CN111882120A - Power load prediction method based on VMD-MQPSO-BPn network - Google Patents

Power load prediction method based on VMD-MQPSO-BPn network Download PDF

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CN111882120A
CN111882120A CN202010673530.8A CN202010673530A CN111882120A CN 111882120 A CN111882120 A CN 111882120A CN 202010673530 A CN202010673530 A CN 202010673530A CN 111882120 A CN111882120 A CN 111882120A
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肖秦琨
张雪
邓雪亚
尹玉婷
张杰韬
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Abstract

The invention relates to a load prediction method based on a VMD-MQPSO-BPn network. The method overcomes the defects of end effect, noise residue and modal aliasing in the prior data preprocessing technology. The method comprises the following steps: taking the acquired historical data of the power load as an original load data sequence signal X (t); decomposing original load data sequence signals into a specified number of intrinsic mode functions by using Variational Mode Decomposition (VMD); constructing BP neural networks with corresponding different structures by using intrinsic mode functions; setting the set values of all parameters of the BP neural network and the MQPSO algorithm; optimizing the weights and the threshold values of BP neural networks with different structures by using a self-adaptive variation quantum particle swarm algorithm, and establishing an MQPSO-BPn prediction model; decomposing the VMD into a plurality of intrinsic mode functions and inputting the intrinsic mode functions into a training set for training; applying the trained MQPSO-BPn prediction model to the test data of each mode function to obtain a corresponding prediction result; and superposing the predicted values of all the modal functions to obtain an actual prediction result.

Description

Power load prediction method based on VMD-MQPSO-BPn network
Technical Field
The invention belongs to the technical field of power load prediction, and relates to a load prediction method based on a VMD-MQPSO-BPn network.
Background
Currently, there are mainly 3 types for load prediction of power systems: the first is a prediction method based on a traditional mathematical statistical model, the second is a prediction algorithm based on machine learning, and the third is a combination method.
The prediction method based on the traditional mathematical statistic model, such as time sequence and other methods, is simple in model, simple in calculation and high in prediction speed, but has poor load prediction capability on a complex nonlinear system and shows strong randomness or unstable characteristics. In the machine learning method, better prediction accuracy is obtained in the nonlinear system prediction, and compared with the traditional algorithm, the method has many advantages, but the prediction result depends on the quality and the quantity of data to a great extent, in practice, load data is unstable and nonlinear, irregular vacancy is difficult to fill in machine learning, and the machine learning algorithm generally has the defects of over-parameter determination disaster, large resource consumption and the like. The method comprises the steps of carrying out future power prediction on a plurality of models in a combined mode, making up the defect of a single model by combining the advantages of all models, enabling power load prediction to be more accurate and practical, combining the prediction models in a mode of obtaining final combined prediction model results from different model prediction results through certain weight, and in a mode of generally adopting the method at present, carrying out data preprocessing on an original sequence, decomposing the original sequence into a plurality of components with different characteristics by utilizing common EMD (empirical mode decomposition) and EEMD (empirical mode decomposition), then respectively establishing a prediction model for each component, and overlapping the prediction results of all the components to obtain a final prediction value. But problems with end-point effects, modal aliasing and noise residues occur.
Disclosure of Invention
The invention aims to provide a power load prediction method based on a VMD-MQPSO-BPn network, which overcomes the defects of end point effect, noise residue and mode aliasing in the existing data preprocessing technology and solves the problems of group diversity loss and local minimum value when PSO optimizes weight.
In order to achieve the purpose of the invention, the technical scheme adopted by the invention is that the power load prediction method based on the VMD-MQPSO-BPn network comprises the following steps:
step 1, obtaining historical data of a power load as an original load data sequence signal X (t);
step 2, decomposing original load data sequence signals into a specified number of intrinsic mode functions by utilizing Variational Mode Decomposition (VMD);
step 3, constructing BP neural networks with corresponding different structures aiming at the intrinsic mode functions decomposed in the step 2;
step 4, setting the set values of all parameters of the BP neural network and the MQPSO algorithm;
step 5, optimizing the weight and the threshold of BP neural networks with different structures by using a self-adaptive variation quantum particle swarm algorithm (MQPSO), and establishing an MQPSO-BPn prediction model;
step 6, decomposing a plurality of intrinsic mode functions by the VMD according to the MQPSO-BPn prediction model, inputting the intrinsic mode functions into a training set, and training to obtain a trained MQPSO-BPn prediction model;
step 7, applying the trained MQPSO-BPn prediction model to the test data of each mode function to obtain a corresponding prediction result;
and 8, superposing the predicted values of all the modal functions in the step 7 to obtain an actual prediction result.
The VMD decomposition in step 2 specifically includes the following contents:
step 2.1: for each mode function u obtained by Hilbert transform of original signalk(t) the single-edge spectrum found is:
Figure BDA0002583221810000021
wherein t represents the t-th time, k represents the kth mode, j represents an imaginary unit, and σ (t) represents the center frequency of the kth mode at the t-th time;
step 2.2: the frequency spectrum of each mode and the mixture of the analysis signals of each mode are used to estimate the center frequency
Figure BDA0002583221810000031
For reference modulation to the corresponding baseband:
Figure BDA0002583221810000032
wherein, wkRepresents the angular frequency of the kth mode;
step 2.3: constructing a constrained variational model as follows:
Figure BDA0002583221810000033
wherein, { u [ [ u ] ]k}＝{u1，…，uKDenotes k mode functions, denotes the initial values of the k mode functions, { wk}＝{w1，…，wKMeans for indicating a k-th center frequency, indicating an initial value of the k-th center frequency; k is 1, 2, 3 … K,
Figure BDA0002583221810000034
represents the partial derivation of t, x (t) represents the original input signal;
step 2.4:
step 2.4.1: the variable model is solved, and an extended Lagrangian expression is formed by introducing a quadratic penalty function term a and a Lagrangian multiplier lambda (t), and is as follows:
Figure BDA0002583221810000035
step 2.4.2: initialization parameters
Figure BDA0002583221810000036
And n
Figure BDA0002583221810000037
Is the initial value of Lagrange multiplication operator, and n is the iteration number;
step 2.4.3: updating by alternating multiplier direction method
Figure BDA0002583221810000041
And λn+1The saddle point of the extended lagrangian expression is sought:
(1)ukthe update formula of (2);
Figure BDA0002583221810000042
(2)wkthe update formula of (2):
Figure BDA0002583221810000043
(3) the updated formula of λ:
Figure BDA0002583221810000044
(4) whether the convergence is judged by adopting a mean square error, and the conditions are as follows:
Figure BDA0002583221810000045
for a given discrimination accuracy e >0, if mse < e, the iteration is stopped, one component U1 is obtained, and the remaining components U2, U3 …, Un can be obtained by repeating step 2.4.3.
The step 5 specifically includes the following steps:
step 5.1: quantum particle swarm algorithm principle (QPSO)
In the QPSO algorithm, the population size is set to M, and the particle position update formula is transformed to:
P＝aPbest(i)+(1-a)×Gbest (9)
Figure BDA0002583221810000051
Figure BDA0002583221810000052
position＝P±|mbest-position|×ln(1/u) (12)
wherein, mbest is the middle position of the individual extreme value of the particle, namely the average optimal value, a and u are random numbers between [0,1], if u is greater than 0.5, the formula (12) is added, otherwise, the formula is subtracted, b is the coefficient of contraction and expansion, the linear reduction is carried out in the searching process, generation is the current evolutionary algebra, and maxgeneration is the set maximum evolutionary algebra;
step 5.2: improved quantum particle swarm algorithm (MQPSO)
Step 5.2.1: group fitness variance σ of a population of particles2：
Figure BDA0002583221810000053
Wherein n is the number of particles in the particle group, fiIs the fitness of the first particle, favgThe function of f is to limit the sigma2The value in the algorithm f adopts the following formula:
Figure BDA0002583221810000054
step 5.2.2: spatial aggregation degree h of particles:
Figure BDA0002583221810000061
Figure BDA0002583221810000062
denoted as the ith particle of the t generation,
Figure BDA0002583221810000063
best position, denoted as t generation, nullThe aggregation degree h of the inter-position reflects the aggregation dispersion degree of the particle individuals in the search space;
step 5.2.3: mutation operation
(1) Probability of structural variation Pm：
Figure BDA0002583221810000064
Wherein the fitness variance σ2Is determined by the formula (13), h is the spatial position concentration determined by the formula (15), σ1Is a given threshold, typically approaching 0. Probability of variation P according to structuremCarrying out mutation operation on part of the particles to enable the particles to have larger search space; generating a random number r ∈ [0,1]]If r < PmPerforming an update operation on each extremum according to Pi＝Pi(1+0.5 η), wherein PiThe current best position of the first particle, η, is the dimensional random vector that follows a (0,1) normal distribution.
The specific steps of the step 6 are as follows:
step 6.1: establishing a BP network, and determining parameters such as the structure, weight and the like of the neural network according to the input and output sample sets of the solved problem; carrying out real number vector coding on the weights and thresholds among all units of the neural network, and corresponding to all individuals in the population, wherein the vector dimension is the space dimension of the particle;
step 6.2: initializing population, initializing population size, particle position, position weight, maximum number of iterations allowed, and the like,
step 6.3: calculating the fitness of the particles; determining the fitness function of an individual as the mean square error of the neural network, comparing the obtained individual extreme values of each particle, wherein the global extreme value is the particle with the best individual extreme value, recording the serial number of the particle, and performing iteration by taking the optimal weight of the neural network as the recorded global extreme value in the next iteration;
step 6.4: updating the extreme value of the particle, calculating and comparing the fitness of each particle, and updating the individual extreme value to the position of the particle if the particle has an individual extreme value better than the current value; if the best individual extreme value in all the particles is better than the current global extreme value, recording the global extreme value as the position of the particle, recording the serial number of the particle, and updating the global extreme value;
6.5; recalculating the fitness value of the particle, updating the inertia weight and searching the optimal position of the particle;
6.6; checking whether a convergence condition is met, if an expected error requirement or the maximum iteration number is met, ending the iteration process, and if the optimal weight and the threshold of the neural network correspond to the global extreme value of the particles, namely the best result of the problem, otherwise, turning to the step 6.3;
step 6.7: and updating the weight value and the threshold value of the network by using the optimal position of the population, and ending the operation of the algorithm.
Compared with the prior art, the invention has the advantages that:
1. the introduced VMD method is a non-recursive and variational self-adaptive mode decomposition mode, can effectively solve the problems of mode aliasing, end effect and the like existing in other common load signal preprocessing methods, and has the advantages of high operation speed and stable decomposition result.
2. The BP network improvement strategy based on the MQPSO algorithm not only effectively solves the problems of group diversity loss and local optimum trapping existing in PSO and QPSO, but also can realize the remarkable improvement of the BP network prediction precision, the acceleration of the convergence speed and the enhancement of the self-adaptive learning capacity by only setting a small number of parameters under the various defects of the BP neural network.
Drawings
FIG. 1 is an overall block diagram of a power load prediction method based on a VMD-MQPSO-BPn network;
FIG. 2 is a MQPSO flow diagram.
Detailed Description
The present invention will be described in detail below with reference to the drawings and examples.
Referring to fig. 1, the invention provides a power load prediction method based on a VMD-MQPSO-BPn network, which includes the following steps:
step 1, obtaining historical data of a power load as an original load data sequence signal X (t);
step 2, decomposing the original load data sequence signals into a specified number of intrinsic mode functions by utilizing Variational Mode Decomposition (VMD): comprises the following steps
Step 2.1: for original signals X (t), each mode function u is obtained by Hilbert transformationk(t) analyzing the signal and obtaining each uk(t) unilateral spectrum of subsequences:
Figure BDA0002583221810000081
wherein t represents the t-th time, k represents the kth mode, j represents an imaginary unit, and σ (t) represents the center frequency of the kth mode at the t-th time;
step 2.2: the frequency spectrum of each mode and the mixture of the analysis signals of each mode are used to estimate the center frequency
Figure BDA0002583221810000082
For reference modulation to the corresponding baseband:
Figure BDA0002583221810000083
wherein, wkRepresents the angular frequency of the kth mode;
step 2.3: squaring L of the gradient of the demodulated signal in step 3.22Norm, estimating the bandwidth u of the signal of each modekThe constrained variational modal decomposition problem is as follows:
Figure BDA0002583221810000091
wherein, { u [ [ u ] ]k}＝{u1，…，uK}，{wk}＝{w1，…，wK}；k＝1，2，3…K，
Figure BDA0002583221810000097
Denotes the derivation of t, X (t)Representing the original input signal;
step 2.4: in step 2.3, the solution of the variational modal decomposition problem comprises the following steps:
step 2.4.1: in order to convert the constraint problem in step 2.3 into an unconstrained problem, a quadratic penalty function term a and a lagrangian multiplier λ (t) are introduced to form an extended lagrangian expression as follows:
Figure BDA0002583221810000092
step 2.4.2: initialization parameters
Figure BDA0002583221810000093
And n; wherein, { uk}＝{u1，…，uKDenotes k mode functions, denotes the initial values of the k mode functions, { wk}＝{w1，…，wKDenotes the kth center frequency, denotes the initial value of this kth center frequency,
Figure BDA0002583221810000094
is the initial value of Lagrange multiplication operator, and n is the iteration number;
step 2.4.3: the problem of variable mode decomposition is solved by adopting an alternative multiplier direction method, and the variable mode decomposition is updated alternately
Figure BDA0002583221810000095
And λn+1The saddle point of the extended lagrangian expression is sought:
(1)ukthe update formula of (2);
Figure BDA0002583221810000096
(2)wkthe update formula of (2):
Figure BDA0002583221810000101
(3) the updated formula of λ:
Figure BDA0002583221810000102
(4) whether the convergence is judged by adopting a mean square error, and the conditions are as follows:
Figure BDA0002583221810000103
for a given discrimination accuracy e >0, if mse < e, the iteration is stopped, one component U1 is obtained, and the remaining components U2, U3 …, Un can be obtained by repeating step 2.4.3.
Step 3, constructing BP neural networks with corresponding different structures aiming at the intrinsic mode functions decomposed in the step 2;
step 4, setting the set values of all parameters of the BP neural network and the MQPSO algorithm;
step 5, optimizing the weight and the threshold of BP neural networks with different structures by using a self-adaptive variation quantum particle swarm algorithm (MQPSO), and establishing an MQPSO-BPn prediction model, which specifically comprises the following steps:
step 5.1: quantum particle swarm algorithm principle (QPSO)
In the QPSO algorithm, the particle position is increased or decreased with a certain probability during the search, the population size is set to M, and the particle position update formula is transformed into:
P＝aPbest(i)+(1-a)×Gbest (9)
Figure BDA0002583221810000111
Figure BDA0002583221810000112
position＝P±|mbest-position|×ln(1/u) (12)
wherein, mbest is the middle position of the individual extreme value of the particle, i.e. the average optimal value, a and u are random numbers between [0,1], if u is greater than 0.5, the formula (12) is added, otherwise, the formula is subtracted, b is the contraction and expansion coefficient, the linear reduction is performed in the searching process, generation is the current evolution algebra, and maxgeneration is the set maximum evolution algebra.
Step 5.2: improved quantum particle swarm algorithm (MQPSO)
Step 5.2.1: group fitness variance σ of a population of particles2：
Figure BDA0002583221810000113
Wherein n is the number of particles in the particle group, fiIs the fitness of the first particle, favgThe function of f is to limit the sigma2The value in the algorithm f adopts the following formula:
Figure BDA0002583221810000114
from the above formula, it can be seen that the variance of population fitness actually reflects the aggregation degree of all particles in a particle swarm, and the larger the aggregation degree is, the smaller the variance value is. And if the value is smaller than the given threshold value, the late search is considered to be carried out, and the premature convergence phenomenon occurs. If the particle swarm optimization algorithm falls into premature convergence, the variance of the population fitness approaches to 0, and then the particle space position is fallen into local convergence when the aggregation degree is small. Step 5.2.2: spatial aggregation degree h of particles:
Figure BDA0002583221810000121
Figure BDA0002583221810000122
denoted as the ith particle of the t generation,
Figure BDA0002583221810000123
the best position represented as the t generation, the aggregation degree h of the spatial position reflects the aggregation dispersion degree of the particles in the search space, if the larger the particles are, the larger the aggregation degree is, the smaller the aggregation degree is, the more the particles areThe greater the probability of being mutated.
Step 5.2.3: mutation operation
(1) Probability of structural variation Pm：
Figure BDA0002583221810000124
Wherein the fitness variance σ2Is determined by the formula (13), h is the spatial position concentration determined by the formula (15), σ1Is a given threshold, typically approaching 0. Probability of variation P according to structuremAnd carrying out mutation operation on part of the particles to enable the particles to have larger search space. Generating a random number r ∈ [0,1]]If r < PmPerforming an update operation on each extremum according to Pi＝Pi(1+0.5 η), wherein PiThe current best position of the first particle, η, is the dimensional random vector that follows a (0,1) normal distribution.
Step 5.3: the MQPSO algorithm flow is as follows
Step 5.3.1: initializing parameters of the particle swarm, including individual extrema, global extrema and the like, and determining the population scale and the particle dimension;
step 5.3.2: calculating the fitness of each particle through the target function, judging whether a convergence condition is met, if the convergence condition is met, turning to step 5.3.6, and if the convergence condition is not met, continuing to execute step 5.3.3;
step 5.3.3: updating the current individual optimal position and the population optimal position according to the particle fitness value, and updating each particle position by adding or subtracting each particle position according to the formulas (9) - (12) with a certain probability to generate a new particle swarm;
step 5.3.4: calculating the fitness variance σ of the particles2And the spatial clustering degree h, and calculating the mutation probability according to the formula (16);
step 5.3.5: generating a random number r if r < P is satisfiedmThen a mutation operation is performed, otherwise go to step 5.3.6;
step 5.3.6: judging whether the particle fitness meets the convergence condition or reaches the set maximum iteration times, if so, finishing the iteration, otherwise, returning to the step 5.3.2;
step 5.3.7: resetting t to t +1, and turning to step 5.3.2;
step 5.3.8: and outputting the global extreme value gbest and the adaptive value thereof. (ii) a
Step 6, referring to fig. 2, decomposing the VMD into a plurality of intrinsic mode functions according to the MQPSO-BPn prediction model, inputting the plurality of intrinsic mode functions into a training set, and training to obtain a trained MQPSO-BPn prediction model, specifically including the following steps:
step 6.1: and (3) creating a BP network, and determining parameters such as the structure and weight of the neural network according to the input and output sample sets of the solved problem. Carrying out real number vector coding on the weights and thresholds among all units of the neural network, and corresponding to all individuals in the population, wherein the vector dimension is the space dimension of the particle;
step 6.2: initializing population, initializing population size, particle position, position weight, maximum number of iterations allowed, and the like,
step 6.3: and calculating the fitness of the particles. Determining the fitness function of an individual as the mean square error of the neural network, comparing the obtained individual extreme values of each particle, wherein the global extreme value is the particle with the best individual extreme value, recording the serial number of the particle, and performing iteration by taking the optimal weight of the neural network as the recorded global extreme value in the next iteration;
step 6.4: and updating the extreme value of the particle, calculating and comparing the fitness of each particle, and updating the individual extreme value to the position of the particle if the particle has an individual extreme value better than the current value. If the best individual extreme value in all the particles is better than the current global extreme value, recording the global extreme value as the position of the particle, recording the serial number of the particle, and updating the global extreme value;
6.5; recalculating the fitness value of the particle, updating the inertia weight and searching the optimal position of the particle;
6.6; checking whether a convergence condition is met, if an expected error requirement or the maximum iteration number is met, ending the iteration process, and if the optimal weight and the threshold of the neural network correspond to the global extreme value of the particles, namely the best result of the problem, otherwise, turning to the step 6.3;
step 6.7: and updating the weight value and the threshold value of the network by using the optimal position of the population, and ending the operation of the algorithm.
Step 7, applying the trained MQPSO-BPn prediction model to the test data of each mode function to obtain a corresponding prediction result;
and 8, superposing the predicted values of all the modal functions in the step 7 to obtain an actual prediction result.

Claims (4)

1. A power load prediction method based on a VMD-MQPSO-BPn network is characterized by comprising the following steps: the method comprises the following steps:
step 1, obtaining historical data of a power load as an original load data sequence signal X (t);
step 2, decomposing original load data sequence signals into a specified number of intrinsic mode functions by utilizing Variational Mode Decomposition (VMD);
step 3, constructing BP neural networks with corresponding different structures aiming at the intrinsic mode functions decomposed in the step 2;
step 4, setting the set values of all parameters of the BP neural network and the MQPSO algorithm;
step 5, optimizing the weight and the threshold of BP neural networks with different structures by using a self-adaptive variation quantum particle swarm algorithm (MQPSO), and establishing an MQPSO-BPn prediction model;
step 6, decomposing a plurality of intrinsic mode functions by the VMD according to the MQPSO-BPn prediction model, inputting the intrinsic mode functions into a training set, and training to obtain a trained MQPSO-BPn prediction model;
step 7, applying the trained MQPSO-BPn prediction model to the test data of each mode function to obtain a corresponding prediction result;
and 8, superposing the predicted values of all the modal functions in the step 7 to obtain an actual prediction result.
2. The power load prediction method based on the VMD-MQPSO-BPn network according to claim 1, characterized in that: the VMD decomposition in step 2 specifically includes the following contents:
step 2.1: to pairEach mode function u obtained by Hilbert transform of original signalk(t) the single-edge spectrum found is:
Figure FDA0002583221800000011
wherein t represents the t-th time, k represents the kth mode, j represents an imaginary unit, and σ (t) represents the center frequency of the kth mode at the t-th time;
step 2.2: the frequency spectrum of each mode and the mixture of the analysis signals of each mode are used to estimate the center frequency
Figure FDA0002583221800000021
For reference modulation to the corresponding baseband:
Figure FDA0002583221800000022
wherein, wkRepresents the angular frequency of the kth mode;
step 2.3: constructing a constrained variational model as follows:
Figure FDA0002583221800000023
wherein, { u [ [ u ] ]k}＝{u1，…，uKDenotes k mode functions, denotes the initial values of the k mode functions, { wk}＝{w1，…，wKMeans for indicating a k-th center frequency, indicating an initial value of the k-th center frequency; k is 1, 2, 3 … K,
Figure FDA0002583221800000024
represents the partial derivation of t, x (t) represents the original input signal;
step 2.4:
step 2.4.1: the variable model is solved, and an extended Lagrangian expression is formed by introducing a quadratic penalty function term a and a Lagrangian multiplier lambda (t), and is as follows:
Figure FDA0002583221800000025
step 2.4.2: initialization parameters
Figure FDA0002583221800000026
And n
Figure FDA0002583221800000027
Is the initial value of Lagrange multiplication operator, and n is the iteration number;
step 2.4.3: updating by alternating multiplier direction method
Figure FDA0002583221800000031
And λn+1The saddle point of the extended lagrangian expression is sought:
(1)ukthe update formula of (2);
Figure FDA0002583221800000032
(2)wkthe update formula of (2):
Figure FDA0002583221800000033
(3) the updated formula of λ:
Figure FDA0002583221800000034
(4) whether the convergence is judged by adopting a mean square error, and the conditions are as follows:
Figure FDA0002583221800000035
for a given discrimination accuracy e >0, if mse < e, the iteration is stopped, one component U1 is obtained, and the remaining components U2, U3 …, Un can be obtained by repeating step 2.4.3.
3. The power load prediction method based on the VMD-MQPSO-BPn network according to claim 1, characterized in that: the step 5 specifically comprises the following steps:
step 5.1: quantum particle swarm algorithm principle (QPSO)
In the QPSO algorithm, the population size is set to M, and the particle position update formula is transformed to:
P＝aPbest(i)+(1-a)×Gbest (9)
Figure FDA0002583221800000041
Figure FDA0002583221800000042
position＝P±|mbest-position|×ln(1/u) (12)
wherein, mbest is the middle position of the individual extreme value of the particle, namely the average optimal value, a and u are random numbers between [0,1], if u is greater than 0.5, the formula (12) is added, otherwise, the formula is subtracted, b is a contraction expansion coefficient, the linear reduction is carried out in the searching process, generation is the current evolution algebra, and max generation is the set maximum evolution algebra;
step 5.2: improved quantum particle swarm algorithm (MQPSO)
Step 5.2.1: group fitness variance σ of a population of particles2：
Figure FDA0002583221800000043
Wherein n is the number of particles in the particle group, fiIs the fitness of the first particle, favgThe function of f is to limit the sigma2The value in the algorithm f adopts the following formula:
Figure FDA0002583221800000044
Figure FDA0002583221800000051
step 5.2.2: spatial aggregation degree h of particles:
Figure FDA0002583221800000052
Figure FDA0002583221800000053
denoted as the ith particle of the t generation,
Figure FDA0002583221800000054
expressing as best position of t generation, the aggregation degree h of the space position reflects the aggregation dispersion degree of the particle individuals in the search space;
step 5.2.3: mutation operation
(1) Probability of structural variation Pm：
Figure FDA0002583221800000055
Wherein the fitness variance σ2Is determined by the formula (13), h is the spatial position concentration determined by the formula (15), σ1Is a given threshold, generally approaching 0, according to the constructed mutation probability PmPerforming mutation operation on part of the particles to make the particles have larger search space, and generating random number r E [0,1 ∈]If r < PmPerforming an update operation on each extremum according to Pi＝Pi(1+0.5 η), wherein PiThe current best position of the first particle, η, is the dimensional random vector that follows a (0,1) normal distribution.
4. The power load prediction method based on the VMD-MQPSO-BPn network according to claim 1, characterized in that: the specific steps of the step 6 are as follows:
step 6.1: establishing a BP network, determining parameters such as the structure and weight of the neural network according to input and output sample sets of the solved problem, carrying out real number vector coding on the weight and threshold values among all units of the neural network, and corresponding to all individuals in a population, wherein the vector dimension is the space dimension of the particles;
step 6.2: initializing population, initializing population size, particle position, position weight, maximum number of iterations allowed, and the like,
step 6.3: calculating the fitness of the particles, determining an individual fitness function as the mean square error of the neural network, comparing the obtained individual extreme values of each particle, wherein the global extreme value is the particle with the best individual extreme value, recording the serial number of the particle, and performing iteration by taking the optimal weight of the neural network as the recorded global extreme value in the next iteration;
step 6.4: updating the extreme value of the particle, calculating and comparing the fitness of each particle, updating the individual extreme value to the position of the particle if the particle has an individual extreme value better than the current individual extreme value, recording the serial number of the particle if the best individual extreme value in all the particles is better than the current global extreme value, and updating the global extreme value;
6.5; recalculating the fitness value of the particle, updating the inertia weight and searching the optimal position of the particle;
6.6; checking whether a convergence condition is met, if an expected error requirement or the maximum iteration number is met, ending the iteration process, and if the optimal weight and the threshold of the neural network correspond to the global extreme value of the particles, namely the best result of the problem, otherwise, turning to the step 6.3;
step 6.7: and updating the weight value and the threshold value of the network by using the optimal position of the population, and ending the operation of the algorithm.
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CN112883886A (en) * 2021-03-01 2021-06-01 兰州理工大学 Parallel accelerated VMD-SVPSO-BP neural network fault diagnosis method
CN113762078A (en) * 2021-08-03 2021-12-07 南昌工程学院 Lake TN prediction method based on VMD-CSSA-LSTM-MLR combined model
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CN115953804A (en) * 2023-01-03 2023-04-11 杭州师范大学 Human body size prediction method based on improved QPSO-BP neural network

Cited By (4)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN112883886A (en) * 2021-03-01 2021-06-01 兰州理工大学 Parallel accelerated VMD-SVPSO-BP neural network fault diagnosis method
CN113762078A (en) * 2021-08-03 2021-12-07 南昌工程学院 Lake TN prediction method based on VMD-CSSA-LSTM-MLR combined model
CN114899844A (en) * 2022-06-13 2022-08-12 华能国际电力股份有限公司德州电厂 Primary frequency modulation control system of small-disturbance thermal power generating unit
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