Inverse-signal analysis with PCA

Current methods for analyzing dynamic measurements from chemical processes and instruments often rely on fitting parametric models to the measured data; the methods assume a predetermined mathematical function for the measurement signal. Principal component analysis (PCA) is a useful technique for extracting condensed descriptors from multivariate data without predetermined functional forms for the signals; however, it assumes linear relationships among signals. In practice, many signals are not adequately modeled by linear techniques; signals which display variation in time scales are especially difficult to model with linear relationships. In this paper, we present a method for transforming such signals in order to efficiently apply PCA without restriction to a pre-defined model. An inversion of the signals is shown to be an effective way to transform signals, with varying time scales, prior to PCA. Two examples are presented that illustrate this methodology, and the results are compared to those obtained from applying PCA without transforming the signals.