Patent Document ID: 20130035910
Application ID: 13391775
Patent Flag: 0

Claim One:
1. A fault detection method in a continuous annealing process based on a recursive kernel principal component analysis (RKPCA), comprising the following steps: Step 1 : collecting data and standardizing the data, the collected data in the continuous annealing industrial process including: roll speed, current and tension of an entry loop (ELP); Step 2 : calculating principal factors P of the fault in the continuous annealing process, i.e., building an initial monitoring model of the continuous annealing process with N standardized samples in Step 1 ; monitoring a new sample x new of the continuous annealing process, if it is abnormal, an alarm will be given, otherwise go to Step 3 ; wherein the extracted principal factor P in the continuous annealing process is as follows: P = Φ ( X ) [ 1 h Φ N - 1 N ( N - 2 ) 0 T - 1 h Φ N - 1 N ( N - 2 ) B A ~ ] U Φ ′ where Φ(X) is a mapping matrix of N samples X=[x 1 ,x 2 ,. .. ,x N ], N is the sample number, the regulating factor of the initial monitoring model in the continuous annealing process is h Φ = N - 1 N ( N - 2 ) 1 - 2 B T k ( X , x 1 ) + B T K ( X ) B , the correcting matrix of the initial monitoring model in the continuous annealing process is B = 1 N - 1 1 N - 1 + A ~ Λ ~ A ~ T ( k ( X ~ , x 1 ) - 1 N - 1 K ( X ~ ) 1 N - 1 ) , k ( X , x 1 ) indicates the inner product of X and x 1 , K(X) indicates the inner product of the sample matrix, k({tilde over (X)}, x 1 ) is the inner product of {tilde over (X)} and x 1 , {tilde over (X)} is the middle matrix, K({tilde over (X)}) indicates the inner product of the middle matrix, {tilde over (Λ)} is the eigenvalues matrix of the middle matrix covariance, U Φ ′ is the eigenvectors matrix of the process variables, 1 N−1 is the unit vector in N−1 column; Extracting the transmission factor of the continuous annealing process, which is expressed as [ 1 h Φ N - 1 N ( N - 2 ) 0 T - 1 h Φ N - 1 N ( N - 2 ) B A ~ ] = A ( U Φ ′ ) - 1 Step 3 : when the continuous annealing process sample x new is normal data, updating the initial monitoring model of the continuous annealing process built in Step 2 and calculating the principal factor {circumflex over (P)} of the fault in the updated continuous annealing process model by using the RKPCA, in which {circumflex over (P)} is expressed as follows: P ^ = Φ ( [ X ~ x new ] ) [ A ~ - 1 h Φ ′ N - 1 N ( N - 2 ) B ′ 0 T 1 h Φ ′ N - 1 N ( N - 2 ) ] U Φ ″ = Φ ( X new ) A ^ where Φ(X new )=Φ([{tilde over (X)} x new ]) is the updated mapping matrix, the regulating factor of the updated monitoring model in the continuous annealing process is h Φ ′ = N - 1 N ( N - 2 ) 1 - 2 B ′ T k ( X ~ , x new ) + B ′ T K ( X ~ ) B ′ , the regulating matrix of the updating monitoring model in the continuous annealing process is B ′ = 1 N - 1 1 N - 1 + A ~ Λ ~ A ~ T ( k ( X ~ , x new ) - 1 N - 1 K ( X ~ ) 1 N - 1 ) , k({tilde over (X)}, x new ) indicates the inner product of {tilde over (X)} and x new ; Step 4 : detecting fault for the continuous annealing process; wherein the fault of the continuous annealing process can be judged by using Hotelling's T 2 statistic and squared prediction error (SPE) statistic, when the T 2 statistic and SPE statistic exceed their confidence limit, a failure is identified; on the contrary, the whole process is normal, go to step 3 to continue to update the initial monitoring model of the continuous annealing process.