CN115438842A - Load prediction method based on adaptive improved dayflies and BP neural network - Google Patents

Load prediction method based on adaptive improved dayflies and BP neural network Download PDF

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CN115438842A
CN115438842A CN202210989752.XA CN202210989752A CN115438842A CN 115438842 A CN115438842 A CN 115438842A CN 202210989752 A CN202210989752 A CN 202210989752A CN 115438842 A CN115438842 A CN 115438842A
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许贤泽
蒋宇飞
徐逢秋
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Abstract

The invention relates to the power load forecasting technology, in particular to a load forecasting method based on self-adaptive improved mayflies and BP neural networks, which is characterized in that the power load data and the corresponding weather characteristic data of a target area in a certain time period are collected and respectively normalized to form an original data set; decomposing an original data set into four wavelets A3, D1, D2 and D3 by utilizing three-layer wavelet decomposition; constructing and determining the structure, learning efficiency, target accuracy and training times of the BP neural network, determining the population size, iteration times, upper and lower search space boundaries and upper and lower search speed boundaries of the self-adaptive improved mayflies algorithm, and determining the mayfly population dimension according to the number of BP neural network parameters; iterative optimization of BP neural network parameters is carried out by utilizing a self-adaptive improved mayflies algorithm, the four wavelets are respectively predicted to obtain predicted data A3', D1', D2 'and D3', and the predicted data A3', D1', D2 'and D3' are superposed to obtain a final load predicted value. The method can more accurately predict the power load of multiple scenes and has strong self-adaptive capacity.

Description

Load prediction method based on adaptive improved dayflies and BP neural network
Technical Field
The invention belongs to the technical field of power load prediction, and particularly relates to a load prediction method based on self-adaptive improved mayflies and BP neural networks.
Background
The load prediction problem is about predicting the power load required by a power enterprise at a specific future time, and is one of the core contents in power grid planning. The power enterprise forecasts the change situation and the development trend of the power load within a period of time in the future according to the historical data analysis of the load and the judgment of the future development trend. An accurate load forecast is crucial to the short-term scheduling arrangement and the long-term system planning of the power enterprise, and is the basis for making power supply planning, development planning, capital financial planning and the like.
The existing power load prediction methods can be roughly divided into two types, one is a traditional prediction method represented by multiple linear regression, time series analysis, gray prediction and the like; another is an artificial intelligence algorithm represented by a neural network, an expert system, or the like. Since the power load change is a highly complex nonlinear process, the prediction accuracy of the conventional prediction method and the conventional artificial intelligence algorithm needs to be improved.
Disclosure of Invention
Aiming at the problems in the background art, the invention provides a load prediction method based on adaptive improved mayflies and BP neural networks.
In order to solve the technical problems, the invention adopts the following technical scheme: a load forecasting method based on self-adaptive improved mayflies and BP neural networks comprises the following steps:
step 1, collecting six types of original data of power load, highest temperature, lowest temperature, average temperature, relative humidity and rainfall of a target area, and normalizing the maximum value and the minimum value to form an original data set; normalization processing of data:
Figure BDA0003803404580000011
wherein x is ij Representing the original value, x, of the jth parameter in the ith class index ij * Is its normalized value, x imax 、x imin Respectively the maximum and minimum values of the parameters in the ith index;
2, decomposing an original data set into four wavelets A3, D1, D2 and D3 by utilizing three-layer wavelet decomposition;
step 3, constructing and determining the structure, learning efficiency, target accuracy and training times of the BP neural network, determining the population size, iteration times, upper and lower search space boundaries and upper and lower search speed boundaries of the self-adaptive improved mayflies algorithm, and determining the mayflies population dimension according to the number of BP neural network parameters;
step 4, utilizing a self-adaptive improved mayfly algorithm to iteratively optimize the weight and the threshold of the BP neural network, establishing a prediction model based on the BP neural network, and respectively predicting the four wavelets by utilizing the prediction model to obtain prediction data A3', D1', D2 'and D3' corresponding to the four wavelets in a prediction time period;
and 5, superposing all the prediction data A3', D1', D2 'and D3' to obtain the power load prediction value of the prediction time period.
In the above load prediction method based on adaptive modified dayflies and BP neural network, the construction of BP neural network in step 3 comprises the following formula:
determining the input quantity of the input layer:
Figure BDA0003803404580000021
wherein, the input quantity of the hidden layer is:
Figure BDA0003803404580000022
the output of the hidden layer is:
Figure BDA0003803404580000023
the Sigmoid function of the hidden layer is:
Figure BDA0003803404580000024
the input quantities of the output layer are:
Figure BDA0003803404580000025
the output of the output layer is:
Figure BDA0003803404580000026
the back propagation error function is:
Figure BDA0003803404580000027
wherein r (k) is a network model output value, and y (k) is an actual output value;
in the error back propagation stage, the value obtained by calculating the back propagation error function is subjected to attached degree correction on the weight coefficients of the hidden layer and the output layer, so that the increment of the weight coefficients from the hidden layer to the output layer is obtained as follows:
Figure BDA0003803404580000028
wherein eta is learning efficiency, and alpha is an inertia coefficient;
the weighting coefficient correction increment of the output layer is as follows:
Figure BDA0003803404580000029
wherein the content of the first and second substances,
Figure BDA00038034045800000210
the weighting factor modification increment of the hidden layer is:
Figure BDA00038034045800000211
wherein the content of the first and second substances,
Figure BDA0003803404580000031
in the above method of load prediction based on the adaptive modified dayflies and BP neural network, the adaptive modified dayflies algorithm in step 4 comprises the following steps:
step 4.1, initializing each parameter, initializing mayfly populations by Sin chaotic map, calculating all individual fitness, recording the optimal individuals and positions of the mayflies respectively;
mayflies population x = { x 1 ,x 2 ,x 3 ...x n }, n is the total mayflies; having x as the ith mayflies i ＝[x i,1 ,x i,2 ,x i,3 ...x i,j ]，x i,j ∈[0,1]J is the total weight threshold of the BP neural network, and any one mayflies represents a weight threshold combination condition of the BP neural network; generating an initial population by using Sin chaotic mapping, wherein the definition is as follows:
x n+1 ＝μsin(πx n )，x n ∈[0,1]
wherein x represents the component of mayflies in any dimension, and μ is in the range of [0,1]The control parameter of (2); enabling the generated initial population to uniformly fill the whole solution space through Sin chaotic mapping; after Sin mapping is complete, linear mapping of dayflies to Ux min ,x max ]Wherein x is max 、x min Respectively representing the upper limit and the lower limit of the weight threshold; for the ith mayflies x i ＝[x i,1 ,x i,2 ,x i,3 ...x i,j ]All weight thresholds of the BP neural network are represented;
step 4.2, movement of female dayflies; the behaviors of mayflies are characterized by flying to males to propagate, taking the total number of mayflies as N;
is provided with
Figure BDA0003803404580000032
Is the current position of the ith male mayflies in search space U at time step t; to distinguish from male mayflies, let
Figure BDA0003803404580000033
Is the current position of the ith mayfly in the search space U at time step t by adding speed to the current position
Figure BDA0003803404580000034
To change the position:
Figure BDA0003803404580000035
mayflies in the range of positions both female and male mayflies [ x ] min ,x max ]If the rate of addition is high
Figure BDA0003803404580000036
If the latter exceeds the range U, the latter is limited back to the nearest limit value;
the attraction process is set to attract the optimal female by the optimal male, and the second optimal male attracts the second optimal female; the mayflies:
Figure BDA0003803404580000037
if the changed speed exceeds the range V min ,V max ]Then it is limited back to the nearest boundary value; wherein, the first and the second end of the pipe are connected with each other,
Figure BDA0003803404580000038
for the speed of the ith mayflies in the time step t in dimension j =1.
Figure BDA0003803404580000039
The position of the ith mayfly in dimension j at time step t; f represents a fitness function, namely substituting each dayfly into a BP neural network to obtain a difference value between a predicted value and an actual value; a is a 3 Represents a positive attraction constant; r is a radical of hydrogen mf The cartesian distance between female dayflies and corresponding male dayflies is calculated as follows:
Figure BDA0003803404580000041
wherein, y i,j As mayflies i Position in dimension j, x i,j As dayflies i A position in dimension j;
g' represents the adaptive gravity coefficient of the incomplete gamma function, fl is the random flight coefficient, used when the female is not attracted by the male, when the female flies randomly, r is a random number between [ -1,1 ]; the iterative formula for fl is:
fl t+1 ＝fl t ·fldamp
wherein, fl t The coefficient is the random flight coefficient at time step t, and fldamp is the random flight damping;
step 4.3, movement of male dayflies; setting the total mayflies to be N;
each male mayflies adjust their position according to their own experience and that of neighbors; is provided with
Figure BDA0003803404580000042
Is the current position of the ith mayfly at time step t in the search space U by adding a speed to the current position
Figure BDA0003803404580000043
To change the position:
Figure BDA0003803404580000044
wherein, mayflies position x i ∈U[x min ,x max ]If the rate of addition is high
Figure BDA0003803404580000045
If the value exceeds U, the value is limited to the nearest boundary value;
speed of male dayflies
Figure BDA0003803404580000046
Comprises the following steps:
Figure BDA0003803404580000047
if the changed speed exceeds the range V min ,V max ]Then it is limited back to the nearest boundary value; wherein the content of the first and second substances,
Figure BDA0003803404580000048
represents the speed of the ith male mayflies in dimension j =1,.., n at time step t,
Figure BDA0003803404580000049
represents the position of the ith mayfly in dimension j at time step t; g' represents an adaptive gravity coefficient of the incomplete gamma function; a is a 1 、a 2 Are positive attraction constants used to scale contributions of cognitive and social components, respectively; β is a fixed visibility coefficient for limiting the visibility of dayflies; and r is p And r g Are each x i And pbest i 、x i The Cartesian distance from the gbest is calculated according to the following formula:
Figure BDA00038034045800000410
wherein x is i,j As mayflies i Position in dimension j, X i Corresponding to pbest i And gbest;
f denotes a fitness function, i.e., the absolute value of the difference between the predicted value and the actual value obtained by substituting each dayfly into the BP neural network, f min The minimum fitness function value in mayflies; mayflies in optimal positions for wedding dances, varying speed, d being the coefficient of wedding dances, r being [ -1,1]A random number in between; the iterative formula of d is:
d t+1 ＝d t ·ddamp
wherein d is t The coefficient of wedding dance at time step t and ddamp the dance damping;
step 4.4, mayflies are crossed and mutated to generate offspring;
selecting the male parent from male mayflies, the female parent from female mayflies, the two having the same rank in identity population fitness; propagating male and female dayflies of the optimal individual to obtain the optimal individual, and repeating the steps to obtain two offspring expressions:
child1＝L·m+(1-L)·f+σN 1 (0,1)
child2＝L·f+(1-L)·m+σN 2 (0,1)
wherein child1 is male progeny, and child2 is female progeny; l is a random number which is in the range of [ -1,1] and obeys Gaussian distribution, m is a male parent, and f is a female parent; σ N (0, 1) represents a random number with a mean of 0 and a variance of 1, subject to a Gaussian distribution;
step 4.5, updating the gravity coefficient, the wedding dance coefficient and the random flight coefficient;
updating the wedding dancing coefficient d and the random flight coefficient fl;
the updating formula of the adaptive gravity coefficient of the incomplete gamma function is as follows:
Figure BDA0003803404580000051
wherein gamma (λ, μ) is an incomplete gamma function, λ is a random variable greater than 0, and is taken to be 0.1; alpha is a gravity coefficient control coefficient, and alpha =1.0 is taken;
step 4.6, performing Tent chaotic mapping and population regulation of Gaussian variation;
let f (x) i ) As a function of the fitness function of the ith mayflies, f a The average value of the population fitness function values is judged as follows:
1) If f (x) i )<f a If the new position fitness function value is lower than the old position, the position is replaced;
2) If f (x) i )≥f a If the divergence phenomenon occurs, performing Tent chaotic mapping, and performing position replacement according to the same principle;
the method comprises the following specific steps:
step 4.6.1, the ith mayflies before changing is recorded as x i ；
Step 4.6.2, judge f (x) i ) And f a Relative size of (d): if the former is smaller, turning to step 4.6.3; otherwise, turning to the step 4.6.4;
step 4.6.3 dayflies are dayflies Ux min ,x max ]Linear mapping to [0,1]Range (c) wherein max 、x min Respectively representing the upper limit and the lower limit of the weight threshold;
introducing a random variable on the basis of Tent chaotic mapping, and adopting improved Tent chaotic mapping, wherein the expression is as follows:
Figure BDA0003803404580000061
wherein x represents the component of the mayflies in any dimension, and N is the number of particles in the chaotic sequence; rand (0, 1) represents a range of [0, 1]]The random number of (2); after Tent mapping is completed, the mapped dayflies are extended from [0, 1']Linear mapping back to Ux min ,x max ]The above step (1); mayflies in a new position marked with x i '; step 4.6.5 is carried out;
step 4.6.4, gaussian variation is adopted, and the expression is as follows:
mutation(x)＝x·[1+σN(0,1)]
wherein x represents the component of mayflies in any dimension, σ N (0, 1) represents a random number with a mean of 0 and a variance of 1 obeying a gaussian distribution; mutation (x) represents a value after mutation; mayflies in new positions marked with x i ′；
Step 4.6.5 the values of the mayflies fitness function f (x) only in the new positions i ') values of the fitness function of mayflies below the home position f (x) i ) Then, mayflies in the old position were replaced with the new position; the expression is as follows:
Figure BDA0003803404580000062
step 4.7, a random reverse learning strategy;
the random reverse learning strategy formula is as follows:
mutation(x)＝x max +x min -r*x
wherein x represents the component of mayflies in any dimension, x max 、x min Respectively represent the upper and lower limits of the weight threshold, r is [0, 1]]A random number in between;
values of fitness functions f (x) only when mayflies in new positions i ') values of fitness function f (x) of mayflies below the original position i ) Then, mayflies in the old position were replaced with the new position; the expression is as follows:
Figure BDA0003803404580000063
step 4.8, updating the iteration number T, exiting if the iteration number T is greater than the maximum iteration number T, outputting the best mayday; otherwise, the step 4.2 is returned.
Compared with the prior art, the invention has the beneficial effects that: the invention is based on the most basic mayflies algorithm, (1) mayflies populations are initialized using Sin chaotic maps; (2) The Tent chaotic mapping and Gaussian variation are introduced to adjust the population individuals; (3) Introducing an incomplete gamma function, and reconstructing a self-adaptive dynamically adjusted gravity coefficient; (4) introducing a random reverse learning strategy (ROBL). The global search capability is enhanced, the search adaptability is improved, and the overall performance of the algorithm is greatly improved. The weight threshold of the BP neural network is optimized by using the self-adaptive improved mayflies algorithm, so that the problem that the traditional BP neural network is easy to fall into local optimum during training is avoided, the problem of power load prediction of multiple scenes can be solved more accurately, and the self-adaptive dynamic mayflies network has stronger self-adaptive capacity.
Drawings
Fig. 1 is a diagram of a BP neural network structure according to an embodiment of the present invention;
FIG. 2 is a flowchart of an adaptive modified mayfly algorithm according to an embodiment of the invention;
FIG. 3 is a load prediction curve plot for the particle swarm optimization algorithm PSO, the base mayfly algorithm MA, the adaptive modified mayfly algorithm IMA in the embodiment of the invention.
Detailed Description
The technical solutions in the embodiments of the present invention will be described clearly and completely with reference to the following embodiments of the present invention, and it is obvious that the described embodiments are only a part of the embodiments of the present invention, and not all of the embodiments. All other embodiments, which can be derived by a person skilled in the art from the embodiments given herein without making any creative effort, shall fall within the protection scope of the present invention.
It should be noted that the embodiments and features of the embodiments may be combined with each other without conflict.
The present invention is further illustrated by the following examples, which are not intended to limit the scope of the invention.
In order to solve the problems of low accuracy and weak self-adaption capability of the current prediction algorithms, the embodiment proposes a load prediction method based on adaptive improved mayflies and BP neural networks, by collecting the electrical load data and the corresponding weather characteristic data of a target area in a certain period of time, respectively normalizing and forming an original data set; decomposing an original data set into four wavelets A3, D1, D2 and D3 by utilizing three-layer wavelet decomposition; constructing and determining the structure, learning efficiency, target accuracy and training times of the BP neural network, determining the population size, iteration times, the upper and lower bounds of the search space, the upper and lower bounds of the search speed of the adaptive improved mayflies, determining the mayflies population dimension in dependence on the number of BP neural network parameters; utilizing an adaptive improved mayflies algorithm to iteratively optimize BP neural network parameters, respectively predicting four wavelets to obtain prediction data A3', D1', D2 'and D3', and superposing the prediction data to obtain a final load prediction value.
The embodiment is realized by the following technical scheme, a load prediction method based on adaptive improved mayflies and BP neural networks, comprising the following steps:
s1, collecting six types of original data including power load, highest temperature, lowest temperature, average temperature, relative humidity and rainfall of a target area, and normalizing the maximum and minimum values to form an original data set, as shown in FIG. 1. The normalization process for the data is as follows:
Figure BDA0003803404580000071
wherein x is ij Representing the original value, x, of the jth parameter in the ith class index ij * Is its normalized value, x imax 、x imin Respectively the maximum and minimum values of the parameters in the i-th index;
s2, decomposing the original data set into four wavelets A3, D1, D2 and D3 by utilizing three-layer wavelet decomposition;
s3, constructing and determining the structure, learning efficiency, target accuracy and training times of the BP neural network, determining the population size, iteration times, upper and lower search space boundaries and upper and lower search speed boundaries of the self-adaptive improved mayflies, and determining the mayflies population dimension according to the number of BP neural network parameters;
the BP neural network is established according to the following formula:
determining the input quantity of the input layer:
Figure BDA0003803404580000081
wherein the content of the first and second substances,
the input quantities of the hidden layer are:
Figure BDA0003803404580000082
the output of the hidden layer is:
Figure BDA0003803404580000083
the Sigmoid function of the hidden layer is:
Figure BDA0003803404580000084
the input quantities of the output layer are:
Figure BDA0003803404580000085
the output of the output layer is:
Figure BDA0003803404580000086
the back propagation error function is:
Figure BDA0003803404580000087
wherein r (k) is a network model output value, and y (k) is an actual output value;
in the error back propagation stage, the value obtained by calculating the back propagation error function is subjected to attached degree correction on the weight coefficients of the hidden layer and the output layer, so that the increment of the weight coefficients from the hidden layer to the output layer is obtained as follows:
Figure BDA0003803404580000088
wherein eta is learning efficiency, and alpha is an inertia coefficient;
the weighting coefficient correction increment of the output layer is as follows:
Figure BDA0003803404580000089
wherein, the first and the second end of the pipe are connected with each other,
Figure BDA00038034045800000810
the weighting factor modification increment of the hidden layer is:
Figure BDA00038034045800000811
wherein the content of the first and second substances,
Figure BDA0003803404580000091
s4, iteratively optimizing the weight and the threshold of the BP neural network by utilizing a self-adaptive improved mayfly algorithm, establishing a prediction model based on the BP neural network, and predicting the four wavelets by utilizing the prediction model respectively to obtain prediction data A3', D1', D2 'and D3' corresponding to the four wavelets in a prediction time period;
as shown in fig. 2, the adaptive modified dayflies algorithm comprises the following steps:
s41, initializing various parameters, initializing maydaydaydaydayflies using Sin chaotic mapping: mayflies population x = { x 1 ,x 2 ,x 3 ...x n }, n is the total number of mayflies. Has x for the ith mayflies i ＝[x i,1 ,x i,2 ,x i,3 ...x i,j ]，x i,j ∈[0,1]J is the total weight threshold of the BP neural network, and any one mayflies represents a weight threshold combination condition of the BP neural network; generating an initial population by using Sin chaotic mapping, wherein the definition is as follows:
x n+1 ＝μsin(πx n )，x n ∈[0,1]
wherein x represents the component of mayflies in any dimension, and μ is in the range of [0,1]The control parameter(s) of (2). The generated initial population can more uniformly fill the whole solution space through Sin chaotic mapping, and the quality of the initial population is improved. After Sin mapping is complete, linear mapping of dayflies to Ux min ,x max ]Wherein x is max 、x min Respectively representing the upper and lower limits of the weight threshold. For the ith mayflies x i ＝[x i,1 ,x i,2 ,x i,3 ...x i,j ]I.e. all weight thresholds representing the BP neural network.
S42, movement of mayflies: the maximum behavior of female mayflies is characterized by flies propagating to males. Let the total number of mayflies be N.
Is provided with
Figure BDA0003803404580000092
Is the current position of the ith mayfly in the search space U at time step t. To distinguish from male mayflies, let
Figure BDA0003803404580000093
Is the current position of the ith female mayfly in search space U at time step tBy adding speed to the current position
Figure BDA0003803404580000094
To change the position:
Figure BDA0003803404580000095
mayflies in the range of positions both female and male mayflies [ x ] min ,x max ]If the rate of addition is high
Figure BDA0003803404580000096
And then out of range U, it is limited back to the nearest boundary value.
The attraction process is set such that the best male attracts the best female and the second best male attracts the second best female. The mayflies:
Figure BDA0003803404580000097
if the changed speed exceeds the range V min ,V max ]It is limited back to the nearest boundary value. Wherein, the first and the second end of the pipe are connected with each other,
Figure BDA0003803404580000098
for the speed of the ith mayflies in the time step t in dimension j =1.
Figure BDA0003803404580000099
The ith mayflies are the positions in dimension j at time step t. f represents a fitness function, i.e., the difference between the predicted value and the actual value obtained by substituting each dayfly into the BP neural network, the smaller the difference, the more adaptative the dayfly. a is a 3 Indicating a positive attraction constant. r is mf The Cartesian distance between female dayflies and correspondent males is the formula for the calculation:
Figure BDA0003803404580000101
wherein, y i,j Dayflies are i Position in dimension j, x i,j As mayflies i The position in dimension j.
g' represents the adaptive gravity coefficient of the incomplete gamma function, the calculation formula of which is noted in S46. fl is a random flight coefficient, used when the female is not attracted to the male, when the female flies randomly, r is a random number between [ -1,1 ]; the iterative formula for fl is:
fl t+1 ＝fl t ·fldamp
wherein, fl t The coefficient of random flight at time step t, fldamp is the random flight damping.
S43, movement of male mayflies:
let the total number of male dayflies be N. Each male mayflies adjust their position according to their own experience and that of neighbors. Suppose that
Figure BDA0003803404580000102
Is the current position of the ith mayfly at time step t in search space U by adding a speed to the current position
Figure BDA0003803404580000103
To change the position:
Figure BDA0003803404580000104
wherein, mayflies position x i ∈U[x min ,x max ]If rate of addition
Figure BDA0003803404580000105
And if U is exceeded, it is limited back to the nearest boundary value. Speeds of male mayflies
Figure BDA0003803404580000106
Comprises the following steps:
Figure BDA0003803404580000107
if the changed speed exceeds the range V min ,V max ]It is limited back to the nearest boundary value. Wherein, the first and the second end of the pipe are connected with each other,
Figure BDA0003803404580000108
represents the speed of the ith male mayflies in dimension j =1,.., n at time step t,
Figure BDA0003803404580000109
represents the position of the ith mayfly at time step t in dimension j. g' represents the adaptive gravity coefficient of the incomplete gamma function, the calculation formula of which is noted in S46. a is 1 、a 2 Are positive attraction constants used to scale the contributions of cognitive and social components, respectively. β is a fixed visibility coefficient for limiting the visibility of dayflies. And r p And r g Are each x i And pbest i 、x i The Cartesian distance from gbest is calculated as follows:
Figure BDA00038034045800001010
wherein x is i,j As dayflies i Position in dimension j, X i Corresponding to pbest i And gbest.
f denotes a fitness function, i.e., the absolute value of the difference between the predicted and actual values obtained by substituting each mayfly into the BP neural network, the smaller the value the more adaptative the mayflies are, the more f min I.e. the minimum fitness function value in the male mayflies. Mayflies in optimal positions for wedding dances, varying speed, d being the coefficient of wedding dances, r being [ -1,1]A random number in between; the iterative formula of d is: d t+1 ＝d t ·ddamp
Wherein d is t The wedding dance coefficient at time step t, ddamp is dance damping.
S44, mayflies crossing and mutating, generating offspring:
the male parent is selected from the male mayflies, the female parent is selected from the female mayflies, which are ranked the same in their individual population fitness. The optimal individual is bred by following the male and female dayflies of the optimal individual, and by analogy, two offspring expressions are obtained:
child1＝L·m+(1-L)·f+σN 1 (0,1)
child2＝L·f+(1-L)·m+σN 2 (0,1)
wherein child1 is a male offspring and child2 is a female offspring. L is a random number in the range of [ -1,1] and obeys Gaussian distribution, m is a male parent, and f is a female parent. σ N (0, 1) represents a random number with a mean of 0 and a variance of 1, subject to a Gaussian distribution.
S45, updating the gravity coefficient, the wedding dance coefficient and the random flight coefficient:
the updating formulas of the wedding dancing coefficient d and the random flying coefficient fl are set forth in S43, S42.
The larger gravity coefficient has good global searching capability; smaller inertial weights have better local exploitation capability. There is a need to introduce a non-linearly decreasing adaptive gravity coefficient to better balance global search and local development capabilities. However, the gravity coefficient with the deterministic mathematical expression is considered to be searched according to a fixed rule, so that the gravity coefficient is easy to fall into local optimum and a real self-adaptive mechanism cannot be realized. The present invention thus achieves the above object by introducing an incomplete gamma function.
The updating formula of the adaptive gravity coefficient of the incomplete gamma function is as follows:
Figure BDA0003803404580000111
where Γ (λ, μ) is an incomplete gamma function, λ is a random variable greater than 0, taken to be 0.1. And alpha is a gravity coefficient control coefficient. Experiments prove that the gravity coefficient control coefficient alpha has certain influence on the optimizing capability of the algorithm, and the self-adaptive improved mayflies algorithm has better searching capability when alpha = 1.0.
S46, population regulation based on Tent chaotic mapping and Gaussian variation:
let f (x) i ) As a function of the fitness function of the ith mayflies, f a The average value of the population fitness function values is judged as follows:
1) If f (x) i )<f a If the new position fitness function value is lower than the old position, the position is replaced;
2) If f (x) i )≥f a Namely, divergence occurs, tent chaotic mapping is carried out, and position replacement is carried out according to the same principle.
The method comprises the following specific steps:
s461, the ith mayfly as x before change i 。
S462, determining f (x) i ) And f a Relative size of (c): if the former is smaller, go to step S463; otherwise, go to step S464.
S463, first, the dayflies are bound by Ux min ,x max ]Linear mapping to [0,1]Range wherein x max 、x min Respectively representing the upper and lower limits of the weight threshold.
Introducing a random variable on the basis of Tent chaotic mapping, and adopting improved Tent chaotic mapping, wherein the expression is as follows:
Figure BDA0003803404580000121
where x represents the component of the mayflies in any dimension and N is the number of particles in the chaotic sequence. rand (0, 1) represents a range of [0, 1]]The random number of (2). After Tent mapping is completed, dayflies [0, 1] after mapping]Linear mapping back to Ux min ,x max ]The above. Mayflies in a new position marked with x i '. Go to step S465.
S464, adopting Gaussian variation, wherein the expression is as follows:
mutation(x)＝x·[1+σN(0,1)]
wherein x represents the component of mayflies in any dimension, σ N (0, 1) represents a random number with a mean of 0 and a variance of 1 obeying a gaussian distribution; the mutation (x) represents a value after mutation. Mayflies in a new position marked with x i ′。
S465 dayflies fitness function value f (x) only in new position i ') values of fitness function f (x) of mayflies below the original position i ) When doing so, mayflies in the old position were replaced with the new position. The expression is as follows:
Figure BDA0003803404580000122
s47, random reverse learning strategy:
in order to enhance the population diversity and improve the capability of the algorithm for avoiding falling into the local optimal solution, a random reverse learning strategy is adopted, and the formula is as follows:
mutation(x)＝x max +x min -r*x
wherein x represents the component of mayflies in any dimension, x max 、x min Respectively represent the upper and lower limits of the weight threshold, r is [0, 1]]A random number in between.
The value of the mayflies fitness function only in the new position f (x) i ') values of fitness function f (x) of mayflies below the original position i ) When doing so, mayflies in the old position were replaced with the new position. The expression is as follows:
Figure BDA0003803404580000123
s48, updating the iteration times T, exiting if the iteration times T are greater than the maximum iteration times T, and outputting the best mayflies; otherwise, the process returns to S42.
And S5, superposing all the prediction data A3', D1', D2 'and D3' to obtain the power load prediction value of the prediction time period.
The embodiment is as follows:
in this embodiment, the method specifically includes the following steps for the power grid data set 1:
1) Six types of original data of the power load, the highest temperature, the lowest temperature, the average temperature, the relative humidity and the rainfall of the power grid data set 1 are obtained, and maximum and minimum normalization is respectively carried out to obtain an original data set.
2) The original data set is decomposed into four wavelets A3, D1, D2, D3 using a three-layer wavelet decomposition.
3) The power load is used as output, other five indexes are used as input, the number of nodes of the single hidden layer is determined to be 12, and the BP neural network structure is 5-12-1; determining that each mayfly individual contains 85 dimensions according to the network structure, with limits of [ -5,5] being set on average, with continuous stride lengths; calculating an individual adaptive value by an individual through a fitness function; obtaining an initial weight and a threshold of the BP neural network according to the mayflies, training the BP neural network by using training data, predicting system output, and marking an absolute value of an error between the predicted output and expected output as an individual fitness value;
4) Iteration is carried out on the BP neural network weight and the threshold by utilizing the self-adaptive improved mayflies algorithm, and the optimal weight and threshold combination is obtained after iteration is circulated to the maximum iteration times. Substituting the obtained optimal weight threshold value into a BP neural network, and respectively predicting four wavelets A3, D1, D2 and D3 to obtain prediction data A3', D1', D2 'and D3';
5) And superposing all the prediction data A3', D1', D2 'and D3' to obtain the power load prediction value of the prediction time period.
6) Comparison verification is carried out, the power grid data set 1 is taken as an experimental object, the BP neural network is optimized by adopting a particle swarm optimization algorithm PSO, a base mayfly algorithm MA and an adaptive improved mayfly algorithm IMA respectively, and load prediction errors are compared. See table 1.
TABLE 1
Figure BDA0003803404580000131
According to the load prediction results of the BP neural network optimized by the three optimization algorithms, as can be seen from analysis table 1, when load prediction is performed on the grid dataset 1, the load prediction results of the BP neural network can be more accurate by the particle swarm optimization algorithm PSO, the base mayfly algorithm MA and the adaptive improved mayfly algorithm IMA, but the adaptive improved mayfly algorithm IMA provided by the invention has the best effect.
As shown in FIG. 3, the iterations of the three optimization algorithms are all set to 600 times, the base mayflies MA, the adaptive improved mayflies IMA converge substantially to the global optimum solution after 600 iterative evolutions, while the particle swarm optimization algorithm PSO still has a certain gap. In the early stage of iteration, the adaptive improved mayfly algorithm IMA can converge to global optimum within 50 iterations, while the base mayfly algorithm MA requires about 550 iterations, and the particle swarm optimization PSO has a convergence rate close to that of MA and IMA in the initial stage of iteration, but is difficult to jump out of local optimum solutions due to small population diversity in the subsequent stage. The adaptive modified mayflies algorithm IMA is modified by four items: (1) initializing mayflies using Sin chaos maps; (2) Tent chaotic mapping and Gaussian variation are introduced to adjust population individuals; (3) Introducing an incomplete gamma function, and reconstructing a self-adaptive dynamically adjusted gravity coefficient; and (4) introducing a random reverse learning strategy (ROBL). The global search capability is enhanced, the search adaptability is improved, the global search capability and the ability of jumping out of the local optimal solution of the MA algorithm are greatly improved, and the algorithm performance is superior to other two algorithms.
While the invention has been described with reference to a preferred embodiment, it will be understood by those skilled in the art that various changes in form and detail may be made therein without departing from the spirit and scope of the invention.

Claims (3)

1. A load prediction method based on adaptive modified dayflies and BP neural networks, characterized in that: the method comprises the following steps:
step 1, collecting six types of original data of power load, highest temperature, lowest temperature, average temperature, relative humidity and rainfall of a target area, and normalizing the maximum value and the minimum value to form an original data set; normalization processing of data:
Figure FDA0003803404570000011
wherein x is ij Representing the original value, x, of the jth parameter in the ith class index ij * Is its normalized value, x imax 、x imin Respectively the maximum and minimum values of the parameters in the ith index;
step 2, decomposing the original data set into four wavelets A3, D1, D2 and D3 by utilizing three-layer wavelet decomposition;
step 3, constructing and determining the structure, learning efficiency, target precision and training times of the BP neural network, determining the population size, iteration times, upper and lower bounds of the search space and upper and lower bounds of the search speed of the adaptive improved mayflies, determining the mayflies population dimension according to the number of BP neural network parameters;
step 4, utilizing a self-adaptive improved mayfly algorithm to iteratively optimize the weight and the threshold of the BP neural network, establishing a prediction model based on the BP neural network, and respectively predicting the four wavelets by utilizing the prediction model to obtain prediction data A3', D1', D2 'and D3' corresponding to the four wavelets in a prediction time period;
and 5, superposing all the prediction data A3', D1', D2 'and D3' to obtain the power load prediction value of the prediction time period.
2. The method for forecasting loads based on adaptive modified dayflies and BP neural networks according to claim 1, characterized in that: the construction of the BP neural network in the step 3 comprises the following formula:
determining the input quantity of the input layer:
Figure FDA0003803404570000012
wherein, the input quantity of the hidden layer is:
Figure FDA0003803404570000013
the output of the hidden layer is:
Figure FDA0003803404570000014
the Sigmoid function of the hidden layer is:
Figure FDA0003803404570000015
the input quantities of the output layer are:
Figure FDA0003803404570000016
the output of the output layer is:
Figure FDA0003803404570000017
the back propagation error function is:
Figure FDA0003803404570000018
wherein r (k) is a network model output value, and y (k) is an actual output value;
in the error back propagation stage, the weight coefficients of the hidden layer and the output layer are subjected to attached degree correction by using values obtained by calculating a back propagation error function, so that the increment of the weight coefficients from the hidden layer to the output layer is obtained as follows:
Figure FDA0003803404570000021
wherein eta is learning efficiency, and alpha is an inertia coefficient;
the weighting coefficient correction increment of the output layer is as follows:
Figure FDA0003803404570000022
wherein the content of the first and second substances,
Figure FDA0003803404570000023
the weighting factor correction increment of the hidden layer is as follows:
Figure FDA0003803404570000024
wherein, the first and the second end of the pipe are connected with each other,
Figure FDA0003803404570000025
3. the method for forecasting loads based on adaptive modified dayflies and BP neural networks according to claim 1, characterized in that: step 4 the adaptive modified dayflies algorithm comprises the following steps:
4.1, initializing various parameters, initializing the mayflies using the Sin chaotic map, calculating all individual fitness levels, recording the optimal individuals and positions of the mayflies respectively;
mayflies x = { x 1 ,x 2 ,x 3 ...x n }, n is the total number of mayflies; has x for the ith mayflies i ＝[x i,1 ,x i,2 ,x i,3 ...x i,j ]，x i,j ∈[0,1]J is the total weight threshold of the BP neural network, and any one mayflies represents a weight threshold combination condition of the BP neural network; generating an initial population by Sin chaotic mapping, wherein the definition is as follows:
x n+1 ＝μsin(πx n )，x n ∈[0,1]
wherein x represents the component of mayflies in any dimension, and μ is in the range of [0,1]The control parameter of (2); enabling the generated initial population to uniformly fill the whole solution space through Sin chaotic mapping; after Sin mapping is complete, linear mapping of dayflies to Ux min ,x max ]Wherein x is max 、x min Respectively representing the upper limit and the lower limit of the weight threshold; for the ith mayflies x i ＝[x i,1 ,x i,2 ,x i, 3 ...x i,j ]All weight thresholds of the BP neural network are represented;
step 4.2, movement of female dayflies; the behavior of female dayflies is characterized by flying to male dayflies for propagation, assuming the total number of female dayflies is N;
is provided with
Figure FDA0003803404570000026
Is the current position of the ith male mayflies in search space U at time step t; distinguished from mayflies, are
Figure FDA0003803404570000027
Is the current position of the ith mayfly in the search space U at time step t by adding speed to the current position
Figure FDA0003803404570000028
To change the position:
Figure FDA0003803404570000031
mayflies in the range of positions both female and male mayflies [ x ] min ,x max ]If rate of addition
Figure FDA0003803404570000032
If the latter exceeds the range U, the latter is limited back to the nearest limit value;
the attraction process is set to attract the optimal female by the optimal male, and the second optimal male attracts the second optimal female; the mayflies:
Figure FDA0003803404570000033
if the changed speed exceeds the range V min ,V max ]Then limit it back to the nearest boundary value; wherein the content of the first and second substances,
Figure FDA0003803404570000034
for the speed of the ith mayflies in time step t in dimension j =1., n,
Figure FDA0003803404570000035
the position of the ith mayfly in dimension j for time step t; f denotes a fitness function, i.e. each dayflySubstituting the predicted value into a BP neural network to obtain a difference value between the predicted value and the actual value; a is 3 Represents a positive attraction constant; r is a radical of hydrogen mf The cartesian distance between female dayflies and corresponding male dayflies is calculated as follows:
Figure FDA0003803404570000036
wherein, y i,j Dayflies are i Position in dimension j, x i,j As dayflies i A position in dimension j;
g' represents the adaptive gravity coefficient of the incomplete gamma function, fl is the random flight coefficient, used when the female is not attracted by the male, when the female flies randomly, r is a random number between [ -1,1 ]; the iterative formula for fl is:
fl t+1 ＝fl t ·fldamp
wherein fl t The coefficient is the random flight coefficient at time step t, and fldamp is the random flight damping;
step 4.3, movement of male dayflies; setting the total mayflies to be N;
each male mayflies adjust their position according to their own experience and the experience of neighbors; is provided with
Figure FDA0003803404570000037
Is the current position of the ith mayfly at time step t in the search space U by adding a speed to the current position
Figure FDA0003803404570000038
To change the position:
Figure FDA0003803404570000039
wherein, mayflies position x i ∈U[x min ,x max ]If rate of addition
Figure FDA00038034045700000310
If the value exceeds U, the value is limited to the nearest boundary value;
speed of male dayflies
Figure FDA00038034045700000311
Comprises the following steps:
Figure FDA00038034045700000312
if the changed speed exceeds the range V min ,V max ]Then it is limited back to the nearest boundary value; wherein, the first and the second end of the pipe are connected with each other,
Figure FDA00038034045700000313
represents the speed of the ith male mayflies in the time step t in dimension j =1.
Figure FDA00038034045700000314
Represents the position of the ith mayfly in dimension j at time step t; g' represents an adaptive gravity coefficient of the incomplete gamma function; a is a 1 、a 2 Are positive attraction constants used to scale contributions of cognitive and social components, respectively; β is a fixed visibility coefficient for limiting the visibility of dayflies; and r is p And r g Are each x i And pbest i 、x i The Cartesian distance from gbest is calculated as follows:
Figure FDA0003803404570000041
wherein x is i,j As dayflies i Position in dimension j, X i Corresponding to pbest i And gbest;
f denotes a fitness function, i.e., the absolute value of the difference between the predicted value and the actual value obtained by substituting each dayfly into the BP neural network, f min The minimum fitness function value in mayflies;mayflies in optimal positions carry out wedding dances, varying speed, d being the coefficient of wedding dances, r being [ -1,1]A random number in between; the iterative formula of d is:
d t+1 ＝d t ·ddamp
wherein, d t The coefficient of the wedding dance at the time step t, and ddamp is dance damping;
step 4.4, mayflies cross and mutate to generate offspring;
selecting male parents from male dayflies and female parents from female dayflies, the two having the same rank in natural-identity population fitness; propagating male and female dayflies of the optimal individual to obtain the optimal individual, and repeating the steps to obtain two offspring expressions:
child1＝L·m+(1-L)·f+σN 1 (0,1)
child2＝L·f+(1-L)·m+σN 2 (0,1)
wherein child1 is male progeny, and child2 is female progeny; l is a random number which is in the range of [ -1,1] and obeys Gaussian distribution, m is a male parent, and f is a female parent; σ N (0, 1) represents a random number with a mean of 0 and a variance of 1, subject to a Gaussian distribution;
step 4.5, updating the gravity coefficient, the wedding dance coefficient and the random flight coefficient;
updating the wedding dancing coefficient d and the random flight coefficient fl;
the updating formula of the self-adaptive gravity coefficient of the incomplete gamma function is as follows:
Figure FDA0003803404570000042
wherein gamma (lambda, mu) is incomplete gamma function, lambda is random variable greater than 0, and is 0.1; alpha is a gravity coefficient control coefficient, and alpha =1.0 is taken;
step 4.6, performing Tent chaotic mapping and population regulation of Gaussian variation;
let f (x) i ) As a function of the fitness function of the ith mayflies, f a The average value of the population fitness function values is judged as follows:
1) If f (x) i )＜f a If the new position fitness function value is lower than the old position, the position is replaced;
2) If f (x) i )≥f a If the divergence phenomenon occurs, performing Tent chaotic mapping, and performing position replacement according to the same principle;
the method comprises the following specific steps:
step 4.6.1, the ith mayflies before changing is recorded as x i ；
Step 4.6.2, judge f (x) i ) And f a Relative size of (c): if the former is smaller, turning to the step 4.6.3; otherwise, turning to the step 4.6.4;
step 4.6.3 dayflies are dayflies by Ux min ,x max ]Linear mapping to [0,1]Range wherein x max 、x min Respectively representing the upper limit and the lower limit of the weight threshold;
introducing a random variable on the basis of Tent chaotic mapping, and adopting improved Tent chaotic mapping, wherein the expression is as follows:
Figure FDA0003803404570000051
wherein x represents the component of the mayflies in any dimension, and N is the number of particles in the chaotic sequence; rand (0, 1) represents a range of [0, 1]]The random number of (2); after Tent mapping is completed, the mapped dayflies are extended from [0, 1']Linear mapping back to Ux min ,x max ]The above step (1); mayflies in a new position marked with x i '; turning to step 4.6.5;
step 4.6.4, gaussian variation is adopted, and the expression is as follows:
mutation(x)＝x·[1+σN(0,1)]
wherein x represents the component of mayflies in any dimension, σ N (0, 1) represents a random number with a mean of 0 and a variance of 1 obeying a gaussian distribution; mutation (x) represents a value after mutation; mayflies in new positions marked with x i ′；
Step 4.6.5, the value of the fitness function f (x) only when the mayflies in the new positions i ') lower than the original positionThe value of the fitness function f (x) of mayflies i ) Dayflies in the old position are replaced by the new position; the expression is as follows:
Figure FDA0003803404570000052
step 4.7, a random reverse learning strategy;
the random reverse learning strategy formula is as follows:
mutation(x)＝x max +x min -r*x
wherein x represents the component of mayflies in any dimension, x max 、x min Respectively represent the upper and lower limits of the weight threshold, r is 0,1]A random number in between;
values of fitness functions f (x) only when mayflies in new positions i ') values of the fitness function of mayflies below the home position f (x) i ) Dayflies in the old position are replaced by the new position; the expression is as follows:
Figure FDA0003803404570000061
step 4.8, updating the iteration number T, exiting if the iteration number T is greater than the maximum iteration number T, outputting the best mayflies;
otherwise, the step 4.2 is returned.
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