1. Principle of fuzzy neural network
Fuzzy Neural Networks (FNN) has the characteristics of high robustness, high learning and high adaptability. The fuzzy neural network consists of an input layer, a fuzzy layer, a fuzzy inference layer, and a clear layer. The topological structure diagram is shown in the figure below.
The first layer: the input layer. Corresponding to the input of the model
The second layer: fuzzy layer. Fuzzify the input, corresponding to each input has 7 fuzzy language sets, {positive large, positive medium, positive small, zero, negative small, negative medium, negative large} = {PB, PM, PS, Z, NS, NM ,NB}, the membership function adopts the Gaussian function, and the central values of the Gaussian function corresponding to {PB,PM,PS,Z,NS,NM,NB} are {6,4,2,0,-2,- 4,-6} with a width of {2,2,2,2,2,2,2}.
The third layer: fuzzy reasoning layer. The fuzzy reasoning layer is connected with the fuzzy layer to complete the matching of fuzzy rules, and the fuzzy operation is realized between each node, that is, the corresponding ignition intensity is obtained through the combination of each node. The output of each node j is the product of all input signals to that node.
The fourth layer: fuzzy reasoning layer. The weight average judgment method is adopted.
The general learning algorithm of fuzzy neural network is BP learning algorithm. The BP learning algorithm has the characteristics of simple implementation and strong local search ability.
2. Code combat
clc
clear
%% 参数初始化
xite=0.001;
alfa=0.05;
%% 网络节点
I=6; %输入节点数
M=12; %隐含节点数
O=1; %输出节点数
%% 系数初始化
p0=0.3*ones(M,1);p0_1=p0;p0_2=p0_1;
p1=0.3*ones(M,1);p1_1=p1;p1_2=p1_1;
p2=0.3*ones(M,1);p2_1=p2;p2_2=p2_1;
p3=0.3*ones(M,1);p3_1=p3;p3_2=p3_1;
p4=0.3*ones(M,1);p4_1=p4;p4_2=p4_1;
p5=0.3*ones(M,1);p5_1=p5;p5_2=p5_1;
p6=0.3*ones(M,1);p6_1=p6;p6_2=p6_1;
%% 参数初始化
c=1+rands(M,I);c_1=c;c_2=c_1;
b=1+rands(M,I);b_1=b;b_2=b_1;
maxgen=100; %进化次数
%% 网络测试数据，并对数据归一化
load data1 input_train output_train input_test output_test
%% 样本输入输出数据归一化
[inputn,inputps]=mapminmax(input_train);
[outputn,outputps]=mapminmax(output_train);
[n,m]=size(input_train);
%% 网络训练
%循环开始，进化网络
for iii=1:maxgen
iii
for k=1:m
x=inputn(:,k);
%输出层结算
for i=1:I
for j=1:M
u(i,j)=exp(-(x(i)-c(j,i))^2/b(j,i));
end
end
%模糊规则计算
for i=1:M
w(i)=u(1,i)*u(2,i)*u(3,i)*u(4,i)*u(5,i)*u(6,i);
end
addw=sum(w);
for i=1:M
yi(i)=p0_1(i)+p1_1(i)*x(1)+p2_1(i)*x(2)+p3_1(i)*x(3)+p4_1(i)*x(4)+p5_1(i)*x(5)+p6_1(i)*x(6);
end
addyw=yi*w';
%网络预测计算
yn(k)=addyw/addw;
e(k)=outputn(k)-yn(k);
%计算p的变化值
d_p=zeros(M,1);
d_p=xite*e(k)*w./addw;
d_p=d_p';
%计算b变化值
d_b=0*b_1;
for i=1:M
for j=1:I
d_b(i,j)=xite*e(k)*(yi(i)*addw-addyw)*(x(j)-c(i,j))^2*w(i)/(b(i,j)^2*addw^2);
end
end
%更新c变化值
for i=1:M
for j=1:I
d_c(i,j)=xite*e(k)*(yi(i)*addw-addyw)*2*(x(j)-c(i,j))*w(i)/(b(i,j)*addw^2);
end
end
p0=p0_1+ d_p+alfa*(p0_1-p0_2);
p1=p1_1+ d_p*x(1)+alfa*(p1_1-p1_2);
p2=p2_1+ d_p*x(2)+alfa*(p2_1-p2_2);
p3=p3_1+ d_p*x(3)+alfa*(p3_1-p3_2);
p4=p4_1+ d_p*x(4)+alfa*(p4_1-p4_2);
p5=p5_1+ d_p*x(5)+alfa*(p5_1-p5_2);
p6=p6_1+ d_p*x(6)+alfa*(p6_1-p6_2);
b=b_1+d_b+alfa*(b_1-b_2);
c=c_1+d_c+alfa*(c_1-c_2);
p0_2=p0_1;p0_1=p0;
p1_2=p1_1;p1_1=p1;
p2_2=p2_1;p2_1=p2;
p3_2=p3_1;p3_1=p3;
p4_2=p4_1;p4_1=p4;
p5_2=p5_1;p5_1=p5;
p6_2=p6_1;p6_1=p6;
c_2=c_1;c_1=c;
b_2=b_1;b_1=b;
end
E(iii)=sum(abs(e));
end
figure(1);
plot(outputn,'r')
hold on
plot(yn,'b')
hold on
plot(outputn-yn,'g');
legend('实际输出','预测输出','误差','fontsize',12)
title('训练数据预测','fontsize',12)
xlabel('样本序号','fontsize',12)
ylabel('水质等级','fontsize',12)
%% 网络预测
%数据归一化
inputn_test=mapminmax('apply',input_test,inputps);
[n,m]=size(inputn_test)
for k=1:m
x=inputn_test(:,k);
%计算输出中间层
for i=1:I
for j=1:M
u(i,j)=exp(-(x(i)-c(j,i))^2/b(j,i));
end
end
for i=1:M
w(i)=u(1,i)*u(2,i)*u(3,i)*u(4,i)*u(5,i)*u(6,i);
end
addw=0;
for i=1:M
addw=addw+w(i);
end
for i=1:M
yi(i)=p0_1(i)+p1_1(i)*x(1)+p2_1(i)*x(2)+p3_1(i)*x(3)+p4_1(i)*x(4)+p5_1(i)*x(5)+p6_1(i)*x(6);
end
addyw=0;
for i=1:M
addyw=addyw+yi(i)*w(i);
end
%计算输出
yc(k)=addyw/addw;
end
%预测结果反归一化
test_simu=mapminmax('reverse',yc,outputps);
%作图
figure(2)
plot(output_test,'r')
hold on
plot(test_simu,'b')
hold on
plot(test_simu-output_test,'g')
legend('实际输出','预测输出','误差','fontsize',12)
title('测试数据预测','fontsize',12)
xlabel('样本序号','fontsize',12)
ylabel('水质等级','fontsize',12)
%% 实际水质预测
load data2 hgsc gjhy dxg
%% 秦玺水厂-------
zssz=hgsc;
%数据归一化
inputn_test =mapminmax('apply',zssz,inputps);
[n,m]=size(zssz);
for k=1:1:m
x=inputn_test(:,k);
%计算输出中间层
for i=1:I
for j=1:M
u(i,j)=exp(-(x(i)-c(j,i))^2/b(j,i));
end
end
for i=1:M
w(i)=u(1,i)*u(2,i)*u(3,i)*u(4,i)*u(5,i)*u(6,i);
end
addw=0;
for i=1:M
addw=addw+w(i);
end
for i=1:M
yi(i)=p0_1(i)+p1_1(i)*x(1)+p2_1(i)*x(2)+p3_1(i)*x(3)+p4_1(i)*x(4)+p5_1(i)*x(5)+p6_1(i)*x(6);
end
addyw=0;
for i=1:M
addyw=addyw+yi(i)*w(i);
end
%计算输出
szzb(k)=addyw/addw;
end
szzbz1=mapminmax('reverse',szzb,outputps);
for i=1:m
if szzbz1(i)<=1.5
szpj1(i)=1;
elseif szzbz1(i)>1.5&&szzbz1(i)<=2.5
szpj1(i)=2;
elseif szzbz1(i)>2.5&&szzbz1(i)<=3.5
szpj1(i)=3;
elseif szzbz1(i)>3.5&&szzbz1(i)<=4.5
szpj1(i)=4;
else
szpj1(i)=5;
end
end
%% 高升水厂------
zssz=gjhy;
inputn_test =mapminmax('apply',zssz,inputps);
[n,m]=size(zssz);
for k=1:1:m
x=inputn_test(:,k);
%计算输出中间层
for i=1:I
for j=1:M
u(i,j)=exp(-(x(i)-c(j,i))^2/b(j,i));
end
end
for i=1:M
w(i)=u(1,i)*u(2,i)*u(3,i)*u(4,i)*u(5,i)*u(6,i);
end
addw=0;
for i=1:M
addw=addw+w(i);
end
for i=1:M
yi(i)=p0_1(i)+p1_1(i)*x(1)+p2_1(i)*x(2)+p3_1(i)*x(3)+p4_1(i)*x(4)+p5_1(i)*x(5)+p6_1(i)*x(6);
end
addyw=0;
for i=1:M
addyw=addyw+yi(i)*w(i);
end
%计算输出
szzb(k)=addyw/addw;
end
szzbz2=mapminmax('reverse',szzb,outputps);
for i=1:m
if szzbz2(i)<=1.5
szpj2(i)=1;
elseif szzbz2(i)>1.5&&szzbz2(i)<=2.5
szpj2(i)=2;
elseif szzbz2(i)>2.5&&szzbz2(i)<=3.5
szpj2(i)=3;
elseif szzbz2(i)>3.5&&szzbz2(i)<=4.5
szpj2(i)=4;
else
szpj2(i)=5;
end
end
%% ----重风水厂
zssz=dxg;
inputn_test =mapminmax('apply',zssz,inputps);
[n,m]=size(zssz);
for k=1:1:m
x=inputn_test(:,k);
%计算输出中间层
for i=1:I
for j=1:M
u(i,j)=exp(-(x(i)-c(j,i))^2/b(j,i));
end
end
for i=1:M
w(i)=u(1,i)*u(2,i)*u(3,i)*u(4,i)*u(5,i)*u(6,i);
end
addw=0;
for i=1:M
addw=addw+w(i);
end
for i=1:M
yi(i)=p0_1(i)+p1_1(i)*x(1)+p2_1(i)*x(2)+p3_1(i)*x(3)+p4_1(i)*x(4)+p5_1(i)*x(5)+p6_1(i)*x(6);
end
addyw=0;
for i=1:M
addyw=addyw+yi(i)*w(i);
end
%计算输出
szzb(k)=addyw/addw;
end
szzbz3=mapminmax('reverse',szzb,outputps);
for i=1:m
if szzbz3(i)<=1.5
szpj3(i)=1;
elseif szzbz3(i)>1.5&&szzbz3(i)<=2.5
szpj3(i)=2;
elseif szzbz3(i)>2.5&&szzbz3(i)<=3.5
szpj3(i)=3;
elseif szzbz3(i)>3.5&&szzbz3(i)<=4.5
szpj3(i)=4;
else
szpj3(i)=5;
end
end
figure(3)
plot(szzbz1,'o-r')
hold on
plot(szzbz2,'*-g')
hold on
plot(szzbz3,'*:b')
xlabel('时间','fontsize',12)
ylabel('预测水质','fontsize',12)
legend('水厂1','水厂2','水厂3','fontsize',12)
The result display:
