2011
IMAACA 2011 Proceeding
Geometric Properties of Kernel Partial Least Squares for Non-Linear Process Monitoring
Authors: José L. Godoy, Germán Bustos, Alejandro H. Gonzalez, Jacinto L. Marchetti
Abstract
This work proposes a new strategy for monitoring non- linear processes based on Kernel Partial Least Squares (KPLS). When strongly non-linear process are considered, a PLS regression model could not be enough accurate. So, the first stage of the proposed method is to map the input data to a high-dimension space, where a linear regression model can be obtained. Then, an implicit linear regression model relating the high-dimension space with output space (output data) is obtained. This model implicitly induces a decomposition of the high-dimension space into the Model subspace and the complementary Residual subspace, being the vectors in the first subspace the effective domain of the linear regression model. Finally, once the space decomposition is understood, new statistics (metrics) for each subspace are proposed to monitor the process and detect possible abnormal behaviours. The effectiveness of the method is tested by means of a synthetic simulation example from the literature.
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