CN112085254B - Prediction method and model based on multi-fractal cooperative measurement gating circulation unit - Google Patents
Prediction method and model based on multi-fractal cooperative measurement gating circulation unit Download PDFInfo
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Abstract
The invention relates to a prediction method and a model based on multi-fractal cooperative measurement gating circulation unit, wherein the method comprises the following steps: preprocessing the input time sequence data to obtain preprocessed time sequence data; the processed time sequence data is segmented by sliding time windows, the spectrum width delta alpha of the multi-fractal spectrum on each time window is calculated by utilizing a multi-fractal algorithm, a spectrum width matrix E of the multi-fractal spectrum of the time sequence data is obtained, an updated gate weight matrix in a gate control circulation unit is improved to a weight matrix related to the spectrum width matrix E, an improved gate control circulation unit is obtained, and a network model is constructed by utilizing the improved gate control circulation unit to predict. The MF-GRU model provided by the invention adopts a multi-fractal technology to extract fluctuation change degree characteristics of time sequence data, and a dynamic adjustment matrix is arranged to replace the change trend of a non-stationary data section in the traditional updated gate weight matrix learning data so as to improve the prediction accuracy of the non-stationary time sequence data.
Description
Technical Field
The invention relates to the technical field of time sequence prediction, in particular to a prediction method and model based on a multi-fractal synergetic measure gating circulation unit.
Background
Time series prediction plays an important role in various fields of society, such as stock price, air quality, voice recognition, and the like. However, the actual timing problem is not stable, so that the accuracy of predicting the non-stable data sequence by the traditional prediction method is not high.
The traditional time sequence prediction method fits time sequence trend by establishing a proper mathematical model, such as an ARMA model, an ES model, a logistic regression model and the like, but the prediction accuracy is lower due to the multi-variable dependency relationship of difficult data processing. The time sequence prediction model based on machine learning, such as support vector regression, K nearest neighbor algorithm and the like, can better process time sequence data dependent on multiple variables, but is easy to cause poor prediction effect due to over fitting. Deep neural networks, as a highly complex nonlinear system, have certain advantages in processing complex time series data of multivariate dependence. The long-term dependence problem exists in the cyclic neural network model, and a gating mechanism is introduced into Hochreater and Schmidhuber on the basis of RNN to provide a long-term and short-term memory model so as to solve the long-term dependence problem of RNN; chung et al, on the basis of which a gating mechanism is simplified, propose a gating circulation unit (Gated Recurrent Unit, GRU) so that the model has faster training efficiency and equivalent accuracy; the minimum gating unit proposed by Zhou et al further simplifies the model structure on the basis of GRU, and the training efficiency is further improved. However, the above model improves efficiency, converges in prediction performance, and has poor prediction effect on non-stationary time series data.
Disclosure of Invention
Aiming at the defects, the invention provides a prediction method and a model based on multi-fractal synergetic measurement gating circulation unit. According to the invention, the fluctuation change degree of the variable to be predicted is quantized through the spectrum width of the multi-fractal spectrum, and an improved gating circulation unit network is established to realize training and prediction of non-stationary time sequence data.
In order to solve the technical problems, the invention adopts the following technical scheme:
the prediction method based on the multi-fractal cooperative measurement gating cycle unit comprises the following steps:
step 4, inputting the preprocessed time sequence data into an improved gate control circulation unit to obtain predicted data; judging whether the current iteration times are greater than or equal to the preset highest iteration times, if so, turning to the step 7, otherwise, turning to the step 4;
and 7, outputting the prediction data.
Further, the method for calculating the spectrum width by using the multi-fractal algorithm in the step 2 specifically includes the following steps:
step 31, dividing the time series data with length N into (N-w) time series with window length w by step length 1, and probability measure P of each window i Expressed as:
wherein I is i (w) is the sum of all sample values in the ith interval (i.e. (1, (N-w)) for a time scale of w;
if the time series has multi-fractal characteristics, the following power law relationship is satisfied within the scale-free interval:
P i (w)∝w α
wherein alpha is a mark P corresponding to the ith interval i Singular index of (w) magnitude reflecting P i (w) varying degrees of singular from interval to interval with w;
N α (w)∝w -f(α)
step 33, defining a distribution function χ of the multi-fractal system q (w) is the q-order moment of the normalized time series data:
wherein χ is q (w) is a time series data P reflecting normalization i (w) statistics of non-uniformity, q being a weight factor;
from the self-similarity of fractal, χ is known q (w) and w satisfy the following power law relationship in the scale-free interval:
χ q (w)∝w τ(q)
the logarithm of the two sides is calculated to obtain ln chi q (w) lnw curve, wherein the slope of the curve τ (q) is the mass index, τ (q) can be determined by ln chi q Performing least square fitting on linear points in the (w) to lnw double logarithmic curve to perform estimation;
wherein Δα=α max -α min The spectrum width of the multi-fractal spectrum of the time sequence data is obtained, and f (alpha) is a multi-fractal spectrum function of the time sequence data.
Further, the improvement method of the improved gating cycle unit in the step 3 is as follows:
splitting the updated gate weight matrix in the gate control circulation unit into two new updated gate matrices W z1 ,W z2 Respectively with activatedMultiplying the multi-fractal spectrum width matrixes sigma (E) and (1-sigma (E)) to obtain temporary gating output
To learn the fluctuation variation characteristics of the data in the non-stationary time series data segment:
outputting temporary gate control
Adding to obtain an integral updated gate z t Participation in calculations, i.e.
Other update rules of the improved gating loop unit are consistent with the gating loop unit:
a t ＝tanh(W h ⊙[r t *h t-1 ,x t ]+b a )
h t ＝h t-1 *(1-z t )+z t *a t
wherein, the liquid crystal display device comprises a liquid crystal display device,
representing two temporary update gates, respectively +.>
Representing two temporary updated gate matrices, respectively, sigma (x) beingSigmoid activation function, E is the spectrum width matrix of multi-fractal spectrum of input data, z t 、r t To represent the calculation results of the update gate and the reset gate at the time t, h t-1 And h t Output at time (t-1) and time t respectively,/represents multiplication of matrix corresponding elements,/represents point-wise multiplication, W * And b * Representing a weight matrix and a bias vector for the network.
Further, the improved gating loop cell network model comprises an input layer, a hidden layer and an output layer, wherein the input layer is used for inputting time sequence data, and a time sequence X= (X) containing n variable sequences is given 1 ,x 2 ,x 3 ,…,x n ) T T represents a time step, n represents an input dimension, and then the time sequence prediction model based on the gating weight unit is expressed as follows:
y^ T+1 ＝F(h 1 ,…,h T-1 ,x 1 ,…,x T )
wherein h is t In the hidden layer state, h t E, R, F () is a nonlinear mapping function which needs to be learned by a model hidden layer, y ^ T+1 Is the prediction target of the model, and is the prediction output of the output layer of the next time point; data sequence x= (X) 1 ,x 2 ,x 3 ,…,x n ) T The input matrix at the whole input layer is denoted as (x 1 ,x 2 ,x 3 ,…,x T )∈R n*T 。
Further, the loss functions in the step 5 and the step 6 are root mean square error loss functions.
Further, the method also comprises the step of training the improved gating cycle unit to obtain model parameters of the improved gating cycle unit, and the training method comprises the following steps:
and 13, calculating average absolute error, root mean square error and average error percentage of the predicted data and the actual data of the training set, evaluating a model by taking the average absolute error, root mean square error and average error percentage as measurement indexes to obtain optimized model parameters of the improved gating circulation unit, and taking the optimized model parameters as initial model parameters of the improved gating circulation unit.
The prediction model based on the multi-fractal cooperative measurement gating cycle unit comprises a data preprocessing unit, a spectrum width calculation unit based on a multi-fractal algorithm and an improved gating cycle unit, wherein the data preprocessing unit is used for preprocessing input data to obtain preprocessed time sequence data; the spectrum width calculation unit based on the multi-fractal algorithm is used for calculating a spectrum function f (alpha) and a spectrum width delta alpha of a multi-fractal spectrum of the preprocessed time sequence data by using the multi-fractal algorithm, and for a time sequence data sequence X= { X with a length of n 1 ,X 2 ,…,X n Setting the length of a sliding time window as w and the step length as 1, and calculating the spectrum width delta alpha of the multi-fractal spectrum on each time window by using a multi-fractal algorithm i Obtaining a spectrum width matrix E=G of the multi-fractal spectrum T ＝[Δα 1 ,Δα 2 ,…,Δα n-w ] T The method comprises the steps of carrying out a first treatment on the surface of the The improved gating circulation unit is used for improving the updated gating weight matrix in the gating circulation unit into a weight matrix related to the spectrum width matrix E, obtaining the improved gating circulation unit, predicting the preprocessed time sequence data, carrying out error back propagation through an optimization algorithm after each prediction, updating the weight matrix and the bias vector of the improved gating circulation unit until the number of times of prediction is greater than or equal to the highest iteration number or the loss function meets the convergence condition, and outputting the predicted data.
The beneficial effects of the invention are as follows: the invention provides an improved gating circulation unit (MF-GRU) based on the improvement of the gating circulation unit (GRU), wherein the updated gating weight matrix of the gating circulation unit (GRU) is improved to a weight matrix related to a spectrum width matrix, the fluctuation change characteristics of non-stationary time sequence data are extracted by introducing a multi-fractal technology, and a dynamic adjustment matrix is arranged to replace the traditional updated gating weight matrix so as to learn the change trend of a non-stationary data segment in the data, so that the prediction precision of the non-stationary data can be improved, and the problem that the traditional deep neural network faces the difficulty of learning the non-stationary time sequence data is solved.
The invention will now be described in detail with reference to the drawings and examples.
Drawings
FIG. 1 is a schematic flow chart of the present invention;
FIG. 2 is a schematic diagram of a modified door cycle unit;
FIG. 3 is a schematic diagram showing the influence of the number of hidden layer nodes in embodiment 1;
FIG. 4 is a schematic diagram showing the effect of the number of hidden layers in embodiment 1;
FIG. 5 is a "open reading" prediction curve for a BAC dataset;
FIG. 6 is a "open value" prediction curve for a C dataset;
FIG. 7 is a "open value" prediction curve for a JPM dataset;
FIG. 8 is a plot of "open reading" predictions for an MS data set;
fig. 9 is a "humidity" prediction curve for the USV dataset.
Detailed Description
The principles and features of the present invention are described below with reference to the drawings, the examples are illustrated for the purpose of illustrating the invention and are not to be construed as limiting the scope of the invention.
As shown in fig. 1, the prediction method based on the multi-fractal synergy metric gating cycle unit comprises the following steps:
step 4, inputting the preprocessed time sequence data into an improved gate control circulation unit to obtain predicted data; judging whether the current iteration times are greater than or equal to the preset highest iteration times, if so, turning to the step 7, otherwise, turning to the step 5;
and 7, outputting the prediction data.
As an implementation manner, the method for calculating the spectrum width by using the multi-fractal algorithm in the step 2 specifically includes the following steps:
step 31, dividing the time series data with length N into (N-w) time series with window length w by step length 1, and probability measure P of each window i Expressed as:
wherein I is i (w) is the sum of all sample values in the ith interval (i.e. (1, (N-w))) for a time scale of w;
if the time series has multi-fractal characteristics, the following power law relationship is satisfied within the scale-free interval:
P i (w)∝w α
wherein alpha is a mark P corresponding to the ith interval i Singular index of (w) magnitude reflecting P i (w) varying degrees of singular from interval to interval with w;
N α (w)∝w -f(α)
step 33, defining a distribution function χ of the multi-fractal system q (w) is the q-order moment of the normalized time series data:
wherein χ is q (w) is a time series data P reflecting normalization i (w) statistics of non-uniformity, q being a weight factor;
from the self-similarity of fractal, χ is known q (w) and w satisfy the following power law relationship in the scale-free interval:
χ q (w)∝w τ(q)
the logarithm of the two sides is calculated to obtain ln chi q (w) lnw curve, wherein the slope of the curve τ (q) is the mass index, τ (q) can be determined by ln chi q Performing least square fitting on linear points in the (w) to lnw double logarithmic curve to perform estimation;
to sum up, by calculating the probability measure P i (w) the score function χ q And (w) and a quality index tau (q), and obtaining alpha and a multi-fractal spectrum function f (alpha) by adopting least square regression fitting. In the f (alpha) -alpha pattern, the spectral width Δalpha (i.e., alpha max -α min ) The size of the fractal structure reflects the non-uniformity degree of the whole fractal structure on probability measure distribution, and the fluctuation degree of time sequence data is immediately drawn. A larger Δα indicates a more uneven distribution of data within the corresponding time-series data segment,the more severe the fluctuation changes. Thus, for a time-series data sequence x= { X of length n 1 ,X 2 ,…,X n Using the length of the time window as w and the step length as 1, calculating the spectrum width delta alpha of the multi-fractal spectrum on each time window by using the multi-fractal algorithm i Finally, a spectrum width matrix E=G of a multi-fractal spectrum of the time sequence data can be obtained T ＝[Δα 1 ,Δα 2 ,…,Δα n-w ] T To extract the characteristic of the fluctuation degree of the time series data.
As shown in fig. 2, as an embodiment, the improved method of the improved gating cycle unit of the step 3 is as follows:
splitting the updated gate weight matrix in the gate control circulation unit into two new updated gate matrices W z1 ,W z2 Multiplying the multi-fractal spectrum width matrices sigma (E) and (1-sigma (E)) with the activated multi-fractal spectrum width matrices respectively to obtain temporary gating output
To learn the fluctuation variation characteristics of the data in the non-stationary time series data segment:
outputting temporary gate control
Adding to obtain an integral updated gate z t Participation in calculations, i.e.
Other update rules of the improved gating loop unit are consistent with the gating loop unit:
a t ＝tanh(W h ⊙[r t *h t-1 ,x t ]+b a )
h t ＝h t-1 *(1-z t )+z t *a t
wherein, the liquid crystal display device comprises a liquid crystal display device,
representing two temporary update gates, respectively +.>
Representing two temporary updated gate matrices respectively, sigma (x) being Sigmoid activation function, E being a spectral width matrix of multi-fractal spectrum of input data, z t 、r t To represent the calculation results of the update gate and the reset gate at the time t, h t-1 And h t Output at time (t-1) and time t respectively,/represents multiplication of matrix corresponding elements,/represents point-wise multiplication, W * And b * Representing a weight matrix and a bias vector for the network.
As one embodiment, the improved gated loop cell network model includes an input layer for the input of time series data, given a time series x= (X) comprising n variable sequences, a hidden layer, and an output layer 1 ,x 2 ,x 3 ,…,x n ) T T represents a time step, n represents an input dimension, and then the time sequence prediction model based on the gating weight unit is expressed as follows:
y ^ T+1 ＝F(h 1 ,…,h T-1 ,x 1 ,…,x T )
wherein h is t In the hidden layer state, h t E, R, F () is a nonlinear mapping function which needs to be learned by a model hidden layer, y ^ T+1 Is the prediction target of the model, and is the prediction output of the output layer of the next time point; data sequence x= (X) 1 ,x 2 ,x 3 ,…,x n ) T The input matrix at the whole input layer is denoted as (x 1 ,x 2 ,x 3 ,…,x T )∈R n*T 。
As an embodiment, the loss function in the step 5 and the step 6 is a root mean square error loss function.
As an embodiment, the method further comprises the step of training the improved gating cycle cell to obtain model parameters of the improved gating cycle cell, and the training method comprises the following steps:
and 13, calculating average absolute error, root mean square error and average error percentage of the predicted data and the actual data of the training set, evaluating a model by taking the average absolute error, root mean square error and average error percentage as measurement indexes to obtain optimized model parameters of the improved gating circulation unit, and taking the optimized model parameters as initial model parameters of the improved gating circulation unit.
The prediction model based on the multi-fractal cooperative measurement gating cycle unit comprises a data preprocessing unit, a spectrum width calculation unit based on a multi-fractal algorithm and an improved gating cycle unit, wherein the data preprocessing unit is used for preprocessing input data to obtain preprocessed time sequence data; the spectrum width calculation unit based on the multi-fractal algorithm is used for calculating a spectrum function f (alpha) and a spectrum width delta alpha of a multi-fractal spectrum of the preprocessed time sequence data by using the multi-fractal algorithm, and for a time sequence data sequence X= { X with a length of n 1 ,X 2 ,…,X n Setting the length of a sliding time window as w and the step length as 1, and calculating the spectrum width delta alpha of the multi-fractal spectrum on each time window by using a multi-fractal algorithm i Obtaining a spectrum width matrix E=G of the multi-fractal spectrum T ＝[Δα 1 ,Δα 2 ,…,Δα n-w ] T The method comprises the steps of carrying out a first treatment on the surface of the The improved gating cyclic unit is used for improving the updated gating weight matrix in the gating cyclic unit into an AND spectrumAnd updating the weight matrix and the bias vector of the improved gating circulating unit until the number of the predictions is greater than or equal to the highest iteration number or the loss function meets the convergence condition, and outputting the predicted data.
Example 1
1. Example data:
aiming at the problem of poor prediction effect of non-stationary time sequence data in the traditional deep learning method, the fluctuation change degree of the feature to be predicted is quantized by adopting a multi-fractal technology, the performances of 3 models of an improved gating circulation unit (MF-GRU), a gating circulation unit (GRU) and a long-term short-term memory network (LSTM) are subjected to comparative analysis by combining 5 non-stationary time sequence data sets, and the prediction effect based on the multi-fractal collaborative metric gating circulation unit is analyzed and evaluated.
Example data: the 5 multivariate time series data sets included 4 market data sets, 1 air humidity index data set. All data are divided into a training set according to the first 60 percent and a testing set according to the last 40 percent;
the 4 stock datasets include: the public data set recorded in the Kaggle Datasets machine learning library mainly records stock data of each big bank, and each data set has 2517 records and comprises 5 effective characteristics (closing price, opening price, lowest price, highest price and bargain). The four stock datasets are respectively noted as "BAC", "C", "JPM", "MS";
1 air humidity index prediction dataset: the public data set recorded in the UCI machine learning storage library and the machine learning library is mainly recorded in sea surface humidity data of the coastal area of Athens. The dataset has 1672 records containing 4 valid features (device number, humidity, temperature, reporting time) and is denoted "USV".
2. Metric index:
average absolute error (MAE) and average absolute percent error (MAPE), root Mean Square Error (RMSE) were chosen as metrics to evaluate model performance. Three metrics are defined as follows:
where n is the total number of samples, y predict Is the predicted value, y real Is a true value.
3. Parameter tuning:
the time sequence prediction based on the improved gating circulating unit needs to set parameters in the model, the setting of the model parameters can have great influence on the performance of the model, and the model parameters mainly comprise a loss function, an optimization algorithm, a learning rate, the number of hidden layer nodes, the number of hidden layer layers, the number of iterations required by model training and the like.
(1) Prediction effect when nodes with same hidden layer number and different hidden layers are used
The number of hidden layer nodes is sequentially selected from the candidate set {8,16,32,64,96,128} and tested. As a result, as shown in fig. 3, as the number of hidden layer nodes increases, the prediction performance increases first, and when the number of hidden layer nodes is 32 or 64 (the two accuracies are very similar), the highest accuracy in the candidate set parameters is reached, and when the number of hidden layer nodes exceeds 64, the accuracy starts to decrease. As shown in table 1, when the number of hidden layer nodes is selected to be 64, all of the 3 metrics are better than the result when the number of neurons is selected to be 32. The experiment set the number of hidden layer nodes to 64.
TABLE 1 influence of hidden layer node quantity schematic form "
Note that: the data represented by gray background is the best result
(2) Prediction effect when same hidden layer node number is different from hidden layer number
After the number of neurons is determined, the number of neurons is set as a fixed value, the number of hidden layers is sequentially selected from a hidden layer number candidate set {1,2 and 3} and tested, the experimental result is drawn into a histogram as shown in fig. 4, the prediction performance is firstly increased along with the increase of the number of hidden layers, and the highest precision in the candidate set parameters is achieved when the number of hidden layers is 2, so that the number of hidden layer numbers is set to 2. As shown in table 2, when the number of hidden layers is 2,3 metrics are optimal;
TABLE 2 influence of number of hidden layers schematic form'
Note that: the data represented by gray background is the best result
As can be seen from the above comparative experiments, when the number of hidden layers is 2 and the number of nodes in each hidden layer is 64, the performance of the GRU network model is optimal. The specific model parameter table is shown in table 3;
TABLE 3 parameter set Table "
| Parameters (parameters) | Value taking |
| Loss function | Root Mean Square Error (RMSE) |
| Optimization algorithm | Adam |
| Output layer activation function | tanh |
| Learning rate | 0.005 |
| Number of input nodes | 4 |
| Number of |
1 |
| Number of |
2 |
| Hidden |
64 |
| Number of iterations | 4000 |
For fairness, all deep learning models in subsequent experiments will use the table 3 parameter settings to set 2 hidden layers, 64 nodes per hidden layer.
4. Comparison of experimental results
In order to verify the performance of the MF-GRU time sequence prediction model, a time sequence prediction model is built based on MF-GRU, LSTM, GRU unit, parameters when GRU takes the best performance and training sets and test sets with the same proportion are adopted for all models to perform time sequence prediction comparison experiments, the precision of each model is compared, and the experimental results of each model on 5 time sequence data sets are shown in table 4. Wherein gray represents the optimal result of the model, as shown in Table 4, the performance of the MF-GRU model on 5 data sets is superior to that of the traditional LSTM and GRU models;
TABLE 4 schematic representation of experimental results "
The 5 data set BAC, C, JPM, MS, USV prediction curves used for the experiments are shown in the corresponding graphs of fig. 5, 6, 7, 8 and 9, respectively. The MF-GRU time sequence prediction model has the most similar non-stationary data segments of data sets BAC (figure 5) 0 to 20, data set C (figure 6) 20 to 30, data set JPM (figure 7) 20 to 30, data set MS (figure 8) 90 to 100 and data set USV (figure 9) 25 to 50 with the true values, and the prediction effect is superior to other models. In addition, when the time sequence data set C is predicted, the overall prediction effect of the MF-GRU is obviously better than that of a GRU model. This is because the weight matrix of the multi-fractal spectrum width can dynamically adjust weights for non-stationary data segments to reduce errors;
the result shows that compared with LSTM and GRU models, the MF-GRU model has better prediction performance and higher precision.
The foregoing is illustrative of the best mode of carrying out the invention, and is not presented in any detail as is known to those of ordinary skill in the art. The protection scope of the invention is defined by the claims, and any equivalent transformation based on the technical teaching of the invention is also within the protection scope of the invention.
Claims (7)
1. The prediction method based on the multi-fractal cooperative measurement gating cycle unit is characterized by comprising the following steps of:
step 1, preprocessing the input air humidity index time sequence data to obtain preprocessed time sequence data;
step 2, calculating the spectrum function f (alpha) and the spectrum width delta alpha of the multi-fractal spectrum of the preprocessed air humidity index time sequence data by using a multi-fractal algorithm, wherein for a time sequence data sequence X=with the length of n
{X 1 ,X 2 ,…,X n Time window lengthThe degree is w, the step length is 1, and the spectrum width delta alpha of the multi-fractal spectrum on each time window is calculated by utilizing the multi-fractal algorithm i Obtaining a spectrum width matrix E=G of the multi-fractal spectrum T ＝[Δα 1 ,Δα 2 ,…,Δα n-w ] T ；
Step 3, improving an updated gate weight matrix in the gate control circulation unit into a weight matrix related to the spectrum width matrix E to obtain an improved gate control circulation unit;
step 4, inputting the preprocessed air humidity index time sequence data into an improved gate control circulating unit to obtain predicted air humidity index data; judging whether the current iteration times are greater than or equal to the preset highest iteration times or not, if so, turning to the step 7, and if not, turning to the step 5;
step 5, calculating a loss function by using the predicted air humidity index data and the actual air humidity index data;
step 6, judging whether the loss function meets the convergence condition, if so, turning to step 7; if not, carrying out error back propagation through an optimization algorithm, updating a weight matrix and a bias vector of the improved gating loop unit, and turning to the step 5 after adding one to the current iteration times;
and 7, outputting predicted air humidity index data.
2. The prediction method based on multi-fractal synergy metric gating cycle unit as recited in claim 1, wherein the method for calculating the spectral width using the multi-analysis algorithm in step 2 specifically comprises the following steps:
step 31, dividing the time series data of the air humidity index with the length N into (N-w) time series with the window length w according to the step length of 1, and measuring the probability P of each window i Expressed as:
wherein I is i (w) is the sum of all sample values in the ith interval at a time scale of w(i∈(1，(N-w)))；
If the time series has multi-fractal characteristics, the following power law relationship is satisfied within the scale-free interval:
P i (w)∝w α
wherein alpha is a mark P corresponding to the ith interval i Singular index of (w) magnitude reflecting P i (w) varying degrees of singular from interval to interval with w;
step 32, counting the number of intervals with the same alpha and time scale w as N α (w) decreasing with w, N α (w) increasing, if there is a multi-scale relationship for this time sequence, the following power law relationship is satisfied within the scale-free interval:
N α (w)∝w -f(α)
step 33, defining a distribution function χ of the multi-fractal system q (w) is the q-order moment of the normalized time series data:
wherein χ is q (w) is a time series data P reflecting normalization i (w) statistics of non-uniformity, q being a weight factor;
from the self-similarity of fractal, χ is known q (w) and w satisfy the following power law relationship in the scale-free interval:
χ q (w)∝w τ(q)
the logarithm of the two sides is calculated to obtain ln chi q (w) lnw curve, wherein the slope of the curve τ (q) is the mass index, τ (q) can be determined by ln chi q Performing least square fitting on linear points in the (w) to lnw double logarithmic curve to perform estimation;
step 34, on the premise of knowing a q-tau (q) curve, alpha (q) and f (alpha) can be obtained from q and tau (q) through Legend transformation (Legendre transformation);
wherein Δα=α max -α min ) The spectrum width of the multi-fractal spectrum of the time sequence data is obtained, and f (alpha) is a multi-fractal spectrum function of the time sequence data.
3. The prediction method based on multi-fractal synergy metric gating cycle unit as recited in claim 1, wherein the improved method of the improved gating cycle unit of step 4 is as follows:
splitting the updated gate weight matrix in the gate control circulation unit into two new updated gate matrices W z1 ,W z2 Multiplying the multi-fractal spectrum width matrices sigma (E) and (1-sigma (E)) with the activated multi-fractal spectrum width matrices respectively to obtain temporary gating output
To learn the fluctuation variation characteristics of the data in the non-stationary time series data segment:
outputting temporary gate control
Adding to obtain an integral updated gate z t Participation in calculations, i.e.
Other update rules of the improved gating loop unit are consistent with the gating loop unit:
h t ＝h t-1 *(1-z t )+z t *a t
wherein the method comprises the steps of
Representing two temporary update gates, respectively +.>
Representing two temporary updated gate matrices respectively, sigma (x) being Sigmoid activation function, E being a spectral width matrix of multi-fractal spectrum of input data, z t 、r t To represent the calculation results of the update gate and the reset gate at the time t, h t-1 And h t Output at time (t-1) and time t respectively,/represents multiplication of matrix corresponding elements,/represents point-wise multiplication, W * And b * Representing a weight matrix and a bias vector for the network.
4. The prediction method based on multi-fractal synergy metric gating cyclic unit as recited in claim 1, wherein the improved gating cyclic unit network model comprises an input layer, a hidden layer and an output layer, the input layer is used for inputting time series data, and a time series x= (X) containing n variable series is given 1 ,x 2 ,x 3 ,...,x n ) T T represents a time step, n represents an input dimension, and then the time sequence prediction model based on the gating weight unit is expressed as follows:
y^ T+1 ＝F(h 1 ,...,h T-1 ,x 1 ,...,x T )
wherein h is t In the hidden layer state, h t E, R, F ()'s are nonlinear mapping functions that the model hidden layer needs to learn, y ≡ T+1 Is the prediction target of the model, and is the prediction output of the output layer of the next time point; data sequence x= (X) 1 ,x 2 ,x 3 ,...,x n ) T Throughout the whole deliveryThe input matrix of the input layer is denoted as (x 1 ,x 2 ,x 3 ,...,x T )∈R n*T 。
5. The prediction method based on multi-fractal synergy metric gating cycle unit as recited in claim 1, wherein the loss function in step 5 and step 6 is a root mean square error loss function.
6. The prediction method based on multi-fractal synergy metric gating cycle unit as recited in claim 1, further comprising the step of training the improved gating cycle unit to obtain model parameters of the improved gating cycle unit, the training method comprising the steps of:
step 11, selecting a part of data from the time sequence data of the input air humidity index as a training set;
step 12, inputting the data of the training set into an improved gating circulation unit to obtain the predicted air humidity index time sequence data of the training set;
and 13, calculating average absolute error, root mean square error and average error percentage of the predicted data and the actual data of the training set, evaluating the model by taking the average absolute error, root mean square error and average error percentage as measurement indexes to obtain optimized model parameters of the improved gating circulation unit, and taking the optimized model parameters as initial model parameters of the improved gating circulation unit.
7. The prediction model based on the multi-fractal cooperative measurement gating circulation unit is characterized by comprising a data preprocessing unit, a spectrum width calculation unit based on a multi-fractal algorithm and an improved gating circulation unit, wherein the data preprocessing unit is used for preprocessing input air humidity index time sequence data to obtain preprocessed air humidity index time sequence data; the spectrum width calculation unit based on the multi-fractal algorithm is used for calculating a spectrum function f (alpha) and a spectrum width delta alpha of a multi-fractal spectrum of the preprocessed time sequence data by using the multi-fractal algorithm, and for a time sequence data sequence X= { X with a length of n 1 ,X 2 ,…,X n Using the length of the time window as w and the step length as 1, calculating the spectrum width delta alpha of the multi-fractal spectrum on each time window by using the multi-fractal algorithm i Obtaining a spectrum width matrix E=G of the multi-fractal spectrum T ＝[Δα 1 ,Δα 2 ,…,Δα n-w ] T The method comprises the steps of carrying out a first treatment on the surface of the The improved gating circulation unit is used for improving an updated gating weight matrix in the gating circulation unit into a weight matrix related to the spectrum width matrix E, obtaining the improved gating circulation unit, predicting the preprocessed air humidity index time sequence data, carrying out error counter propagation through an optimization algorithm after each prediction, updating the weight matrix and the bias vector of the improved gating circulation unit until the number of predictions is greater than or equal to the highest iteration number or when a loss function meets a convergence condition, and outputting the predicted air humidity index time sequence data.
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