CN111257934A - Prediction method of ground motion peak acceleration based on second-order neuron deep neural network - Google Patents

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

Prediction method of ground motion peak acceleration based on second-order neuron deep neural network

technical field

The invention belongs to the field of earthquake engineering, and in particular relates to a method for predicting the peak acceleration of ground motion based on a second-order neuron deep neural network.

Background technique

From ancient times to the present, the losses brought to the society by every major earthquake are immeasurable. In order to reduce and control the losses caused by earthquakes, it is the most important measure to fortify buildings against earthquakes. Risk Analysis. In earthquake hazard analysis, in order to evaluate earthquake intensity through different parameters, it is very important to establish ground motion prediction equation.

At present, the traditional prediction method mainly performs empirical regression based on the existing seismic records. This method has good prediction accuracy and uniform residual distribution. However, due to the high uncertainty of each variable in the equation, the ground motion records suitable for this method are less.

In recent years, with the development of computer technology and technology, deep neural network has achieved good results in data regression, so a peak acceleration prediction method based on second-order neuron deep neural network is proposed.

SUMMARY OF THE INVENTION

The purpose of the present invention is to provide a ground motion peak acceleration prediction method based on a second-order neuron deep neural network in order to solve the technical problem of low accuracy of ground motion prediction.

The method for predicting the ground motion peak acceleration based on the second-order neuron deep neural network of the present invention is implemented according to the following steps:

Step 1: Collect ground motion records and build a data set:

The magnitude (M), projection distance (R _JB ), shear wave velocity (V _S30 ), region (Region), overburden thickness (Z ₁ ), fault type (Fault Type) and period (T) were selected in the dataset as Input parameters, the corresponding ground motion peak acceleration is the target parameter, and the value of the input parameter and the target parameter is between -0.5 and 0.5 through the standardization method, and the ground motion data set is obtained;

Step 2: Build a deep neural network with second-order neurons:

A deep neural network with three hidden layers is established. The neurons are all second-order elements. The hyperbolic tangent function (Tanh) is used as the activation function, and the mean square error function (MSE) and the Adam adaptive optimization function are used for backpropagation. Taking the mean absolute error function (MAE) as the evaluation function, the deep neural network model is obtained;

Step 3: Deep neural network model training:

The deep neural network model is trained, and the training accuracy is guaranteed by the mean square error function (MSE) and the mean absolute error function (MAE), and the decay curve is smoothly decreased, and the trained deep neural network model is obtained;

Step 4: Peak acceleration prediction:

Use the deep neural network model trained in step 3 to predict the ground motion input parameters and output the ground motion peak acceleration, thereby realizing the prediction of the ground motion peak acceleration;

The operation formula inside the second-order element in step 2 is as follows:

Among them: k: the current neuron is located in the kth layer;

n: the number of neurons in the k-th layer network;

σ: activation function, using the hyperbolic tangent function (Tanh);

ω _ir : the first weight parameter corresponding to the i-th neuron of the k-th layer network;

ω _ig : the second weight parameter corresponding to the i-th neuron of the k-th layer network;

ω _ib : the third weight parameter corresponding to the i-th neuron of the k-th layer network;

b ₁ : the first bias parameter corresponding to the k-th layer network;

b ₂ : the second bias parameter corresponding to the k-th layer network;

b ₃ : the third bias parameter corresponding to the k-th layer network;

x _i : Input parameters.

The invention selects more than 20,900 ground motion records from the global scope (NGA-West2 database), and adopts a multi-input structure and a second-order neuron network, which can not only improve the prediction accuracy, but also ensure the applicability of the deep neural network model.

Compared with the traditional empirical formula, the ground motion peak acceleration prediction method based on the second-order neuron deep neural network of the present invention contains the most data sets, has higher precision, better applicability, and is also easy to use.

Description of drawings

Fig. 1 is the overall framework flow chart of the ground motion peak acceleration prediction method based on the second-order neuron deep neural network according to the embodiment;

2 is a network structure diagram of a second-order neuron deep neural network model in an embodiment;

Figure 3 is the test chart of using ASK14 to predict the peak acceleration of ground motion;

Fig. 4 is the test chart of using BSSA14 to predict the peak acceleration of ground motion;

Figure 5 is a test chart of using CB14 to predict the peak acceleration of ground motion;

Figure 6 is a test chart of using CY14 to predict the peak acceleration of ground motion;

Fig. 7 is the test chart of using ANN to predict the peak acceleration of ground motion;

Fig. 8 is the test chart that adopts embodiment RSO-DNN to predict the ground motion peak acceleration;

9 is a comparison diagram of the peak acceleration decay curve between the embodiment and the BSSA14 model, wherein the solid line represents the RSO-DNN, the dotted line represents the BSSA14, and the M magnitudes along the arrow direction are 4, 5, 6, 7 and 8 in turn.

Detailed ways

Embodiment 1: The method for predicting the ground motion peak acceleration based on the second-order neuron deep neural network in this embodiment is implemented according to the following steps:

Step 1: Collect ground motion records and build a data set:

The magnitude (M), projection distance (R _JB ), shear wave velocity (V _S30 ), region (Region), overburden thickness (Z ₁ ), fault type (Fault Type) and period (T) are selected in the dataset as Input parameters, the corresponding ground motion peak acceleration is the target parameter, and the value of the input parameter and the target parameter is between -0.5 and 0.5 through the standardization method, and the ground motion data set is obtained;

Step 2: Build a deep neural network with second-order neurons:

A deep neural network with three hidden layers is established. The neurons are all second-order elements. The hyperbolic tangent function (Tanh) is used as the activation function, and the mean square error function (MSE) and the Adam adaptive optimization function are used for backpropagation. Taking the mean absolute error function (MAE) as the evaluation function, the deep neural network model is obtained;

Step 3: Deep neural network model training:

The deep neural network model is trained, and the training accuracy is guaranteed by the mean square error function (MSE) and the mean absolute error function (MAE), and the decay curve is smoothly decreased, and the trained deep neural network model is obtained;

Step 4: Peak acceleration prediction:

Use the deep neural network model trained in step 3 to predict the ground motion input parameters and output the ground motion peak acceleration, thereby completing the ground motion peak acceleration prediction method based on the second-order neuron deep neural network;

The operation formula inside the second-order element in step 2 is as follows:

Among them: k: the current neuron is located in the kth layer;

n: the number of neurons in the k-th layer network;

σ: activation function, using the hyperbolic tangent function (Tanh);

ω _ir : the first weight parameter corresponding to the i-th neuron of the k-th layer network;

ω _ig : the second weight parameter corresponding to the i-th neuron of the k-th layer network;

ω _ib : the third weight parameter corresponding to the i-th neuron of the k-th layer network;

b ₁ : the first bias parameter corresponding to the k-th layer network;

b ₂ : the second bias parameter corresponding to the k-th layer network;

b ₃ : the third bias parameter corresponding to the k-th layer network;

x _i : Input parameters.

Embodiment 2: The difference between this embodiment and Embodiment 1 is that the ground motion records in step 1 are selected from the NGA-West2 database.

Embodiment 3: The difference between this embodiment and Embodiment 1 or 2 is that in step 1, the magnitude (M) takes the natural logarithm value, and the projection distance (R _JB ) takes the natural logarithmic value.

Embodiment 4: The difference between this embodiment and one of Embodiments 1 to 3 is that each hidden layer in Step 2 includes 30 second-order neurons.

Embodiment 5: The difference between this embodiment and one of Embodiments 1 to 4 is that the deep neural network described in step 2 is a multi-input network, and the input parameters are divided into four groups and input into independent sub-networks, each independent The sub-network includes 30 second-order neurons, and the input parameters are processed by four independent sub-networks to obtain four sets of data, and the concatenate function is used to connect the four sets of data into one group and then input it to the next hidden layer.

The independent sub-network described in this embodiment is a hidden layer.

Embodiment 6: The difference between this embodiment and Embodiment 3 or 5 is that the input parameters are divided into four groups: A, B, C and D. In group A, fault type (Fault Type) and magnitude (M) are used as input parameters. Group C takes magnitude (M), projection distance (R _JB ) and region (Region) as input parameters, while Group C takes magnitude (M), projection distance (R _JB ), region (Region), shear wave velocity (V _S30 ) and The cover layer thickness (Z ₁ ) is used as the input parameter, and the D group takes the period (T) as the input parameter.

Embodiment 7: The difference between this embodiment and one of Embodiments 1 to 6 is that the expression of the mean square error function (MSE) described in step 2 is as follows:

Among them: y _i —true value; y _i ^pre —predicted value.

Embodiment 8: The difference between this embodiment and one of Embodiments 1 to 7 is that the algorithm of the Adam adaptive optimization function is as follows:

(1) Calculate the first-order moment estimation and the second-order moment estimation of the gradient, and the calculation formula is:

m _t =β ₁ ·m _t-1 +(1-β ₁ )·g _t , ν _t =β ₂ ·ν _t-1 +(1-β ₂ )·g _t ² ;

In the formula, g _t is the gradient, where m _t is the average value of the gradient at time t, ν _t is the non-central variance value of the gradient at time t, m _t-1 is the average value of the gradient at time t-1, and V _t-1 is the non-central variance value of the gradient at time t-1, the exponential decay rates β ₁ and β ₂ of the moment estimation are in the interval [0,1), β ₁ takes 0.9, and β ₂ takes 0.999;

(2) For the correction of the first-order moment estimation and the second-order moment estimation, the calculation formula is:

(3) The final formula for parameter update is:

In the formula, θ _t is the updated parameter, η is the learning rate, ε is a small constant used for numerical stability, and ε is taken as 10 ^-8 .

Embodiment 9: The difference between this embodiment and one of Embodiments 1 to 8 is that the batch size (Batchsize) of the deep neural network model trained in step 3 is 325, the training round (Epoch) is 15, and the learning rate is 0.001.

Embodiment: The method for predicting the peak acceleration of ground motion based on the second-order neuron deep neural network in this embodiment is implemented according to the following steps:

Step 1: Collect ground motion records and build a data set:

More than 20,900 ground motion records were selected from the NGA-West2 database, and the magnitude (M), projection distance (R _JB ), shear wave velocity (V _S30 ), region (Region), and overburden thickness (Z ₁ ) were selected from the dataset. , fault type (Fault Type) and period (T) are input parameters, magnitude (M) takes the natural logarithm value, projection distance (R _JB ) takes the natural logarithmic value, and the corresponding ground motion peak acceleration is the target parameter, through the standardization method Make the value of the input parameter and the target parameter between -0.5 and 0.5 to obtain the ground motion data set;

The formula for the described normalization method is as follows:

Among them: x ^* : data after normalization; x _max : data maximum value; x _min : data minimum value; x: data before normalization;

Step 2: Divide the dataset;

The ground motion dataset is randomly divided into training set, validation set and test set, and the ratio of training set, validation set and test set is 8:1:1;

Step 3: Build a deep neural network with second-order neurons:

Establish a deep neural network with three hidden layers. The deep neural network is a multi-input network. The input parameters are divided into four groups and input into independent sub-networks. The input parameters are divided into A group, B group, C group and D group, A group Taking the fault type (FaultType) and magnitude (M) as input parameters, group B takes magnitude (M), projection distance (R _JB ) and region (Region) as input parameters, group C takes magnitude (M), projection distance (R) _JB ), region (Region), shear wave velocity (V _S30 ) and cover layer thickness (Z ₁ ) as input parameters, group D takes period (T) as input parameter, each independent sub-network includes 30 second-order neurons The input parameters get four sets of data after four independent sub-network operations, use the concatenate function to connect the four sets of data into one group and then input it to the next hidden layer, each hidden layer includes 30 second-order neurons, using The hyperbolic tangent function (Tanh) is the activation function, the mean square error function (MSE) and the Adam adaptive optimization function are used for backpropagation, and the mean absolute error function (MAE) is used as the evaluation function to obtain the deep neural network model;

Step 4: Deep neural network model training:

The deep neural network model is trained, the training accuracy is guaranteed by the mean square error function (MSE) and the mean absolute error function (MAE), and the applicability is guaranteed according to the shape of the decay curve, and the trained deep neural network model RSO-DNN is obtained. The batch size (Batchsize) of the deep neural network model is 325, the training epoch (Epoch) is 15, and the learning rate is 0.001;

Step 5: Peak acceleration prediction:

The trained deep neural network model trained in step 4 is used to predict the ground motion input parameters and output the ground motion peak acceleration, thereby completing the ground 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:

Among them: k: the current neuron is located in the kth layer;

n: the number of neurons in the k-th layer network;

σ: activation function, using the hyperbolic tangent function (Tanh);

ω _ir : the first weight parameter corresponding to the i-th neuron of the k-th layer network;

ω _ig : the second weight parameter corresponding to the i-th neuron of the k-th layer network;

ω _ib : the third weight parameter corresponding to the i-th neuron of the k-th layer network;

b ₁ : the first bias parameter corresponding to the k-th layer network;

b ₂ : the second bias parameter corresponding to the k-th layer network;

b ₃ : the third bias parameter corresponding to the k-th layer network;

x _i : Input parameters.

With the development of computer technology and the expansion of data sets, the neural network is developing towards a deeper layer, and the neurons are developing towards a higher-order direction, but the contribution of the neural network to the establishment of ground motion prediction equations is very limited. The accuracy and applicability of models established by traditional empirical regression methods such as BSSA14, ASK14, CB14, CY14, I14 and artificial neural networks trained by Deras are very good, but there is still room for improvement. Therefore, the present invention selects 5 empirical formulas to compare with 1 artificial neural network model (ANN), wherein in the traditional linear neural network (ANN), the operation formula inside each neuron is as follows:

Among them: k: the current neuron is located in the kth layer;

n: the number of neurons in the k-th layer network;

ω _i : the weight parameter corresponding to the i-th neuron of the k-th layer network;

b: the bias parameter corresponding to the k-th layer network;

x _i : input parameter;

σ: activation function.

The comparison results are shown in Table 1, and the comparison diagrams are shown in Figures 3-8. Through the calculation and comparison of the peak acceleration prediction accuracy and the observation and comparison of the gathering effect, the deep neural network model trained in this embodiment has the best performance.

Table 1 The present invention is compared with empirical formula and linear artificial neural network peak acceleration prediction result

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;

ω_ira first weight parameter corresponding to the ith neuron of the k-th layer network;

ω_iga second weight parameter corresponding to the ith neuron of the k-th layer network;

ω_iba 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;

x_iinput 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 is_i-the true value; y is_i ^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:

m_t＝β₁·m_t-1+(1-β₁)·g_t，ν_t＝β₂·ν_t-1+(1-β₂)·g_t ²；

in the formula, g_tIs a gradient in which m_tIs the mean value of the gradient at time t, v_tIs the non-central variance value, m, at time t of the gradient_t-1Is the mean value at time t-1 of the gradient, V_t-1The exponential decay rate β of the moment estimate for the non-central variance value at time t-1 of the gradient₁And β₂Within the interval [0,1 ], β₁Take 0.9, β₂Taking 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, theta_tFor 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.

Images