Influence of a harmonic in the response on randomdec signature

Abstract

Operational Modal Analysis (OMA) extracts modal parameters of a structure using their output response, during operation in general. OMA, when applied to mechanical engineering structures is often faced with the problem of harmonics present in the output response, and can cause erroneous modal extraction. The random decrement (RD) method of OMA helps extract randomdec signature data that can be further processed to obtain modal parameters of a structure. This paper for the first time analyses influence of a harmonic in the response on randomdec signature. Fundamental equations based on probability are derived for analyzing the influence of a harmonic on randomdec signature. These probabilistic equations are then used to predict the amplitude of the harmonic in randomdec signature. Randomdec signature of a pure harmonic signal is also derived and it is shown that it is of the same frequency as that of the harmonic signal, but has an amplitude equal to the trigger level used to find the randomdec. Based on the developed theory, new insights into the influence of harmonic on randomdec are presented based on an example. It is shown that the influence of the harmonic on randomdec is characterized by the conditional probability density function of the harmonic. It is found that more unsymmetrical is this PDF, more is the amplitude of the harmonic that is present in the randomdec signature. The amplitude of the harmonic in the randomdec is shown to be the conditional expected value of the harmonic. It is also shown that as the random component of the response increases then the amplitude of the harmonic in the randomdec decreases and in the limit can be completely eliminated.