CN112926266B - Underground air supply quantity estimation method based on regularized incremental random weight network - Google Patents
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Abstract
The application discloses an underground air supply quantity estimation method based on a regularized incremental random weight network, which comprises the following steps: a group of variables influencing the change of underground air supply quantity are obtained through analysis of the switching process of the main mine ventilator and are used as the input of a data-driven underground air supply quantity model; setting initialization parameters of a 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 hidden layer node with the best quality from the candidate hidden layer nodes as a newly added hidden layer node; 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 modeling is finished when the set maximum hidden layer node number is reached or acceptable tolerance is met, and obtaining an underground air supply volume estimation model based on a regularized incremental random weight network. The method can not only effectively improve the estimation precision of the model, but also avoid the problem of over fitting.
Description
Technical Field
The application relates to the technical field of mine ventilation, in particular to an underground air supply quantity estimation method based on a regularized incremental random weight network.
Background
The main ventilator switching process is widely used to ensure continuous safe production of mines. According to the requirements of the coal mine safety regulations, the mine adopts a mode of 'one main fan and one standby fan' to alternately operate the two main fans. One of the running fans is called a working fan, and the other is called a standby fan. The underground air supply quantity is used as a key operation index of the switching process of the main ventilator, so that the underground operation is greatly affected, and accurate measurement is needed to ensure the stability and safety of the switching process of the main ventilator and provide sufficient underground air supply quantity. However, due to the severe environment, the pressure-taking hole of the air volume measuring device is easy to be blocked, frequent maintenance is required, and the change of underground air volume supply is difficult to monitor in real time for mine staff. Therefore, an accurate reliability model of the underground air supply quantity is necessary to be established, and the underground air supply quantity information is reflected for workers.
Currently, a common method is to estimate it using a mechanism model or a data driven model. The mechanism model is generally based on some theoretical assumption, and important parameters of the model are difficult to accurately acquire, so that certain deviation can be generated when the mechanism model is used for estimating the operation index. The modeling technology based on data driving can establish an estimation model of the operation index by using input and output data without knowing complex changes of the switching process, so that the estimation of the operation index is carried out by adopting the model based on the data.
In recent years, BP (back propagation) neural networks, elman neural networks, and RBF (radial basis function) neural networks have been widely used in the estimation of operation indexes. However, these neural networks use a gradient descent method with slow convergence to train parameters, resulting in learning at a rate far below the expected rate. As a single hidden layer feedforward neural network, the hidden parameters of the incremental random weight network are randomly generated, and the output weight of the network is obtained by solving a linear equation. Meanwhile, in the process of constructing the network, only one newly added node is added each time until the modeling task is completed. Thus, the incremental random weight network has a simple structure and extremely fast learning speed. However, when the hidden layer nodes are too many, the network structure becomes complex, and the problem of over fitting is easy to generate, so that the generalization performance is reduced, and the practical application of the model is limited.
Disclosure of Invention
The application aims to provide an underground air supply quantity estimation method based on a regularized incremental random weight network, which not only has higher estimation precision, but also can effectively avoid the problem of overfitting in a conventional incremental random weight network, and can be well applied to underground air supply quantity estimation.
The application provides an underground air supply quantity estimation method based on a regularized incremental random weight network, which comprises the following steps of:
s1, obtaining a group of variables influencing the change of underground air supply quantity through analysis of a switching process of a main mine ventilator, and taking the variables as input of a data-driven underground air supply quantity model;
s2, setting initialization parameters of a model;
s3, establishing a new constraint condition to generate a group of candidate hidden layer nodes according to the characteristics of the network residual errors in iterative learning;
s4, selecting one hidden layer node with the best quality from the candidate hidden layer nodes as a newly added hidden layer node;
s5, introducing a 2-norm regularization term into a secondary loss function, and updating the output weight of the whole network by adopting a global regularization least square method until modeling is finished when the set maximum hidden layer node number is reached or acceptable tolerance is met, so as to obtain an underground air supply volume estimation model based on the regularized incremental random weight network.
Further, the step S1 includes:
the method takes a group of variables with the strongest relevance to the underground air supply quantity as input variables of a model, and comprises the following steps: horizontal air door windage R of two main ventilators 1s and R2s Vertical damper wind resistance R 1c and R2c Pressure head H 1d and H2d Wind resistance R of underground mine 0 The output variable is the underground air supply quantity.
Further, the step S2 includes:
parameters required for training a given model include: maximum hidden layer node number L max Regularization coefficient C, recessive parameter configuration times T max Tolerance error epsilon, learning parameter r, adjusting factor gamma, recessive parameter selection range gamma: = { λ min :Δλ:λ max The initial hidden layer node number of the record model is theta 1 Residual is e 0 And let e 0 For the output T of the sample, training of the model is performed from Θ 1 Initially, hidden layer nodes are added one by one.
Further, the step S3 includes:
when adding the kth hidden layer node, respectively fromVariable symmetry interval [ -lambda [ -lambda ]] d And [ -lambda ]]Randomly generated implicit parameters and />
Substituting the generated hidden parameters into an activation function, and establishing an output matrix of the kth hidden layer node:
taking the newly added hidden layer node meeting the following inequality constraint as a candidate hidden layer node:
ξ k ≥0
wherein ,
further, the step S4 includes:
calculating xi corresponding to candidate hidden layer node k Obtaining a set of variables, i.e
Finding the maximum ζ from the set of variables k Corresponding hidden parameters are used as optimal hidden parameters meeting inequality constraint and />
If the generated implicit parameters do not meet the constraint conditions, the learning parameters r need to be adjusted: increasing the value of r to relax the constraint and repeating steps S3 and S4, i.e., r=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 network k The method comprises the following steps:
wherein ,
further, the step S5 includes:
updating the output weight of the whole network by a ridge regression method:
the residual error of the current network is calculated as follows: e, e k ＝T-H k β * ；
If the current network residual error e k Within the tolerable error epsilon range or k greater than the preset maximum hidden layer node number L max And (3) no new hidden layer node is added, and modeling is completed.
The beneficial effects are that:
the application discloses an underground air supply quantity estimation method based on a regularized incremental random weight network, which starts from a small-size model, adopts compact inequality constraint to optimize hidden parameters (input weight and bias) and obtains a high-quality newly-added hidden layer node. Meanwhile, the 2-norm regularization method is introduced to balance modeling precision and model complexity to avoid the problem of overfitting, so that estimation precision is ensured, and network complexity is reduced.
Drawings
FIG. 1 is a flow chart of a method for estimating the underground air supply quantity based on a regularized incremental random weight network;
FIG. 2 is a schematic diagram of a primary ventilator switching process for an embodiment I, wherein 1. The underground mine 2. The downhole supply wind flow 3. The vertical damper 4. The horizontal damper 5. The impeller 6. The motor 7. The vertical damper 8. The horizontal damper 9. The impeller 10. The motor II;
FIG. 3 is an effect diagram of the method for estimating the underground air supply quantity based on the regularized incremental random weight network.
Detailed Description
Embodiments of the present application will be described in detail below with reference to examples of embodiments shown in the drawings.
According to the embodiment of the application, as shown in fig. 1, the method for estimating the underground air supply quantity based on the regularized incremental random weight network comprises the following specific steps:
s1, a group of variables influencing the change of underground air supply quantity are obtained through analysis of a switching process of a main mine ventilator, and are used as input of a data-driven underground air supply quantity model.
The inputs to the regularized incremental random weight network soft measurement model are a set of variables highly correlated to the supply air volume downhole, comprising: horizontal air door windage R of two main ventilators 1s and R2s Vertical damper wind resistance R 1c and R2c Pressure head H 1d and H2d Wind resistance R of underground mine 0 The method comprises the steps of carrying out a first treatment on the surface of the The output variable is the underground air supply quantity.
Next, to implement the method for estimating the underground air supply volume based on the regularized incremental random weight network according to the embodiment of the present application, a given number of main ventilator switching process data sets needs to be generated and preprocessed. Specifically, let x= { X for a given main ventilator switching process data set containing N samples 1 ,x 2 ,...,x N },To input data, t= { T 1 ,t 2 ,...,t N },/>And finally, carrying out normalization processing on all input and output data for outputting samples.
S2, setting initialization parameters of a model.
The parameters involved in regularized incremental random weight network training are as follows: maximum hidden layer node number L max Regularization coefficient C, recessive parameter configuration times T max Tolerance error epsilon, learning parameter r, adjusting factor gamma, recessive parameter selection range gamma: = { λ min :Δλ:λ max The initial hidden layer node number of the record model is theta 1 Residual is e 0 And let e 0 For the output T of the sample, training of the model is performed from Θ 1 Initially, hidden layer nodes are added one by one.
S3, establishing a new constraint condition to generate a group of candidate hidden layer nodes according to the characteristics of the network residual errors in iterative learning.
The implicit parameters (input weight w and bias b) are randomly selected from the variable symmetry interval [ -lambda, lambda ], remain the implicit parameters satisfying the inequality constraint, and are used to construct candidate hidden layer nodes.
Specifically, when constructing the kth hidden layer node, the variable symmetry interval [ -lambda ] is firstly respectively selected from] d And [ -lambda ]]Randomly generated implicit parameters and />Then, the hidden parameters are sent into an activation function (such as a sigmoid activation function) to form an output matrix of hidden layer nodes: />And finally, screening the generated hidden layer nodes by adopting the following inequality constraint, wherein the hidden layer nodes meeting the constraint serve as candidate hidden layer nodes:
ξ k ≥0
wherein ,
it should be noted that, the current network residual error drop amount is:
wherein ,/>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 hidden layer node parameters.
S4, selecting one hidden layer node with the best quality from the candidate hidden layer nodes as a newly added hidden layer node.
And finding out the hidden parameter which makes the network residual error decrease the most as the optimal hidden parameter, and substituting the optimal hidden parameter into the activation function to form the newly added hidden layer node. If no candidate hidden layer node meeting the constraint can be found, the constraint of the inequality on the hidden parameters is relaxed: updating r=r+τ, where τ is a random number within the interval (0, 1-r), and repeating steps S3 and S4.
Specifically, the candidate hidden layer node which is preserved through inequality constraint screening is substituted into xi k Calculating to obtain a group ofAnd then the maximum zeta is found out by comparison k The corresponding hidden parameter is the optimal hidden parameter which is subjected to inequality constraint screening +.> and />If the hidden parameter does not exist, the learning parameter r needs to be adjusted: relaxing the constraint of the inequality and repeating steps S3 and S4, i.e. r=r+τ, where τ e (0, 1-r) until the best implicit parameters are foundUntil that point. It should be noted that r may be set to a positive number close to 1 in order to find the implicit parameter satisfying the inequality constraint more easily. At this time, the hidden layer output matrix H of the incremental random-weight network k The method comprises the following steps:
wherein ,
s5, introducing a 2-norm regularization term into a secondary loss function, and updating the output weight of the whole network by adopting a global regularization least square method until modeling is finished when the set maximum hidden layer node number is reached or acceptable tolerance is met, so as to obtain an underground air supply volume estimation model based on the regularized incremental random weight network.
Specifically, the output weight of the network is calculated by a global regularized least square method:
the residual error of the current network is calculated as follows: e, e k ＝T-H k β * ；
At the current network residual e k Within the tolerable error epsilon range or k greater than the preset maximum hidden layer node number L max When the method is used, new hidden layer nodes are not added, modeling is completed, and the built regularized incremental random weight network can be used for estimating underground air supply quantity.
The method according to the application will be described in detail below with reference to the example of a main ventilator switching process shown in fig. 2, in which 1 is an underground mine and is connected to a common duct, 2 is the underground supply air volume flowing from the underground mine, and this common duct is divided into two air ducts, each air duct being connected to the common duct by means of an arrow, a vertical damper being arranged at the location where each air duct is connected to the common duct, a horizontal air damper being arranged above each air duct after the vertical damper, and an impeller being arranged inside each air duct after the horizontal damper and being connected to a motor for rotation. 3. And 4, 5 and 6 are respectively a vertical air door, a horizontal air door, a first impeller and a first motor, and 7, 8, 9 and 10 are respectively a vertical air door, a horizontal air door, an impeller and a motor on the second main ventilator.
Firstly, in the switching process of a main ventilator, seven variables which are highly related to the underground air supply quantity are selected as the input of an estimation model, so that the estimation of the underground air supply quantity is realized; setting initialization parameters of a model; obtaining candidate hidden layer nodes through constraint screening according to the given number of the candidate hidden layer nodes; finding out the node which is the most rapid in the network residual error from the candidate hidden layer nodes as a newly added node; the weight of the whole network is updated through a global regularized least square method, and after modeling is completed, the current underground supply air quantity is estimated according to the main ventilator switching process data acquired in real time, so that the operation index of the underground supply air quantity is obtained.
With reference to the above embodiment, the method for estimating the underground air supply volume based on the regularized incremental random weight network according to the embodiment of the present application includes the following steps:
the first step: in the switching process of the main ventilator, the process variable with the greatest influence on the underground air supply quantity is found to serve as an input variable, so that the underground air supply quantity is estimated. Wherein the input variable involved is the wind resistance R of the horizontal air door of the two main ventilators 1s (Kg/m 7) and R2s (Kg/m 7 ) Vertical damper wind resistance R 1c (Kg/m 7) and R2c (Kg/m 7 ) Pressure head H 1d(Pa) and H2d (Pa) and wind resistance R of underground mine 0 (Kg/m 7 ) The output variable is the underground air supply quantity. 1500 data samples were collected during the actual main ventilator switching process, 1400 samples were used as training data set for the model, and the remaining 100 samples constituted the test data set, namely: x= { X 1 ,x 2 ,...,x 1400 },To input samples, t= { T 1 ,t 2 ,...,t 1400 },/>To output samples. Wherein x is i ＝[R 1s ,R 2s ,R 1c ,R 2c ,H 1d ,H 2d ,R 0 ]. Then, the input and output samples described above are normalized.
And a second step of: setting initialization parameters of a learning model and setting the maximum hidden layer node number L max =50, regularization coefficient c=2 4 Implicit parameter configuration times T max 200, tolerable error ε=0.02, learning parameter r=0.9, adjustment factor γ=3, implicit parameter selection range γ: = {1:0.1:5}, initial hidden layer node number Θ of model 1 =1, residual is e 0 =t, choosing the Sigmoid function as the activation function.
And a third step of: when the kth hidden layer node is added, 200 groups of hidden parameters (input weight w and bias b) are randomly generated in a variable hidden parameter selection interval according to given hidden parameter configuration times, and a corresponding hidden layer output matrix h is obtained k . Then, constraint by inequalityHidden layer nodes meeting the constraint are screened out and used as candidate hidden layer nodes.
Fourth step: causing xi in candidate node k The maximum hidden parameter is used as the optimal hidden parameter, and a new node is formed and added into the network; simultaneously obtain the output matrix of the newly added nodesWhen no candidate hidden layer node satisfying the constraint is found, then the value of r is changed to relax the constraint of the inequality, i.e. r=r+τ, where τ e (0, 1-r), followed by repeating the third and fourth steps.
Fifth step: according to the calculated output matrix of the candidate hidden layer nodeImplicit layer transport to compose a current networkGo out matrix->And calculates the output weight of the network by global regularization least square methodThereby obtaining the residual error e of the current network k ＝T-H k β * 。
And stopping the construction of the network and ending the modeling when the number of hidden layer nodes is more than 50 or the current network residual error falls in the [0,0.02] interval. Finally the remaining 100 samples were used for testing. Fig. 3 is a graph of the effect of regularized incremental random weight network model on the estimation of the air supply quantity downhole. From fig. 3, it can be seen that the estimated value of the model substantially coincides with the true value, which illustrates that the model modeling accuracy provided by the application is high.
Claims (6)
1. The underground air supply quantity estimation method based on the regularized incremental random weight network is characterized by comprising the following steps of:
s1, obtaining a group of variables influencing the change of underground air supply quantity through analysis of a switching process of a main mine ventilator, and taking the variables as input of a data-driven underground air supply quantity model;
s2, setting initialization parameters of a model;
s3, establishing a new constraint condition to generate a group of candidate hidden layer nodes according to the characteristics of the network residual errors in iterative learning;
s4, selecting one hidden layer node with the best quality from the candidate hidden layer nodes as a newly added hidden layer node;
s5, introducing a 2-norm regularization term into a secondary loss function, and updating the output weight of the whole network by adopting a global regularization least square method until modeling is finished when the set maximum hidden layer node number is reached or acceptable tolerance is met, so as to obtain an underground air supply volume estimation model based on the regularized incremental random weight network.
2. The method for estimating the air supply quantity under the well based on the regularized incremental random weight network according to claim 1, wherein the step S1 comprises:
the method takes a group of variables with the strongest relevance to the underground air supply quantity as input variables of a model, and comprises the following steps: horizontal air door windage R of two main ventilators 1s and R2s Vertical damper wind resistance R 1c and R2c Pressure head H 1d and H2d Wind resistance R of underground mine 0 The output variable is the underground air supply quantity.
3. The method for estimating the air supply quantity under the well based on the regularized incremental random weight network according to claim 1, wherein the step S2 comprises:
parameters required for training a given model include: maximum hidden layer node number L max Regularization coefficient C, recessive parameter configuration times T max Tolerance error epsilon, learning parameter r, adjusting factor gamma, recessive parameter selection range gamma: = { λ min :Δλ:λ max The initial hidden layer node number of the record model is theta 1 Residual is e 0 And let e 0 For the output T of the sample, training of the model is performed from Θ 1 Initially, hidden layer nodes are added one by one.
4. The method for estimating the supply air volume under the well based on the regularized incremental random weight network according to claim 3, wherein the step S3 comprises:
when the kth hidden layer node is added, the variable symmetry interval [ -lambda ] is respectively used for] d And [ -lambda ]]Randomly generated implicit parameters and />
Substituting the generated hidden parameters into an activation function, and establishing an output matrix of the kth hidden layer node:
taking the newly added hidden layer node meeting the following inequality constraint as a candidate hidden layer node:
ξ k ≥0
wherein ,
5. the method for estimating the air supply quantity under the well based on the regularized incremental random weight network according to claim 4, wherein the step S4 comprises:
calculating xi corresponding to candidate hidden layer node k Obtaining a set of variables, i.e
Finding the maximum ζ from the set of variables k Corresponding hidden parameters are used as optimal hidden parameters meeting inequality constraint and />
If the generated implicit parameters do not meet the constraint conditions, the learning parameters r need to be adjusted: increasing the value of r to relax the constraint and repeating steps S3 and S4, i.e., r=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 network k The method comprises the following steps:
wherein ,
6. the method for estimating the air supply quantity under the well based on the regularized incremental random weight network according to claim 5, wherein the step S5 comprises:
updating the output weight of the whole network by a ridge regression method:
the residual error of the current network is calculated as follows: e, e k ＝T-H k β * ；
If the current network residual error e k Within the tolerable error epsilon range or k greater than the preset maximum hidden layer node number L max And (3) no new hidden layer node is added, and modeling is completed.
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