CN115438729A - Tunnel uplift prediction method based on unit linear regression - Google Patents
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Abstract
The invention provides a tunnel uplift prediction method based on unit linear regression, which comprises the following steps: acquiring original data of the thickness (H) of an open-cut soil body above a tunnel and the original covering thickness (H) of the top of the tunnel of an existing tunnel, calculating to obtain data of a residual buried depth ratio (i), and forming an original data group (i, S) by the data and a corresponding tunnel bulge value (S); visualizing a two-dimensional scatter diagram of the residual burial depth ratio (i) and the tunnel uplift value (S), and selecting a proper prediction function; encoding the raw data set (i, S) into training samples (x, y) based on a linear regression algorithm according to the selected prediction function; training sample data based on a unit linear regression algorithm to obtain an empirical fitting formula; the method adopts the existing tunnel uplift prediction method based on unit linear regression, predicts the tunnel uplift by using a large amount of empirical data, obtains an empirical fitting formula and provides data reference for subsequent mining work.
Description
Technical Field
The invention relates to the technical field of existing tunnel uplift prediction, in particular to a tunnel uplift prediction method based on unit linear regression.
Background
In recent years, with the continuous development of urban construction in China, the influence range of tunnel uplift caused by excavation of foundation pits above the existing tunnel on traffic safety is continuously expanded, and the operation safety of the tunnel is influenced in the past. Due to the fact that foundation pits above the existing tunnel are excavated, soil is unloaded, surrounding strata above the tunnel are caused to move, and the tunnel is bulged, wherein the thickness of the soil excavated and removed by open excavation above the tunnel and the initial thickness of soil covering above the tunnel are main factors influencing bulging deformation of the existing tunnel.
Aiming at the problems, the tunnel uplift value is predicted in advance according to the tunnel uplift factor and corresponding support measures are taken, but a mature prediction method is provided at present. The machine learning theory has the advantages of high efficiency, accuracy, wide application range and the like, and can be widely applied to the engineering industry in recent years to achieve good effects. How to apply the machine learning theory to realize the prediction of the tunnel bulge is an urgent problem to be solved.
In view of the above, there is a need for an existing tunnel ridge prediction method based on unit linear regression to solve the problems in the prior art.
Disclosure of Invention
The invention aims to provide a tunnel ridge prediction method based on unit linear regression aiming at the existing problems, which is used for establishing a tunnel ridge prediction model based on residual buried depth ratio data and providing data reference for subsequent mining.
In order to achieve the above object, the present invention provides a tunnel ridge prediction method based on unit linear regression, which comprises the following steps:
calculating a residual buried depth ratio (i) according to historical data of the existing tunnel, wherein the residual buried depth ratio is obtained by the ratio of the thickness (H) of an open-cut soil body above the existing tunnel to the original soil covering thickness (H) of the top of the existing tunnel;
taking the residual burial depth ratio (i) and the tunnel uplift value (S) at the excavation as an original data set; selecting a function relation corresponding to the original data group according to the original data group to obtain a selected function relation;
encoding data in an original data group into a training sample (x, y) based on a linear regression algorithm, wherein x represents the characteristics of the training sample, y represents the label value of the training sample, and fitting the training sample through a hypothesis function h (x) = omega x + b to obtain an empirical fitting formula; wherein, omega is a weight coefficient of the characteristic x, and b is a bias coefficient;
and obtaining a fitting value according to a fitting formula, substituting the fitting value into the selected functional relation, and decoding to obtain a tunnel uplift predicted value.
Furthermore, after the original earth covering excavation of the top of the existing tunnel, the thickness of the residual earth covering on the top of the tunnel is smaller than 1 time of the diameter of the tunnel.
Further, the residual burial depth ratio (i) is calculated by the formula,
further, the empirical fitting formula is obtained by:
setting iteration times w and a hyper-parameter alpha, initializing weight coefficients (omega, b), namely (omega) 0 ，b 0 ) Setting a loop to iteratively update the weight coefficient, and outputting the latest weight coefficient (omega) after the loop operation is finished w ，b w ) Terminating the training to obtain an empirical formula based on the training samples (x, y);
after repeating the loop w times, the weight coefficients (ω, b) are updated to (ω) w ，b w )；
After the loop operation is finished, the final weight coefficient (ω) is output w ，b w ) An empirical formula based on the training samples (x, y) is obtained:
h(x)＝ω w x+b w 。
further, the update formula of the weight coefficient ω is:
wherein, ω is 0 Setting the value to be 0, setting the alpha as a hyperparameter to be 0.01, and representing the number of samples in the training set by m;
further, the update formula of the bias coefficient b is as follows:
wherein, b 0 Set to 0;
further, the obtaining a fitting value according to a fitting formula and substituting the fitting value into the selected functional relation to decode to obtain a predicted tunnel ridge value includes: acquiring the thickness (h) of the open cut soil body above the newly acquired existing tunnel Testing ) The original thickness of the earth covering on the top of the existing tunnel (H) Testing of ) Calculating the residual buried depth ratio (i) Testing ) It is coded as a sample characteristic x based on a linear regression algorithm Testing of And substituting into an empirical fitting formula to obtain h (x) Testing ) Decoding the tunnel crown prediction value according to the selected functional relation；
The method specifically comprises the following steps:
obtaining the thickness (h) of the open cut soil body above the tunnel of the existing tunnel Testing of ) Original thickness of covering soil (H) with tunnel top Testing ) According to
Calculating the residual buried depth ratio (i) Testing )；
According to the selected functional relation, the residual buried depth ratio (i) Testing ) Encoding as sample features x based on a linear regression algorithm Testing And substituting h (x) = ω w x+b w To obtain h (x) Testing )：
h(x Testing of )＝ω w x Testing +b w 。
Selecting a functional relation of h (x) Testing ) And decoding the predicted tunnel bump value to finish the prediction of the existing tunnel bump value.
After the method is adopted, the following beneficial effects are achieved:
the invention provides a tunnel uplift prediction method based on unit linear regression starting from a tunnel residual burial depth ratio. Converting original data into training samples of unit linear regression according to the correlation between the residual embedding depth ratio and the tunnel ridge, simplifying the relationship between the converted residual embedding depth ratio and the tunnel ridge by using a linear regression algorithm, converting the linear relationship into the correlation between the actual residual embedding depth ratio and the tunnel ridge after the training is finished, and finally inputting the newly acquired sample to be detected into a prediction model to predict the existing tunnel ridge value. With the continuous increase of open cut engineering on the upper part of the existing tunnel, more and more samples are obtained, the samples are merged into original data, the training data volume is enlarged, and a prediction model is continuously updated so as to achieve the purpose of continuously optimizing the prediction effect, so that the method has great significance for accurately predicting the uplift value of the existing tunnel.
Drawings
FIG. 1 is a flow chart of an existing tunnel bump prediction method based on unit linear regression according to the present invention;
FIG. 2 is a scatter plot of residual burial depth ratio and mound value in raw data;
FIG. 3 is a graph of a functional relationship between a tunnel uplift value and a residual buried depth ratio in original data obtained by training;
fig. 4 is a graph of measured versus predicted values of a ridge value for a test sample;
FIG. 5 is a graph of updated tunnel bump values as a function of residual buried depth ratio after raw data expansion and retraining.
Detailed Description
The present invention will now be described more fully hereinafter with reference to the accompanying examples, in order to better illustrate the invention, it being understood that the examples described are only a few, but not all, of the embodiments of the invention. The following examples are provided to give a more thorough understanding of the disclosure of the invention.
The method is suitable for large-area earthwork excavation right above the existing tunnel, and when the thickness of residual covering soil excavated to the top of the tunnel is smaller than 1 time of the diameter of the tunnel, attention needs to be paid to strengthen the protection of the existing tunnel structure.
As shown in fig. 1 to fig. 5, in this embodiment, a tunnel crown prediction method based on unit linear regression with a subway shield tunnel as a project background includes the following steps:
step S1: acquiring historical data of an existing shield tunnel, wherein the historical data comprises the thickness (H) of an open-cut soil body above the existing tunnel and the original covering thickness (H) of the top of the existing tunnel, and calculating a residual buried depth ratio (i) expressed as:
and forming an original data set (i, S) with the corresponding tunnel crown value (S), wherein the original data sets obtained after the preliminary excavation of the subway shield tunnel are respectively (0.22, 0.80), (0.32, 1.10), (0.46, 1.50), (0.54, 5.17), (0.65, 11.0), (0.76, 20.05);
step S2: visualizing the data relationship between the residual buried depth ratio (i) and the tunnel uplift value (S) in the step S1, drawing a two-dimensional scatter diagram, as shown in FIG. 2, observing and estimating the correlation relationship between the residual buried depth ratio (i) and the tunnel uplift value (S), selecting a function type which accords with the correlation relationship between the residual buried depth ratio (i) and the tunnel uplift value (S), selecting an exponential function to represent the correlation relationship between the residual buried depth ratio (i) and the tunnel uplift value (S), and obtaining a selected function relation formula, wherein the expression is as follows:
S＝ce di formula 2) below is given,
where c, d represent the coefficients of the above functions.
And step S3: according to the exponential function type selected in the step S2, taking logarithms on two sides of the equation of the formula 2), wherein the expression is as follows:
lnS = di + ln c formula 3).
Then let y = lnS, x = i, β = lnc. The raw data set (i, S) in step S1 is encoded as training samples (x, y) based on a linear regression algorithm, x representing features of the training samples, y representing label values of the training samples, the transformed training samples being (0.22, ln (0.8)), (0.32, ln (1.10)), (0.46, ln (1.5)), (0.54, ln (5.17)), (0.65, ln (11.0)), (0.76, ln (20.05)). Formula 3) to:
y = dx + β formula 4).
It is then fitted with the following hypothesis function:
h (x) = ω x + b formula 5),
where ω is a weight coefficient of the feature x, and b is an offset coefficient.
And step S4: training the sample data in the step S3 based on a unit linear regression algorithm to obtain an empirical fitting formula, wherein the training process specifically comprises the following steps:
setting a proper iteration number w and a hyper-parameter alpha, setting w =100 and alpha =0.01. The weight coefficients (ω, b) are initialized, i.e., (ω) 0 ，b 0 ) Setting a loop to perform iterative update on the weight coefficient omega, wherein the update formula of the weight coefficient omega is as follows:
wherein, ω is 0 Is 0; alpha is a hyperparameter and is 0.01; m represents the number of training set samples and is 6; i is an index of the number of samples.
The update formula of the bias coefficient b is as follows:
wherein, b 0 Is 0.
After the loop operation is finished, the latest weight coefficient (omega) is output w ，b w ) I.e. (6.374, -1.909), terminating the training, resulting in an empirical formula based on the training samples (x, y):
h (x) =6.374x-1.909 formula 8).
Equation 8) is reduced to an actual exponential function, namely, the functional relation y =0.1481e between the tunnel crown value and the residual buried depth ratio 6.374x See fig. 3.
Step S5: acquiring the thickness (h) of the open cut soil body above the newly acquired tunnel of the existing shield tunnel Testing of ) Thickness of original covering soil (H) with tunnel top Testing ) Calculating the residual buried depth ratio (i) Testing ) According to the function type selected in the step S3, the function type is coded into a sample characteristic x based on a linear regression algorithm Testing of And substituting the empirical formula in step S4 to obtain h (x) Testing ) It is decoded into a tunnel bump prediction value according to the function type selected in step S3. The method specifically comprises the following steps:
step S51: obtaining the thickness (h) of the open cut soil body above the existing tunnel of the subway tunnel Testing ) The original thickness of the earth covering on the top of the existing tunnel (H) Testing ) Calculating the residual buried depth ratio (i) according to the step S1, formula 1) Testing ) And 5 residual buried depth ratio data are obtained: (0.52, 0.35,0.50,0.60, 0.80);
step S52: according to the function type selected in step S3, the residual buried depth ratio (i) in step S51 is compared Testing ) Encoding as sample features x based on a linear regression algorithm Testing Since x = i has been set in step S3, the sample feature x is Testing Is i Testing As such, (0.52, 0.35,0.50,0.60, 0.80) are respectively substituted into empirical formula 8 in step S4 to obtain h (x) Testing ) Is (1.4046, 0.3210,1.2771,1.9145, 3.1893)
Step S53: depending on the type of function selected in step S3, y = lnS has been set,h (x) in step S52 Testing ) Decoding into tunnel ridge prediction values, i.e.
The prediction of the existing tunnel ridge value is completed to be (4.0738, 1.3785,3.5862,6.7835, 24.2714), and the prediction effect is very good by plotting the prediction result and the measured value of the tunnel ridge value in fig. 4.
Step S6: adding the new acquired data in the step S5 into the original data, repeatedly executing the steps S1 to S4, and training to obtain a new empirical formula, namely y =0.1974e 5.9215x As shown in fig. 5, the result is more reliable than the result predicted by the empirical formula using only 6 raw data, so as to achieve the purpose of improving the accuracy of the empirical formula.
After the method is adopted, the beneficial effects of the embodiment are as follows: the embodiment provides a tunnel uplift prediction method based on unit linear regression, which comprises the steps of converting original data into a training sample of the unit linear regression according to a correlation between a residual burial depth ratio and tunnel uplift, simplifying the relationship between the converted residual burial depth ratio and the tunnel uplift by using a linear regression algorithm, converting the linear relationship into the correlation between the actual residual burial depth ratio and the tunnel uplift after the training is finished, and inputting a newly acquired sample to be detected into a prediction model to predict the existing tunnel uplift value. With the continuous increase of open cut projects on the upper portion of the existing tunnel, more and more samples are obtained, the samples are merged into original data, the training data volume is enlarged, the prediction model is continuously updated, the purpose of continuously optimizing the prediction effect is achieved, and the method has great significance for accurately predicting the uplift value of the existing tunnel.
The above description is only a preferred embodiment of the present invention and is not intended to limit the present invention, and various modifications and changes may be made by those skilled in the art. Any modification, equivalent replacement, or improvement made within the spirit and principle of the present invention should be included in the protection scope of the present invention.
Claims (7)
1. A tunnel bump prediction method based on unit linear regression is characterized by comprising the following steps:
calculating a residual buried depth ratio (i) according to historical data of the existing tunnel, wherein the residual buried depth ratio is obtained by the ratio of the thickness (H) of an open-cut soil body above the existing tunnel to the original soil covering thickness (H) of the top of the existing tunnel;
taking the residual burial depth ratio (i) and the tunnel uplift value (S) at the excavation as an original data set; selecting a functional relation corresponding to the original data group according to the original data group to obtain a selected functional relation;
encoding data in an original data group into a training sample (x, y) based on a linear regression algorithm, wherein x represents the characteristics of the training sample, y represents the label value of the training sample, and fitting the training sample through a hypothesis function h (x) = omega x + b to obtain an empirical fitting formula; wherein, omega is a weight coefficient of the characteristic x, and b is a bias coefficient;
and obtaining a fitting value according to a fitting formula, substituting the fitting value into the selected functional relation formula, and decoding to obtain a tunnel uplift predicted value.
2. The tunnel uplift prediction method based on unit linear regression as claimed in claim 1, wherein the residual earth thickness of the top of the tunnel after the original earth covering excavation of the top of the existing tunnel is less than 1 time of the diameter of the tunnel.
3. The tunnel ridge prediction method based on unit linear regression of claim 1, wherein the residual burial depth ratio (i) is calculated by the formula,
4. the tunnel lifting prediction method based on unit linear regression according to any of claims 1-3, characterized in that the empirical fitting formula is obtained by:
setting iteration times w and a hyper-parameter alpha, initializing weight coefficients (omega, b) to be (omega 0 ，b 0 ) Setting a loop to iteratively update it, the loopAfter the loop operation is completed, the latest weight coefficient (ω) is output w ，b w ) Terminating the training to obtain an empirical formula based on the training samples (x, y);
after repeating the loop for w times, the weight coefficients (ω, b) are updated to (ω) w ，b w )；
After the loop operation is finished, the final weight coefficient (ω) is output w ，b w ) An empirical formula based on the training samples (x, y) is obtained:
h(x)＝ω w x+b w 。
5. the method of predicting tunnel uplift based on unit linear regression as claimed in claim 4, wherein the weight coefficient ω is updated by the formula:
wherein, ω is 0 Set to 0, alpha is the hyper-parameter set to 0.01, m represents the training set sample number.
6. The method of predicting tunnel uplift based on unit linear regression as claimed in claim 5, wherein the update formula of the bias coefficient b is:
wherein, b 0 Is set to 0.
7. The method of claim 6, wherein the obtaining the fitted value according to the fitting formula and substituting the fitted value into the selected functional relation to decode to obtain the predicted value of the tunnel ridge comprises: acquiring the thickness (h) of the open cut soil body above the newly acquired existing tunnel Testing ) The original thickness of the earth covering on the top of the existing tunnel (H) Testing of ) Calculating the residual buried depth ratio (i) Testing of ) It is coded as a sample characteristic x based on a linear regression algorithm Testing And substituting the obtained result into an empirical fitting formula to obtain h (x) Testing of ) And decoding the tunnel bump prediction value according to the selected functional relation.
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