Joint inversion method for one-dimensional soil layer model based on physics-guided neural network

Abstract

The one-dimensional soil layer model joint inversion method based on physical guided neural network is designed to solve the problems of the current one-dimensional soil layer model joint inversion method, such as high cost, high sensitivity to the initial assumptions of the profile, and difficulty in determining the optimal number of inversions. 1. Collect surface seismic acceleration records and corresponding underground seismic acceleration records; 2. Establish a physical guided neural network; 3. Construct a network training data set; 4. Conduct physical guided neural network training; 5. Obtain soil layer parameters obtained by inversion. The present invention uses physical guided neural network to impose obvious physical constraints on the inversion. In addition, it proposes a physically restricted loss function to further restrict the parameter space, effectively reducing the uncertainty of the inversion and greatly improving the accuracy of the inversion.

Description

Technical Field

[0001] The invention belongs to the field of earthquake engineering, and in particular relates to a one-dimensional soil layer model joint inversion method based on a physics-guided neural network. Background Art

[0002] The characteristics of earthquake ground motions, including their intensity, duration, and frequency content, can be significantly affected by site conditions, leading to the appearance of destructive ground motions, a phenomenon often referred to as site effects. Site effects are generally studied and quantified in engineering through one-dimensional soil response analysis. In soil response analysis, the subsurface medium is generally assumed to consist of horizontally stratified, homogeneous, and transversely isotropic material that extends infinitely in the horizontal direction. In addition, the input motion is assumed to consist of plane waves that are vertically propagating, horizontally polarized shear waves. Two basic site parameters are the shear wave velocity (V) and the shear wave velocity (V). S ) profile and damping are used to characterize the stiffness of the soil layer and the dissipation of energy in the soil, respectively.

[0003] At present, different technologies are generally used to perform V S Estimation of profile and damping. Estimation of V S The methods of profile measurement can be divided into two categories: invasive methods and non-invasive methods. Although the former can measure more accurate shear wave velocity profiles than the latter, the former requires drilling at least one borehole, which significantly increases the measurement cost. Therefore, non-invasive methods have received widespread attention and application due to their performance and economy. Non-invasive techniques are based on single-station or multi-station measurement data and use various inversion methods to obtain V S Damping can be estimated using various field seismic methods that rely on the attenuation of surface waves, P waves, or S waves. However, these techniques have difficulty distinguishing between geometric and intrinsic attenuation, thus limiting their effectiveness. In addition, researchers have found that estimating V alone is not effective. S The profile and damping may cause a mismatch between the two estimates. The observed mismatch can be attributed to the use of different constitutive models when estimating each parameter separately. S The elastic constitutive model is generally used when estimating the cross-section, while the viscoelastic constitutive model is used when estimating the damping. In addition, the correlation between the two parameters is also ignored. To solve these problems, some researchers have proposed the V S Joint inversion methods for profile and damping. However, these joint methods still have disadvantages such as high cost, high sensitivity to the initial assumptions of the profile, and difficulty in determining the optimal number of inversions.

[0004] With the development of computer technology and deep learning in recent years, physics-guided deep learning has attracted widespread attention due to its excellent interpretability and generalization performance. The integration of traditional physics-based models with deep learning techniques, so-called physics-guided deep learning, makes it possible to take advantage of tools inherent in the deep learning framework, including automatic differentiation, Adam optimizer, and mini-batch strategy. The use of these integrated tools has shown insensitivity to initial profiles, accelerated convergence, and a trend of reduced computational overhead in the context of inversion problems. Summary of the invention

[0005] The purpose of the present invention is to solve the technical problems of the current one-dimensional soil layer model joint inversion method, such as high cost, high sensitivity to the initial assumptions of the profile and difficulty in determining the optimal number of inversions, and to provide a one-dimensional soil layer model joint inversion method based on a physics-guided neural network.

[0006] The one-dimensional soil layer model joint inversion method based on physical guided neural network of the present invention is implemented according to the following steps:

[0007] Step 1: Collect surface earthquake acceleration records and corresponding underground earthquake acceleration records;

[0008] Step 2: Establish a physical guided neural network:

[0009] The physical guided neural network consists of multiple complex fully connected layers, and the activation functions are all linear activation functions. The number of complex fully connected layers of the physical guided neural network is equal to the number of layers of the soil layer model, and the weights and bias values ​​of each network layer are consistent with the parameters of each soil layer to be determined (V S The parameters of each soil layer have physical meaning.

[0010] (1) Frequency domain method for one-dimensional soil response analysis

[0011] The propagation of shear waves in infinite viscoelastic media is described by the one-dimensional motion equation (1), which is expressed as:

[0012]

[0013] Where τ represents stress, η represents viscous damping, G represents shear modulus, γ represents shear strain, u represents displacement, t represents time, and z represents depth. For a simple harmonic wave with a frequency of ω, the general solution of the one-dimensional motion equation is obtained by the following equation (2):

[0014]

[0015] Where A and B are the incident wave amplitude and the reflected wave amplitude respectively. is the complex wave number, ρ represents the medium density, G* =G(2+2iβ) is the complex shear modulus, β is the damping ratio, and the corresponding stress solution is:

[0016]

[0017] For a viscoelastic system consisting of N layers of soil and a half space, assuming that each layer of soil has a local coordinate system Z, the displacement and stress at the top and bottom of the nth layer of soil are:

[0018] u n | z＝0 =(A n +B n ) iωt (4)

[0019]

[0020]

[0021]

[0022] Among them A n , B n , h n They represent the incident wave amplitude, reflected wave amplitude, complex wave number, complex shear modulus and thickness of the nth layer of soil respectively;

[0023] The following recursive formula is obtained from the displacement continuity and stress continuity of the interface:

[0024]

[0025]

[0026] in is the complex impedance ratio, A n+1 , B n+1 , and ρ n+1 are the incident wave amplitude, reflected wave amplitude, complex shear modulus, complex wave number and density of the n+1th layer of soil respectively; and then the incident wave amplitude and reflected wave amplitude of any layer of soil are obtained through the recursive formula;

[0027] (2) Physical guidance of neural network construction

[0028] Using matrix to express recursive formulas (8) and (9), we can obtain:

[0029]

[0030] For a single-layer neural network with two input and output neurons, the mathematical formula is as follows:

[0031]

[0032] Then, the recursive formula is expressed by the physical guided neural network. The parameter definition of the physical guided neural network is shown in formula (12). The physical guided neural network corresponding to the multi-layer soil is established.

[0033]

[0034] Where y1 and y2 represent the two outputs of the current soil network and are also the two inputs of the next soil network, x1 and x2 represent the two inputs of the current soil network, ω 11 represents the weight between the first neuron of the current soil layer network and the first neuron of the next soil layer network, ω 12 represents the weight between the first neuron of the current soil layer network and the second neuron of the next soil layer network, ω 21 represents the weight between the second neuron of the current soil layer network and the first neuron of the next soil layer network, ω 22 represents the weight between the second neuron of the current soil layer network and the second neuron of the next soil layer network, b1 represents the bias value of the current soil layer network, and b2 represents the bias value of the next soil layer network, thereby establishing the physical guidance neural network NN corresponding to the multi-layer soil;

[0035] Step 3: Build a network training data set:

[0036] The surface earthquake records and underground earthquake records collected in step 1 are respectively subjected to discrete Fourier transform to obtain the amplitude of each frequency component. For the (digital) acceleration records containing m equidistant element values, they are decomposed into the following form:

[0037]

[0038] where ω s is the sth equidistant frequency, a s and b s Respectively represent the frequency corresponding to ω s and -ω s The complex Fourier magnitude of ;

[0039] An input data set is constructed based on the amplitude of each frequency component of the surface seismic records, and a label data set is constructed using the amplitude of the corresponding frequency component of the underground seismic records;

[0040] Step 4: Conduct physical guided neural network training:

[0041] The amplitude of the component with frequency ω in the surface earthquake acceleration record is A g (ω), the amplitude of the component with frequency ω in the underground seismic acceleration record is Ad (ω); For the physical guided neural network NN, when the input is A g (ω), the network parameters are continuously updated through training so that the corresponding output is A d (ω), that is:

[0042] A d (ω) = NN(A g (ω)) (18)

[0043] The total loss function for training a physics-guided neural network is:

[0044]

[0045] Where λ1 and λ2 are weight coefficients;

[0046] The Where m represents the number of equally spaced elements in the observation record, that is, the number of frequency components, is an operator for the real part of a complex number, is an operator for finding the imaginary part of a complex number, A d (ω s )and Represent the amplitude of the sth frequency of the target and prediction respectively;

[0047] The Where N represents the number of soil layers in the soil layer model, p i are soil layer model parameters, including V S and damping ratio, p max is the maximum value in the soil layer model parameter space, p min is the minimum value of the soil layer model parameter space, relu() is the rectified linear unit function;

[0048] Step 5: Get the soil layer parameters obtained by inversion:

[0049] Since physics guides the neural network parameter weights and bias values ​​​​to be related to V S The profile is related to the damping ratio. When the physical guidance neural network training is completed, V is obtained through the network parameters. S cross section and damping ratio.

[0050] The present invention utilizes the similarity between the principle of one-dimensional soil layer response analysis frequency domain method and the principle of neural network to build a physically guided neural network. Each parameter in the network has a strict physical meaning, which greatly enhances the interpretability and generalization performance of the network. At the same time, prior knowledge constraints are added to the loss function, which significantly reduces the uncertainty and difficulty of inversion, and provides strong technical support for the inversion of one-dimensional soil layer models.

[0051] Compared with the current one-dimensional soil layer model joint inversion method, the one-dimensional soil layer model joint inversion method based on the physical guided neural network of the present invention has lower cost, is insensitive to the initial assumptions of the profile, and only requires one inversion to obtain the optimal result. Therefore, it is more practical and more convenient and quick in actual use. BRIEF DESCRIPTION OF THE DRAWINGS

[0052] Figure 1 Schematic diagram of a viscoelastic system consisting of N layers of soil and a half space in the embodiment;

[0053] Figure 2 Schematic diagram of a single-layer neural network structure with two input and output neurons in an embodiment, wherein f(·), ω and b are activation function, weight and bias, respectively;

[0054] Figure 3 A schematic diagram of a single-layer physical guided neural network structure in an embodiment;

[0055] Figure 4 Schematic diagram of the structure of a multi-layer physical guided neural network in an embodiment, wherein all bias values ​​of neurons are set to 0, and the activation function used is a linear activation function;

[0056] Figure 5 A flowchart of inverting underground soil parameters using a physical guided deep neural network based on underground array data in an embodiment, wherein DFT is used to transform surface and underground records from the time domain to the frequency domain to generate input and label data, respectively;

[0057] Figure 6 is the surface seismic time history and the corresponding Fourier amplitude spectrum selected under the noise-free working condition in the embodiment;

[0058] Figure 7 The shear wave velocity profile obtained by joint inversion using the present invention under noise-free conditions in the embodiment;

[0059] Figure 8 The damping ratio changes with Epochs in the joint inversion process using the present invention under noise-free conditions in the embodiment;

[0060] Fig. 9 It is the underground ground motion record and transfer function calculated by using the one-dimensional soil layer model obtained by joint inversion using the present invention under noise-free working conditions in the embodiment;

[0061] Fig.10 It is a one-dimensional soil layer model and a corresponding transfer function obtained by performing joint inversion using the present invention under actual working conditions in the embodiment. DETAILED DESCRIPTION

[0062] Specific implementation method 1: This implementation method is based on the one-dimensional soil layer model joint inversion method of the physical guided neural network according to the following steps:

[0063] Step 1: Collect surface earthquake acceleration records and corresponding underground earthquake acceleration records;

[0064] Step 2: Establish a physical guided neural network:

[0065] The physical guided neural network consists of multiple complex fully connected layers, and the activation functions are all linear activation functions. The number of complex fully connected layers of the physical guided neural network is equal to the number of layers of the soil layer model, and the weights and bias values ​​of each network layer are consistent with the parameters of each soil layer to be determined (V S The parameters of each soil layer have physical meaning.

[0066] (1) Frequency domain method for one-dimensional soil response analysis

[0067] The propagation of shear waves in infinite viscoelastic media is described by the one-dimensional motion equation (1), which is expressed as:

[0068]

[0069] Where τ represents stress, η represents viscous damping, G represents shear modulus, γ represents shear strain, u represents displacement, t represents time, and z represents depth. For a simple harmonic wave with a frequency of ω, the general solution of the one-dimensional motion equation is obtained by the following equation (2):

[0070]

[0071] Where A and B are the incident wave amplitude and the reflected wave amplitude respectively. is the complex wave number, ρ represents the medium density, G * =G(2+2iβ) is the complex shear modulus, β is the damping ratio, and the corresponding stress solution is:

[0072]

[0073] For a viscoelastic system consisting of N layers of soil and a half space, assuming that each layer of soil has a local coordinate system Z, the displacement and stress at the top and bottom of the nth layer of soil are:

[0074] u n | z＝0 =(A n +B n ) iωt (4)

[0075]

[0076]

[0077]

[0078] Among them A n , B n , h n They represent the incident wave amplitude, reflected wave amplitude, complex wave number, complex shear modulus and thickness of the nth layer of soil respectively;

[0079] The following recursive formula is obtained from the displacement continuity and stress continuity of the interface:

[0080]

[0081]

[0082] in is the complex impedance ratio, A n+1 , B n+1 , and ρ n+1 are the incident wave amplitude, reflected wave amplitude, complex shear modulus, complex wave number and density of the n+1th layer of soil respectively; and then the incident wave amplitude and reflected wave amplitude of any layer of soil are obtained through the recursive formula;

[0083] (2) Physical guidance of neural network construction

[0084] Using matrix to express recursive formulas (8) and (9), we can obtain:

[0085]

[0086] For a single-layer neural network with two input and output neurons, the mathematical formula is as follows:

[0087]

[0088] Then, the recursive formula is expressed by the physical guided neural network. The parameter definition of the physical guided neural network is shown in formula (12). The physical guided neural network corresponding to the multi-layer soil is established.

[0089]

[0090] Where y1 and y2 represent the two outputs of the current soil network and are also the two inputs of the next soil network, x1 and x2 represent the two inputs of the current soil network, ω 11 Represents the weight between the first neuron of the current soil layer network and the first neuron of the next soil layer network, ω 12represents the weight between the first neuron of the current soil layer network and the second neuron of the next soil layer network, ω 21 represents the weight between the second neuron of the current soil layer network and the first neuron of the next soil layer network, ω 22 represents the weight between the second neuron of the current soil layer network and the second neuron of the next soil layer network, b1 represents the bias value of the current soil layer network, and b2 represents the bias value of the next soil layer network, thereby establishing the physical guidance neural network NN corresponding to the multi-layer soil;

[0091] Step 3: Build a network training data set:

[0092] The surface earthquake records and underground earthquake records collected in step 1 are respectively subjected to discrete Fourier transform to obtain the amplitude of each frequency component. For the (digital) acceleration records containing m equidistant element values, they are decomposed into the following form:

[0093]

[0094] where ω s is the sth equidistant frequency, a s and b s Respectively represent the frequency corresponding to ω s and -ω s The complex Fourier magnitude of ;

[0095] An input data set is constructed based on the amplitude of each frequency component of the surface seismic records, and a label data set is constructed using the amplitude of the corresponding frequency component of the underground seismic records;

[0096] Step 4: Conduct physical guided neural network training:

[0097] The amplitude of the component with frequency ω in the surface earthquake acceleration record is A g (ω), the amplitude of the component with frequency ω in the underground seismic acceleration record is A d (ω); For the physical guided neural network NN, when the input is A g (ω), the network parameters are continuously updated through training so that the corresponding output is A d (ω), that is:

[0098] A d (ω) = NN(A g (ω)) (18)

[0099] The total loss function for training a physics-guided neural network is:

[0100]

[0101] Where λ1 and λ2 are weight coefficients;

[0102] The Where m represents the number of equally spaced elements in the observation record, that is, the number of frequency components, is an operator for the real part of a complex number, is an operator for finding the imaginary part of a complex number, A d (ω s )and Represent the amplitude of the sth frequency of the target and prediction respectively;

[0103] The Where N represents the number of soil layers in the soil layer model, p i are soil layer model parameters, including V S and damping ratio, p max is the maximum value in the soil layer model parameter space, p min is the minimum value of the soil layer model parameter space, relu() is the rectified linear unit function;

[0104] Step 5: Get the soil layer parameters obtained by inversion:

[0105] Since physics guides the neural network parameter weights and bias values ​​​​to be related to V S The profile is related to the damping ratio. When the physical guidance neural network training is completed, V is obtained through the network parameters. S cross section and damping ratio.

[0106] Specific implementation method 2: This implementation method is different from specific implementation method 1 in that the record observed by the surface acceleration recorder in step 1 is the surface seismic acceleration record, and the record observed by the underground acceleration recorder is the underground seismic acceleration record.

[0107] Specific implementation method three: This implementation method is different from specific implementation method two in that the underground acceleration recorder in step one is selected from the IWTH08 station in the Japanese Kik-Net array.

[0108] Specific embodiment 4: This embodiment is different from specific embodiments 1 to 3 in that the density when calculating the complex shear modulus in step 2 is calculated by the following empirical formula:

[0109] ρ=0.914V s 0.122

[0110] Where V s represents the shear wave velocity.

[0111] Specific implementation method 5: This implementation method is different from the specific implementation methods 1 to 4 in that the top of the first layer of soil in step 2 satisfies the free surface condition, that is, the stress is 0, so it can be obtained:

[0112] A1=B1 (10).

[0113] Specific implementation method 6: This implementation method is different from the specific implementation methods 1 to 5 in that the step 3 s The calculation formula is as follows:

[0114]

[0115] Where Δt is the time interval.

[0116] Specific implementation method 7: This implementation method is different from the specific implementation methods 1 to 6 in that a s and b s Calculate using the following formula:

[0117]

[0118]

[0119] Specific implementation method 8: This implementation method is different from the specific implementation methods 1 to 7 in that the total loss function formula in step 4 is mask max =relu(p i -p max ), mask min =relu(p min -p i ), relu() is the rectified linear unit function.

[0120] Specific implementation method 9: This implementation method is different from any one of specific implementation methods 1 to 8 in that the shear wave velocity profile and the damping ratio in step 4 are initially set to 1000 m / s and 0.01, respectively.

[0121] Specific implementation method ten: The difference between this implementation method and specific implementation methods one to nine is that in step four, the minibatch gradient descent method is used for training, the batch size is set to 64, the optimizer is the Adam algorithm, the learning rate is set to 10, and the training round epochs is set to 400.

[0122] Embodiment: The one-dimensional soil layer model joint inversion method based on physical guided neural network in this embodiment is implemented according to the following steps:

[0123] Step 1: Collect surface earthquake acceleration records and corresponding underground earthquake acceleration records;

[0124] Since the proposed method relies on the one-dimensional site assumption, the IWTH08 station that meets the one-dimensional site assumption was selected from the Japanese Kik-Net array, and both noise-free and actual noise-containing conditions were considered. In order to generate the data required for the noise-free condition, a surface record corresponding to a magnitude of 5.4 was selected from the historical records of the IWTH08 station (e.g. Figure 6 Based on the soil profile provided by IWTH08 station (as shown in Table 1) and the one-dimensional soil response analysis frequency domain method, the underground seismic acceleration record was inverted. In addition, 12 pairs of earthquakes with epicenter distances within 200 km and amplitudes between 30-50 cm / s were collected. 2 The surface-downhole seismic records within the range are used as the data for inversion in the actual noisy working conditions, and the specific parameters are shown in Table 2;

[0125] Table 1. Shear wave velocity profile at station IWTH08

[0126]

[0127]

[0128] Table 2. Related parameters of 12 selected pairs of surface-underground ground motion records

[0129]

[0130] Step 2: Establish a physical guided neural network:

[0131] The physical guided neural network consists of multiple complex fully connected layers, and the activation functions are all linear activation functions. The shear wave velocity profile and damping ratio are initially 1000 m / s and 0.01, respectively. The number of layers of the physical guided neural network is equal to the number of layers of the soil layer model, and the weights and bias values ​​of each network layer are the same as the parameters of each soil layer to be determined (V S The profile and damping ratio are related and can be determined by the principle of frequency domain method for one-dimensional soil response analysis, so each parameter has obvious physical meaning;

[0132] (1) Frequency domain method for one-dimensional soil response analysis

[0133] The propagation of shear waves in infinite viscoelastic media is described by the one-dimensional motion equation (1), which is expressed as:

[0134]

[0135] Where τ represents stress, η represents viscous damping, G represents shear modulus, γ represents shear strain, u represents displacement, t represents time, and z represents depth. For a simple harmonic wave with a frequency of ω, the general solution of the one-dimensional motion equation is obtained by the following equation (1):

[0136]

[0137] Where A and B are the incident wave amplitude and the reflected wave amplitude respectively. is the complex wave number, ρ represents the medium density, G * =G(2+2iβ) is the complex shear modulus, β is the damping ratio, and the corresponding stress solution is:

[0138]

[0139] For a viscoelastic system consisting of N layers of soil and a half space, assuming that each layer of soil has a local coordinate system Z, the displacement and stress at the top and bottom of the nth layer of soil are:

[0140] u n | z＝0 =(A n +B n ) iωt (4)

[0141]

[0142]

[0143]

[0144] Among them A n , B n , h n Represent the incident wave amplitude, reflected wave amplitude, complex wave number, complex shear modulus and thickness of the nth layer of soil respectively. The following recursive formula is obtained from the displacement continuity and stress continuity of the interface:

[0145]

[0146]

[0147] in is the complex impedance ratio, A n+1 , B n+1 , and ρ n+1 are the incident wave amplitude, reflected wave amplitude, complex shear modulus, complex wave number and density of the n+1th layer of soil respectively; and then the incident wave amplitude and reflected wave amplitude of any layer of soil are obtained through the recursive formula;

[0148] (2) Physical guidance of neural network construction

[0149] Using matrix to express recursive formulas (8) and (9), we can obtain:

[0150]

[0151] For a single-layer neural network with two input and output neurons, the mathematical formula is as follows:

[0152]

[0153] Then, the recursive formula is expressed by the physical guided neural network. The parameter definition of the physical guided neural network is shown in formula (13). The physical guided neural network corresponding to the multi-layer soil is established.

[0154]

[0155] Where y1 and y2 represent the two outputs of the current soil network and are also the two inputs of the next soil network, x1 and x2 represent the two inputs of the current soil network, ω 11 Represents the weight between the first neuron of the current soil layer network and the first neuron of the next soil layer network, ω 12 represents the weight between the first neuron of the current soil layer network and the second neuron of the next soil layer network, ω 21 represents the weight between the second neuron of the current soil layer network and the first neuron of the next soil layer network, ω 22 represents the weight between the second neuron of the current soil layer network and the second neuron of the next soil layer network, b1 represents the bias value of the current soil layer network, and b2 represents the bias value of the next soil layer network, thereby establishing the physical guidance neural network NN corresponding to the multi-layer soil;

[0156] Step 3: Build a network training data set:

[0157] The surface earthquake records and underground earthquake records collected in step 1 are respectively subjected to discrete Fourier transform to obtain the amplitude of each frequency component. For the (digital) acceleration records containing m equidistant element values, they are decomposed into the following form:

[0158]

[0159] where ω s is the sth equidistant frequency:

[0160]

[0161] a s and b s Respectively represent the frequency corresponding to ω s and -ω s The complex Fourier amplitude of is calculated by the following formula:

[0162]

[0163]

[0164] The input data set is constructed based on the amplitude of each frequency component of the surface seismic record, and the label data set is constructed using the amplitude of the corresponding frequency component of the underground seismic record, and the frequency components with a frequency ≥ 20 Hz are cut off to improve the training efficiency;

[0165] Step 4: Conduct physical guided neural network training:

[0166] The amplitude of the component with frequency ω in the surface earthquake acceleration record is A g (ω), the amplitude of the component with frequency ω in the underground seismic acceleration record is A d (ω); For the physical guided neural network NN, when the input is A g (ω), the network parameters are continuously updated through training so that the corresponding output is A d (ω), that is:

[0167] A d (ω) = NN(A g (ω)) (18)

[0168] The loss function used to train the network consists of two parts. The first part is used to penalize the generated and the real A d The difference between (ω):

[0169]

[0170] Where m represents the number of elements in the observation record, that is, the number of frequency components, is an operator for the real part of a complex number, is the operator for the imaginary part of the complex number; the other part is the physical constraint loss. S The damping ratio is only distributed within a certain range. Therefore, in order to avoid inversion to obtain unreal physical parameters while reducing the uncertainty of inversion and the difficulty of inversion, the physical constraint loss is imposed:

[0171]

[0172] Where N represents the number of soil layers in the soil layer model, p i are soil layer model parameters, including V S and damping ratio, p max is the maximum value in the soil layer model parameter space, p min is the minimum value of the soil layer model parameter space, relu() is the rectified linear unit function, and V S The maximum and minimum values ​​of are 5000 and 50 respectively, and the maximum and minimum values ​​of the damping ratio are 0.25 and 0.001 respectively, that is:

[0173] 50m / s≤V s,i ≤5000m / s,0.001≤β i ≤0.25,for i=1,……,N+1 (21) In summary, the total loss function used to train the network is:

[0174]

[0175] Where λ1 and λ2 are weight coefficients, which are set to 1 and 10 in all experiments. 6 ;

[0176] Step 5: Get the soil layer parameters obtained by inversion:

[0177] Since physics guides the neural network parameter weights and bias values ​​​​to be related to V S The profile is related to damping. When the physical guidance neural network training is completed, V is obtained through the network parameters. S cross section and damping ratio.

[0178] In step 4 of this embodiment, the Adam optimizer is used to train the network parameters, the batch size is set to 64, the learning rate is set to 10, the training rounds epochs are set to 400, and the order of the data arranged from small to large according to frequency is not disrupted when traversing the data in each epoch.

[0179] Figure 8 and 9 The results of the joint inversion of the joint one-dimensional soil layer model using the method proposed in the present invention under noise-free conditions are given. It can be clearly seen that although the initial assumptions of the soil layer parameters are far from the true solution, the inversion results of extremely high accuracy are still obtained using the method proposed in the present invention, indicating that this method can effectively avoid the uncertainty of the inversion results caused by the local optimum and accurately converge to the global optimal solution. Unlike other methods, there is no need to carry out inversion under multiple different initial assumptions and finally take the average to reduce the uncertainty of the inversion results caused by multiple solutions. At the same time, it also proves the insensitivity of the proposed method to the initial model. In addition, bedrock seismic inversion and transfer function calculation were carried out based on the soil layer model obtained by the joint inversion, and compared with the actual bedrock seismic motion and the theoretical transfer function, as shown in the figure. Fig.10 As shown, the high degree of consistency shown in the figure further proves the excellent performance of the method proposed in the present invention.

[0180] When using actual seismic data to invert soil layer models, it is necessary to consider the uncertainty caused by factors such as noise and changes in soil layer structure over time. At present, the engineering community often uses multiple pairs of surface-underground seismic records to carry out inversion and then take the average to reduce this uncertainty. This paper selects 12 pairs of surface-underground seismic records to carry out joint inversion of one-dimensional soil layer models. The inversion results are as follows: Fig.10 As shown in Table 3. It can be seen that the theoretical transfer function calculated based on the mean model obtained by inversion is consistent with the empirical transfer function, and can fully capture the main frequency information that is most concerned in engineering, indicating that the method proposed in the present invention can still have good performance under actual working conditions.

[0181] Table 3. Damping ratio values ​​and corresponding mean damping ratios obtained by inverting 12 pairs of surface-underground seismic records

[0182]

[0183] In summary, the one-dimensional soil layer model joint inversion method based on physics-guided neural network is effective and realistic. This method uses physics-guided neural network to impose obvious physical constraints on the inversion. In addition, a physical restriction loss function is proposed to further limit the parameter space, effectively reducing the uncertainty of the inversion and greatly improving the accuracy of the inversion. This method not only shows excellent performance under noise-free conditions, but also has been verified under real conditions. It can effectively capture the main frequency of the site model, which is helpful to improve seismic design, improve seismic performance, assess seismic risks, and ensure the safety of buildings and foundations.

Claims

1. A one-dimensional soil layer model joint inversion method based on a physics-guided neural network, characterized by The one-dimensional soil layer model joint inversion method is implemented in the following steps: Step 1: Collect surface earthquake acceleration records and corresponding underground earthquake acceleration records; Step 2: Establish a physical guided neural network: The physics-guided neural network consists of multiple complex fully connected layers, and the activation functions are all linear activation functions. The number of complex fully connected layers of the physics-guided neural network is equal to the number of layers of the soil layer model. The weights and bias values ​​of each network layer are related to the parameters of each soil layer to be determined and are determined by the one-dimensional soil layer response analysis frequency domain method. Therefore, the parameters of each soil layer have physical meanings. (1) Frequency domain method for one-dimensional soil response analysis The propagation of shear waves in infinite viscoelastic media is described by the one-dimensional motion equation (1), which is expressed as: Where τ represents stress, η represents viscous damping, G represents shear modulus, γ represents shear strain, u represents displacement, t represents time, and z represents depth. For a simple harmonic wave with a frequency of ω, the general solution of the one-dimensional motion equation is obtained by the following equation (2): Where A and B are the incident wave amplitude and the reflected wave amplitude respectively. is the complex wave number, ρ represents the medium density, G * =G(2+2iβ) is the complex shear modulus, β is the damping ratio, and the corresponding stress solution is: For a viscoelastic system consisting of N layers of soil and a half space, assuming that each layer of soil has a local coordinate system Z, the displacement and stress at the top and bottom of the nth layer of soil are: u n | z＝0 =(A n +B n )and iωt (4) Among them A n , B n , h n They represent the incident wave amplitude, reflected wave amplitude, complex wave number, complex shear modulus and thickness of the nth layer of soil respectively; The following recursive formula is obtained from the displacement continuity and stress continuity of the interface: in is the complex impedance ratio, A n+1 , B n+1 , and ρ n+1 are the incident wave amplitude, reflected wave amplitude, complex shear modulus, complex wave number and density of the n+1th layer of soil respectively; and then the incident wave amplitude and reflected wave amplitude of any layer of soil are obtained through the recursive formula; (2) Physical guidance of neural network construction Using matrix to express recursive formulas (8) and (9), we can obtain: For a single-layer neural network with two input and output neurons, the mathematical formula is as follows: Then, the recursive formula is expressed by the physical guided neural network. The parameter definition of the physical guided neural network is shown in formula (12). The physical guided neural network corresponding to the multi-layer soil is established. Where y1 and y2 represent the two outputs of the current soil network and are also the two inputs of the next soil network, x1 and x2 represent the two inputs of the current soil network, ω 11 Represents the weight between the first neuron of the current soil layer network and the first neuron of the next soil layer network, ω 12 represents the weight between the first neuron of the current soil layer network and the second neuron of the next soil layer network, ω 21 represents the weight between the second neuron of the current soil layer network and the first neuron of the next soil layer network, ω 22 represents the weight between the second neuron of the current soil layer network and the second neuron of the next soil layer network, b1 represents the bias value of the current soil layer network, and b2 represents the bias value of the next soil layer network, thereby establishing the physical guidance neural network NN corresponding to the multi-layer soil; Step 3: Build a network training data set: The surface seismic records and underground seismic records collected in step 1 are respectively subjected to discrete Fourier transform to obtain the amplitude of each frequency component. For the acceleration records containing m equidistant element values, they are decomposed into the following form: where ω s is the sth equidistant frequency, a s and b s Respectively represent the frequency corresponding to ω s and -ω s The complex Fourier magnitude of ; An input data set is constructed based on the amplitude of each frequency component of the surface seismic records, and a label data set is constructed using the amplitude of the corresponding frequency component of the underground seismic records; Step 4: Conduct physical guided neural network training: The amplitude of the component with frequency ω in the surface earthquake acceleration record is A g (ω), the amplitude of the component with frequency ω in the underground seismic acceleration record is A d (ω); For the physical guided neural network NN, when the input is A g (ω), the network parameters are continuously updated through training so that the corresponding output is A d (ω), that is: A d (ω)=NN(A g (oh)) (18) The total loss function for training a physics-guided neural network is: Where λ1 and λ2 are weight coefficients; represents the number of equally spaced elements in the observation record, that is, the number of frequency components, and R(·) is an operator for finding the real part of a complex number. I(·) is an operator for finding the imaginary part of a complex number, A d (ω s )and Represent the amplitude of the sth frequency of the target and prediction respectively; The Where N represents the number of soil layers in the soil layer model, p i are soil layer model parameters, including V S and damping ratio, p max is the maximum value in the soil layer model parameter space, p min is the minimum value of the soil layer model parameter space, mask max =relu(p i -p max ), mask min =relu(p min -p i ), relu() is the rectified linear unit function; Step 5: Get the soil layer parameters obtained by inversion: Since physics guides the neural network parameter weights and bias values ​​​​to be related to V S The profile is related to the damping ratio. When the physical guidance neural network training is completed, V is obtained through the network parameters. S cross section and damping ratio.

2. The one-dimensional soil layer model joint inversion method based on physical guided neural network according to claim 1 is characterized in that In step 1, the record observed by the acceleration recorder on the surface is the surface seismic acceleration record, and the record observed by the acceleration recorder underground is the underground seismic acceleration record.

3. The one-dimensional soil layer model joint inversion method based on physical guided neural network according to claim 1 is characterized in that The underground accelerometer in step 1 is selected from the IWTH08 station in the Japanese Kik-Net array.

4. The one-dimensional soil layer model joint inversion method based on physical guided neural network according to claim 1 is characterized in that The density when calculating the complex shear modulus in step 2 is calculated using the following empirical formula: p=0.914V s 0.122 Where V s represents the shear wave velocity.

5. The one-dimensional soil layer model joint inversion method based on physical guided neural network according to claim 1 is characterized in that The top of the first layer of soil in step 2 meets the free surface condition, that is, the stress is 0, so we can get: A1=B1(10).

6. The one-dimensional soil layer model joint inversion method based on physical guided neural network according to claim 1 is characterized in that Step 3 s The calculation formula is as follows: Where Δt is the time interval.

7. The one-dimensional soil layer model joint inversion method based on physical guided neural network according to claim 1 is characterized in that Step 3a s and b s Calculate using the following formula:

8. The one-dimensional soil layer model joint inversion method based on physical guided neural network according to claim 1 is characterized in that In step 4, the shear wave velocity profile and damping ratio are initially set to 1000 m / s and 0.01, respectively.

9. The one-dimensional soil layer model joint inversion method based on physical guided neural network according to claim 1 is characterized in that In step 4, the minibatch gradient descent method is used for training, the batch size is set to 64, the optimizer is the Adam algorithm, the learning rate is set to 10, and the training round epochs is set to 400.

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