Small sample regression prediction method for tunnel blasting effect

Abstract

The invention provides a tunnel blasting effect small sample regression prediction method. The tunnel blasting effect small sample regression prediction method specifically comprises the following steps that feature data before blasting and blasting effect data after blasting are obtained and sorted; performing data normalization processing on the data, and selecting input features of a regression prediction model by using grey correlation analysis; establishing a generative adversarial network model, and augmenting and expanding the training data set; establishing a blasting effect multi-kernel Gaussian process regression prediction model; searching and predicting model hyper-parameters based on a multi-strategy integrated optimization sparrow algorithm; and predicting the new blasting effect based on the prediction model under the optimal parameter. According to the method, the unbalanced problems that blasting engineering data are difficult to collect, the number of samples is small, and meanwhile the number of samples with the excellent effect is large and the number of samples with the poor effect is small are effectively solved. The prediction precision and prediction efficiency of the blasting effect are improved, the generalization ability of blasting effect prediction is improved to the greatest extent, and the construction safety and efficiency of an engineering project are guaranteed.

Description

Technical Field

[0001] The invention belongs to the technical field of tunnel blasting, and in particular relates to a small sample regression prediction method for tunnel blasting effect. Background Art

[0002] The drilling and blasting method is widely used in mountain tunnel projects due to its advantages of high efficiency, economy, flexibility and wide application range. However, due to differences in blasting design, tunnel structure and surrounding rock properties, the effects of blasting impact on the blasthole wall vary, which may lead to undesirable blasting effects such as over-excavation and under-excavation of tunnels, insufficient settlement of step blast piles, and large blocks, affecting construction safety and efficiency. Therefore, it is of great engineering value to predict and evaluate the blasting effect before the blasting operation and adjust the blasting design in a timely and reasonable manner.

[0003] For the problem of blasting effect prediction, most methods only use the characteristic data before blasting and deep learning algorithms to predict the characteristic parameters of blasting effect. However, blasting engineering data is difficult to collect, and the data shows an imbalanced characteristic of more samples with good effects and fewer samples with poor effects while the number of samples is small. Deep learning algorithms often require a large amount of data to train and adjust the weight parameters and bias parameters in the neural network so that the model can extract the characteristics and patterns of the data. This is in conflict with the data characteristics of blasting engineering, making it difficult to obtain the optimal prediction model. Therefore, how to fully consider the small sample characteristics of the characteristic data of the blasting process and achieve accurate prediction of tunnel blasting effects is a technical problem that needs to be solved in this field. Summary of the invention

[0004] The purpose of the present invention is to solve the technical problems in the above background and propose a small sample regression prediction method for tunnel blasting effect, comprising the following steps:

[0005] S1. Collect characteristic data before blasting and blasting effect data after blasting;

[0006] S2, data normalization, and use grey relational analysis to select input features of the regression prediction model;

[0007] S3. Establish a generative adversarial network model to augment and expand the training data set;

[0008] S4. Establish a multi-kernel Gaussian process regression prediction model for blasting effect;

[0009] S5. Sparrow algorithm search prediction model hyperparameters based on multi-strategy integrated optimization;

[0010] S6. Predict blasting effects.

[0011] In a preferred solution, in step S1, the characteristic data collected before blasting are characteristic data related to blasting effect selected according to expert experience, including blasting parameters, surrounding rock parameters, tunnel design and other aspects, which may specifically include but are not limited to: surrounding rock type, rock mass compressive strength, rock mass integrity coefficient, cross-sectional area, drilling depth, external insertion angle, blasting unit consumption, trenching angle and peripheral hole spacing, which are expressed in the following matrix form:

[0012]

[0013] In the formula, n represents the number of feature data collected before blasting, and m represents the dimension of the features collected before blasting;

[0014] The collected post-blasting effect data are characteristic data that can reflect the quality of the blasting effect, including but not limited to: over-excavation, under-excavation, footage, half-hole rate and block size, which are expressed in the following matrix form:

[0015]

[0016] In the formula, n represents the number of blasting effect feature data collected, and p represents the dimension of the blasting effect features collected;

[0017] The data normalization method in step S2 is:

[0018]

[0019] In the formula, x norm is the normalized data value, x norm ∈[0,1]; x is the original data value; x max , x min Respectively represent the maximum and minimum values ​​of the parameter column.

[0020] In a preferred solution, the specific process of selecting the model input features in step S2 includes:

[0021] First, calculate the range from the comparison feature column to the reference feature column:

[0022]

[0023] In the formula, a and b are the minimum and maximum differences between the two poles, y kp is the kth row of data of the reference feature in the pth column, x im It is the kth row of data of the mth column comparison feature;

[0024] Calculate the correlation:

[0025]

[0026] In the formula, r mpis the correlation between the comparison feature in the mth column and the reference feature in the pth column, that is, the correlation between the feature parameters before blasting and the blasting effect. ρ is the resolution coefficient;

[0027] In the preferred solution, step S2 further includes: arranging the correlation degrees of the pre-blasting features in descending order, setting the feature selection dimension, and taking the comparative features with the highest correlation degrees as the input feature data after correlation degree screening according to the set feature selection dimension Ni;

[0028] The filtered input feature data and blasting effect data are divided into training data set and test data set.

[0029] In a preferred solution, the generative adversarial network model established in step S3 comprises a one-dimensional convolutional layer, a fully connected layer and an activation function layer;

[0030] The input of the generator network is a noise vector of (Ni+No) dimension and conforming to the Gaussian distribution, and the output is a generated sample of (Ni+No) dimension; the discriminator network contains two fully connected layers and a Sigmoid activation function layer. The network output is a scalar from 0 to 1, which indicates the probability estimate of the discriminator network that the input data vector is real data, that is, the distribution similarity between the input data and the real data;

[0031] The loss of the discriminator network in the training process is composed of the sum of the losses of the real burst data and the generated samples; the loss of the generated network is calculated by whether the discriminator believes that the data generated by the generator is real data, and the loss function is the binary cross entropy loss function:

[0032] BCELoss=-(ylog(p)+(1-y)log(1-p)),

[0033] Where y is the true label, the label corresponding to the real blasting data is 1, and the label corresponding to the generated sample is 0; p is the output probability estimate of the Sigmoid activation function layer of the discriminator network.

[0034] In the preferred solution, during the adversarial game training of GAN, the generator network gradually improves its ability to generate realistic data, and the discriminator improves its ability to distinguish whether the data is a real blasting sample. After reaching the maximum number of training times, the generative model is saved. The generated samples of the generative model are used to augment the original training data set to obtain an augmented data set containing generated samples and real samples.

[0035] In the preferred solution, the process of establishing the Gaussian process regression prediction model of the blasting effect in step S4 is as follows:

[0036] Gaussian process regression is a Bayesian inference non-parametric regression method, and its regression model expression is:

[0037] y=f(x)+ε;

[0038] In the formula, x represents the input pre-blasting feature, y represents the actual observed blasting effect, ε is the noise variable, and ε obeys f(x) is the predicted blasting effect, assuming that it obeys the Gaussian process f(x)~GP(m(x),k(x,x * ), whose mean function is determined by the training data and the covariance function is determined by the kernel function:

[0039]

[0040] Where x and x * represents any two different characteristic data before blasting, m is the mean function, E is the mathematical expectation, and k is the covariance function;

[0041] From this, we can get the prior distribution of the actual observed explosion effect y:

[0042]

[0043] Assume that X is the pre-blasting feature data in the training set, where K = K(X,X) = k ij is a positive definite covariance matrix of size n×n, k ij = k(x i ,x j ) is used to measure x i With x j The correlation between them; k = k (X * ,X * );K * =K(X * ,X) is the n×1 order covariance matrix between the test point and the training set; I n is an n-order unit matrix. The posterior distribution of the predicted value is obtained as follows:

[0044]

[0045] In the formula, Represents the mean of the predicted values, cov(f * ) represents the variance.

[0046] In the preferred solution, further, the blasting effect multi-kernel Gaussian process regression prediction model in step S4, the fusion kernel function construction process includes:

[0047] (1) RBF kernel is used to extract local features of data, and its covariance function is:

[0048]

[0049] (2) Matérn kernel is a generalization of RBF kernel, which is used to extract local correlation characteristics. Its covariance function is:

[0050]

[0051] (3) Linear kernel, used to describe the linear correlation between data, the covariance function is:

[0052]

[0053] (4) Polynomial kernel, used to describe the nonlinear relationship between data, the covariance function is:

[0054]

[0055] Where δ1~δ9 are the kernel function hyperparameters that need to be set;

[0056] Multiple kernel functions form a fusion kernel function in the following way:

[0057] k M (x i ,x j )=δ 10 ·k RBF (x i ,x j )+δ 11 ·k Matern (x i ,x j )+δ 12 ·k l (x i ,x j )+δ 13 ·k P (x i ,x j ),

[0058] Where δ 10 ~δ 13 is the covariance weight of different kernel functions;

[0059] Finally, the augmented dataset containing generated samples and real samples is divided into training set, validation set and test set. The training set is used to train the multi-kernel Gaussian process regression prediction model, the validation set is used to tune the model's hyperparameters and select the best model, and the test set is used to evaluate the model performance and generalization ability. The model performance evaluation indicators are:

[0060]

[0061] Where MAE, RMSE, and R2 represent the mean absolute error, root mean square error, and determination coefficient, respectively. i , y′ irepresent the true sample value and the predicted value respectively. Represents the sample mean.

[0062] In the preferred solution, the multi-strategy integrated optimization sparrow algorithm in step S5, the optimization strategies include: chaotic mapping mechanism, dynamic adaptive weight, improved scout position update method, fusion Cauchy mutation and random reverse learning strategy, the specific search model hyperparameter process includes:

[0063] S501, setting hyperparameters δ1~δ in the fusion kernel function 13 is the search solution of the sparrow algorithm, the polynomial kernel hyperparameter δ9 is the highest degree of the polynomial, and the value range is set to [1,2,3,4,5,6]. The value range of other hyperparameters is set to [0,1]. The number of discoverers, the proportion of scouts, and the safety threshold are set;

[0064] S502. Initialize the position of the sparrow population through the ICMIC chaotic mapping model:

[0065]

[0066] Where Z is the generated chaotic sequence, x i is the i-th individual of the sparrow population generated according to the chaotic mapping sequence, x lb 、x ub They are the lower and upper limits of the range of each individual in the search dimension respectively. The polynomial hyperparameter δ9 still needs to be rounded after initialization.

[0067] S503, calculating the fitness of individuals in the population, sorting them according to the fitness and determining the best and worst individuals, and the fitness value of each sparrow in the population is calculated according to the following formula:

[0068] f FIT =RMSE+MAE+(1-R2);

[0069] S504: Use a finder location update method with an adaptive weight to update the finder location:

[0070]

[0071] Where ω is the dynamic adaptive weight of the detector position change; k is the control weight value range [0,2]; T max Indicates the maximum number of iterations; It represents the position information of the i-th sparrow when the number of iterations in the j-dimension is t; They represent the optimal fitness and the worst fitness of the individuals in the population when the number of iterations is t; R∈[0,1] represents the warning value; ST∈[0.5,1] represents the safety threshold. When R<ST, the sparrow conducts a global search for food. When R>ST, the sparrow walks randomly with a normal distribution; Q is a random number that obeys a normal distribution;

[0072] S505, update the joiner's position:

[0073]

[0074] In the formula, It is the position with the best fitness value among the current discoverers; is the position with the worst global fitness; A + =A T (AA T ) -1 ; A represents a single column vector of the same dimension as the individual sparrow, and its internal elements are randomly composed of 1 and -1; n is the population size, when i≤n / 2, the joiner will actively follow the discoverer to move towards a better foraging position; when i>n / 2, the joiner will get rid of the current poor foraging position.

[0075] S506. Randomly select m×n sparrows as scouts, where m is the proportion of scouts in the population, to undertake the early warning task. The traditional scout update formula easily causes the scout position to be out of control and deviate from the optimal position.

[0076] Update the scout position using the following optimizations:

[0077]

[0078] is the optimal individual position when the iteration number is t; β is a random number that obeys a normal distribution with a mean of 0 and a variance of 1;

[0079] The improved position update formula means that if the sparrow is in the current optimal position, it will fly to any random position between the optimal position and the worst position; otherwise, it will choose to fly to any random position between itself and the optimal position;

[0080] S507, introduce random factors and use random reverse learning to avoid the algorithm from falling into the local optimal solution and improve population diversity:

[0081]

[0082] In the formula, is the reverse solution of the optimal solution at the tth iteration; x ub 、x lb are the upper and lower bounds; r is a random value between 0 and 1; represents the individual position of the optimal solution individual after random reverse learning in t iterations; b1 is the information exchange control parameter;

[0083] S508. At the same time, the Cauchy mutation strategy is introduced to improve the tendency of the algorithm to fall into the local optimal solution due to the competition between joiners and discoverers for foraging:

[0084]

[0085] Where cauchy(0,1) is the standard Cauchy distribution;

[0086] S509, select and update the optimal individual position through a dynamic selection strategy:

[0087]

[0088] When rand(1,e)>P s When , the position update based on the random reverse learning strategy is selected, otherwise the position update based on the Cauchy mutation perturbation strategy is selected;

[0089] S510, determine whether the maximum number of iterations has been reached, and proceed to the next step if the maximum number of iterations has been reached, otherwise repeat S53;

[0090] S511. Output the optimal individual position, that is, the optimal hyperparameter combination of the multi-kernel Gaussian process regression prediction model for blasting effect.

[0091] In the preferred solution, in step S6, the blasting effect prediction is performed by using a multi-kernel Gaussian process regression prediction model established using the optimal hyperparameter combination output in step S5, and the blasting effect is predicted by inputting new data.

[0092] The beneficial effects of the present invention are as follows: the method of the present invention has the advantages of high accuracy, simple prediction model structure, strong model generalization ability, etc. in predicting small samples of blasting effects. Specifically:

[0093] 1) In view of the characteristics of the blasting data, such as more normal evaluation samples, fewer abnormal evaluation samples, and less data volume, the generative adversarial network is used to supplement the data set, which reduces the difficulty of training the prediction model;

[0094] 2) To address the problems of small sample high dimension, small sample and nonlinear prediction accuracy, multi-kernel Gaussian process regression is used to improve the generalization ability and prediction accuracy of the prediction model;

[0095] 3) In order to solve the problem of setting mixed kernel hyperparameters in the multi-kernel Gaussian process regression prediction model, the sparrow algorithm with multi-strategy integrated optimization is used to search for the optimal prediction hyperparameters, which further enhances the prediction accuracy of the prediction model. BRIEF DESCRIPTION OF THE DRAWINGS

[0096] Figure 1 Overall flow chart.

[0097] Figure 2 Grey relational analysis chart.

[0098] Figure 3 Generate adversarial network to obtain augmented data architecture diagram.

[0099] Figure 4 Diagram of the optimal fitness iteration process.

[0100] Figure 5 Comparison chart of prediction effects. DETAILED DESCRIPTION

[0101] like Figures 1 to 5 As shown in the figure, a small sample regression prediction method for tunnel blasting effect is proposed. The specific implementation steps are as follows:

[0102] S1.1 Select characteristic data related to blasting effect before blasting based on expert experience, including blasting parameters, surrounding rock parameters, tunnel design and other aspects, including but not limited to: surrounding rock type, rock mass compressive strength, rock mass integrity coefficient, cross-sectional area, drilling depth, external insertion angle, blasting unit consumption, trenching angle, peripheral hole spacing, etc. and express it in the following matrix form:

[0103]

[0104] Where n represents the number of feature data collected before blasting, and m represents the dimension of the features collected before blasting.

[0105] S1.2 Collect characteristic data that can reflect the quality of the blasting effect after blasting, including but not limited to: over-excavation and under-excavation, footage, half-hole rate, block size, etc. and express it in the following matrix form:

[0106]

[0107] In the formula, n represents the number of collected blasting effect feature data, and p represents the dimension of the collected blasting effect features.

[0108] S2.1 Normalize the collected data:

[0109]

[0110] In the formula, x norm is the normalized data value, x norm ∈[0,1]; x is the original data value; x max , x min Respectively represent the maximum and minimum values ​​of the parameter column.

[0111] S2.2 takes the features before blasting as the comparison feature column, and the effect data after blasting as the reference feature column, and calculates the correlation between each feature before blasting and the blasting effect through grey correlation analysis. Calculate the range of the comparison feature column and the reference feature column:

[0112]

[0113] In the formula, a and b are the minimum and maximum differences between the two poles, y kp is the kth row of data of the reference feature in the pth column, x im It is the k-th row of data with the m-th column comparison feature.

[0114] S2.3 Calculate the correlation:

[0115]

[0116] In the formula, r mp is the correlation between the comparison feature in the mth column and the reference feature in the pth column, that is, the correlation between the feature parameters before blasting and the blasting effect. ρ is the resolution coefficient, which is generally 0.5.

[0117] S2.4 Arrange the correlation of each pre-blasting feature in descending order (see Figure 2 ), set the feature selection dimension, and take the comparative features with the highest correlation according to the set feature selection dimension Ni as the input feature data after correlation screening. The screened input feature data (dimension Ni) and the blasting effect data (dimension No) are divided into a training data set and a test data set.

[0118] S3.1 Establish a generative adversarial network model. The generative network consists of a one-dimensional convolutional layer, a fully connected layer, and an activation function layer. The input of the generator network is a noise vector of (Ni+No) dimension and conforms to the Gaussian distribution, and the output is a generated sample of (Ni+No) dimension; the discriminator network contains two layers of fully connected layers and a Sigmoid activation function layer.

[0119] S3.2 Train the discriminator network and the generator network. The loss of the discriminator network during the training process is composed of the sum of the losses of the real burst data and the generated samples. The loss of the generator network is calculated by whether the discriminator believes that the data generated by the generator is real data. The loss function is the binary cross entropy loss function:

[0120] BCELoss=-(ylog(p)+(1-y)log(1-p))

[0121] Where y is the true label. If it is real blasting data, this label is 1, and if it is a generated sample, this label is 0. p is the output probability estimate of the Sigmoid activation function layer of the discriminator network.

[0122] S3.3 Save the generator network. Input a noise vector that conforms to the Gaussian distribution to generate samples to augment the original data set to obtain an augmented data set. The specific structure of the architecture of the generative adversarial network to obtain augmented data is shown in Figure 3 .

[0123] S4.1 Establish a Gaussian process regression model:

[0124] y=f(x)+ε

[0125] In the formula, x represents the input pre-blasting feature, y represents the actual observed blasting effect, ε is the noise variable, and ε obeys f(x) is the predicted blasting effect, assuming that it obeys the Gaussian process f(x)~GP(m(x),k(x,x * ), whose mean function is determined by the training data and the covariance function is determined by the kernel function:

[0126]

[0127] Where x and x * represents any two different characteristic data before blasting, m is the mean function, E is the mathematical expectation, and k is the covariance function.

[0128] S4.2 obtains the prior distribution of the actual observed explosion effect y:

[0129]

[0130] Assume that X is the pre-blasting feature data in the training set, where K = K(X,X) = k ij is a positive definite covariance matrix of size n×n, k ij = k(x i ,x j ) is used to measure x i With x j The correlation between them; k = k (X * ,X * );K * =K(X * ,X) is the n×1 order covariance matrix between the test point and the training set; I n is the n-th order identity matrix.

[0131] S4.3 obtains the posterior distribution of the predicted value:

[0132]

[0133] In the formula, Represents the mean of the predicted values, cov(f * ) represents the variance.

[0134] S4.4 constructs the fusion kernel function:

[0135] 1) RBF kernel is used to extract local features of data, and its covariance function is:

[0136]

[0137] 2) Matérn kernel, which is a generalization of RBF kernel, is also used to extract local correlation characteristics. Its covariance function is:

[0138]

[0139] 3) Linear kernel, used to describe the linear correlation between data, the covariance function is:

[0140]

[0141] 4) Polynomial kernel, used to describe the nonlinear relationship between data, the covariance function is:

[0142]

[0143] Where δ1~δ9 are the kernel function hyperparameters that need to be set.

[0144] Multiple kernel functions form a fusion kernel function in the following way:

[0145] k M (x i ,x j )=δ 10 ·k RBF (x i ,x j )+δ 11 ·k Matern (x i ,x j )+δ 12 ·k l (x i ,x j )+δ 13 ·k P (x i ,x j )

[0146] Where δ 10 ~δ 13 is the covariance weight of different kernel functions.

[0147] S4.5 divides the augmented data set containing generated samples and real samples into a training set and a validation set. The training set is used to train the multi-kernel Gaussian process regression prediction model, and the validation set is used to tune the model's hyperparameters and select the best model. The model performance evaluation indicators are as follows:

[0148]

[0149] Where MAE, RMSE, and R2 represent the mean absolute error, root mean square error, and determination coefficient, respectively. i , y′ i Represent the true sample value and the predicted value respectively. Represents the sample mean.

[0150] S5.1 Setting the hyperparameters δ1~δ in the fusion kernel function 13 is the search solution of the sparrow algorithm. The polynomial kernel hyperparameter δ9 is the highest degree of the polynomial, and the value range is set to [1,2,3,4,5,6]. The value range of other hyperparameters is set to [0,1]. Set the number of discoverers, the proportion of scouts, and the safety threshold.

[0151] S5.2 initializes the position of the sparrow population through the ICMIC chaos mapping model:

[0152]

[0153] Where Z is the generated chaotic sequence, x i is the i-th individual of the sparrow population generated according to the chaotic mapping sequence, x lb 、x ub are the lower and upper limits of the range of each individual in the search dimension. In particular, the polynomial hyperparameter δ9 still needs to be rounded after initialization.

[0154] S5.3 Calculate the fitness of individuals in the population. According to the individual parameters of the sparrow, a multi-kernel Gaussian process regression prediction model is established with the process in S4, and the augmented data set is input for training and verification. Calculate the performance index and fitness function, sort by fitness and determine the best and worst individuals. The fitness value of each sparrow in the population is calculated according to the following formula:

[0155] f FIT =RMSE+MAE+(1-R2)

[0156] S5.4 Update finder location:

[0157]

[0158] Where ω is the dynamic adaptive weight of the detector position change; k is the control weight value range [0,2]; T max Indicates the maximum number of iterations; It represents the position information of the i-th sparrow when the number of iterations in the j-dimension is t; They represent the optimal fitness and the worst fitness of individuals in the population when the number of iterations is t; R∈[0,1] represents the warning value; ST∈[0.5,1] represents the safety threshold. When R<ST, the sparrow conducts a global search for food; when R>ST, the sparrow performs a random walk with a normal distribution; Q is a random number that obeys the normal distribution.

[0159] S5.5 Update Joiner Location:

[0160]

[0161] In the formula, It is the position with the best fitness value among the current discoverers; is the position with the worst global fitness; A + =A T (AA T ) -1 ; A represents a single column vector of the same dimension as the individual sparrow, and its internal elements are randomly composed of 1 and -1; n is the population size, when i≤n / 2, the joiner will actively follow the discoverer to move towards a better foraging position; when i>n / 2, the joiner will get rid of the current poor foraging position.

[0162] S5.6 randomly selects m×n sparrows as scouts, where m is the proportion of scouts in the population, to undertake the early warning task and update the scout position:

[0163]

[0164] is the optimal individual position when the iteration number is t; β is a random number that follows a normal distribution with a mean of 0 and a variance of 1. The improved position update formula means that if the sparrow individual is in the current optimal position, it will fly to any random position between the optimal position and the worst position; otherwise, it will choose to fly to any random position between itself and the optimal position.

[0165] S5.7 introduces random factors and uses random reverse learning to prevent the algorithm from falling into local optimal solutions and improve population diversity:

[0166]

[0167] In the formula, is the reverse solution of the optimal solution at the tth iteration; x ub 、x lb are the upper and lower bounds; r is a random value between 0 and 1; It represents the individual position of the optimal solution individual after random reverse learning in t iterations; b1 is the information exchange control parameter.

[0168] S5.8 introduces the Cauchy mutation strategy to improve the tendency of the algorithm to fall into the local optimal solution due to the competition between joiners and discoverers for foraging:

[0169]

[0170] Where cauchy(0,1) is the standard Cauchy distribution;

[0171] S5.9 selects and updates the optimal individual position through a dynamic selection strategy:

[0172]

[0173] If rand(1,e)>P s Then the position update based on the random reverse learning strategy is selected, otherwise the position update based on the Cauchy mutation perturbation strategy is selected.

[0174] S5.10 determines whether the maximum number of iterations has been reached. If not, repeat S5.3. If reached, continue. The optimal fitness iteration process is shown in Figure 4 .

[0175] S5.11 outputs the optimal individual position, that is, the optimal hyperparameter combination of the multi-kernel Gaussian process regression prediction model for blasting effect, and establishes the optimal multi-kernel Gaussian process regression prediction model for blasting effect under the optimal hyperparameter combination through processes S4.1-S4.5.

[0176] S6 saves the optimal prediction model of multi-kernel Gaussian process regression for blasting effect under the optimal hyperparameter combination, inputs the test data set, obtains the prediction of blasting effect of the test data set, and compares the prediction accuracy of the commonly used prediction models SVM (support vector machine), BP (back propagation neural network), RF (random forest), GPR (single kernel Gaussian process regression) and the patent model (MGPR) (see Figure 5 ).

[0177] The above embodiments are only used to illustrate the technical solutions of the present invention, rather than to limit the same. Although the present invention has been described in detail with reference to the aforementioned embodiments, those skilled in the art should understand that the technical solutions described in the aforementioned embodiments may still be modified, or some of the technical features may be replaced by equivalents. However, these modifications or replacements do not deviate the essence of the corresponding technical solutions from the spirit and scope of the technical solutions of the embodiments of the present invention.

Claims

1. A small sample regression prediction method for tunnel blasting effect, characterized by: The following steps are involved: S1. Collect characteristic data before blasting and blasting effect data after blasting; S2, data normalization, and use grey relational analysis to select input features of the regression prediction model; S3. Establish a generative adversarial network model to augment and expand the training data set; S4. Establish a multi-kernel Gaussian process regression prediction model for blasting effect; S5. Sparrow algorithm search prediction model hyperparameters based on multi-strategy integrated optimization; S6. Predict blasting effects.

2. According to the small sample regression prediction method of tunnel blasting effect in claim 1, it is characterized by: In step S1, the characteristic data collected before blasting are characteristic data related to blasting effect selected according to expert experience, including blasting parameters, surrounding rock parameters, tunnel design and other aspects, specifically including: surrounding rock type, rock mass compressive strength, rock mass integrity coefficient, cross-sectional area, drilling depth, external insertion angle, blasting unit consumption, trenching angle and peripheral hole spacing, which are expressed in the following matrix form: In the formula, n represents the number of feature data collected before blasting, and m represents the dimension of the features collected before blasting; The collected post-blasting effect data are characteristic data that can reflect the quality of the blasting effect, including but not limited to: over-excavation and under-excavation, footage, half-hole rate and block size, which are expressed in the following matrix form: In the formula, n represents the number of blasting effect feature data collected, and p represents the dimension of the blasting effect features collected; The data normalization method in step S2 is: In the formula, x norm is the normalized data value, x norm ∈[0,1]; x is the original data value; x max , x min Respectively represent the maximum and minimum values ​​of the parameter column.

3. According to claim 1, a small sample regression prediction method for tunnel blasting effect is characterized by: The specific process of selecting the model input features in step S2 includes: First, calculate the range from the comparison feature column to the reference feature column: In the formula, a and b are the minimum and maximum differences between the two poles, y kp is the kth row of data of the reference feature in the pth column, x im It is the kth row of data of the mth column comparison feature; Calculate the correlation: In the formula, r mp is the correlation between the comparison features in the mth column and the reference features in the pth column, that is, the correlation between the characteristic parameters before blasting and the blasting effect, and ρ is the resolution coefficient.

4. According to claim 1, a small sample regression prediction method for tunnel blasting effect is characterized by: Step S2 also includes: arranging the correlation degrees of each pre-blasting feature in descending order, setting the feature selection dimension, and taking the comparative features with the highest correlation degree as the input feature data after correlation degree screening according to the set feature selection dimension Ni; The filtered input feature data and blasting effect data are divided into training data set and test data set.

5. According to claim 1, a small sample regression prediction method for tunnel blasting effect is characterized by: The generative adversarial network model established in step S3, the generative network includes a one-dimensional convolutional layer, a fully connected layer and an activation function layer; The input of the generator network is a noise vector of (Ni+No) dimension and conforming to the Gaussian distribution, and the output is a generated sample of (Ni+No) dimension; the discriminator network contains two fully connected layers and a Sigmoid activation function layer. The network output is a scalar from 0 to 1, which indicates the probability estimate of the discriminator network that the input data vector is real data, that is, the distribution similarity between the input data and the real data; The loss of the discriminator network in the training process is composed of the sum of the losses of the real burst data and the generated samples; the loss of the generated network is calculated by whether the discriminator believes that the data generated by the generator is real data, and the loss function is the binary cross entropy loss function: BCELoss=-(ylog(p)+(1-y)log(1-p)), Where y is the true label, the label corresponding to the real blasting data is 1, and the label corresponding to the generated sample is 0; p is the output probability estimate of the Sigmoid activation function layer of the discriminator network.

6. According to the small sample regression prediction method for tunnel blasting effect in claim 1, it is characterized by: During the adversarial game training of GAN, the generative network gradually improves its ability to generate realistic data, and the discriminator improves its ability to distinguish whether the data is a real blasting sample. After reaching the maximum number of training times, the generative model is saved, and the original training data set is augmented using the generated samples of the generative model to obtain an augmented data set containing generated samples and real samples.

7. According to claim 1, a small sample regression prediction method for tunnel blasting effect is characterized by: The process of establishing the Gaussian process regression prediction model for the blasting effect in step S4 is as follows: Gaussian process regression is a Bayesian inference non-parametric regression method, and its regression model expression is: y=f(x)+ε; In the formula, x represents the input pre-blasting feature, y represents the actual observed blasting effect, ε is the noise variable, and ε obeys f(x) is the predicted blasting effect, assuming that it obeys the Gaussian process f(x)~GP(m(x),k(x,x * ), whose mean function is determined by the training data and the covariance function is determined by the kernel function: Where x and x * represents any two different characteristic data before blasting, m is the mean function, E is the mathematical expectation, and k is the covariance function; The prior distribution of the actual observed explosion effect y is obtained as follows: Assume that X is the pre-blasting feature data in the training set, where K = K(X,X) = k ij is a positive definite covariance matrix of size n×n, k ij = k(x i ,x j ) is used to measure x i With x j The correlation between them; k = k (X * ,X * );K * =K(X * ,X) is the n×1 order covariance matrix between the test point and the training set; I n is the n-order identity matrix, from which the posterior distribution of the predicted value is obtained: In the formula, represents the mean of the predicted values, cov(f * ) represents the variance.

8. According to claim 1, a small sample regression prediction method for tunnel blasting effect is characterized by: Furthermore, the multi-kernel Gaussian process regression prediction model of the blasting effect in step S4, the fusion kernel function construction process includes: The RBF kernel is used to extract local features of data, and its covariance function is: The Matérn kernel is a generalization of the RBF kernel and is used to extract local correlation characteristics. Its covariance function is: Linear kernel is used to describe the linear correlation between data. The covariance function is: Polynomial kernel is used to describe the nonlinear relationship between data. The covariance function is: Where δ1~δ9 are the kernel function hyperparameters that need to be set; Multiple kernel functions form a fusion kernel function in the following way: k M (x i ,x j )=δ 10 ·k RBF (x i ,x j )+δ 11 ·k Matern (x i ,x j )+δ 12 ·k l (x i ,x j )+δ 13 ·k P (x i ,x j ), Where δ 10 ~δ 13 is the covariance weight of different kernel functions; Finally, the augmented dataset containing generated samples and real samples is divided into training set, validation set and test set. The training set is used to train the multi-kernel Gaussian process regression prediction model, the validation set is used to tune the model's hyperparameters and select the best model, and the test set is used to evaluate the model performance and generalization ability. The model performance evaluation indicators are: Where MAE, RMSE, and R2 represent the mean absolute error, root mean square error, and determination coefficient, respectively. i , y′ i represent the true sample value and the predicted value respectively. Represents the sample mean.

9. The small sample regression prediction method for tunnel blasting effect according to claim 1 is characterized by: The multi-strategy integrated optimization sparrow algorithm in step S5 has optimization strategies including: chaotic mapping mechanism, dynamic adaptive weight, improved scout position update method, fusion of Cauchy mutation and random reverse learning strategy. The specific process of searching model hyperparameters includes: S501, setting hyperparameters δ1~δ in the fusion kernel function 13 is the search solution of the sparrow algorithm, the polynomial kernel hyperparameter δ9 is the highest degree of the polynomial, and the value range is set to [1,2,3,4,5,6]. The value range of other hyperparameters is set to [0,1]. The number of discoverers, the proportion of scouts, and the safety threshold are set; S502. Initialize the position of the sparrow population through the ICMIC chaotic mapping model: Where Z is the generated chaotic sequence, x i is the i-th individual of the sparrow population generated according to the chaotic mapping sequence, x lb 、x ub are the lower and upper limits of the range of each individual in the search dimension, respectively. The polynomial hyperparameter δ9 still needs to be rounded after initialization; S503, calculating the fitness of individuals in the population, sorting them according to the fitness and determining the best and worst individuals, and the fitness value of each sparrow in the population is calculated according to the following formula: f FIT =RMSE+MAE+(1-R2); S504: Use a finder location update method with an adaptive weight to update the finder location: Where, ω is the dynamic adaptive weight of the discoverer's position change; k is the control weight with a value range of [0, 2]; T max represents the maximum number of iterations; represents the position information of the i-th sparrow at the j-th dimension and the t-th iteration; respectively represent the optimal fitness and the worst fitness values of the population individuals at the t-th iteration; R ∈ [0, 1] represents the warning value; ST ∈ [0.5, 1] represents the safety threshold. When R < ST, the sparrows conduct global search for food. When R > ST, the sparrows perform random walks in a normal distribution; Q is a random number that follows a normal distribution; S505, update the joiner's position: In the formula, It is the position with the best fitness value among the current discoverers; is the position with the worst global fitness; A + =A T (AA T ) -1 ; A represents a single column vector of the same dimension as the individual sparrow, and its internal elements are randomly composed of 1 and -1; n is the population size, when i≤n / 2, the joiner will actively follow the discoverer to move to a better foraging position; when i>n / 2, the joiner will get rid of the current poor foraging position; S506. Randomly select m×n sparrows as scouts, where m is the proportion of scouts in the population, to undertake the early warning task. The traditional scout update formula easily causes the scout position to be out of control and deviate from the optimal position. Update the scout position using the following optimizations: is the optimal individual position when the iteration number is t; β is a random number that obeys a normal distribution with a mean of 0 and a variance of 1; The improved position update formula means that when the sparrow is at the current optimal position, it will fly to any random position between the optimal position and the worst position; otherwise, the sparrow will choose to fly to any random position between itself and the optimal position; S507, introduce random factors and use random reverse learning to avoid the algorithm from falling into the local optimal solution and improve population diversity: In the formula, is the reverse solution of the optimal solution at the tth iteration; x ub 、x lb are the upper and lower bounds; r is a random value between 0 and 1; represents the individual position of the optimal solution individual after random reverse learning in t iterations; b1 is the information exchange control parameter; S508. At the same time, the Cauchy mutation strategy is introduced to improve the tendency of the algorithm to fall into the local optimal solution due to the competition between joiners and discoverers for foraging: Where cauchy(0,1) is the standard Cauchy distribution; S509, select and update the optimal individual position through a dynamic selection strategy: When rand(1,e)>P s When , the position update based on the random reverse learning strategy is selected, otherwise the position update based on the Cauchy mutation perturbation strategy is selected; S510, determine whether the maximum number of iterations has been reached, and proceed to the next step if the maximum number of iterations has been reached, otherwise repeat S53; S511. Output the optimal individual position, that is, the optimal hyperparameter combination of the multi-kernel Gaussian process regression prediction model for blasting effect.

10. The small sample regression prediction method for tunnel blasting effect according to claim 1 is characterized by: In step S6, the blasting effect prediction is to use the multi-kernel Gaussian process regression prediction model established by the optimal hyperparameter combination output in step S5, and the blasting effect is predicted by inputting new data.

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