A brief introduction of BP neural network prediction algorithm
Note: Section 1.1 mainly summarizes and helps to understand the principle of BP neural network algorithm considering the influence factors, that is, the conventional TRAINING principle of BP model is explained (whether to skip according to their own knowledge). Section 1.2 begins with the BP neural network prediction model based on the influence of historical values.
When BP neural network is used for prediction, there are mainly two types of models from the perspective of input indexes to be considered:
1.1 BP neural network algorithm principle affected by relevant indicators
As shown in Figure 1, when BP is trained with the newff function of MATLAB, it can be seen that most cases are three-layer neural networks (namely, input layer, hidden layer and output layer). 1) Input layer: the input layer is equivalent to the human five senses. The five senses obtain external information, which corresponds to the input port of the neural network model in the process of receiving input data. 2) Hidden Layer: corresponding to the human brain, the brain analyzes and thinks about the data transmitted by the five senses. The hiddenLayer of the neural network maps the data x transmitted by the input Layer, which can be simply understood as a formula hiddenLayer_output=F(W *x+ B). Where w and b are weight and threshold parameters, F() is mapping rule, also called activation function, and hiddenLayer_output is the output value of the hidden layer for the transmitted data mapping. In other words, the hidden layer maps the input influence factor data X to produce the mapped value. 3) Output layer: it can correspond to human limbs. After thinking about the information from the five senses (hidden layer mapping), the brain controls the limbs to perform actions (responding externally). Similarly, output layer of BP neural network maps hiddenLayer_output again, outputLayer_output= W *hiddenLayer_output+ B. Where w and B are weight and threshold parameters, and outputLayer_output is the output value (also called simulation value and predicted value) of the neural network output layer (understood as the external execution action of human brain, such as the baby tapping the table). 4) Gradient descent algorithm: by calculating the deviation between outputLayer_output and the y value passed in by the neural network model, the algorithm is used to adjust parameters such as weight and threshold accordingly. This process, you can think of it as the baby slaps the table, misses it, adjusts its body depending on how far it misses so that the arm that is swinging again gets closer and closer to the table and hits.
Here’s another example to deepen your understanding:
The BP neural network shown in Figure 1 has an input layer, a hidden layer and an output layer. How does BP realize the output value outputLayer_output of the output layer through the three-layer structure, constantly approaching the given Y value, so as to obtain an accurate model by training?
From the ports strung together in the picture, one can think of a process: taking the subway. Imagine figure 1 as a subway line. One day wang went home by subway: Get on the bus at the input starting station, pass through many stations (hiddenLayer), and then find that the seat is too far (outputLayer corresponds to the current position), then Wang xx will be based on the distance from home (Target) (Error) of the current position, Return to the hiddenLayer and take the subway again (error reverse transmission, using the gradient descent algorithm to update w and b). If wang makes a mistake again, the adjustment process will be carried out again.
From the example of baby beating the table and Wang taking the subway, consider the problem: the complete training of BP needs to first input data to input, and then through the mapping of the hidden layer, the output layer gets the BP simulation value. According to the error between the simulation value and the target value, adjust the parameters, so that the simulation value constantly approaches the target value. For example, (1) infants react to external interference factors (X) and thus predict. The brain continuously adjusts the position of arms and controls the accuracy of limbs (Y and Target). (2) Wang got on the bus (X), passed through the station (predict), and kept returning to the halfway station to adjust his position and arrived home (Y and Target).
In these links, influencing factor data X and Target value data Y (Target) are involved. According to x and y, BP algorithm is used to find the rule between X and Y, and x is mapped to approximate Y. This is the role of BP neural network algorithm. One more word, all the processes mentioned above are BP model training, so though the model finally obtained is accurate in training, is the BP network found accurate and reliable? Then, we put X1 into the trained BP network to obtain the corresponding BP output value (predicted value) predicT1. By drawing and calculating the indicators such as Mse, Mape and R square, we can compare the closeness of predicT1 and Y1, so as to know whether the prediction of the model is accurate. This is the testing process of BP model, that is, to realize the prediction of data and verify the accuracy of the prediction by comparing with the actual value.
FIG. 1 structure diagram of 3-layer BP neural network
1.2 BP neural network based on the influence of historical values
Taking the power load forecasting problem as an example, the two models are distinguished. When predicting the power load within a certain period of time:
One way is to predict the load value at time T by considering the climatic factors at time T, such as the influence of air humidity X1, temperature X2 and holidays X3, etc. This is the model described in 1.1 above.
Another approach is to think that the change of power load value is related to time. For example, the power load value at t-1, T-2 and T-3 is related to the load value at t, which satisfies the formula Y (t)=F(y(t-1), Y (t-2),y(t-3)). When BP neural network is used to train the model, the influencing factor values input into the neural network are historical load values Y (t-1), Y (T-2),y(t-3). In particular, 3 is called autoregressive order or delay. The output value given to the target in the neural network is y(t).
Second, sparrow algorithm
Optimization is a popular problem in scientific research and engineering practice. Most intelligent optimization algorithms are inspired by human intelligence, the sociality of biological groups or the laws of natural phenomena, and carry out global optimization in solution space. Sparrow algorithm was first proposed by Xue Jiankai [1] in 2020. It is a new intelligent optimization algorithm based on the foraging and anti-predation behavior of sparrow population.
Sparrow search algorithm specific steps and formula description:
Building sparrow population:
Where, D represents the dimension of the problem to be optimized, and N represents the number of sparrow population. The fitness function of all sparrow populations can be expressed as follows:
Where, Fx represents the fitness function value.
Sparrows in the sparrow algorithm are divided into two categories: finders and entrants. Finders are responsible for finding food for the whole population and providing foraging directions for entrants. Therefore, the foraging search scope of finders is larger than that of entrants. During each iteration, the discoverer iterates according to Formula (3).
T said the current number of iterations, Xij said of the ith the sparrow population in the first j d location information, alfa said random number of 0 and 1, itermax said the largest number of iterations, Q means a obey the normal distribution of random Numbers, L is a 1 * d and all elements of 1 matrix, R2 belong to early warning value of 0 and 1 is the location of the sparrow population, ST belongs to the safe value of 0.5-1 indicating the position of sparrow population.
When R2<ST, it means that the warning value is less than the safe value. At this time, there is no predator in the foraging environment, and the finder can conduct extensive search operations. When R2>ST, it means that some sparrows in the population have found the predator, and give warning to other sparrows in the population. All sparrows need to fly to the safe area for foraging.
In the process of foraging, part of the entrants will monitor the discoverers all the time. When the discoverers find better food, the entrants will compete with them. If they succeed, they will get the discoverers’ food immediately.
Where, XP represents the optimal location discovered by the discoverer, Xworst represents the global worst location, and A represents the 1* D matrix whose elements are randomly assigned to 1 or -1 and meet the following relations:
L is still a 1 times d matrix with all 1’s. When I >n/2, it indicates that the ith entrant has no food and is hungry. At this time, he/she needs to fly to other places for food so as to obtain more energy.
In the sparrow population, the number of sparrows aware of danger accounts for 10% to 20% of the total number. The positions of these sparrows are randomly generated, and the positions of sparrows aware of danger are constantly updated according to Formula (5).
Where, Xbest represents the current global optimal position, is the random number that follows the standard normal distribution and is used as the step size control parameter, beta is a random number ranging from -1 to 1, Fi represents the fitness value of the current individual sparrow, FG represents the global best fitness value, fw represents the global worst fitness value, Does the one like the left ear read “Il Buzeno”? “One not zeno” means a constant that avoids a zero in the denominator. When FI >fg, sparrows are at the edge of the population and vulnerable to predators. When FI = FG, sparrows in the middle of the population are also in danger and need to be close to other sparrows to reduce the risk of being preyed on.
Three, part of the code
function [FoodFitness,FoodPosition,Convergence_curve]=SSA(N,Max_iter,lb,ub,dim,fobj) if size(ub,1)==1 ub=ones(dim,1)*ub; lb=ones(dim,1)*lb; end Convergence_curve = zeros(1,Max_iter); %Initialize the positions of salps SalpPositions=initialization(N,dim,ub,lb); FoodPosition=zeros(1,dim); FoodFitness=inf; %calculate the fitness of initial salps for i=1:size(SalpPositions,1) SalpFitness(1,i)=fobj(SalpPositions(i,:)); end [sorted_salps_fitness,sorted_indexes]=sort(SalpFitness); for newindex=1:N Sorted_salps(newindex,:)=SalpPositions(sorted_indexes(newindex),:); end FoodPosition=Sorted_salps(1,:); FoodFitness=sorted_salps_fitness(1); %Main loop l=2; % start from the second iteration since the first iteration was dedicated to calculating the fitness of salps while l<Max_iter+1 c1 = 2*exp(-(4*l/Max_iter)^2); % Eq. (3.2) in the paper for I =1:size(SalpPositions,1) SalpPositions= SalpPositions'; if i<=N/2 for j=1:1:dim c2=rand(); c3=rand(); % % % % % % % % % % % % % % Eq. (3.1) in the paper % % % % % % % % % % % % % % if c3 < 0.5 SalpPositions(j,i)=FoodPosition(j)+c1*((ub(j)-lb(j))*c2+lb(j)); else SalpPositions(j,i)=FoodPosition(j)-c1*((ub(j)-lb(j))*c2+lb(j)); end %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% end elseif i>N/2 && i<N+1 point1=SalpPositions(:,i-1); point2=SalpPositions(:,i); SalpPositions(:,i)=(point2+point1)/2; % % Eq. (3.4) in the paper end SalpPositions= SalpPositions'; end for i=1:size(SalpPositions,1) Tp=SalpPositions(i,:)>ub'; Tm=SalpPositions(i,:)<lb'; SalpPositions(i,:)=(SalpPositions(i,:).*(~(Tp+Tm)))+ub'.*Tp+lb'.*Tm; SalpFitness(1,i)=fobj(SalpPositions(i,:)); if SalpFitness(1,i)<FoodFitness FoodPosition=SalpPositions(i,:); FoodFitness=SalpFitness(1,i); end end Convergence_curve(l)=FoodFitness; l = l + 1; endCopy the code4. Simulation results
Five, reference and code private message blogger
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