Concrete penetration depth prediction method, device, equipment and medium

Abstract

The invention discloses a concrete penetration depth prediction method, device, equipment and medium, and relates to the technical field of concrete anti-penetration performance analysis, and the technical scheme is as follows: constructing a state vector according to a physical variable set generated in a rigid elastic body penetration concrete process; constructing a dimension matrix according to the state vector, and performing singular value decomposition on the dimension matrix to obtain a null space orthogonal base; performing linear mapping on the null space orthogonal base through a pre-trained learnable parameter matrix to obtain a feature index matrix; inputting the logarithm mapping result of the state vector and the feature index matrix into a neural network for forward propagation calculation, and outputting dimensionless features; inputting the dimensionless features into a multi-objective optimization algorithm, searching in an operator space of the multi-objective optimization algorithm, and outputting an analytic formula of the dimensionless penetration depth when the Pareto front of formula complexity and fitting loss reaches an optimal solution; and predicting the penetration depth of the concrete based on the analytical formula.

Description

Technical Field

[0001] This invention relates to the field of concrete penetration resistance analysis technology, and more specifically, to a method, apparatus, equipment, and medium for predicting concrete penetration depth. Background Technology

[0002] Analysis of the penetration resistance of concrete structures is a core aspect of concrete engineering protection design.

[0003] Traditional prediction methods primarily rely on semi-empirical formulas (such as the Forrestal formula) or purely empirical formulas based on cavity expansion theory. However, these methods have the following limitations: First, classical formulas are usually based on the assumption of geometric similarity, but in large-caliber conditions (such as projectile diameter > 76.2 mm), the prediction results often show significant deviations (underestimating the penetration depth) due to neglecting the mesoscopic heterogeneity of concrete (the influence of aggregate size). Existing pure data-driven machine learning models (such as BP neural networks and random forests), although having high fitting loss, are black-box models, lacking physical consistency constraints. The intermediate calculation process may violate dimensional homogeneity, and they cannot output explicit analytical formulas, making them difficult to promote and apply in practical engineering. Traditional dimensional analysis relies on experts manually selecting dimensionless terms (such as Johnson numbers), which easily overlooks key physical coupling mechanisms (such as the relative aggregate size effect). Real experimental data is usually sparse and contains high noise, and directly using symbolic regression is prone to getting trapped in local optima or producing complex formulas that overfit. Summary of the Invention

[0004] The purpose of this invention is to provide a method, apparatus, equipment, and medium for predicting concrete penetration depth, in order to solve the problems of large prediction deviations caused by neglecting the mesoscopic aggregate scale effect under large-diameter conditions and the lack of physical interpretability of the prediction process.

[0005] The above-mentioned technical objective of the present invention is achieved through the following technical solution:

[0006] In a first aspect, the present invention provides a method for predicting the penetration depth of concrete, the method comprising:

[0007] Obtain the set of physical variables generated during the process of a rigid projectile penetrating concrete, and construct a state vector based on the set of physical variables;

[0008] A dimensional matrix is ​​constructed based on the state vector, and singular value decomposition is performed on the dimensional matrix to obtain a null space orthogonal basis.

[0009] The feature exponent matrix is ​​obtained by linearly mapping the null space orthogonal basis using a pre-trained learnable parameter matrix.

[0010] The logarithmic mapping result of the state vector and the feature exponent matrix are input into the neural network for forward propagation calculation, and the dimensionless features are output; wherein, the dimensionless features include Johnson number, mass ratio and relative aggregate size;

[0011] The dimensionless features are input into a multi-objective optimization algorithm, and a search is performed in the operator space of the multi-objective optimization algorithm. When the optimal solution is reached in the Pareto front of the formula complexity and fitting loss, the analytical formula of the dimensionless penetration depth is output.

[0012] Predicting the penetration depth of concrete based on an analytical formula for dimensionless penetration depth.

[0013] In one implementation, the set of physical variables includes impact velocity, target density, projectile diameter, concrete compressive strength, projectile mass, and maximum aggregate particle size.

[0014] In one implementation, constructing a dimensional matrix based on the state vector includes: deriving the elements within the state vector based on a fundamental dimensional set to obtain the dimensional matrix; wherein the dimensional matrix describes the power of each physical variable on the fundamental dimensional set, which includes length, mass, and time.

[0015] In one implementation, the training method for the learnable parameter matrix includes:

[0016] Obtain multiple sets of actual physical variables for projectile penetration into concrete, and the actual penetration depth corresponding to each set of actual physical variables;

[0017] Each set of actual physical variables is input into a pre-built fully connected neural network for forward propagation, and the predicted penetration depth is output.

[0018] The loss value between the predicted penetration depth and the actual penetration depth is calculated using a loss function consisting of a prediction error term and a decoupling penalty term.

[0019] When the loss value converges, the weight matrix is ​​output, and the weight matrix is ​​subjected to the simplest transformation to obtain the learnable parameter matrix.

[0020] In one implementation, a Frobenius norm term is introduced to constrain the parameter space complexity for the prediction error term.

[0021] For the decoupling penalty term, an L1 sparse regularization term is introduced to induce the features to converge to the simplest form matrix.

[0022] In one implementation, the expression for the loss function is:

[0023] Where t represents the normalized training process, For the prediction error term, The balance parameter for the prediction error term. The characteristic index matrix, for The Frobenius norm, To balance the decoupling penalty term, For decoupling penalty terms, The balancing parameter for the L1 sparse regularization term is... for L1 sparse regularization terms.

[0024] In one implementation, the input to the multi-objective optimization algorithm further includes a warhead shape factor;

[0025] When the Pareto front reaches the optimal solution in terms of formula complexity and fitting loss, an analytical formula for dimensionless penetration depth is output, including: using the elbow method to determine an analytical formula on the Pareto curve that takes into account both formula complexity and fitting loss.

[0026] A second aspect of the present invention provides a device for predicting the penetration depth of concrete, the method comprising:

[0027] A state vector construction unit is used to obtain the set of physical variables generated during the process of a rigid projectile penetrating concrete, and to construct a state vector based on the set of physical variables.

[0028] A matrix decomposition unit is used to construct a dimensional matrix based on the state vector and perform singular value decomposition on the dimensional matrix to obtain a null space orthogonal basis.

[0029] A linear mapping unit is used to perform a linear mapping on the null space orthogonal basis through a pre-trained learnable parameter matrix to obtain a feature exponent matrix;

[0030] A dimensionless feature calculation unit is used to input the logarithmic mapping result of the state vector and the feature exponent matrix into a neural network for forward propagation calculation and output dimensionless features; wherein, the dimensionless features include Johnson number, mass ratio and relative aggregate size;

[0031] The analytical formula output unit is used to input the dimensionless feature into the multi-objective optimization algorithm, search in the operator space of the multi-objective optimization algorithm, and output the analytical formula of the dimensionless penetration depth when the Pareto front of the formula complexity and fitting loss reaches the optimal solution.

[0032] The prediction unit is used to predict the penetration depth of concrete based on an analytical formula for dimensionless penetration depth.

[0033] A third aspect of the present invention provides an electronic device, including a memory and a processor;

[0034] A memory for storing computer programs, the computer programs including program instructions;

[0035] A processor is configured to execute the program instructions to cause the electronic device to perform the steps of a concrete penetration depth prediction method as provided in the first aspect of the invention.

[0036] A fourth aspect of the present invention provides a computer-readable storage medium comprising a computer program that, when executed by one or more processors, implements a method for predicting concrete penetration depth as provided in the first aspect of the present invention.

[0037] Compared with the prior art, the present invention has the following beneficial effects:

[0038] This invention determines the null space orthogonal basis of the dimensional matrix through singular value decomposition. A pre-trained learnable parameter matrix is ​​used to linearly map this null space orthogonal basis to obtain a feature exponent matrix. This strictly restricts the search space of the neural network weights to the null space, thereby forcibly constraining the dimensionless features of the neural network output in subsequent processes to satisfy Buckingham's π theorem (i.e., maintaining dimensional homogeneity). Therefore, it can automatically decouple and extract key dimensionless features such as Johnson number and mass ratio from physical variables without the intervention of expert prior knowledge. Secondly, it is applicable to large-diameter working conditions. To address the significant prediction bias caused by neglecting the mesoscopic aggregate scale effect, this paper incorporates the maximum aggregate particle size into the set of physical variables. It identifies and extracts the dimensionless feature of relative aggregate size, which is ignored by traditional theories. This dimensionless feature quantitatively characterizes the physical phenomenon of decreased penetration resistance as the projectile diameter increases and the aggregate interlocking effect weakens, effectively correcting the prediction bias caused by neglecting the mesoscopic aggregate scale effect. Finally, a multi-objective optimization algorithm is used for regression to obtain an analytical formula for the dimensionless penetration depth. This process distills an analytical formula that combines physical simplicity and numerical accuracy from the neural network weights. This mechanism combines the nonlinear fitting capability of deep learning with the interpretability of symbolic regression, ultimately achieving accurate prediction of concrete penetration depth and automatic discovery of its physical evolution laws. Attached Figure Description

[0039] The accompanying drawings, which are included to provide a further understanding of embodiments of the invention and form part of this application, do not constitute a limitation thereof. In the drawings:

[0040] Figure 1 A flowchart illustrating a method for predicting concrete penetration depth provided in an embodiment of the present invention;

[0041] Figure 2A flowchart illustrating a method for predicting concrete penetration depth provided in an embodiment of the present invention;

[0042] Figure 3 Pareto front diagram provided for embodiments of the present invention;

[0043] Figure 4 A comparison chart of predicted values ​​and actual values ​​obtained using the prediction method provided by the present invention, provided for an embodiment of the present invention;

[0044] Figure 5 This is a schematic diagram of a concrete penetration depth prediction device provided in an embodiment of the present invention. Detailed Implementation

[0045] To make the objectives, technical solutions, and advantages of the present invention clearer, the present invention will be further described in detail below with reference to the embodiments and accompanying drawings. The illustrative embodiments and descriptions of the present invention are only used to explain the present invention and are not intended to limit the present invention.

[0046] It should be noted that the terms "comprising" or "may include" used in the various embodiments of this application indicate the presence of the claimed function, operation, or element, and do not limit the addition of one or more functions, operations, or elements. Furthermore, as used in the various embodiments of this application, the terms "comprising," "having," and their cognates are intended only to indicate a specific feature, number, step, operation, element, component, or combination of the foregoing, and should not be construed as primarily excluding the presence of one or more other features, numbers, steps, operations, elements, components, or combinations of the foregoing, or adding one or more combinations of the foregoing.

[0047] It should be understood that terms such as "first" and "second" are used for descriptive purposes only and should not be construed as indicating or implying relative importance or implicitly specifying the number of technical features indicated. Therefore, a feature defined as "first" or "second" may explicitly or implicitly include one or more of that feature. In the description of this invention, "a plurality of" means two or more, unless otherwise explicitly specified.

[0048] Before providing a further detailed description of the embodiments of this application, the nouns and terms involved in the embodiments of this application will be explained, and the nouns and terms involved in the embodiments of this application shall be interpreted as follows.

[0049] 1. Neural Networks: This invention is based on a prediction method constructed using a Multilayer Perceptron (MLP) within a neural network. Neural networks are a method with powerful nonlinear prediction capabilities. Key parameters include the number of hidden layers, the number of neurons per layer, the activation function, the learning rate, the optimization method, the loss function, the dropout rate, and K-fold cross-validation.

[0050] 2. Buckingham's π Theorem: Consider an ovoid projectile normally penetrating a semi-infinite thickness concrete target system. The system's state is determined by n independent physical variables. (e.g., V is the impact velocity,) Where D is the target density and D is the projectile diameter. (where M represents the compressive strength of concrete and M represents the mass of the projectile, etc.). These physical variables can be derived from the basic dimensional set. (L is length, M is mass, T is time) Derived. Regarding the concrete penetration problem, based on Buckingham... Theorem (Buckingham) Both theorem and the objective function f can be represented by a simplified set of dimensionless parameters. It means that, among them, The target output variable must be the dimensionless penetration depth P / d (or P / L). Therefore, the learning objective is to find a direct mapping. Transform into discovery mapping , so that: .

[0051] According to Buckingham's π theorem, any equation with physical meaning must satisfy the dimensional homogeneity constraint. That is, the above physical relationship is a functional mapping between k = n - m dimensionless invariants (π terms). Traditional semi-empirical models (such as Forrestal formulas) rely on expert prior knowledge to heuristically construct the π term form, lacking the ability to adaptively represent complex nonlinear characteristics (especially the mesoscopic heterogeneity effect introduced by aggregate particle size dagg). To address this limitation, this application constructs a two-stage physical discovery network neural symbolic computation framework, such as... Figure 2As shown, the first stage is the differentiable dimensional inference in step one, and the second stage is the symbolic regression of physical constraints in step two. This framework employs a cascaded computational path of first reducing dimensionality and decoupling, then performing symbolic evolution, establishing an automated discovery process from high-dimensional experimental data to explicit physical laws. In the first stage of differentiable dimensional inference, a neural network with embedded null space topological constraints is constructed. Utilizing a dynamic curriculum learning strategy, the optimal dimensionless basis set controlling the physical process is automatically identified and orthogonalized during data fitting. Based on this, the second stage, the symbolic evolution module based on dimensional constraints, uses the orthogonal dimensionless basis set decoupled in the first stage as a physical prior, performing a restricted symbolic search on the original experimental observation manifold. This drives a genetic algorithm to directly solve for an explicit analytical expression from noisy observation data that possesses physical parsimony, robustness, and high-fidelity.

[0052] The embodiments of this application will now be described with reference to the accompanying drawings.

[0053] Please refer to Figure 1 This application provides a method for predicting the penetration depth of concrete, the method comprising:

[0054] S101, Obtain the set of physical variables generated during the process of a rigid projectile penetrating concrete, and construct a state vector based on the set of physical variables.

[0055] Specifically, the set of physical variables includes the target impact velocity V and the target density. Projectile diameter D, concrete compressive strength Projectile mass M and maximum aggregate particle size The physical variables included in the above set can be obtained through experimental measurement. For example, the impact velocity can be measured using a light curtain target velocity measurement system or a Doppler radar velocimeter. Specifically, with the light curtain target velocity measurement system, two sets of light curtain targets are arranged parallel to each other at a certain distance in front of the target body, with the light curtain plane perpendicular to the projectile's trajectory. The projectile passes through the two sets of light curtains in sequence, and the time difference Δt between the curtain passes is recorded. Combined with the distance L between the two sets of light curtains, the impact velocity V = L / Δt is calculated. With the Doppler radar velocimeter, the radar is mounted to the side of the trajectory, aligned with the projectile's flight path. The radar captures the Doppler frequency shift signal of the projectile in real time and directly outputs the projectile's velocity curve throughout its entire flight. The velocity value of the projectile at the moment of contact with the target body is extracted as the impact velocity. Since the testing of physical variables is a conventional technique well-known to those skilled in the art, this embodiment will not provide a detailed description of the measurement methods for the remaining physical variables.

[0056] It should be noted that, due to the technical difficulty that the classical semi-empirical formulas provided by the existing technology have in predicting failure under large-diameter conditions because they ignore the mesoscopic heterogeneity of concrete, the maximum aggregate particle size is added to the physical variable set in this embodiment.

[0057] Therefore, the expression for the state vector is: In this embodiment, n=7, including It should be noted that the dimensionless warhead shape factor CRH does not participate in dimensionless inference.

[0058] S102, construct a dimensional matrix based on the state vector, and perform singular value decomposition on the dimensional matrix to obtain a null space orthogonal basis.

[0059] In this embodiment, the aim is to construct a neural network input layer with embedded physical hard constraints, forcing the neural network to perform feature search on a dimensionless manifold, and ensuring that the output dimensionless features satisfy Buckingham's π theorem under any weight update.

[0060] In one embodiment, the elements within the state vector are derived based on a fundamental set of dimensions to obtain a dimensional matrix; wherein the dimensional matrix describes the power of each physical variable on the fundamental set of dimensions, which includes length, mass, and time.

[0061] To transform the power-law product form in the physical formula into a linear combination form that neural networks excel at, a logarithmic mapping is performed on the state vector to obtain... .

[0062] At the same time, based on the basic dimensional set (mass, length, time), construct a dimensional matrix (where k=3), elements of the dimension matrix This represents the power of the j-th physical variable on the i-th fundamental dimension.

[0063] According to the principle of dimensional homogeneity, any dimensionless quantity The exponential vector W must satisfy the system of linear equations. This means that an effective weight vector must lie within the dimensional matrix. Within the zero space.

[0064] To explicitly parameterize this constraint, this invention modifies the dimensional matrix. Perform Singular Value Decomposition (SVD): Select the right singular vectors corresponding to the zero singular values ​​to form a set of orthogonal basis vectors for the null space. ,in, Let m be the number of independent dimensionless numbers, for example, m=4.

[0065] S103, the null space orthogonal basis is linearly mapped using a pre-trained learnable parameter matrix to obtain the feature exponent matrix.

[0066] Specifically, in the first layer of the neural network, i.e., the input layer, the neural network used in this embodiment is a fully connected neural network (MLP). As those skilled in the art will understand, radial basis function networks (RBF), Gaussian process regression (GPR), or other deep learning models with universal approximation capabilities can also be used instead of MLP. For example, the fully connected neural network (MLP) contains 3 hidden layers, each with 64 neurons, and the activation function is GELU.

[0067] Instead of directly using weights as learnable parameters in the input layer, a set of unconstrained learnable parameter matrices is introduced. And project it back to the physical parameter space through the null basis; the formula for the linear mapping is: , Describes an orthogonal basis. This represents the characteristic index matrix.

[0068] S104, the logarithmic mapping result of the state vector and the feature index matrix are input into the neural network for forward propagation calculation, and the dimensionless features are output; wherein, the dimensionless features include Johnson number, mass ratio and relative aggregate size.

[0069] Specifically, the forward propagation calculation formula for a neural network is defined as follows: Regardless of how the learnable parameter matrix Q is updated during backpropagation, the generated feature exponent matrix... Always strictly meet This constraint, this mathematical construction, fundamentally eliminates the possibility of dimensional inconsistencies in model generation, expanding the search space from the entire real number field. Compressed to a physically permissible low-dimensional manifold .

[0070] Because this invention incorporates the maximum aggregate particle size into the set of physical variables, and combined with the learnable parameter matrix provided in this embodiment, it can automatically search for nonlinear coupling relationships between physical variables in the neural network, thereby identifying and extracting the relative aggregate size correction term that is ignored by traditional theory. This quantitatively characterizes the physical phenomenon that the penetration resistance decreases as the projectile diameter increases, due to the weakening of the aggregate interlocking effect. This effectively corrects the prediction bias when extrapolating across scales.

[0071] In one embodiment, the learnable parameter matrix is ​​trained as follows: First, multiple sets of actual physical variables of the projectile penetrating concrete are obtained, along with the actual penetration depth corresponding to each set of actual physical variables. Then, each set of actual physical variables is input into a pre-constructed fully connected neural network for forward propagation, outputting the predicted penetration depth. Second, a loss function consisting of a prediction error term and a decoupling penalty term is used to calculate the loss value between the predicted penetration depth and the actual penetration depth. Finally, when the loss value converges, the weight matrix is ​​output, and the weight matrix is ​​subjected to a simplified transformation to obtain the learnable parameter matrix.

[0072] To robustly identify the optimal dimensionless basis set in noisy experimental data, this application introduces a joint optimization strategy of noise suppression and dynamic evolution. In the preprocessing stage, outliers with relative errors exceeding 50% are automatically removed based on the reconstruction residuals to clean up the input space. In the training stage, a dynamic loss function based on curriculum learning is constructed. Its definition is as follows: Where t represents the normalized training process, For the prediction error term, The balance parameter for the prediction error term. The characteristic index matrix, for The Frobenius norm, To balance the decoupling penalty term, For decoupling penalty terms, The balancing parameter for the L1 sparse regularization term is... for L1 sparse regularization terms.

[0073] It should be noted that, and Linear growth strategies are employed to gradually introduce physical constraints, while The process is only initiated in the latter half of training (t>0.5) to perform fine-tuning, provided that the physical features have been largely locked. This time-varying loss surface ensures that the optimization path always converges along the direction with the clearest physical meaning.

[0074] In the initial stage of training, the optimization objective is determined by the prediction error. The dominant driving force enables the network to quickly identify dominant patterns in the data, while utilizing the Frobenius norm. Constraining parameter space complexity and suppressing overfitting. As training progresses, the system uses dynamic weights... Gradually introduce decoupling penalty terms Strongly correlated physical quantities are forcibly separated, and the features are induced to converge to the simplest form matrix through an L1 sparse regularization term. Finally, the converged weight matrix undergoes a simplest form transformation, automatically outputting a set of orthogonal, complete, and physically meaningful dimensionless features. During training, the Adam optimizer is used with a learning rate of 0.001, combined with 5-fold cross-validation to prevent overfitting.

[0075] In summary, based on steps S101-S104 above, the settings are as follows: The layer output dimension is 3. The MLP contains 3 hidden layers, each with 64 neurons. The activation function is GELU, and the loss function is as described above. CRH itself is dimensionless, therefore it is not used as an input feature of the π layer. The neural network successfully outputs three highly physically meaningful dimensionless features: (Johnson number), (mass ratio) and (Relative aggregate size). To ensure integrity, (Warhead shape factor) is directly added as a dimensionless input parameter to the second stage of knowledge distillation.

[0076] S105, the dimensionless feature is input into a multi-objective optimization algorithm, and a search is performed in the operator space of the multi-objective optimization algorithm. When the Pareto front of the formula complexity and fitting loss reaches the optimal solution, the analytical formula of the dimensionless penetration depth is output.

[0077] Specifically, Figure 2 The second stage input is dimensionless features, and the fitting objective is an analytical formula for the dimensionless penetration depth. Therefore, a genetic programming algorithm is used in the operator space. The search is performed within the framework. Explicit analytical relationships are decoupled from implicit neural network weights. Multi-objective optimization: A Pareto Frontier is constructed to balance formula complexity and fit accuracy (MSE). To ensure the physical interpretability of the final formula, a Strict Physics Validator is integrated into the evolution process. This module acts as a topological screening operator, forcibly eliminating any candidate individuals containing non-real exponents or illegal dimensional nesting structures. The final output selection follows the Pareto Optimality principle. It is understandable that multi-objective optimization, besides genetic programming algorithms, can also utilize variants of genetic programming algorithms, as well as reinforcement learning (RL)-driven symbolic search or gradient-based symbolic regression methods.

[0078] Here, during the optimization process, the elbow method is used to determine an analytical formula on the Pareto curve that balances formula complexity and fitting loss, such as... Figure 3 As shown, Figure 3 The red dot represents the "elbow point," the ordinate is the fitting loss, and the abscissa is the formula complexity. We selected an abscissa point with a complexity of 24. Finally, the analytical formula for the dimensionless penetration depth is expressed as follows: This formula clearly reveals the variation of penetration resistance with relative aggregate size. That is, as... As the projectile size increases (i.e., the projectile becomes larger relative to the aggregate), the aggregate interlocking effect weakens, leading to a nonlinear decrease in normalized penetration resistance. The exponential weight of the relative scale term is automatically assigned statistical significance during evolution, proving that within a given physical space, this term is indispensable for correcting deviations in the classical similarity law. Through these two stages of processing, it is evident that this application has completed a paradigm shift from empirical parameter fitting to the discovery of physical laws, providing a physically based analytical formula for the accurate extrapolation of large-caliber penetration laws.

[0079] like Figure 4 As shown, in the low dimensionless penetration depth range (typically corresponding to small-caliber or low-velocity conditions), the ACE model agrees well with experimental data, with data points clustered near the y=x reference line, indicating that its empirical parameters remain valid within the calibration range. However, with increasing penetration depth and projectile size, the prediction accuracy of these empirical models decreases significantly, with predicted values ​​generally lower than experimental observations. The TSPDN model proposed in this application accurately captures the drag attenuation mechanism that accompanies scale increase, thereby effectively eliminating the underfitting phenomenon in the deep penetration range and demonstrating superior fitting accuracy compared to empirical models.

[0080] S106, Predicting the penetration depth of concrete based on an analytical formula for dimensionless penetration depth.

[0081] Specifically, based on the formula described above, the penetration depth of concrete can be predicted by substituting the physical variables generated during the actual process of a rigid projectile penetrating concrete into the formula.

[0082] Please refer to Figure 5 This application provides a concrete penetration depth prediction device, the method of which includes:

[0083] The state vector construction unit 510 is used to obtain the set of physical variables generated during the process of rigid projectile penetrating concrete, and to construct a state vector based on the set of physical variables.

[0084] Matrix decomposition unit 520 is used to construct a dimensional matrix based on the state vector and perform singular value decomposition on the dimensional matrix to obtain a null space orthogonal basis.

[0085] The linear mapping unit 530 is used to perform a linear mapping on the null space orthogonal basis through a pre-trained learnable parameter matrix to obtain a feature exponent matrix.

[0086] The dimensionless feature calculation unit 540 is used to input the logarithmic mapping result of the state vector and the feature index matrix into the neural network for forward propagation calculation and output dimensionless features; wherein, the dimensionless features include Johnson number, mass ratio and relative aggregate size;

[0087] The analytical formula output unit 550 is used to input the dimensionless feature into the multi-objective optimization algorithm, search in the operator space of the multi-objective optimization algorithm, and output the analytical formula of the dimensionless penetration depth when the Pareto front of the formula complexity and fitting loss reaches the optimal solution.

[0088] Prediction unit 560 is used to predict the penetration depth of concrete based on an analytical formula for dimensionless penetration depth.

[0089] This application provides a concrete penetration depth prediction device, which is similar to the above-mentioned... Figure 1 The concrete penetration depth prediction method shown is a technical solution based on the same inventive concept. Through the detailed description of the concrete penetration depth prediction method provided in the above embodiments, those skilled in the art can clearly understand the implementation process of the concrete penetration depth prediction device in this embodiment. Therefore, for the sake of brevity, it will not be described again here.

[0090] Accordingly, this application determines the null space orthogonal basis of the dimensional matrix through singular value decomposition, and obtains the feature index matrix by linearly mapping the null space orthogonal basis through a pre-trained learnable parameter matrix. This strictly restricts the search space of the neural network weights to the null space, thereby forcibly constraining the dimensionless features of the neural network output in the subsequent process to satisfy Buckingham's π theorem (i.e., maintaining dimensional homogeneity). Therefore, it can automatically decouple and extract key dimensionless features such as Johnson number and mass ratio from physical variables without the intervention of expert prior knowledge. Secondly, for large-diameter industrial applications... To address the significant prediction bias caused by neglecting the mesoscopic aggregate size effect, this paper incorporates the maximum aggregate particle size into the set of physical variables. It identifies and extracts the dimensionless feature of relative aggregate size, which is ignored by traditional theories. This dimensionless feature quantitatively characterizes the physical phenomenon of decreased penetration resistance as the projectile diameter increases and the aggregate interlocking effect weakens, effectively correcting the prediction bias caused by neglecting the mesoscopic aggregate size effect. Finally, a multi-objective optimization algorithm is used for regression to obtain an analytical formula for the dimensionless penetration depth. This process distills an analytical formula with both physical simplicity and numerical accuracy from the neural network weights. This mechanism combines the nonlinear fitting capability of deep learning with the interpretability of symbolic regression, ultimately achieving accurate prediction of concrete penetration depth and automatic discovery of its physical evolution laws.

[0091] This invention also provides an electronic device. The electronic device includes a processor, a memory, a communication interface, and at least one communication bus for connecting the processor, the memory, and the communication interface. The memory includes, but is not limited to, random access memory (RAM), read-only memory (ROM), erasable programmable read-only memory (PROM), or portable read-only memory (CD-ROM), and is used for related instructions and data.

[0092] The communication interface is used to receive and send data. The processor can be one or more CPUs; if the processor is a single CPU, it can be a single-core CPU or a multi-core CPU. The processor in the electronic device reads one or more programs stored in memory, performs the following operations: obtains a set of physical variables generated during the rigid projectile's penetration of concrete, and constructs a state vector based on the set of physical variables; constructs a dimensional matrix based on the state vector, and performs singular value decomposition on the dimensional matrix to obtain a null-space orthogonal basis; performs a linear mapping on the null-space orthogonal basis using a pre-trained learnable parameter matrix to obtain a feature exponent matrix; inputs the logarithmic mapping result of the state vector and the feature exponent matrix into a neural network for forward propagation calculation, outputting dimensionless features; wherein the dimensionless features include Johnson number, mass ratio, and relative aggregate size; inputs the dimensionless features into a multi-objective optimization algorithm, searches in the operator space of the multi-objective optimization algorithm, and outputs an analytical formula for the dimensionless penetration depth when the Pareto front of the formula complexity and fitting loss reaches the optimal solution; and predicts the penetration depth of concrete based on the analytical formula for the dimensionless penetration depth.

[0093] It should be noted that the specific implementation of each operation can be described above. Figure 1 The corresponding description of the method embodiments shown indicates that the electronic device can be used to execute a concrete penetration depth prediction method according to the above method embodiments of this application, which will not be described in detail here.

[0094] This invention also provides a computer-readable storage medium, which is a memory device in a computer device for storing programs and data. It is understood that the computer-readable storage medium here can include both built-in storage media in the computer device and extended storage media supported by the computer device. The computer-readable storage medium provides storage space that stores the operating system of the terminal. Furthermore, the storage space also stores one or more instructions suitable for loading and execution by a processor. These instructions can be one or more computer programs (including program code). It should be noted that the computer-readable storage medium here can be high-speed RAM or non-volatile memory, such as at least one disk storage device. The processor can load and execute one or more instructions stored in the computer-readable storage medium to implement the corresponding steps of the concrete penetration depth prediction method in the above embodiments. Those skilled in the art should understand that embodiments of the present invention can be provided as methods, systems, or computer program products. Therefore, the present invention can take the form of a completely hardware embodiment, a completely software embodiment, or an embodiment combining software and hardware aspects. Furthermore, the present invention can take the form of a computer program product implemented on one or more computer-usable storage media (including but not limited to disk storage, CD ROM, optical storage, etc.) containing computer-usable program code.

[0095] The specific embodiments described above further illustrate the purpose, technical solution, and beneficial effects of the present invention. It should be understood that the above description is only a specific embodiment of the present invention and is not intended to limit the scope of protection of the present invention. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of the present invention should be included within the scope of protection of the present invention.

Claims

1. A method for predicting the penetration depth of concrete, characterized in that the method... include: Obtain the set of physical variables generated during the process of a rigid projectile penetrating concrete, and construct a state vector based on the set of physical variables; A dimensional matrix is ​​constructed based on the state vector, and singular value decomposition is performed on the dimensional matrix to obtain a null space orthogonal basis. The feature exponent matrix is ​​obtained by linearly mapping the null space orthogonal basis using a pre-trained learnable parameter matrix. The logarithmic mapping result of the state vector and the feature exponent matrix are input into the neural network for forward propagation calculation, and the dimensionless features are output; wherein, the dimensionless features include Johnson number, mass ratio and relative aggregate size; The dimensionless features are input into a multi-objective optimization algorithm, and a search is performed in the operator space of the multi-objective optimization algorithm. When the optimal solution is reached in the Pareto front of the formula complexity and fitting loss, the analytical formula of the dimensionless penetration depth is output. Predicting the penetration depth of concrete based on an analytical formula for dimensionless penetration depth.

2. The method according to claim 1, characterized in that, The set of physical variables includes impact velocity, target density, projectile diameter, concrete compressive strength, projectile mass, and maximum aggregate particle size.

3. The method according to claim 1, characterized in that, Constructing a dimensional matrix based on the state vector includes: deriving the elements within the state vector based on a basic dimensional set to obtain a dimensional matrix; wherein the dimensional matrix describes the power of each physical variable on the basic dimensional set, which includes length, mass, and time.

4. The method according to claim 1, characterized in that, The training methods for the learnable parameter matrix include: Obtain multiple sets of actual physical variables for projectile penetration into concrete, and the actual penetration depth corresponding to each set of actual physical variables; Each set of actual physical variables is input into a pre-built fully connected neural network for forward propagation, and the predicted penetration depth is output. The loss value between the predicted penetration depth and the actual penetration depth is calculated using a loss function consisting of a prediction error term and a decoupling penalty term. When the loss value converges, the weight matrix is ​​output, and the weight matrix is ​​subjected to the simplest transformation to obtain the learnable parameter matrix.

5. The method according to claim 4, characterized in that, For the prediction error term, a Frobenius norm term is introduced to constrain the parameter space complexity; For the decoupling penalty term, an L1 sparse regularization term is introduced to induce the features to converge to the simplest form matrix.

6. The method according to claim 5, characterized in that, The expression for the loss function is: Where t represents the normalized training process, For the prediction error term, The balance parameter for the prediction error term. The characteristic index matrix, for The Frobenius norm, To balance the decoupling penalty term, For decoupling penalty terms, The balancing parameter for the L1 sparse regularization term is... for L1 sparse regularization terms.

7. The method according to claim 1, characterized in that, The input to the multi-objective optimization algorithm also includes the warhead shape factor; When the Pareto front reaches the optimal solution in terms of formula complexity and fitting loss, an analytical formula for dimensionless penetration depth is output, including: using the elbow method to determine an analytical formula on the Pareto curve that takes into account both formula complexity and fitting loss.

8. A device for predicting the penetration depth of concrete, characterized in that, The methods include: A state vector construction unit is used to obtain the set of physical variables generated during the process of a rigid projectile penetrating concrete, and to construct a state vector based on the set of physical variables. A matrix decomposition unit is used to construct a dimensional matrix based on the state vector and perform singular value decomposition on the dimensional matrix to obtain a null space orthogonal basis. A linear mapping unit is used to perform a linear mapping on the null space orthogonal basis through a pre-trained learnable parameter matrix to obtain a feature exponent matrix; A dimensionless feature calculation unit is used to input the logarithmic mapping result of the state vector and the feature exponent matrix into a neural network for forward propagation calculation and output dimensionless features; wherein, the dimensionless features include Johnson number, mass ratio and relative aggregate size; The analytical formula output unit is used to input the dimensionless feature into the multi-objective optimization algorithm, search in the operator space of the multi-objective optimization algorithm, and output the analytical formula of the dimensionless penetration depth when the Pareto front of the formula complexity and fitting loss reaches the optimal solution. The prediction unit is used to predict the penetration depth of concrete based on an analytical formula for dimensionless penetration depth.

9. An electronic device, characterized in that, Including memory and processor; A memory for storing computer programs, the computer programs including program instructions; A processor is configured to execute the program instructions to cause the electronic device to perform the steps of a concrete penetration depth prediction method as described in any one of claims 1 to 7.

10. A computer-readable storage medium, characterized in that, The computer-readable storage medium includes a computer program that, when executed by one or more processors, implements a method for predicting concrete penetration depth as described in any one of claims 1 to 7.

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