)+C2loss idf (θ)+C3loss exp (θ)+C4loss bc (θ)+C5loss dr (θ),

[0021] Wherein, loss(θ, α) is the total residual; θ is the weight and bias parameter in the fully connected neural network and is the undetermined parameter; α is the explosive parameter and is the undetermined parameter; loss pde (θ, α) is the corresponding residual component of the detonation time control equation; loss idf (θ) is the corresponding residual component of the initial wavefront; loss exp (θ) is the corresponding residual component of the detonation time of the measuring point; loss bc (θ) is the residual component corresponding to the boundary condition; loss dr (θ) is the residual component corresponding to the propagation direction law; C1-C5 are preset weight values ​​and C5 is greater than C1, C2, C3, and C4.

[0022] Optionally, the expression of the corresponding residual component of the initial wavefront is:

[0023]

[0024] Among them, loss idf (θ) is the corresponding residual component of the initial wavefront; N idf is the number of sample points of the initial wavefront; is the sample point location coordinate The corresponding predicted detonation time; is the sample point location coordinate The corresponding actual detonation time;

[0025] The expression of the corresponding residual component of the detonation time control equation is:

[0026]

[0027] Among them, loss pde (θ) is the corresponding residual component of the detonation time control equation; N pde is the number of sample points of the detonation time control equation; is the sample point location coordinate The corresponding predicted detonation time gradient; α′ is the explosive parameter and is a known parameter; k is the detonation wave front curvature; D CJ For the explosive CJ detonation speed.

[0028] Optionally, the expression of the residual component corresponding to the detonation time of the measuring point is:

[0029]

[0030] Among them, loss exp (θ) is the corresponding residual component of the detonation time of the measuring point; N exp is the number of sample points of the measuring point; is the sample point location coordinate The corresponding predicted detonation time; is the sample point location coordinate The corresponding actual detonation time.

[0031] Optionally, the expression of the corresponding residual component of the detonation time control equation is:

[0032]

[0033] Among them, loss pde (θ, α) is the corresponding residual component of the detonation time control equation; N pde is the number of sample points of the detonation time control equation; is the sample point location coordinate The corresponding predicted detonation time gradient; k is the detonation wave front curvature; D CJ For the explosive CJ detonation speed.

[0034] Optionally, the corresponding residual component of the boundary condition includes a first boundary residual and a second boundary residual, the first boundary residual is a material boundary constraining the propagation direction of the detonation wave, and the second boundary residual is a symmetric boundary constraining the propagation direction of the detonation wave;

[0035] The expression of the first boundary residual is:

[0036]

[0037] Among them, loss bc1 (θ) is the first boundary residual; N bc1 is the number of sample points at the boundary of the material; is the sample point location coordinate The corresponding detonation wavefront unit external normal vector; is the sample point location coordinate The corresponding material boundary unit external normal vector; is the sample point location coordinate The corresponding predicted detonation time gradient; ω c is the boundary threshold angle; max is the upper limit set by the clamp function;

[0038] The expression of the second boundary residual is:

[0039]

[0040] Among them, loss bc2 (θ) is the second boundary residual; N bc2 is the number of sample points of the symmetric boundary; is the sample point location coordinate The corresponding detonation wavefront unit external normal vector; is the sample point location coordinate The corresponding symmetry boundary unit external normal vector; is the sample point location coordinate The corresponding predicted detonation time gradient.

[0041] Optionally, the expression of the residual component corresponding to the propagation direction law is:

[0042]

[0043] Among them, loss dr is the residual component corresponding to the propagation direction law; N dr is the number of sample points of the propagation direction law; is the position coordinate of the first sample point The corresponding predicted detonation time; is the position coordinate of the second sample point The corresponding predicted detonation time; the first sample point and the second sample point are the position coordinates of adjacent sample points in the same detonation wave propagation direction; max is the upper limit set by the clamp function.

[0044] Optionally, the iterative optimization of the determined parameters according to the total residual until a preset convergence condition is satisfied includes:

[0045] Based on the total residual, the Adam optimizer is used to iteratively optimize the undetermined parameters until the relative error of the predicted detonation time is less than a preset threshold, and the preset convergence condition is met.

[0046] Compared with the prior art, the multifunctional calculation method for detonation wave propagation by integrating data and physical information provided by the present invention has the following beneficial effects:

[0047] The multifunctional calculation method for the propagation of detonation waves that integrates data and physical information provided by the embodiment of the present invention constructs a fully connected neural network by acquiring the position coordinates of the sample points and known physical information. The physical information includes the detonation time control equation, boundary conditions and propagation direction law; the fully connected neural network includes an input layer, an output layer and a hidden layer; the input data of the input layer is the coordinates, and the output data of the output layer is the predicted detonation time. According to the known physical information and the predicted detonation time corresponding to the position coordinates of the sample points, as well as other known conditions provided by different scenarios, a total residual is established; according to the total residual, the parameters to be determined are iteratively optimized until the preset convergence conditions are met, thereby solving the problems in different scenarios. In addition, simulation based on a fully connected neural network can meet the computational requirements of high-precision and fast calculation of detonation wave propagation simulation. BRIEF DESCRIPTION OF THE DRAWINGS

[0048] In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the drawings required for use in the embodiments or the description of the prior art will be briefly introduced below. Obviously, the drawings described below are only embodiments of the present invention. For ordinary technicians in this field, other drawings can be obtained based on the provided drawings without paying creative work.

[0049] Figure 1 A schematic flow chart of a multifunctional calculation method for detonation wave propagation that integrates data and physical information provided by an embodiment of the present invention;

[0050] Figure 2a A schematic diagram of the shape of an arc-shaped explosive in an embodiment of the present invention;

[0051] Figure 2b A schematic diagram of a rectangular explosive in an embodiment of the present invention;

[0052] Figure 3 This is a schematic diagram of a fully connected neural network structure in an embodiment of the present invention;

[0053] Figure 4a This is a functional schematic diagram of a detonation wave scenario 1 in an embodiment of the present invention;

[0054] Figure 4b This is a functional schematic diagram of the second detonation wave scenario in an embodiment of the present invention;

[0055] Figure 4c It is a schematic diagram of three functions of a detonation wave scene in an embodiment of the present invention;

[0056] Figure 5It is a schematic diagram of a prior art method for detonation wave scenario 2 in an embodiment of the present invention;

[0057] Figure 6a Schematic diagram of arc-shaped explosive in scene 1 in an embodiment of the present invention;

[0058] Figure 6b Schematic diagram of total residual variation in the simulation of explosion wave propagation in scenario 1 according to an embodiment of the present invention;

[0059] Figure 6c This is a schematic diagram of a simulation result of a visual detonation wave propagation in scenario 1 according to an embodiment of the present invention;

[0060] Figure 7 This is a schematic diagram of measurement point data for scenario 2 in an embodiment of the present invention;

[0061] Figure 8a It is a schematic diagram of the total residual change of the explosion wave propagation simulation in scenario 2 in an embodiment of the present invention;

[0062] Figure 8b This is a schematic diagram of a simulation result of a visualized detonation wave propagation in scenario 2 according to an embodiment of the present invention;

[0063] Fig. 9 Schematic diagram of changes in explosive parameters for the simulation of detonation wave propagation in scenario three of an embodiment of the present invention. DETAILED DESCRIPTION

[0064] In order to make the above-mentioned objects, features and advantages of the present invention more obvious and easy to understand, specific embodiments of the present invention are described in detail below with reference to the accompanying drawings.

[0065] The embodiment of the present invention provides a multifunctional calculation method for detonation wave propagation that integrates data and physical information. Figure 1 A schematic flow chart of a multifunctional calculation method for detonation wave propagation integrating data and physical information is shown, the method comprising the following steps:

[0066] S110, obtaining the position coordinates of the sample points and known physical information.

[0067] Among them, the known physical information includes the detonation time control equation, boundary conditions and propagation direction laws.

[0068] S120, build a fully connected neural network.

[0069] The fully connected neural network includes an input layer, an output layer and a hidden layer; the input data of the input layer are coordinates, and the output data of the output layer are predicted detonation time.

[0070] S130, establishing a total residual according to the known physical information and the predicted detonation time corresponding to the position coordinates of the sample points.

[0071] Optionally, the known physical information also includes the initial wavefront. The step S130 includes: loss(θ)=A1loss pde (θ)+A2loss idf (θ)+A3loss bc (θ)+A4loss dr (θ),

[0072] Among them, loss(θ) is the total residual; θ is the weight and bias parameter in the fully connected neural network, and is a parameter to be determined; loss pde (θ) is the corresponding residual component of the detonation time control equation; loss idf (θ) is the corresponding residual component of the initial wavefront; loss bc (θ) is the residual component corresponding to the boundary condition; loss dr (θ) is the residual component corresponding to the propagation direction law; A1-A4 are preset weight values ​​and A4 is greater than A1, A2, and A3.

[0073] It should be noted that the initial wavefront is the isosurface of the initial detonation time, and the explosive parameter is the influence coefficient of the detonation wavefront curvature on the CJ detonation velocity of the explosive.

[0074] Optionally, the known physical information also includes the detonation time of the measuring point. The step S130 includes:

[0075] loss(θ)=B1loss pde (θ)+B2loss exp (θ)+B3loss bc (θ)+B4loss dr (θ),

[0076] Among them, loss(θ) is the total residual; θ is the weight and bias parameter in the fully connected neural network, and is a parameter to be determined; loss pde (θ) is the corresponding residual component of the detonation time control equation; loss exp (θ) is the corresponding residual component of the detonation time of the measuring point; loss bc (θ) is the residual component corresponding to the boundary condition; loss dr (θ) is the residual component corresponding to the propagation direction law; B1-B4 are preset weight values ​​and B4 is greater than B1, B2, and B3.

[0077] Optionally, the known physical information also includes the initial wavefront and the detonation time of the measuring point. The step S130 includes:

[0078] loss(θ,α)=

[0079] C1loss pde (θ, α)+C2loss idf (θ)+C3loss exp (θ)+C4loss bc (θ)+C5loss dr (θ),

[0080] Among them, loss(θ, α) is the total residual; θ is the weight and bias parameter in the fully connected neural network and is a parameter to be determined; α is the explosive parameter and is a parameter to be determined; loss pde (θ, α) is the corresponding residual component of the detonation time control equation; loss idf (θ) is the corresponding residual component of the initial wavefront; loss exp (θ) is the corresponding residual component of the detonation time of the measuring point; loss bc (θ) is the residual component corresponding to the boundary condition; loss dr (θ) is the residual component corresponding to the propagation direction law; C1-C5 are preset weight values ​​and C5 is greater than C1, C2, C3, and C4.

[0081] It should be noted that the measuring point is a measuring point located inside the explosive (not the initial wavefront) with a known detonation time; the above preset weights are all positive numbers.

[0082] S140, iteratively optimizing the parameters to be determined according to the total residual until a preset convergence condition is met.

[0083] Optionally, the above step S140 includes:

[0084] Based on the total residual, the Adam optimizer is used to iteratively optimize the fully connected neural network or explosive parameters until the relative error of the predicted detonation time is less than the preset threshold, and the preset convergence condition is met.

[0085] Optionally, the expression of the corresponding residual component of the initial wavefront is:

[0086]

[0087] Among them, loss idf (θ) is the corresponding residual component of the initial wavefront; N idf is the number of sample points of the initial wavefront; is the sample point location coordinate The corresponding predicted detonation time; is the sample point location coordinate The corresponding actual detonation time.

[0088] The expression of the corresponding residual component of the detonation time control equation is:

[0089]

[0090] Among them, loss pde (θ) is the corresponding residual component of the detonation time control equation; N pde is the number of sample points of the detonation time control equation; is the sample point location coordinate The corresponding predicted detonation time gradient; α′ is the explosive parameter and is a known parameter; k is the detonation wave front curvature; D CJ For the explosive CJ detonation speed.

[0091] Optionally, the expression of the corresponding residual component of the detonation time of the measuring point is:

[0092]

[0093] Among them, loss exp (θ) is the corresponding residual component of the detonation time of the measuring point; N exp is the number of sample points of the measurement points; is the sample point location coordinate The corresponding predicted detonation time; is the sample point location coordinate The corresponding actual detonation time.

[0094] Optionally, the expression of the corresponding residual component of the detonation time control equation is:

[0095]

[0096] Among them, loss pde (θ, α) is the corresponding residual component of the detonation time control equation; N pde is the number of sample points of the detonation time control equation; is the sample point location coordinate The corresponding predicted detonation time gradient; κ is the detonation wave front curvature; D CJ For the explosive CJ detonation speed.

[0097] It should be noted that the embodiment of the present invention directly focuses on the detonation time t(x), which is different from the level-set function of the existing method. The time dimension is reduced. The isosurface of the detonation time t is the detonation wavefront. The detonation physics information includes the detonation time control equation, boundary conditions and propagation direction law. The control equation of the detonation time t is:

[0098]

[0099] in, represents the gradient of the detonation time t, is the magnitude of the gradient, D n represents the wavefront normal velocity.

[0100] According to DSD theory, D n Determined by the wavefront curvature. Without loss of generality, the following uses a linear relationship as an example to illustrate, D n The expression is:

[0101] D n =f(D CJ , k) = D CJ (1-αk),

[0102] Among them, α is the explosive parameter. The larger α is, the higher the normal velocity D n The greater the influence of curvature K. The relationship between total curvature K and detonation time t is:

[0103]

[0104] in, is the divergence of the unit external normal vector of the wavefront.

[0105] Optionally, the corresponding residual components of the above boundary conditions include a first boundary residual and a second boundary residual, wherein the first boundary residual is the constraint of the material boundary on the propagation direction of the detonation wave, and the second boundary residual is the constraint of the symmetric boundary on the propagation direction of the detonation wave.

[0106] The expression of the first boundary residual is:

[0107]

[0108] Among them, loss bc1 (θ) is the first boundary residual; N bc1 is the number of sample points at the material boundary; is the sample point location coordinate The corresponding detonation wavefront unit external normal vector; is the sample point location coordinate The corresponding material boundary unit external normal vector; is the sample point location coordinate The corresponding predicted detonation time gradient; ω c is the boundary threshold angle; max is the upper limit set by the clamp function.

[0109] The expression of the second boundary residual is:

[0110]

[0111] Among them, loss bc2 (θ) is the second boundary residual; N bc2 is the number of sample points of the symmetric boundary; is the sample point location coordinate The corresponding detonation wavefront unit external normal vector; is the sample point location coordinate The corresponding symmetry boundary unit external normal vector; is the sample point location coordinate The corresponding predicted detonation time gradient.

[0112] It should be noted that this embodiment introduces boundary condition information, wherein the boundary condition information includes material boundary conditions and symmetric boundary conditions.

[0113] Specifically, the material boundary condition is the restriction of the explosive material boundary on the propagation direction of the detonation wave. In the embodiment of the present invention, the constraint of the material boundary condition is obtained by limiting the angle between the detonation wave and the boundary on the explosive boundary to not exceed a certain angle, that is,

[0114] ω≤ω c ,

[0115] Among them, the angle 0<ω c <90°, which can be obtained by the impact polar curve analysis method of the explosives and inert materials on both sides of the boundary. For example, see Figure 2a The schematic diagram of the arc-shaped explosive shape is shown in the figure. The inner arc boundary condition is ω≤ω c1 ,ω c1 =45°; the outer arc boundary condition is ω≤ω c2 ,ω c2 =90°.

[0116] In addition, the symmetric boundary condition is a restriction on the propagation direction of the detonation wave due to the symmetry of the explosive shape. In the embodiment of the present invention, the constraint of the symmetric boundary condition is obtained by limiting the detonation wave on the explosive boundary to be perpendicular to the boundary, that is, ω = 90°. For example, see Figure 2b The schematic diagram of the rectangular explosive shape is shown in the figure. The initial wavefront in the rectangular explosive is a circular arc at the lower left corner, and the left boundary and the lower boundary are perpendicular to the detonation wavefront. The detonation wavefront is an arc line with equal detonation time at each point, such as Figure 2b As shown by the solid grey line. By making the rectangular explosive symmetrical with the left boundary as the axis of symmetry, and then making it symmetrical with the lower boundary as the axis of symmetry, a complete explosive with material shape symmetry can be obtained; for the above explosive, only the rectangular explosive part needs to be studied to predict the detonation wave propagation of the complete explosive.

[0117] Optionally, the expression of the residual component corresponding to the above propagation direction law is:

[0118]

[0119] Among them, loss dris the residual component corresponding to the propagation direction law; N dr is the number of sample points of the propagation direction law; is the position coordinate of the first sample point The corresponding predicted detonation time; is the position coordinate of the second sample point The corresponding predicted detonation time; the first sample point and the second sample point are the position coordinates of adjacent sample points in the same detonation wave propagation direction; max is the upper limit set by the clamp function.

[0120] It should be noted that the embodiment of the present invention introduces the propagation direction regularity information; the propagation direction regularity information is the variation regularity of the detonation time on the specific curve inside the explosive. It should also be noted that although the detonation time of each point of the explosive is unknown, the propagation direction of the detonation wave inside the explosive can be roughly determined; along the above propagation direction, the corresponding detonation time gradually increases.

[0121] For example, see Figure 2a , the initial wavefront in the arc-shaped explosive is the lower curve, which can determine that the detonation wave propagates from bottom to top in the arc-shaped explosive. The propagation direction regularity information is to take a series of concentric arcs starting from the initial wavefront, such as Figure 2a As shown in the solid grey line, on these arcs, the detonation time should increase monotonically in the direction of the arrow.

[0122] In summary, the embodiments of the present invention can enhance the model training effect and improve the accuracy of detonation wave propagation simulation by introducing the above-mentioned propagation direction regularity information.

[0123] Different from the existing method of discretizing the continuous space, the embodiment of the present invention directly adopts the neural network defined on the continuous space. Approximate the detonation time distribution t(x) on the explosive, that is, A neural network is a nonlinear function with a large number of undetermined parameters. The undetermined neural network parameters include weights and biases, which are represented by θ. The embodiment of the present invention adopts a fully connected neural network. Figure 3 The schematic diagram of the fully connected neural grid structure is shown in the figure. The network input is the coordinates of the spatial point, and the output is the detonation time. Once the parameters of the fully connected neural network are determined, the mapping relationship between the coordinates and the detonation time is also determined, that is, the detonation time distribution is determined, and the simulation of the detonation wave propagation is realized.

[0124] Among them, the parameters of the fully connected neural network are solved by quantifying the degree of deviation of the neural network from the known conditions as the total residual and minimizing the total residual. The known conditions include two types of information: data information and physical information. The data information is the detonation time of several points, including the measurement point data and initial wavefront obtained from various channels such as experiments or literature. The physical information is the physical condition constraints, including the detonation time control equation, boundary conditions and propagation direction laws; by establishing the total residual, the fully connected neural network is suitable for simulating a variety of detonation wave propagation scenarios. In addition, simulation based on the fully connected neural network can meet the computational requirements of high-precision and fast calculation of detonation wave propagation simulation.

[0125] As a feasible implementation method, regarding the data information residual, the measurement point data includes N exp Measurement points The corresponding detonation time is The residual of the fully connected neural network at these measurement points is the mean square value of the difference between the network result and the measurement point result, and the corresponding residual is:

[0126]

[0127] Randomly select N on the initial wavefront idf Sample points The residual of the neural network at these sample points is the mean square value of the difference between the network result and the initial detonation time, and the corresponding residual is:

[0128]

[0129] As a feasible implementation method, regarding the residual of the control equation of the detonation time, N random values ​​are taken inside the explosive. pde Sample points If the residual of the explosive parameter is the parameter to be determined, the control equation of the detonation time is:

[0130]

[0131] If the residual of explosive parameters is a known parameter, the control equation of detonation time is:

[0132]

[0133] As a feasible implementation method, regarding the boundary condition residual, N random samples are drawn from the explosive boundary. bc Sample points According to the material boundary conditions, the unit external normal vector between the wave front and the material boundary and n bc The dot product should satisfy Therefore, since the shape of the explosive is known, the material boundary sample points The boundary unit normal vector on It is also known that, in addition, the unit external normal vector of the detonation wave front is:

[0134]

[0135] Furthermore, the material boundary residual can be obtained as:

[0136]

[0137] Among them, the function clamp is used to limit the upper and lower limits.

[0138]

[0139] Among them, maxval and minval are given constants. Since only the max parameter is set in the material boundary residual formula, the material boundary residual loss bc1 (θ) means when Not less than cos(ω c ) satisfies the boundary condition and the residual at this point is zero; Less than cos(ω c ) does not meet the boundary conditions, and the residual at this point is and cos(ω c ) squared.

[0140] According to the symmetric boundary condition, the unit external normal vector between the wavefront and the symmetric boundary and n bc The dot product should be equal to 0, so since the shape of the explosive is known, the symmetric boundary sample points The boundary unit normal vector on It is also known that, in addition, the unit external normal vector of the detonation wave front is:

[0141]

[0142] Furthermore, the symmetric boundary residual can be obtained as:

[0143]

[0144] As a feasible implementation method, regarding the propagation direction regularity residual, for a line segment that can determine the propagation direction, N dr Sample points A calculation example can take multiple line segments. The detonation time of each line segment increases monotonically, that is, Therefore, taking a line segment as an example, the residual of its propagation direction law is:

[0145]

[0146] Among them, since only the max parameter is set in the propagation direction law residual formula, the propagation direction law residual loss dr (θ) means when Not less than When the boundary condition is met, the residual at this point is zero; when Less than The boundary condition is not met when , and the residual at this point is and The difference.

[0147] As a feasible implementation method, regarding the wavefront symmetry boundary residual, if the detonation wavefront is symmetrical and the symmetry can be roughly determined, then the detonation time at the symmetrical points should be equal. The wavefront symmetry residual of a detonation wave is:

[0148]

[0149] Among them, loss sym (θ) is the wavefront symmetry boundary residual; N sym is the number of symmetrical sample point groups; is the sample point coordinate The corresponding predicted detonation time; is the sample point coordinate The corresponding predicted detonation time; and is the coordinate point where the detonation wave front is symmetrical.

[0150] There are three possible scenarios in the detonation wave propagation problem, and the three scenarios directly correspond to the three functions. Figure 4a The function diagram of the detonation wave scenario 1 is shown in the figure. The function required for scenario 1 is to calculate the detonation time at any point based on the initial waveform and explosive parameters. Figure 4b The function diagram of the detonation wave scenario 2 is shown in the figure. The function required for this type of inverse problem in scenario 2 is to calibrate the initial wavefront based on the known detonation time of the measuring point (the moment when the detonation wave reaches the point) and the explosive parameters. Figure 4c The function diagram of the detonation wave scenario 3 is shown in the figure. The function required for the inverse problem of scenario 3 is to calibrate the explosive parameters based on the known measurement point detonation time (the time when the detonation wave reaches the point) and the initial wavefront. The known measurement point detonation time may come from experiments or other methods. The disadvantage of the existing technology is that it is only applicable to scenario 1 and difficult to be efficiently applied to scenarios 2 and 3. Taking the calibration of the initial wavefront in scenario 2 as an example, see Figure 5The schematic diagram of the prior art method for the second detonation wave scenario is shown. The prior method first generates the initial wavefront based on certain experience using the detonation time of the known point, then calculates the propagation process, and finally verifies the calculation result at the known point. If the error does not meet the requirements, the initial wavefront needs to be adjusted until the error meets the requirements. The calibration of explosive parameters in scenario three follows a similar process. It can be seen that in scenarios two and three, the existing method requires manual repeated adjustment and participation, which leads to low efficiency, and the adjustment of the initial wavefront or explosive parameters according to the error situation relies on experience, which makes it difficult to make full use of known data.

[0151] The method provided by the embodiment of the present invention has three functions required for direct application in three scenarios. The implementation process of the three functions is the same: the total residual is minimized through the optimization algorithm. When applied to the two types of inverse problems in scenarios 2 and 3, each known point data All recorded in the residual loss exp In this paper, the full utilization of known data is realized. The following takes arc explosives as an example to illustrate the implementation steps and technical effects of the method provided by the embodiment of the present invention in three scenarios. The network structure of the three scenarios is the same, all of which use a fully connected network, including two hidden layers, and 50 nodes in each hidden layer. The construction and training of the network are implemented using the pytorch package in the python language. The derivative of the network output to the input is calculated through the automatic differentiation module (autograd) provided by pytorch. The optimization of the residual adopts the widely used adam optimizer, and the optimization process is a multi-step iterative process.

[0152] Scenario 1: In solving the positive problem in scenario 1, the wavefront position at the initial time t0 is known. The detonation time at each point is calculated based on the initial wavefront and the explosive parameters. Figure 6a The scene shown is a schematic diagram of an arc-shaped explosive. The inner and outer radii of the explosive are r1=2 and r2=4 respectively, and the inner arc boundary condition is ω c1 =45°, the outer arc boundary condition is ω c2 =90°. The upper and lower boundaries are the wavefront symmetry boundaries. Take (1.5,2.0) and (3.5,0.0) as the error test points. The initial wavefront is shown as the inner curve below the arc-shaped explosive, with the coordinates (-4.0,-3.0) as the center and the radius The explosive parameter α is set to 0.1.

[0153] 1) Build a fully connected network

[0154] The network consists of four layers, including 1 input layer, 1 output layer and two hidden layers. The input layer is the coordinate (x1, x2), the output layer is the detonation time t, and each hidden layer is set with 50 nodes, so the number of nodes in each layer is (2, 50, 50, 1). It should be noted that if the coordinates are the coordinates of the three-dimensional space point (x1, x2, x3), the input layer is set to 3 nodes.

[0155] 2) Establish residual

[0156] The total residual consists of four parts, corresponding to the detonation time control equation, initial wavefront, boundary conditions and propagation direction, and the expression is:

[0157] loss(θ)=loss pde (θ)+loss idf (θ)+loss bc (θ)+1000loss dr (θ),

[0158] Among them, loss bc (θ) consists of three parts, corresponding to the inner arc boundary, the outer arc boundary and the wavefront symmetry boundary, respectively. bc (θ)=loss bc-r1 (θ)+loss bc-r2 (θ)+loss bc-sym (θ).

[0159] loss dr (θ) consists of five parts, which come from five arcs concentric with the inner and outer boundaries, two of which are the inner and outer boundaries. The radii of the five arcs are 2, 2.5, 3.0, 3.5 and 4.0 respectively. dr (θ) is not equal to 0, which means that the propagation direction is abnormal, indicating a qualitative error. Therefore, a large weight (here 1000) is multiplied before this term to ensure that the propagation direction is strictly satisfied. The weights of other terms can be adjusted according to the convergence situation, and a larger weight can be multiplied for the residual that converges slowly. For example, all weights except the propagation direction rule are 1.

[0160] loss pde (θ) is the residual corresponding to 10,000 random sample points in the explosive, loss idf (θ) is the residual corresponding to 200 random sample points on the initial wavefront, loss bc The two parts of (θ) are the residuals corresponding to 200 random sample points on each boundary, loss dr The five parts of (θ) are the residuals corresponding to the 200 sequential sample points on each arc.

[0161] 3) Optimize training and results

[0162] The Adam optimizer provided by pytorch is used to optimize loss(θ) to find the minimum value, the learning rate lr = 0.001, and other parameters are set by default. Figure 6b Schematic diagram of the total residual change in the blast wave propagation simulation of scenario 1 and Figure 6c The diagram of the simulation results of the blast wave propagation in scenario 1 is shown in the figure. After 3000 steps of iterative optimization, the total residual is reduced to the order of 0.01. At this time, the distribution of the detonation time represented by the neural network is as follows: Figure 6c The relative errors of the two test points are both less than 0.7%.

[0163] Scenario 2: Calculate the initial wavefront based on known data and explosive parameters, and continue to use Figure 6a Arc charge shown. See Figure 7 The schematic diagram of the measurement point data of scenario 2 is shown in Figure 1. It is known that the measurement points are distributed on 4 straight lines, with angles of ±22.5° and ±67.5° with the x-axis respectively. There are 11 points on each straight line. Figure 7 As shown by the dotted line, the explosive parameter α is 0.1.

[0164] 1) Build a fully connected network

[0165] The network structure is the same as that of the above scenario 1 and will not be described in detail here.

[0166] 2) Establish residual

[0167] The total residual consists of four parts, corresponding to the detonation time control equation, known measurement point data, boundary conditions and propagation direction, and the expression is:

[0168] loss(θ)=loss pde (θ)+loss exp (θ)+loss bc (θ)+1000loss dr (θ),

[0169] Among them, loss exp (θ) is the residual of the measured point data on the four straight lines, and the establishment method of other residuals is the same as that of scenario 1.

[0170] 3) Optimize training and results

[0171] The optimizer and settings are the same as in scenario 1. Figure 8a Schematic diagram of the total residual change in the explosion wave propagation simulation of scenario 2 and Figure 8b The diagram shows the simulation results of the detonation wave propagation in scenario 2. After 3000 steps of iterative optimization, the total residual is reduced to the order of 0.01, and the relative error at the two error test points is also less than 1%. The contour line at time 0 is the initial wavefront.

[0172] Scenario 3: The total residual of the equation includes not only network parameters but also D n The explosive parameter α in Scenario 3 is an unknown parameter to be determined. The explosive parameter α is calibrated according to the known measurement point data and the initial wavefront. The initial waveform and known data are the same as those in Scenario 1 and 2, respectively, and the corresponding true value of the explosive parameter to be determined is α=0.1.

[0173] 1) Build a fully connected network

[0174] The network structure is the same as that of the above scenario 1 and will not be described in detail here.

[0175] 2) Establish residual

[0176] The total residual consists of five parts, corresponding to the detonation time control equation, initial wavefront, known measurement point data, boundary conditions and propagation direction, and the expression is:

[0177] loss(θ, α) = loss pde (θ,α)+loss idf (θ)+loss exp (θ)+loss bc (θ)+1000loss dr (θ),

[0178] Among them, the explosive parameter α is unknown, and the residual of the equation contains two unknown parameters, θ and α. The method of establishing each residual is the same as that of scenarios one and two.

[0179] 3) Optimize training and results

[0180] The optimizer and settings are the same as in scenario 1. Fig. 9 The schematic diagram of the change of explosive parameters in the simulation of detonation wave propagation in scenario 3 is shown in the figure. The initial value of the explosive parameter α is 1. The convergence process in the iterative optimization process is as follows: Fig. 9 As shown in the figure, the explosive parameter α gradually approaches the true value at a very slow speed after a short rapid increase and rapid decrease at the beginning of training. At 7000 steps, α = 0.10067, and its relative error is less than 0.7%.

[0181] It should be noted that the fully connected neural network in the embodiment of the present invention introduces a nonlinear factor, namely, an activation function. For example, the default activation function ReLU of pytorch is used.

[0182] Of course, those skilled in the art can understand that all or part of the processes in the above-mentioned embodiment methods can be implemented by instructing the control device through a computer, and the program can be stored in a computer-readable storage medium. When the program is executed, it may include the processes of the above-mentioned method embodiments, wherein the storage medium may be a memory, a disk, an optical disk, etc.

[0183] Finally, it should be noted that, in this article, relational terms such as first and second, etc. are only used to distinguish one entity or operation from another entity or operation, and do not necessarily require or imply any such actual relationship or order between these entities or operations. Moreover, the terms "include", "comprise" or any other variants thereof are intended to cover non-exclusive inclusion, so that a process, method, article or device including a series of elements includes not only those elements, but also other elements not explicitly listed, or also includes elements inherent to such process, method, article or device. In the absence of further restrictions, the elements defined by the sentence "comprise a ..." do not exclude the presence of other identical elements in the process, method, article or device including the elements.

[0184] The various embodiments in this specification are described in a progressive manner, and each embodiment focuses on the differences from other embodiments. The same or similar parts between the various embodiments can be referenced to each other.

[0185] Although the present invention is disclosed as above, the present invention is not limited thereto. Any person skilled in the art can make various changes and modifications without departing from the spirit and scope of the present invention. Therefore, the protection scope of the present invention shall be subject to the scope defined by the claims.

Claims

1. A multifunctional calculation method for detonation wave propagation integrating data and physical information, characterized in that: The method comprises the following steps: Acquire the sample point position coordinates and known physical information, wherein the known physical information includes a detonation time control equation, boundary conditions, and propagation direction law; Constructing a fully connected neural network, the fully connected neural network comprising an input layer, an output layer and a hidden layer; the input data of the input layer is the coordinates, and the output data of the output layer is the predicted detonation time; Establishing a total residual according to the known physical information and the predicted detonation time corresponding to the position coordinates of the sample points; The determined parameters are iteratively optimized according to the total residual until a preset convergence condition is met.

2. The method according to claim 1, characterized in that The known physical information also includes the initial wave front; The step of establishing a total residual according to the known physical information and the predicted detonation time corresponding to the position coordinates of the sample points includes: loss(θ)=A1loss pde (θ)+A2loss idf (θ)+A3loss bc (θ)+A4loss dr (i), Wherein, loss(θ) is the total residual; θ is the weight and bias parameter in the fully connected neural network, and is the undetermined parameter; loss pde (θ) is the corresponding residual component of the detonation time control equation; loss idf (θ) is the corresponding residual component of the initial wavefront; loss bc (θ) is the residual component corresponding to the boundary condition; loss dr (θ) is the residual component corresponding to the propagation direction law; A1-A4 are preset weight values ​​and A4 is greater than A1, A2, and A3.

3. The method according to claim 1, characterized in that The known physical information also includes the detonation time of the measuring point; The step of establishing a total residual according to the known physical information and the predicted detonation time corresponding to the position coordinates of the sample points includes: loss(θ)=B1loss pde (θ)+B2loss exp (θ)+B3loss bc (θ)+B4loss dr (i), Wherein, loss(θ) is the total residual; θ is the weight and bias parameter in the fully connected neural network, and is the undetermined parameter; loss pde (θ) is the corresponding residual component of the detonation time control equation; loss exp (θ) is the corresponding residual component of the detonation time of the measuring point; loss bc (θ) is the residual component corresponding to the boundary condition; loss dr (θ) is the residual component corresponding to the propagation direction law; B1-B4 are preset weight values ​​and B4 is greater than B1, B2, and B3.

4. The method according to claim 1, characterized in that The known physical information also includes the initial wavefront and the detonation time of the measuring point; The step of establishing a total residual according to the known physical information and the predicted detonation time corresponding to the position coordinates of the sample points includes: loss(θ,α)=C1loss pde (θ,α)+C2loss idf (θ)+C3loss exp (θ)+C4loss bc (θ)+C5loss dr (i), Wherein, loss(θ,α) is the total residual; θ is the weight and bias parameter in the fully connected neural network and is the undetermined parameter; α is the explosive parameter and is the undetermined parameter; loss pde (θ, α) is the corresponding residual component of the detonation time control equation; loss idf (θ) is the corresponding residual component of the initial wavefront; loss exp (θ) is the corresponding residual component of the detonation time of the measuring point; loss bc (θ) is the residual component corresponding to the boundary condition; loss dr (θ) is the residual component corresponding to the propagation direction law; C1-C5 are preset weight values ​​and C5 is greater than C1, C2, C3, and C4.

5. The method according to claim 2 or 3, characterized in that: The expression of the corresponding residual component of the initial wavefront is: Among them, loss idf (θ) is the corresponding residual component of the initial wavefront; N idf is the number of sample points of the initial wavefront; is the sample point location coordinate The corresponding predicted detonation time; is the sample point location coordinate The corresponding actual detonation time; The expression of the corresponding residual component of the detonation time control equation is: Among them, loss pde (θ) is the corresponding residual component of the detonation time control equation; N pde is the number of sample points of the detonation time control equation; is the sample point location coordinate The corresponding predicted detonation time gradient; α′ is the explosive parameter and is a known parameter; k is the detonation wave front curvature; D CJ For the explosive CJ detonation speed.

6. The method according to claim 2 or 4, characterized in that: The expression of the corresponding residual component of the detonation time of the measuring point is: Among them, loss exp (θ) is the corresponding residual component of the detonation time of the measuring point; N exp is the number of sample points of the measuring point; is the sample point location coordinate The corresponding predicted detonation time; is the sample point location coordinate The corresponding actual detonation time.

7. The method according to claim 4, characterized in that The expression of the corresponding residual component of the detonation time control equation is: Among them, loss pde (θ, α) is the corresponding residual component of the detonation time control equation; N pde is the number of sample points of the detonation time control equation; is the sample point location coordinate The corresponding predicted detonation time gradient; ε is the detonation wave front curvature; D CJ For the explosive CJ detonation speed.

8. The method according to any one of claims 2 to 4, characterized in that: The corresponding residual components of the boundary conditions include a first boundary residual and a second boundary residual, wherein the first boundary residual is a material boundary constraining the propagation direction of the detonation wave, and the second boundary residual is a symmetric boundary constraining the propagation direction of the detonation wave; The expression of the first boundary residual is: Among them, loss bc1 (θ) is the first boundary residual; N bc1 is the number of sample points at the boundary of the material; is the sample point location coordinate The corresponding detonation wavefront unit external normal vector; is the sample point location coordinate The corresponding material boundary unit external normal vector; is the sample point location coordinate The corresponding predicted detonation time gradient; ω c is the boundary threshold angle; max is the upper limit set by the clamp function; The expression of the second boundary residual is: Among them, loss bc2 (θ) is the second boundary residual; N bc2 is the number of sample points of the symmetric boundary; is the sample point location coordinate The corresponding detonation wavefront unit external normal vector; is the sample point location coordinate The corresponding symmetry boundary unit external normal vector; is the sample point location coordinate The corresponding predicted detonation time gradient.

9. The method according to any one of claims 2 to 4, characterized in that: The expression of the residual component corresponding to the propagation direction law is: Among them, loss dr is the residual component corresponding to the propagation direction law; N dr is the number of sample points of the propagation direction law; is the position coordinate of the first sample point The corresponding predicted detonation time; is the position coordinate of the second sample point The corresponding predicted detonation time; the first sample point and the second sample point are the position coordinates of adjacent sample points in the same detonation wave propagation direction; max is the upper limit set by the clamp function.

10. The method according to claim 1, characterized in that The iterative optimization of the determined parameters according to the total residual until a preset convergence condition is satisfied includes: Based on the total residual, the Adam optimizer is used to iteratively optimize the undetermined parameters until the relative error of the predicted detonation time is less than a preset threshold, and the preset convergence condition is met.

Images