CN107145665B - Roadway surrounding rock stress modeling and prediction method - Google Patents
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Abstract
The invention relates to the technical field of rock and soil detection, and particularly discloses a roadway surrounding rock stress modeling and prediction method. Firstly, selecting a plurality of actual detection values of stress and strain of roadway surrounding rock, and carrying out normalization processing; then, establishing a traditional ELM model for a part of normalized strain stress data, and optimizing the input layer weight of the ELM by using a greedy algorithm to establish an optimized quantitative analysis mathematical model; then, the stress is obtained for the known roadway allergy prediction based on the mathematical model. The method applies the ELM model to the modeling of the stress strain of the surrounding rock of the roadway for the first time, thereby realizing the prediction of the stress under the condition of only knowing the stress strain of the surrounding rock, and utilizes the computer to model and calculate, thereby having short analysis period, low cost, simple operation steps, improved working efficiency and reduced human errors.
Description
Technical Field
The invention relates to the technical field of rock and soil detection, in particular to a tunnel surrounding rock stress modeling and prediction method.
Background
And (4) excavating the roadway, releasing the energy of the surrounding rock, and generating partial stress in the surrounding rock. The surrounding rock stress is the superposition of original rock stress and partial stress, and the partial stress can control the rock mass to be destroyed. For constructors, the safety classification of surrounding rocks of the roadway is an important guideline before construction. The correct classification can reduce the construction cost, improve the construction efficiency and avoid potential danger. At present, roadway surrounding rock safety level classification mainly based on quantitative indexes becomes a development direction. The strain and the stress of the surrounding rock of the roadway are two important quantitative indexes, in actual engineering, the strain measurement of the surrounding rock of the roadway is easy, but the stress measurement of the surrounding rock of the roadway is difficult, and the cost is high.
The existing sensor capable of effectively measuring stress is large in size, inconvenient to operate, high in price and difficult to realize large-scale long-time measurement, manual intermittent observation and collection are mainly adopted for measurement, and monitoring results are delayed. The existing numerical analysis modeling method utilizes a numerical calculation method, such as a finite difference method, a finite element method, a boundary element method, a discrete element method and the like, for example, a famous simulation calculation software FLAC3D is compiled based on the finite difference method, and according to a series of static parameters of elasticity modulus, shear modulus, density, tensile strength and the like of rock and soil, the stress and strain of the surrounding rock of a roadway can be simulated to obtain ideal data.
At present, no method exists for accurately predicting roadway stress under the condition of only knowing the strain of surrounding rocks, and no method exists for predicting the roadway stress value and trend in the tested part.
Disclosure of Invention
Technical problem to be solved
In order to solve the problems in the prior art, the invention provides a tunnel surrounding rock stress modeling and prediction method. The method has the advantages of short analysis period, easy operation, strong operability, improved precision by a computer and high accuracy.
(II) technical scheme
In order to achieve the purpose, the invention adopts the main technical scheme that:
a roadway surrounding rock stress modeling and prediction method comprises the following steps:
s1, measuring and acquiring stress values and strain values of N points of the roadway surrounding rock, and recording data of the strain values and the strain values of each point of the roadway surrounding rock in each day of M days; wherein the roadway is of a horseshoe shape;
s2, carrying out normalization processing on the data obtained in the first step, and processing the strain value and the stress value into numerical values between-1 and 1;
and S3, establishing an improved ELM algorithm quantitative analysis mathematical model by using the numerical value normalized by the S2, testing the strain data needing to be predicted based on the mathematical model, and obtaining the stress value and the trend of the predicted part.
The method as described above, preferably, the S2 includes the following steps:
s101, respectively making strain value data of the N points of the roadway surrounding rock in the vertical and horizontal directions into an M multiplied by 2N matrix A; and making the stress value data of one point into an M multiplied by 1 matrix B;
s201, performing normalization processing on the matrix A, B obtained in the step S101; the maximum data in the matrix A, B is recorded as Cmax and the minimum data is recorded as Cmin, and the difference between the Cmax and the Cmin is obtainedr，CtThe formula one is satisfied;
s202, replacing the C value with the numerical value in the matrix A, B respectively, and substituting the numerical value into the formula I to obtain the matrixes At and Bt respectively.
The method as described above, preferably, the S3 includes the following steps:
s301, taking one part of the normalized data as a training sample, and taking the other part of the normalized data as a test sample;
substituting the matrix of the training sample into a traditional ELM stress model for modeling, substituting the test sample into the modeled stress model to obtain a predicted output test stress, and comparing the predicted output test stress with actually measured data to obtain a variance E between the predicted output test stress and the actually measured stress;
s302, establishing an improved ELM algorithm quantitative analysis mathematical model by using the variance E, and predicting the stress of the surrounding rock according to the strain of the surrounding rock.
The method as described above, preferably, the modeling of the conventional ELM stress model, includes the following steps:
s30101, taking sigmoid from an activation function g (x) in the ELM model;
s30102, generating a matrix w of l × n random input layers:
wherein, the l represents that the hidden layer has l neurons, and the n represents that the hidden layer has n groups of input variables; let the output layer weight and hidden layer offset be:
wherein m is m sets of output variables;
the input layer X is the training sample in the matrix At, and the output layer Y is the training sample in the matrix Bt:
n in the input layer X is expressed as n groups of vectors of the input layer X, and each vector has Q elements; in output layer Y, m denotes that output layer Y has m sets of vectors, each vector having p elements,
the output T is:
hidden layer output H is:
h ═ g (w · X + b) formula seven
Wherein g is a sigmoid function, w is an input layer weight, X is an input layer, b is a hidden layer offset, and the following can be obtained according to the (6) and the (7):
β＝H+T
wherein β is the weight of the output layer, and H is the weight of the output layer+Represents the Moore-Penrose generalized inverse of the hidden layer output matrix H.
The method preferably comprises the following steps of:
s30201, defining a search step t, and taking an input layer weight wijA value;
s30202, order wij'＝wij+ t, updating the weight β ' of the output layer again according to the traditional ELM method, and recalculating to obtain the variance E ', if E '<E, keeping new weight wij' and β ', and E ═ E ', proceed with wij'＝wij+t；
S30203, if said E'>E, selecting another weight and executing S30201; s30204, if w is performed for the first timeij'＝wij+ t, said E'>E, then look up w in reverseij'＝wij-t; if E'<E, continue wij'＝wij-t, up to E'>E, another weight is selected, and S30201 is performed.
The method of the invention utilizes an improved algorithm (weight modification of an input layer) of ELM to establish a tunnel surrounding rock stress and strain quantitative analysis mathematical model, and utilizes the established mathematical model to quantitatively obtain the stress value under the condition of only knowing the strain.
(III) advantageous effects
The invention has the beneficial effects that: the modeling and predicting method for the roadway surrounding rock stress can rapidly and accurately predict the roadway stress according to the roadway strain. The modeling and predicting method has the advantages of short analysis period, simple operation steps, low cost, modeling and calculating by using a computer, improved testing precision and improved working efficiency. In addition, the method reduces the investment of instruments and a large amount of labor, has low working strength, saves the cost of production investment, reduces human errors, and greatly improves the accuracy of the predicted result which is far higher than that of the method in the prior art.
Drawings
FIG. 1 is a flow chart of a modeling method of roadway surrounding rock strain and stress;
FIG. 2 is a flowchart illustrating the specific step of S2 in FIG. 1;
FIG. 3 is a flow chart of a conventional ELM stress model building;
FIG. 4 is a flow chart of optimizing ELM input layer weights using a greedy algorithm in accordance with the present invention;
FIG. 5 is a comparison graph of simulation results output using an optimized ELM and an unoptimized ELM model training set in accordance with the present invention;
fig. 6 is a schematic position diagram of a detection point of a tunnel cross section in embodiment 2 of the present invention;
FIG. 7 is a diagram showing the test results of embodiment 2 of the present invention and the conventional method.
Detailed Description
For the purpose of better explaining the present invention and to facilitate understanding, the present invention will be described in detail by way of specific embodiments with reference to the accompanying drawings.
Example 1
The invention establishes a tunnel surrounding rock stress modeling and prediction method, the modeling method is to establish a quantitative analysis mathematical model of tunnel surrounding rock strain and stress by using an ELM algorithm after input weight is improved, and the stress of the tunnel surrounding rock is predicted by using the established mathematical model under the condition that only the surrounding rock strain is known.
The detailed process of applying the modeling of the stress and the strain of the surrounding rock of the roadway to predicting the stress of the surrounding rock of the roadway is as follows:
preparation work: and (3) collecting a stress and stress value sample in the surrounding rock of the mine iron ore in front of the hole of the saddle steel, and recording the stress and the strain value of part of the interface of the surrounding rock of the tunnel for a plurality of days.
The method specifically comprises the following steps: as shown in figure 1 of the drawings, in which,
s1, measuring strain values of 5 points of the roadway surrounding rock in the vertical and horizontal directions by using a convergence instrument and a three-dimensional measuring instrument, and monitoring for 106 days to obtain 106 multiplied by 10 groups of sample data; the stress value of one point is measured, and 106 groups of sample data are obtained.
S2, normalizing the sample data, as shown in the flowchart of fig. 2, the implementation process is as follows:
s101, standardizing data, and making the obtained data of 106 multiplied by 10 strain values into a matrix A of 106 multiplied by 10; 106 sets of stress values are obtained, a matrix B of 106 x 1 is made,
step S201, normalizing the data:
respectively substituting the obtained matrix A and matrix B into the following formula I for normalization treatment, wherein the normalization treatment is respectively carried out on the matrix A and the matrix BThe maximum data in the matrix A, B is recorded as Cmax and the minimum data is recorded as Cmin, and the difference between them is calculated to obtain Cr；CtThe formula one is satisfied:
step S202, adding CtAnd replacing the original matrix A or B to obtain the normalized matrix At and the normalized matrix Bt.
In the embodiment, the roadway surrounding rock strain value with a small actual value and the roadway surrounding rock stress value with a large actual value are compressed to be between-1 and 1 through normalization, so that a model with accurate description is conveniently established.
S3, establishing an improved ELM algorithm quantitative analysis mathematical model by using the numerical value normalized by S2, testing strain data to be predicted based on the mathematical model, and obtaining a stress value and a trend in a predicted part; the method comprises the steps of establishing a traditional ELM algorithm quantitative analysis model by using normalized data in S2, optimizing the whole model by using a greedy algorithm, testing strain data to be predicted based on the optimized model, and obtaining a stress value and a trend in a predicted part.
The method comprises the following specific steps:
s301, using the obtained random 90 groups of data as training samples A90、B90The normalized data is At90、Bt90Marking; the remaining 16 sets of data were obtained as test samples A16、B16The normalized data is At16、Bt16Marking for later use; training the matrix At90、Bt90Substituting the model into a traditional ELM stress model for modeling, bringing the test sample into the modeled model to obtain a predicted output test stress, comparing the predicted output test stress with actually measured data to obtain a variance of the predicted output test stress and the actually measured stress, and marking the variance as E;
s302, establishing an improved ELM algorithm quantitative analysis mathematical model by using the variance E, and predicting the stress of the surrounding rock by Matlab under the condition of knowing the strain of the surrounding rock.
In the invention, an ELM model is improved by mainly utilizing a greedy algorithm, input layer weights of the traditional ELM network are randomly generated, once the input layer weights are generated, the values of the input layer weights are unchanged until the training is finished, so that the output layer weights β can be calculated only by determining an activation function of hidden layer neurons, the number of the hidden layer neurons and the number of network hidden layers.
The method comprises the following specific steps:
step S30101, an activation function G (x) in the ELM model is used to obtain a sigmoid function, and the number of hidden layer nodes is 20.
Step S30102, establishing a traditional ELM model by using the normalized training samples, namely 90 groups of roadway strain and stress data, and specifically comprising the following steps:
generating a matrix w of l × n random input layers:
wherein, let l denote that the hidden layer has l neurons, and n denote that there is an input layer with n sets of input variables.
Let the output layer weight and hidden layer offset be:
where m refers to m sets of output variables, m being n in this embodiment.
The input layer X is the training sample in the matrix At, and the output layer Y is the training sample in the matrix Bt:
n in the input layer X means that the input layer X has n sets of vectors, each vector having Q elements, Q being 10 in this embodiment. In the output layer Y, m represents that the output layer Y has m groups of vectors, each vector has p elements, and p is 1 in the embodiment;
the output T is:
t may be considered as the output Y;
hidden layer output H is:
h ═ g (w · X + b) formula seven
Wherein g is a sigmoid function, w is an input layer weight, x is an input layer, and b is a hidden layer offset. According to the formula six and the formula seven, the method can obtain:
h β ═ T equation eight
In the formula eight, H is the hidden layer output, β is the output layer weight, the output T of the training sample is known, and finally the output weight is calculated to calculate the output weight β, β is H+T, here H+And representing Moore-Penrose generalized inverse of the hidden layer output matrix H, and thus, completing the establishment of the traditional ELM stress model.
And S30103, bringing the latter 16 groups of data into the established model to obtain the prediction output.
Step S30104, the obtained prediction output is compared with the data collected by the sensor, and the variance between the stress output calculated by the ELM and the actually measured stress is the variance E, and a specific flowchart thereof is shown in fig. 3.
The modeling method of the conventional ELM is described in equations 2 to 8.
Next, modeling is performed by further improving the ELM by using a greedy algorithm: before modeling, modeling is carried out according to the traditional ELM, and the weight of an input layer is wijAnd the weight of the output layer is β, and the error E is obtained after calculation, as shown in the flow chart of fig. 4, the specific steps are as follows:
step S30201, firstDefining search step length t, and taking an input layer weight wijThe value is obtained.
Step S30202, let wij'＝wij+ t, where i, j are the number in row i and column j in the matrix, output layer weight β ' is re-updated according to conventional ELM methods, and variance E ' is re-calculated if E '<E, keeping new weight wij' and β ', and E ═ E ', proceed with wij'＝wij+t。
In step S30203, if E' > E. If the weight value is updated in the previous S302, the local minimum point is found, the next weight value is selected by jumping out, and at this time, another weight value is selected, and S30201 is executed; if the first calculation of S302 is greater than E, the next step S30204 is performed.
Step S30204, if w is performed for the first timeij'＝wij+ t is E'>E, then look up w in reverseij'＝wij-t, if E'<E, continue wij'＝wij-t, up to E'>E, another weight is selected, i.e., S30201 is performed.
And S30205, substituting the strain matrix to be predicted into the optimized ELM model, and simulating and calculating to obtain the stress of the surrounding rock through Matlab.
And modeling the stress and strain of the surrounding rock of the roadway to be detected by using the optimized ELM, wherein the modeling method adopts a greedy algorithm to optimize the weight of an input layer in the ELM, so that a quantitative analysis mathematical model of the stress and strain of the surrounding rock of the roadway is established, and the stress of the surrounding rock can be predicted by using the established mathematical model under the condition that only the stress of the surrounding rock is known.
And substituting the last 16 groups of test data into Matlab to realize the simulation of the model, and making images according to the accuracy of the test data to obtain a comparison graph of the prediction effect of the improved ELM and the traditional ELM on the stress of the roadway surrounding rock, as shown in FIG. 5, wherein the ＊ expected value is the real value measured by using a sensor, ○ is the predicted value of the optimized ELM, and □ is the predicted value of the traditional ELM, and as is obvious from FIG. 5, the optimized ELM is closer to the real value than the unoptimized ELM, and the accuracy of the former is far higher than that of the latter.
Example 2
The method established in the embodiment 1 is applied to a tunnel to predict the stress of surrounding rocks of an excavation roadway, 4 sections of different tunnel sections are selected, each section is provided with a detection point selected as shown in fig. 6, a vertex is composed of two points (ID6061 and ID21461), the vertex is provided with the ID21461 of the left point, and the vertical and horizontal strains of the 5 points ID18941, ID20341, ID21461, ID4941 and ID3541 are obtained as input. The vertex (ID21461) vertical stress is used as an input. And then carrying out training by taking the traditional ELM and the optimized ELM into the model. Finally, 3 other sections were selected, and strain and stress data were obtained in the same manner and used as test samples to be tested in the method established in example 1. A graph of the results shown in fig. 7 was obtained. The expected stress curve is a real value obtained by detection of a specific practical application sensor, the stress curve predicted by the traditional ELM is a stress value obtained by a traditional ELM model, and the stress curve predicted by the optimized ELM is a stress value obtained by prediction by using the method of the embodiment 1.
The result shows that the difference between the predicted stress value obtained by the modeling and predicting method of the tunnel surrounding rock stress established by the invention and the actually measured stress value is minimum, and the predicted stress value can be used as a true value.
Example 3
Compared with the prior art, the method established by the invention is used for comparative analysis of the stress test of the surrounding rock of the same roadway, the following methods are respectively adopted,
control group 1: measuring the stress of surrounding rock by using a three-dimensional measuring instrument on the market;
control group 2: the prior art method of using FLAC3D values;
experimental group 1: non-optimized traditional ELM modeling methods;
the modeling method described in embodiment 1 is applied to predicting roadway surrounding rock stress.
The difference, time consumption and cost of the error between the predicted stress obtained by the method and the actual measurement are shown in the following table 1.
TABLE 1 test results
| Test object | Difference in error | Measuring elapsed time | Cost of consuming |
| |
-- | >1 |
300 ten thousand |
| Control group | |||
| 2 | Ideally small | >1 |
10 |
| Experimental group | |||
| 1 | Big (a) | 2 seconds | 4000 yuan |
| Example 1 | Small | 40 minutes | 4000 yuan |
As can be seen from table 1: the stress of surrounding rock is measured by a three-dimensional measuring instrument on the market, the obtained real value can be regarded as a real value, but the required time is long, and the price of the sensor is up to millions of RMB. In addition, some chemical laboratory instrumentation and human cost investment are also indispensable. The existing numerical method is adopted for analysis, the cost is low, but the numerical method can obtain a good effect only when the surrounding rock of the roadway is in an ideal state, and the practicability is not enough. By adopting an unoptimized traditional ELM modeling method, strain of surrounding rocks of a roadway needs to be obtained by using a strain sensor, the total price of the strain sensor is about 4000 yuan, the cost is relatively low, and the traditional ELM modeling method is high in speed but large in error. In contrast, the optimized ELM modeling method needs about 4000 yuan of strain investment cost for obtaining the tunnel surrounding rock by using the strain sensor, is low in relative labor cost, small in detection result error, high in prediction result, close to the detection result of the stress sensor with high price and high precision, and has considerable benefit.
Therefore, the modeling method has the advantages of short analysis period and simple operation steps, and utilizes the computer to model and calculate, thereby improving the test precision and the working efficiency. In addition, the method reduces the instrument investment and the large manpower investment, has low working strength, saves the cost of production investment, and reduces human errors.
The above is only a preferred embodiment of the present invention, and it should be noted that the above preferred embodiment should not be considered as limiting the present invention, and the protection scope of the present invention should be subject to the scope defined by the claims. It will be apparent to those skilled in the art that various modifications and adaptations can be made without departing from the spirit and scope of the invention, and these modifications and adaptations should be considered within the scope of the invention.
Claims (1)
1. A roadway surrounding rock stress modeling and prediction method is characterized by comprising the following steps:
s1, measuring and acquiring stress values and strain values of N points of the roadway surrounding rock, and recording data of the strain values and the strain values of each point of the roadway surrounding rock in each day of M days; wherein the roadway is of a horseshoe shape;
s2, carrying out normalization processing on the data obtained in the step S1, and processing the strain value and the stress value into numerical values between-1 and 1;
s3, establishing an improved ELM algorithm quantitative analysis mathematical model by using the numerical value normalized by the S2, testing strain data to be predicted based on the mathematical model, and obtaining a stress value and a trend in a predicted part;
wherein the S2 includes the steps of:
s101, respectively making strain value data of the N points of the roadway surrounding rock in the vertical and horizontal directions into an M multiplied by 2N matrix A; and making the stress value data of one point into an M multiplied by 1 matrix B;
s201, performing normalization processing on the matrix A, B obtained in the step S101; taking the maximum data in the matrix A as Cmax and the minimum data as Cmin, and taking the difference between Cmax and Cmin to obtain Cr，CtObtaining a formula I;
S202, replacing the value C with the numerical value in the matrix A, substituting the numerical value into the formula I to obtain a matrix At, and simultaneously performing the same processing on the matrix B to obtain a matrix Bt;
the step S3 includes the steps of:
s301, taking one part of the normalized data as a training sample, and taking the other part of the normalized data as a test sample;
substituting the matrix of the training sample into a traditional ELM stress model for modeling, substituting the test sample into the modeled stress model to obtain a predicted output test stress, and comparing the predicted output test stress with actually measured data to obtain a variance E between the predicted output test stress and the actually measured stress;
s302, establishing an improved ELM algorithm quantitative analysis mathematical model by using the variance E, and predicting the stress of the surrounding rock according to the strain of the surrounding rock;
the modeling of the traditional ELM stress model comprises the following steps:
s30101, taking sigmoid from an activation function g (x) in the ELM model;
s30102, generating a matrix w of l × n random input layers:
Wherein, the l represents that the hidden layer has l neurons, and the n represents that the hidden layer has n groups of input variables; w is ai,jAnd (i 1.. l, j 1.. n) is an input layer weight value connecting the ith input node and the jth hidden layer node, and the output layer weight value β and the hidden layer offset b are made as follows:
Wherein m is m groups of output variables βi,j(i 1.. l, j 1.. m) is an output layer weight value connecting the ith hidden layer node and the jth output node; bi(i 1.. l) is the bias of the ith hidden layer node;
the input layer X is the training sample in the matrix At, and the output layer Y is the training sample in the matrix Bt:
N in the input layer X is expressed as n groups of vectors of the input layer X, and each vector has Q elements; in output layer Y, m denotes that output layer Y has m sets of vectors, each vector having p elements,
the output of the conventional ELM model, i.e., output T, is:
Hidden layer output H is:
h ═ g (w · X + b) formula seven
G is a sigmoid function, w is an input layer matrix, X is an input layer, b is a hidden layer offset, and the method can be obtained according to the formula six and the formula seven:
β＝H+T
wherein β is the weight of the output layer, and H is the weight of the output layer+Representing Moore-Penrose generalized inverse of the hidden layer output matrix H;
the method for establishing the improved ELM algorithm quantitative analysis mathematical model comprises the following specific steps:
s30201, defining a search step t, and taking an input layer weight wijAnd calculating a variance E;
s30202, order wij'＝wij+ t, re-updating the output layer weight according to the traditional ELM method, wherein the updated output weight is β ', and re-calculating to obtain the variance, wherein the re-calculated variance is E';
s30203, judging the relation between E and E';
if E'<E, let wij＝wij', β ═ β ' and let E ═ E ', proceed to S30202;
if E'>E, judging whether the execution of w is the first timeij'＝wij+ t, if not the first time, executing S30204, if the first time, executing 30205;
s30204 output wijExecuting S30201;
s30205, order wij'＝wijT, re-updating the weight of the output layer according to the traditional ELM method, wherein the updated output weight is β ', re-calculating the variance, and re-calculating to obtain the variance E';
s30206, judging the relation between E and E';
if E'<E, let wij＝wij', β ═ β ' and let E ═ E ', proceed to S30205;
if E'>E, output wijS30201 is executed.
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| CN104182622A (en) * | 2014-08-12 | 2014-12-03 | 大连海事大学 | Feedback analytical method and feedback analytical device during tunnel construction and based on extreme learning machine |
| CN105260575A (en) * | 2015-11-17 | 2016-01-20 | 中国矿业大学 | Roadway surrounding rock deformation predicting method based on neural network |
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| CN105260575A (en) * | 2015-11-17 | 2016-01-20 | 中国矿业大学 | Roadway surrounding rock deformation predicting method based on neural network |
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