The prediction of nonlinear and non-stationary systems is a research topic of great scientific significance. Some recent work has used the Convergent Cross Mapping (CCM) algorithm to detect the causal relationship between variables. In the CCM algorithm, the points close to each other in the phase space have similar trends and trajectories in time. Therefore, this method can try to be applied to the prediction experiment research of nonlinear and non-stationary systems. Therefore, in this paper the CCM algorithm was applied to the prediction of the Lorenz system and the actual climate time series respectively, and different phase space reconstruction methods were investigated on the prediction skill. The preliminary results are as follows: (1) Regardless of the ideal Lorenz model or the actual climate series, for the three reconstruction phase space methods of univariate, multivariate, and multiview embedding method, the multiview embedding method has the best predictive skill. Indicating that for a given length of time series, the more information contained in the reconstructed phase space, the stronger its predictive ability. (2) Adding data of NAM (Northern Hemisphere Annular Mode) to the reconstructed phase space of SAT (Surface Air Temperature) can improve the prediction effect on prediction of SAT. Using univariable, multivariable, and multiview embedding methods for prediction, the characteristics of common information in the complex system were considered, the length of the time series is fixed, the complexity of the dynamic system can be used to increase the information of the system. Based on causality detection, through the extraction of quantitative information of data, it provides a novel idea for the improvement of predictive skills in nonlinear and non-stationary systems.

：Briefly introduces the current situation of techniques and applications of China's high-speed train wheels, and the several major problems influencing the operation quality, safe operation and transportation costs of high-speed trains. In these problems the most concerned one is the wheel out of roundness or called polygonal wear of wheel. The domestic and foreign researches the polygonal wear and its countermeasures are briefly reviewed. The situation and characteristics of polygonal wear of high-speed wheels of China are clearly classified and its characteristics shows that the polygonal wear includes 2 to 3 main wavelengths, they are respectively the eccentricity wear (called one-order polygonal wear), 14-order and 23-order polygonal wear (called high-order polygons). A basic condition for the initiation and fast development of the polygonal wear is established. It is found that in several special stages of wheel diameter change the polygonal wear develops fast if the basic condition is satisfied. The effects of the polygonal wear on the dynamical behavior and noise of high-speed vehicle, the impact load of wheel/rail, and the fatigue of the parts are discussed briefly. The basic factors affecting the formation and rapid development of wheel polygons are discussed in detail. Several countermeasures to suppress the development of the polygonal wear are discussed, and some of them have been proved to be very effective in field operation experience. The paper also puts forward the maintenance strategy of the polygonal wear wheel and the key research problems that need to be carried out urgently at present.

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