Nonlinear Fault Separation for Redundancy Process Variables Based on FNN in MKFDA Subspace

Table 1

Steps designed in this paper.

Inputs	𝑇={(𝐱1,𝑦1),(𝐱2,𝑦2),…,(𝐱𝑁,𝑦𝑁)}, 𝐱𝑖∈𝐑^𝑑, 𝑦𝑖∈{+1,−1}, 𝑖=1,2,…,𝑁
Step  1	Initiate 𝜆∈[0,1] and compute 𝐮𝑖, 𝑖=1,2
Step  2	Select suitable multikernel function
Step  3	Compute the kernel mean vector between two kinds with 𝐤𝑤𝑖=∑^𝑁𝑖𝑗=1𝐊𝐱^𝑖𝑗−𝐮𝑖𝐊𝐱^𝑖𝑗−𝐮𝑖^𝑇
Step  4	Compute the kernel scatter matrix of intraclass 𝐤𝑤=𝜆𝐤𝑤1+(1−𝜆)𝐤𝑤2
Step  5	Compute 𝜶^∗=𝐤𝑤^−1𝐮1−𝐮2, 𝐲0=𝜶^𝑇𝐮1−𝐮2
Step  6	Get the optimal solution of (16)
Step  7	Place the inspected process variable as zero in original samples
Step  8	Project the new samples into the feature space
Step  9	Compute the contribution of one variable at one time with FNN in MKFDA
Step  10	Repeat the above course for the remaining variables
Outputs	The distance measure 𝜹=𝛿1,𝛿2,…,𝛿𝑛 of each original variable is obtained