A method for modelling the non-stationary behaviour of structures in deformation analysis

Abstract

The standard description and modelling of the normal behaviour of structures under influence of factors like temperature or tides is done by means of correlation functions and power spectra that assume the condition of stationarity of the observed process. As a consequence of influencing parameters with highly irregular patterns, aging or damage to the structure the measured reaction of the structure may have non-stationary characteristics. Hence these functions give only a coarse description of the object's reaction and more detailed analysis techniques are needed. For these cases a method of data analysis based on the discrete wavelet decomposition and variance homogeneity testing of the wavelet coefficients is applied in this paper. After identifying the frequencies with high energy in a spectral analysis, the signal is decomposed on a scale base in order to analyse the different stationary and non-stationary components separately. The wavelet coefficients of each scale are separated into intervals with homogeneous variance by performing a test based on the cumulative sum of squares. The amplitude and phase shift of the detected frequencies are calculated for each interval in an adjustment step. Finally, using the modelled data the signal is reconstructed by wavelet synthesis. Because the wavelet transform is done without loss of information, an objective evaluation of the modelled data is possible. Continuously recorded tilt measurements at the tower of a wind energy plant were analysed both in the classical manner and with the proposed method, in order to test the latter's performance. It is shown that the new method performs well and lowers the standard deviation of the residuals by 30%, while the standard procedure does not remove the high energy components. © Springer-Verlag Berlin Heidelberg 2007.