Modal Identification Algorithm with Unmeasured Input

Abstract

This paper investigates the possibility of generating a time‐domain modal identification algorithm that does not need measurements of the input signals. Such a technique is useful when complete input data acquisition cannot be performed. The approach is based on the Yule‐Walker equations, extended to the case where the input signal is not white noise. The algorithm is written recursively both to minimize data acquisition and to be flexible enough when time‐varying modal parameters are tracked. Natural frequencies and damping ratios are extracted with an error magnitude inferior to impulse response techniques but superior to methods using the input time history. From a computational aspect, the algorithm only introduces scalar inversions, which presents an important gain of time and stability. Examples and comparisons with other techniques are presented. The case where a change in the modal parameter values occur is also highlighted. A normalized error, taking into account the quality and the swiftness of the new estimation, is introduced.