Fault Diagnosis of Complex Industrial Process Using KICA and Sparse SVM

Algorithm 1

SVM based on the modified Newton optimization.

Function: 𝛽=PrimalSVM_ENM(𝐾,𝑦,𝜆)

sv←{1,…,𝑛}; 𝛽_old=0

Repeat

𝛽=0;

𝛽_sv=(𝜆𝐼_𝑛sv+𝐾_sv,sv)⁻¹𝑦_sv;

step=𝛽−𝛽_old;

𝛾=1;

 While Ω(𝛽+𝛾⋅step)>Ω(𝛽)+𝜇𝛾⋅(∇^𝑇⋅step)

  𝛾←𝜌⋅𝛾;

 End

 𝛽←𝛽+𝛾⋅step;

 𝛽_old←𝛽;

   sv←𝑖,𝑖 satisfy 𝑦_𝑖(𝐾^𝑇_𝑖𝛽)<1;

Until sv has not changed.

  Where 𝜇∈(0,0.5), 𝜌∈(0,1).