Wavelet Analysis And Catastrophe Theory In The Deformation Analysis

Deformation monitoring is a fringe topic in the field of prevention and reduction of disaster in geodesy both an home and aboard. Because of the continual applications of Global Position System(GPS), survey robots and highly advanced technology, such as sensor integrated system, deformation monitoring accumulates a great deal of information and datum, it will possess theory meaning and practical value that how to proceed excavating efficiently from abundant information of short-term or medium term or long term forecast in deformation. Deformation analysis generally includes deformation data preprocessing and deformation forecast. This dissertation principally studies the deformation based on wavelet analysis and catastrophe theory.Soft computing methods, which received much recognition in natural science in recent years, includes wavelet analysis, catastrophe theory, and so on. These soft computing methods are applied in analyzing deformation observation data. On the one hand, deformation monitoring theories are enriched and developed; on the other hand, some deficiencies of routine monitoring methods, such as model cannot reflect nonlinear characters, forecast results influenced by model factors and their correlation, are made up. The main contents include:(1)By taking advantages of wavelet transformation in signal treatment, abnormal errors detection, noise reduction of deformation observation data are researched.(2)Through mathematic transformation, displacement of observation point is switched to standard format of cusp catastrophe model's potential function. Taking the method of the wavelet analysis and cusp catastrophe model combined. By calculating symbol of discriminant, displacement continuity of the system can be estimated. Thus to determine the stability of the system.