Nonlinear parameter prediction of fossil power plant based on OSC-KPLS

Constrained kernelized partial least squares

“…Our solution was to add a regularizing diagonal matrix to the second kernel in Equation (16) in order to prevent rank deficiency. This problem is more prevalent in the kernel case as the optimization problem is a generalized eigenvalue problem.…”

“…As in the ordinary PLS context, once each component is calculated, the kernel is deflated, and the new kernel is used in (16) to extract the subsequent principal components. The advantage of using kernels is twofold; first, in this case where n < k, all matrix operations are performed in the smaller dimension (n) of X.…”

“…The α solving (15) is the eigenvector associated with the largest generalized eigenvalue of (16). Once α is calculated, t can be calculated directly from K as…”

“…In order to overcome the nonlinearity problem, several methods such as principal curves [8], locally linear PCA methods [9], the nonlinear iterative PLS algorithm for PLS [10,11] and kernel PCA [12][13][14] have been introduced and applied in practice [15][16][17]. In order to overcome the nonlinearity problem, several methods such as principal curves [8], locally linear PCA methods [9], the nonlinear iterative PLS algorithm for PLS [10,11] and kernel PCA [12][13][14] have been introduced and applied in practice [15][16][17].…”

“…In the case where X and Y are related through some nonlinear relationship Y = Φ(X), direct application of linear LV methods or the OSC methods fails to provide optimal results. In order to overcome the nonlinearity problem, several methods such as principal curves [8], locally linear PCA methods [9], the nonlinear iterative PLS algorithm for PLS [10,11] and kernel PCA [12][13][14] have been introduced and applied in practice [15][16][17]. Nonlinear kernel regression methods were further extended to kernel PLS (KPLS) methods [18][19][20][21].…”