CN111257934B - Seismic oscillation peak acceleration prediction method based on second-order neuron deep neural network - Google Patents
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Abstract
The invention discloses a seismic oscillation peak acceleration prediction method based on a second-order neuron deep neural network, belongs to the field of seismic engineering, and aims to solve the technical problem of low accuracy of seismic oscillation prediction. The earthquake motion peak acceleration prediction method comprises the following steps: selecting a seismic magnitude, a projection distance, a shear wave velocity, an area, a covering layer thickness, a fault type and a period as input parameters in a data set, wherein the corresponding seismic oscillation peak acceleration is a target parameter; establishing a deep neural network comprising three hidden layers, wherein neurons are second-order elements, a hyperbolic tangent function is adopted as an activation function, a mean square error function and an Adam self-adaptive optimization function are adopted for back propagation, and an average absolute error function is taken as an evaluation function; thirdly, training a deep neural network model; and fourthly, predicting the peak acceleration. The invention adopts a multi-input structure and a second-order neural network, which can not only improve the precision of predicting the earthquake motion peak acceleration, but also ensure the applicability of a deep neural network model.
Description
Technical Field
The invention belongs to the field of seismic engineering, and particularly relates to a seismic oscillation peak acceleration prediction method based on a second-order neuron deep neural network.
Background
From ancient times to present, the loss of society caused by each major earthquake is immeasurable, in order to reduce and control the loss caused by the earthquake, the earthquake fortification of buildings is the most important measure, and the basis of the earthquake fortification is the earthquake danger analysis. In earthquake risk analysis, in order to evaluate earthquake intensity through different parameters, establishing an earthquake motion prediction equation is a very important link.
At present, the traditional prediction method is mainly to carry out empirical regression according to the existing seismic records, the method has good prediction precision and uniform residual distribution, but the seismic record applicable to the method is less due to the uncertainty of the height of each variable in an equation.
In recent years, with the development of computer technology, the deep neural network achieves better performance in data regression, and therefore a peak acceleration prediction method based on a second-order neuron deep neural network is provided.
Disclosure of Invention
The invention aims to solve the technical problem of low accuracy of seismic motion prediction, and provides a seismic motion peak acceleration prediction method based on a second-order neuron deep neural network.
The seismic oscillation peak acceleration prediction method based on the second-order neuron deep neural network is realized according to the following steps:
the method comprises the following steps: collecting seismic motion records, and establishing a data set:
selecting magnitude (M) and projection distance (R) in the data setJB) Shear wave velocity (V)S30) Region (Region), cover thickness (Z)1) The Fault Type (Fault Type) and the period (T) are used as input parameters, the corresponding earthquake motion peak acceleration is used as a target parameter, and the values of the input parameters and the target parameter are between-0.5 and 0.5 through a standardization method to obtain an earthquake motion data set;
step two: establishing a deep neural network with second-order neurons:
establishing a deep neural network comprising three hidden layers, wherein neurons are second-order elements, a hyperbolic tangent function (Tanh) is adopted as an activation function, a mean square error function (MSE) and an Adam self-adaptive optimization function are adopted for back propagation, and an average absolute error function (MAE) is adopted as an evaluation function to obtain a deep neural network model;
step three: deep neural network model training:
training the deep neural network model, ensuring the training precision through a mean square error function (MSE) and an average absolute error function (MAE), and enabling an attenuation curve to smoothly descend to obtain the trained deep neural network model;
step four: predicting the peak acceleration:
predicting earthquake motion input parameters and outputting earthquake motion peak acceleration by using the deep neural network model trained in the step three, so that the earthquake motion peak acceleration is predicted;
the operation formula in the second order element in the step two is as follows:
wherein: k is that the current neuron is positioned at the kth layer;
n is the number of neurons in the k-th layer network;
σ: an activation function, which adopts a hyperbolic tangent function (Tanh);
ωira first weight parameter corresponding to the ith neuron of the k-th layer network;
ωiga second weight parameter corresponding to the ith neuron of the k-th layer network;
ωiba third weight parameter corresponding to the ith neuron of the k-th layer network;
b1a first bias parameter corresponding to the k-th layer network;
b2a second bias parameter corresponding to the k-th layer network;
b3a third bias parameter corresponding to the k-th layer network;
xiinput parameters.
The invention selects more than 20900 earthquake motion records from the global scope (NGA-West2 database), adopts a multi-input structure and a second-order neuron network, can improve the prediction precision and ensure the applicability of a deep neural network model.
Compared with the traditional empirical formula, the seismic oscillation peak acceleration prediction method based on the second-order neuron deep neural network has the advantages of most data sets, higher precision, better applicability and the same simplicity and convenience in use.
Drawings
FIG. 1 is a general framework flowchart of an embodiment seismic peak acceleration prediction method based on a second-order neuron deep neural network;
FIG. 2 is a diagram of a second-order neuron deep neural network model according to an embodiment;
FIG. 3 is a test chart for predicting seismic peak acceleration by using ASK 14;
FIG. 4 is a test chart for predicting seismic peak acceleration using BSSA 14;
FIG. 5 is a test chart of seismic peak acceleration prediction by using CB 14;
FIG. 6 is a test chart for predicting seismic peak acceleration by using CY 14;
FIG. 7 is a test chart of seismic peak acceleration prediction using ANN;
FIG. 8 is a test chart of seismic peak acceleration prediction using an embodiment RSO-DNN;
fig. 9 is a graph of the peak acceleration decay curve of the embodiment compared to BSSA14 model, wherein the solid line represents RSO-DNN and the dashed line represents BSSA14, with sequential magnitudes of 4, 5, 6, 7, and 8 along arrow direction M.
Detailed Description
The first embodiment is as follows: the earthquake motion peak acceleration prediction method based on the second-order neuron deep neural network is implemented according to the following steps:
the method comprises the following steps: collecting seismic motion records, and establishing a data set:
selecting magnitude (M) and projection distance (R) in the data setJB) Shear wave velocity (V)S30) Region (Region), cover thickness (Z)1) The Fault Type (Fault Type) and the period (T) are input parameters, the corresponding earthquake motion peak acceleration is a target parameter, and the values of the input parameters and the target parameter are between-0.5 and 0.5 through a standardization method to obtain an earthquake motion data set;
step two: establishing a deep neural network with second-order neurons:
establishing a deep neural network comprising three hidden layers, wherein neurons are second-order elements, a hyperbolic tangent function (Tanh) is adopted as an activation function, a mean square error function (MSE) and an Adam self-adaptive optimization function are adopted for back propagation, and an average absolute error function (MAE) is adopted as an evaluation function to obtain a deep neural network model;
step three: deep neural network model training:
training the deep neural network model, ensuring the training precision through a mean square error function (MSE) and an average absolute error function (MAE), and enabling an attenuation curve to smoothly descend to obtain the trained deep neural network model;
step four: predicting the peak acceleration:
predicting earthquake motion input parameters by using the deep neural network model trained in the step three and outputting earthquake motion peak acceleration, thereby completing the earthquake motion peak acceleration prediction method based on the second-order neuron deep neural network;
the operation formula in the second order element in the step two is as follows:
wherein: k is that the current neuron is positioned at the kth layer;
n is the number of neurons in the k-th layer network;
σ: an activation function, which adopts a hyperbolic tangent function (Tanh);
ωira first weight parameter corresponding to the ith neuron of the k-th layer network;
ωiga second weight parameter corresponding to the ith neuron of the k-th layer network;
ωiba third weight parameter corresponding to the ith neuron of the k-th layer network;
b1a first bias parameter corresponding to the k-th layer network;
b2a second bias parameter corresponding to the k-th layer network;
b3a third bias parameter corresponding to the k-th layer network;
xiinput parameters.
The second embodiment is as follows: this embodiment differs from the embodiment in that the seismic record in step one is selected from the NGA-West2 database.
The third concrete implementation mode: the difference between this embodiment and the first or second embodiment is that the first step, the middle magnitude (M), is obtained from the natural logarithm, and the projection distance (R)JB) Taken from the natural log value.
The fourth concrete implementation mode: the difference between this embodiment and one of the first to third embodiments is that each hidden layer in step two includes 30 second-order neurons.
The fifth concrete implementation mode: the difference between this embodiment and one of the first to the fourth embodiments is that the deep neural network described in step two is a multi-input network, the input parameters are divided into four groups and respectively input into independent sub-networks, each independent sub-network includes 30 second-order neurons, the input parameters are subjected to four independent sub-network operations to obtain four groups of data, and the four groups of data are connected into one group by using a catenate function and then input into the next hidden layer.
The independent sub-network described in this embodiment is a hidden layer.
The sixth specific implementation mode: the third or fifth difference from the specific embodiment is that the input parameters are divided into A, B, C and D groups, wherein the A group takes the Fault Type (Fault Type) and the magnitude (M) as the input parameters, and the B group takes the magnitude (M) and the projection distance (R)JB) And Region (Region) as input parameters, and C group is the magnitude (M) and projection distance (R)JB) Region, shear wave velocity (V)S30) And the thickness (Z) of the covering layer1) As input parameters, the D group takes the period (T) as an input parameter.
The seventh embodiment: the difference between this embodiment and one of the first to sixth embodiments is that the expression of the mean square error function (MSE) in step two is as follows:
wherein: y isi-the true value;
-a predicted value.
The specific implementation mode is eight: the difference between this embodiment and one of the first to seventh embodiments is that the algorithm of the Adam adaptive optimization function is as follows:
(1) calculating a first moment estimate and a second moment estimate of the gradient by the following formula:
mt＝β1·mt-1+(1-β1)·gt，νt＝β2·νt-1+(1-β2)·gt 2；
in the formula, gtIs a gradient in which mtIs the mean value of the gradient at time t, vtIs the non-central variance value, m, at time t of the gradientt-1Is the mean value at time t-1 of the gradient, Vt-1The exponential decay rate beta of the moment estimate, which is the non-central variance value at time t-1 of the gradient1And beta2Within the interval [0,1 ], beta1Take 0.9, beta2Taking 0.999;
(2) correcting the first order moment estimate and the second order moment estimate by calculating the formula:
(3) the final formula for parameter update is:
in the formula, thetatFor updated parameters, η is the learning rate, ε is a small constant for numerical stability, ε is taken to be 10-8。
The specific implementation method nine: the present embodiment is different from the first to eighth embodiments in that the batch size (batch size) of the deep neural network model after training in step three is 325, the training round (Epoch) is 15, and the learning rate is 0.001.
Example (b): the earthquake motion peak acceleration prediction method based on the second-order neuron deep neural network is implemented according to the following steps:
the method comprises the following steps: collecting seismic motion records, and establishing a data set:
selecting 20900 seismic records from the NGA-West2 database, and selecting the magnitude (M) and the projection distance (R) in the data setJB) Shear wave velocity (V)S30) Region (Region), cover thickness (Z)1) Fault Type and period (T) as input parameters, magnitude (M) is taken from natural logarithm value, projection distance (R)JB) Taking a natural logarithm value, taking the corresponding seismic oscillation peak acceleration as a target parameter, and enabling the values of the input parameter and the target parameter to be between-0.5 and 0.5 through a standardization method to obtain a seismic oscillation data set;
the formula of the normalization method is as follows:
wherein: x is the number of*Standardized data; x is the number ofmax: maximum value of data; x is the number ofmin: a data minimum value; x is data before standardization;
step two: dividing a data set;
randomly dividing the seismic data set into a training set, a verification set and a test set, wherein the proportion of the training set, the verification set and the test set is 8: 1: 1;
step three: establishing a deep neural network with second-order neurons:
establishing a deep neural network comprising three hidden layers, wherein the deep neural network is a multi-input network, input parameters are divided into four groups and are respectively input into independent sub-networks, the input parameters are divided into an A group, a B group, a C group and a D group, the A group takes a Fault Type (Fault Type) and a magnitude (M) as the input parameters, and the B group takes the magnitude (M) and a projection distance (R) as the input parametersJB) And Region (Region) as input parameters, and the C group is in magnitude(M), projection distance (R)JB) Region, shear wave velocity (V)S30) And the thickness (Z) of the covering layer1) The D group takes a period (T) as an input parameter, each independent sub-network comprises 30 second-order neurons, the input parameter is operated by four independent sub-networks to obtain four groups of data, the four groups of data are connected into a group by using a concatenate function and then input into a next hidden layer, each hidden layer comprises 30 second-order neurons, a hyperbolic tangent function (Tanh) is used as an activation function, a mean square error function (MSE) and an Adam self-adaptive optimization function are used for back propagation, and a mean absolute error function (MAE) is used as an evaluation function to obtain a deep neural network model;
step four: deep neural network model training:
training the deep neural network model, ensuring the training precision through a mean square error function (MSE) and a mean absolute error function (MAE), ensuring the applicability according to the shape of an attenuation curve, and obtaining the trained deep neural network model RSO-DNN, wherein the batch size (Batchsize) of the trained deep neural network model is 325, the training round (Epoch) is 15, and the learning rate is 0.001;
step five: predicting the peak acceleration:
and predicting the earthquake motion input parameters by using the trained deep neural network model trained in the step four and outputting earthquake motion peak acceleration, thereby completing the earthquake motion peak acceleration prediction method based on the second-order neuron deep neural network.
The network selected in this embodiment includes three hidden layers, all neurons are second-order elements, and the internal operation formula of the second-order elements is as follows:
wherein: k is that the current neuron is positioned at the kth layer;
n is the number of neurons in the k-th layer network;
σ: an activation function, which adopts a hyperbolic tangent function (Tanh);
ωira first weight parameter corresponding to the ith neuron of the k-th layer network;
ωiga second weight parameter corresponding to the ith neuron of the k-th layer network;
ωiba third weight parameter corresponding to the ith neuron of the k-th layer network;
b1a first bias parameter corresponding to the k-th layer network;
b2a second bias parameter corresponding to the k-th layer network;
b3a third bias parameter corresponding to the k-th layer network;
xiinput parameters.
With the development of computer technology and the amplification of data sets, neural networks are developed towards deep layers, and neurons are developed towards higher orders, but the contribution of the neural networks in the aspect of building earthquake motion prediction equations is very limited. Models established by traditional empirical regression methods, such as BSSA14, ASK14, CB14, CY14, I14, and Derras trained artificial neural networks, are very good in accuracy and applicability, but have room for improvement. Therefore, the present invention selects 5 empirical formulas to compare with 1 artificial neural network model (ANN), wherein in the conventional linear neural network (ANN), the operation formula inside each neuron is as follows:
wherein: k is that the current neuron is positioned at the kth layer;
n is the number of neurons in the k-th layer network;
ωithe weighting parameter corresponding to the ith neuron of the k-th layer network;
b, bias parameters corresponding to the k-th layer network;
xiinputting parameters;
σ: the function is activated.
The comparison results are shown in table 1, and the comparison graphs are shown in fig. 3 to 8. Through the calculation comparison of the peak acceleration prediction precision and the observation comparison of the gathering effect, the deep neural network model trained by the embodiment has the best performance.
TABLE 1 comparison of the present invention with empirical formulas and linear artificial neural network peak acceleration prediction results
Claims (9)
1. The earthquake motion peak acceleration prediction method based on the second-order neuron deep neural network is characterized by comprising the following steps of:
the method comprises the following steps: collecting seismic motion records, and establishing a data set:
selecting an earthquake magnitude, a projection distance, a shear wave velocity, an area, a covering layer thickness, a fault type and a period in the data set as input parameters, taking the corresponding earthquake motion peak acceleration as a target parameter, and enabling the values of the input parameters and the target parameter to be between-0.5 and 0.5 through a standardization method to obtain an earthquake motion data set;
step two: establishing a deep neural network with second-order neurons:
establishing a deep neural network comprising three hidden layers, wherein neurons are second-order elements, a hyperbolic tangent function is adopted as an activation function, a mean square error function and an Adam self-adaptive optimization function are adopted for back propagation, and an average absolute error function is adopted as an evaluation function to obtain a deep neural network model;
step three: deep neural network model training:
training the deep neural network model, ensuring the training precision through a mean square error function and an average absolute error function, and enabling an attenuation curve to smoothly descend to obtain the trained deep neural network model;
step four: predicting the peak acceleration:
predicting earthquake motion input parameters and outputting earthquake motion peak acceleration by using the deep neural network model trained in the step three, so that the earthquake motion peak acceleration is predicted;
the operation formula in the second order element in the step two is as follows:
wherein: k is that the current neuron is positioned at the kth layer;
n is the number of neurons in the k-th layer network;
σ: activating a function by adopting a hyperbolic tangent function;
ωira first weight parameter corresponding to the ith neuron of the k-th layer network;
ωiga second weight parameter corresponding to the ith neuron of the k-th layer network;
ωiba third weight parameter corresponding to the ith neuron of the k-th layer network;
b1a first bias parameter corresponding to the k-th layer network;
b2a second bias parameter corresponding to the k-th layer network;
b3a third bias parameter corresponding to the k-th layer network;
xiinput parameters.
2. The method for predicting earthquake peak acceleration based on the second-order neuron depth neural network as claimed in claim 1, wherein the earthquake record in the first step is selected from NGA-West2 database.
3. The method of claim 1, wherein the seismic peak acceleration prediction method based on the second-order neuron depth neural network is characterized in that in the first step, the seismic magnitude is a natural logarithm value, and the projection distance is a natural logarithm value.
4. The method of predicting earthquake peak acceleration based on the second-order neuron deep neural network as claimed in claim 1, wherein each hidden layer in the second step comprises 30 second-order neurons.
5. The method of predicting earthquake peak acceleration based on the quadratic neuron deep neural network of claim 1, wherein the deep neural network in the second step is a multi-input network, the input parameters are divided into four groups and respectively input into independent sub-networks, each independent sub-network comprises 30 quadratic neurons, the input parameters are subjected to four groups of data obtained by four independent sub-network operations, and the four groups of data are connected into one group by using a catenate function and then input into the next hidden layer.
6. The method of predicting earthquake peak acceleration based on the second-order neuron depth neural network as claimed in claim 3 or 5, wherein the input parameters are divided into A, B, C and D groups, wherein A group takes the fault type and the magnitude as input parameters, B group takes the magnitude, the projection distance and the area as input parameters, C group takes the magnitude, the projection distance, the area, the shear wave velocity and the cover layer thickness as input parameters, and D group takes the period as input parameters.
7. The method for predicting earthquake peak acceleration based on the second-order neuron deep neural network as claimed in claim 1, wherein the expression of the mean square error function in the second step is as follows:
wherein: y isi-the true value; y isi pre-a predicted value.
8. The seismic peak acceleration prediction method based on the second-order neuron depth neural network of claim 1, characterized in that the algorithm of the Adam adaptive optimization function is as follows:
(1) calculating a first moment estimate and a second moment estimate of the gradient by the following formula:
mt＝β1·mt-1+(1-β1)·gt，νt＝β2·νt-1+(1-β2)·gt 2；
in the formula, gtIs a gradient in which mtIs the mean value of the gradient at time t, vtIs the non-central variance value, m, at time t of the gradientt-1Is the mean value at time t-1 of the gradient, Vt-1The exponential decay rate beta of the moment estimate, which is the non-central variance value at time t-1 of the gradient1And beta2Within the interval [0,1 ], beta1Take 0.9, beta2Taking 0.999;
(2) correcting the first order moment estimate and the second order moment estimate by calculating the formula:
(3) the final formula for parameter update is:
in the formula, thetatFor updated parameters, η is the learning rate, ε is a small constant for numerical stability, ε is taken to be 10-8。
9. The method of predicting earthquake motion peak acceleration based on the second-order neuron deep neural network of claim 1, wherein the batch size of the deep neural network model after training in step three is 325, the training round is 15, and the learning rate is 0.001.
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