Subway tunnel blasting vibration prediction method

Abstract

The invention discloses a subway tunnel blasting vibration prediction method. The method comprises the following steps: S1, obtaining surface blasting vibration peak velocity measured data; s2, calculating a correlation degree between each influence factor and blasting vibration through an entropy weight method, extracting a main influence factor from each influence factor, and constructing a training set and a test set; s3, optimizing a penalty coefficient and a kernel function width of a support vector machine method by adopting a firefly algorithm, and constructing an SPSS-FFA-SVR combined prediction model; s4, predicting a blast vibration peak value by using the trained prediction set, and completing blast vibration peak value speed prediction based on the SPSS-FFA-SVR combined prediction model; according to the subway tunnel blasting vibration prediction method, by predicting the blasting vibration peak speed, the comprehensiveness and accuracy of research on the dynamic response characteristics of the subway tunnel under the blasting load are improved, and a reliable basis is provided for safe construction of a subway tunnel drilling and blasting method in an urban sensitive environment.

Description

Technical Field

[0001] The invention relates to the technical field of tunnel blasting vibration control, and in particular to a subway tunnel blasting vibration prediction method. Background Art

[0002] The blasting time of subway tunnel engineering is very short. Explosives need to release huge amounts of energy in a very short time, so the action process is very violent and will have significant negative impacts on the rock and soil near the explosion source and its surface buildings (structures). However, with the rapid development of the scale and number of urban subway tunnels, it is urgent to accurately predict and evaluate the blasting disturbance caused by tunnel drilling and blasting construction.

[0003] There have been many studies on blasting vibration prediction models in the prior art, among which the most widely used are multivariate linear regression and neural network algorithms, but they each have certain limitations. For example, the support vector regression algorithm (SVR) model is relatively simple. It is based on structural risk minimization, can ensure globality, and effectively achieve accurate fitting of small-capacity samples, nonlinear problems and high-dimensional data, and has good generalization ability. However, the penalty coefficient c and kernel function parameter G in the SVR prediction model have a great influence on the prediction effect, and it is necessary to manually verify the parameters of the prediction model one by one. This method is labor-intensive and cumbersome. Summary of the invention

[0004] The purpose of the present invention is to provide a subway tunnel blasting vibration prediction method to solve the problem of accurately and efficiently controlling the blasting construction in the subway tunnel.

[0005] To achieve the above object, the present invention provides the following technical solution: a method for predicting subway tunnel blasting vibration, the method comprising the following steps:

[0006] S1: Obtain the measured data of the peak velocity of surface blasting vibration;

[0007] S2: Calculate the correlation between each influencing factor and blasting vibration by entropy weight method, extract the main influencing factors from each influencing factor, and construct training set and test set;

[0008] S3: Firefly algorithm is used to optimize the penalty coefficient and kernel function width of the support vector machine method, and the SPSS-FFA-SVR combined prediction model is constructed;

[0009] S4: Use the trained prediction set to predict the blasting vibration peak value and complete the blasting vibration peak velocity prediction based on the SPSS-FFA-SVR combined prediction model.

[0010] Preferably, step S2 includes taking the blasting vibration influence factor as an input parameter to construct a data set as a training sample and a prediction sample, making the original data of the data set constructed by the training sample and the prediction sample dimensionless, and normalizing the data; using the following formula:

[0011]

[0012] Where: x n is the dimensionless value after normalization; x is the original data; x min is the minimum value of the original data, x max is the maximum value of the original data.

[0013] Preferably, the step S2 includes performing a weight analysis on the blasting vibration influencing factor based on the entropy weight method (SPSS) to obtain a weight value of the blasting vibration influencing factor, which satisfies the following formula:

[0014]

[0015] Obtaining the information entropy δ of the factors affecting subway blasting vibration i , the information entropy δ i The calculation formula is as follows:

[0016]

[0017] Calculate the weight value ω of each influencing factor i , the expression weight value ω i As shown below:

[0018] The weight value of the key influencing factors is defined as greater than 80%, the weight value of the secondary influencing factors is between 50% and 80%, and the weight value of the weak influencing factors is less than 50%. The weak influencing factors are filtered out and only the key and secondary influencing factors are considered.

[0019] Preferably, the step S3 includes performing principal component analysis on the factors affecting blasting vibration;

[0020] Based on the field measured data, we can get n (X1, X2, ..., X n ) has m-dimensional variable samples, denoted as

[0021]

[0022] For the matrix X m×n After removing the mean value, the calculation formula is as follows:

[0023]

[0024] Calculating the Matrix The covariance matrix C m×m, the calculation formula is as follows:

[0025]

[0026] Calculate the covariance matrix C m×m The eigenvalues ​​(λ1,…,λ m ) and the eigenvector V m×m , the calculation formula is as follows:

[0027] Arrange the eigenvalues ​​and eigenvectors in descending order. The variance contribution rate of the i-th principal component satisfies the following formula: According to the variance contribution rate, the first q principal components are obtained. When the cumulative contribution rate of the first q principal components reaches more than 85%, the first q principal components are taken as new indicators for analysis.

[0028] Preferably, the FFA algorithm is used in S3 to optimize the penalty coefficient c and kernel function parameter g of the SVR model, and the specific steps include: mapping the two parameters that need to be optimized by SVR into the position parameters of the firefly individuals, and initializing the parameters and positions of each firefly individual; calculating the fitness value (firefly brightness) of the individual according to the objective function, and the fitness value satisfies the following formula:

[0029]

[0030] Among them, β(r) represents fitness, β0 is the initial attraction, and its value is 1; r is the distance between the two fireflies, unit: m, and γ is the absorption coefficient of the medium to light.

[0031] The firefly position is updated according to the fitness value of each individual firefly; the position update formula is as follows:

[0032]

[0033] Where t is the number of iterations of the algorithm; ε i It is a random number obtained by Gaussian distribution, uniform distribution, etc., and α is the random term coefficient. The formula consists of three parts. The first part is the current position information of the firefly, the second term is the attraction term, and the third term is a random term with a specific coefficient.

[0034] If the algorithm reaches the maximum number of iterations, the optimal firefly position found will be output as the optimal solution.

[0035] Preferably, the training set is trained using an SVR prediction model, and the specific steps include the SVR prediction model mapping nonlinear sample data in a low-dimensional space to a high-dimensional feature space through a nonlinear mapping function, and performing linear regression processing on the samples in the high-dimensional space.

[0036] The regression function of the high-dimensional space satisfies the following formula:

[0037]

[0038] Where: f(x) is the regression function, x is the sample set; w is the regression weight; is the mapping function; b is the threshold.

[0039] Preferably, in step S3, the firefly algorithm is used to optimize the penalty coefficient and kernel function width of the support vector machine method. According to the principle of structural risk minimization, the regression equation is used to solve the optimal problem of the model. The regression equation can be calculated by the following formula:

[0040]

[0041] where ξ i , is the slack variable; C is the penalty coefficient; the constraint condition is to satisfy the following formula:

[0042]

[0043] Where s, t; means "restricted to"; ε is the insensitive loss function.

[0044] Preferably, in step S3, the Lagrangian function and the kernel function are introduced to solve the model dimension problem, and the regression function is converted into a dual form, and the expression is as follows:

[0045]

[0046] where α i , is the Lagrange multiplier; K(x i ,x j ) is the kernel function,

[0047] The kernel function with a width of σ Gaussian radial basis is selected, which satisfies the KKT (Karush-Kuhn-Tucker, KKT) constraint condition. The above kernel function can be expressed as:

[0048]

[0049] Where σ is the kernel function width; g is the kernel function parameter;

[0050] Evaluate and select the optimal position of the entire firefly individual, and find the optimal penalty coefficient c and kernel function parameter g.

[0051] Preferably, in step S4, the prediction set is predicted using the SPSS-FFA-SVR prediction model, and the mean square error (MSE) is used as the prediction model performance evaluation index, and the calculation formula is as follows:

[0052]

[0053] Where: M is the total number of samples, i is the sequence number of the current sample, y i For the predicted data, is the original data.

[0054] It can be seen from the above technical solution that the present invention has the following beneficial effects:

[0055] The subway tunnel blasting vibration prediction method adopts the entropy weight method to calculate the correlation between each influencing factor and the blasting vibration, uses the principal component analysis method to extract the principal component from the influencing factors, constructs a training set and a test set, adopts the firefly algorithm (FFA) algorithm to optimize the penalty coefficient and kernel function width of the support vector machine method (SVR), and constructs an FFA-SVR combined prediction model. The present invention improves the comprehensiveness and accuracy of the study on the dynamic response characteristics of the subway tunnel under the blasting load by predicting the peak velocity of the blasting vibration, solves the problem of quickly and efficiently selecting the parameters of the SVR, solves the problem of accurately and efficiently controlling the blasting construction of the subway tunnel, and provides a reliable basis for the safe construction of the subway tunnel drilling and blasting method in the sensitive environment of the city. BRIEF DESCRIPTION OF THE DRAWINGS

[0056] Figure 1 is a flow chart of the method of the present invention;

[0057] Figure 2 This is a flow chart of the SPSS-FFA-SVR prediction model of the present invention. DETAILED DESCRIPTION

[0058] The following will be combined with the drawings in the embodiments of the present invention to clearly and completely describe the technical solutions in the embodiments of the present invention. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without creative work are within the scope of protection of the present invention.

[0059] like Figure 1 and Figure 2 As shown, a subway tunnel blasting vibration prediction method comprises the following steps:

[0060] S1: Obtain the measured data of the peak velocity of surface blasting vibration;

[0061] S2: Calculate the correlation between each influencing factor and blasting vibration by entropy weight method, extract the main influencing factors from each influencing factor, and construct training set and test set;

[0062] S3: Firefly algorithm is used to optimize the penalty coefficient and kernel function width of the support vector machine method, and the SPSS-FFA-SVR combined prediction model is constructed;

[0063] S4: Use the trained prediction set to predict the blasting vibration peak value and complete the blasting vibration peak velocity prediction based on the SPSS-FFA-SVR combined prediction model.

[0064] In step S1, a blasting vibration monitoring instrument is used to record the speed-related data of the blasting vibration, and the influencing factors of the blasting vibration in the blasting engineering site are obtained. The influencing factors of the blasting vibration include: uniaxial compressive strength reflecting engineering geological conditions, unit: GPa; rock mass integrity coefficient; blasting center distance, unit: m; explosive unit consumption reflecting blasting excavation parameters, unit: kg·m -3 ; Slot hole spacing, unit: m; auxiliary hole spacing, unit: m; peripheral hole spacing, unit: m; maximum charge per shot, unit: kg; delay time, unit, ms.

[0065] Furthermore, in step S2, the blasting vibration influence factor is used as an input parameter to construct a data set as a training sample and a prediction sample, and the original data of the data set constructed by the training sample and the prediction sample are dimensionless, and the data is normalized at the same time; the following formula is used:

[0066]

[0067] Where: x n is the dimensionless value after normalization; x is the original data; x min is the minimum value of the original data, x max is the maximum value of the original data.

[0068] Furthermore, based on the entropy weight method (SPSS), a weight analysis is performed on the blasting vibration influencing factor to obtain the weight value of the blasting vibration blasting influencing factor, which satisfies the following formula:

[0069]

[0070] Obtaining the information entropy δ of the factors affecting subway blasting vibration i , the information entropy δ i The calculation formula is as follows:

[0071]

[0072] Calculate the weight value ω of each influencing factor i, the expression weight value ω i As shown below:

[0073] The weight value of the key influencing factors is defined as greater than 80%, the secondary influencing factors are between 50% and 80%, and the weak influencing factors are less than 50%. The weak influencing factors are filtered out and only the key and secondary influencing factors are considered. The entropy method adopted in the present invention can determine the key factors affecting blasting vibration, effectively avoiding the subjective randomness of the manual judgment method.

[0074] Further, in step S2, principal component analysis is performed on the factors affecting blasting vibration;

[0075] Based on the field measured data, we can get n (X1, X2, ..., X n ) has m-dimensional variable samples, denoted as

[0076]

[0077] For the matrix X m×n After removing the mean value, the calculation formula is as follows:

[0078]

[0079] Calculating the Matrix The covariance matrix C m×m , the calculation formula is as follows:

[0080]

[0081] Calculate the covariance matrix C m×m The eigenvalues ​​(λ1,…,λ m ) and the eigenvector V m×m , the calculation formula is as follows:

[0082] Arrange the eigenvalues ​​and eigenvectors in descending order. The variance contribution rate of the i-th principal component satisfies the following formula: According to the variance contribution rate, the first q principal components are obtained. When the cumulative contribution rate of the first q principal components reaches more than 85%, the first q principal components are taken as new indicators for analysis. The present invention adopts the principal component analysis method to perform data dimensionality reduction processing, thereby saving the key information of the original data with the least dimension and realizing the effective processing of high-dimensional data.

[0083] In step S3, the penalty coefficient c and kernel function parameter g of the SVR model are optimized by using the FFA algorithm. The specific steps include: mapping the two parameters that need to be optimized by SVR into the position parameters of the firefly individuals, and initializing the parameters and positions of each firefly individual; calculating the fitness value (firefly brightness) of the individual according to the objective function, and the fitness value satisfies the following formula:

[0084]

[0085] Among them, β(r) represents fitness, β0 is the initial attraction, and its value is 1; r is the distance between the two fireflies, unit: m, and γ is the absorption coefficient of the medium to light.

[0086] The firefly position is updated according to the fitness value of each individual firefly; the position update formula is as follows:

[0087]

[0088] Where t is the number of iterations of the algorithm; ε i It is a random number obtained by Gaussian distribution, uniform distribution, etc., and α is the random term coefficient. The formula consists of three parts. The first part is the current position information of the firefly, the second term is the attraction term, and the third term is a random term with a specific coefficient.

[0089] If the algorithm reaches the maximum number of iterations, the optimal firefly position searched is output as the optimal solution, and the FFA optimal solution is used as the SVR model parameter to construct the FFA-SVR prediction model. The present invention uses the FFA algorithm to optimize the penalty coefficient c and kernel function parameter g of SVR, further adjusts the search optimization range, and improves the prediction accuracy, modeling efficiency and generalization ability of the SVR model.

[0090] The training set is trained using the SVR prediction model. The specific steps include: the SVR prediction model maps the nonlinear sample data in the low-dimensional space to the high-dimensional feature space through a nonlinear mapping function, and performs linear regression processing on the samples in the high-dimensional space.

[0091] The regression function of the high-dimensional space satisfies the following formula:

[0092]

[0093] Where: f(x) is the regression function, x is the sample set; w is the regression weight; is the mapping function; b is the threshold.

[0094] Furthermore, in step S3, the firefly algorithm is used to optimize the penalty coefficient and kernel function width of the support vector machine method. According to the principle of structural risk minimization, the regression equation is used to solve the optimal problem of the model. The regression equation can be calculated by the following formula:

[0095]

[0096] where ξ i , is the slack variable; C is the penalty coefficient; the constraint condition is to satisfy the following formula:

[0097]

[0098] Where s, t; means "restricted to"; ε is the insensitive loss function.

[0099] The Lagrangian function and kernel function are introduced to solve the model dimension problem and the regression function is converted into a dual form. The expression is as follows:

[0100]

[0101] where α i , is the Lagrange multiplier; K(x i ,x j ) is the kernel function,

[0102] The kernel function with a width of σ Gaussian radial basis is selected, which satisfies the KKT (Karush-Kuhn-Tucker, KKT) constraint condition. The above kernel function can be expressed as:

[0103]

[0104] Where σ is the kernel function width; g is the kernel function parameter;

[0105] Return to step S2 to evaluate and select the optimal position of the entire firefly individual, find the optimal penalty coefficient c and kernel function parameter g, the present invention adopts the FFA intelligent algorithm to find the optimal solution, reduces the modeling time, and greatly improves the accuracy of the prediction model.

[0106] The SPSS-FFA-SVR prediction model is used to predict the prediction set, and the relative error (MRE) is used as the performance evaluation index of the prediction model. The calculation formula is as follows:

[0107]

[0108] Where: n is the total number of samples, i is the sequence number of the current sample, Y i For the predicted data, The smaller the relative error is, the better the fitting effect of the model is.

[0109] Furthermore, in order to evaluate the accuracy of the prediction precision of the FFA-SVR model, the traditional Sadovsky model and SVR model were constructed with the same training samples and parameters of the prediction model to predict the prediction samples, and the results were compared with the present FFA-SVR model. The table shows the prediction model prediction experimental results and relative errors.

[0110] Prediction model predicts experimental results and relative errors

[0111]

[0112] Compared with several other prediction models, FFA-SVR has the best prediction effect, and the relative error is controlled within 50%. From the results, it can be seen that the FFA algorithm is used to optimize the penalty coefficient and kernel function parameters of SVR, and a combined prediction model based on FFA-SVR is established. The prediction accuracy has been significantly improved compared with the traditional Savage prediction model and the single SVR prediction model.

[0113] In summary, the present invention improves the comprehensiveness and accuracy of the research on the subway tunnel blasting vibration prediction method, solves the problem of selecting parameters for the SVR prediction model quickly and efficiently, and the prediction results are more accurate. Therefore, the present invention effectively overcomes the various shortcomings of the prior art and has a high industrial utilization value.

[0114] Although embodiments of the present invention have been shown and described, it will be appreciated by those skilled in the art that various changes, modifications, substitutions and variations may be made to the embodiments without departing from the principles and spirit of the present invention, and that the scope of the present invention is defined by the appended claims and their equivalents.

Claims

1. A method for predicting subway tunnel blasting vibration, characterized in that: The method comprises the following steps: S1: Obtain the measured data of the peak velocity of surface blasting vibration; S2: Calculate the correlation between each influencing factor and blasting vibration by entropy weight method, extract the main influencing factors from each influencing factor, and construct training set and test set; S3: Firefly algorithm is used to optimize the penalty coefficient and kernel function width of the support vector machine method, and the SPSS-FFA-SVR combined prediction model is constructed; S4: Use the trained prediction set to predict the blasting vibration peak value and complete the blasting vibration peak velocity prediction based on the SPSS-FFA-SVR combined prediction model.

2. A subway tunnel blasting vibration prediction method according to claim 1, characterized in that: The step S2 includes using the blasting vibration influence factor as an input parameter to construct a data set as a training sample and a prediction sample, making the original data of the data set constructed by the training sample and the prediction sample dimensionless, and normalizing the data; Use the following formula: Where: x n is the dimensionless value after normalization; x is the original data; x min is the minimum value of the original data, x max is the maximum value of the original data.

3. A subway tunnel blasting vibration prediction method according to claim 1, characterized in that: The step S2 includes performing a weight analysis on the blasting vibration influencing factor based on the entropy weight method (SPSS) to obtain a weight value of the blasting vibration influencing factor, which satisfies the following formula: Obtaining the information entropy δ of the factors affecting subway blasting vibration i , the information entropy δ i The calculation formula is as follows: Calculate the weight value ω of each influencing factor i , the expression weight value ω i As shown below: The weight value of the key influencing factors is defined as greater than 80%, the weight value of the secondary influencing factors is between 50% and 80%, and the weight value of the weak influencing factors is less than 50%. The weak influencing factors are filtered out and only the key and secondary influencing factors are considered.

4. A subway tunnel blasting vibration prediction method according to claim 2, characterized in that: The step S2 includes performing principal component analysis on the factors affecting blasting vibration; Based on the field measured data, we can get n (X1, X2, ..., X n ) has m-dimensional variable samples, denoted as For the matrix X m×n After removing the mean value, the calculation formula is as follows: Calculating the Matrix The covariance matrix C m×m , the calculation formula is as follows: Calculate the covariance matrix C m×m The eigenvalues ​​(λ1,…,λ m ) and the eigenvector V m×m , the calculation formula is as follows: Arrange the eigenvalues ​​and eigenvectors in descending order. The variance contribution rate of the i-th principal component satisfies the following formula: According to the variance contribution rate, the first q principal components are obtained. When the cumulative contribution rate of the first q principal components reaches more than 85%, the first q principal components are taken as new indicators for analysis.

5. The subway tunnel blasting vibration prediction method according to claim 1, characterized in that: In S3, the penalty coefficient c and kernel function parameter g of the SVR model are optimized by using the FFA algorithm. The specific steps include: mapping the two parameters that need to be optimized by the SVR into the position parameters of the firefly individuals, and initializing the parameters and positions of each firefly individual; calculating the fitness value (firefly brightness) of the individual according to the objective function, and the fitness value satisfies the following formula: Among them, β(r) represents fitness, β0 is the initial attraction, and its value is 1; r is the distance between the two fireflies, unit: m, and γ is the absorption coefficient of the medium to light. The firefly position is updated according to the fitness value of each individual firefly; the position update formula is as follows: Where t is the number of iterations of the algorithm; ε i It is a random number obtained by Gaussian distribution, uniform distribution, etc., and α is the random term coefficient. The formula consists of three parts. The first part is the current position information of the firefly, the second term is the attraction term, and the third term is a random term with a specific coefficient. If the algorithm reaches the maximum number of iterations, the optimal firefly position found will be output as the optimal solution.

6. A subway tunnel blasting vibration prediction method according to claim 1, characterized in that: The training set is trained using the SVR prediction model, and the specific steps include the SVR prediction model mapping nonlinear sample data in a low-dimensional space to a high-dimensional feature space through a nonlinear mapping function, and performing linear regression processing on the samples in the high-dimensional space. The regression function of the high-dimensional space satisfies the following formula: Where: f(x) is the regression function, x is the sample set; w is the regression weight; is the mapping function; b is the threshold.

7. A subway tunnel blasting vibration prediction method according to claim 1, characterized in that: In step S3, the firefly algorithm is used to optimize the penalty coefficient and kernel function width of the support vector machine method. According to the principle of structural risk minimization, the regression equation is used to solve the optimal problem of the model. The regression equation can be calculated by the following formula: where ξ i , is the slack variable; C is the penalty coefficient; the constraint condition is to satisfy the following formula: Where s, t; means "restricted to"; ε is the insensitive loss function.

8. The method for predicting subway tunnel blasting vibration according to claim 1, characterized in that: In step S3, the Lagrangian function and the kernel function are introduced to solve the model dimension problem, and the regression function is converted into a dual form, and the expression is as follows: where α i , is the Lagrange multiplier; K(x i ,x j ) is the kernel function, The kernel function with a width of σ Gaussian radial basis is selected, which satisfies the KKT (Karush-Kuhn-Tucker, KKT) constraint condition. The above kernel function can be expressed as: Where σ is the kernel function width; g is the kernel function parameter; Evaluate and select the optimal position of the entire firefly individual, and find the optimal penalty coefficient c and kernel function parameter g.

9. A subway tunnel blasting vibration prediction method according to claim 1, characterized in that: In step S4, the SPSS-FFA-SVR prediction model is used to predict the prediction set, and the relative error (MRE) is used as the prediction model performance evaluation index. The calculation formula is as follows: Where: n is the total number of samples, i is the sequence number of the current sample, Y i For the predicted data, is the original data.

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