Local polynomial prediction method of multivariate chaotic time series and its application

To improve the prediction accuracy of chaotic time series, a new methodformed on the basis of local polynomial prediction is proposed. The multivariate phase spacereconstruction theory is utilized to reconstruct the phase space firstly, and on its basis, apolynomial function is applied to construct the prediction model, then the parameters of the modelaccording to the data matrix built with the embedding dimensions are estimated and a one-stepprediction value is calculated. An estimate and one-step prediction value is calculated. Finally,the mean squared root statistics are used to estimate the prediction effect. The simulation resultsobtained by the Lorenz system and the prediction results of the Shanghai composite index show thatthe local polynomial prediction errors of the multivariate chaotic time series are small and itsprediction accuracy is much higher than that of the univariate chaotic time series.

The improved local linear prediction of chaotic time series

Based on the Bayesian information criterion, this paper proposes the improved local linear prediction method to predict chaotic time series. This method uses spatial correlation and temporal correlation simultaneously. Simulation results show that the improved local linear prediction method can effectively make multi-step and one-step prediction of chaotic time series and the multi-step prediction performance and one-step prediction accuracy of the improved local linear prediction method are superior to those of the traditional local linear prediction method.

KLT-based local linear prediction of chaotic time series

In the reconstructed phase space, based on the Karhunen-Loeve transformation （KLT）, the new local linear prediction method is proposed to predict chaotic time series. ＆ noise-free chaotic time series and a noise added chaotic time series are analyzed. The simulation results show that the KLT-based local linear prediction method can effectively make one-step and multi-step prediction for chaotic time series, and the one-step and multi-step prediction accuracies of the KLT-based local linear prediction method are superior to that of the traditional local linear prediction.

Quantifying local predictability of the Lorenz system using the nonlinear local Lyapunov exponent

The nonlinear local Lyapunov exponent（NLLE） can be used as a quantification of the local predictability limit of chaotic systems. In this study, the phase-spatial structure of the local predictability limit over the Lorenz-63 system is investigated. It is found that the inner and outer rims of each regime of the attractor have a high probability of a longer than average local predictability limit, while the center part is the opposite. However, the distribution of the local predictability limit is nonuniformly organized, with adjacent points sometimes showing quite distinct error growth.The source of local predictability is linked to the local dynamics, which is related to the region in the phase space and the duration on the current regime.

Prediction and predictability of a catastrophic local extreme precipitation event through cloud-resolving ensemble analysis and forecasting with Doppler radar observations

Local extreme rain usually resulted in disasters such as flash floods and landslides. Upon today, it is still one of the most difficult tasks for operational weather forecast centers to predict those events accurately. In this paper, we simulate an extreme precipitation event with ensemble Kalman filter(En KF) assimilation of Doppler radial-velocity observations, and analyze the uncertainties of the assimilation. The results demonstrate that, without assimilation radar data, neither a single initialization of deterministic forecast nor an ensemble forecast with adding perturbations or multiple physical parameterizations can predict the location of strong precipitation. However, forecast was significantly improved with assimilation of radar data, especially the location of the precipitation. The direct cause of the improvement is the buildup of a deep mesoscale convection system with En KF assimilation of radar data. Under a large scale background favorable for mesoscale convection, efficient perturbations of upstream mid-low level meridional wind and moisture are key factors for the assimilation and forecast. Uncertainty still exists for the forecast of this case due to its limited predictability. Both the difference of large scale initial fields and the difference of analysis obtained from En KF assimilation due to small amplitude of initial perturbations could have critical influences to the event's prediction. Forecast could be improved through more cycles of En KF assimilation. Sensitivity tests also support that more accurate forecasts are expected through improving numerical models and observations.

Prediction of Maximum Section Flattening of Thin-walled Circular Steel Tube in Continuous Rotary Straightening Process

Cross-sectional ovalization of thin-walled circular steel tube because of large plastic bending,also known as the Brazier effect,usually occurs during the initial stage of tube′s continuous rotary straightening process.The amount of ovalization,defined as maximal cross section flattening,is an important technical parameter in tube′s straightening process to control tube′s bending deformation and prevent buckling.However,for the lack of special analytical model,the maximal section flattening was determined in accordance with the specified charts developed by experienced operators on the basis of experimental data;thus,it was inevitable that the localized buckling might occur during some actual straightening operations.New normal strain component formulas were derived based on the thin shell theory.Then,strain energy of thin-walled tube（per unit length）was obtained using the elastic-plastic theory.A rational model for predicting the maximal section flattening of the thin-walled circular steel tube under its straightening process was presented by the principle of minimum potential energy.The new model was validated by experiments and numerical simulations.The results show that the new model agrees well with the experiments and the numerical simulations with error of less than 10%.This new model was expected to find its potential application in thin-walled steel tube straightening machine design.

Accelerating the detection of unfeasible hypothetical zeolites via symmetric local interatomic distance criteria

In silico prediction of potential synthetic targets is the prerequisite for function-led discovery of new zeolites. Millions of hypothetical zeolitic structures have been predicted via various computational methods, but most of them are experimentally inaccessible under conventional synthetic conditions.Screening out unfeasible structures is crucial for the selection of synthetic targets with desired functions.The local interatomic distance（LID） criteria are a set of structure rules strictly obeyed by all existing zeolite framework types. Using these criteria, many unfeasible hypothetical structures have been detected. However, to calculate their LIDs, all hypothetical structures need to be fully optimized without symmetry constraints. When evaluating a large number of hypothetical structures, such calculations may become too computationally expensive due to the forbiddingly high degree of freedom. Here, we propose calculating LIDs among structures optimized with symmetry constraints and using them as new structure evaluation criteria, i.e., the LIDsymcriteria, to screen out unfeasible hypothetical structures. We find that the LIDsymcriteria can detect unfeasible structures as many as the original non-symmetric LID criteria do, yet require at least one order of magnitude less computation at the initial geometry optimization stage.

Dynamic single-index model for functional data

We propose a new functional single index model, which called dynamic single-index model for functional data, or DSIM, to efficiently perform non-linear and dynamic relationships between functional predictor and functional response. The proposed model naturally allows for some curvature not captured by the ordinary functional linear model. By using the proposed two-step estimating algorithm, we develop the estimates for both the link function and the regression coefficient function, and then provide predictions of new response trajectories. Besides the asymptotic properties for the estimates of the unknown functions, we also establish the consistency of the predictions of new response trajectories under mild conditions. Finally, we show through extensive simulation studies and a real data example that the proposed DSIM can highly outperform existed functional regression methods in most settings.