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⛄ 内容介绍
本文使用鲸鱼优化算法(WOA)来优化GRU的初始参数,并以此建立了WOA-GRU软测量模型。最后,将该方法应用于丙烯精馏塔中塔顶丙烷浓度的预测,实验结果表明,在动态建模方面WOA-GRU具有更高的预测精度。
⛄ 部分代码
clc; clear; close all;
%Model Parameters and excitation
%--------------------------------------------------------------------------
M=[1 0; 0 1];
K=[2 -1; -1 1]*5;
C=0.1*M+0.1*K;
f=2*randn(2,10000);
fs=100;
%Apply modal superposition to get response
%--------------------------------------------------------------------------
n=size(f,1);
dt=1/fs; %sampling rate
[Vectors, Values]=eig(K,M);
Freq=sqrt(diag(Values))/(2*pi); % undamped natural frequency
steps=size(f,2);
Mn=diag(Vectors'*M*Vectors); % uncoupled mass
Cn=diag(Vectors'*C*Vectors); % uncoupled damping
Kn=diag(Vectors'*K*Vectors); % uncoupled stifness
wn=sqrt(diag(Values));
zeta=Cn./(sqrt(2.*Mn.*Kn)); % damping ratio
wd=wn.*sqrt(1-zeta.^2);
fn=Vectors'*f; % generalized input force matrix
t=[0:dt:dt*steps-dt];
for i=1:1:n
h(i,:)=(1/(Mn(i)*wd(i))).*exp(-zeta(i)*wn(i)*t).*sin(wd(i)*t); %transfer function of displacement
hd(i,:)=(1/(Mn(i)*wd(i))).*(-zeta(i).*wn(i).*exp(-zeta(i)*wn(i)*t).*sin(wd(i)*t)+wd(i).*exp(-zeta(i)*wn(i)*t).*cos(wd(i)*t)); %transfer function of velocity
hdd(i,:)=(1/(Mn(i)*wd(i))).*((zeta(i).*wn(i))^2.*exp(-zeta(i)*wn(i)*t).*sin(wd(i)*t)-zeta(i).*wn(i).*wd(i).*exp(-zeta(i)*wn(i)*t).*cos(wd(i)*t)-wd(i).*((zeta(i).*wn(i)).*exp(-zeta(i)*wn(i)*t).*cos(wd(i)*t))-wd(i)^2.*exp(-zeta(i)*wn(i)*t).*sin(wd(i)*t)); %transfer function of acceleration
qq=conv(fn(i,:),h(i,:))*dt;
qqd=conv(fn(i,:),hd(i,:))*dt;
qqdd=conv(fn(i,:),hdd(i,:))*dt;
q(i,:)=qq(1:steps); % modal displacement
qd(i,:)=qqd(1:steps); % modal velocity
qdd(i,:)=qqdd(1:steps); % modal acceleration
end
x=Vectors*q; %displacement
v=Vectors*qd; %vecloity
a=Vectors*qdd; %vecloity
%Add noise to excitation and response
%--------------------------------------------------------------------------
f2=f+0.0*randn(2,10000);
a2=a+0.0*randn(2,10000);
v2=v+0.0*randn(2,10000);
x2=x+0.0*randn(2,10000);
%Plot displacement of first floor without and with noise
%--------------------------------------------------------------------------
figure;
subplot(2,2,1)
plot(t,f(1,:)); xlabel('Time (sec)'); ylabel('Force1'); title('First Floor');
subplot(2,2,2)
plot(t,f(2,:)); xlabel('Time (sec)'); ylabel('Force2'); title('Second Floor');
subplot(2,2,3)
plot(t,x(1,:)); xlabel('Time (sec)'); ylabel('DSP1');
subplot(2,2,4)
plot(t,x(2,:)); xlabel('Time (sec)'); ylabel('DSP2');
%Identification using neural network
%--------------------------------------------------------------------------
X=f2; %Input of neural network is forces
T=x2; %Output of neural network is displacement
[X,~] = tonndata(X,1,0); %Change format of input data
[T,~] = tonndata(T,1,0); %Change format of output data
net = narxnet(0,1,2); %Create (nonlinear autoregressive with external input) network with 0 input delays and 1 output delays
[Xs,Xi,Ai,Ts] = preparets(net,X,{},T); %Prepares data for training
net = train(net,Xs,Ts,Xi,Ai); %Train the network
view(net) %View the network
Yopen = net(Xs,Xi,Ai); %Predict Output
net = closeloop(net); %convert to closed loop neural network
view(net); %view closed-loop network
[Xs,Xi,Ai,Ts] = preparets(net,X,{},T); %Prepares data for training
net = train(net,Xs,Ts,Xi,Ai); %Train the network
Yclosed = net(Xs,Xi,Ai); %Predict Output
%Plot output with predicted output
%--------------------------------------------------------------------------
T=cell2mat(T);
Yopen=cell2mat(Yopen);
Yclosed=cell2mat(Yclosed);
figure;
subplot(2,1,1);
plot(t(1,2:end),T(1,2:end),'b-',t(1,2:end),Yopen(1,:),'r--',t(1,2:end),Yclosed(1,:),'k-.'); xlabel('Time (sec)'); ylabel('DSP1');
legend('Actual','Predicted (openloop)','Predicted (closedloop)');
subplot(2,1,2);
plot(t(2:end),T(2,2:end),'b-',t(2:end),Yopen(2,:),'r--',t(1,2:end),Yclosed(2,:),'k-.'); xlabel('Time (sec)'); ylabel('DSP2');
⛄ 运行结果
⛄ 参考文献
[1]王康, 龚文杰, 段晓燕,等. 基于PSO算法优化GRU神经网络的短期负荷预测[J]. 广东电力, 2020, 33(4):7.
[2]李祚敏, 秦江涛. 基于WOA-GRU的销售预测研究[J]. 软件导刊, 2020, 19(9):4.
[3]杨丽娜, 赵鹏, 王佩哲. 基于GRU神经网络的数据中心能耗预测模型研究[J]. 电力信息化, 2021, 019(003):10-18.
