A multifunctional calculation method for detonation wave propagation integrating data and physical information

Abstract

The present invention relates to the field of detonation wave simulation and calculation. Specifically, it relates to a multifunctional calculation method for detonation wave propagation that integrates data and physical information, suitable for solving various detonation wave propagation scenarios. This method constructs a fully connected neural network by acquiring the position coordinates of sample points and known physical information. This physical information includes the detonation time governing equations, boundary conditions, and propagation direction patterns. Based on this known physical information and other known conditions provided by different scenarios, a total residual is established. By iteratively solving the total residual minimum problem through an optimization algorithm, solutions for different scenarios are achieved, and the solution accuracy meets application requirements.

Description

Technical Field

[0001] The present invention relates to the field of detonation wave simulation calculation, and in particular to a multifunctional calculation method for detonation wave propagation that integrates 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 the 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. The solution is then gradually solved over time steps, calculating the next time step based on the results of the previous time step to simulate the propagation of the detonation wave. However, this method can only solve specific scenarios, requiring the wavefront position at a certain initial moment to calculate the subsequent propagation process. Furthermore, traditional numerical solution methods have significant limitations, primarily manifested in difficulties in mesh generation in complex geometric areas, high computational overhead, 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 that integrates data and physical information. The method includes the following steps:

[0006] Obtaining the sample point location coordinates and known physical information, wherein the known physical information includes an initiation time control equation, boundary conditions, and propagation direction laws;

[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 based on the known physical information and the predicted detonation time corresponding to the position coordinates of the sample points;

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

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

[0011] The step of establishing a total residual based on the known physical information and the predicted detonation time corresponding to the sample point position coordinates 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 further includes the detonation time of the measuring point;

[0015] The step of establishing a total residual based on the known physical information and the predicted detonation time corresponding to the sample point position coordinates 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 residual component corresponding to 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 further includes the initial wavefront and the detonation time of the measurement point;

[0019] The step of establishing a total residual based on the known physical information and the predicted detonation time corresponding to the sample point position coordinates 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 residual component corresponding to 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 residual component corresponding to 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 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; The coordinates of the first sample point The corresponding predicted detonation time; The position coordinates 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 iteratively optimizing the parameters to be determined 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 that integrates data and physical information provided by the present invention has the following beneficial effects:

[0047] The multifunctional calculation method for detonation wave propagation, which integrates data and physical information, provided by an embodiment of the present invention, constructs a fully connected neural network by acquiring the position coordinates of sample points and known physical information. The physical information includes the detonation time governing equations, boundary conditions, and propagation direction patterns. The fully connected neural network comprises 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. Based on 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. Based on this total residual, the parameters to be determined are iteratively optimized until the preset convergence conditions are met, thereby solving problems in different scenarios. Furthermore, simulations based on the fully connected neural network can meet the computational requirements for high-precision and fast detonation wave propagation simulations. 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 following briefly introduces the drawings required for use in the embodiments or the description of the prior art. Obviously, the drawings described below are merely embodiments of the present invention. For ordinary technicians in this field, other drawings can be obtained based on the provided drawings without paying any 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 This is a schematic diagram of the shape of the arc-shaped explosive in an embodiment of the present invention;

[0051] Figure 2b Schematic diagram of the rectangular explosive shape in an embodiment of the present invention;

[0052] Figure 3 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 in an embodiment of the present invention;

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

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

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

[0057] Figure 6a Schematic diagram of arc-shaped explosives in scenario 1 according to an embodiment of the present invention;

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

[0059] Figure 6c Schematic diagram of the simulation results of 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 Schematic diagram of total residual variation in the explosion wave propagation simulation of scenario 2 in an embodiment of the present invention;

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

[0063] Figure 9 Schematic diagram of explosive parameter changes in the detonation wave propagation simulation of scenario three in 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 that integrates data and physical information is shown, the method comprising the following steps:

[0066] S110, obtaining the sample point position coordinates 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 is the coordinates, and the output data of the output layer is the predicted detonation time.

[0070] S130 , establishing a total residual based on 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. 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 an 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.

[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 an undetermined parameter; loss pde (θ) is the corresponding residual component of the detonation time control equation; loss exp (θ) is the residual component corresponding to 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 above 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 residual component corresponding to 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 optimize 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 residual component corresponding to the initiation time of the measurement 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 governing equation, boundary conditions, and propagation direction law. The governing equation of the detonation time t is:

[0098]

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

[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 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 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 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, which includes material boundary conditions and symmetry 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 analyzing the impact extreme curve of explosives and inert materials on both sides of the boundary. For example, see Figure 2a The schematic diagram of the arc-shaped explosive 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 rectangular explosive shape diagram shown in the figure shows that the initial wavefront in the rectangular explosive is the arc in the lower left corner, and the left and lower boundaries are perpendicular to the detonation wavefront. The detonation wavefront is an arc line with equal detonation time at each point, as shown in the figure. Figure 2b As shown by the medium gray solid line, the rectangular explosive is symmetrically formed with its left boundary as the axis of symmetry, and then vertically and horizontally with its lower boundary as the axis of symmetry. This yields a complete explosive with material shape symmetry. For this explosive, only the rectangular portion 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 with regular propagation direction; The position coordinates of the first sample point The corresponding predicted detonation time; The coordinates 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 this embodiment of the present invention incorporates propagation direction information; this information represents the variation of the detonation time along a specific curve within the explosive. Furthermore, while the detonation time at each point in the explosive is unknown, the propagation direction of the detonation wave within the explosive can be roughly determined; along this 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 confirm 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 On these arcs, the detonation time should increase monotonically in the direction of the arrows.

[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 uses 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 diagram shows a fully connected neural grid structure. The network input is the coordinates of a spatial point, and the output is the detonation time. Once the parameters of the fully connected neural network are determined, the mapping relationship between coordinates and detonation time is also determined, thus determining the detonation time distribution and enabling detonation wave propagation simulation.

[0124] The parameters of the fully connected neural network are solved by quantifying the degree of deviation between the neural network and the known conditions as a 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 sources 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 various 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 measuring 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 the explosive parameters is a known parameter, the control equation of the detonation time is:

[0132]

[0133] As a feasible implementation method, regarding the boundary condition residual, N random samples are taken from the explosive boundary. bc Sample points According to the material boundary conditions, the unit external normal vector of the wavefront 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 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 that when Not less than cos(ω c ) satisfies the boundary condition and the residual at this point is zero; when 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 of 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 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 the 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 that when Not less than When the boundary condition is met, the residual at this point is zero; when Less than When the boundary condition is not met, 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 certain 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; The coordinates of the sample points The corresponding predicted detonation time; The coordinates of the sample points The corresponding predicted detonation time; and is the coordinate point where the detonation wavefront 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 the inverse problem of scenario 2 is to calibrate the initial wavefront based on the known initiation time of the measuring point (the time 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 detonation time of the measuring point (the time when the detonation wave reaches the point) and the initial wavefront. The known detonation time of the measuring point may be obtained from experiments or other means. The disadvantage of the existing technology is that it is only applicable to scenario 1 and is difficult to be effectively applied to scenarios 2 and 3. Taking the calibration of the initial wavefront in scenario 2 as an example, see Figure 5The diagram below shows a schematic diagram of a prior art method for detonation wave scenario 2. The prior art method first generates an initial wavefront based on empirical experience using the detonation time at a known point, then calculates the propagation process, and finally verifies the calculated result at the known point. If the error does not meet the required error, the initial wavefront is adjusted again until the error meets the required error. A similar process is followed for scenario 3, where explosive parameter calibration is performed. As can be seen in scenarios 2 and 3, the prior art method requires repeated manual adjustments, resulting in low efficiency. Furthermore, adjusting the initial wavefront or explosive parameters based on error depends on empirical experience, making it difficult to fully utilize 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, full utilization of known data is achieved. The following uses 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 using a fully connected network with two hidden layers and 50 nodes in each hidden layer. The network construction and training are implemented using the PyTorch package in the Python language. The automatic differentiation module (Autograd) provided by PyTorch is used to calculate the derivative of the network output with respect to the input. The widely used Adam optimizer is used for residual optimization, and the optimization process is a multi-step iterative process.

[0152] Scenario 1: In solving the direct problem of 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. 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 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: one input layer, one output layer, and two hidden layers. The input layer is the coordinates (x1, x2), the output layer is the detonation time t, and each hidden layer has 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 a three-dimensional point (x1, x2, x3), then 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, respectively. 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, loss 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 If (θ) is not equal to 0, it 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 based on the convergence situation, and larger weights can be multiplied for residuals that converge more slowly. For example, all weights except the propagation direction 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, with a learning rate of lr = 0.001 and other parameters using default settings. Figure 6b The diagram of the total residual change of the blast wave propagation simulation in scenario 1 is shown in Figure 1. 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 detonation time distribution 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. Figure 7 The schematic diagram of the measurement point data of scene 2 is shown. 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 repeated 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, respectively. 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 measurement point data on the four straight lines. 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 those in scenario 1. Figure 8a Schematic diagram of the total residual change of the explosion wave propagation simulation in the scenario 2 shown and Figure 8b The diagram below shows the results of a visualization of the detonation wave propagation simulation for scenario 2. After 3000 iterations of optimization, the total residual was reduced to 0.01, and the relative error at the two error test points was less than 1%. The contour line at time 0 represents 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 unknown. The explosive parameter α is calibrated based on 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. 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 repeated 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] The explosive parameter α is unknown, and the residuals in the equation contain two unknown parameters, θ and α. The method for establishing each residual is the same as in scenarios one and two.

[0179] 3) Optimize training and results

[0180] The optimizer and settings are the same as in scenario 1. Figure 9 The schematic diagram of explosive parameter changes in the simulation of explosion wave propagation in scenario 3 is shown in the figure. The initial value of explosive parameter α is 1. The convergence process in the iterative optimization process is as follows: Figure 9 As shown in the figure, the explosive parameter α undergoes a brief rapid increase and rapid decrease at the beginning of training, and then gradually approaches the true value at a very slow rate. 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 will 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 program, 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 document, relational terms such as first and second, etc., are used only to distinguish one entity or operation from another entity or operation, and do not necessarily require or imply any actual relationship or order between these entities or operations. Moreover, the terms "comprises," "comprising," or any other variations thereof are intended to cover non-exclusive inclusion, such that a process, method, article, or device comprising a series of elements includes not only those elements, but also other elements not explicitly listed, or elements inherent to such process, method, article, or device. In the absence of further limitations, an element defined by the phrase "comprising a ..." does not exclude the presence of additional identical elements in the process, method, article, or device comprising the element.

[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 scope of protection of the present invention should be based on the scope defined by the claims.

Claims

1. A multifunctional calculation method for detonation wave propagation that integrates data and physical information, characterized in that: The method comprises the following steps: Acquiring the position coordinates of the sample point and known physical information, wherein the known physical information includes an initiation time control equation, boundary conditions, and propagation direction law; the known physical information also includes an initial wavefront, or an initiation time of the measuring point, or both the initial wavefront and the initiation time of the measuring point; 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; A total residual is established based on the known physical information and the predicted detonation time corresponding to the sample point position coordinates; the residual components corresponding to the boundary conditions include a first boundary residual and a second boundary residual, the first boundary residual is a material boundary that constrains the propagation direction of the detonation wave, and the second boundary residual is a symmetric boundary that constrains the propagation direction of the detonation wave; The expression of the residual component corresponding to the propagation direction law is: ， in, is the residual component corresponding to the propagation direction law; is the number of sample points of the propagation direction law; The position coordinates of the first sample point The corresponding predicted detonation time; The coordinates 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; for The upper limit set by the function; When the known physical information further includes an initial wavefront, establishing a total residual based on the known physical information and the predicted detonation time corresponding to the sample point position coordinates includes: ， in, is the total residual; are the weight and bias parameters in the fully connected neural network, and are to be determined; is the corresponding residual component of the detonation time control equation; is the corresponding residual component of the initial wavefront; is the residual component corresponding to the boundary condition; A1-A4 are preset weight values ​​and A4 is greater than A1, A2, and A3; The expression of the corresponding residual component of the initial wavefront is: ， in, 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: ， in, is the number of sample points of the detonation time control equation; is the sample point location coordinate The corresponding predicted detonation time gradient; are explosive parameters and are known parameters; is the detonation wavefront curvature; For explosives CJ detonation speed; The parameters to be determined 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 When the known physical information further includes the detonation time of the measurement point: establishing the total residual according to the known physical information and the predicted detonation time corresponding to the position coordinates of the sample point includes: ， in, is the residual component corresponding to the detonation time of the measuring point; B1-B4 are preset weight values ​​and B4 is greater than B1, B2, and B3.

3. The method according to claim 1, characterized in that When the known physical information further includes the initial wavefront and the detonation time of the measurement point: establishing the total residual according to the known physical information and the predicted detonation time corresponding to the position coordinates of the sample point includes: ， in, is the explosive parameter and is to be determined; is the corresponding residual component of the detonation time control equation; C1-C5 are preset weight values ​​and C5 is greater than C1, C2, C3, and C4.

4. The method according to claim 2 or 3, characterized in that The expression of the corresponding residual component of the detonation time of the measuring point is: , in, 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.

5. The method according to claim 3, characterized in that The expression of the corresponding residual component of the detonation time control equation is: ， in, is the number of sample points of the detonation time control equation; is the sample point location coordinate The corresponding predicted detonation time gradient; is the detonation wavefront curvature; For the explosive CJ detonation speed.

6. The method according to any one of claims 1 to 3, characterized in that The expression of the first boundary residual is: ， ， in, is the first boundary residual; 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; is the boundary threshold angle; for The upper limit set by the function; The expression of the second boundary residual is: ， ， in, is the second boundary residual; 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.

7. 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 parameters to be determined until the relative error of the predicted detonation time is less than a preset threshold, and the preset convergence condition is met.

Images