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function ho1()
% Example of how to create a higher order DBN
% Written by Rainer Deventer <deventer@informatik.uni-erlangen.de> 3/28/03
bnet = createBNetNL();
%%%%%%%%%%%%
function bnet = createBNetNL(varargin)
% Generate a Bayesian network, which is able to model nonlinearities at
% the input. The only input is the order of the dynamic system. If this
% parameter is missing, the an order of two is assumed
if nargin > 0
order = varargin{1}
else
order = 2;
end
ss = 6; % For each time slice the following nodes are modeled
% ud(t_k) Discrete node, which decides whether saturation is reached.
% Node number 2
% uv(t_k) Visible input node with node number 2
% uh(t_k) Hidden input node with node number 3
% y(t_k) Modeled output, Number 4
% z(t_k) Disturbing variable, number 5
% q(t_k), number6 6
intra = zeros(ss,ss);
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% Within each timeslice ud(t_k) is connected with uv(t_k) and uh(t_k) %
% This part is used to model saturation %
% A connection from uv(t_k) to uh(t_k) is omitted %
% Additionally y(t_k) is connected with q(t_k). To model the disturbing%
% value z(t_k) is connected with q(t_k). %
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
intra(1,2:3) = 1; % Connections ud(t_k) -> uv(t_k) and ud(t_k) -> uh(t_k)
intra(4:5,6) = 1; % Connectios y(t_k) -> q(t_k) and z(t_k) -> q(t_k)
inter = zeros(ss,ss,order);
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% The Markov assumption is not met as connections from time slice t to t+2 %
% exist. %
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
for i = 1:order
if i == 1
inter(1,1,i) = 1; %Connect the discrete nodes. This is necessary to improve
%the disturbing reaction
inter(3,4,i) = 1; %Connect uh(t_{k-1}) with y(t_k)
inter(4,4,i) = 1; %Connect y(t_{k-1}) with y(t_k)
inter(5,5,i) = 1; %Connect z(t_{k-1}) with z(t_k)
else
inter(3,4,i) = 1; %Connect uh(t_{k-i}) with y(t_k)
inter(4,4,i) = 1; %Connect y(t_{k-i}) with y(t_k)
end
end
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% Define the dimensions of the discrete nodes. Node 1 has two states %
% 1 = lower saturation reached %
% 2 = Upper saturation reached %
% Values in between are model by probabilities between 0 and 1 %
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
node_sizes = ones(1,ss);
node_sizes(1) = 2;
dnodes = [1];
eclass = [1:6;7 2:3 8 9 6;7 2:3 10 11 6];
bnet = mk_higher_order_dbn(intra,inter,node_sizes,...
'discrete',dnodes,...
'eclass',eclass);
cov_high = 400;
cov_low = 0.01;
weight1 = randn(1,1);
weight2 = randn(1,1);
weight3 = randn(1,1);
weight4 = randn(1,1);
numOfNodes = 5 + order;
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% Nodes of the first time-slice %
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% Discrete input node,
bnet.CPD{1} = tabular_CPD(bnet,1,'CPT',[1/2 1/2],'adjustable',0);
% Modeled visible input
bnet.CPD{2} = gaussian_CPD(bnet,2,'mean',[0 10],'clamp_mean',1,...
'cov',[10 10],'clamp_cov',1);
% Modeled hidden input
bnet.CPD{3} = gaussian_CPD(bnet,3,'mean',[0, 10],'clamp_mean',1,...
'cov',[0.1 0.1],'clamp_cov',1);
% Modeled output in the first timeslice, thus there are no parents
% Usuallz the output nodes get a low covariance. But in the first
% time-slice a prediction of the output is not possible due to
% missing information
bnet.CPD{4} = gaussian_CPD(bnet,4,'mean',0,'clamp_mean',1,...
'cov',cov_high,'clamp_cov',1);
%Disturbance
bnet.CPD{5} = gaussian_CPD(bnet,5,'mean',0,...
'cov',[4],...
'clamp_mean',1,...
'clamp_cov',1);
%Observed output.
bnet.CPD{6} = gaussian_CPD(bnet,6,'mean',0,...
'clamp_mean',1,...
'cov',cov_low,'clamp_cov',1,...
'weights',[1 1],'clamp_weights',1);
% Discrete node at second time slice
bnet.CPD{7} = tabular_CPD(bnet,7,'CPT',[0.6 0.4 0.4 0.6],'adjustable',0);
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% Node for the model output %
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
bnet.CPD{8} = gaussian_CPD(bnet,10,'mean',0,...
'cov',cov_high,...
'clamp_mean',1,...
'clamp_cov',1);
% 'weights',[0.0791 0.9578]);
%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% Node for the disturbance %
%%%%%%%%%%%%%%%%%%%%%%%%%%%%
bnet.CPD{9} = gaussian_CPD(bnet,11,'mean',0,'clamp_mean',1,...
'cov',[4],'clamp_cov',1,...
'weights',[1],'clamp_weights',1);
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% Node for the model output %
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
bnet.CPD{10} = gaussian_CPD(bnet,16,'mean',0,'clamp_mean',1,...
'cov',cov_low,'clamp_cov',1);
% 'weights',[0.0188 -0.0067 0.0791 0.9578]);
%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% Node for the disturbance %
%%%%%%%%%%%%%%%%%%%%%%%%%%%%
bnet.CPD{11} = gaussian_CPD(bnet,17,'mean',0,'clamp_mean',1,...
'cov',[0.2],'clamp_cov',1,...
'weights',[1],'clamp_weights',1);
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