Series-Nonuniform Rational B-Spline Modeling Method And Its Application

Time series may reveal the variation of the phenomenon on some extent. For the actual complex systems, studying the development process and internal rule of the system through analysising time series is widely used. As we all know, Non-Uniform Rational B-Spline (NURBS) is a kind of excellent geometrical modeling method, and it provides a unified mathematical form for all standard shapes and freedom curves. But, the modeling technique has long not been used for time series modeling analysis, the main reason is that the modeling method lack of time variable, it can’t well describe the system evolution process. Therefore, our team had put forward to introduce time parameter into NURBS geometrical modeling and then obtained the series-NURBS (called S-NURBS for short) model, which can be used for time series analysis and application effectively.In this thesis, firstly, S-NURBS model to be further improved are discussed. Then, we explore the practical applications of S-NURBS modeling technique. From the properties and the superiority of S-NURBS, we consider to use it in time series missing value recovery and construct the specially external chaos periodic signal generator. Then we put forward an interpolation method that combining S-NURBS with window interpolation adjustment and an chaos control method based on S-NURBS signal feedback.The experiments for real world time series demonstrate that the proposed interpolation method that combining S-NURBS and window interpolation adjustment based on time sequence features is feasible, we can get reliable interpolation for missing data through flexible weight value adjustment for data points and window interpolation adjustment, and then we can analyze the physical properties of the real system easily. Actually, it provides a new technical means for the time series pretreatment. In addition, the compared results show that the geometrical method we proposed is superior than other traditional interpolation methods, such as the Linear interpolation, the Piecewise Cubic Hermite interpolating polynomial, and the Cubic B-Spline interpolation.Finally, The chaos control method based on S-NURBS signal feedback is applied to control the Van der Pol oscillator chaos system and Lorenz chaos system, it has confirmed the conclusion that the method is not only simple, but also not needs precise mathematical model of the system, all we need to do is to design suitable control signals with the discrete time sequence points sampled from chaos system and adjust the feedback weight K. Obviously, this kind of method provides an effective chaos control idea for many practical problems, especially when the mathematical expression of the nonlinear dynamic system is unclear.