An efficient method for the quantification of the frequency domain statistical properties of short response time series of dynamic systems

Abstract

For the development of innovative materials, construction types or maintenance strategies, experimental investigations are inevitable to validate theoretical models in praxis. Numerical simulations are alternatives to expensive experimental investigations. The statistical properties of the response in the frequency domain obtained from continuously measured data are often the basis for many approaches, such as the optimization of damage indicators for structural health monitoring systems. Two straightforward numerical simulation methods exist to derive the statistics of a response due to random excitation. One method is the sample-based technique, wherein for each excitation sample a time integration solution is needed. This can be computationally very expensive if a high accuracy of the statistical properties is of interest. The other method consists in using Fourier transforms and frequency response functions, wherein an infinite weakly stationary process is assumed. In this paper, a novel method is proposed that overcomes the limitation of both straightforward methods, by providing a fast probabilistic framework to determine accurately the statistics of the response for short time series. The influences of signal processing techniques, such as windowing, are considered as well. The performance of the algorithm is demonstrated on a three-degree-of-freedom system.