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).
Atomic search algorithm
Atom Search Optimization (Atom Search Optimization) is a novel intelligent algorithm based on molecular dynamics model proposed in 2019. In a molecular system composed of atoms, the displacement of atoms is simulated due to the interaction force and system binding force. In a molecular system, there are interaction forces (attractive and repulsive forces) between adjacent atoms, and the globally optimal atoms exert geometric constraints on other atoms. Gravity forces the atoms to extensively explore the entire search space, and repulsion allows them to efficiently exploit potential regions. It has the characteristics of strong searching ability and fast convergence. 1. Principle of atomic optimization algorithm
3. Steps of ASO to optimize BP neural network
Step1: initialize weights and thresholds of BP neural network Step2: calculate the length of decision variables of the improved atomic search optimization algorithm based on Logistic chaos mapping, and select the mean square error as the objective function of optimization. Step3: Set the algorithm stop criterion, and use the genetic optimization algorithm to optimize the weight and threshold parameters of the neural network. Step4: Assign weight and threshold parameters obtained by optimization to BP neural network. Step5: The optimized BP neural network is trained and tested, and the error analysis and precision comparison are made with the BP neural network before optimization.
Three, demo code
%-------------------------------------------------------------------------- % Atom Search Optimization. function [X_Best,Fit_XBest,Functon_Best]=ASO(alpha,beta,Fun_Index,Atom_Num,Max_Iteration) % Dim: Dimension of search space. % Atom_Pop: Population (position) of atoms. % Atom_V: Velocity of atoms. % Acc: Acceleration of atoms. % M: Mass of atoms. % Atom_Num: Number of atom population. % Fitness: Fitness of atoms. % Max_Iteration: Maximum of iterations. % X_Best: Best solution (position) found so far. % Fit_XBest: Best result corresponding to X_Best. % Functon_Best: The fitness over iterations. % Low: The low bound of search space. % Up: The up bound of search space. % alpha: Depth weight. % beta: Multiplier weight alpha=50; Beta = 0.2; Iteration=1; [Low,Up,Dim]=Test_Functions_Range(Fun_Index); % Randomly initialize positions and velocities of atoms. if size(Up,2)==1 Atom_Pop=rand(Atom_Num,Dim).*(Up-Low)+Low; Atom_V=rand(Atom_Num,Dim).*(Up-Low)+Low; end if size(Up,2)>1 for i=1:Dim Atom_Pop(:,i)=rand(Atom_Num,1).*(Up(i)-Low(i))+Low(i); Atom_V(:,i)=rand(Atom_Num,1).*(Up(i)-Low(i))+Low(i); end end % Compute function fitness of atoms. for i=1:Atom_Num Fitness(i)=Test_Functions(Atom_Pop(i,:),Fun_Index,Dim); end Functon_Best=zeros(Max_Iteration,1); [Max_Fitness,Index]=min(Fitness); Functon_Best(1)=Fitness(Index); X_Best=Atom_Pop(Index,:); % Calculate acceleration. Atom_Acc=Acceleration(Atom_Pop,Fitness,Iteration,Max_Iteration,Dim,Atom_Num,X_Best,alpha,beta); % Iteration for Iteration=2:Max_Iteration Functon_Best(Iteration)=Functon_Best(Iteration-1); Atom_V=rand(Atom_Num,Dim).*Atom_V+Atom_Acc; Atom_Pop=Atom_Pop+Atom_V; for i=1:Atom_Num % Relocate atom out of range. TU= Atom_Pop(i,:)>Up; TL= Atom_Pop(i,:)<Low; Atom_Pop(i,:)=(Atom_Pop(i,:).*(~(TU+TL)))+((rand(1,Dim).*(Up-Low)+Low).*(TU+TL)); %evaluate atom. Fitness(i)=Test_Functions(Atom_Pop(i,:),Fun_Index,Dim); end [Max_Fitness,Index]=min(Fitness); if Max_Fitness<Functon_Best(Iteration) Functon_Best(Iteration)=Max_Fitness; X_Best=Atom_Pop(Index,:); else r=fix(rand*Atom_Num)+1; Atom_Pop(r,:)=X_Best; end % Calculate acceleration. Atom_Acc=Acceleration(Atom_Pop,Fitness,Iteration,Max_Iteration,Dim,Atom_Num,X_Best,alpha,beta); end Fit_XBest=Functon_Best(Iteration);Copy the code4. Simulation results
Five, reference and code private message blogger
Forecasting of Water Resources Demand in Ningxia Based on BP Neural Network