CN101118610A - Sparseness data process modeling approach - Google Patents

Sparseness data process modeling approach Download PDF

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CN101118610A
CN101118610A CNA2007100127765A CN200710012776A CN101118610A CN 101118610 A CN101118610 A CN 101118610A CN A2007100127765 A CNA2007100127765 A CN A2007100127765A CN 200710012776 A CN200710012776 A CN 200710012776A CN 101118610 A CN101118610 A CN 101118610A
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关守平
尤富强
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Northeastern University China
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Abstract

The present invention relates to a method applying a procedure neural network to establish a procedure predicting model for sparse data. On the basis of the pretreatment of the sparse sample data, a learning algorithm based upon the discrete Walsh transform is applied to increase the learning efficiency and the modeling precision of the procedure neural network. To ensure that the established procedure predicting model can amend the prediction deviations timely, a method of data sampling periodic network rolling learning is adopted based upon the characteristics of the sparse data procedure to conduct an on-line amendment to the network predicting model timely through up-to-date sampled data, thereby improving the accuracy of the predicting model further. The present invention provides an effective approach for solving the modeling problem related to a kind of sparse data procedure.

Description

Sparse data process modeling method
(I) technical field
The invention relates to a process modeling method applying an intelligent information processing technology, in particular to a modeling method of a sparse data process.
(II) background of the invention
In many industrial processes, due to the influence of factors such as field conditions, technological processes, detection equipment and the like, the time interval for acquiring sample data is long, the data volume is limited, and the sample data is sparse. Therefore, how to establish a prediction model of the process according to the characteristics of the sparse data process and generate relatively continuous intensive forecast data through the prediction model is an important research topic, which is beneficial to process control.
In the aspect of system modeling, an identification modeling method represented by a neural network is developed rapidly at present. However, most of the existing neural networks used for system modeling are feed-forward networks, and are characterized in that network inputs are constants irrelevant to time, so that the problem of mapping on a data space is mainly solved, and the method is very effective for modeling of a dense sampling data process. However, for sparse data processes, in order to fully utilize the information contained in limited data, it is not enough to consider only the spatial aggregation effect of the data, but also to fully consider the time accumulation effect of the data, because the data in industrial processes is often time-dependent. Therefore, the space and time effects of the sparse data are utilized simultaneously to generate dense process forecast data, and forecast errors of the network model are corrected in time, so that process monitoring and optimization control are facilitated, and the method is a problem which is difficult to solve by a traditional neural network modeling method.
Disclosure of the invention
The invention aims to provide a modeling method based on a process neural network aiming at the defects of the prior art, so as to solve the problem of modeling of a sparse data process and provide an effective way for modeling of the sparse data process.
The invention is realized by the following technical scheme: data preprocessing, data expansion, process neural network modeling and online rolling learning. Smoothing pseudo data generated by interference in the sampled data by preprocessing the sampled data; then expanding the processed data to generate more dense data with required time intervals for network model training, aiming at enabling a network prediction model to output data at required time points and solving the problems of rare actual sampling data and difficulty in effectively monitoring and controlling the process due to difficult detection; the method comprises the steps of establishing a neural network model of the process by applying process neurons, wherein the input and weight of the process neurons are functions or processes changing along with time, the aggregation operation of the process neurons comprises multi-input aggregation on space and cumulative aggregation on a time process, and space and time information contained in sparse data can be fully utilized; after the processed offline data are used for offline training the process neural network model, the network model is put into an actual prediction process, existing actual data are immediately processed when a predicted value is detected to be incorrect at a sampling time interval, and the processed data are used for online training the network, so that the network learns new information in the training process. The sampling period of the sparse data process is long, and some sparse data process even detects data offline, so the method for the rolling learning of the sampling time interval is feasible.
The present invention is further described below, specifically as follows:
1. data pre-processing
Supposing that n groups of field sampling data are provided, the sampling number of each group is m, and the average value of different groups of sampling data at the same timeThe variance is sigma, if the sampling values of each group corresponding to the same time are all in
Figure A20071001277600072
Indicating that no dummy data is present in the set of data. If a certain sampling value x nm Is out of position
Figure A20071001277600073
In between, then
Figure A20071001277600074
When it is takenWhen in use
Figure A20071001277600076
When it is taken
Figure A20071001277600077
And after smoothing the sampled data, normalizing the sample data. Considering that the excitation function of each layer of the neural network selects a Sigmoid function, the input and output data of the network are limited in a [0,1] interval, and the input and output variables of the network are approximated to normal standard distribution by applying the transformation of the formula (1).
Figure A20071001277600078
In the formula: x is sampling data processed by pseudo data;
Figure A20071001277600079
the data is normalized; x is the number of min Is the minimum value of the neural network input or output; x is the number of max The maximum value of the input or output quantity of the neural network is rho which is a proportionality coefficient and is generally rho = 0.1-0.9.
2. Data expansion
The method adopts a recursive adjacent mean generation method to expand data, namely, a method which firstly generates middle expanded data by using data at two ends and then expands all data by using the data at two ends and the obtained middle data. I.e. the original sequence [ X ]]＝[X(1)，X(2)，…，X(n)]Expanded into a sequence [ X (1), phi ] 1 (k 1 )，…，Φ 1 (k i )，…，Φ 1 (k m )，X(2)，Φ 2 (k 1 )，…，Φ 2 (k i )，Φ 2 (k m )，…，X(n)]Wherein phi j (k i ) And (i =1,2, … m, j =1,2, …, n-1) is the augmented data.
Take phi i (k 0 )＝X(j)，Φ j (k m+1 ) = X (j + 1), then
Figure A200710012776000710
In the formula (I), the compound is shown in the specification,
Figure A200710012776000711
i min for expanding arraysLeft-end known data sequence number, i max The data sequence number is known to the right of the augmented sequence. Repeating the formula (2) to obtain the required extended data sequenceΦ j (k i )。
3. Process neuron network modeling
The process neuron is composed of three parts of weighting, aggregation and excitation, and the structure diagram is shown in FIG. 1. In the figure, x 1 (t)，x 2 (t)，…，x n (t) is the process neuron input function; w is a 1 (t)，w 2 (t)，…，w n (t) is the corresponding weight function; k (t) is the time-aggregated basis function of the process neuron; f (-) is an excitation function, and can be a linear function, a Sigmoid function, a Gauss type function and the like. The relationship between the input and output of a process neuron is
Y＝f((W(t)⊕X(t))K(·)-θ) (3)
Where θ is the process neuron output threshold, y is the output value of the process neuron, # indicates some spatial aggregation operation, and  indicates some temporal (process) aggregation operation. Here, the spatial aggregation operation is taken as a weighted sum, and the temporal aggregation operation is taken as an integral.
A process neuron network model with a 4-layer structure is constructed on the basis of process neurons, as shown in figure 2, the topological structure is n-m-K-1, namely a network input layer is provided with n nodes, a process neuron hidden layer is provided with m nodes, a non-time-varying general neuron hidden layer is provided with K nodes, and an output layer is provided with 1 node. The process neuron hidden layer is used for extracting the process mode characteristics of the input information and performing time aggregation operation, and the time-invariant general neuron hidden layer is used for improving the mapping capability of a network on complex relations between the input and the output of a system.
As can be seen from FIG. 2, the relationship between the inputs and outputs of the process neural network is
Figure A20071001277600081
The input of the model in the figure is X (t) = (X) 1 (t)，x 2 (t)，…，x n (t)), the model output is y, [0,T]Is a time sampling interval, w ij (t) is the connection weight function of the input layer and the 1 st hidden layer, v jk Is the connection weight of the 1 st hidden layer and the 2 nd hidden layer, mu k Is the connection weight, theta, from the 2 nd hidden layer to the output layer j (1) Output threshold, θ, for the 1 st hidden layer jth process neuron k (2) The output threshold of the kth process neuron of the hidden layer 2 is defined as f, the excitation function of the hidden layer 1 is defined as f, and g is the excitation function of the hidden layer 2. Taking the excitation functions of all layers as Sigmoid functions, i.e.
Figure A20071001277600082
Walsh transformation is carried out on discrete sampling data which change along with time, the discrete sampling data are directly used as input of a neural network, the middle fitting process is reduced, fitting errors are eliminated, and the transformation process is as follows:
given Q sequences of length 2 p If the discrete sequence length is not 2 p Can be obtained by smooth interpolation): (x) q1 (t l )，x q2 (t l )，…，x qn (t l )，d q ) Wherein Q =1,2, …, Q,l＝0，1，…，N-1，N＝2 p p is a natural number satisfying the interpolation accuracy requirement, d i Is the desired output. Walsh transform is applied to the learning samples to obtain (wal (x) q1 (t l ))，wal(x q2 (t l ))，…，wal(x qn (t l ))，d q )。
Discrete data is input into the network through Walsh transformation, so that the input and output relations of the network are
Figure A20071001277600091
Wherein
Figure A20071001277600092
The error function of the network is
Figure A20071001277600093
The process neural network action process is shown in figure 3. And (3) performing off-line training on the neural network model in the process by applying a BP algorithm of error back propagation to obtain expected network approximation accuracy. The learning algorithm is shown as follows:
Figure A20071001277600094
wherein alpha, beta, gamma, eta and lambda are network learning rates.
4. Online rolling learning
At the kth sampling moment, comparing the predicted value with the sampling value, if the error exceeds the precision requirement, processing the acquired data and then performing online network learning, otherwise, keeping the output of a network model; at time k +1, the above detection and learning process is repeated. This "learn-predict-learn" scrolling flow is illustrated in FIG. 4
The method fully utilizes the characteristics of the sparse data process, utilizes the process neurons and combines the data processing technology to carry out modeling work of a class of sparse data process in the industrial process, effectively solves the problem that the monitoring and optimization control of the process are difficult to effectively implement due to the fact that process sampling data are rare due to the difficulty in detection in the industrial process, provides an effective way for modeling of the sparse data process, and lays a foundation for implementing optimization control of the class of industrial process.
Description of the drawings
FIG. 1 is a schematic diagram of a process neuron architecture.
FIG. 2 is a schematic diagram of a neural network structure of a double hidden layer process.
Fig. 3 is a schematic diagram of the action process of the neural network.
Fig. 4 is a schematic diagram of network model rolling learning.
(V) detailed description of the preferred embodiments
In order to better understand the technical scheme of the invention, the monosodium glutamate fermentation process is taken as an example in the following, and the modeling of the thallus concentration prediction model is carried out on the monosodium glutamate fermentation process.
The monosodium glutamate fermentation process is a complex biochemical reaction process, and due to the influence of factors such as field conditions, technological processes, detection equipment and the like, sample data of thallus concentration can be obtained usually every 3 hours, and the monosodium glutamate fermentation process belongs to a sparse data process. In the fermentation process, the air intake and the thallus concentration are determined to have a certain relation according to actual data and the experience of field engineers. Therefore, the current intake air volume and the current thallus concentration are used as two input nodes of the network, and the thallus concentration is predicted to be an output node. The specific steps for establishing the prediction model of the thallus concentration in the monosodium glutamate fermentation process are as follows:
1. data pre-processing
Table 1 shows the field data of partial thallus concentration and air intake, the thallus concentration is sparse data, a group of sample data is obtained at intervals of 3 hours, and the ventilation volume is continuous dense data.
TABLE 1 partial field data
Time- Hour(s) Group 1 2 groups of Group 3
Intake air quantity is greater or less Per minute of cubic meter The number of the thallus is- OD Intake air volume Per minute of cubic meter The number of the thallus is- OD Intake air quantity is greater or less Per minute of cubic meter The number of the thallus is- OD
0.0 15 0.10 15 0.08 15 0.075
0.5 15 15 15
1.0 15 15 15
1.5 20 15 15
2.0 20 15 15
2.5 25 20 25
3.0 25 0.30 20 0.25 25 0.30
3.5 30 25 30
4.0 30 25 30
4.5 40 30 40
5.0 40 30 40
5.5 45 40 45
6.0 45 0.72 40 0.62 45 0.67
6.5 45 45 45
7.0 45 45 45
7.5 45 45 45
8.0 45 45 45
8.5 45 45 45
9.0 45 0.86 45 0.85 45 0.87
9.5 45 45 45
10.0 45 45 45
10.5 45 45 45
11.0 45 45 45
11.5 45 45 45
12.0 45 0.97 45 0.94 45 0.96
12.5 45 45 45
13.0 45 45 45
13.5 45 45 45
14.0 45 45 45
14.5 45 45 45
15.0 45 1.00 45 0.85 45 1.0
15.5 45 45 45
16.0 45 45 45
16.5 40 45 45
17.0 40 45 45
17.5 40 40 45
18.0 40 1.05 40 1.02 40 1.02
18.5 40 40 40
19.0 40 40 40
19.5 40 40 40
20.0 40 40 40
20.5 40 40 40
21.0 40 1.04 40 1.04 40 1.02
21.5 40 40 40
22.0 40 40 40
22.5 40 35 40
23.0 40 35 40
23.5 40 35 40
24.0 35 1.02 35 1.05 40 1.00
24.5 35 35 40
25.0 35 35 40
25.5 35 35 40
26.0 35 35 40
26.5 35 35 40
27.0 35 1.00 35 1.01 40 1.00
27.5 35 35 35
28.0 35 35 35
28.5 35 35 35
29.0 35 35 35
29.5 35 35 35
30.0 35 0.98 35 1.00 35 1.00
Considering the 15 th hour cell concentration data in group 3, the mean value of the 3 groups of sampling data at this time point is:
Figure A20071001277600121
the variance is:
Figure A20071001277600122
therefore, the sampled data at that time should be in the interval
Figure A20071001277600123
Among them. From this, it was found that the group 2 cell concentration data at 15 hours was pseudo data, and the lower limit of the interval was defined, that is, 0.909 was used instead of the pseudo dataThe value of 0.85 at that time.
The minimum value of the thallus concentration is x by field data analysis 1min =0.07, maximum value x 1max =1.10; the minimum value of the intake air is x 2min =15, maximum value x 2max =50, and thereby the data in table 1 is normalized by applying equation (1) in which the proportionality coefficient is ρ =0.8. The data after normalization are shown in table 2.
2. Data expansion
The sparse sample data of the bacterial cell concentration is expanded, and the sample data after expansion is obtained according to the time interval of 0.5 hour by adopting a recursive adjacent mean generation method, and is shown in table 2.
TABLE 2 normalized and extended sample data
Time-or Hour(s) Group 1 2 groups of Group 3
Intake air quantity is greater or less Per minute of cubic meter The number of the thallus is- OD Intake air volume Per minute of cubic meter The number of the thallus is- OD Intake air quantity is greater or less Per minute of cubic meter The number of the thallus is- OD
0.0 0.100 0.1233 0.100 0.1078 0.100 0.1039
0.5 0.100 0.1614 0.100 0.1408 0.100 0.1476
1.0 0.100 0.1809 0.100 0.1573 0.100 0.1694
1.5 0.214 0.2005 0.100 0.1738 0.100 0.1913
2.0 0.214 0.2395 0.100 0.2068 0.100 0.2349
2.5 0.329 0.2591 0.214 0.2233 0.329 0.2568
3.0 0.329 0.2786 0.214 0.2398 0.329 0.2786
3.5 0.443 0.3602 0.329 0.3116 0.443 0.3505
4.0 0.443 0.4010 0.329 0.3476 0.443 0.3864
4.5 0.671 0.4417 0.443 0.3835 0.671 0.4223
5.0 0.671 0.5233 0.443 0.4554 0.671 0.4941
5.5 0.786 0.5641 0.671 0.4913 0.786 0.5301
6.0 0.786 0.6049 0.671 0.5272 0.786 0.5660
6.5 0.786 0.6321 0.786 0.5718 0.786 0.6048
7.0 0.786 0.6457 0.786 0.5942 0.786 0.6243
7.5 0.786 0.6593 0.786 0.6165 0.786 0.6437
8.0 0.786 0.6864 0.786 0.6612 0.786 0.6825
8.5 0.786 0.7000 0.786 0.6835 0.786 0.7020
9.0 0.786 0.7136 0.786 0.7058 0.786 0.7214
9.5 0.786 0.7349 0.786 0.7233 0.786 0.7389
10.0 0.786 0.7456 0.786 0.7320 0.786 0.7476
10.5 0.786 0.7563 0.786 0.7408 0.786 0.7564
11.0 0.786 0.7776 0.786 0.7582 0.786 0.7738
11.5 0.786 0.7883 0.786 0.7670 0.786 0.7826
12.0 0.786 0.7990 0.786 0.7757 0.786 0.7913
12.5 0.786 0.8048 0.786 0.7697 0.786 0.7991
13.0 0.786 0.8077 0.786 0.7667 0.786 0.8029
13.5 0.786 0.8107 0.786 0.7636 0.786 0.8068
14.0 0.786 0.8165 0.786 0.7577 0.786 0.8146
14.5 0.786 0.8194 0.786 0.7547 0.786 0.8184
15.0 0.786 0.8223 0.786 0.7517 0.786 0.8223
15.5 0.786 0.8320 0.786 0.7732 0.786 0.8262
16.0 0.786 0.8369 0.786 0.7839 0.786 0.8281
16.5 0.671 0.8418 0.786 0.7947 0.786 0.8300
17.0 0.671 0.8515 0.786 0.8162 0.786 0.8338
17.5 0.671 0.8563 0.671 0.8270 0.786 0.8358
18.0 0.671 0.8612 0.671 0.8377 0.671 0.8377
18.5 0.671 0.8592 0.671 0.8416 0.671 0.8377
19.0 0.671 0.8583 0.671 0.8436 0.671 0.8377
19.5 0.671 0.8573 0.671 0.8456 0.671 0.8377
20.0 0.671 0.8554 0.671 0.8495 0.671 0.8377
20.5 0.671 0.8544 0.671 0.8514 0.671 0.8377
21.0 0.671 0.8534 0.671 0.8534 0.671 0.8377
21.5 0.671 0.8495 0.671 0.8554 0.671 0.8338
22.0 0.671 0.8475 0.671 0.8563 0.671 0.8319
22.5 0.671 0.8456 0.557 0.8573 0.671 0.8300
23.0 0.671 0.8416 0.557 0.8592 0.671 0.8262
23.5 0.671 0.8397 0.557 0.8602 0.671 0.8242
24.0 0.557 0.8377 0.557 0.8612 0.671 0.8223
24.5 0.557 0.8338 0.557 0.8534 0.671 0.8223
25.0 0.557 0.8319 0.557 0.8495 0.671 0.8223
25.5 0.557 0.8300 0.557 0.8457 0.671 0.8223
26.0 0.557 0.8262 0.557 0.8379 0.671 0.8223
26.5 0.557 0.8242 0.557 0.8340 0.671 0.8223
27.0 0.557 0.8223 0.557 0.8301 0.671 0.8223
27.5 0.557 0.8184 0.557 0.8281 0.557 0.8223
28.0 0.557 0.8165 0.557 0.8272 0.557 0.8223
28.5 0.557 0.8146 0.557 0.8262 0.557 0.8223
29.0 0.557 0.8107 0.557 0.8243 0.557. 0.8223
29.5 0.557 0.8087 0.557 0.8233 0.557 0.8223
30.0 0.557 0.8068 0.557 0.8223 0.557 0.8223
3. Process neuron network modeling
The topological structure of the network is selected to be 2-20-9-1, namely 2 input nodes, 20 process neuron hidden nodes, 9 time-invariant general neuron hidden nodes and 1 thallus concentration output node. The number of discrete Walsh basis functions taken for the input function and the number of discrete Walsh basis functions used for the weight basis spreading are both 64. The bacterial concentration and the intake air amount in table 2 are input into a process neural network for training, the learning rate α =0.65, β =0.8, γ =0.7, η =0.8, λ =0.71, the error precision is 0.01, the network converges after 1000 times of training, and the process neural network is used as a bacterial concentration prediction model.
4. Online rolling learning
And putting the off-line trained process neural network prediction model into on-line operation, and outputting thallus concentration prediction data with the time interval of 0.5 hour. Comparing the model predicted value with the sampling value at sampling points for 3, 6, 9, 12, 15, 18, 21, 24, 27 and 30 hours, immediately processing the acquired data if the error precision is more than 1%, and then performing online network learning; otherwise, the output of the network model is maintained. A set of prediction data using this "learning-prediction-learning" mode is shown in table 3 (only data at sampling points are shown in the table). To increase the contrast, table 3 shows the model prediction data of the non-rolling learning mode, and it can be seen that the accuracy of the output value predicted by the rolling learning method is higher than the accuracy of the output value predicted by the non-rolling learning method.
TABLE 3 Online prediction data of cell concentration
Time Hour/hour Actual output value /OD Non-rolling learning mode Rolling learning mode
Predicted output value /OD Relative error /％ Predicted output value /OD Relative error/%)
0 0.11
3 0.37 0.3609 2.46 0.3609 2.46
6 0.78 0.7501 3.83 0.7665 1.73
9 0.91 0.8792 3.38 0.8954 1.61
12 1.00 0.9656 3.44 0.9903 0.97
15 1.05 1.0232 2.55 1.0425 0.71
18 1.06 1.0215 3.63 1.0487 1.07
21 1.06 1.0147 4.27 1.0507 0.88
24 1.05 1.0126 3.56 1.0404 0.91
27 1.03 1.0011 2.81 1.0213 0.85
30 1.01 0.9702 3.76 0.9993 1.05

Claims (5)

1. A modeling method of a sparse data process comprises three steps of data preprocessing, process neural network modeling and online rolling learning, and is characterized in that:
the data processing comprises correction of pseudo data and filling of sparse data; the correction of the pseudo data is to carry out smooth correction and processing on the pseudo data existing in the sampling data and carry out normalization processing on the smoothed data; the filling of the sparse data is to expand the sparse data, make up unknown data at known moments and obtain dense data at proper time intervals;
the process neural network modeling is to apply process neurons to form a double-hidden-layer process neural network model, and apply preprocessing data to train the neural network model to obtain a process neural network model meeting the precision requirement; the process neuron consists of three parts of weighting, aggregation and excitation; the inputs and weights are functions that vary with time; the network consists of an input layer, a process neuron hidden layer, a non-time-varying general neuron hidden layer and an output layer, and the learning training is carried out on the network by adopting a discrete Walsh transform-based method;
x 1 (t)，x 2 (t)，…，x n (t) is the process neuron input function; w is a 1 (t)，w 2 (t)，…，w n (t) is the corresponding weight function; k (t) is the time-aggregated basis function of the process neuron; f (-) is an excitation function, and can be a linear function, a Sigmoid function, a Gauss type function and the like; the relationship between the input and output of the process neuron is:
Y＝f((W(t)⊕X(t))K(·)-θ) (1)
where θ is the process neuron output threshold, y is the process neuron output value,. Indicates ^ a certain spatial aggregation operation,  indicates a certain temporal (process) aggregation operation; taking the space aggregation operation as a weighted sum and the time aggregation operation as an integral;
constructing a process neuron network model with a four-layer structure on the basis of process neurons, wherein the topological structure is n-m-K-1, the network input layer is provided with n nodes, the process neuron hidden layer is provided with m nodes, the time-invariant general neuron hidden layer is provided with K nodes, and the output layer is provided with 1 node; the process neuron hidden layer is used for extracting process mode characteristics of input information and performing time aggregation operation, and the time-invariant general neuron hidden layer is used for improving the mapping capability of a network on complex relations between input and output of a system;
the relationship between the process neural network inputs and outputs is:
Figure A2007100127760002C1
the input of the model is X (t) = (X) 1 (t)，x 2 (t)，…，x n (t)), the model output is y, [0,T]Is a time sampling interval, w ij (t) is the connection weight function of the input layer and the 1 st hidden layer, v jk Is a connection of a 1 st hidden layer and a 2 nd hidden layerIs connected to the weight value, mu k Is the connection weight, theta, from the 2 nd hidden layer to the output layer j (1) Is the output threshold, θ, of the jth process neuron of the 1 st hidden layer k (2) An output threshold value of a kth process neuron of a hidden layer 2, f is an excitation function of the hidden layer 1, and g is an excitation function of the hidden layer 2; taking the excitation functions of all layers as Sigmoid functions, i.e.
Figure A2007100127760003C1
Walsh transformation is carried out on discrete sampling data which change along with time, the discrete sampling data are directly used as input of a neural network, the middle fitting process is reduced, fitting errors are eliminated, and then the transformation process is as follows:
given Q sequences of length 2 p If the learning samples are discrete sequencesLength not equal to 2 p The following can be obtained by smooth interpolation: (x) q1 (t l )，x q2 (t l )，…，x qn (t l )，d q ) Wherein Q =1,2, …, Q, l =0,1, …, N-1, N =2 p P is a natural number satisfying the interpolation accuracy requirement, d i Is the desired output; walsh transform is applied to the learning samples to obtain (wal (x) q1 (t l ))，wal(x q2 (t l ))，…，wal(x qn (t l ))，d q )；
Discrete data is input into the network through Walsh transformation, so that the input and output relations of the network are
Figure A2007100127760003C2
Wherein
Figure A2007100127760003C3
s＝1，2，…，N
The error function of the network is
Figure A2007100127760003C4
The neural network model in the process is trained offline by applying a BP algorithm of error back propagation to obtain expected network approximation accuracy. The learning algorithm is as follows:
Figure A2007100127760003C5
wherein alpha, beta, gamma, eta and lambda are network learning rates;
the online rolling learning is that at the interval of sampling time, when the predicted value is detected to be incorrect, the existing actual data is processed, and the network is retrained by adopting the processed data, so that the network learns new information in the training process; at the kth sampling moment, comparing the predicted value with the sampling value, if the error exceeds the precision requirement, carrying out online network learning after processing the acquired data, and otherwise, keeping the output of a network model; at time k +1, the above detection and learning process is repeated.
2. The sparse data process modeling method of claim 1, wherein: correction of the above-mentioned dummy data: n groups of sampling data are set, the sampling number of each group is m, and the average value of different groups of sampling data at the same time is
Figure A2007100127760004C1
The variance is sigma, if the sampling values of each group corresponding to the same time are all in
Figure A2007100127760004C2
Indicates that no dummy data exists in the set of data; if a certain sampling value x nm Is out of position
Figure A2007100127760004C3
In between, then
Figure A2007100127760004C4
When it is taken
Figure A2007100127760004C5
When in use
Figure A2007100127760004C6
When it is taken
Figure A2007100127760004C7
Obtaining data suitable for training and learning of the neural network model;
smoothing the sampled data and normalizing the sample data; limiting the input and output data of the network in the interval of [0,1], and applying a formula
Figure A2007100127760004C8
Approximating the input and output variables of the network to normal standard distribution;
in the formula: x is sampled data processed by pseudo data；
Figure A2007100127760004C9
The data is normalized; x is the number of min Is the minimum value of the neural network input or output; x is the number of max The maximum value of the input or output quantity of the neural network is rho which is a proportionality coefficient and is generally rho = 0.1-0.9.
3. The sparse data process modeling method of claim 1, wherein: the filling of the sparse data is a method for expanding data by adopting a recursive adjacent mean generation method, namely, the data at two ends are used for firstly generating middle expanded data, and then the data at two ends and the obtained middle data are used for expanding all data;
i.e., the original sequence of numbers [ X ] = [ X (1), X (2), …, X (n) ],
expanded into a sequence [ X (1), phi ] 1 (k 1 )，…，Φ 1 (k i )，…，Φ 1 (k m )，X(2)，Φ 2 (k 1 )…，Φ 2 (k i )，…，Φ 2 (k m )，…，X(n)]Wherein phi j (k i ) For augmented data, i =1,2, … m; j =1,2, …, n-1;
get phi j (k 0 )＝X(j)，Φ j (k m+1 ) = X (j + 1), then
Figure A2007100127760004C10
In the formula
Figure A2007100127760004C11
i min For expanding the left-hand known data sequence number of the sequence, i max Knowing the data sequence number for the right end of the extended sequence; the formula (8) is repeatedly applied to obtain the required extended data sequence phi j (k i )。
4. The sparse data process modeling method of claim 1, wherein: forming a process neural network model of a double-hidden layer by adopting process neurons; the process neuron is composed of a weighting part, an aggregation part and an excitation part 3, and the input and the weight are functions which change along with time; the network consists of an input layer, a process neuron hidden layer, a non-time-varying general neuron hidden layer and an output layer, and the learning training of the network is carried out by adopting a discrete Walsh transform-based method.
5. The sparse data process modeling method of claim 1, wherein: the learning of the process neural network model adopts a learning mode combining off-line learning and on-line rolling learning; performing offline learning of the network model by using the preprocessed offline data, and putting the network prediction model into online application after the required prediction error precision is achieved; at the kth sampling moment, comparing the predicted value with the sampling value, if the error exceeds the precision requirement, processing the acquired data and then performing online network learning, otherwise, keeping the output of a network model; at time k +1, the above detection and learning process is repeated.
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