Ground subsidence prediction method

Abstract

The invention relates to a land subsidence prediction method which comprises the following steps: assuming that n subsidence monitoring points, including n1 known points and n2 points to be inserted, are arranged in a region; according to the spatial position information of the known points, the ground subsidence of all the subsidence monitoring points is fitted by using a quadric surface fitting method; calculating the settlement deviation of n1 known points, and taking the spatial position information and the settlement deviation of the known points as training samples; a PPLN network model is constructed, the input is spatial position information and a quadric surface fitting value, the output is settlement deviation, the training sample is utilized to train the PPLN network model, and a land subsidence prediction model is obtained; and predicting the predicted settlement of the n2 points to be inserted by using the trained land subsidence prediction model. According to the method, the advantages of the quadric surface fitting method and the PPLN method are fully utilized, the gross error influence can be reduced, the signal estimation value with the minimum mean square error can be fitted by adjusting the parameters through self-learning, and therefore the interpolation precision is improved.

Description

Technical Field

[0001] The invention relates to the technical field of engineering geological survey, and in particular to a method for predicting ground subsidence. Background Art

[0002] Land subsidence refers to the drop in the elevation of ground level points, which is generally discovered by measuring the changes in the elevation of ground level points. Using the data from ground subsidence monitoring points to estimate the amount of ground subsidence at interpolated unmonitored points is a mathematical interpolation problem. Any interpolation method is based on a large correlation between data points. It is generally believed that land subsidence is mainly caused by the ups and downs of the earth's crust (including fault activity) and human activities. A large number of research results have shown that the extent of urban land subsidence is closely related to the extraction of groundwater, which is mainly manifested in the excessive exploitation of groundwater, which causes the water level to continue to drop, resulting in a gradual decrease in pore water pressure and a gradual increase in effective pressure, causing ground subsidence.

[0003] The process of estimating the attribute values ​​of non-observation points or non-sampling points within the area covered by the observation points is called spatial interpolation. Spatial interpolation methods can be divided into two categories: global interpolation and local interpolation. The global interpolation method uses the data of all known points in the study area to fit the characteristics of the entire area; the local interpolation method only uses neighboring data points to estimate the values ​​of unknown points. For discrete ground subsidence monitoring points, local interpolation methods such as linear interpolation, nearest neighbor point method, moving fitting method and weighted average method can be used. However, there is still a large difference between the prediction results obtained using existing methods and the actual observed values. Summary of the invention

[0004] The present invention provides a ground subsidence prediction method to solve the above technical problems.

[0005] In order to solve the above technical problems, the present invention provides a method for predicting land subsidence, comprising the following steps:

[0006] Step 1: Assume that there are n settlement monitoring points in the area, including n1 known points and n2 points to be inserted;

[0007] Step 2: According to the spatial position information of the known points, the ground settlement amounts of all settlement monitoring points are fitted using a quadratic surface fitting method;

[0008] Step 3: Calculate the settlement deviations of n1 known points, and use the spatial position information and settlement deviations of the known points as training samples;

[0009] Step 4: constructing a PPLN network model, wherein the input of the PPLN network model is spatial position information and quadratic surface fitting value, and the output is settlement deviation, and the PPLN network model is trained using the training samples to obtain a ground settlement prediction model;

[0010] Step 5: Use the trained ground subsidence prediction model to predict the predicted subsidence of n2 points to be inserted.

[0011] Preferably, the number n1 of the known points is greater than the number of parameters to be determined of the quadratic surface in the quadratic surface fitting method.

[0012] Preferably, the number n1 of the known points is greater than 6.

[0013] Preferably, the spatial position information of the known point at least includes the coordinates of the known point and the actual settlement amount.

[0014] Preferably, the modeling method of the PPLN network model is divided into a forward growth process and a backward pruning process.

[0015] Preferably, a part of the training samples is used as training data, and the other part is used as test data, and the ratio of training data to test data is 7:3.

[0016] Preferably, the settlement monitoring points in the training data are evenly distributed in the entire area.

[0017] Preferably, the convergence control parameters of the PPLN network model include a relative error threshold of the loss function and the number of hidden layer nodes.

[0018] Preferably, the number of hidden layer nodes is 4 to 8.

[0019] Preferably, the number of hidden layer nodes is 7.

[0020] Compared with the prior art, the ground subsidence prediction method provided by the present invention has the following advantages: the present invention makes full use of the advantages of the quadratic surface fitting method and the PPLN method. The quadratic surface fitting method is simple and convenient to calculate, reduces the influence of gross errors, and is a closer fit to the subsidence trend. The PPLN method can adjust its own parameters through self-learning according to the information of known points to fit the signal estimation with the minimum mean square error. BRIEF DESCRIPTION OF THE DRAWINGS

[0021] Figure 1 A flow chart of a method for predicting land subsidence in a specific embodiment of the present invention;

[0022] Figure 2 A network topology diagram of a PPLN in a specific implementation manner of the present invention;

[0023] Figure 3 It is a network structure diagram of a hybrid interpolation model of land subsidence based on spatial location information in a specific implementation manner of the present invention. DETAILED DESCRIPTION

[0024] In order to describe the technical solution of the above invention in more detail, specific embodiments are listed below to demonstrate the technical effects; it should be emphasized that these embodiments are used to illustrate the present invention but not to limit the scope of the present invention.

[0025] The method for predicting land subsidence provided by the present invention is as follows: Figure 1 As shown, the following steps are included:

[0026] Step 1: Assume that there are n settlement monitoring points in the area, including n1 known points and n2 points to be inserted.

[0027] Step 2: Based on the spatial position information of the known points, the ground settlement of all settlement monitoring points is fitted using the quadratic surface fitting method; the spatial position information of the known points at least includes the coordinates of the known points and the actual settlement. In some embodiments, the spatial position information of the known points also includes the location distribution information of groundwater extraction wells and the annual extraction volume of each wellhead.

[0028] Step 3: Calculate the settlement deviations of n1 known points, and use the spatial position information and settlement deviations of the known points as training samples.

[0029] Step 4: Construct a PPLN network (projection pursuit learning network) model, wherein the input of the PPLN network model is spatial position information and quadratic surface fitting value, and the output is settlement deviation. The PPLN network model is trained using the training samples to obtain a ground settlement prediction model.

[0030] Step 5: Use the trained ground subsidence prediction model to predict the predicted subsidence of n2 points to be inserted.

[0031] The present invention makes full use of the advantages of the quadratic surface fitting method and the PPLN method. The quadratic surface fitting method is simple and convenient to calculate, reduces the influence of gross errors, and is a closer fit to the settlement trend. The PPLN method can adjust its own parameters through self-learning according to the information of known points to fit the signal estimation with the minimum mean square error.

[0032] The quadratic surface fitting method is to first establish a mathematical model with coordinates as independent variables and settlement as dependent variable, then use the X, Y, and L of the known monitoring points for fitting, and use the fitted mathematical model to calculate the settlement of other points to be inserted. Its mathematical model is generally not greater than quadratic, and the quadratic surface model is widely used:

[0033] L=a0+a1x+a2y+a3xy+a4x 2 +a5y 2 (1)

[0034] In the formula, x and y are the coordinates of the point, and L is the settlement of the point in a certain period, which is generally taken as the difference between two observed elevations. There are 6 undetermined coefficients in the model, so there must be at least 6 known points.

[0035] The quadratic surface model actually establishes a trend surface of urban land subsidence, which will be different from the actual observed value. This difference cannot be simply expressed by a function. After removing the trend surface, if the observed value contains both signal and noise (and the signal and noise expectations are both 0, and the covariance of the two is also zero), the linear interpolation method with the minimum residual square sum of the signal estimation can be obtained, including interpolation, filtering and estimation.

[0036] The combination of projection pursuit and neural network methods has produced the Projection Pursuit Learning Network (PPLN) method. PPLN can solve problems existing in artificial neural networks, such as the estimation of a large number of free parameters; the appropriate definition of the model dimension size (i.e., the appropriate number of hidden layer units); and the selection of nonlinear functions.

[0037] The topology of PPLN is as follows: Figure 2 As shown, it is expressed as follows: Let X = (x1, x2, ..., x p ) T is the input of PPLN; Y=(y1,y2,…,y q ) T is the desired output; is the actual output of the network, where satisfy:

[0038]

[0039] Where: i∈[1,q]; is the connection weight vector between the input layer and the hidden layer, k = 1,…,m, and ||α k ||=1,f k is the kth smoothing function of the hidden layer, k = 1, ..., m, α kj is the jth element x of the input layer j and the kth smooth function f in the hidden layer k The connection weights between them, k∈[1,m],j∈[1,p],β ik is the kth smooth function f in the hidden layer k and the i-th element y of the output layer i The connection weights are k∈[1,m],i∈[1,q].

[0040] PPLN uses an alternating optimization algorithm to determine three types of parameters: input layer weight αkj ,1≤k≤m,1≤j≤p, hidden layer smoothing function f k , 1≤k≤m and the output layer weight β ik ,1≤k≤m,1≤i≤q. The specific approach is: divide all parameters into m groups, each group is associated with a hidden layer smoothing function, that is, α kj ,1≤j≤p,β ik ,1≤i≤q and f k Classify into a group, k = 1, ..., m, there are m groups in total. Starting from the first group, train the parameters of each group in turn. When training the k0th group parameters When , first fix the first k0-1 group, and then divide the k0 group into three subgroups Fix two of the subgroups, assign initial values, and find the best value for the third subgroup. After the result is obtained, use the subgroup parameter value as the initial value, and select another subgroup parameter to find the best value under this initial value. Repeatedly optimize the three subgroup parameters until the relative error of the loss function converges, then stop optimizing the k0th group. L2 is the loss function, and They represent the loss functions before and after the optimization of a subgroup's parameters.

[0041] The PPLN network modeling method is mainly divided into two steps: forward growth process and backward pruning process.

[0042] In the forward growth process, hidden neurons are added to the network one by one. For example, if we consider adding the kth hidden neuron, we train and learn all the parameters connected to this neuron. Then, we use the backfitting method to adjust the parameters of the previously fixed neurons. That is, we loop through each existing neuron in the network and find the minimum value of the residual square. Update the parameter α associated with the kth neuron k ,f k ,{β ik}, so that the loss function L2 can be further reduced.

[0043] Once the network hidden layer neurons reach m * (m * >m), the backward pruning process is performed, one neuron is pruned at a time, and the number of neurons is reduced to m neurons in sequence. Where m * and m can be pre-specified in size. Pruning is determined by the importance of neurons. The simplest importance measures are:

[0044]

[0045] in yes The output weights of the hidden layer neuron model. Obviously, if Ik A smaller value indicates that the contribution of the kth neuron to the network output is small and can be ignored. j The meaning is the same as above. i =1 / Var(y i ).

[0046] So the pruning process is to start from Select m neurons with the largest importance measure from the neurons. Then, according to the above return fitting method, loop through and optimize the parameters of k neurons Minimize the loss function L2.

[0047] To determine the value of m, we can first assume that there are p nodes in the input layer of the network and determine the appropriate value of m* for the specific problem. When the value of p is small, such as p≤4, then m * ≥p; when the p value is large, m * <p. Then, for each neuron Calculate the FUV (fraction of unexplained variance) value, also known as the weighted sum of squared residuals:

[0048]

[0049] Y i for y i The mathematical expectation value of . Select the optimized values ​​of α, f and β to minimize the FUV value. As the number of neurons increases, The value is decreasing, based on this, a relative A downward curve. When the neuron hour, The value decreases faster; hour, The value decreases very slowly. Therefore, the backward pruning process of PPLN is performed twice. The first time, m=1 is set, so that we can find a suitable m0 value; the second time, m=m0 is set, and pruning is performed again to obtain the final network structure.

[0050] The specific idea of ​​the hybrid interpolation model based on spatial position information of this application is as follows:

[0051] (1) Assuming that there are n points in the area, among which there are n1 known settlement monitoring points, the number of points to be interpolated is n2 = n-n1; the number of known points n1 should be greater than the number of parameters to be determined for the quadratic surface.

[0052] (2) Based on the information of n1 known points (X, Y, and L are all known), the ground subsidence of all points (n points) is fitted using the quadratic surface method.

[0053] (3) Calculate the settlement deviation of n1 known points △L = L0-L; where L0 = H2-H1 is the difference between the two elevation observations, and L is the quadratic surface fitting value.

[0054] (4) All the information of the above n1 known points constitutes the training learning samples of PPLN, that is,

[0055] (x i ,y i ,L i ;ΔL)i=1,2,…,n1

[0056] Among them: x, y, L are network input units; △L is the network output unit. Figure 3 The PPLN method is used to simulate the settlement deviation △L, that is, n1 learning samples are used to train the PPLN network.

[0057] (5) Using the trained PPLN network to calculate the n2 points to be calculated, the settlement deviation △L of each point can be obtained, and the settlement of the point to be calculated can be calculated:

[0058] L0=L+ΔL (5)

[0059] Where: L is the fitting value of the point to be calculated on the quadratic surface, and △L is the deviation of the settlement simulated by the PPLN method.

[0060] The experimental data has a total of 60 monitoring points, 42 of which are selected as network learning samples; 18 points are used as network test samples, i.e. interpolation verification data (the ratio of network learning samples to network test samples is 7:3). The network learning samples (i.e. training samples) are evenly distributed in the entire area.

[0061] According to the principle of least squares method, using 42 known points, the unknown parameters in the quadratic surface fitting method can be obtained, that is, a0, a1, ..., a5 in formula (1), and then the settlement deviation values ​​of all 60 points can be obtained using these 6 parameters. The specific results are shown in Table 1. The settlement deviation △L = L0-L; where L0 = H2-H1 is the difference between the two elevation observations, and L is the quadratic surface fitting value.

[0062] Table 1 Sedimentation fitting results of quadratic surface fitting method

[0063]

[0064]

[0065] The plane coordinates x, y, quadratic surface fitting value L, and sedimentation deviation △L of 42 known points constitute the training learning samples of PPLN, as shown in Table 2 (due to space limitations, only part of the data is listed):

[0066] Table 2 PPLN training data format for hybrid interpolation model

[0067]

[0068] The UI model still uses the relative error threshold of the loss function and the number of hidden layer nodes as convergence control parameters. In order to examine their influence on the experimental results, several experiments were carried out. The experimental results are shown in Table 3.

[0069] Table 3 Effect of model parameters on the error in mixed interpolation of land subsidence

[0070]

[0071] Note: a is the number of hidden layer nodes, b is the relative error threshold of the loss function; m1 is the learning error; m2 is the error in the test set, and the unit of the error is millimeter.

[0072] From Table 3, we can see that:

[0073] ① The learning error and the test error of multiple simulation results are relatively close, indicating that the performance of the hybrid interpolation model constructed in this application is relatively stable;

[0074] ②The relative error threshold of the loss function and the number of hidden nodes have an impact on the interpolation error. When the number of hidden nodes is 3 or 4, when the relative error threshold of the loss function changes from 0.1 to 0.00001, the error in the test set goes from large to small and then becomes large again, indicating that when there are too few hidden nodes, the threshold is set too small and the interpolation accuracy cannot be significantly improved.

[0075] ③ When the number of hidden layer nodes is 9, no matter what the relative error threshold of the loss function is, the fitting of the learning samples is relatively good, but the error in the test set is large and the interpolation accuracy is relatively low, indicating that the number of hidden layer nodes is the main factor affecting the interpolation accuracy of the model, and the appropriate number of hidden layer nodes is 4 to 8.

[0076] ④ From the data with 4 or 9 hidden layer nodes, it can be seen that when the error in learning is less than 3 mm, the error in the test set is significantly larger, indicating that PPLN cannot overfit the learning samples, otherwise it will reduce the network's generalization ability and lead to reduced interpolation accuracy.

[0077] ⑤ When the number of hidden layer nodes is 7, the learning error and the test set error are relatively stable, and as the relative error threshold of the loss function decreases, the error decreases and the accuracy continues to improve. Finally, the test set error reaches 4.2mm.

[0078] The accuracy of the two ground subsidence interpolation methods is compared below.

[0079] The fitting effect of known monitoring points is judged by internal consistency, according to the formula

[0080]

[0081] Calculate the mean error respectively. △ represents the residual, [] represents the algebraic sum, t represents the number of parameters to be estimated, and n1 represents the total number of data used to fit the quadratic surface. In this experiment, t=6 and n1=42.

[0082] The interpolation accuracy of the check point is judged by external conformity, according to the formula

[0083]

[0084] Calculate the mean error. △ represents the residual, [] represents the algebraic sum, n2 represents the total number of check data, and in this experiment n2 = 18. The residual maximum value and the external accuracy are used as the basis for evaluating the interpolation method.

[0085] In order to compare the interpolation effect of the UI model, the same 42 known monitoring points were used to establish the trend surface, and 18 points were used as check points. The 18 verification data were substituted into two land subsidence interpolation methods: the quadratic surface fitting method (CFM) and the hybrid interpolation method (UI, i.e., the method proposed in this application), and the residuals between the interpolated values ​​and the measured values ​​were obtained as shown in Table 4.

[0086] Table 4 Residuals of two land subsidence interpolation methods

[0087] dot number CFM UI dot number CFM UI 2 -9 -4 42 12 8 3 2 -1 44 1 7 8 8 7 45 5 3 10 -5 3 49 1 3 19 -1 4 51 10 8 25 11 3 52 -6 -2 33 1 0 53 0 1 36 -4 -1 57 2 0 37 4 4 58 0 1

[0088] The accuracy statistics are shown in Tables 5 and 6.

[0089] Table 5 Accuracy statistics of different interpolation methods

[0090]

[0091] Table 6 Check point residual distribution table of different interpolation methods

[0092]

[0093] Analysis shows that:

[0094] 1. Table 5 shows that the residual errors of the UI method are relatively concentrated, and the residual percentage within 5 mm is greater than that of the quadratic surface fitting. The absolute values ​​of the residuals of the UI method are all less than 10 mm, and the residual value of UI is the smallest, which is 8 mm.

[0095] 2. From Table 5, we can see that the maximum residual of CFM is 12 mm, located at point 42. Combined with Table 4, we can see that the residuals of most check points of UI method are smaller than those of CFM method, which shows that UI improves the interpolation accuracy by simulating the residuals.

[0096] In summary, the ground subsidence prediction method provided by the present invention fully utilizes the advantages of the quadratic surface fitting method and the PPLN method. The quadratic surface fitting method is simple and convenient to calculate, reduces the influence of gross errors, and is a closer fit to the subsidence trend, while the PPLN can adjust its own parameters through self-learning according to known sample points to fit the signal estimation with the minimum mean square error. The essence of the hybrid interpolation model is to use the PPLN network to detect and reduce the mathematical model error of the quadratic surface fitting method and improve the interpolation accuracy. Experimental results show that the accuracy can be improved by 30%. Therefore, the ground subsidence hybrid interpolation model based on spatial position information is used to interpolate the ground subsidence of unknown points, which has certain advantages and practical value.

[0097] Obviously, those skilled in the art can make various changes and modifications to the invention without departing from the spirit and scope of the invention. Thus, if these modifications and variations of the invention fall within the scope of the claims of the invention and their equivalents, the invention is also intended to include these modifications and variations.

Claims

1. A method for predicting land subsidence, characterized in that: The steps include: Step 1: Assume that there are n settlement monitoring points in the area, including n1 known points and n2 points to be inserted; Step 2: According to the spatial position information of the known points, the ground settlement amounts of all settlement monitoring points are fitted using a quadratic surface fitting method; Step 3: Calculate the settlement deviations of n1 known points, and use the spatial position information and settlement deviations of the known points as training samples; Step 4: constructing a PPLN network model, wherein the input of the PPLN network model is spatial position information and quadratic surface fitting value, and the output is settlement deviation, and the PPLN network model is trained using the training samples to obtain a ground settlement prediction model; Step 5: Use the trained ground subsidence prediction model to predict the predicted subsidence of n2 points to be inserted.

2. The method for predicting land subsidence according to claim 1, characterized in that: The number n1 of the known points is greater than the number of parameters to be determined of the quadratic surface in the quadratic surface fitting method.

3. The method for predicting land subsidence according to claim 2, characterized in that: The number n1 of the known points is greater than 6.

4. The method for predicting land subsidence according to claim 1, characterized in that: The spatial position information of the known point at least includes the coordinates of the known point and the actual settlement amount.

5. The method for predicting land subsidence according to claim 1, characterized in that: The modeling method of the PPLN network model is divided into a forward growth process and a backward pruning process.

6. The method for predicting land subsidence according to claim 1, characterized in that: A part of the training samples is used as training data, and the other part is used as test data, and the ratio of training data to test data is 7:

3.

7. The method for predicting land subsidence according to claim 6, characterized in that: The settlement monitoring points in the training data are evenly distributed in the entire area.

8. The method for predicting land subsidence according to claim 1, characterized in that: The convergence control parameters of the PPLN network model include a relative error threshold of a loss function and the number of hidden layer nodes.

9. The method for predicting land subsidence according to claim 8, characterized in that: The number of hidden layer nodes is 4 to 8.

10. The method for predicting land subsidence according to claim 9, characterized in that: The number of hidden layer nodes is 7.

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