Mathematical modeling for war preparation 34-bp neural network prediction 2

Catalog

One 、 Prediction of octane number

1- Topic analysis and principle introduction

2- Neural network building process

3- Analysis of prediction results

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BP Neural network model , Include input layer , The hidden layer and the output layer , The forward propagation process is through the input samples to the input layer , Through the input layer, the hidden layer passes through each layer , Finally, it reaches the output layer ; If the output value of the output layer does not match the output of the expected value , And then the error propagates back , Correct the weight of each unit , When the error of the network output reaches an acceptable level or the preset number of learning times is reached . I won't introduce the theory part this time , Look directly at the example , Need to learn the theory part , You can see my last neural network blog .

One 、 Prediction of octane number

1- Topic analysis and principle introduction

Let's take a look at this example 1,  about 50 Group data , We think of it as a large sample , It can be considered to establish a neural network model for prediction , Because octane number is the object of prediction , We use absorbance as input , Octane number as output .

Using neural networks to predict , We need to know three nouns ： Training set , Verification set , Test set , The details are as follows , We choose 70% As a training set , The remaining 30% As validation set and test set respectively .

About just starting to use Matlab Writing neural networks appears Input data size does not match net.inputs{1}.size problem , Because the input and output dimensions of training data are inconsistent , Make sure that the number of input columns is equal to the number of output columns .

2- Neural network building process

Take absorbance as input , Octane number as output , Building neural networks , The number of hidden layer neurons is 7 individual , The number of neurons in the output layer is 1 individual , As follows ：

 50 Group data , front 40 Group as training set , Back 10 Group as test set , Training set training model , Test set for generalization capability evaluation , We calculate root mean square error and mean error . Finally, 10 Group data for prediction .

Train the network , Then make predictions ,MATLAB Code and the future 10 The forecast results for the year are as follows ：

clear; clc
load data_Octane.mat

%% First step   Reading data 
input=X;  % Load input data 
output=Y;  % Load output data 

%%  The second step   Set training data and prediction data 
input_train = input(1:40,:)';
output_train =output(1:40,:)';
input_test = input(41:50,:)';
output_test =output(41:50,:)';
input_10 =  new_X(1:10,:)' ;
output_10 = zeros(10,1)' ;
% Number of nodes 
inputnum=2; %  Enter the number of layer nodes 
hiddennum=7;%  Number of hidden layer nodes 
outputnum=1; %  Number of output layer nodes 
%%  The third book   Training sample data normalization 
[inputn,inputps]=mapminmax(input_train);% Normalize to [-1,1] Between ,inputps To do the same normalization next time 
[outputn,outputps]=mapminmax(output_train);
%%  Step four   structure BP neural network 
net=newff(inputn,outputn,hiddennum,{'tansig','purelin'},'trainlm');%  Build a model , The transfer function uses purelin, The gradient descent method is used to train 

W1= net. iw{1, 1};% Input the weight from layer to middle layer 
B1 = net.b{1};% Threshold of neurons in the middle layer 

W2 = net.lw{2,1};% The weight from the middle layer to the output layer 
B2 = net. b{2};% The threshold of each neuron in the output layer 

%%  Step five   Network parameter configuration （  Training times , Learning rate , Minimum error of training target, etc ）
net.trainParam.epochs=1000;         %  Training times , I'm going to set it to 1000 Time 
net.trainParam.lr=0.01;                   %  Learning rate , I'm going to set it to 0.01
net.trainParam.goal=0.00001;                    %  The minimum error of training target , I'm going to set it to 0.00001

%%  Step six  BP Neural network training 
net=train(net,inputn,outputn);% Start training , among inputn,outputn Input and output samples respectively 

%%  Step seven   Test sample normalization 
inputn_test=mapminmax('apply',input_test,inputps);%  Normalize the sample data 
inputn_10 = mapminmax('apply',input_10,inputps);

%%  Step eight  BP Neural networks predict 
an=sim(net,inputn_test); % Use the trained model for simulation 
an1 = sim(net,inputn_10) ;% Last 10 Group prediction 

%%  Step nine   Inverse normalization of prediction results and error calculation      
test_simu=mapminmax('reverse',an,outputps); % Restore the simulated data to the original order of magnitude 
output_10 = mapminmax('reverse',an1,outputps);
error=test_simu-output_test;      % The error between the predicted value and the real value 

%% Step 10   Comparison of error between real value and predicted value 
figure(1);
plot(output_test,'bo-')
hold on
plot(test_simu,'r*-')
hold on
plot(error,'square','MarkerFaceColor','b')
legend(' Expectations ',' Predictive value ',' error ')
xlabel(' Number of data groups ')
ylabel(' Sample value ')
title('BP Comparison between predicted value and actual value of neural network test set ')

[c,l]=size(output_test);
MAE1=sum(abs(error))/l;
MSE1=error*error'/l;
RMSE1=MSE1^(1/2);
disp(['----------------------- Error calculation --------------------------']);
disp([' The number of hidden layer nodes is ',num2str(hiddennum),' The error results are as follows ：']);
disp([' Mean absolute error MAE by ：',num2str(MAE1)]);
disp([' Mean square error MSE by ：       ',num2str(MSE1)]);
disp([' Root mean square error RMSE by ：  ',num2str(RMSE1)]);
disp(' Last 10 The predicted result of group octane is ：') ;
disp(output_10) ;
figure(2);
plot(51:60,output_10,'o-') ;
xlabel(' sample ID');
ylabel(' Octane predicted value ') ;

3- Analysis of prediction results

Let's take a look at the comparison between the predicted value and the real value of the test set , It can be found that the error is very small , Almost close to 0, It can be considered that the model training is better .

Then let's take a look at , Last 10 Prediction results of group octane number , As follows ：

  Let's look at the mean square error and mean error of the prediction , As follows ：

Let's take a look at the training set 、 Verification set 、 The change of mean square error of test set and population with training times , Basically, validation sets and test sets 5 It converges every time , Training set Essentials 6 More than once .

Regress the fitting value to the true value , The higher the goodness of fit , It shows that the better the fitting effect , We can see that the goodness of fit of the set is close to 1 Of .