Nonparametric Statistical Modeling of Spatiotemporal Dynamics Based on recorded Data

Experimental analysis of spatially extended processes is based on measured data of characteristic dynamic variables in space and time. The basic aim of the analysis is to extract a field evolution law from data thus recorded. We present a nonparametric statistical modeling of field evolution, following a state space reconstruction technique. For this purpose a novel state reconstruction is proposed that properly describes chaotic field evolution on short- as well as statistically on long-term basis. From the reconstructed state vectors, deterministic and random parts of field evolution are then approximated by employing a conditional average estimator. The performance of such statistical modeling is demonstrated by predicting simulated stochastic fields, and experimental fields generated by cutting and welding manufacturing processes. The results presented indicate that the proposed method of modeling can be successfully utilized for experimental characterization of different stochastic processes.

[1]  Jaroslav Stark,et al.  Reconstruction and cross-prediction in coupled map lattices using spatio-temporal embedding techniques , 1998 .

[2]  David M. Rubin,et al.  Use of forecasting signatures to help distinguish periodicity, randomness, and chaos in ripples and other spatial patterns. , 1992, Chaos.

[3]  P. Collet,et al.  The Definition and Measurement of the Topological Entropy per Unit Volume in Parabolic PDE's , 1998 .

[4]  Igor Grabec,et al.  Synergetics of Measurement, Prediction and Control , 1997 .

[5]  Igor Grabec,et al.  Continuation of Chaotic Fields by RBFNN , 1997, IWANN.

[6]  H. Kantz,et al.  Nonlinear time series analysis , 1997 .

[7]  Igor Grabec,et al.  Experimental Modeling of Chaotic Fields , 2003 .

[8]  Holger Kantz,et al.  FITTING PARTIAL DIFFERENTIAL EQUATIONS TO SPACE-TIME DYNAMICS , 1999 .

[9]  David J. Whitehouse,et al.  Handbook of Surface Metrology , 2023 .

[10]  Martin Casdagli,et al.  Nonlinear Modeling And Forecasting , 1992 .

[11]  Jianqing Fan.  Nonlinear Time Series , 2003 .

[12]  Fraser,et al.  Independent coordinates for strange attractors from mutual information. , 1986, Physical review. A, General physics.

[13]  E. Lorenz.  Deterministic nonperiodic flow , 1963 .

[14]  M. Cross,et al.  Pattern formation outside of equilibrium , 1993 .

[15]  Marco Paniconi,et al.  STATIONARY, DYNAMICAL, AND CHAOTIC STATES OF THE TWO-DIMENSIONAL DAMPED KURAMOTO-SIVASHINSKY EQUATION , 1997 .

[16]  E. Govekar,et al.  TIME SERIES ANALYSIS IN METAL CUTTING : CHATTER VERSUS CHATTER-FREE CUTTING , 1998 .

[17]  L. Tsimring,et al.  The analysis of observed chaotic data in physical systems , 1993 .

[18]  Igor Grabec,et al.  Statistical Approach to Modeling of Spatiotemporal Dynamics , 2001, Int. J. Bifurc. Chaos.

[19]  R. Friedrich,et al.  Analysis of data sets of stochastic systems , 1998 .

[20]  A. Vulpiani,et al.  Predictability: a way to characterize complexity , 2001, nlin/0101029.

[21]  M. J. Bunner,et al.  Identification of continuous, spatiotemporal systems. , 1998 .

[22]  Parlitz,et al.  Prediction of spatiotemporal time series based on reconstructed local states , 2000, Physical review letters.

[23]  Carlo Novara,et al.  Nonlinear Time Series , 2003 .

[24]  J. Kurths,et al.  Amplitude equations from spatiotemporal binary-fluid convection data , 1999 .

[25]  Schreiber,et al.  Noise reduction in chaotic time-series data: A survey of common methods. , 1993, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics.

[26]  Olbrich,et al.  Local estimates for entropy densities in coupled map lattices , 2000, Physical review letters.

[27]  Ulrich Parlitz,et al.  Experimental Nonlinear Physics , 1997 .