Adaptive Fault Detection for Complex Dynamic Processes Based on JIT Updated Data Set

Pseudocode 1

for𝑖=1∶𝑚

 for𝑗=1∶𝑚

  cov(𝑖,𝑗)=sum((𝑥(∶,𝑖)−mean(𝑥(∶,𝑖))).

  ∗(𝑥(∶,𝑗)−mean(𝑥(∶,𝑗))))/(size(𝑥,1)−1);

 end

end

𝐙=𝐗;

𝑠𝑠1=eig(cov);

[𝑠𝑚1,𝑠𝑛1]=size(𝑠𝑠1);

𝑙𝑚𝑑1=0

for𝑖=1∶𝑠𝑚1

 𝑙𝑚𝑑1=𝑙𝑚𝑑1+𝑠𝑠1(𝑖);

end

while1

[𝑝,𝑞]=size(𝐙)

for𝑖=1∶𝑞

 for𝑗=1∶𝑞

  cov(𝑖,𝑗)=sum((𝑧(∶,𝑖)−mean(𝑧(∶,𝑖))).

  ∗(𝑧(∶,𝑗)−mean(𝑧(∶,𝑗))))/(size(𝑧,1)−1);

 end

end

𝑠𝑠=eig(cov);

[𝑠𝑚,𝑠𝑛]=size(𝑠𝑠)

𝑙𝑚𝑑=0

for𝑖=1∶𝑠𝑚

 𝑙𝑚𝑑=𝑙𝑚𝑑+𝑠𝑠(𝑖);

end

if𝑙𝑚𝑑/𝑙𝑚𝑑1<𝜖||𝑙𝑚𝑑/𝑙𝑚𝑑1>1

 break

end

[𝑛,𝑚]=size(𝐙);

𝑑=zeros(𝑛,𝑛);

𝐌=𝐙;

for𝑖=1∶𝑛

 for𝑗=1∶𝑛

  𝑑(𝑖,𝑗)=𝑑(𝑖,𝑗)+(𝑧(𝑖,∶)−𝑧(𝑗,∶))∗inv(cov)

  ∗(𝑧(𝑖,∶)−𝑧(𝑗,∶))^𝑇

 end

end

𝑚𝑑=zeros(𝑛−1,𝑛−1);

for𝑖=1∶𝑛

 for𝑗=1∶𝑛

  if𝑑(𝑖,𝑗)>0

   𝑚𝑑(𝑖,𝑗)=𝑑(𝑖,𝑗);

  else

   𝑚𝑑(𝑖,𝑗)=10000;

  end

 end

end

[The_Min,The_Min_ID]=min(𝑚𝑑^′)

𝑣=The_Min;

𝑝=The_Min_ID;

[The_Min,The_Min_ID]=min(𝑣);

𝑖=The_Min_ID;

𝑗=𝑝(𝑖);

𝑧(𝑖,∶)=(𝑧(𝑖,∶)+𝑧(𝑗,∶))/2;

𝑧(𝑗,∶)=[];

end