The type-oriented algorithm for baseline correction of acceleration time histories

Abstract

This paper presents the development of an exhaustive approach to baseline correction of acceleration signals that amalgamates several existing methods to provide a more powerful and flexible toolkit for scientific software implementation. The proposed type-oriented baseline correction algorithm employs the traditional methodology of subtracting a least squares polynomial from the raw time series, but it is seeded by a specified combination of correction types that can vary in both polynomial order and kinematic variable considered (i.e., acceleration, velocity, or displacement). The result is a dramatic expansion in the number of corrections possible with current commercial software, which tend to consider only one kinematic variable while also restricting the polynomial order used. The proposed algorithm incorporates seven unique correction types based on permutations of kinematic variables adjusted in sequence. Different numerical methods are evaluated to solve the system of normal equations of the least squares polynomial approximation of the one-dimensional real function. The result is an algorithm that achieves practically unlimited polynomial order. The external behavior of the algorithm is evaluated by presenting a set of parametric tests that use different correction types. It is shown that the optimal correction of some vibration signals, particularly those with low frequency content occurring over many cycles, cannot be obtained without adjusting the time histories by high order best-fits of more than one kinematic variable. The importance of baseline correction in the context of finite element analysis is discussed, and several implementation examples are provided in different programming languages.