CN111915560A - Rock strength parameter determination method based on deep convolutional neural network - Google Patents

Rock strength parameter determination method based on deep convolutional neural network Download PDF

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CN111915560A
CN111915560A CN202010612710.5A CN202010612710A CN111915560A CN 111915560 A CN111915560 A CN 111915560A CN 202010612710 A CN202010612710 A CN 202010612710A CN 111915560 A CN111915560 A CN 111915560A
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rock
value
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何明明
庞帆
李宁
张志强
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Xian University of Technology
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Abstract

The invention discloses a rock strength parameter determination method based on a deep convolutional neural network, which comprises the steps of firstly collecting unconfined compressive strength UCS, cohesive force and internal friction angle of various common rocks as basic data of a database; data collection during drilling operations using DPMA; then training the established CNN model by using the obtained data; and finally, predicting the cohesive force, the internal friction angle and UCS of the complete rock, and outputting the predicted values as rock strength parameters. The invention solves the problem of large limitation of the rock strength parameter determination method in the prior art.

Description

Rock strength parameter determination method based on deep convolutional neural network
Technical Field
The invention belongs to the technical field of geotechnical engineering in-situ testing, and particularly relates to a rock strength parameter determination method based on a deep convolutional neural network.
Background
Reliable determination of mechanical properties of rock masses (e.g. unconfined compressive strength, cohesion, internal friction angle) is important for the design of underground structures built in rock (e.g. nuclear waste storage spaces, oil and gas storage systems and water transport tunnels). At present, Unconfined Compressive Strength (UCS) of rock has become the most common measure of strength in most rock mass classification systems, also the rock mass strength limits used in civil engineering, mining and oil engineering. Laboratory testing to determine UCS requires the preparation of adequate samples, however the sample preparation process is time consuming, expensive, and difficult, especially in terms of finishing and polishing of the sample ends. For these reasons, scholars at home and abroad choose indirect methods such as point load testing, scratch testing, schmidt hammer test and block impact strength index testing to estimate UCS. Despite the tremendous efforts in measuring UCS, indirect methods suffer from a number of drawbacks, the results of which provide only limited information about the rock in situ, and do not necessarily reflect the properties of the rock in situ, as they do not effectively assess the associated impact of complex site conditions on the strength of the rock in situ. Drilling has proven to be another promising method for determining rock strength using drilling logging parameters. The method utilizes the relevant parameters measured in the drilling process to determine the on-site rock strength, and can be applied as a quasi-nondestructive site method besides the advantage of continuous measurement because the method does not need sampling, is simple to move and is easy to realize. Another significant advantage of drilling technology is that it can provide field condition assessment for the measurement of rock strength. Researchers have also established many methods for estimating rock strength based on drilling data of force limits and energy balances, including "indentation models", "shear models" and "bit models". However, existing models suffer from certain disadvantages or limitations, such as high plastic deformation during drilling, ground stress, and complex field conditions, which result in less accurate measurements.
Disclosure of Invention
The invention aims to provide a rock strength parameter determination method based on a deep convolutional neural network, and solves the problem that the rock strength parameter determination method in the prior art is high in limitation.
The technical scheme adopted by the invention is that a rock strength parameter determination method based on a deep convolutional neural network is implemented according to the following steps:
step 1, collecting unconfined compressive strength UCS, cohesive force and internal friction angle of various common rocks as basic data of a database;
step 2, using DPMA to collect data during drilling work;
step 3, training the established CNN model by using the data in the step 1 and the step 2;
and 4, predicting the cohesive force, the internal friction angle and the UCS of the complete rock, and outputting the predicted values serving as rock strength parameters finally.
The present invention is also characterized in that,
the step 1 is implemented according to the following steps:
collecting a plurality of rock samples, wherein the unconfined compressive strength UCS of the rock samples is between 10 and 95MPa, the cohesive force is between 1 and 20MPa, and the internal friction angle is between 30 and 60 degrees.
Step 2, collecting data including drilling speed, rotating speed, torque and feeding force related data during the drilling work.
Step 3 is specifically implemented according to the following steps:
step 3.1, converting the drilling performance parameters obtained in the step 2 into an M × M matrix, wherein M is a positive integer;
step 3.2, establishing a CNN model;
and 3.3, training the CNN model by adopting a reverse gradient descent algorithm.
Step 3.1 is specifically carried out according to the following steps:
step 3.1.1, converting the obtained data set of drilling speed, rotating speed, torque and feeding force into diX M drilling performance parameter matrix, where i ═ 1,2,3,4, where i ═ 1 represents drilling rate, i ═ 2 represents rotation speed, i ═ 3 represents torque, i ═ 4 represents feed force, and d for each rock is addediExpanding the XM drilling performance parameter matrix into an M XM matrix, wherein M is 76;
step 3.1.2, normalize the mxm drilling performance parameter matrix using equation (1), convert the drilling performance parameters to the grey values of the image:
y＝255×(x-xmin)/(xmax-xmin) (1)
wherein y is a grey scale value, x is a drilling performance parameter, xminIs the minimum value, x, of the drilling performance parametermaxIs the maximum value of the drilling performance parameter;
and 3.1.3, converting the gray value obtained in the step 3.1.2 into an image of M multiplied by M pixels.
The CNN model established in step 3.2 is specifically as follows:
the method comprises a convolutional layer, a random pooling layer and softmax loss, wherein the convolutional layer learns the characteristics of the gray level image obtained in the step 3.1.2, the pooling layer reduces the dimensionality of the gray level image learned by the convolutional layer, the convolutional layer extracts the gray level image characteristics, more abstract characteristics are formed after combination, finally all parameters are normalized into a one-dimensional array to form a complete connection layer, the complete connection layer provides complete connection with the previous layer, non-linear mapping between the image characteristics is represented, and rock strength parameters are finally output.
The CNN model established in step 3.2 contains two convolutional layers for respectively obtaining line, edge and corner features from the grayscale image obtained in step 3.1.2, each output feature map combines multiple input maps with the convolutional layers, a sigmoid function is applied to detailed implementation of CNN, and the unit value at the position (x, y) of the ith layer of the jth feature map
Figure BDA0002562686430000041
The calculation is as follows:
Figure BDA0002562686430000042
wherein, i, j, x and y are all positive integers, j represents the jth characteristic diagram, i represents the ith layer of the jth characteristic diagram,
Figure BDA0002562686430000043
is the unit value at position (x, y) of the ith layer of the jth feature map, bijIs the deviation of the ith layer feature map of the jth feature map, piIs the height of the ith nucleus, qjIs the width of the core of the i-th layer,
Figure BDA0002562686430000044
is the kernel weight value of the ith layer of the jth feature map at the (p, q) location, p being the height of the kernel, q being the width of the kernel;
in the pooling layer, sub-sampling layers in CNN are replaced by random layers, and random pools are randomly selected for activation to reduce variance according to polynomial distribution, first, using probabilities in the random pools
Figure BDA0002562686430000045
PiIs the i-th layer probability, a is the feature vector, RjTo obtain P distribution (P) in the pooling area of the jth feature map1，…，P|RjI) then, sample from the P-polynomial based distribution, then, represent the random pool operation using a random function Stochastic(s), the random function Stochastic(s) for each feature map being obtained by:
Figure BDA0002562686430000046
wherein u (i, j) represents a weighted window function,
Figure BDA0002562686430000047
an activation feature value representing the neuron (p, q) position in the l-th layer feature map k;
the probability of x classification is calculated using equation (4):
Figure BDA0002562686430000048
ψ(θh)＝(-1)kcos(mθh)-2k,θh∈[kπ/m,(k+1)π/m] (5)
wherein k is [0, m-1]]Is an integer, i, h, m and k are all positive integers, whIs the h-th column matrix weight, θhIs an input feature vector ahAnd h columnWeight matrix whAngle a ofhIs an input feature vector, ψ (θ)h) Is (-1)kcos(mθh)-2k。
Step 3.3, when the reverse gradient descent algorithm is adopted to train the CNN model, the CNN model comprises a feedforward transmission stage and a reverse propagation transmission stage, and the CNN model specifically comprises the following steps:
step 3.3.1, feed forward transfer phase, the squared error function is expressed as:
Figure BDA0002562686430000051
wherein E isNAs an error function, yNInput value, ONOutput value, ykIs the value of the kth output layer, okThe value of the kth input layer, N, k, N and c are positive integers;
step 3.3.2 CNN model according to error ENDetermines whether the model converges, and obtains the back propagation error from equation (7) using sigmoid function as the activation function:
Figure BDA0002562686430000052
wherein the content of the first and second substances,Lcounter-propagating error, L being a positive integer representing the output layer, f' (z)L) As a derivative of the activation function, yNInput value, ONOutput value, ykIs the value of the kth output layer, okIs the value of the kth input layer, N, k, N and c are all positive integers;
step 3.3.3, back propagation transfer phase, back propagation error is transferred from higher layer to lower layer, residual error of l layer is calculated(l)Comprises the following steps:
(l)＝((W(l))T (l+1))·f'(z(l)) (8)
where L is the current layer, L is the output layer, is the input layer residual,(l)residual error of layer l, W(l)Is the current layer weight, l is a positive integer
Step 3.3.4, update weight W of each layer(l)And deviation of
Figure BDA0002562686430000053
The calculation is as follows:
Figure BDA0002562686430000054
Figure BDA0002562686430000061
wherein a is the learning rate, a(l)Is the l-th layer learning rate, E is the error function; l is the current layer of the video stream,
Figure BDA0002562686430000062
is the first layer deviation, b is the deviation, i is a positive integer, W(l)Is the current layer weight
The CNN training model enables drilling performance parameters to form a gray image, and the gray image is converted into related parameter values of rock cohesion, internal friction angle and unconfined compressive strength UCS through formulas (2) to (10).
The step 4 is as follows:
and (4) outputting relevant parameter values of the cohesive force, the internal friction angle and the unconfined compressive strength UCS of the rock obtained in the step (3).
The rock strength parameter determination method based on the deep convolutional neural network has the advantages that the rock strength parameter determination method based on the deep convolutional neural network is characterized in that a strength parameter database is established through laboratory tests; data collection during drilling operations using DPM; training a proposed CNN model using a database; and predicting the cohesive force, the internal friction angle and UCS of the complete rock, and using the rock strength parameters as final output. The present invention overcomes some of the major limitations of extreme balance based drilling methods, such as the effects of specific drilling energy and high plastic deformation at low depths of cut during drilling, especially in soft rock. The method of the invention can provide high resolution, continuous on-site measurement of rock strength parameters, and in addition, the speed of predicting rock strength parameters by the invention is several orders of magnitude faster than standard laboratory tests. Finally, the inventive method shows great potential for use in rock engineering due to the low requirements for test preparation.
Drawings
FIG. 1 shows the mechanical parameters of rock measured by laboratory tests;
FIG. 2 is the steps required to obtain an M pixel image;
FIG. 3 is a deep Convolutional Neural Network (CNN) composition framework;
FIG. 4 is an overview of a deep Convolutional Neural Network (CNN) computation framework;
FIG. 5(a) shows the predicted results of cohesion prediction compared to standard tests;
FIG. 5(b) shows the comparison of the predicted results of internal friction angle with standard tests;
fig. 5(c) shows the predicted results of Unconfined Compressive Strength (UCS) compared to standard tests.
Detailed Description
The present invention will be described in detail below with reference to the accompanying drawings and specific embodiments.
The invention relates to a rock strength parameter determination method based on a deep convolutional neural network, which is implemented according to the following steps:
step 1, collecting unconfined compressive strength UCS, cohesive force and internal friction angle of various common rocks as basic data of a database;
the step 1 is implemented according to the following steps:
collecting a plurality of rock samples, wherein the unconfined compressive strength UCS of the rock samples is between 10 and 95MPa, the cohesive force is between 1 and 20MPa, and the internal friction angle is between 30 and 60 degrees.
Step 2, using DPMA to collect data during drilling work;
step 2, collecting data including drilling speed, rotating speed, torque and feeding force related data during the drilling work.
Step 3, training the established CNN model by using the data in the step 1 and the step 2;
step 3 is specifically implemented according to the following steps:
step 3.1, converting the drilling performance parameters obtained in the step 2 into an M × M matrix, wherein M is a positive integer;
step 3.2, establishing a CNN model;
and 3.3, training the CNN model by adopting a reverse gradient descent algorithm.
As shown in fig. 2, step 3.1 is specifically performed according to the following steps:
step 3.1.1, converting the obtained data set of drilling speed, rotating speed, torque and feeding force into diX M drilling performance parameter matrix, where i ═ 1,2,3,4, where i ═ 1 represents drilling rate, i ═ 2 represents rotation speed, i ═ 3 represents torque, i ═ 4 represents feed force, and d for each rock is addediExpanding the XM drilling performance parameter matrix into an M XM matrix, wherein M is 76;
step 3.1.2, normalize the mxm drilling performance parameter matrix using equation (1), convert the drilling performance parameters to the grey values of the image:
y＝255×(x-xmin)/(xmax-xmin) (1)
wherein y is a grey scale value, x is a drilling performance parameter, xminIs the minimum value, x, of the drilling performance parametermaxIs the maximum value of the drilling performance parameter;
and 3.1.3, converting the gray value obtained in the step 3.1.2 into an image of M multiplied by M pixels.
As shown in fig. 3, the CNN model established in step 3.2 is specifically as follows:
the method comprises a convolutional layer, a random pooling layer and softmax loss, wherein the convolutional layer learns the characteristics of the gray level image obtained in the step 3.1.2, the pooling layer reduces the dimensionality of the gray level image learned by the convolutional layer, the convolutional layer extracts the gray level image characteristics, more abstract characteristics are formed after combination, finally all parameters are normalized into a one-dimensional array to form a complete connection layer, the complete connection layer provides complete connection with the previous layer, non-linear mapping between the image characteristics is represented, and rock strength parameters are finally output.
The CNN model built in step 3.2 contains two convolutional layers for use in step 3 respectively1.2 obtaining line, edge and corner features in the gray scale image, each output feature map combining multiple input maps with convolutional layers, sigmoid function applied to detailed implementation of CNN, unit value at position (x, y) of ith layer of jth feature mapThe calculation is as follows:
Figure BDA0002562686430000082
wherein, i, j, x and y are all positive integers, j represents the jth characteristic diagram, i represents the ith layer of the jth characteristic diagram,
Figure BDA0002562686430000083
is the unit value at position (x, y) of the ith layer of the jth feature map, bijIs the deviation of the ith layer feature map of the jth feature map, piIs the height of the ith nucleus, qjIs the width of the core of the i-th layer,
Figure BDA0002562686430000091
is the kernel weight value of the ith layer of the jth feature map at the (p, q) location, p being the height of the kernel, q being the width of the kernel;
in the pooling layer, sub-sampling layers in CNN are replaced by random layers, and random pools are randomly selected for activation to reduce variance according to polynomial distribution, first, using probabilities in the random pools
Figure BDA0002562686430000092
PiIs the i-th layer probability, a is the feature vector, RjTo obtain P distribution (P) in the pooling area of the jth feature map1，…，P|RjI) then, sample from the P-polynomial based distribution, then, represent the random pool operation using a random function Stochastic(s), the random function Stochastic(s) for each feature map being obtained by:
Figure BDA0002562686430000093
wherein u (i, j) represents a weighted window function,
Figure BDA0002562686430000094
an activation feature value representing the neuron (p, q) position in the l-th layer feature map k;
the probability of x classification is calculated using equation (4):
Figure BDA0002562686430000095
ψ(θh)＝(-1)kcos(mθh)-2k,θh∈[kπ/m,(k+1)π/m] (5)
wherein k is [0, m-1]]Is an integer, i, h, m and k are all positive integers, whIs the h-th column matrix weight, θhIs an input feature vector ahAnd h column weight matrix whAngle a ofhIs an input feature vector, ψ (θ)h) Is (-1)kcos(mθh)-2k。
Step 3.3, when the reverse gradient descent algorithm is adopted to train the CNN model, the CNN model comprises a feedforward transmission stage and a reverse propagation transmission stage, and the CNN model specifically comprises the following steps:
step 3.3.1, feed forward transfer phase, the squared error function is expressed as:
Figure BDA0002562686430000101
wherein E isNAs an error function, yNInput value, ONOutput value, ykIs the value of the kth output layer, okThe value of the kth input layer, N, k, N and c are positive integers;
step 3.3.2 CNN model according to error ENDetermines whether the model converges, and obtains the back propagation error from equation (7) using sigmoid function as the activation function:
Figure BDA0002562686430000102
wherein the content of the first and second substances,Lcounter-propagating error, L being a positive integer representing the output layer, f' (z)L) As a derivative of the activation function, yNInput value, ONOutput value, ykIs the value of the kth output layer, okIs the value of the kth input layer, N, k, N and c are all positive integers;
step 3.3.3, back propagation transfer phase, back propagation error is transferred from higher layer to lower layer, residual error of l layer is calculated(l)Comprises the following steps:
(l)＝((W(l))T (l+1))·f'(z(l)) (8)
where L is the current layer, L is the output layer, is the input layer residual,(l)residual error of layer l, W(l)Is the current layer weight, l is a positive integer
Step 3.3.4, update weight W of each layer(l)And deviation of
Figure BDA0002562686430000103
The calculation is as follows:
Figure BDA0002562686430000104
Figure BDA0002562686430000105
wherein a is the learning rate, a(l)Is the l-th layer learning rate, E is the error function; l is the current layer of the video stream,
Figure BDA0002562686430000106
is the first layer deviation, b is the deviation, i is a positive integer, W(l)Is the current layer weight
The CNN training model enables drilling performance parameters to form a gray image, and the gray image is converted into related parameter values of rock cohesion, internal friction angle and unconfined compressive strength UCS through formulas (2) to (10).
Step 4, predicting the cohesive force, the internal friction angle and UCS of the complete rock, and outputting the predicted values as rock strength parameters finally, wherein the parameters are as follows:
and (4) outputting relevant parameter values of the cohesive force, the internal friction angle and the unconfined compressive strength UCS of the rock obtained in the step (3).
Examples
In this embodiment, the invention is illustrated by taking the drilling test of the tunnel rock mass at a certain place of the Hanjiang to Weihe project constructed in China as an example.
(1) Engineering background
The traffic tunnel is located below the right bank of the hydropower station of the Chinese Hanjiang river dam and is located on a steep slope, and the steep slope has good stability and good geological conditions and is 45-52 degrees in gradient. The shapes of the region are mainly mountains and valleys, the two sides of the region are steep, and the surrounding rock is composed of hundreds of rock types such as retention system marble rock, sandstone, limestone, granite, tuff, shale, phyllite, gneiss, quartzite, slate and the like. Drilling tests were carried out along the tunnel path (about 0-25 m) from the entrance section to the first fault, in the test area, there were weak structural surfaces, including fissures, bedding surfaces.
(2) Brief introduction to drilling testing
The main equipment of this field drilling test is the drilling process monitoring equipment (DPM), and DPM is used to collect drilling performance parameters. DPM can be used for on-site drilling with 60mm inner diameter, 70mm outer diameter and 50m borehole depth, and it can continuously measure and record drilling data, such as thrust (F)n) Torque (T), penetration speed (v), rotational speed (w), drilling depth and penetration depth per revolution (h). Thrust (F) measurement using two different servomotorsn) And torque (T). The thrust servo motor can provide a maximum thrust of 18kN for penetration, while the torque servo motor can provide a maximum reliable thrust of 2458 nM for the cutting process, the thrust servo motor and the torque servo motor operating independently during the drilling process. DPM can accurately measure thrust, torque and drilling depth in a self-controlled manner, and automatically stores drilling operation data as drilling depth increasesIn an Excel file, a DPM capable of collecting 500 data per second at most can accurately complete hundreds of sets of drilling data storage.
(3) Laboratory Standard test
The cores were obtained by drilling in situ, machined to standard cylinders of 50mm x 100mm (diameter x height) strictly according to ISRM standards, and the sample end faces were finished and polished. And (3) carrying out a triaxial compression test on the standard sample, wherein the triaxial compression test is carried out on a WDT-1500 multifunctional material testing machine of the institute of geotechnical university of Western Ann, the Unconfined Compressive Strength (UCS), cohesive force and internal friction angle of the rock are measured through the triaxial compression test, and the test result is shown in figure 1. A total of 30 rock samples were tested in the laboratory to determine UCS, internal friction angle and cohesion, with UCS varying between 10 and 95MPa, cohesion varying between 1 and 20MPa and internal friction angle varying between 30 ° and 60 °.
(4) Collecting drilling performance parameters
To build a wide range of drilling performance parameter databases for different rock types, drilling speed was set to a wide range of 0.1-1.5mm/s, the rotational speed was increased from 200rpm to 600rpm, and the drilling force and rotational torque were recorded for each rock. For example, a data set consisting of drilling performance parameters for complete sandstone consists of 76 sets of data (see table 1).
TABLE 1 drilling Performance data
Figure BDA0002562686430000121
Figure BDA0002562686430000131
(1) Training proposed CNN models using databases
The drilling performance parameters for each type of rock are represented by a two-dimensional (2D) matrix of size D × M, which cannot be used directly for the proposed CNN model, the training data for the CNN model must be an n × n matrix, and we convert the case of the drilling performance parameters into an image of M × M pixels to preserve the details of the input drilling performance parameters and increase the dimensionality of the training data, as shown in fig. 4, and to obtain an image of M × M pixels, the following steps need to be performed. (i) Expanding the dXM drilling performance parameter matrix for each rock into an MXM matrix by repeatedly inserting the dXM matrix 18 times in the 2D matrix; (ii) normalizing the matrix of M × M drilling performance parameters using equation (1) to convert the drilling performance parameters to grayscale values of the image; (iii) the obtained gray values were converted into an image of M × M pixels using a MATLAB program.
y＝255×(x-xmin)/(xmax-xmin) (1)
Where y is the grey scale value, x is the drilling performance parameter, xminIs the minimum value, x, of the drilling performance parametermaxIs the maximum value of the drilling performance parameter.
CNN consists of convolutional layers, stochastic pooling layers and softmax loss (fig. 3), which, in the current problem of estimating rock strength characteristics using drilling parameter information, aim to learn the characteristic quantities of the drilling parameter information, map the drilling parameter information to the characteristic quantity space through the convolutional layers and the stochastic pooling layers, the fully connected layers provide full connection with the previous layers, represent non-linear mapping between the characteristic quantities, and the rock strength parameters as final output.
The proposed hierarchical architecture of the CNN model contains two convolutional layers for obtaining low-level features and high-level features, including lines, edges and corners, respectively, from the input image, each output feature map combining multiple input maps with convolutional layers, a sigmoid function can be applied to a detailed implementation of CNN, the jth feature map and the unit value at the location (x, y) of the ith layer
Figure BDA0002562686430000141
Can be calculated as:
Figure BDA0002562686430000142
where sigmoid (. cndot.) is a sigmoid function, bijIs the deviation of the feature map, PiAnd QjRespectively the height and width of the nucleus，
Figure BDA0002562686430000143
Is the core weight value (i, j) level of the location (p, q) to which it is connected.
In the pooling layer, the sub-sampling layers in the proposed CNN are replaced with random layers, which may randomly select activations to reduce variance according to a polynomial distribution. First, probabilities in a random pool are used
Figure BDA0002562686430000144
In obtaining P distribution (P)1，…，P|RjI) we can sample from the P-based polynomial distribution to select the location i within the region, then represent the random pool operation using a random(s), which is obtained for each feature map by:
Figure BDA0002562686430000145
where u (i, j) is a weighted window function, and
Figure BDA0002562686430000146
is the activation of neurons in the layer i feature map k. The realization of the random pooling layer not only improves the generalization ability of the model, but also enables the proposed CNN to realize faster convergence and avoids overfitting.
Softmax loss is essentially a combination of Softmax, which can translate predictions into non-negative values and normalize them by Softmax to obtain a probability distribution over classes, and multinomial logic losses, which we use to compute Softmax loss. In softmax regression, we calculate the probability of classifying x into a class using equation (4):
Figure BDA0002562686430000151
ψ(θj)＝(-1)kcos(mθj)-2k,θj∈[kπ/m,(k+1)π/m] (5)
wherein k ∈ [0, m-1] is an integer.
The proposed CNN is trained using an inverse gradient descent algorithm, which includes a feed-forward pass stage where a multi-class problem with c classes and N training samples is considered, and a back-propagation pass stage, where the squared error function is expressed as:
Figure BDA0002562686430000152
finally, CNN determines whether the model converges according to the value of E, given an activation function f, a residual may be obtained from equation (7), the sigmoid function being used as the activation function:
Figure BDA0002562686430000153
in the back propagation pass phase, the residual is passed from the higher layer to the lower layer, and then the remaining residual of layer l can be calculated as:
(l)＝((W(l))T (l+1))·f'(z(l)) (8)
where L is the current layer, L is the output layer, and s is the input layer. Update weight W of each layer(l)And deviation of
Figure BDA0002562686430000154
Can be calculated as:
Figure BDA0002562686430000155
Figure BDA0002562686430000156
where a is the learning rate.
(2) Comparison of predicted results with Standard tests
Cohesion, internal friction angle and UCS obtained from laboratory tests were used as test measurements, as these test results provided training data. According to the proposed CNN model, predicted values of internal friction angles of red sandstone, limestone, blackboard rock, marble and granite are 43.1 °, 48.3 °, 60.2 °, 51.3 °, 53.8 ° and 60.9 °, respectively, and as can be seen from fig. 5(a), errors of the proposed CNN are 4.6%, 1.2%, 4.3%, 1.9%, 1.3% and 1.1%, respectively; based on the CNN model, predicted values of cohesion for these rocks were 3.1, 4.6, 10.1, 14.5, 13.6, and 16.5MPa, respectively, and as can be seen from fig. 5(b), errors of proposed CNNs were 8.8%, 6.97%, 5.2%, 2.0%, 3.03%, and 5.7%, respectively; based on the CNN model, UCS predicted values of these rocks were 16.5, 25.8, 74.3, 79.5, 85.7 and 127.8MPa, respectively, and errors of proposed CNNs were 9.8%, 4.9%, 4.1%, 2.5%, 1.7% and 1.8%, respectively, as can be seen from fig. 5 (c). The strength parameters of these types of rocks, predicted based on the CNN model, proved to be very consistent with those obtained from standard laboratory tests, especially for medium-hard rocks. Predicted values and experimental measurements of cohesion, internal friction angle and UCS were measured along a 1: line 1 has a very significant correlation (FIG. 5). In this case, we demonstrate that the proposed CNN can predict cohesion, internal friction angle and UCS within 10% error of laboratory test values, thanks to the proposed CNN model, which is well reflective of the response of drilling data to the complete rock mechanics.
The approximability of UCS estimated values obtained by the CNN method shows that the drilling performance parameters have good response to the rock strength parameters, and the effectiveness and the accuracy of the CNN model are verified. The proposed method of training a database using drilling performance parameters can therefore be applied to the estimation of the rock UCS.
A DCNN model is established based on a random pooling method and softmax loss, and the proposed CNN model framework comprises: (1) collecting drilling logging performance parameters of the complete rock; (2) establishing an intensity parameter database through a standard laboratory test; (3) training a CNN model by using images generated by drilling logging performance parameters and rock strength parameters (unconfined compressive strength (UCS), cohesion and internal friction angle) data; (4) a new prediction is performed to evaluate the reliability of the trained CNN model. The test results show that the predicted rock strength parameters are within 10% of the acceptable error range compared to the results of the conventional standard tests. Compared with Mohr-Coulomb criterion, the proposed CNN has better performance for UCS estimation of different rock types and obtains higher precision, particularly the proposed method can overcome the main limitation of the current indoor test, the method can continuously and reliably measure the rock strength parameter at a speed several orders of magnitude faster than the standard test, the technology is applied to an engineering problem of the engineering from Hanjiang to Weihe in China, and the application potential of the technology in rock engineering is displayed.

Claims (9)

1. A rock strength parameter determination method based on a deep convolutional neural network is characterized by comprising the following steps:
step 1, collecting unconfined compressive strength UCS, cohesive force and internal friction angle of various common rocks as basic data of a database;
step 2, using DPMA to collect data during drilling work;
step 3, training the established CNN model by using the data in the step 1 and the step 2;
and 4, predicting the cohesive force, the internal friction angle and the UCS of the complete rock, and outputting the predicted values serving as rock strength parameters finally.
2. The method for determining the rock strength parameter based on the deep convolutional neural network as claimed in claim 1, wherein the step 1 is implemented according to the following steps:
collecting a plurality of rock samples, wherein the unconfined compressive strength UCS of the rock samples is between 10 and 95MPa, the cohesive force is between 1 and 20MPa, and the internal friction angle is between 30 and 60 degrees.
3. The method for determining rock strength parameters based on the deep convolutional neural network as claimed in claim 1, wherein the step 2 collected data comprises drilling speed, rotating speed, torque and feeding force related data during drilling work.
4. The method for determining the rock strength parameter based on the deep convolutional neural network as claimed in claim 3, wherein the step 3 is implemented according to the following steps:
step 3.1, converting the drilling performance parameters obtained in the step 2 into an M × M matrix, wherein M is a positive integer;
step 3.2, establishing a CNN model;
and 3.3, training the CNN model by adopting a reverse gradient descent algorithm.
5. The method for determining the rock strength parameter based on the deep convolutional neural network as claimed in claim 4, wherein the step 3.1 is implemented according to the following steps:
step 3.1.1, converting the obtained data set of drilling speed, rotating speed, torque and feeding force into diX M drilling performance parameter matrix, where i ═ 1,2,3,4, where i ═ 1 represents drilling rate, i ═ 2 represents rotation speed, i ═ 3 represents torque, i ═ 4 represents feed force, and d for each rock is addediExpanding the XM drilling performance parameter matrix into an M XM matrix, wherein M is 76;
step 3.1.2, normalize the mxm drilling performance parameter matrix using equation (1), convert the drilling performance parameters to the grey values of the image:
y＝255×(x-xmin)/(xmax-xmin) (1)
wherein y is a grey scale value, x is a drilling performance parameter, xminIs the minimum value, x, of the drilling performance parametermaxIs the maximum value of the drilling performance parameter;
and 3.1.3, converting the gray value obtained in the step 3.1.2 into an image of M multiplied by M pixels.
6. The method for determining the rock strength parameter based on the deep convolutional neural network as claimed in claim 5, wherein the CNN model established in the step 3.2 is specifically as follows:
the method comprises a convolutional layer, a random pooling layer and softmax loss, wherein the convolutional layer learns the characteristics of the gray level image obtained in the step 3.1.2, the pooling layer reduces the dimensionality of the gray level image learned by the convolutional layer, the convolutional layer extracts the gray level image characteristics, more abstract characteristics are formed after combination, finally all parameters are normalized into a one-dimensional array to form a complete connection layer, the complete connection layer provides complete connection with the previous layer, non-linear mapping between the image characteristics is represented, and rock strength parameters are finally output.
7. The method of claim 6, wherein the CNN model created in step 3.2 comprises two convolutional layers for obtaining line, edge and corner features from the grayscale image obtained in step 3.1.2, each output feature map combines multiple input maps with convolutional layers, sigmoid function is applied to detailed implementation of CNN, unit value at position (x, y) of ith layer of jth feature map
Figure FDA0002562686420000031
The calculation is as follows:
Figure FDA0002562686420000032
wherein, i, j, x and y are all positive integers, j represents the jth characteristic diagram, i represents the ith layer of the jth characteristic diagram,
Figure FDA0002562686420000033
is the unit value at position (x, y) of the ith layer of the jth feature map, bijIs the deviation of the ith layer feature map of the jth feature map, piIs the height of the ith nucleus, qjIs the width of the core of the i-th layer,
Figure FDA0002562686420000034
is the weight value of the core at the (p, q) position of the ith layer of the jth feature map, p is the height of the core, q isThe width of the nucleus;
in the pooling layer, sub-sampling layers in CNN are replaced by random layers, and random pools are randomly selected for activation to reduce variance according to polynomial distribution, first, using probabilities in the random pools
Figure FDA0002562686420000035
PiIs the i-th layer probability, a is the feature vector, RjTo obtain P distribution (P) in the pooling area of the jth feature map1，…，P|RjI) then, sample from the P-polynomial based distribution, then, represent the random pool operation using a random function Stochastic(s), the random function Stochastic(s) for each feature map being obtained by:
Figure FDA0002562686420000036
wherein u (i, j) represents a weighted window function,
Figure FDA0002562686420000037
an activation feature value representing the neuron (p, q) position in the l-th layer feature map k;
the probability of x classification is calculated using equation (4):
Figure FDA0002562686420000038
ψ(θh)＝(-1)kcos(mθh)-2k,θh∈[kπ/m,(k+1)π/m] (5)
wherein k is [0, m-1]]Is an integer, i, h, m and k are all positive integers, whIs the h-th column matrix weight, θhIs an input feature vector ahAnd h column weight matrix whAngle a ofhIs an input feature vector, ψ (θ)h) Is (-1)kcos(mθh)-2k。
8. The method for determining rock strength parameters based on the deep convolutional neural network as claimed in claim 4, wherein the step 3.3 comprises a feedforward transfer stage and a back propagation transfer stage when training the CNN model by using an inverse gradient descent algorithm, specifically as follows:
step 3.3.1, feed forward transfer phase, the squared error function is expressed as:
Figure FDA0002562686420000041
wherein E isNAs an error function, yNInput value, ONOutput value, ykIs the value of the kth output layer, okThe value of the kth input layer, N, k, N and c are positive integers;
step 3.3.2 CNN model according to error ENDetermines whether the model converges, and obtains the back propagation error from equation (7) using sigmoid function as the activation function:
Figure FDA0002562686420000042
wherein the content of the first and second substances,Lcounter-propagating error, L being a positive integer representing the output layer, f' (z)L) As a derivative of the activation function, yNInput value, ONOutput value, ykIs the value of the kth output layer, okIs the value of the kth input layer, N, k, N and c are all positive integers;
step 3.3.3, back propagation transfer phase, back propagation error is transferred from higher layer to lower layer, residual error of l layer is calculated(l)Comprises the following steps:
(l)＝((W(l))T (l+1))·f'(z(l)) (8)
where L is the current layer, L is the output layer, is the input layer residual,(l)residual error of layer l, W(l)Is the current layer weight, l is a positive integer
Step 3.3.4, update weight W of each layer(l)And deviation of
Figure FDA0002562686420000043
The calculation is as follows:
Figure FDA0002562686420000051
Figure FDA0002562686420000052
wherein a is the learning rate, a(l)Is the l-th layer learning rate, E is the error function; l is the current layer of the video stream,
Figure FDA0002562686420000053
is the first layer deviation, b is the deviation, i is a positive integer, W(l)Is the current layer weight
The CNN training model enables drilling performance parameters to form a gray image, and the gray image is converted into related parameter values of rock cohesion, internal friction angle and unconfined compressive strength UCS through formulas (2) to (10).
9. The method for determining the rock strength parameter based on the deep convolutional neural network as claimed in claim 7, wherein the step 4 is as follows:
and (4) outputting relevant parameter values of the cohesive force, the internal friction angle and the unconfined compressive strength UCS of the rock obtained in the step (3).
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