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CN112926266A - Underground supply air volume estimation method based on regularized incremental random weight network - Google Patents

Underground supply air volume estimation method based on regularized incremental random weight network Download PDF

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CN112926266A
CN112926266A CN202110230904.3A CN202110230904A CN112926266A CN 112926266 A CN112926266 A CN 112926266A CN 202110230904 A CN202110230904 A CN 202110230904A CN 112926266 A CN112926266 A CN 112926266A
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王前进
陆群
杨晓冬
辅小荣
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Yancheng Institute of Technology
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Abstract

The invention discloses an underground supply air volume estimation method based on a regularization incremental random weight network, which comprises the following steps: a group of variables influencing the change of the underground supply air volume are obtained through the analysis of the switching process of the main mine ventilator and are used as the input of a data-driven underground supply air volume model; setting initialization parameters of the model; establishing a new constraint condition to generate a group of candidate hidden layer nodes according to the characteristics of network residual errors in iterative learning; selecting one node with the best quality from the candidate hidden layer nodes as a new hidden layer node; and introducing a 2-norm regularization term into a secondary loss function, updating the output weight of the whole network by adopting a global regularization least square method until the modeling is finished when the set maximum hidden layer node number is reached or the acceptable tolerance is met, and obtaining the underground supply air volume estimation model based on the regularization incremental random weight network. The method can effectively improve the estimation precision of the model and avoid the over-fitting problem.

Description

Underground supply air volume estimation method based on regularized incremental random weight network
Technical Field
The invention relates to the technical field of mine ventilation, in particular to an underground supply air volume estimation method based on a regularization incremental random weight network.
Background
The main ventilator switching process is widely used to ensure continuous safe production in mines. According to the requirements of coal mine safety regulations, a mine adopts a mode of' one main ventilator and one standby ventilator to alternately operate. Wherein, one of the operation is called a working fan, and the other is called a standby fan. The underground supply air volume is used as a key operation index of the switching process of the main ventilator and has great influence on underground operation, so that the underground supply air volume is required to be accurately measured to ensure the stability and the safety of the switching process of the main ventilator and provide sufficient underground supply air volume. However, due to the harsh environment, the pressure tapping hole of the air volume measuring device is easily blocked, frequent maintenance is required, and it is difficult for mine workers to monitor the change of the underground supplied air volume in real time. Therefore, it is necessary to establish an accurate and reliable model of the underground supply air quantity to reflect the underground supply air quantity information for the working personnel.
Currently, a common method is to estimate the mechanism model or the data-driven model. The mechanism model is generally based on some theoretical assumptions, and important parameters of the model are difficult to obtain accurately, so that certain deviation is generated when the mechanism model is used for estimating the operation index. The data-driven modeling technology does not need to know the complex change of the switching process, and can establish an estimation model of the operation index only by using input and output data, so that the data-based model is mostly adopted for estimating the operation index.
In recent years, bp (back propagation) neural networks, Elman neural networks, and rbf (radial basis function) neural networks have been widely used for estimation of operation indexes. However, these neural networks use a gradient descent method with a slow convergence rate to train parameters, resulting in a learning rate far from the expected rate. As a single hidden layer feedforward neural network, hidden parameters of an incremental random weight network are randomly generated, and an output weight of the network is obtained by solving a linear equation. Meanwhile, in the process of network construction, only one newly added node is added each time until the modeling task is completed. Therefore, the incremental random weight network has a simple structure and a very fast learning speed. However, when the number of hidden layer nodes is too many, the network structure becomes complex, an overfitting problem is easily generated, generalization performance is reduced, and practical application of the model is limited.
Disclosure of Invention
The invention aims to provide a method for estimating the underground supply air volume based on a regularized incremental random weight network, which not only has higher estimation precision, but also can effectively avoid the over-fitting problem in the conventional incremental random weight network and can be well applied to estimation of the underground supply air volume.
The invention provides a method for estimating underground supply air volume based on a regularized incremental random weight network, which comprises the following steps:
s1, analyzing the switching process of the main mine ventilator to obtain a group of variables influencing the change of the underground supply air volume, and using the variables as the input of a data-driven underground supply air volume model;
s2, setting initialization parameters of the model;
s3, establishing a new constraint condition to generate a group of candidate hidden layer nodes according to the characteristics of the network residual error in iterative learning;
s4, selecting one node with the best quality from the candidate hidden layer nodes as a new hidden layer node;
and S5, introducing a 2-norm regularization term into a secondary loss function, updating the output weight of the whole network by adopting a global regularization least square method until the modeling is finished when the set maximum number of hidden layer nodes is reached or the acceptable tolerance is met, and obtaining the underground supply air volume estimation model based on the regularization incremental random weight network.
Further, the step S1 includes:
a group of variables with the strongest correlation with the underground supply air volume are used as input variables of the model, and the method comprises the following steps: wind resistance R of horizontal air door of two main ventilators1s and R2sVertical air door windage R1c and R2cPressure head H1d and H2dAnd wind resistance R of underground mine0And the output variable is the underground supply air quantity.
Further, the step S2 includes:
parameters required for model training are given, including: maximum number of hidden layer nodes LmaxRegularization coefficient C, implicit parameter configuration times TmaxTolerable error epsilon, learning parameter r, adjusting factor gamma, recessive parameter selection range gamma: λ ═ λmin:Δλ:λmaxThe initial hidden layer node number of the model is theta1Residual error of e0And order e0For the output T of the sample, the training of the model is from Θ1Initially, the hidden layer nodes are added one by one.
Further, the step S3 includes:
when adding the kth hidden layer node, respectively from the variable symmetry interval [ - λ [ - λ [ ]]dAnd [ - λ [ ]]In generating recessive parameters at random
Figure BDA0002957950460000021
And
Figure BDA0002957950460000022
substituting the generated implicit parameters into an activation function to establish an output matrix of the kth implicit layer node:
Figure BDA0002957950460000023
and taking the newly added hidden layer node satisfying the following inequality constraint as a candidate hidden layer node:
ξk≥0
wherein ,
Figure BDA0002957950460000031
further, the step S4 includes:
calculating xi corresponding to the nodes of the candidate hidden layerkObtain a set of variables, i.e.
Figure BDA0002957950460000032
Finding the maximum ξ from the set of variableskCorresponding implicit parameters are taken as the optimal implicit parameters meeting inequality constraints
Figure BDA0002957950460000033
And
Figure BDA0002957950460000034
if the generated implicit parameter does not meet the constraint condition, the learning parameter r needs to be adjusted: increasing the value of r to relax the constraint and repeating the steps S3 and S4, i.e., r + τ, where τ is a random number within the interval (0, 1-r);
at this time, the hidden layer output matrix H of the incremental random weight networkkComprises the following steps:
Figure BDA0002957950460000035
wherein ,
Figure BDA0002957950460000036
further, the step S5 includes:
updating the output weight of the whole network by a ridge regression method:
Figure BDA0002957950460000037
the residual error of the current network is calculated as: e.g. of the typek=T-Hkβ*
If the current network residual ekWithin a tolerable error epsilon or k is greater than a predetermined maximum number L of hidden layer nodesmaxAnd then, no new hidden layer node is added, and the modeling is completed.
Has the advantages that:
the invention discloses a method for estimating underground supply air volume based on a regularized incremental random weight network. Meanwhile, the 2 norm regularization method is introduced to balance modeling precision and model complexity to avoid the over-fitting problem, so that not only is estimation precision ensured, but also the complexity of a network is reduced.
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FIG. 1 is a flow chart of a downhole supply air volume estimation method based on a regularization incremental random weight network according to the present application;
fig. 2 is a structural diagram of a switching process of a main ventilator according to a first embodiment, wherein 1 is an underground mine, 2 is an underground supply air flow, 3 is a first vertical air door, 4 is a first horizontal air door, 5 is a first impeller, 6 is a first motor, 7 is a second vertical air door, 8 is a second horizontal air door, 9 is a second impeller, and 10 is a second motor;
fig. 3 is an effect diagram of the downhole supply air volume estimation method based on the regularization incremental random weight network.
Detailed Description
Embodiments of the invention will be described in detail hereinafter with reference to the examples of embodiments shown in the drawings.
As shown in fig. 1, the method for estimating the downhole supply air volume based on the regularized incremental random weight network according to the embodiment of the present invention specifically includes the following steps:
and S1, analyzing the switching process of the main mine ventilator to obtain a group of variables influencing the change of the underground supply air volume, and using the variables as the input of a data-driven underground supply air volume model.
The input of the regularized incremental random weight network soft measurement model is a set of variables highly correlated with the underground supply air volume, and comprises the following steps: wind resistance R of horizontal air door of two main ventilators1s and R2sVertical air door windage R1c and R2cPressure head H1d and H2dAnd wind resistance R of underground mine0(ii) a The output variable is the downhole supply air volume.
Next, to implement the method for estimating the underground supply air volume based on the regularization incremental random weight network according to the embodiment of the present invention, a given number of main ventilator switching process data sets need to be generated and preprocessed. In particular, for a given main ventilator switching process data set containing N samples, let X ═ { X ═ X1,x2,...,xN},
Figure BDA0002957950460000041
For input data, T ═ T1,t2,...,tN},
Figure BDA0002957950460000042
And finally, normalizing all input and output data to output samples.
And S2, setting initialization parameters of the model.
Parameters involved in regularization incremental random weight network training are as follows: maximum number of hidden layer nodes LmaxRegularization coefficient C, implicit parameter configuration times TmaxTolerable error epsilon, learning parameter r, adjusting factor gamma, recessive parameter selection range gamma: λ ═ λmin:Δλ:λmaxThe initial hidden layer node number of the model is theta1Residual error of e0And order e0For the output T of the sample, the training of the model is from Θ1Initially, the hidden layer nodes are added one by one.
And S3, establishing a new constraint condition to generate a group of candidate hidden layer nodes according to the characteristics of the network residual error in the iterative learning.
And (3) randomly selecting implicit parameters (input weight w and bias b) from the variable symmetric interval [ -lambda, lambda ], reserving the implicit parameters meeting inequality constraints, and using the implicit parameters to form candidate hidden layer nodes.
Specifically, when constructing the kth hidden layer node, the kth hidden layer node is firstly and respectively divided from the variable symmetric regionM [ - λ [ ]]dAnd [ - λ [ ]]In generating recessive parameters at random
Figure BDA0002957950460000051
And
Figure BDA0002957950460000052
then, the recessive parameters are sent to an activation function (such as a sigmoid activation function) to form an output matrix of the hidden layer node:
Figure BDA0002957950460000053
and finally, screening the generated hidden layer nodes by adopting the following inequality constraints, wherein the hidden layer nodes meeting the constraints are taken as candidate hidden layer nodes:
ξk≥0
wherein ,
Figure BDA0002957950460000054
it should be noted that the current amount of network residual error reduction is:
Figure BDA0002957950460000055
wherein ,
Figure BDA0002957950460000056
and outputting a reference variable of the weight value for the kth hidden layer node. Thus, the inequality described above may be used to guide the configuration of the hidden layer node parameters.
And S4, selecting one node with the best quality from the candidate hidden layer nodes as a new hidden layer node.
And finding out the implicit parameter which enables the network residual error to be reduced maximally as the optimal implicit parameter, and substituting the optimal implicit parameter into the activation function to form a newly-added implicit layer node. If candidate hidden layer nodes meeting the constraint cannot be found, relaxing the constraint of the inequality on the hidden parameters: r + τ is updated, where τ is a random number within the section (0,1-r), and steps S3 and S4 are repeated.
Specifically, the method is firstly retained through inequality constraint screeningSubstituting next candidate hidden layer node into xikCalculating to obtain a group
Figure BDA0002957950460000057
Then finding out the maximum xi by comparisonkThe corresponding implicit parameter is the best implicit parameter after inequality constraint screening
Figure BDA0002957950460000058
And
Figure BDA0002957950460000059
if the implicit parameter does not exist, the learning parameter r needs to be adjusted: the constraints of the inequality are relaxed and steps S3 and S4 are repeated, i.e., r ═ r + τ where τ e (0,1-r) until the best implicit parameter is found. It should be noted that r can be set to a positive number close to 1 in order to find implicit parameters satisfying inequality constraints more easily. At this time, the hidden layer output matrix H of the incremental random weight networkkComprises the following steps:
Figure BDA00029579504600000510
wherein ,
Figure BDA00029579504600000511
and S5, introducing a 2-norm regularization term into a secondary loss function, updating the output weight of the whole network by adopting a global regularization least square method until the modeling is finished when the set maximum number of hidden layer nodes is reached or the acceptable tolerance is met, and obtaining the underground supply air volume estimation model based on the regularization incremental random weight network.
Specifically, the output weights of the network are calculated by a global regularized least squares method:
the residual error of the current network is calculated as: e.g. of the typek=T-Hkβ*
At the current network residual ekWithin a tolerable error eIn range or k is greater than a predetermined maximum number L of hidden layer nodesmaxAnd then, a new hidden layer node is not added, modeling is completed, and the established regularization incremental random weight network can be used for estimating the underground supply air volume.
The method of the present invention will be described in detail with reference to an example of the switching process of the main blower shown in fig. 2, in which 1 is an underground mine and is connected to a common duct, 2 is the underground supply air flow from the underground mine and flows in the direction indicated by the arrow, the common duct is divided into two air ducts, a vertical air door is installed at the position where each air duct is connected to the common duct, a horizontal air door is installed above each air duct after the vertical air door, and an impeller is installed inside each air duct after the horizontal air door and connected to a motor to rotate the air duct. 3. 4, 5 and 6 are respectively a vertical air door, a horizontal air door, an impeller and a motor, and 7, 8, 9 and 10 are respectively a vertical air door, a horizontal air door, an impeller and a motor on a second main ventilator.
Firstly, selecting seven variables highly related to the underground supply air volume as the input of an estimation model in the switching process of a main ventilator to realize the estimation of the underground supply air volume; setting initialization parameters of the model; obtaining candidate hidden layer nodes through constraint screening according to the given number of the candidate hidden layer nodes; finding out nodes which enable the network residual error to be reduced most quickly from the candidate hidden layer nodes as new nodes; and updating the weight of the whole network by using a global regularization least square method, and estimating the current underground supply air volume according to the main ventilator switching process data acquired in real time after modeling is completed, so as to obtain the operation index of the whole network.
Referring to the above embodiment, the method for estimating the downhole supply air volume based on the regularized incremental random weight network according to the embodiment of the present invention includes the following steps:
the first step is as follows: and in the switching process of the main ventilator, finding out the process variable which has the greatest influence on the underground supply air volume as an input variable so as to realize the estimation of the underground supply air volume. Wherein, the related input variable is the windage R of the horizontal air door of the two main ventilators1s(Kg/m7) and R2s(Kg/m7) Vertical air door windage R1c(Kg/m7) and R2c(Kg/m7) Pressure head H1d(Pa) and H2d(Pa) and underground mine wind resistance R0(Kg/m7) And the output variable is the underground supply air quantity. 1500 data samples were collected during the actual main ventilator switching process, wherein 1400 samples were used as the training data set of the model, and the remaining 100 samples constitute the test data set, i.e.: x ═ X1,x2,...,x1400},
Figure BDA0002957950460000061
For the input sample, T ═ T1,t2,...,t1400},
Figure BDA0002957950460000062
To output samples. Wherein x isi=[R1s,R2s,R1c,R2c,H1d,H2d,R0]. Then, normalization processing is performed on the input and output samples described above.
The second step is that: setting the initialization parameters of the learning model, and setting the maximum number L of hidden layer nodes max50, regularization coefficient C24Implicit parameter configuration times Tmax200, tolerable error epsilon is 0.02, learning parameter r is 0.9, regulating factor gamma is 3, recessive parameter selection range upsilon: 1:0.1:5, the initial number of hidden layer nodes Θ of the model11, residual error e0And selecting a Sigmoid function as an activation function.
The third step: when the kth hidden layer node is added, according to the given hidden parameter configuration times, in a variable hidden parameter selection interval, 200 groups of hidden parameters (input weight w and bias b) are randomly generated, and a corresponding hidden layer output matrix h is solvedk. Then, constrained by inequality
Figure BDA0002957950460000071
And screening hidden layer nodes meeting the constraint as candidate hidden layer nodes.
The fourth step: make xi in the candidate nodekThe maximum implicit parameter is used as the optimal implicit parameter, and a newly added node is formed and added into the network; simultaneously obtaining output matrix of newly added node
Figure BDA0002957950460000072
When no candidate hidden layer node satisfying the constraint is found, then the value of r is changed to relax the inequality constraint, i.e., r + τ, where τ ∈ (0,1-r), and then the third and fourth steps are repeated.
The fifth step: according to the output matrix of the candidate hidden layer node obtained by calculation
Figure BDA0002957950460000073
Hidden layer output matrix composing current network
Figure BDA0002957950460000074
And calculating the output weight of the network by global regularization least square method
Figure BDA0002957950460000075
Further obtaining the residual error e of the current networkk=T-Hkβ*
And when the number of the hidden layer nodes is more than 50 or the current network residual error is in the interval of [0,0.02], stopping the construction of the network and ending the modeling. The remaining 100 samples were finally used for testing. FIG. 3 is a diagram of the effect of estimating the downhole supply air volume of a regularized incremental random weight network model. As can be seen from FIG. 3, the estimated values of the model substantially match the real values, which illustrates the high modeling accuracy of the model provided by the present invention.

Claims (6)

1. A downhole supply air volume estimation method based on a regularization incremental random weight network is characterized by comprising the following steps:
s1, analyzing the switching process of the main mine ventilator to obtain a group of variables influencing the change of the underground supply air volume, and using the variables as the input of a data-driven underground supply air volume model;
s2, setting initialization parameters of the model;
s3, establishing a new constraint condition to generate a group of candidate hidden layer nodes according to the characteristics of the network residual error in iterative learning;
s4, selecting one node with the best quality from the candidate hidden layer nodes as a new hidden layer node;
and S5, introducing a 2-norm regularization term into a secondary loss function, updating the output weight of the whole network by adopting a global regularization least square method until the modeling is finished when the set maximum number of hidden layer nodes is reached or the acceptable tolerance is met, and obtaining the underground supply air volume estimation model based on the regularization incremental random weight network.
2. The method for estimating downhole supply air volume based on the regularized incremental random weight network according to claim 1, wherein the step S1 comprises:
a group of variables with the strongest correlation with the underground supply air volume are used as input variables of the model, and the method comprises the following steps: wind resistance R of horizontal air door of two main ventilators1s and R2sVertical air door windage R1c and R2cPressure head H1d and H2dAnd wind resistance R of underground mine0And the output variable is the underground supply air quantity.
3. The method for estimating downhole supply air volume based on the regularized incremental random weight network according to claim 1, wherein the step S2 comprises:
parameters required for model training are given, including: maximum number of hidden layer nodes LmaxRegularization coefficient C, implicit parameter configuration times TmaxTolerable error epsilon, learning parameter r, adjusting factor gamma, recessive parameter selection range gamma: λ ═ λmin:Δλ:λmaxThe initial hidden layer node number of the model is theta1Residual error of e0And order e0For the output T of the sample, the training of the model is from Θ1Initially, the hidden layer nodes are added one by one.
4. The method for estimating downhole supply air volume based on the regularized incremental random weight network according to claim 1, wherein the step S3 comprises:
when adding the kth hidden layer node, respectively from the variable symmetry interval [ - λ [ - λ [ ]]dAnd [ - λ [ ]]In generating recessive parameters at random
Figure FDA0002957950450000011
And
Figure FDA0002957950450000012
substituting the generated implicit parameters into an activation function to establish an output matrix of the kth implicit layer node:
Figure FDA0002957950450000013
and taking the newly added hidden layer node satisfying the following inequality constraint as a candidate hidden layer node:
ξk≥0
wherein ,
Figure FDA0002957950450000021
5. the method for estimating downhole supply air volume based on the regularized incremental random weight network according to claim 1, wherein the step S4 comprises:
calculating xi corresponding to the nodes of the candidate hidden layerkObtain a set of variables, i.e.
Figure FDA0002957950450000022
Finding the maximum ξ from the set of variableskCorresponding implicit parameters are taken as the optimal implicit parameters meeting inequality constraints
Figure FDA0002957950450000023
And
Figure FDA0002957950450000024
if the generated implicit parameter does not meet the constraint condition, the learning parameter r needs to be adjusted: increasing the value of r to relax the constraint and repeating the steps S3 and S4, i.e., r + τ, where τ is a random number within the interval (0, 1-r);
at this time, the hidden layer output matrix H of the incremental random weight networkkComprises the following steps:
Figure FDA0002957950450000025
wherein ,
Figure FDA0002957950450000026
6. the method for estimating downhole supply air volume based on the regularized incremental random weight network according to claim 1, wherein the step S5 comprises:
updating the output weight of the whole network by a ridge regression method:
Figure FDA0002957950450000027
the residual error of the current network is calculated as: e.g. of the typek=T-Hkβ*
If the current network residual ekWithin a tolerable error epsilon or k is greater than a predetermined maximum number L of hidden layer nodesmaxAnd then, no new hidden layer node is added, and the modeling is completed.
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CN114186771B (en) * 2021-10-22 2024-07-02 盐城工学院 Mixed regularized random configuration network industrial process operation index estimation method

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