CN116993181A - RBF-ARX-based comprehensive energy system time sequence probability multi-element load prediction method and system - Google Patents
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Abstract
The invention belongs to the field of multi-element load prediction of a comprehensive energy system, and provides a time sequence probability multi-element load prediction method and a time sequence probability multi-element load prediction system of the comprehensive energy system based on RBF-ARX, wherein the technical scheme is as follows: carrying out correlation analysis by adopting a maximum information coefficient method, and selecting proper external factors and IES loads with stronger coupling relations as input of a model according to a correlation analysis result; decomposing the original multi-element load data into a deterministic component and a stochastic component based on a fast fourier transform; based on the RBF-ARX mixed model, carrying out time sequence prediction on the deterministic component; based on Gaussian mixture model and Markov Monte Carlo algorithm, probability prediction is carried out on the random component, and then the random component is added with time sequence prediction result of deterministic component to be used as the whole prediction result. The method has the advantages of higher prediction precision, higher calculation speed and certain generalization.
Description
Technical Field
The invention belongs to the field of multi-element load prediction of a comprehensive energy system, and particularly relates to a time sequence probability multi-element load prediction method and system of the comprehensive energy system based on RBF-ARX.
Background
The statements in this section merely provide background information related to the present disclosure and may not necessarily constitute prior art.
The integrated energy system (Integrated energy system, IES) serves as a novel energy supply mode, and flexible conversion, efficient distribution and organic coordination among different energy sources are achieved through a plurality of energy conversion and storage devices in the integrated energy system. Compared with the traditional single energy system, the comprehensive energy system can improve the energy utilization efficiency, effectively reduce the carbon emission and has the characteristics of flexibility, cleanness and high efficiency. While accurate short-term predictions for multiple loads (including primarily cooling, thermal, electrical loads) are a precondition to ensure reliable, economical operation of IES. On one hand, various forms of energy sources can be reasonably configured according to the multi-element load prediction result, so that the energy source utilization efficiency and the economical efficiency of system operation are improved; on the other hand, a demand response plan can be formulated according to the load prediction result, so that energy supply and demand balance is realized, and the running reliability of the system is improved. Therefore, the development of multi-element load prediction research for the comprehensive energy system has important significance.
At present, load prediction methods are mainly classified into two types, namely a statistical method and a machine learning method. Classical statistical algorithms include exponential smoothing, autoregressive moving average (ARMA), autoregressive integral moving average (ARIMA), etc., where the time frame that such methods can predict is short and where the prediction accuracy is degraded when a longer prediction time frame is required. The machine learning method comprises Support Vector Regression (SVR), a big data analysis technology, an artificial neural network and the like, wherein the artificial neural network is widely applied in the field of load prediction by virtue of good nonlinear approximation characteristics and excellent performance in space-time sequence prediction.
In recent years, in order to further improve the prediction performance of nonlinear time series such as IES load, a learner has proposed to combine another model or technique with an artificial neural network to construct a hybrid model with better performance for the prediction of time series, wherein RBF-ARX is a more typical hybrid model. Compared with the traditional single neural network, the RBF-ARX combined model has higher prediction precision, and the application of the RBF-ARX in the prediction of the multiple loads can greatly improve the precision of the prediction of the multiple loads. However, IES multiple loads have greater volatility and randomness than conventional electrical loads of a single power system, and therefore tend to affect the predictive effect of RBF-ARX.
Disclosure of Invention
In order to solve at least one technical problem in the background art, the invention provides the RBF-ARX-based comprehensive energy system time sequence probability multi-element load prediction method, which adopts an RBF-ARX mixed model, has higher prediction precision and higher calculation speed, and has certain generalization. Meanwhile, the method combines the neural network time sequence prediction and the statistical probability prediction, and considers the time sequence and the probability of the IES load, thereby achieving better prediction effect.
In order to achieve the above purpose, the present invention adopts the following technical scheme:
the first aspect of the invention provides a comprehensive energy system time sequence probability multi-element load prediction method based on RBF-ARX, which comprises the following steps:
acquiring multi-element load data of the comprehensive energy system, performing correlation analysis, and screening to obtain multi-element load data with external factors and coupling relations meeting conditions;
decomposing the multi-element load data meeting the conditions into a deterministic component and a random component;
optimizing the RBF-ARX mixed model parameters by adopting a variable projection algorithm, and then carrying out time sequence prediction on deterministic components;
fitting the randomness component, obtaining a predicted value of the randomness component through sampling after obtaining a probability density function of the fitting randomness component, and carrying out probability prediction on the randomness component; the timing predictions of the deterministic component and the probability predictions of the stochastic component are added as final predictions.
The second aspect of the invention provides a comprehensive energy system time sequence probability multi-element load prediction system based on RBF-ARX, comprising:
the correlation analysis module is used for acquiring the multi-element load data of the comprehensive energy system, performing correlation analysis, and screening to obtain multi-element load data with external factors and coupling relations meeting the conditions;
a data decomposition module for decomposing the conditional multi-element load data into a deterministic component and a stochastic component;
the time sequence prediction module is used for performing time sequence prediction on the deterministic component after optimizing the RBF-ARX mixed model parameters by adopting a variable projection algorithm;
the probability prediction module is used for fitting the randomness component, acquiring a predicted value of the randomness component through sampling after obtaining a probability density function of the fitted randomness component, and carrying out probability prediction on the randomness component;
and a prediction result output module for adding the time-series prediction result of the deterministic component and the probability prediction of the stochastic component as final prediction results.
A third aspect of the present invention provides a computer-readable storage medium.
A computer readable storage medium having stored thereon a computer program which when executed by a processor performs the steps in the RBF-ARX based integrated energy system time series probability multiple load prediction method as described above.
A fourth aspect of the invention provides a computer device.
A computer device comprising a memory, a processor and a computer program stored on the memory and executable on the processor, the processor implementing the steps in the RBF-ARX based integrated energy system time series probability multiple load prediction method as described above when the program is executed.
Compared with the prior art, the invention has the beneficial effects that:
1. the multi-element load prediction method combines the neural network time sequence prediction and the statistical probability prediction based on the RBF-ARX mixed model, considers the time sequence and the probability of the IES load, predicts the deterministic component and the random component of the IES load respectively, increases the prediction step on the surface, reduces the difficulty degree of direct prediction in practice and improves the efficiency of the IES load prediction. The prediction accuracy is higher, the calculation speed is faster, and the method has certain generalization.
2. The prediction method of the invention can be popularized and applied to IES loads with complex coupling relations and a large number of fluctuation and probability components.
Additional aspects of the invention will be set forth in part in the description which follows and, in part, will be obvious from the description, or may be learned by practice of the invention.
Drawings
The accompanying drawings, which are included to provide a further understanding of the invention and are incorporated in and constitute a part of this specification, illustrate embodiments of the invention and together with the description serve to explain the invention.
FIG. 1 is a flow chart of a comprehensive energy system time sequence probability multi-element load prediction method based on RBF-ARX;
FIGS. 2 (a) -2 (b) are graphs showing the results of analyzing correlations between multiple loads and external factors using the maximum information coefficient method provided by the present invention;
fig. 3 is a graph of the results of decomposing the raw IES payload data using a fast fourier transform method provided by the present invention.
Detailed Description
The invention will be further described with reference to the drawings and examples.
It should be noted that the following detailed description is illustrative and is intended to provide further explanation of the invention. Unless defined otherwise, all technical and scientific terms used herein have the same meaning as commonly understood by one of ordinary skill in the art to which this invention belongs.
It is noted that the terminology used herein is for the purpose of describing particular embodiments only and is not intended to be limiting of exemplary embodiments according to the present invention. As used herein, the singular is also intended to include the plural unless the context clearly indicates otherwise, and furthermore, it is to be understood that the terms "comprises" and/or "comprising" when used in this specification are taken to specify the presence of stated features, steps, operations, devices, components, and/or combinations thereof.
Example 1
As shown in fig. 1, the embodiment provides a comprehensive energy system time sequence probability multi-element load prediction method based on RBF-ARX, which comprises the following steps:
step 1: adopting a maximum information coefficient method to analyze the correlations between the multiple loads and external factors, and selecting proper external factors and IES loads with stronger coupling relations as the input of a model according to correlation analysis results; the analysis results are shown in FIG. 2 (a) -FIG. 2 (b).
Step 2: preprocessing the multi-element load data by adopting a moving window method and a 3 sigma criterion based on the multi-element load data obtained in the step 1 to obtain preprocessed multi-element load data;
step 3: decomposing the multi-element load data preprocessed in the step 2 into a deterministic component and a random component based on fast Fourier transform; the analysis results are shown in FIG. 3.
Step 4: based on the RBF-ARX mixed model, carrying out time sequence prediction on the deterministic component;
step 5: based on Gaussian mixture model and Markov Monte Carlo algorithm, probability prediction is carried out on the random component, and then the random component is added with time sequence prediction result of deterministic component to be used as the whole prediction result.
In step 1, the analysis of the correlation between the multiple loads and external factors by using the maximum information coefficient method specifically includes:
the MIC is calculated based on the principle of mutual information, and the correlation between two variables, mainly cold, heat, electrical load, and external factors such as temperature, air pressure, humidity, are measured by joint probability, and are represented by x and y.
The calculation equation for MIC is as follows:
wherein a and b represent the number of grids divided in x-axis and y-axis directions; s is the total number of grids, which is 0.6 times of the data sample; p (x, y) represents the probability that the variable samples are distributed in grids x and y. The mutual information is obtained by calculating the joint probability of sample distribution in the grid, and the MIC takes the maximum value of the normalized mutual information.
In step 2, the decomposing the original multi-element load data into a deterministic component and a stochastic component based on the fast fourier transform specifically includes:
the original time series of inputs constitutes a vector X of length N, each data point in the vector being represented by X (N). Obtaining a representation result X of the time sequence in the frequency domain through FFT process DFT (k)：
X DFT (k) The calculation formula of (2) is as follows:
where k is the frequency domain representation result X DFT (k) The number corresponding to each data point in the vector X is n.
By setting a threshold level L, X is filtered out DFT (k) In frequency components related to the original time series randomness component:
thereafter for screening X DFT (k) Performing an IFFT operation to obtain a deterministic component separated from the original time series as follows:
finally, the original data and the deterministic component are subjected to difference to obtain a randomness component, and the calculation formula is as follows:
X rand (n)＝X(n)-X cert (n),0≤n≤N-1 (6)
further, in step 3, the performing timing prediction on the deterministic component based on the RBF-ARX hybrid model specifically includes:
when a Gaussian function is used as the basis function of the RBF neural network, the RBF-ARX model can be expressed as:
wherein the method comprises the steps ofFor the output at time t, +.>For the input at time t-i, X (t-1) is a state variable at time t-1; n is n y For the number of inputs, nu is the number of outputs, p, q, m and n X Dim { X (t-1) } is the order of the model; phi (phi) y,i And phi u,i Is a state dependent function coefficient, approximated by a set of RBF neural networks; />And->The center and the scaling factors of the RBF network are respectively; />And->Linear weight of RBF network; the terms "vector" and "vector" - "E (t) is the white noise sequence, +.>And->Is the offset of RBF network, phi 0 And phi j,i Is a coefficient of a state dependent function, y (t-i) and u (t-i) are the output and input at time t-i, < >>And->The center and the scaling factors of the RBF network are respectively, u and y are input variables and output variables of the RBF-ARX model, and y represents the time sequence prediction result of the deterministic component.
Parameter optimization of the RBF-ARX model belongs to the separable nonlinear least squares (SNLLS) problem,
the embodiment adopts a Variable Projection (VP) algorithm proposed by Golub and Pereyera and the like to optimize model parameters, and the specific steps are as follows:
the parameter optimization problem of the RBF-ARX model is as follows:
wherein the method comprises the steps ofThe written vector is in the form of:
wherein θ is L ＝(c 0 ,c 1 ,···,c m ,c 1,0 ,···,c 1,m ,c p,0 ,···,c p,m ) T As a linear parameter of the model,θ N is a nonlinear parameter of the model.
For a fixed nonlinear parameter, the VP algorithm solves the linear least squares problem:
the method comprises the following steps:
θ L ＝Φ(θ N ) + y (11)
wherein phi (theta) N ) + Is a matrix phi (theta) N ) Moore-Penrose, by substituting formula (11) into formula (10):
wherein recordFor the orthographic projection operator, the equation (12) only relates to nonlinear parameters, and the VP algorithm completes the simplification of the problem.
Then solving the nonlinear least square problem by a Levenberg-Marquardt (LM) method, and performing iterative updating steps:
where k represents the number of iteration steps, β k Is the search direction, d k Is a step size coefficient. Step size coefficient d k Is determined by the following equation:
wherein the method comprises the steps ofDamping parameter gamma k Determining d k Is of a size and orientation of (c). When gamma is k Approaching 0, d k Along the Newton-Gaussian direction; when gamma is k Approaching infinity, d k Along the steepest descent direction.
The form of the jacobian matrix given by Golub and Pereyra is as follows (simple parameters omitted from the expression):
where D is the Frechet derivative of a map, Φ - Is the generalized inverse of Φ symmetry.
And finally, after parameter optimization of the RBF-ARX model, the obtained variable y represents a deterministic component time sequence prediction result.
In step 4, probability prediction is performed on the random component based on a gaussian mixture model and a markov monte carlo algorithm, and then the probability prediction is added with a time sequence prediction result of the deterministic component, so that the overall prediction result is obtained, and the method specifically comprises the following steps:
the construction method of the Gaussian mixture model comprises the following steps:
based on the statistical knowledge, a gaussian mixture model GMM is built, which can be expressed as:
wherein the parameter alpha n The weight coefficient in the Gaussian mixture model satisfies that the sum of the weights is 1;representing a gaussian density function; θ n ＝(μ n ,σ n 2 )，μ n Is the mean value of Gaussian function, sigma n 2 Is the covariance matrix of the gaussian function.
Fitting the randomness component to obtain a corresponding probability density function, wherein a parameter optimization method adopted in the fitting process is a greatly expected algorithm, and the specific algorithm steps are as follows:
1) Inputting random component sample data X rand (n)＝(x 1 ,x 2 ,x 3 ,..), the maximum number of iterations is J, and the number of gaussian distribution members is N.
2) The probability density distribution p (x|θ) of the random component sample data is estimated, and the condition distribution p (z|x, θ) is estimated.
3) Estimating the weight coefficient alpha of the GMM model n ，μ n ，σ 2 n Record theta n ＝{α n ,μ n ,σ 2 n }。
4) Select θ 0 As an initial parameter of the model.
5) Iteration is started, j=1, 2, 3.
6) Calculating a conditional probability distribution P (z j |x j ,θ j )。
7) Calculating the conditional expectation L (θ, θ) of the joint distribution j ) E.g. formula (17)
8) Maximizing L (θ, θ) j ) Determine θ j E.g. formula (18)
θ j ＝arg max L(θ,θ j-1 ) (18)
9) Judging theta j Whether or not to converge.
10 If the algorithm converges, ending the iteration and outputting the parameters of the GMM, and if the algorithm does not converge, continuing the iteration until the algorithm converges.
After obtaining a probability density function fitting the random component, sampling by using a Markov Monte Carlo algorithm to obtain a predicted value of the random component, and finally adding the predicted value with a time sequence predicted result of the deterministic component to obtain an overall predicted result, wherein the specific algorithm steps are as follows:
1) The state transition matrix Q of the arbitrary selected Markov chain is input, the target is distributed smoothly pi (x), the state transition times N1 are set, and the required sample number N2 is set.
2) From any one ofFinding the initial state value x obtained by that sampling in the probability distribution 0 。
3) Circulation was performed, t=0, 1,..n1+n2-1.
4) From a conditional probability distribution Q (x|x t ) Mid-sampling to obtain sample x * 。
5) Sampling u-uniform [0,1] from the uniform distribution, u being the generated uniform distribution.
6) If it isAccept transfer x t →x * I.e. x t+1 ＝x * The method comprises the steps of carrying out a first treatment on the surface of the Otherwise, not accepting the transfer, which is x t+1 ＝x t Wherein, alpha (x t ,x * ) For the set acceptance rate coefficient matrix, pi (j) is the target stable distribution, Q (j, i) is the state transition matrix, x t+1 Is a predictive value of the randomness component.
In order to verify the practicability of the multi-element load prediction method provided by the invention, simulation tests are carried out on a relevant platform based on historical data of a comprehensive energy system of a certain university.
The dataset contained 15 minute scale load and meteorological data throughout 2018, with 7 days of data extracted per season for the experiment and at 5:2 to divide the training set and the test set. Five cases were set up in total, each case being set up specifically as follows, wherein case 5 is the method proposed by the present invention.
Case 1: the time sequence probability decomposition is not carried out on the IES load data, and the LSTM is directly utilized for carrying out time sequence prediction on the load.
Case 2: the time sequence probability decomposition is not carried out on the IES load data, and the Bi-LSTM is directly utilized for carrying out time sequence prediction on the load.
Case 3: and carrying out time sequence probability decomposition on the IES load data, carrying out time sequence prediction on deterministic components by using LSTM, and carrying out probability prediction on random components by using Gaussian mixture model.
Case 4: and carrying out time sequence probability decomposition on the IES load data, carrying out time sequence prediction on deterministic components by using Bi-LSTM, and carrying out probability prediction on random components by using a Gaussian mixture model.
Case 5: and (3) carrying out time sequence probability decomposition on the IES load data, carrying out time sequence prediction on deterministic components by using RBF-ARX, and carrying out probability prediction on random components by using a Gaussian mixture model.
Tables 1 to 2 show the average values of the ten-step prediction errors in spring and autumn, respectively, by learning the model.
Table 1 spring IES load lead ten step prediction error average
TABLE 2 mean value of ten-step predictive error for IES load lead in autumn
From tables 1 and 2, it can be obtained that: in the cold, hot and electric load prediction in spring and autumn, the prediction errors RMSE and MAPE of case 5 are obviously smaller than those of the other four cases, which shows that case 5 adopting time sequence probability decomposition and RBF-ARX has the best prediction performance. For case 5, the prediction error of the electric load and the cold load in spring and autumn is smaller, the MAPE change is relatively stable within 2%, and the prediction precision is higher. In summary, the practicability and effectiveness of the multi-element load prediction method provided by the invention can be demonstrated.
Example two
The embodiment provides a comprehensive energy system time sequence probability multi-element load prediction system based on RBF-ARX, which comprises the following components:
the correlation analysis module is used for acquiring the multi-element load data of the comprehensive energy system, performing correlation analysis, and screening to obtain multi-element load data with external factors and coupling relations meeting the conditions;
the data preprocessing module is used for preprocessing multi-element load data meeting the conditions by adopting a moving window method and a 3 sigma rule, cleaning the multi-element load data and screening abnormal values in the data;
the data decomposition module is used for decomposing the preprocessed multi-element load data into a deterministic component and a random component;
the time sequence prediction module is used for performing time sequence prediction on the deterministic component after optimizing the RBF-ARX mixed model parameters by adopting a variable projection algorithm;
the probability prediction module is used for fitting the randomness component, acquiring a predicted value of the randomness component through sampling after obtaining a probability density function of the fitted randomness component, and carrying out probability prediction on the randomness component;
and a prediction result output module for adding the time-series prediction result of the deterministic component and the probability prediction of the stochastic component as final prediction results.
Example III
The present embodiment provides a computer readable storage medium having stored thereon a computer program which when executed by a processor performs the steps of the RBF-ARX based integrated energy system time-series probability multiple load prediction method according to embodiment one.
Example IV
The embodiment provides a computer device, which comprises a memory, a processor and a computer program stored on the memory and capable of running on the processor, wherein the processor executes the program to realize the steps in the comprehensive energy system time sequence probability multi-element load prediction method based on RBF-ARX according to the embodiment.
It will be appreciated by those skilled in the art that embodiments of the present invention may be provided as a method, system, or computer program product. Accordingly, the present invention may take the form of a hardware embodiment, a software embodiment, or an embodiment combining software and hardware aspects. Furthermore, the present invention may take the form of a computer program product embodied on one or more computer-usable storage media (including, but not limited to, magnetic disk storage, optical storage, and the like) having computer-usable program code embodied therein.
The present invention is described with reference to flowchart illustrations and/or block diagrams of methods, apparatus (systems) and computer program products according to embodiments of the invention. It will be understood that each flow and/or block of the flowchart illustrations and/or block diagrams, and combinations of flows and/or blocks in the flowchart illustrations and/or block diagrams, can be implemented by computer program instructions. These computer program instructions may be provided to a processor of a general purpose computer, special purpose computer, embedded processor, or other programmable data processing apparatus to produce a machine, such that the instructions, which execute via the processor of the computer or other programmable data processing apparatus, create means for implementing the functions specified in the flowchart flow or flows and/or block diagram block or blocks.
These computer program instructions may also be stored in a computer-readable memory that can direct a computer or other programmable data processing apparatus to function in a particular manner, such that the instructions stored in the computer-readable memory produce an article of manufacture including instruction means which implement the function specified in the flowchart flow or flows and/or block diagram block or blocks.
These computer program instructions may also be loaded onto a computer or other programmable data processing apparatus to cause a series of operational steps to be performed on the computer or other programmable apparatus to produce a computer implemented process such that the instructions which execute on the computer or other programmable apparatus provide steps for implementing the functions specified in the flowchart flow or flows and/or block diagram block or blocks.
Those skilled in the art will appreciate that implementing all or part of the above-described methods in accordance with the embodiments may be accomplished by way of a computer program stored on a computer readable storage medium, which when executed may comprise the steps of the embodiments of the methods described above. The storage medium may be a magnetic disk, an optical disk, a Read-Only Memory (ROM), a Random access Memory (Random AccessMemory, RAM), or the like.
The above description is only of the preferred embodiments of the present invention and is not intended to limit the present invention, but various modifications and variations can be made to the present invention by those skilled in the art. Any modification, equivalent replacement, improvement, etc. made within the spirit and principle of the present invention should be included in the protection scope of the present invention.
Claims (10)
1. The comprehensive energy system time sequence probability multi-element load prediction method based on RBF-ARX is characterized by comprising the following steps:
acquiring multi-element load data of the comprehensive energy system, performing correlation analysis, and screening to obtain multi-element load data with external factors and coupling relations meeting conditions;
decomposing the multi-element load data meeting the conditions into a deterministic component and a random component;
optimizing the RBF-ARX mixed model parameters by adopting a variable projection algorithm, and then carrying out time sequence prediction on deterministic components;
fitting the randomness component, obtaining a predicted value of the randomness component through sampling after obtaining a probability density function of the fitting randomness component, and carrying out probability prediction on the randomness component; the timing predictions of the deterministic component and the probability predictions of the stochastic component are added as final predictions.
2. The RBF-ARX-based comprehensive energy system time-series probability multiple load prediction method as claimed in claim 1, wherein correlation between multiple loads and external factors is analyzed by using a maximum information coefficient method.
3. The RBF-ARX-based comprehensive energy system time-series probability multiple load prediction method of claim 1, wherein said decomposing conditional multiple load data into deterministic and stochastic components comprises:
the qualified multi-element load data X (n) is subjected to FFT to obtain a representation result X of a time sequence in a frequency domain DFT (k)；
By setting a threshold level, X is filtered out DFT (k) Frequency components related to the X (n) randomness component;
for screening X DFT (k) Performing IFFT operation to obtain deterministic component X separated from original time sequence cert ；
The randomness component X can be obtained by differencing the original data with the deterministic component rand (n)。
4. The method for predicting the time sequence probability multiple loads of the comprehensive energy system based on RBF-ARX according to claim 1, wherein the method is characterized in that based on an RBF-ARX hybrid model, a variable projection algorithm is adopted to optimize model parameters, and the method specifically comprises the following steps:
writing the RBF-ARX mixed model as an optimization problem of model linear parameters and nonlinear parameters;
for nonlinear parameters, obtaining the relation between the model linear parameters and the nonlinear parameters by solving the linear least square problem;
simplifying the optimization problem based on the relation between the model linear parameters and the nonlinear parameters to obtain an expression only containing the nonlinear parameters as the simplified optimization problem;
solving the nonlinear least square problem by an LM method, and taking the obtained result as a time sequence prediction result of a deterministic component.
5. The method for predicting the time sequence probability multiple load of the comprehensive energy system based on RBF-ARX according to claim 1, wherein a Gaussian mixture model is adopted to fit the random components, so as to obtain a probability density function of the corresponding fit random components.
6. The method for predicting the time sequence probability multiple loads of the comprehensive energy system based on RBF-ARX according to claim 5, which is characterized by comprising the following steps: fitting the randomness component by adopting a Gaussian mixture model to obtain a probability density function of the corresponding fitting randomness component, wherein the probability density function specifically comprises the following steps:
inputting random component sample data, the maximum iteration number and the number of Gaussian distribution members;
estimating probability density distribution of the random component to obtain a conditional distribution p (z|x, theta);
estimating the weight coefficient alpha of a Gaussian mixture model n ，μ n ，σ 2 n Record theta n ＝{α n ,μ n ,σ 2 n }；
Select θ 0 As an initial parameter of the model, iteration is started, and a conditional probability distribution P (z j |x j ,θ j ) And conditional expectation L (θ, θ) of joint distribution j )；
Maximizing the conditional expectation of the joint distribution, solving the parameter theta j Judging the parameter theta j If the algorithm is converged, ending iteration and outputting parameters of the Gaussian mixture model, and if the algorithm is not converged, continuing iteration until the algorithm is converged, and obtaining a probability density function of the corresponding fitting randomness component.
7. The RBF-ARX based comprehensive energy system time-series probability multivariate load prediction method of claim 1, wherein the sampling using markov monte carlo algorithm to obtain the predicted value of the randomness component comprises:
inputting a state transition matrix Q of a random selected Markov chain, stably distributing pi (x) of a target, setting state transition times N1 and the number of required samples N2;
finding sampled initial state values x from arbitrary probability distributions 0 ；
Performing a loop from the conditional probability distribution Q (x|x t ) Mid-sampling to obtain sample x * Sampling u-uniform [0,1] from uniform distribution]；
If it isAccept transfer x t →x * I.e. x t+1 ＝x * The method comprises the steps of carrying out a first treatment on the surface of the Otherwise, not accepting the transfer, which is x t+1 ＝x t In the following，α(x t ,x * ) For the set acceptance rate coefficient matrix, pi (j) is the target stable distribution, Q (j, i) is the state transition matrix, x t+1 Is a predictive value of the randomness component.
8. The comprehensive energy system time sequence probability multi-element load prediction system based on RBF-ARX is characterized by comprising:
the correlation analysis module is used for acquiring the multi-element load data of the comprehensive energy system, performing correlation analysis, and screening to obtain multi-element load data with external factors and coupling relations meeting the conditions;
a data decomposition module for decomposing the conditional multi-element load data into a deterministic component and a stochastic component;
the time sequence prediction module is used for performing time sequence prediction on the deterministic component after optimizing the RBF-ARX mixed model parameters by adopting a variable projection algorithm;
the probability prediction module is used for fitting the randomness component, acquiring a predicted value of the randomness component through sampling after obtaining a probability density function of the fitted randomness component, and carrying out probability prediction on the randomness component;
and a prediction result output module for adding the time-series prediction result of the deterministic component and the probability prediction of the stochastic component as final prediction results.
9. A computer readable storage medium having stored thereon a computer program, which when executed by a processor, implements the steps of the RBF-ARX based integrated energy system time series probability multiple load prediction method as recited in any of claims 1-7.
10. A computer device comprising a memory, a processor and a computer program stored on the memory and executable on the processor, wherein the processor performs the steps in the RBF-ARX based integrated energy system time sequential multi-load prediction method as recited in any of claims 1-7.
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| CN118246770B (en) * | 2024-05-23 | 2024-09-10 | 华北电力科学研究院有限责任公司 | Method, system, medium and electronic equipment for predicting load harmonic current of power distribution network |
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