Designing shape-preserving descriptors for classifying signals with application to vibrations of large mechanical structures

Abstract

The main contribution of this paper is introduction of descriptors based on the moments of the Bernstein–Durrmeyer polynomials. As it is demonstrated, their distinctive feature is their ability to preserve knowledge about the shapes of the signals such as monotonicity and convexity, without imposing any a priori constraints. These descriptors act in time-domain as shape-preserving knowledge extractors. For their empirical version, the asymptotic unbiasedness and MSE consistency are also proved without additional pre-filtering.Another significant contribution is the method of designing an autoencoder for selecting the number of descriptors suitable for a whole class of underlying signals. For this purpose, a generalized version of Akaike’s information criterion (AIC) is derived, and its approximate version is proposed and tested. It serves as the main nonlinear part of the autoencoder. Its linear part computes the descriptors, while the decoder part computes the AIC for all particular signals from a considered family.To demonstrate the usefulness of the proposed methodology, we consider the problem of classifying signals based on knowledge about their shapes gathered by the descriptors. First, a general scheme of selecting an appropriate classifier from a predefined list is proposed. Then, the proposed approach is applied to classifying vibrations of a large excavator in an open pit mine.