A robust model structure selection method for small sample size and multiple datasets problems

Abstract In model identification, the existence of uncertainty normally generates negative impact on the accuracy and performance of the identified models, especially when the size of data used is rather small. With a small data set, least squares estimates are biased, the resulting models may not be reliable for further analysis and future use. This study introduces a novel robust model structure selection method for model identification. The proposed method can successfully reduce the model structure uncertainty and therefore improve the model performances. Case studies on simulation data and real data are presented to illustrate how the proposed metric works for robust model identification.

[1]  Peter Xiaoping Liu,et al.  Adaptive Neural Control of Nonlinear Systems With Unknown Control Directions and Input Dead-Zone , 2018, IEEE Transactions on Systems, Man, and Cybernetics: Systems.

[2]  Stephen A. Billings,et al.  Model structure selection using an integrated forward orthogonal search algorithm assisted by squared correlation and mutual information , 2008, Int. J. Model. Identif. Control..

[3]  S. A. Billings,et al.  Using the NARMAX OLS-ERR algorithm to obtain the most influential coupling functions that affect the evolution of the magnetosphere , 2011 .

[4]  G. Maire,et al.  Sensitivity and uncertainty analysis of the carbon and water fluxes at the tree scale in Eucalyptus plantations using a metamodeling approach , 2016 .

[5]  N. Robinson,et al.  Identification and interpretation of sources of uncertainty in soils change in a global systems-based modelling process , 2015 .

[6]  Stephen A. Billings,et al.  Generalized Cellular Neural Networks (Gcnns) Constructed Using Particle Swarm Optimization for Spatio-Temporal Evolutionary Pattern Identification , 2008, Int. J. Bifurc. Chaos.

[7]  David G. Sibeck,et al.  Kp forecast models , 2005 .

[8]  Peter Xiaoping Liu,et al.  Adaptive fuzzy decentralized control for a class of interconnected nonlinear system with unmodeled dynamics and dead zones , 2016, Neurocomputing.

[9]  Miroslav Kubat,et al.  Neural networks: a comprehensive foundation by Simon Haykin, Macmillan, 1994, ISBN 0-02-352781-7. , 1999, The Knowledge Engineering Review.

[10]  Hua-Liang Wei,et al.  Analysis of the relationship between lifestyle and life satisfaction using transparent and nonlinear parametric models , 2016, 2016 22nd International Conference on Automation and Computing (ICAC).

[11]  Weiguo Xia,et al.  Adaptive Fuzzy Hierarchical Sliding-Mode Control for a Class of MIMO Nonlinear Time-Delay Systems With Input Saturation , 2017, IEEE Transactions on Fuzzy Systems.

[12]  Simon Haykin,et al.  Neural Networks: A Comprehensive Foundation , 1998 .

[13]  Steve A. Billings,et al.  A unified wavelet-based modelling framework for non-linear system identification: the WANARX model structure , 2004 .

[14]  Peter Norvig,et al.  Artificial Intelligence: A Modern Approach , 1995 .

[15]  Stephen A. Billings,et al.  Improved parameter estimates for non-linear dynamical models using a bootstrap method , 2009, Int. J. Control.

[16]  C G Billings,et al.  The prediction of in-flight hypoxaemia using non-linear equations. , 2013, Respiratory medicine.

[17]  S. A. Billings,et al.  A century of variation in the dependence of Greenland iceberg calving on ice sheet surface mass balance and regional climate change , 2014, Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences.

[18]  Lotfi A. Zadeh,et al.  Fuzzy Sets , 1996, Inf. Control..

[19]  Xiaodong Liu,et al.  Multivariate time series prediction using a hybridization of VARMA models and Bayesian networks , 2016 .

[20]  Stephen A. Billings,et al.  Non-linear system identification using neural networks , 1990 .

[21]  S. A. Billings,et al.  The wavelet-NARMAX representation: A hybrid model structure combining polynomial models with multiresolution wavelet decompositions , 2005, Int. J. Syst. Sci..

[22]  Stephen A. Billings,et al.  A new class of wavelet networks for nonlinear system identification , 2005, IEEE Transactions on Neural Networks.

[23]  S. A. Billings,et al.  Using the NARMAX approach to model the evolution of energetic electrons fluxes at geostationary orbit , 2011 .

[24]  Stephen A. Billings,et al.  Improved model identification for non-linear systems using a random subsampling and multifold modelling (RSMM) approach , 2009, Int. J. Control.

[25]  Francisco Herrera,et al.  A Historical Account of Types of Fuzzy Sets and Their Relationships , 2016, IEEE Transactions on Fuzzy Systems.

[26]  Sheng Chen,et al.  Representations of non-linear systems: the NARMAX model , 1989 .

[27]  Shen Yin,et al.  Adaptive Fuzzy Control of Strict-Feedback Nonlinear Time-Delay Systems With Unmodeled Dynamics , 2016, IEEE Transactions on Cybernetics.

[28]  Qinghua Zhang,et al.  Wavelet networks , 1992, IEEE Trans. Neural Networks.

[29]  Sheng Chen,et al.  Orthogonal least squares methods and their application to non-linear system identification , 1989 .

[30]  Stephen A. Billings,et al.  International Journal of Control , 2004 .

[31]  T. Chai,et al.  Root mean square error (RMSE) or mean absolute error (MAE)? – Arguments against avoiding RMSE in the literature , 2014 .

[32]  S. A. Billings,et al.  Forecasting relativistic electron flux using dynamic multiple regression models , 2010 .

[33]  Steve A. Billings,et al.  Term and variable selection for non-linear system identification , 2004 .

[34]  Stephen A. Billings,et al.  A novel logistic-NARX model as a classifier for dynamic binary classification , 2017, Neural Computing and Applications.

[35]  Stephen A. Billings,et al.  An adaptive orthogonal search algorithm for model subset selection and non-linear system identification , 2008, Int. J. Control.

[36]  Julia L. Blanchard,et al.  Quantifying heterogeneous responses of fish community size structure using novel combined statistical techniques , 2016, Global change biology.

[37]  Stephen A. Billings,et al.  Identification of nonlinear time-varying systems using an online sliding-window and common model structure selection (CMSS) approach with applications to EEG , 2016, Int. J. Syst. Sci..