Structural dynamic response calculation method and system based on adaptive physical base network

Abstract

The present application relates to a method and system for calculating the dynamic response of a structure based on an adaptive physical base network. The method includes: determining the first n-order modes that contribute the most to the dynamic response of the structure; based on the vibration mode decomposition method, decoupling the m differential equations that characterize the mutually coupled dynamic response of the structure into independent equations corresponding to the first n-order modes; characterizing the load characteristics under different load conditions with scalar parameters under each modal coordinate according to the independent equations corresponding to the first n-order modes; inputting the adaptive physical base network of the n-order mode corresponding to the time input to predict the response components of the first n-order modes of the structure under unit load in the modal space; multiplying the modal response components with the scalar parameters that characterize the load characteristics to obtain the modal response components under the actual load conditions; converting the modal response components in the modal space into the dynamic response in the physical space. It solves the problem that the dynamic response of multi-degree-of-freedom structures based on the PINN network framework is difficult to solve and the load conditions are difficult to generalize.

Description

Technical Field

[0001] The present application relates to the fields of artificial intelligence technology and structural dynamic response technology, and in particular to a structural dynamic response calculation method, device, computer equipment, storage medium and computer program product based on an adaptive physical base network. Background Art

[0002] With the development of computer technology, in recent years, multi-layer perceptron (MLP) has been used to solve partial differential equations and has attracted people's attention. Among them, physical information neural network (PINN) has great potential in the field of solving partial differential equations. This method embeds known prior knowledge into the neural network to guide the learning of the network, so that the network can achieve non-target learning.

[0003] However, this method (PINN) can generally only be used for relatively simple physical problems. In the field of civil engineering, the calculation of structural dynamic response is an important part of structural analysis. However, for general civil engineering structures, there are thousands of degrees of freedom, and structural dynamic analysis involves a large number of coupled dynamic partial differential equations. Traditional neural networks cannot adapt to such complex dynamic systems. Summary of the invention

[0004] Based on this, it is necessary to provide a structural dynamic response calculation method, device, computer equipment, computer readable storage medium and computer program product based on an adaptive physical base network to address the above-mentioned technical problems, which can solve the problem that the dynamic response of multi-degree-of-freedom structures in a network framework based on PINN is difficult to solve, and solve the problem that load conditions in a network framework based on PINN are difficult to generalize.

[0005] Furthermore, due to the spectral deviation of the multilayer perceptron, it is difficult to capture the high-frequency features in the partial differential equations, so the traditional physical information neural network (PINN) is difficult to accurately calculate the high-frequency part of the structural response. To address this problem, a physical information radial basis network (PIRBN) has been proposed to solve differential equations containing high-frequency features. However, in order to maintain the local approximation ability of the physical information radial basis network, each neuron center needs to be manually set to a fixed value at the beginning of the model training, and does not participate in the parameter update during the model training process. Although some studies have given a recommended initialization method for the neuron center in the computational domain, the initialization distribution is not the optimal initialization distribution of the neuron center, which limits the network's ability to fit high-frequency functions. In addition, in the selection of the radial basis function, only its physical characteristics are specifically specified, while its physical meaning is ignored. To address this problem, this application introduces an adaptive neuron center parameter based on the boundedness of the Tanh function and proposes an adaptive physical basis network. This parameter can adaptively search for the best neuron center distribution during the neural network training process, thereby improving the accuracy of the neural network's high-frequency differential equation calculation.

[0006] In addition, the existing physical information radial basis network has weak physical interpretation in network structure, and each hyperparameter has no clear physical meaning. Although specific physical information is embedded in the network constraints, it is still a "black box" model at the structural level. To address this problem, this application proposes an adaptive physical basis network, which selects wavelet basis functions as the activation function of the radial basis network, so that the hyperparameters of the neural network have clear physical meanings, and the neural network has strong physical interpretability.

[0007] Finally, almost all physical information neural network models, including physical information radial basis networks, can only solve partial differential equations, but cannot provide information about partial differential equations in the frequency domain. To address this problem, the adaptive physical basis network proposed in this application selects appropriate wavelet basis functions, and while calculating the solution of partial differential equations, it also provides its distribution information in the frequency domain based on the physical interpretability of each hyperparameter.

[0008] In summary, in a first aspect, the present application provides a method for calculating structural dynamic response based on an adaptive physical-based network. The method comprises:

[0009] Determine the first n modes that contribute most to the structural dynamic response;

[0010] Based on the mode decomposition method, the m differential equations that characterize the mutually coupled dynamic response of the structure are decoupled into independent equations corresponding to the first n modes.

[0011] According to the independent equations corresponding to the first n-order modes, the load characteristics under different load conditions are characterized by scalar parameters in the coordinates of each order mode;

[0012] The adaptive physical basis network of the nth mode corresponding to the time input predicts the response components of the first n modes of the structure under unit load in the modal space;

[0013] The modal response components are multiplied by the scalar parameters that characterize the load characteristics to obtain the modal response components under the actual load conditions, and the modal response components in the modal space are converted into dynamic responses in the physical space.

[0014] In one embodiment, for the first n modes, an adaptive physical base network is built corresponding to each mode;

[0015] According to the characteristics and requirements of the differential equations corresponding to the n modes, a suitable wavelet basis function is selected to construct the neuron activation function of the adaptive physical basis network, where the one-dimensional wavelet basis function can be expressed as:

[0016]

[0017] in, is the wavelet function, b is the time shift factor, a is the scale factor, t For time;

[0018] According to the computational domain of the differential equation to be solved, the width of the hidden layer of the radial basis network is set appropriately, and then the neuron center parameters of the adaptive physical basis network are constructed to decouple the neurons in the computational domain.

[0019] The parameters Set to freeze part With the trainable part ,in,

[0020]

[0021]

[0022]

[0023] In the formula, Representative neurons, is an adaptive neuron center parameter, which is used to control the trainable range of the neuron center. This parameter is set according to the size of the computational domain and the number of radial basis network neurons. c i It is a trainable parameter that is optimized as the training progresses;

[0024] Among them, the parameter freezing part Used to control the local influence area of ​​each neuron, the parameters can be trained Used to search for the most appropriate neuron center distribution corresponding to the differential equation to be solved.

[0025] In one embodiment, the loss function of the adaptive physical base network is:

[0026]

[0027] in, is the residual loss of the partial differential equation, is the initial condition loss; is the weight parameter;

[0028]

[0029]

[0030] in, W is the number of sampling points, For the i The displacement response under the first mode, express The acceleration of time, express The speed of time, represents the modal space i The modal response component corresponding to the order mode, The structure of i The modal frequency, For the i The modal damping ratio of the order; For the i Generalized loads under the order mode, For the i Generalized mass in the first mode.

[0031] In one embodiment, the independent equations corresponding to the first n modes are:

[0032] ；

[0033] in, The structure of i The modal frequency, For the i The modal damping ratio of the order is Indicates i Generalized loads under the first mode, Indicates i The generalized mass under the order mode, Indicates i The displacement components under the first mode.

[0034] In one embodiment, the independent equations corresponding to the first n-order modes are used to characterize the load characteristics under different load conditions with scalar parameters in the coordinates of each order mode, including:

[0035] According to the independent equations corresponding to the first n-order modes, the amplification factor of each modal response is obtained: U , the amplification factor is used to represent the scalar parameter of the load characteristics under different load conditions in each order of modal coordinates;

[0036]

[0037] in, is the load applied in the physical space, For the i The vibration shape vector of the first mode j The relative displacement of the degrees of freedom, Indicates i The generalized mass under the first mode, the load characteristics contain information related to the load position, direction, and magnitude.

[0038] In one embodiment, converting the modal response components in the modal space into dynamic responses in the physical space includes:

[0039] The modal response components under unit load are multiplied by the scalar parameters that characterize the load characteristics to obtain the modal response components under actual load conditions. According to the coordinate transformation relationship between the modal space and the physical space, the modal response components in the modal space are converted into the physical space and superimposed to obtain the dynamic response.

[0040] In one embodiment, the structural dynamic response components in the modal space under the initial condition are calculated as follows:

[0041]

[0042] In the formula, is the nth-order modal frequency, is the nth-order modal damping ratio, , is the free vibration response of the nth mode in the modal space;

[0043] in:

[0044]

[0045] In a second aspect, the present application also provides a structural dynamic response calculation device based on an adaptive physical base network. The device comprises:

[0046] The order determination module is used to determine the first n modes that contribute most to the dynamic response of the structure;

[0047] The decoupling module is used to decouple the m mutually coupled differential equations representing the structural dynamic response into independent equations corresponding to the first n modes based on the vibration mode decomposition method;

[0048] A feature processing module, used to characterize the load characteristics under different load conditions with scalar parameters in each modal coordinate according to the independent equations corresponding to the first n-order modes;

[0049] A prediction module is used to input the time into the adaptive physical base network of the n-order mode corresponding to the time, and predict the response components of the first n-order modes of the structure under unit load in the modal space;

[0050] The conversion module is used to multiply the modal response component with the scalar parameter representing the load characteristics to obtain the modal response component under the actual load condition, and convert the modal response component in the modal space into the dynamic response in the physical space.

[0051] In a third aspect, the present application further provides a computer device, which includes a memory and a processor, wherein the memory stores a computer program, and when the processor executes the computer program, the steps of the structural dynamic response calculation method based on the adaptive physical base network are implemented.

[0052] In a fourth aspect, the present application further provides a computer-readable storage medium having a computer program stored thereon, which, when executed by a processor, implements the steps of a method for calculating structural dynamic response based on an adaptive physical-based network.

[0053] In a fifth aspect, the present application also provides a computer program product, which includes a computer program, and when the computer program is executed by a processor, the steps of the structural dynamic response calculation method based on the adaptive physical base network are implemented. BRIEF DESCRIPTION OF THE DRAWINGS

[0054] Figure 1 A schematic diagram of a flow chart of a method for calculating structural dynamic response based on an adaptive physical base network in one embodiment;

[0055] Figure 2 A schematic diagram of another process of calculating the structural dynamic response based on an adaptive physical network in another implementation;

[0056] Figure 3 A schematic diagram of an equation decoupling process in an embodiment;

[0057] Figure 4is a schematic diagram illustrating load generalization in one embodiment;

[0058] Figure 5 A schematic diagram of a network structure of a one-dimensional input of an adaptive physical base network in one embodiment;

[0059] Figure 6 A schematic diagram of a network structure of a two-dimensional input of an adaptive physical base network in one embodiment;

[0060] Figure 7 It is a schematic diagram of setting the neuron center parameters in one embodiment;

[0061] Figure 8 is a schematic diagram of a tanh function curve graph in one embodiment;

[0062] Fig. 9 A schematic diagram of a comparison between a solution result of a differential equation using an adaptive physical base network and a theoretical value in one embodiment;

[0063] Fig.10 A schematic diagram of a comparison between a solution result of a differential equation using a physical information radial basis network and a theoretical value in one embodiment;

[0064] Fig.11 Schematic diagram of Loss iteration curves of an adaptive physical basis network and a physical information radial basis network in one embodiment;

[0065] Fig.12 is a schematic diagram of a plane rigid frame in one embodiment;

[0066] Fig.13 is a schematic diagram of working condition 1 in an embodiment;

[0067] Fig.14 This is a schematic diagram of the structural response results for working condition 1;

[0068] Fig.15 is a schematic diagram of working condition 2 in an embodiment;

[0069] Fig.16 This is a schematic diagram of the structural response results of working condition 2;

[0070] Fig.17 is a schematic diagram of working condition 3 in an embodiment;

[0071] Fig.18 This is a schematic diagram of the structural response results of working condition 3;

[0072] Fig.19 A structural block diagram of a structural dynamic response calculation device based on an adaptive physical base network in one embodiment;

[0073] Fig. 20FIG. 4 is a diagram showing the internal structure of a computer device in one embodiment. DETAILED DESCRIPTION

[0074] In order to make the purpose, technical solution and advantages of the present application more clearly understood, the present application is further described in detail below in conjunction with the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are only used to explain the present application and are not used to limit the present application.

[0075] Modal parameters are the natural vibration characteristics of a structure, which are completely dependent on the physical properties of the structure itself (mass, stiffness, damping, etc.) and its boundary constraints, and have nothing to do with external excitation. Specifically, any discrete or continuum system with infinite degrees of freedom has corresponding infinite modes. Each mode consists of independent modal frequency, modal vibration shape, and corresponding modal damping ratio parameters, which together describe the natural vibration behavior of the system in this mode.

[0076] The modal vibration shape refers to the vector composed of the relative displacement of multiple degrees of freedom of the structure under a certain vibration mode. The modal vibration shape of the structure satisfies the orthogonality of the mass matrix and the orthogonality of the stiffness matrix respectively. This is actually a manifestation of the elastic force and inertial force of the structure satisfying the principle of virtual work.

[0077] The modal decomposition method is a special application method for structural modal vibration modes. The modal decomposition method means that for a certain structure, its dynamic response under any excitation can be decomposed into modal response components with mutually orthogonal modal vibration vectors as the basis. The feasibility of the modal decomposition method lies in that after the modal decomposition, the dynamic response of each mutually coupled degree of freedom is decoupled into modal response components in the modal space that are independent of each other, thereby simplifying the solution process.

[0078] Physically-informed neural networks (PINNs) are a type of neural network that incorporates prior physical knowledge and was proposed in recent years. This method explicitly encodes known physical or scaling laws in the form of mathematical equations into the standard structure of a neural network. This method integrates any existing knowledge that can be expressed in partial differential equations during the learning process, significantly improving predictability while reducing the amount of data required to achieve the desired accuracy.

[0079] Physical Information Radial Basis Network (PIRBN) is a special radial basis network that combines physical information. The network uses the radial basis network as the basic architecture. By setting a suitable radial basis "activation" function and using a special neuron center initialization method, the network can maintain local approximation characteristics during training. Thanks to its unique structure, the network is effective in solving differential equations with high-frequency characteristics.

[0080] Structural dynamic analysis is widely used in civil engineering, mechanical engineering, aerospace engineering and other fields. Based on the dynamic response of the structure, the safety performance of the structure can be evaluated. In addition, in the design of the structure, its dynamic performance is also an important reference indicator. The calculation of dynamic response is the basis for structural dynamic analysis. Traditional structural dynamic response calculations are mostly based on finite element theory, with the help of related calculation software to obtain the dynamic time history of the structure. However, the finite element method, especially for large structures, requires a large number of numerical iterations, which is extremely time-consuming, and requires repeated modeling for different engineering structures, different load conditions and initial conditions, which is extremely inefficient.

[0081] With the development of deep learning technology, neural network-based methods are widely used in structural intelligence. With the help of the neural network model's ability to approximate nonlinear functions, a parameterized space can be established, and an effective proxy model can be constructed for specific structural response calculation tasks. However, most common neural network-based dynamic response calculation methods are data-driven, requiring a large number of data samples to train the model, and the modeling cost is extremely high. Some people also solve the dynamic response of the structure based on physical information neural network (PINN), by embedding physical partial differential equations related to the problem to be solved to guide the training of the network so that it no longer relies on a large number of data samples. However, due to the spectral bias of the multi-layer perceptron, traditional PINN is also difficult to capture the high-frequency components in the structural response. Based on this problem, some scholars have proposed a physical information radial basis network (PIRBN) for solving differential equations containing high-frequency features. However, since the center of the neuron in this network needs to be fixed artificially, even if there is a corresponding initialization method, the initialization method is not the optimal initialization distribution of the center of the neuron, which limits the network's ability to fit high-frequency functions.

[0082] The finite element method is the main numerical analysis tool for solving structural dynamic response problems. The basic idea is to first discretize the continuous structure into a component mesh model with a finite number of degrees of freedom, and then solve it by establishing a set of dynamic differential equations using numerical integration (such as midpoint integration, Newmark-β, etc.). The advantages of the finite element method are clear principles, precise calculations, and strong interpretability. However, the disadvantage is that it requires operators to have high professional knowledge, and the calculations for large structures are time-consuming, and different structural forms, load conditions, and initial conditions require repeated modeling.

[0083] The calculation method based on physical information neural network (PINN) is a recently emerging intelligent computing method. This method introduces physical knowledge into the neural network structure, so that the network training no longer depends on a large amount of labeled data. The traditional PINN method can only calculate relatively simple structural systems. For multi-degree-of-freedom systems, hundreds of mutually coupled dynamic equations are involved, and it is difficult for neural networks to solve so many dynamic equations at the same time. In addition, it is difficult to model different load conditions and initial conditions into the network framework, so they are mostly customized for a single condition and do not have a wide range of applications.

[0084] The Physical Information Radial Basis Network (PIRBN) is a recently proposed network architecture, but few scholars have conducted further research on it. Regarding the initialization of the neuron center in this network architecture, the proposer of this network architecture has conducted comparative experiments on different initialization methods. Studies have shown that uniform initialization is a better way to initialize the neuron center than random initialization. However, this initialization method is artificially specified based on experience, without considering the characteristics of the differential equation itself. For different differential equations, the most suitable distribution of neuron centers is different. This limits the fitting ability of the physical information radial basis network to a certain extent.

[0085] Based on the above problems, this application provides a method for calculating the structural dynamic response based on an adaptive physical base network, such as Figure 1 and Figure 2 As shown, the method includes:

[0086] Step 102, determining the first n modes that contribute most to the structural dynamic response.

[0087] Specifically, the structural model is established by finite element method, assuming that the total number of degrees of freedom of the established model is m. The overall stiffness matrix, overall mass matrix, and the vibration mode and frequency of its mode are obtained. According to the spectrum characteristics of the excitation, a small number of n-order modes are selected from its modes as the main modes involved in the response calculation, and other modes are discarded.

[0088] Step 104, based on the mode decomposition method, the m differential equations that characterize the mutually coupled structural dynamic response are decoupled into independent equations corresponding to the first n-order modes. The decoupling process is as follows: Figure 3 As shown in the figure, for solving the structural dynamic response, the dynamic equations are based on:

[0089] (1)

[0090] in, M is the structurally consistent mass matrix, C is the damping matrix, K is the stiffness matrix, Fis the load matrix. The above equations are multiple mutually coupled differential equations of motion expressed in geometric coordinates, and the displacement of each degree of freedom can be expressed as:

[0091] (2)

[0092] In the formula, m is the total number of degrees of freedom of the structure. Now, the vibration mode vectors of the first n modes are used as the basis to convert the geometric space into the modal space. Then, the displacement of each degree of freedom in the modal space is expressed as:

[0093] (3)

[0094] Expands to:

[0095] (4)

[0096] in, For the i The vibration shape vector of the order mode, represents the modal space i The modal response component corresponding to the first mode. Through coordinate transformation, the original structural motion differential equations can be converted into the following form:

[0097] (5)

[0098] The above formula can be transformed into:

[0099] (6)

[0100] in, = , called the generalized mass matrix, = , called the generalized stiffness matrix, according to the first and second orthogonal conditions of the vibration mode, and are all diagonal matrices. This achieves the decoupling of mass and stiffness. For the damping matrix C , using Rayleigh damping:

[0101] (7)

[0102] (8)

[0103] in Based on the calculated damping coefficient, the damping ratio of each modal can be obtained as

[0104] (9)

[0105] The generalized damping matrix is: = It is also transformed into a diagonal matrix, thus achieving decoupling. Therefore, the motion differential equation of the structure in the modal space can be decoupled and written as follows:

[0106] (10)

[0107] , , , , Respectively represent i The generalized mass, generalized damping, generalized stiffness, displacement components and generalized loads under the order mode. Furthermore, ， ,in: is the i-th modal frequency of the structure, For the i The modal damping ratio of the order, the above formula can be changed to:

[0108] (11)

[0109] In this way, the original differential equations of motion with multiple degrees of freedom coupled to each other are decoupled into independent differential equations of motion with single degree of freedom.

[0110] Step 106 , characterizing the load characteristics under different load conditions with scalar parameters in the coordinates of each modal order according to the independent equations corresponding to the first n-order modes.

[0111] Based on the mode decomposition method, after decoupling the coupled dynamic differential equations into a single independent differential equation, the characteristics related to the load position, magnitude, and direction are presented in scalar form under each modal coordinate. The specific presentation form is as follows: Figure 4 shown.

[0112] The specific change process is:

[0113] (12)

[0114] (13)

[0115] Divide both sides of equation (10) by the generalized mass , the amplification factor U of each modal response can be obtained:

[0116] (14)

[0117] in: is applied in the geometric space j The loads of the degrees of freedom, For the i The vibration shape vector of the first mode j The relative displacement of the degrees of freedom contains information about the position, direction, and magnitude of the load.

[0118] Therefore, loads of different positions, directions, and forms can be uniquely represented by the load magnification coefficient under each mode. In this way, the pre-trained network can predict the response under different load conditions, which to a certain extent overcomes the drawback that traditional neural networks can only calculate a single load condition.

[0119] For the initial conditions, the initial conditions can also be converted to the modal space based on the vibration mode decomposition method, and converted into a single degree of freedom problem under each mode. The initial velocity and displacement originally represented in the form of vectors appear in the single degree of freedom system in the form of scalars. Therefore, it is only necessary to substitute the initial conditions into the formula of free vibration of a single degree of freedom under initial excitation:

[0120] (15)

[0121] In the formula, is the nth-order modal frequency, is the nth-order modal damping ratio, , is the free vibration response of the nth mode in the modal space

[0122] in:

[0123] (16)

[0124] (17)

[0125] In this way, the structural dynamic response components in the modal space under the initial conditions are superimposed with the forced vibration response components under the zero initial state to be predicted by the adaptive physical base network in the next step to obtain the complete dynamic response of the structure in the modal space under a certain initial condition and a certain load form.

[0126] Step 108 , input the time to the adaptive physical base network of the n-order mode corresponding to the time, and predict the response components of the first n-order modes of the structure under unit load in the modal space.

[0127] Step 110: multiply the modal response component by a scalar parameter representing the load characteristic to obtain the modal response component under the actual load condition.

[0128] Specifically, n similar adaptive physical base networks are built to predict the response components of the first n modes of the structure in the modal space. -- . Figure 2 The model1 - model n in is the adaptive physical base network.

[0129] For the first n modes, an adaptive physical base network needs to be built for each mode. Figure 5 Shown and Figure 6 shown.

[0130] First, according to the characteristics of the differential equations corresponding to the n modes to be solved and the specific needs, select the appropriate wavelet basis function and construct the neuron activation function. The one-dimensional wavelet basis function can be expressed as:

[0131] (18)

[0132] in, is the wavelet function, b is the time shift factor, a is the scale factor.

[0133] Then, according to the computational domain of the differential equation to be solved, the width of the hidden layer of the radial basis network is set appropriately, and then the center parameters of the neurons of the adaptive physical basis network are constructed to decouple the neurons in the computational domain. In the previous step, by setting a wavelet function with compact support characteristics as the activation function, the local approximation property of each neuron is guaranteed.

[0134] The original physical information radial basis network has weak physical interpretability in network structure, and each hyperparameter has no clear physical meaning. Although specific physical information is embedded in the network constraints, it is still a "black box" model at the structural level. In response to this problem, the present application proposes an adaptive physical basis network. By selecting a wavelet basis function with tight support characteristics as an activation function, the forward reasoning process of the adaptive physical basis network corresponds to the wavelet transform, and each hyperparameter has a certain physical meaning, so that the neural network has a strong physical interpretability. In addition, almost all physical information neural network models, including the physical information radial basis network, can only solve partial differential equations, but cannot provide information about partial differential equations in the frequency domain. In response to this problem, the adaptive physical basis network proposed in the present application selects a suitable wavelet basis function. While calculating the solution of the partial differential equation, it also provides its distribution information in the frequency domain based on the physical interpretability of each hyperparameter.

[0135] In order to ensure that the entire neural network has good local approximation properties, the coupling between neurons needs to be further reduced. From formula (18), we know that the time shift factor It controls the location of the local area of ​​the computation domain that each neuron is responsible for. Therefore, by initializing the parameters The coupling of each neuron is weakened by the way. Compared with the existing method, the central parameters of neurons are initialized and frozen. Different from the method, this application will parameter Set to freeze part With the trainable part .in

[0136] (19)

[0137] (20)

[0138] (twenty one)

[0139] In the formula Representative neurons, is an adaptive neuron center parameter, which is used to control the trainable range of the neuron center. This parameter is set according to the size of the computational domain and the number of radial basis network neurons. c i It is a trainable parameter that is optimized as the training progresses.

[0140] like Figure 7 As shown, the parameter freezing part Used to control the local influence area of ​​each neuron. Trainable parameters Used to search for the most appropriate neuron center distribution corresponding to the differential equation to be solved.

[0141] In order to ensure the weak coupling between neurons, as shown in Equations (19) and (20), a bounded function is introduced: tanh , thus ensuring that during the parameter update process, the neuron center fluctuates in a small range around the fixed parameter b. tanh Function curve Figure 8 This can prevent the weak coupling of each neuron from being destroyed and ensure that the entire neural network always has good local fitting ability during the training process. The freezing parameter is set in the parameters related to the center position of the neuron. and trainable parameters The two parts enable the center position of neurons to adaptively search for the optimal distribution according to specific problems, so that the adaptive physical basis network proposed in this application has a stronger fitting ability than the physical information radial basis network.

[0142] Since multi-layer perceptrons have spectral bias and are difficult to capture high-frequency features in partial differential equations, traditional physical information neural networks (PINNs) are difficult to accurately calculate the high-frequency part of structural responses. To address this problem, some scholars have proposed a physical information radial basis network (PIRBN) for solving differential equations containing high-frequency features. However, in order to maintain the local approximation capability of the physical information radial basis network, each neuron center needs to be manually set to a fixed value at the beginning of model training and does not participate in parameter updates during model training. Although some studies have given recommended initialization methods for neuron centers in the computational domain, this initialization distribution is not the optimal initialization distribution for neuron centers, which limits the network's ability to fit high-frequency functions. In addition, in the selection of radial basis functions, only specific provisions are made for their physical characteristics, while ignoring their physical meanings. To address this problem, this application is based on tanh The boundedness of the function is considered, and an adaptive physical basis network is proposed by introducing an adaptive neuron center parameter. This parameter can adaptively search for the optimal neuron center distribution during the neural network training process, thereby improving the accuracy of the high-frequency differential equation calculation of the neural network. Finally, the loss function of the network is constructed as:

[0143] (twenty two)

[0144] (twenty three)

[0145] (twenty four)

[0146] The meanings of the characters in the formula are the same as above. W is the number of sampling points, For the i The displacement response under the first mode, is a weight parameter, which needs to be set according to the situation. is the residual loss of the partial differential equation, is the initial condition loss.

[0147] Step 112: convert the modal response components in the modal space into dynamic responses in the physical space.

[0148] According to the coordinate transformation formula, neural network is used to obtain -- After that, the modal components are superimposed to obtain the response in the geometric space. , the specific process is as follows:

[0149] (25)

[0150] (26)

[0151] After the above superposition process, the dynamic response of the structure in the geometric space can be obtained.

[0152] In this way, the established dynamic response model only needs to obtain the modal parameters of the structure to realize the rapid calculation of the dynamic response. The calculation speed can be more than dozens of times that of the finite element method. In addition, different structural forms are characterized in the form of modal parameters in the present invention as parameters of the equations to be solved in the adaptive physical base network. Therefore, there is no need to repeat modeling for different structural forms.

[0153] The structural dynamic response calculation method based on the adaptive physical basis network of the present application first selects the first n-order modes that contribute most to the structural dynamic response, and based on the coordinate transformation, uses the vibration mode vector of the n-order mode as the basis of the spatial coordinate, and respectively builds the corresponding adaptive physical radial basis network in the corresponding modal space. After training, each independent network can realize the rapid calculation of the dynamic response of the structure under a certain order of modal coordinates, and finally superimposes the modal response components of each order of mode to obtain the dynamic response of the structure in the physical space. For a certain mode of the PINN network, its loss function is a dynamic partial differential equation constructed based on the modal frequency, modal damping, and modal vibration mode of the order. In order to achieve the generalization of load conditions, the adaptive physical basis network predicts the response components of the first n-order modes of the structure under unit load in the modal space, and then multiplies the modal response components with the scalar parameters that characterize the load characteristics to obtain the modal response components under the actual load conditions.

[0154] In order to verify the effectiveness of the algorithm of the present application, a high frequency function is further fitted for verification.

[0155] The algorithm proposed in this application is verified by taking the ordinary differential equation shown in formula (27) as an example

[0156] (27)

[0157] (28)

[0158] The independent variable of the differential equation is , for u For independent variables x The second derivative of .

[0159] In order to verify the effectiveness of the adaptive neuron center hyperparameter configuration method proposed in this application for solving differential equations in physical information radial basis networks, the differential equation solution results without setting the adaptive neuron center were used as the control group. The purpose of this comparative analysis is to verify the superiority of the proposed algorithm in performance.

[0160] Since the theoretical solution of the differential equation to be solved has obvious high-frequency characteristics, the nonlinear characteristics are obvious. Therefore, in the example of setting the adaptive neuron center, the width of the adaptive physical base network is set to 121, and the scale factor Initialized to 10, adaptive neuron center parameter = 10, freeze parameters , so Interpolate evenly between 19.8 and 22.2. In the case where the adaptive neuron center is not set, the parameter = 0, which is the same as the trainable parameter The corresponding weight is equal to 0, and the other hyperparameters are set to the same as the example of adaptive neuron center. Loss Function It can be expressed as

[0161] (29)

[0162] (30)

[0163] (31)

[0164] Wherein, equation (30) corresponds to the control equation, and equation (31) corresponds to the initial condition. For the sake of comparison, the training times of both examples are 150,000. Fig. 9 To compare the solution results of differential equations using adaptive physical basis networks with theoretical values, Fig.10 In order to compare the solution results of differential equations using physical information radial basis network with theoretical values, Fig.11 The two algorithms correspond to Loss Iteration curve.

[0165] according to Fig. 9 and Fig.10 From the display, it can be clearly observed that, without setting the adaptive neuron center, the calculation results of the physical information radial basis network are significantly different from the actual solution of the differential equation. However, the results of the adaptive physical basis network with adaptive neuron parameters for the differential equation are almost perfectly consistent with the theoretical solution. In addition, from Fig.11 shown Loss It can be seen from the iteration curve that the model not only converges quickly but also reduces the loss function to a lower value using the algorithm proposed in this application. In contrast, the model using the original algorithm converges slowly and after stabilization Loss The value of the function is relatively high, especially in the early stages of model training. LossThe function stops decreasing. This difference can be attributed to the fact that the wavelet basis function used in this application is used as the activation function of the neuron, which makes the forward reasoning process of the model directly related to the wavelet transform. For different differential equations, the time shift factor of each wavelet basis function is and scale factor They are different and are not fixed. After the hidden layer width of the model is determined, the basis function used for wavelet transform is also determined. The most suitable time shift factor and scale factor The value of is closely related to the time-frequency distribution of the differential equation. This application introduces a trainable parameter in the adaptive physical base network. , allowing each neuron center to automatically find the optimal position during model training according to the characteristics of the differential equation. This adaptive mechanism significantly improves the solution accuracy of the algorithm.

[0166] Next, we will take a plane frame as an example to explain the proposed method for calculating the structural dynamic response based on an adaptive physical network. The specific structure and parameters of the frame are as follows: Fig.12 shown.

[0167] The beam and column adopt the same cross section, which is a square solid cross section with a side length of 0.13 m and a cross-sectional area of , material elastic modulus .

[0168] According to different working conditions, the method of this application and the numerical method Newmark-beta method are used to calculate the structural response under three working conditions. Fig.13 The corresponding structural response results are shown in Fig.14 As shown, working condition 2 is Fig.15 The corresponding structural response results are shown in Fig.16 As shown, working condition 3 is Fig.17 The corresponding structural response results are shown in Fig.18 shown.

[0169]

[0170]

[0171] The calculation time consumption under different working conditions is as follows:

[0172] Table 1 Network computing time comparison table

[0173]

[0174] As can be seen from the table above, based on the calculation method of this application, the calculation speed of the dynamic response is more than 20 times that based on the finite element method. And for different load conditions, there is no need for repetitive modeling, which greatly improves the calculation efficiency.

[0175] In summary, the structural dynamic response calculation method based on the adaptive physical base network of the present application has the following effects:

[0176] (1) Based on the boundedness of the tanh function, a trainable parameter is introduced , so that the neuron center of the adaptive physical basis network can not only automatically search for the most suitable position as the model is trained, but also ensure that the local approximation property of the adaptive physical basis network is not destroyed. This makes the adaptive physical basis network have a stronger high-frequency feature extraction capability than the physical information radial basis network.

[0177] (2) By selecting a wavelet basis function with compact support characteristics as the activation function, the neurons are weakly coupled, ensuring the local approximation properties of the adaptive physical basis network. In addition, this method makes all the hyperparameters of the model have certain physical meanings.

[0178] (3) Based on the mode superposition method, the characteristics related to the load direction, magnitude, and position are presented in the form of scalar parameters. The real modal response components are obtained by multiplying the scalar with the modal components predicted by the neural network, thereby achieving a certain degree of generalization of the load. This allows the trained network to adapt to different working conditions without the need to repeatedly train the model.

[0179] (4) This application uses the mode decomposition method to decouple the coupled dynamic equations of a multi-degree-of-freedom system with complex topological relationships into independent equations, making it possible to use a neural network to solve the dynamic response of the multi-degree-of-freedom system.

[0180] (5) After training, the proposed adaptive physical base network can simultaneously provide the solution and time-frequency information of the differential equation to be solved.

[0181] (6) In the dynamic response calculation model designed in this application, the features related to the initial conditions do not participate in the network training, but are calculated based on the theoretical formula. Therefore, the model does not need to be repeatedly modeled for different initial conditions, and can achieve generalization of different initial conditions.

[0182] (7) The model of this application embeds physical mechanisms during training, does not require any sample data, and has extremely low modeling costs, thus expanding the application scope of neural networks in civil engineering.

[0183] (8) The model established in this application can calculate the dynamic response of a structure by simply obtaining the modal parameters of the structure. Therefore, the model is applicable to any structural form. There is no need to repeat the modeling for different structures, which greatly improves the efficiency of the calculation.

[0184] (8) The computational model established in this application does not need to calculate the response based on numerical iteration, and the calculation speed is more than ten times that of finite element method.

[0185] The structural dynamic response calculation method based on the adaptive physical-based network of the present application can be applied to a computing device, which can be a server or a terminal. A user can realize structural response prediction through the computer device.

[0186] It should be understood that, although the various steps in the flowcharts involved in the above-mentioned embodiments are displayed in sequence according to the indication of the arrows, these steps are not necessarily executed in sequence according to the order indicated by the arrows. Unless there is a clear explanation in this article, the execution of these steps is not strictly limited in order, and these steps can be executed in other orders. Moreover, at least a part of the steps in the flowcharts involved in the above-mentioned embodiments can include multiple steps or multiple stages, and these steps or stages are not necessarily executed at the same time, but can be executed at different times, and the execution order of these steps or stages is not necessarily carried out in sequence, but can be executed in turn or alternately with other steps or at least a part of the steps or stages in other steps.

[0187] Based on the same inventive concept, the embodiment of the present application also provides a structural dynamic response calculation device based on an adaptive physical base network for implementing the structural dynamic response calculation method based on an adaptive physical base network involved above. The implementation scheme for solving the problem provided by the device is similar to the implementation scheme recorded in the above method, so the specific limitations in the embodiments of one or more structural dynamic response calculation devices based on an adaptive physical base network provided below can refer to the limitations of the structural dynamic response calculation method based on an adaptive physical base network above, and will not be repeated here.

[0188] In one embodiment, Fig.19 As shown, a structural dynamic response calculation device based on an adaptive physical base network is provided, comprising:

[0189] An order determination module 1302 is used to determine the first n modes that contribute most to the structural dynamic response;

[0190] A decoupling module 1304 is used to decouple m mutually coupled differential equations representing the dynamic response of the structure into independent equations corresponding to the first n-order modes based on the mode decomposition method;

[0191] A feature processing module 1306 is used to characterize the load characteristics under different load conditions with scalar parameters in each modal coordinate according to the independent equations corresponding to the first n-order modes;

[0192] The prediction module 1308 is used to input the time into the adaptive physical basis network of the n-order mode corresponding to the time, and predict the response components of the first n-order modes of the structure under the unit load in the modal space.

[0193] The conversion module 1310 is used to multiply the modal response component with the scalar parameter representing the load characteristics to obtain the modal response component under the actual load condition, and convert the modal response component in the modal space into the dynamic response in the physical space.

[0194] Each module in the above-mentioned adaptive physical network-based structural dynamic response calculation device can be implemented in whole or in part by software, hardware, or a combination thereof. Each of the above-mentioned modules can be embedded in or independent of a processor in a computer device in the form of hardware, or can be stored in a memory in a computer device in the form of software, so that the processor can call and execute operations corresponding to each of the above modules.

[0195] In one embodiment, a computer device is provided. The computer device may be a server, and its internal structure diagram may be as follows: Fig. 20 As shown. The computer device includes a processor, a memory and a network interface connected through a system bus. Among them, the processor of the computer device is used to provide computing and control capabilities. The memory of the computer device includes a non-volatile storage medium and an internal memory. The non-volatile storage medium stores an operating system, a computer program and a database. The internal memory provides an environment for the operation of the operating system and the computer program in the non-volatile storage medium. The network interface of the computer device is used to communicate with an external terminal through a network connection. The computer program is executed by the processor to implement a structural dynamic response calculation method based on an adaptive physical base network.

[0196] Those skilled in the art will understand that Fig. 20 The structure shown in the figure is only a block diagram of a part of the structure related to the solution of the present application, and does not constitute a limitation on the computer device to which the solution of the present application is applied. The specific computer device may include more or fewer components than those shown in the figure, or combine certain components, or have a different arrangement of components.

[0197] In one embodiment, a computer device is provided, including a memory and a processor, wherein a computer program is stored in the memory, and when the processor executes the computer program, the steps of a method for calculating structural dynamic response based on an adaptive physical base network are implemented.

[0198] In one embodiment, a computer-readable storage medium is provided, on which a computer program is stored. When the computer program is executed by a processor, the steps of a method for calculating structural dynamic response based on an adaptive physical base network are implemented.

[0199] In one embodiment, a computer program product is provided, comprising a computer program, which, when executed by a processor, implements the steps of a method for calculating structural dynamic response based on an adaptive physical-based network.

[0200] Those of ordinary skill in the art can understand that all or part of the processes in the above-mentioned embodiment methods can be completed by instructing the relevant hardware through a computer program, and the computer program can be stored in a non-volatile computer-readable storage medium. When the computer program is executed, it can include the processes of the embodiments of the above-mentioned methods. Among them, any reference to the memory, database or other medium used in the embodiments provided in this application can include at least one of non-volatile and volatile memory. Non-volatile memory can include read-only memory (ROM), magnetic tape, floppy disk, flash memory, optical memory, high-density embedded non-volatile memory, resistive random access memory (ReRAM), magnetoresistive random access memory (MRAM), ferroelectric random access memory (FRAM), phase change memory (PCM), graphene memory, etc. Volatile memory can include random access memory (RAM) or external cache memory, etc. As an illustration and not limitation, RAM can be in various forms, such as static random access memory (SRAM) or dynamic random access memory (DRAM). The database involved in each embodiment provided in this application may include at least one of a relational database and a non-relational database. Non-relational databases may include distributed databases based on blockchains, etc., but are not limited to this. The processor involved in each embodiment provided in this application may be a general-purpose processor, a central processing unit, a graphics processor, a digital signal processor, a programmable logic device, a data processing logic device based on quantum computing, etc., but are not limited to this.

[0201] The technical features of the above embodiments may be combined arbitrarily. To make the description concise, not all possible combinations of the technical features in the above embodiments are described. However, as long as there is no contradiction in the combination of these technical features, they should be considered to be within the scope of this specification.

[0202] The above-described embodiments only express several implementation methods of the present application, and the descriptions thereof are relatively specific and detailed, but they cannot be understood as limiting the scope of the present application. It should be pointed out that, for a person of ordinary skill in the art, several variations and improvements can be made without departing from the concept of the present application, and these all belong to the protection scope of the present application. Therefore, the protection scope of the present application shall be subject to the attached claims.

Claims

1. A method for calculating structural dynamic response based on an adaptive physical base network, characterized in that: include: Determine the first n modes that contribute most to the structural dynamic response; Based on the mode decomposition method, the m differential equations that characterize the mutually coupled dynamic response of the structure are decoupled into independent equations corresponding to the first n modes. According to the independent equations corresponding to the first n-order modes, the amplification factor of each modal response is obtained: U , the amplification factor is used to represent the scalar parameter of the load characteristics under different load conditions in each order of modal coordinates; ； in, is the load applied in the physical space, is the first vibration mode vector in the i-th mode. j The relative displacement of the degrees of freedom, Indicates i The generalized mass under the first mode, the load characteristics contain information related to the load position, direction and magnitude; The adaptive physical information radial basis network of the n-order mode corresponding to the time input is used to predict the response components of the first n-order modes of the structure under unit load in the modal space; The modal response components are multiplied by the scalar parameters that characterize the load characteristics to obtain the modal response components under the actual load conditions; Convert the modal response components in the modal space into dynamic responses in the physical space; Among them, for the first n modes, an adaptive physical information radial basis network is built for each mode; According to the characteristics and requirements of the differential equations corresponding to the n modes, a suitable wavelet basis function is selected to construct the neuron activation function of the adaptive physical information radial basis network, where the one-dimensional wavelet basis function can be expressed as: in, is the wavelet function, b is the time shift factor, a is the scale factor, t For time; According to the computational domain of the differential equation to be solved, the width of the hidden layer of the radial basis network is set appropriately, and then the neuron center parameters of the adaptive physical information radial basis network are constructed to decouple the neurons in the computational domain; The parameters Set to freeze part With the trainable part ,in, In the formula, Representative neurons, is an adaptive neuron center parameter, which is used to control the trainable range of the neuron center. This parameter is set according to the size of the computational domain and the number of radial basis network neurons. c i It is a trainable parameter that is optimized as the training progresses; Among them, the parameter freezing part Used to control the local influence area of ​​each neuron, the parameters can be trained Used to search for the most appropriate neuron center distribution corresponding to the differential equation to be solved.

2. The method for calculating structural dynamic response based on an adaptive physical-based network according to claim 1 is characterized in that: The loss function of the adaptive physical information radial basis network is: in, is the residual loss of the partial differential equation, is the initial condition loss; is the weight parameter; in, W is the number of sampling points, For the i The displacement response under the first mode, represents the modal space i The modal response component corresponding to the order mode, is the i-th modal frequency of the structure, For the i The modal damping ratio of the order; For the i Generalized loads under the order mode, For the i Generalized mass in the first mode.

3. The method for calculating structural dynamic response based on an adaptive physical-based network according to any one of claims 1 to 2, characterized in that: The independent equations corresponding to the first n modes are: ； in, For the structure i The modal frequency, For the i The modal damping ratio of the order is Indicates i Generalized loads under the first mode, Indicates i The generalized mass under the order mode, Indicates i The displacement components under the first mode.

4. The method for calculating structural dynamic response based on an adaptive physical-based network according to claim 1 is characterized in that: The converting the modal response components in the modal space into the dynamic response in the physical space comprises: According to the coordinate transformation relationship between the modal space and the physical space, the modal response components in the modal space are converted into the physical space and superimposed to obtain the dynamic response.

5. The method for calculating structural dynamic response based on an adaptive physical-based network according to claim 1 is characterized in that: The structural dynamic response components in the modal space under the initial conditions are calculated as follows: In the formula, is the nth-order modal frequency, is the nth-order modal damping ratio, , is the free vibration response of the nth mode in the modal space; in: 。 6. A structural dynamic response calculation system based on an adaptive physical base network, characterized in that: The system comprises: The order determination module is used to determine the first n modes that contribute most to the dynamic response of the structure; The decoupling module is used to decouple the m differential equations that characterize the mutually coupled structural dynamic response into independent equations corresponding to the first n-order modes based on the vibration mode decomposition method; the feature processing module is used to obtain the amplification factor of each modal response according to the independent equations corresponding to the first n-order modes. U , the amplification factor is used to represent the scalar parameter of the load characteristics under different load conditions in each order of modal coordinates; ； in, is the load applied in the physical space, is the vibration shape vector of the i-th mode. j The relative displacement of the degrees of freedom, Indicates i The generalized mass under the first mode, the load characteristics contain information related to the load position, direction and magnitude; A prediction module is used to input the adaptive physical information radial basis network of the n-order mode corresponding to the time input, and predict the response components of the first n-order modes of the structure under unit load in the modal space; A conversion module, used for multiplying the modal response component with the scalar parameter representing the load characteristics to obtain the modal response component under the actual load condition, and converting the modal response component in the modal space into the dynamic response in the physical space; Among them, for the first n modes, an adaptive physical information radial basis network is built for each mode; According to the characteristics and requirements of the differential equations corresponding to the n modes, a suitable wavelet basis function is selected to construct the neuron activation function of the adaptive physical information radial basis network, where the one-dimensional wavelet basis function can be expressed as: in, is the wavelet function, b is the time shift factor, a is the scale factor, t For time; According to the computational domain of the differential equation to be solved, the width of the hidden layer of the radial basis network is set appropriately, and then the neuron center parameters of the adaptive physical information radial basis network are constructed to decouple the neurons in the computational domain; The parameters Set to freeze part With the trainable part ,in, In the formula, Representative neurons, is an adaptive neuron center parameter, which is used to control the trainable range of the neuron center. This parameter is set according to the size of the computational domain and the number of radial basis network neurons. c i It is a trainable parameter that is optimized as the training progresses; Among them, the parameter freezing part Used to control the local influence area of ​​each neuron, the parameters can be trained Used to search for the most appropriate neuron center distribution corresponding to the differential equation to be solved.

7. A computer device comprising a memory and a processor, wherein the memory stores a computer program, characterized in that: When the processor executes the computer program, the steps of the method according to any one of claims 1 to 5 are implemented.

8. A computer-readable storage medium having a computer program stored thereon, characterized in that: When the computer program is executed by a processor, the steps of the method according to any one of claims 1 to 5 are implemented.

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