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).
Whale algorithm
1, inspired
Whale optimization Algorithm (WOA) is a new swarm intelligence optimization algorithm proposed by Mirjalili et al from Griffith University in Australia in 2016. Its advantages lie in simple operation, few parameters and strong ability to jump out of local optimum.
2. Surround the prey
Humpback whales recognize the location of prey and circle it. Since the position of the optimal position in the search space is unknown, the WOA algorithm assumes that the current best candidate solution is the target prey or close to the optimal solution. After the best candidate solution is defined, the other candidate locations attempt to move to the best and update their positions. This line is represented by the following equation:
3. Hunting behavior
According to the hunting behavior of humpback whales, it swims toward prey in spiral motion, so the mathematical model of hunting behavior is as follows:
4. Hunt for prey
The mathematical model is as follows:
Three, part of the code
%__________________________________________ % fobj = @YourCostFunction % dim = number of your variables % Max_iteration = maximum number of generations % SearchAgents_no = number of search agents % lb=[lb1,lb2,...,lbn] where lbn is the lower bound of variable n % ub=[ub1,ub2,...,ubn] where ubn is the upper bound of variable n % If all the variables have equal lower bound you can just % define lb and ub as two single number numbers % To run ALO: [Best_score,Best_pos,cg_curve]=ALO(SearchAgents_no,Max_iteration,lb,ub,dim,fobj) % The Whale Optimization Algorithm function [Leader_score,Leader_pos,Convergence_curve]=WOA(SearchAgents_no,Max_iter,lb,ub,dim,fobj,handles,value) % initialize position vector and score for the leader Leader_pos=zeros(1,dim); Leader_score=inf; %change this to -inf for maximization problems %Initialize the positions of search agents Positions=initialization(SearchAgents_no,dim,ub,lb); Convergence_curve=zeros(1,Max_iter); t=0; % Loop counter % Main loop while t<Max_iter for i=1:size(Positions,1) % Return back the search agents that go beyond the boundaries of the search space Flag4ub=Positions(i,:)>ub; Flag4lb=Positions(i,:)<lb; Positions(i,:)=(Positions(i,:).*(~(Flag4ub+Flag4lb)))+ub.*Flag4ub+lb.*Flag4lb; % Calculate objective function for each search agent fitness=fobj(Positions(i,:)); All_fitness(1,i)=fitness; % Update the leader if fitness<Leader_score % Change this to > for maximization problem Leader_score=fitness; % Update alpha Leader_pos=Positions(i,:); end end a=2-t*((2)/Max_iter); 19:00 :00 :00 :00 :00 :00 :00 :00 :00 :00 :00 :00 :00 :00 :00 :00 :00 :00 :00 :00 :00 :00 :00 :00 :00 :00 :00 :00 :00 :00 :00 :00 :00 :00 :00 :00 :00 :00 :00 a2=-1+t*((-1)/Max_iter); % Update the Position of search agents for i=1:size(Positions,1) r1=rand(); % r1 is a random number in [0,1] r2=rand(); % r2 is a random number in [0,1] a =2*a*r1-a; % Eq. (2.3) in the paper C=2*r2; % Eq. (2.4) in the paper b=1; % parameters in Eq. (2.5) l=(a2-1)*rand+1; % parameters in Eq. (2.5) p = rand(); % p in Eq. (2.6) for j=1:size(Positions,2) if P <0.5 if ABS (A)>=1 rand_leader_index = floor(SearchAgents_no*rand()+1); X_rand = Positions(rand_leader_index, :); D_X_rand=abs(C*X_rand(j)-Positions(i,j)); % Eq. (2.7) Positions (I, j) = X_rand (j) - A * D_X_rand; % Eq. (2.8) elseif ABS (A)<1 D_Leader= ABS (C*Leader_pos(j) -positions (I,j)); % Eq. (2.1) Positions (I, j) = Leader_pos (j) - A * D_Leader; % Eq. (2.2) end elseif P >=0.5 distance2Leader=abs(Leader_pos(j) -positions (I,j)); % Eq. (2.5) Positions (I, j) = distance2Leader * exp (b. * l). * cos (2 * PI * l.) + Leader_pos (j); end end end t=t+1; Convergence_curve(t)=Leader_score; if t>2 line([t-1 t], [Convergence_curve(t-1) Convergence_curve(t)],'Color','b') xlabel('Iteration'); ylabel('Best score obtained so far'); drawnow end set(handles.itertext,'String', ['The current iteration is ', num2str(t)]) set(handles.optimumtext,'String', ['The current optimal value is ', num2str(Leader_score)]) if value==1 hold on scatter(t*ones(1,SearchAgents_no),All_fitness,'.','k') end endCopy the code4. Simulation results
FIG. 2 Convergence curve of whale algorithm
The following table shows the test statistics
The test results
Test set accuracy rate
Correct rate of training set
BP neural network
100%
95%
WOA-BP
100%
99.8%
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