CN112364527A - Debutanizer soft measurement modeling method based on ALIESN online learning algorithm - Google Patents

Debutanizer soft measurement modeling method based on ALIESN online learning algorithm Download PDF

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CN112364527A
CN112364527A CN202011402628.6A CN202011402628A CN112364527A CN 112364527 A CN112364527 A CN 112364527A CN 202011402628 A CN202011402628 A CN 202011402628A CN 112364527 A CN112364527 A CN 112364527A
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岳文琦
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Abstract

The invention discloses a debutanizer soft measurement modeling method based on an ALIESN online learning algorithm. The method normalizes key variables to obtain auxiliary variables and main variables, and then carries out dynamic modeling to convert the auxiliary variables and the main variables which only have a time sequence with static characteristics into ALIESN input variables with dynamic characteristics; then, performing off-line training learning on the first n data of the ALIESN input variables by adopting an ALIESN ridge regression off-line learning algorithm to obtain a neural network off-line training output weight; and finally, taking the upper numerical value as an initial weight of online learning, starting online output weight training by inputting the n +1 th data of the variable by the ALIESN, and obtaining a final network output weight and a predicted output variable. The method has the advantages of simple and quick learning algorithm, low cost, less training data, strong approximation capability of a dynamic nonlinear system and the like, is high in network output weight speed, improves the prediction precision of butane content, and meets the requirement of real-time learning in the fine chemical engineering process.

Description

Debutanizer soft measurement modeling method based on ALIESN online learning algorithm
Technical Field
The invention relates to a debutanizer soft measurement modeling method based on an Augmented Leakage Integral Echo State Network (ALIESN) fast online learning algorithm, belongs to the field of soft measurement, and particularly relates to a debutanizer soft measurement modeling method based on an ALIESN online learning algorithm.
Background
In the chemical process, the real-time online monitoring of important variables plays an extremely important role in product quality control. However, these variables are often in the environment of high temperature, strong nonlinearity, strong radiation and rapid change in the chemical process, and cannot be directly, timely and accurately measured and collected, so that the soft measurement technology is applied.
In recent decades, the soft measurement technology has been developed rapidly, and particularly, the soft measurement modeling method based on the neural network has been applied to the actual chemical process by many enterprises and scientific research institutions, so that a good application effect is achieved. However, in the existing soft measurement modeling method based on the neural network in the chemical process, the problems of complex algorithm, need of learning and training by a large data set, long sampling time of input and output variables, long learning time, high learning cost, incapability of rapidly achieving high learning precision in real time and the like generally exist, so that the monitoring of important variables cannot meet the relevant precision requirements of the fine chemical industry.
Disclosure of Invention
The invention aims to provide a debutanizer soft measurement modeling method based on an Augmented Leakage Integral Echo State Network (ALIESN) fast online learning algorithm. The method comprises the steps of firstly carrying out normalization pretreatment on collected key variables to obtain auxiliary variables and main variables, and then carrying out dynamic modeling on the auxiliary variables and the main variables by using a nonlinear autoregressive model (NARX), so that the auxiliary variables and the main variables only having a static characteristic time sequence are converted into ALIESN input variables having dynamic characteristics; then, performing off-line training learning on the first n data of the ALIESN input variables by adopting an ALIESN ridge regression off-line learning algorithm to obtain a neural network off-line training output weight; and finally, taking the neural network training output weight as an initial weight for online learning, and starting online output weight training by inputting the n +1 th data of the variable by ALIESN to obtain a final network output weight and a predicted output variable. The method has the advantages of simple and quick learning algorithm, low learning cost, less training data, strong approximation capability of a dynamic nonlinear system and the like, is high in network output weight speed, improves the prediction precision of butane content, and meets the requirement of real-time learning in the fine chemical engineering process.
In order to achieve the purpose, the debutanizer soft measurement modeling method based on the ALIESN online learning algorithm comprises the following steps:
firstly, carrying out normalization pretreatment on key variables acquired by a sensor to obtain auxiliary variables and main variables, and carrying out dynamic modeling on the auxiliary variables and the main variables by adopting an NARX model to generate ALIESN input variables with dynamic characteristics;
secondly, performing off-line training learning on the first n data of the ALIESN input variables by adopting an ALIESN ridge regression off-line learning algorithm to obtain a neural network off-line training output weight;
and finally, taking the neural network offline training output weight as an initial weight for online learning, and carrying out online training on the output weight from the (n +1) th data of the ALIESN input variable to obtain a final network output weight and a predicted output variable.
The debutanizer soft measurement modeling method based on the ALIESN online learning algorithm comprises the following steps: the method comprises the following steps:
(1) collecting data under normal conditions of key variables in a butane production process, the key variables comprising essentially X1Top temperature value, X2Top pressure value, X3Top butane reflux value, X4Butane flow value, X, to the next process5Temperature value X of ═ plate6Temperature value X in the bottom 1 region7Storing the data into a database respectively according to the temperature value of the bottom 2 area and the butane concentration y at the bottom of the debutanizer, wherein the sampling period of all variables is 12 min;
(2) preprocessing the key variables based on a Z-Score normalization method, and then removing abnormal value variables far greater than 1 to obtain a new data set with a zero mean value and a 1 variance, wherein the new data set is a time sequence consisting of auxiliary variables and main variables;
(3) adopting an NARX model to dynamically model the auxiliary variable and the main variable to obtain an ALIESN input variable with dynamic characteristics, wherein the ALIESN input variable with dynamic characteristics comprises a time sequence data set containing past information;
(4) inputting ALIESN of the previous n time sequences into a variable data set for off-line learning, and obtaining a neural network off-line training output weight based on a least square method through an ALIESN ridge regression off-line learning algorithm;
(5) taking Mean Square Error (MSE) as an evaluation index of network learning precision, calculating MSE of an output variable obtained by an offline learning algorithm and an output variable obtained by actual sampling, and performing the next step when the obtained MSE meets the precision requirement, or adding newly acquired data to an offline training data set for retraining until the precision requirement is met;
(6) after the neural network offline training output weight meeting the precision requirement is obtained, the output weight is used as an initial output weight for RLS online learning, online training of the output weight is carried out from the n +1 th data of the ALIESN input variable, and the final network output weight and the predicted output variable are obtained.
The key variables are X ═ { xi ∈ Rm } i ═ 1,2, …, n, y ∈ Rn, R is a real number set, wherein n is the number of samples, m is the number of auxiliary variables, and the number of main variables is 1.
The step (1) of collecting the key variables specifically comprises the following steps:
reading the values of primary input variable and primary output variable every 12min, storing 8 variables into database, and setting to x1(n) a top temperature value; x is the number of2(n) top pressure value; x is the number of3(n) top butane reflux value; x is the number of4(n) the butane flow rate to the next process; x is the number of5(n) a tray temperature value; x is the number of6(n) the temperature value of the bottom 1; x is the number of7(n) the temperature value of the bottom 2; y (n) bottom butane concentration value;
the step (2) of normalizing the key variables specifically comprises the following steps:
the data were preprocessed by a normalization method with a mean of 0 and a variance of 1 using the Z-Score method, to obtain the auxiliary variables and the dominant variables, and the Z-Score calculation is defined as follows: u ═ x- μ)/σ; the x is an original score, u is a numerical value of a converted [0,1] interval, mu is a score mean value of the overall sample space, and sigma is a standard deviation of the overall sample space;
the step (4) of performing NARX dynamic modeling on the auxiliary variable and the main variable specifically comprises the following steps:
the following NARX model is adopted to convert 7 auxiliary variables and 1 main variable into 13 ALIESN input variables, and the input variables are input into a neural network to start learning:
y(k)=f(u1(k),u2(k),u3(k),u4(k),u5(k),u5(k-1),u5(u-2),u5(k-3),(u6(k)+u7(k))/2,y(k-1),y(k-2),y(k-3),y(k-4))。
the step (4) is specifically as follows:
setting the dimensions of variables of an input layer, a hidden layer and an output layer of the ALIESN network as K-13, N-50 and L-1 respectively, wherein neurons of the input layer, the hidden layer and the output layer of the network at N time are as follows:
Figure BDA0002812953750000041
the input connection weight matrix, the SR internal connection weight matrix, the output connection weight matrix and the feedback connection weight matrix fed back to the SR by the output are respectively expressed as:
Figure BDA0002812953750000042
the dimensions of each weight are as follows: dimension N × K, dimension N × N, dimension L × 2(K + N + L), dimension N × L;
② an input/output sequence with length T equal to 238 is given:
(u (1), d (1)), (u (2), d (2)), …, (u (T), d (T)) and input to the network, training the ALIESN network so that its output y (n) approximates the output d (n);
initializing the network, randomly taking value of SR initial state x (0), and inputting connection weight matrix WinAnd feedback connection weight matrix WbackTaking a value which follows normal uniform distribution, and internally connecting a sparse connection coefficient of a weight matrix W and a sparse matrix with the sparsity of min (10/N,1) in the SR;
the ALIESN (n +1) th moment state updating equation is as follows:
x(n+1)=(1-a)x(n)+f(Winu(n+1)+Wx(n)+Wbackd (n)), wherein when n is 0, d (0) is 0, x (0) is 0, and f is usually a symmetric Sigmoid function;
from time T0After 1, the "augmented" state (u (n), u) of double size was collected2(n))=(u1(n),...,uK+N+L(n),u1 2(n),...,uK+N+L 2(n)) enter the state collection matrix. This will produce an output weight matrix W of size 1 × 2(K + N + L)outThe order of the matrix M is (T-T)0+1) × 2(K + N + L); computing a pseudo-inverse (generalized inverse) M of M-1Similarly, the inverse hyperbolic tangent function tanh of the output state d (n)-1d (n) is collected to a matrix T with the order of (T-T)0+1) xL; collected in T is tanh-1d (n) instead of tanh-1d (n-1), T before discard0The purpose of the state is to eliminate the effect of the initial transient of the network, and T can be determined0The network is no longer affected by the initial transient state after the moment;
output weight W of neural networkoutIs (W)out)T=M-1T, will be (W) in the formulaout)TTranspose to obtain Wout
The calculation output equation is:
y(n+1)=fout(Wout(x(n+1),u(n+1),y(n),x2(n+1),u2(n+1),y2(n))), wherein,
u(n+1),x(n+1),y(n),u2(n+1),x2(n+1),y2(n) represents u (n +1), x (n +1), y (n), u2(n+1)、x2(n+1)、y2(n), merging of the six vectors; f. ofoutUsually taking a symmetric Sigmoid function or a linear function.
The step (5) is specifically as follows:
after the neural network offline learning output is obtained through the step (4), according to an MSE (mean square error) formula: calculating the mean square error of the network training,
Figure BDA0002812953750000051
judging whether the learning error precision in the learning process meets the requirement or not according to the expert experienceIf the production requirement is met, entering the step (6), otherwise, firstly retraining the neural network, wherein the neural network training method comprises the following steps: a. adjusting the sparsity and sparse connection coefficient of the reserve pool parameter W; b. changing an initial state of the network; c. adjusting an input weight matrix WinAnd feedback connection weight matrix WbackThe value range of (a); d. by increasing the number of learning samples, off-line learning is started from the beginning; and (6) entering the step until the learning precision meets the requirement of expert experience.
The step (6) is specifically as follows:
firstly, the neural network obtained in the step (4) is offline learned and output with weight WoutSet as the initial output weight W of online learningout,Wout∈R1×2(K+N+L)
When n is 1,2, …, T, the following iterative operation is completed: obtaining the state x (n) at the time n by using the step (4); define a column vector of dimension N + K + 1:
q(n):q(n)=[x(n-1),u(n),y(n-1),x2(n-1),u2(n),y2(n-1)]and calculating the output of the network at the time n: y (n) tanh (w)out(n-1)q(n));
Calculating prior estimation error of the network at n moments: ξ (n) ═ tanh-1(yd(n)-wout(n-1)q(n));
Fourthly, calculating a gain vector k (n) at the time n:
Figure BDA0002812953750000061
calculating matrix P (N) < lambda >-1[P(n-1)-k(n)q(n)TP(n-1)]Then, the network output weight at n time is updated as: w is aout(n)=wout(n-1)+ξ(n)k(n)T
Sixthly, the step of repeating the calculation is carried out along with the continuous sampling of the new data;
seventhly, testing the network to obtain a testing mean square error:
Figure BDA0002812953750000062
wherein, TeRepresenting the length of the test data; if the testing mean square error meets the requirement, the training is finished, otherwise, the network is retrained until the satisfactory testing mean square error is obtained.
The invention discloses a debutanizer soft measurement modeling method based on ALIESN online learning algorithm, which has the beneficial effects that: according to the method, a NARX time sequence model is adopted to model related input and output variables in the butane production process, a small sample set is trained and learned through an augmented leakage integral echo state network based on an offline learning algorithm, an offline learning output weight of the network is obtained, and the weight is used as an initial weight of an online learning algorithm; performing online learning through an rls algorithm, and outputting real-time online prediction; according to experiments, the algorithm only needs a small number of samples (260) to enable the mean square error to reach 10-5The larger the learning sample, the lower the error.
Drawings
FIG. 1.1 is a residual map of the offline learning algorithm of example 1;
FIG. 1.2 is a learning error curve of the off-line learning algorithm of embodiment 1;
FIG. 1.3 is an error curve for example 1 entering an online learning algorithm;
FIG. 2.1 is a residual map of the offline learning algorithm of example 2;
FIG. 2.2 is a learning error curve of the off-line learning algorithm of embodiment 2;
FIG. 2.3 is an error curve for example 2 entering an online learning algorithm;
FIG. 3.1 is a residual map of the offline learning algorithm of example 3;
FIG. 3.2 is a learning error curve of the off-line learning algorithm of embodiment 3;
FIG. 3.3 is an error curve for example 3 entering an online learning algorithm;
fig. 4 is a learning flowchart of the method.
Detailed Description
Example 1
As shown in fig. 1.1, fig. 1.2, and fig. 1.3, the invention provides a debutanizer soft measurement modeling method based on an ali esn online learning algorithm, which includes the following steps:
firstly, measuring numerical values of key variables in real time by using a measuring instrument installed in butane tower equipment, carrying out normalization pretreatment, and respectively recording 7 auxiliary variables xi and 1 main variable y, wherein xi is composed of sample data of the ith process variable, i belongs to {1, 2, …, 7} and respectively corresponds to tower top temperature, tower top pressure, reflux flow, bottom product outlet flow, 6 th layer tower plate temperature, tower bottom temperature A and tower bottom temperature B, and then modeling is carried out on the 7 auxiliary variables and the 1 main variable by adopting an NARX model to serve as input variables of ALIESN;
secondly, performing off-line training learning on the first n data of the ALIESN input variables by adopting an ALIESN ridge regression off-line learning algorithm to obtain a neural network off-line training output weight;
and finally, taking the neural network training output weight as an initial weight for online learning, and carrying out online training on the output weight from the n +1 th data of the ALIESN input variable to obtain a final network output weight and a predicted output variable.
The mean square error value is calculated to be 1.5466215709364227 x 10-5
Example 2
As shown in fig. 2.1, 2.2, and 2.3, learning was performed under the same conditions as in example 1 to obtain a mean square error value of 1.466215709364227 × 10-5
Example 3
As shown in fig. 3.1, 3.2, and 3.3, learning was performed under the same conditions as in examples 1 and 2 to obtain a mean square error value of 2.757009214241490 × 10-5
Comparative examples
A soft measurement dynamic modeling method based on a leakage integral echo state network and application [ J ]. CIESC Journal (chemical science report), 2014,65(10):4004-4014.doi: 10.3969/j.issn.0438-1157.2014.10.034;
Fortuna L,Graziani S,Xibilia M G.Soft sensors for product quality monitoring in debutanizer distillation columns[J].Control Engineering Practice,2005,13(4):499-508。
the above requires at least 1000 data sets for learning training, but the mean square error values are all lower than the present invention.
In conclusion: the invention adopts the augmented leakage integral echo state network, can rapidly process a strong nonlinear system, obtains a satisfactory output weight in a short time and under the condition of a small amount of data sets, increases the real-time property of soft measurement modeling, and further improves the model prediction precision.

Claims (7)

1. A debutanizer soft measurement modeling method based on ALIESN online learning algorithm is characterized in that: the method comprises the following steps:
firstly, carrying out normalization pretreatment on key variables acquired by a sensor to obtain auxiliary variables and main variables, and carrying out dynamic modeling on the auxiliary variables and the main variables by adopting an NARX model to generate ALIESN input variables with dynamic characteristics;
secondly, performing off-line training learning on the first n data of the ALIESN input variables by adopting an ALIESN ridge regression off-line learning algorithm to obtain a neural network off-line training output weight;
and finally, taking the neural network offline training output weight as an initial weight for online learning, and carrying out online training on the output weight from the (n +1) th data of the ALIESN input variable to obtain a final network output weight and a predicted output variable.
2. The debutanizer soft measurement modeling method based on the ALIESN online learning algorithm according to claim 1, characterized in that: the method comprises the following steps:
(1) collecting data under normal conditions of key variables in a butane production process, the key variables comprising essentially X1Top temperature value, X2Top pressure value, X3Top butane reflux value, X4Butane flow value, X, to the next process5Temperature value X of ═ plate6In the region of the base 1Temperature value, X7Storing the data into a database respectively according to the temperature value of the bottom 2 area and the butane concentration y at the bottom of the debutanizer, wherein the sampling period of all variables is 12 min;
(2) preprocessing the key variables based on a Z-Score normalization method, and then removing abnormal value variables far greater than 1 to obtain a new data set with a zero mean value and a 1 variance, wherein the new data set is a time sequence consisting of auxiliary variables and main variables;
(3) adopting an NARX model to dynamically model the auxiliary variable and the main variable to obtain an ALIESN input variable with dynamic characteristics, wherein the ALIESN input variable with dynamic characteristics comprises a time sequence data set containing past information;
(4) inputting ALIESN of the previous n time sequences into a variable data set for off-line learning, and obtaining a neural network off-line training output weight based on a least square method through an ALIESN ridge regression off-line learning algorithm;
(5) taking Mean Square Error (MSE) as an evaluation index of network learning precision, calculating MSE of an output variable obtained by an offline learning algorithm and an output variable obtained by actual sampling, and performing the next step when the obtained MSE meets the precision requirement, or adding newly acquired data to an offline training data set for retraining until the precision requirement is met;
(6) after the neural network offline training output weight meeting the precision requirement is obtained, the output weight is used as an initial output weight for RLS online learning, online training of the output weight is carried out from the n +1 th data of the ALIESN input variable, and the final network output weight and the predicted output variable are obtained.
3. The debutanizer soft measurement modeling method based on the ALIESN online learning algorithm according to claim 2, characterized in that: the key variables are X ═ { xi ∈ Rm } i ═ 1,2, …, n, y ∈ Rn, R is a real number set, wherein n is the number of samples, m is the number of auxiliary variables, and the number of main variables is 1.
4. The debutanizer soft measurement modeling method based on the ALIESN online learning algorithm according to claim 3, characterized in that:
the step (1) is specifically as follows:
reading the values of the key variables every 12min, storing 8 key variables into a database, and respectively setting the key variables as x1(n) a top temperature value; x is the number of2(n) top pressure value; x is the number of3(n) top butane reflux value; x is the number of4(n) the butane flow rate to the next process; x is the number of5(n) a tray temperature value; x is the number of6(n) the temperature value of the bottom 1; x is the number of7(n) the temperature value of the bottom 2; y (n) bottom butane concentration value;
the step (2) is specifically as follows:
and (3) carrying out normalization pretreatment on the data by using a Z-Score method, wherein the mean value is 0, the variance is 1, and auxiliary variables and main variables are obtained, and the calculation of the Z-Score is defined as follows: u ═ x- μ)/σ; the x is an original score, u is a numerical value of a converted [0,1] interval, mu is a score mean value of the overall sample space, and sigma is a standard deviation of the overall sample space;
the step (3) is specifically as follows:
the following NARX model is adopted to convert 7 auxiliary variables and 1 main variable into 13 ALIESN input variables, and the input variables are input into a neural network to start learning:
y(k)=f(u1(k),u2(k),u3(k),u4(k),u5(k),u5(k-1),u5(u-2),u5(k-3),(u6(k)+u7(k))/2,y(k-1),y(k-2),y(k-3),y(k-4))。
5. the debutanizer soft measurement modeling method based on the ALIESN online learning algorithm according to claim 2, characterized in that: the step (4) is specifically as follows:
setting the dimensions of variables of an input layer, a hidden layer and an output layer of the ALIESN network as K-13, N-50 and L-1 respectively, wherein neurons of the input layer, the hidden layer and the output layer of the network at N time are as follows:
Figure FDA0002812953740000031
the input connection weight matrix, the SR internal connection weight matrix, the output connection weight matrix and the feedback connection weight matrix fed back to the SR by the output are respectively expressed as:
Figure FDA0002812953740000034
W=(wij),
Figure FDA0002812953740000033
the dimensions of each weight are as follows: dimension N × K, dimension N × N, dimension L × 2(K + N + L), dimension N × L;
giving an input/output sequence with length T ═ n:
(u (1), d (1)), (u (2), d (2)), …, (u (T), d (T)) and input to the network, training the ALIESN network so that its output y (n) approximates the output d (n);
initializing the network, randomly taking value of SR initial state x (0), and inputting connection weight matrix WinAnd feedback connection weight matrix WbackTaking a value which follows normal uniform distribution, and internally connecting a sparse connection coefficient of a weight matrix W and a sparse matrix with the sparsity of min (10/N,1) in the SR;
the ALIESN (n +1) th moment state updating equation is as follows:
x(n+1)=(1-a)x(n)+f(Winu(n+1)+Wx(n)+Wbackd (n)), wherein when n is 0, d (0) is 0, x (0) is 0, and f is usually a symmetric Sigmoid function;
from time T0After 1, the "augmented" state (u (n), u) of double size was collected2(n))=(u1(n),...,uK+N+L(n),u1 2(n),...,uK+N+L 2(n)) entering a state collection matrix; this will result in an output weight matrix Wout of size 1 × 2(K + N + L), the order of matrix M being (T-T)0+1) × 2(K + N + L); computing a pseudo-inverse (generalized inverse) M of M-1Similarly, the inverse hyperbolic tangent function of the output state d (n)tanh-1d (n) is collected to a matrix T with the order of (T-T)0+1) xL; collected in T is tanh-1d (n) instead of tanh-1d (n-1), T before discard0The purpose of the state is to eliminate the effect of the initial transient of the network, and T can be determined0The network is no longer affected by the initial transient state after the moment;
output weight W for off-line training of neural networkoutIs (W)out)T=M-1T, will be (W) in the formulaout)TTranspose to obtain Wout
The calculation output equation is:
y(n+1)=fout(Wout(x(n+1),u(n+1),y(n),x2(n+1),u2(n+1),y2(n))), wherein,
u(n+1),x(n+1),y(n),u2(n+1),x2(n+1),y2(n) represents u (n +1), x (n +1), y (n), u2(n+1)、x2(n+1)、y2(n), merging of the six vectors; f. ofoutUsually taking a symmetric Sigmoid function or a linear function.
6. The debutanizer soft measurement modeling method based on the ALIESN online learning algorithm according to claim 2, characterized in that: the step (5) is specifically as follows:
after the primary neural network output weight is obtained in the step (4), according to an MSE (mean square error) formula: calculating the mean square error of the network training,
Figure FDA0002812953740000041
judging whether the learning error precision in the learning process meets the production requirement according to expert experience, if so, entering the step (6), otherwise, firstly retraining the neural network, wherein the neural network training method comprises the following steps: a. adjusting the sparsity and sparse connection coefficient of the reserve pool parameter W; b. changing an initial state of the network; c. adjusting an input weight matrix WinAnd feedback connection weight matrix WbackThe value range of (a); d. by increasing the number of learning samples, off-line learning is started from the beginning; and (6) entering the step until the learning precision meets the requirement of expert experience.
7. The debutanizer soft measurement modeling method based on the ALIESN online learning algorithm according to claim 2, characterized in that: the step (6) is specifically as follows:
firstly, the neural network obtained in the step (4) is offline learned and output with weight WoutSet as the initial output weight W of online learningout,Wout∈R1×2(K+N+L)
When n is 1,2, …, T, the following iterative operation is completed: obtaining the state x (n) at the time n by using the step (4); define a column vector of dimension N + K + 1:
q(n):q(n)=[x(n-1),u(n),y(n-1),x2(n-1),u2(n),y2(n-1)]and calculating the output of the network at the time n: y (n) tanh (w)out(n-1)q(n));
Calculating prior estimation error of the network at n moments: ξ (n) ═ tanh-1(yd(n)-wout(n-1)q(n));
Fourthly, calculating a gain vector k (n) at the time n:
Figure FDA0002812953740000051
calculating matrix P (N) < lambda >-1[P(n-1)-k(n)q(n)TP(n-1)]Then, the network output weight at n time is updated as: w is aout(n)=wout(n-1)+ξ(n)k(n)T
Sixthly, the step of repeating the calculation is carried out along with the continuous sampling of the new data;
seventhly, testing the network to obtain a testing mean square error:
Figure FDA0002812953740000052
wherein, TeRepresenting the length of the test data; if it is measuredAnd if the mean square error meets the requirement, ending the training, otherwise, retraining the network until a satisfactory test mean square error is obtained.
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