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Copy pathIBP_mod_MTLK.m
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IBP_mod_MTLK.m
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function [t,E_stat,E_ind,E_rad,P] = IBP_mod_MTLK(maxA,t1,t2,v,H1,Hm,H2,x0,y0,T1,...
T2,t_step,lamda1,lamda2,x,y,dh,alpha)
% User Inputs
if nargin == 0
a=struct( ...
'maxA' , {-420} , ...
't1' , {10e-006} , ...
't2' , {32.0e-006} , ...
'v' , {2.0e8} , ...
'H1' , {7600} , ...
'H2' , {8400} , ...
'x0' , {0} , ...
'y0' , {0} , ...
'T1' , {-1e-004} , ...
'T2' , {10e-004} , ...
't_step' , {1.0000e-007}, ...
'lamda1', {1.5}, ...
'lamda2', {4}, ...
'alpha', {10} , ...
'x' , {2800} , ...
'y' , {0} ,...
'dh', {10} , ...
'Hm', {7900} ...
);
else
a.maxA = maxA;
a.t1 = t1;
a.t2 = t2;
a.v = v;
a.H1 = H1;
a.Hm = Hm;
a.H2 = H2;
a.x0 = x0;
a.y0 = y0;
a.T1 = T1;
a.T2 = T2;
a.t_step = t_step;
a.lamda1 = lamda1;
a.lamda2 = lamda2;
a.x = x;
a.y = y;
a. dh = dh;
a.alpha = alpha;
end
%% Start modeling
% lamda serves a purpose similar to the characteristic length in RB
% dH = abs(a.H1 - a.H2);
% a.lamda = dH/log(dH);
a.k = (a.t2-a.t1)/a.t1;
% a.alpha = 10/a.t2;
eps0 = 8.8542e-12; % Permitivity of free space
c = 299792458/1.0003; % Speed of light in air
% get the horizontal distance from the pulse to sensors
a.x = a.x - a.x0;
a.y = a.y - a.y0;
D=sqrt(a.x^2+a.y^2);
% Counter
i=0;
ln=length(a.T1:a.t_step:a.T2);
if a.H2 > a.H1
Z = (a.H1:a.dh:a.H2)';
else
Z = (a.H1:-a.dh:a.H2)';
a.maxA = -a.maxA;
end
E_ind = zeros(1,ln);
E_rad = E_ind;
E_stat = E_ind;
%wbh = waitbar(0,'Please wait...','Name','IBP Modeler');
intgr=0;
for t=a.T1:a.t_step:a.T2
i=i+1;
% try
% waitbar(i/ln,wbh,sprintf('Please Wait... %.0f%%',i*100/ln))
% catch
% disp('NBP Program Stopped by User!')
% return
% end
% Current and derivation of current
[ii,didt]=current(Z,t-abs(Z-a.H1)/a.v-((D^2+Z.^2).^0.5)/c,a);
% figure(100)
%plot(ii,Z)
%ylim([Z(1) Z(end)])
%xlim()
% Radiation term
Y = (-1/2/pi/eps0)*D^2./(c^2*(D^2+Z.^2).^1.5).*didt;
E_rad(i) = trapz(Z,Y);
% Induction Term
Y = (1/2/pi/eps0)*((2*Z.^2-D^2)./(c*((Z.^2+D^2).^2))).*ii;
E_ind(i) = trapz(Z,Y);
% Electro Static Term
%Y=(1/2/pi/eps0)*(2*Z.^2 - D^2)./((D^2+Z.^2).^2.5).*intI;
intgr = int_i(Z,t-abs(Z-a.H1)/a.v-(D^2+Z.^2).^0.5/c,a,intgr);
Y=(1/2/pi/eps0)*(2*Z.^2 - D^2)./((D^2+Z.^2).^2.5).*intgr;
E_stat(i) = trapz(Z,Y);
% figure(500)
% plot(Y)
end
% Charge moment
P = trapz(Z,intgr);
t=(a.T1:a.t_step:a.T2);
% figure
% hold all
% tools2fig
% plot(t,E_rad)
% plot(t,E_ind)
% plot(t,E_stat)
%delete(wbh)
function [ii didt]=current(z,t,a)
ii=zeros(size(z));
didt=zeros(size(z));
sig = (a.Hm - a.H1)^2;
for j=1:length(t)
if t(j) <= a.t1
% MTLEI
%ii(j)=a.maxA*exp((z(j)-a.H1)/a.lamda)*exp(-a.alpha^2*(t(j)-a.t1)^2);
%didt(j)=exp((z(j)-a.H1)/a.lamda)*(-2)*a.maxA*a.alpha^2*(t(j)-a.t1)*exp(-a.alpha^2*(t(j)-a.t1)^2);
% TL
% ii(j)=a.maxA*exp(-a.alpha^2*(t(j)-a.t1)^2);
% didt(j)=(-2)*a.maxA*a.alpha^2*(t(j)-a.t1)*exp(-a.alpha^2*(t(j)-a.t1)^2);
% MTLL
%ii(j)=a.maxA*(1 - (z(j)-a.H1)/a.H1)*exp(-a.alpha^2*(t(j)-a.t1)^2);
%didt(j)=(1 - (z(j)-a.H1)/a.H1)*(-2)*a.maxA*a.alpha^2*(t(j)-a.t1)*exp(-a.alpha^2*(t(j)-a.t1)^2);
% MTLE
%ii(j) = a.maxA*exp(-(z(j)-a.H1)/a.lamda)*exp(-a.alpha^2*(t(j)-a.t1)^2);
%didt(j)= exp(-(z(j)-a.H1)/a.lamda)*(-2)*a.maxA*a.alpha^2*(t(j)-a.t1)*exp(-a.alpha^2*(t(j)-a.t1)^2);
% MTLEID
% if z(j) <= a.Hm
% ii(j) = a.maxA*exp((z(j)-a.H1)/a.lamda1)*exp(-a.alpha^2*(t(j)-a.t1)^2);
% didt(j)= exp((z(j)-a.H1)/a.lamda1)*(-2)*a.maxA*a.alpha^2*(t(j)-a.t1)*exp(-a.alpha^2*(t(j)-a.t1)^2);
% else
% ii(j) = exp((a.Hm-a.H1)/a.lamda1)*a.maxA*exp(-(z(j)-a.H1)/a.lamda2)*exp(-a.alpha^2*(t(j)-a.t1)^2);
% didt(j)= exp((a.Hm-a.H1)/a.lamda1)*exp(-(z(j)-a.H1)/a.lamda2)*(-2)*a.maxA*a.alpha^2*(t(j)-a.t1)*exp(-a.alpha^2*(t(j)-a.t1)^2);
% end
% MTLR
% ii(j) = a.maxA*(z(j)-a.H1)/sig*exp(-(z(j)-a.H1)^2/sig)*exp(-a.alpha^2*(t(j)-a.t1)^2);
% didt(j)= (z(j)-a.H1)/sig*exp(-(z(j)-a.H1)^2/sig)*(-2)*a.maxA*a.alpha^2*(t(j)-a.t1)*exp(-a.alpha^2*(t(j)-a.t1)^2);
% MTLKumaraswami
ii(j)=a.maxA*(abs(z(j)-a.H1)/abs(a.H2-a.H1)).^(a.lamda1-1).*((1-(abs(z(j)-a.H1)/abs(a.H2-a.H1)).^a.lamda1).^(a.lamda2-1))*exp(-a.alpha^2*(t(j)-a.t1)^2);
didt(j)=(abs(z(j)-a.H1)/abs(a.H2-a.H1)).^(a.lamda1-1).*((1-(abs(z(j)-a.H1)/abs(a.H2-a.H1)).^a.lamda1).^(a.lamda2-1))*(-2)*a.maxA*a.alpha^2*(t(j)-a.t1)*exp(-a.alpha^2*(t(j)-a.t1)^2);
else
% MTLEI
%ii(j)=a.maxA*exp((z(j)-a.H1)/a.lamda)*exp(-(a.alpha/a.k)^2*(t(j)-a.t1)^2);
%didt(j)=exp((z(j)-a.H1)/a.lamda)*(-2)*a.maxA*(a.alpha/a.k)^2*(t(j)-a.t1).*exp(-(a.alpha/a.k)^2*(t(j)-a.t1)^2);
% % TL
% ii(j)=a.maxA*exp(-(a.alpha/a.k)^2*(t(j)-a.t1)^2);
% didt(j)=(-2)*a.maxA*(a.alpha/a.k)^2*(t(j)-a.t1).*exp(-(a.alpha/a.k)^2*(t(j)-a.t1)^2);
%
% MTLL
%ii(j)=a.maxA*(1 - (z(j)-a.H1)/a.H1)*exp(-(a.alpha/a.k)^2*(t(j)-a.t1)^2);
%didt(j)=(1 - (z(j)-a.H1)/a.H1)*(-2)*a.maxA*(a.alpha/a.k)^2*(t(j)-a.t1).*exp(-(a.alpha/a.k)^2*(t(j)-a.t1)^2);
% MTLE
% ii(j)=a.maxA*exp(-(z(j)-a.H1)/a.lamda)*exp(-(a.alpha/a.k)^2*(t(j)-a.t1)^2);
% didt(j)=exp(-(z(j)-a.H1)/a.lamda)*(-2)*a.maxA*(a.alpha/a.k)^2*(t(j)-a.t1).*exp(-(a.alpha/a.k)^2*(t(j)-a.t1)^2);
% MTLEID
% if z(j) <= a.Hm
% ii(j)=a.maxA*exp((z(j)-a.H1)/a.lamda1)*exp(-(a.alpha/a.k)^2*(t(j)-a.t1)^2);
% didt(j)=exp((z(j)-a.H1)/a.lamda1)*(-2)*a.maxA*(a.alpha/a.k)^2*(t(j)-a.t1).*exp(-(a.alpha/a.k)^2*(t(j)-a.t1)^2);
% else
% ii(j)=exp((a.Hm-a.H1)/a.lamda1)*a.maxA*exp(-(z(j)-a.H1)/a.lamda2)*exp(-(a.alpha/a.k)^2*(t(j)-a.t1)^2);
% didt(j)=exp((a.Hm-a.H1)/a.lamda1)*exp(-(z(j)-a.H1)/a.lamda2)*(-2)*a.maxA*(a.alpha/a.k)^2*(t(j)-a.t1).*exp(-(a.alpha/a.k)^2*(t(j)-a.t1)^2);
%
% end
% MTLR
% ii(j)=a.maxA*(z(j)-a.H1)/sig*exp(-(z(j)-a.H1)^2/sig)*exp(-(a.alpha/a.k)^2*(t(j)-a.t1)^2);
% didt(j)=(z(j)-a.H1)/sig*exp(-(z(j)-a.H1)^2/sig)*(-2)*a.maxA*(a.alpha/a.k)^2*(t(j)-a.t1).*exp(-(a.alpha/a.k)^2*(t(j)-a.t1)^2);
%MTLKumaraswami
ii(j)=a.maxA*(abs(z(j)-a.H1)/abs(a.H2-a.H1)).^(a.lamda1-1).*((1-(abs(z(j)-a.H1)/abs(a.H2-a.H1)).^a.lamda1).^(a.lamda2-1))*exp(-(a.alpha/a.k)^2*(t(j)-a.t1)^2);
didt(j)=(abs(z(j)-a.H1)/abs(a.H2-a.H1)).^(a.lamda1-1).*((1-(abs(z(j)-a.H1)/abs(a.H2-a.H1)).^a.lamda1).^(a.lamda2-1))*(-2)*a.maxA*(a.alpha/a.k)^2*(t(j)-a.t1).*exp(-(a.alpha/a.k)^2*(t(j)-a.t1)^2);
end
end
function intgr=int_i(z,t,a,intgr)
tau=t-a.t_step:a.t_step/1:t;
inti=zeros(size(z));
for j=1:length(z)
cr=zeros(size(tau));
for kk=1:length(tau)
cr(kk)= current(z(j),tau(kk),a);
end
inti(j)=trapz(tau,cr);
end
intgr=inti+intgr;