Weighted prediction of multi-parameter chaotic time series using least squares support vector regression (LS-SVR)

To our knowledge, there does not exist in the open literature the multi-parameter prediction that is weighted. Our weighted prediction of multi-parameter chaotic time series uses the LS-SVR. Through considering not only the single-parameter chaotic time series prediction but also all the information on related parameters' chaotic time series, section 1 of the full paper reconstructs the phase space of multi-parameter chaotic times series. Using the new information priority theory and LS-SVR theory, section 2 combines the characteristics of chaotic time series development and proposes the weighted prediction by establishing two adaptive LS-SVR models for large sample in long term and small sample in short term. Sections 3 and 4 select the parameters of the LS-SVR prediction model with the chaos optimization method and derive the objective function as shown in eq. (10) to minimize the root-mean-square error. Section 5 presents the five-step LS-SVR weighted prediction procedure. Section 6 analyzes the prediction results of the simulation example of a certain aircraft rotor's wear faults. The analysis of the prediction results, given in Tables 1 and 2, indicates preliminarily that the LS-SVR weighted prediction model is effective.