CN114169585A - Wind power generation power prediction method based on Markov chain and combined model - Google Patents

Abstract

The invention discloses a wind power generation power prediction method of a Markov chain and a combined model, which specifically comprises the following steps: step 1, collecting data recorded in a wind power place, and judging whether the collected data has chaotic characteristics or not by calculating a maximum Lyapunov exponent; step 2, reconstructing a phase space according to the Takens theory by using the judgment result in the step 1 to obtain an input data set of the prediction model; step 3, optimizing the BP neural network by using a Genetic Algorithm (GA) to obtain an initial value of an optimal weight and a threshold value, and predicting the data in the step 2 by using a radial basis function neural network algorithm; and 4, dynamically adjusting the weight coefficients of the different prediction models in the step 3 at different time by adopting a Markov chain, and outputting a final prediction result. The invention can be combined with different prediction models, and the weights of the different prediction models are dynamically determined through the Markov chain.

Description

Wind Power Prediction Method Based on Markov Chain and Combination Model

technical field

The invention belongs to the technical field of wind power prediction, and relates to a wind power prediction method based on a Markov chain and a combined model.

Background technique

Wind power output has randomness and uncertainty. In order to effectively dispatch wind power and reduce the adverse effects caused by the intermittent and variability of wind power, the research on the chaotic characteristics of wind power time series and the realization of wind power prediction are beneficial to reduce wind power. The impact of grid connection on the power system. However, there are also urgent problems to be solved in the process of developing and utilizing wind power generation. Among them, the randomness, intermittency and uncertainty of wind energy are the main problems of wind power grid connection difficulties. In order to ensure the normal grid connection of wind power, it is necessary to predict the future wind power with high precision in advance. On the one hand, high-precision wind power prediction can be used as a reference for the power sector to effectively adjust the power dispatch plan; It can improve the utilization rate of wind turbines economically and safely. Therefore, in order to realize the effective utilization of wind power, it is crucial to improve the technical ability of short-term forecasting of wind power and the accuracy of short-term forecasting.

Scholars have proposed a variety of models to accurately predict wind power changes, which can be divided into statistical models and artificial intelligence models. Statistical model is a method of modeling and forecasting by finding the mapping relationship between the historical data of the wind farm and the wind speed or power of the wind farm, that is, the functional relationship. The application of statistical models is simple and the original data is single, so the prediction accuracy will be limited. The artificial intelligence model has strong nonlinear modeling ability and excellent data recognition ability. Therefore, artificial intelligence models have been widely recognized in the field of wind power forecasting.

The prediction accuracy of the existing single prediction model is limited, and most combined models cannot guarantee the accuracy of short-term and long-term prediction.

SUMMARY OF THE INVENTION

The purpose of the present invention is to provide a Markov chain and combined model wind power prediction method, which can combine different prediction models and dynamically determine the weights of different prediction models through the Markov chain.

The technical solution adopted in the present invention is a wind power prediction method based on Markov chain and combined model, which specifically includes the following steps:

Step 1: Collect the data recorded by the wind farm, and determine whether the collected data has chaotic characteristics by calculating the maximum Lyapunov exponent;

Step 2, using the judgment result in Step 1, and reconstructing the phase space according to the Takens theory, to obtain the input data set of the prediction model;

Step 3, use the GA genetic algorithm to optimize the BP neural network to obtain the initial values of the optimal weights and thresholds, and use the radial basis function neural network algorithm to predict the data in step 2;

In step 4, the Markov chain is used to dynamically adjust the weight coefficients of different prediction models in step 3 at different times, and output the final prediction result.

The feature of the present invention also lies in:

The specific process of step 1 is:

Step 1.1, collect the total power generation time series of all operating wind turbines in a wind farm;

Step 1.2, analyze the chaotic characteristics of the power generation time series collected in step 1.1, specifically:

First, it is assumed that there is a one-dimensional map x(t+1)=f[x(t)] in the power generation time series, the initial condition is x(t ₀ ), and x(t ₀ ) is transformed into f ⁿ (t ₀ ) after n iterations ; After disturbing ε at x(t ₀ ), another initial condition x ₀ +ε is obtained, and after n iterations, it becomes f ⁿ (t ₀ +ε), then the distance between the two trajectories is expressed as:

When ε→0, n→∞:

In the above formula, λ(x(t ₀ )) refers to the degree of exponential separation between two trajectories, and λ(x(t ₀ )) is defined as the Lyapunov exponent. In practical applications, formula (2) has nothing to do with the initial value. Formula (2) is rewritten as:

where λ represents the Lyapunov exponent;

When the maximum Lyapunov exponent is greater than zero, it is determined that the time series of wind power collected in step 1.1 is a chaotic time series.

The specific process of step 2 is:

In step 2.1, the C-C solution method based on the embedding window method is used to reconstruct the phase space of the chaotic time series obtained in step 1. The relationship between the delay time τ and the embedding dimension m established according to the embedding window method is:

τ _w =(m-1)τ,τ _w >τ _p (4);

where τ _w represents the embedded window, and τ _p is the average orbital period of the chaotic system;

Step 2.2, let the chaotic time series be x={x(t)|t=1,2,...,}, assuming that the reconstructed phase space is X _m (t)={x(t),x( t+τ),...,x(t+(m-1)τ)},t=1,2,...,M, then the associated integral of the embedded time series C(m,N,r,τ) for:

where N is the length of the time series, r is the neighborhood radius, and θ(x) is the Heaviside unit function, which is expressed by the following formula (6):

The correlation dimension D(m,τ) is:

定义检验统计量S：in,

Define the test statistic S:

S(m,N,r,τ)=C( ^m ,N,r,τ)-Cm(1,N,r,τ) (8);

In the formula, S(m, N, r, τ) reflects the autocorrelation of the time series, so the delta is defined:

表示对所有r的最大偏差；In the formula, j≠k,

represents the maximum deviation for all r;

make:

In the formula, n _m and n _u are integers, which define the indicators:

Therefore, the embedded bed window τ _w is obtained by finding the global minimum point of S _cor (t), and then the embedding dimension m is obtained by τ _w =(m-1)τ; according to the delay time τ and the embedding dimension m, the chaotic time The sequence is reconstructed in phase space, and the input data set of the prediction model is obtained after reconstruction.

The specific process of step 3 is:

Step 3.1, optimize the BP neural network to obtain the initial values of the optimal weights and thresholds;

Step 3.2, establish a radial basis neural network, and perform wind power prediction through the radial basis neural network;

Step 3.3, divide the input data set after phase space reconstruction in step 2 into training set and test set; use the training set data to train the GA-BP and RBF neural network models, and use the test set to test the GA-BP and RBF neural networks The prediction performance of the model, the network prediction output of GA-BP and RBF is obtained in turn.

The specific process of step 4 is:

Step 4.1, since the final predicted value is a linear combination of the predicted value of the GA-BP and RBF neural network model, the following formula (13) is used to calculate the output value of the combined prediction model

Among them, _yi is the predicted value of the ith prediction model, and _wi is the weight coefficient of _yi ;

Step 4.2, assuming that the time parameter of the random process is X={X _n ,n∈T}, T={0,1,2...}, and the state space E is discrete, define E={i ₀ ,i ₁ ,...}, X is called a Markov chain, if for any n∈R,i ₀ ,i ₁ ,...i _n ∈E, there is the following formula:

Among them, P( ) represents the probability, P _ij represents the probability of transitioning from the state S _i at time t to the state S _j at time t+1, all the probabilities form a state transition matrix P, which represents the transition from one state to another state The probability distribution of transition, then the Markov probability state transition matrix is expressed as:

Step 4.3, when training the Markov chain according to the method of step 4.2, first determine the initial probability matrix, let π={π _i }, π _i =P{X ₁ =S _i }, 1≤i≤N, for represents the probability that the network state is in state _Si at the initial time;

In step 4.4, the state transition probability between different models in the Markov chain result obtained in step 4.3 is brought into the following formula (16) to obtain the final prediction output result y _t :

Among them, p _it is the probability of the ith prediction model at time t, and y _it is the predicted value of the ith prediction model at time t.

The beneficial effects of the present invention are as follows:

1. The present invention can effectively use the GA genetic algorithm to optimize the defect that the BP neural network is easy to fall into the local minimum value, and is linked with the delay time and the embedded dimension, two important parameters of phase space reconstruction, and improves the performance. The training samples make the prediction results more scientific. The improved BP converges faster and does not fall into local minima, and has higher prediction accuracy.

2. The present invention can effectively use the weighted Markov chain as the basis for adjusting the weight coefficient of the combination of the two algorithms, establish a new combined prediction model, and through simulation calculation, it is verified that the combined prediction model is compared with the prediction of a separate neural network. The advantages.

Description of drawings

Fig. 1 is the general flow chart of the wind power prediction method based on Markov chain and combined model of the present invention;

Fig. 2 is the structure diagram of BP neural network in the wind power prediction method based on Markov chain and combined model of the present invention; in the figure, X _i represents the input of the neuron, Y _i represents the output of the hidden layer, and O _i represents the output of the neuron , d _i expected output value, Δ _i is the error between the expected output and the actual output.

Fig. 3 is the improved GA-BP prediction flow chart in the wind power generation power prediction method based on Markov chain and combined model of the present invention;

FIG. 4 is a structural diagram of the RBF neural network in the wind power prediction method based on the Markov chain and the combined model of the present invention.

Detailed ways

The present invention will be described in detail below with reference to the accompanying drawings and specific embodiments.

The present invention is based on the Markov chain and the combined model of the wind power prediction method.

Step 1: Collect the total power generation time series of all operating wind turbines in a wind farm, and analyze the chaotic characteristics of the time series. Using the wind power time series, the maximum Lyapunov exponent of the wind power time series calculated by the small data volume method is used, and then the least squares method is used to obtain a regression line, but the slope is greater than 0, indicating that the wind power time series Has chaotic properties. If the conclusion of a non-chaotic system is obtained, the period of the system needs to be doubled, which will gradually lose its periodic behavior and enter chaos. in the power system.

Step 1 is specifically:

Step 1.1, collect the time series of the total generated power of all operating wind turbines in a wind farm.

Step 1.2, analyze the chaotic characteristics of the time series of power generation, and determine whether the system has chaotic attributes. Using the small amount of data method, it is first assumed that there is a one-dimensional map x(t+1)=f[x(t)] for the chaotic time series of wind power, the initial condition is x(t ₀ ), and x(t ₀ ) becomes f ⁿ (t ₀ ); after perturbing ε at x(t ₀ ), another initial condition x ₀ +ε is obtained, and also after n iterations to f ⁿ (t ₀ +ε), the distance between the two trajectories is expressed as for:

When ε→0, n→∞:

In the above formula, λ(x(t ₀ )) refers to the degree of exponential separation between two trajectories, which is defined as the Lyapunov exponent. In practice, the above formula has nothing to do with the initial value and can be rewritten as:

Step 1.3, substitute the input data according to the above formula, if the maximum Lyapunov exponent is greater than zero, the system can be judged as a chaotic system; if the conclusion of a non-chaotic system is obtained, the period of the system needs to be doubled, which will gradually lose the period. The behavior enters into chaos. This method of transforming the system into chaos using the period-doubling bifurcation method is very common in various nonlinear dynamical systems.

In step 2, the time series of wind power obtained in step 1 is a chaotic time series, and phase space reconstruction can be used to further process the input data. Specifically:

Using the C-C solution method based on the embedding window method, the relationship between the delay time τ and the embedding dimension m is:

τ _w =(m-1)τ,τ _w >τ _p (4);

where τ _p is the average orbital period of the chaotic system, and τ _w represents the embedding window. From this, the delay time τ and the embedding dimension m can be calculated.

Let the wind power time series be x={x(t)|t=1,2,...,}, and assume that the reconstructed phase space is X _m (t)={x(t), x(t+ τ),...,x(t+(m-1)τ)},t=1,2,...,M, then the associated integral of the embedded time series is:

where N is the length of the time series, r is the neighborhood radius, θ(x) is the Heaviside unit function, and its expression is:

The associated dimension is:

关联积分其实是累计分部积分，表示相空间中，小于r的可能性(r为任意两个具体位置之间的距离)。然后定义检验统计量S，求解延迟时间τ的方法如下in,

The correlation integral is actually a cumulative integral by parts, indicating the possibility of being less than r in the phase space (r is the distance between any two specific positions). Then define the test statistic S, and the method for solving the delay time τ is as follows

S(m,N,r,τ)=C( ^m ,N,r,τ)-Cm(1,N,r,τ) (8);

In the formula, S(m, N, r, τ) reflects the autocorrelation of the time series. The most suitable delay time τ is the first zero point of S(m, N, r, τ) or the time when the difference of all r is the smallest. So define the delta:

表示对所有r的最大偏差。最合适的延迟时间为S(m,N,r,τ)的第一个零点或者是

的第一个局部极小值点。以此求出延迟时间τ，再根据τ与m的关系式则可求取嵌入维数m；where N is the length of the time series, r is the neighborhood radius, τ is the delay time, m is the embedding dimension, C is the correlation integral, S is the defined test statistic, j≠k,

represents the maximum deviation over all r. The most suitable delay time is the first zero of S(m, N, r, τ) or

the first local minimum point of . In this way, the delay time τ can be obtained, and then the embedding dimension m can be obtained according to the relationship between τ and m;

The average block idea is used in the calculation:

In the formula, n _m , n _u are integers. Define metrics:

To sum up, the embedded bed window τ _w can be obtained by finding the global minimum point of S _cor (t), and the embedded dimension m can be obtained by τ _w =(m-1)τ.

According to the optimal parameter values determined by the above steps: delay time τ and embedding dimension m, the time series is reconstructed in phase space, and the input data set of the prediction model is obtained after reconstruction.

Step 3, use the GA genetic algorithm to optimize the BP neural network (GA-BP) to obtain the initial g part of the optimal weights and thresholds, and predict the data in step 2; establish an RBF neural network for the data in step 2. Predict; as shown in Figures 2 to 4, specifically: in Figure 2, X ₁ , X ₂ , ...... X _n represent the input of neurons, Y ₁ , Y ₂ , ...... Y _j represents the output of the hidden layer, O ₁ , O ₂ , ......O _k represents the output of the neuron, d ₁ , d ₂ , ...... d _m expected output value, Δ ₁ , Δ ₂ , ......, Δ _m is the error between the expected output and the actual output. In Fig. 4, x ₁ , x ₂ ,..., x _p represent the input of the neuron, c ₁ , _{c 2} ,..., ch represent the output of the hidden layer, w ₁ , w ₂ , ..., w _h represent the weights between the hidden layer and the output layer, and y represents the actual output of the network.

Step 3.1, using the genetic algorithm GA to optimize the BP neural network The specific steps are as follows:

3.1.1, BP neural network includes input layer, hidden layer and output layer. Determine the value range of the connection weights between the neural networks of each layer. The training of the given training sample is carried out according to the given training times and training error. After the training is completed, the maximum value u _max and the minimum value u _min of the qualified weight coefficients are obtained, and then the value range of the network connection weight can be determined. [u _min -δ ₁ , u _max -δ ₂ ] (δ ₁ ,δ ₂ are adjustment constants).

3.1.2, the fitness function is defined as:

In the above formula: Tk is the expected output value of the _kth neuron, _Qk is the output of the kth neuron, N is the number of populations, b is the number of neurons in the output layer, and k and q are the number of neurons.

3.1.3, encode the chromosomes in the determined network connection weight range, use floating-point numbers to encode the weight coefficients and thresholds, and connect them into a length of L=m×l+l+l×n+n. Long strings, the long strings formed correspond to a set of network layer connection weights respectively.

3.1.4, generate initial samples: generate L random distribution numbers on [u _min -δ ₁ , u _max -δ ₂ ], input training samples, and calculate the fitness of each individual by the above formula (13). The individuals with the highest fitness are selected and copied to the next generation, and they do not participate in the crossover and mutation calculations in the program.

The crossover operator used is as follows:

代表交叉前的个体，

代表交叉后的个体,c_i取[0,1]的均匀分布随机数。以概率p_m对交叉后的第i个个体进行变异，变异算子为：In the above formula,

represents the individual before the crossover,

Represents the individuals after crossover, and c _i takes a uniformly distributed random number of [0,1]. The ith individual after crossover is mutated with probability p _m , and the mutation operator is:

是变异前的个体，

是变异后的个体，为确保编译后的个体不超过搜索范围，

取此区间上的均匀分布随机数。In the above formula,

is the individual before mutation,

is the mutated individual. To ensure that the compiled individual does not exceed the search range,

Take a uniformly distributed random number over this interval.

3.1.5, Generating Next Generation Groups.

3.1.6, repeat the input training samples to generate the next generation population, and observe the evolving population until the H generation. Finally, the individuals with the best fitness in the H-th generation are screened out and decoded to obtain the corresponding connection weights between the layers of the neural network.

Step 3.2, establish a radial basis neural network (RBF neural network) for wind power prediction, and the establishment process steps are as follows:

3.2.1, Initialization of network structure and parameters. The parameters that need to be initialized are: the training input is X=[x ₁ ,x ₂ ,...,x _p ] ^T , the actual output is Y=[y ₁ ,y ₂ ,...,y _q ] ^T , the expected output is Z=[z ₁ , z ₂ ,...,z _q ] ^T ; the initial value of the weight vector to be updated in learning is W _k =[w _k1 ,w _k2 ,...,w _kq ] ^T ; The initial value of the central parameter of the basis function of the hidden layer node is c=[c ₁ ,c ₂ ,...,c _N ] ^T ; the standard deviation σ _k , the expression is:

In the above formula, _ck is the kth neuron center of the selected hidden layer, and N represents the number of hidden layer nodes.

3.2.2, calculate the output value of the kth node of the hidden layer:

是由径向基网络通常选取高斯函数作为基函数给出的，c_k＝[c_k1,c_k2,...,c_km]是根据中间层第k个节点对应于输入层所有节点的中心分量构成的向量，σ_k为中间层第k个节点的标准差。In the above formula,

is given by the radial basis network usually selects the Gaussian function as the basis function, c _k = [c _k1 ,c _k2 ,...,c _km ] is the center of all nodes in the input layer corresponding to the kth node in the middle layer A vector composed of components, σ _k is the standard deviation of the kth node in the middle layer.

3.2.3, calculate the RBF neural network output Y=[y ₁ , y ₂ ,...,y _q ] ^T

3.2.4. Finally, iterative calculation of weight parameters is performed. By continuously updating the center, variance,

weights to obtain the optimal learning strategy.

Step 4, the Markov chain is used to dynamically adjust the weight coefficients of the two different prediction models in step 3 at different times, and output the final prediction result. Specifically:

The state transition probability between different models in the Markov chain result obtained by training is brought into the following formula to obtain the final prediction output result y _t :

In the above formula, p _it is the probability of the ith prediction model at time t, and y _it is the predicted value of the ith prediction model at time t.

Example

The data set used in the present invention comes from the time series of generated power recorded in all the running wind turbines in a wind farm, and the chaotic characteristics of the wind power data are studied, and the obtained Lyapunov exponent is greater than 0, so The wind power time series has chaotic characteristics, and the phase space is reconstructed according to the Takens theory, and the dynamic information of the original system is recovered, which is conducive to the prediction of the next prediction model.

Using GA genetic algorithm to optimize the defect of BP which is easy to fall into local minimum value, and link the two important parameters of phase space reconstruction, delay time and embedding dimension, improve the training samples; establish RBF neural network Predictive model of the network.

Using the weighted Markov chain as the basis for adjusting the weight coefficient of the combination of the two algorithms, a new combined prediction model is established. Through simulation calculation, the advantages of the combined prediction model compared with the single neural network prediction are verified.

Claims (5)

1. The wind power generation power prediction method based on the Markov chain and the combined model is characterized by comprising the following steps: the method specifically comprises the following steps:

step 1, collecting data recorded in a wind power place, and judging whether the collected data has chaotic characteristics or not by calculating a maximum Lyapunov exponent;

step 2, reconstructing a phase space according to the Takens theory by using the judgment result in the step 1 to obtain an input data set of the prediction model;

step 3, optimizing the BP neural network by using a Genetic Algorithm (GA) to obtain an initial value of an optimal weight and a threshold value, and predicting the data in the step 2 by using a radial basis function neural network algorithm;

and 4, dynamically adjusting the weight coefficients of the different prediction models in the step 3 at different time by adopting a Markov chain, and outputting a final prediction result.

2. The method of Markov chain and combination model based wind power generation power prediction of claim 1, wherein: the specific process of the step 1 is as follows:

step 1.1, collecting the total generated power time sequence of all the operating wind turbine generators in a certain wind power plant;

step 1.2, performing chaotic characteristic analysis on the generated power time sequence acquired in the step 1.1, specifically:

firstly, a one-dimensional mapping x (t +1) ═ f [ x (t) of the time series of the generated power is assumed to exist]The initial condition is x (t)₀)，x(t₀) Through n iterations to fⁿ(t₀) (ii) a At x (t)₀) Is disturbed to obtain another initial condition x₀+ ε, likewise over n iterations to fⁿ(t₀+ epsilon), the distance between two tracks is expressed as:

when → ∞ of → 0, epsilon:

in the above formula, λ (x (t)₀) Denotes the degree of exponential separation between the two traces, will be lambda (x (t)₀) Defined as Lyapunov exponent, in practical application, formula (2) is independent of the initial value, and formula (2) is rewritten as:

wherein λ represents the Lyapunov exponent;

and when the maximum Lyapunov index is larger than zero, judging that the wind power time sequence acquired in the step 1.1 is a chaotic time sequence.

3. The method of Markov chain and combination model based wind power generation power prediction of claim 2, wherein: the specific process of the step 2 is as follows:

step 2.1, performing phase-space reconstruction on the chaotic time sequence obtained in the step 1 by adopting a C-C solving method based on an embedded window method, wherein the relation between the delay time tau and the embedded dimension m established according to the embedded window method is as follows:

τ_w＝(m-1)τ,τ_w＞τ_p (4)；

in the formula, τ_wRepresents an embedding window, τ_pIs the average orbit period of the chaotic system;

step 2.2, let the chaotic time sequence be X ═ { X (t) | t ═ 1,2, · then }, and assume that the reconstructed phase space is X_m(t) { x (t), x (t + τ),. times, x (t + (M-1) τ) }, t ═ 1,2.. times, M, then the associated integral C (M, N, r, τ) of the embedding time series is:

where N is the time series length, r is the neighborhood radius, and θ (x) is the hervesseld unit function, expressed by the following equation (6):

the correlation dimension D (m, τ) is:

wherein,

defining a test statistic S:

S(m,N,r,τ)＝C(m,N,r,τ)-C^m(1,N,r,τ) (8)；

in the formula, S (m, N, r, τ) reflects the autocorrelation of the time series, thus defining the dispersion:

▽S(m,τ)＝max[S(m,N,r_j,τ)]-min[S(m,N,r_k,τ)] (9)；

in the formula, j is not equal to k,

represents the maximum deviation for all r;

order:

in the formula, n_m、n_uIs an integer, the index is defined as:

thus, find S_cor(t) obtaining the global minimum point, i.e. the embedding bed window τ_wThen from τ_wSolving the embedding dimension m as (m-1) tau; and according to the delay time tau and the embedding dimension m, carrying out phase space reconstruction on the chaotic time sequence, and obtaining an input data set of the prediction model after reconstruction.

4. A method for wind power generation power prediction based on markov chains and combined models according to claim 3, characterized in that: the specific process of the step 3 is as follows:

step 3.1, optimizing the BP neural network to obtain an optimal weight and an initial value of a threshold;

step 3.2, establishing a radial basis function neural network, and predicting the wind power through the radial basis function neural network;

step 3.3, dividing the input data set subjected to the phase space reconstruction in the step 2 into a training set and a test set; and training the GA-BP and RBF neural network models by using the training set data, and testing the prediction performance of the GA-BP and RBF neural network models by using the test set to sequentially obtain the network prediction output of the GA-BP and the RBF.

5. The Markov chain and combination model based wind power generation power prediction method of claim 4, wherein: the specific process of the step 4 is as follows:

step 4.1, because the final predicted value is the linear combination of the GA-BP and the RBF neural network model predicted value, the output value of the combined prediction model is calculated by using the following formula (13)

Wherein, y_iIs the predicted value of the ith prediction model, w_iIs y_iThe weight coefficient of (a);

step 4.2, assume that the time parameter of the random process is X ═ X_nN ∈ T }, T ═ {0,1,2. }, and state space E is discrete, defining E ═ { i }₀,i₁,., call X a Markov chain if for any n ∈ R, i₀,i₁,...i_nE has the following formula:

wherein P (-) represents the probability, P_ijRepresenting state S from time t_iS transferred to t +1 time_jThe probabilities of the states, all forming a state transition matrix P, representing the probability distribution of transitions from one state to another, the markov probability state transition matrix is then represented as:

step 4.3, when training the markov chain according to the method of step 4.2, first determine the initial probability matrix, let pi ═ pi { (pi }_i},π_i＝P{X₁＝S_i1 ≦ i ≦ N for indicating the network state is in state S at the initial time_iThe probability of (d);

step 4.4, substituting the state transition probability among different models in the Markov chain result obtained by training in step 4.3 into the following formula (16) to obtain the final prediction output result y_t：

Wherein p is_itIs the probability of the ith prediction model at time t, y_itIs the predicted value of the ith prediction model at time t.

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