Theory Of Wavelet Analysis And Its Application In Deformation Monitoring

Abstract:The wavelet analysis theory has been widely used in the field of deformation monitoring because of its excellent feature of time-frequency localization and capability of multiresolution analysis. However, the wavelet theory, currently, still has three problems which are not fully resolved in the field of deformation analysis. More specifically, the first one is how to evaluate the effect of de-noising accurately, and the second one is how to de-noise with high precision for different types of measurement data, then the last one is how to extract the feature information from the deformation monitoring data. So considering the current research status and problems, to establish the relevant methods of wavelet analysis and the theories of precision evaluation and quality control, then to study its applications in the areas of deformation monitoring that are all urgently needed with much value. Therefore, the main contents are as follow:(1) Under the limitations of existing traditional evaluations in comparing with the de-noising effect, a composite evaluation is proposed. It is a reliable wavelet de-noising quality evaluation which can solve the problems of optimal parameter selection such as decomposition levels and wavelet basis functions in wavelet analysis.(2) A comparative study of the de-noising effects of several filter methods is investigated in the data processing of GPS deformation monitoring under the different noise pollution. And an improved composite filtering method combined with the advantages of wavelet filter, median filter and mean filter is proposed which is based on the frequency domain and the spatial domain. Then its effect is better than the other traditional methods.(3) Aiming at the shortcomings of traditional wavelet and wavelet packet analysis, the method of wavelet packet de-noising with multi-threshold criteria based on frequency order is put forward. Then it is applied successfully into the areas of high precision deformation analysis.(4) For high sampling frequency GPS deformation monitoring data, an improved hybrid filter method based on wavelet packet analysis that combined with high-frequency coefficient weighted median filter and the overall weighted mean filter is used to preprocess the data.(5) During the analysis of the time series of deformation monitoring, a multi-scale analysis based on wavelet transform method is proposed. And it can extract the random terms, periodic terms, trend terms and other information to be analysed with satisfactory results.25figures,17tables,89references.