Pub. Date:
Springer Berlin Heidelberg
Adaptive Modelling, Estimation and Fusion from Data: A Neurofuzzy Approach / Edition 1

Adaptive Modelling, Estimation and Fusion from Data: A Neurofuzzy Approach / Edition 1

by Chris Harris, Xia Hong, Qiang Gan


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This book brings together for the first time the complete theory of data based neurofuzzy modelling and the linguistic attributes of fuzzy logic in a single cohesive mathematical framework. After introducing the basic theory of data based modelling new concepts including extended additive and multiplicative submodels are developed. All of these algorithms are illustrated with benchmark examples to demonstrate their efficiency. The book aims at researchers and advanced professionals in time series modelling, empirical data modelling, knowledge discovery, data mining and data fusion.

Product Details

ISBN-13: 9783540426868
Publisher: Springer Berlin Heidelberg
Publication date: 06/20/2002
Series: Advanced Information Processing
Edition description: 2002
Pages: 323
Product dimensions: 6.10(w) x 9.25(h) x (d)

Table of Contents

1. An introduction to modelling and learning algorithms.- 1.1 Introduction to modelling.- 1.2 Modelling, control and learning algorithms.- 1.3 The learning problem.- 1.4 Book philosophy and contents overview.- 1.4.1 Book overview.- 1.4.2 A historical perspective of adaptive modelling and control.- 2. Basic concepts of data-based modelling.- 2.1 Introduction.- 2.2 State-space models versus input-output models.- 2.2.1 Conversion of state-space models to input-output models.- 2.2.2 Conversion of input-output models to state-space models.- 2.3 Nonlinear modelling by basis function expansion.- 2.4 Model parameter estimation.- 2.5 Model quality.- 2.5.1 The bias-variance dilemma.- 2.5.2 Bias-variance balance by model structure regularisation.- 2.6 Reproducing kernels and regularisation networks.- 2.7 Model selection methods.- 2.7.1 Model selection criteria.- 2.7.2 Model selection criteria sensitivity.- 2.7.3 Correlation tests.- 2.8 An example: time series modelling.- 3. Learning laws for linear-in-the-parameters networks.- 3.1 Introduction to learning.- 3.2 Error or performance surfaces.- 3.3 Batch learning laws.- 3.3.1 General learning laws.- 3.3.2 Gradient descent algorithms.- 3.4 Instantaneous learning laws.- 3.4.1 Least mean squares learning.- 3.4.2 Normalised least mean squares learning.- 3.4.3 NLMS weight convergence.- 3.4.4 Recursive least squares estimation.- 3.5 Gradient noise and normalised condition numbers.- 3.6 Adaptive learning rates.- 4. Fuzzy and neurofuzzy modelling.- 4.1 Introduction to fuzzy and neurofuzzy systems.- 4.2 Fuzzy systems.- 4.2.1 Fuzzy sets.- 4.2.2 Fuzzy operators.- 4.2.3 Fuzzy relation surfaces.- 4.2.4 Inferencing.- 4.2.5 Fuzzification and defuzzification.- 4.3 Functional mapping and neurofuzzy models.- 4.4 Takagi-Sugeno local neurofuzzy model.- 4.5 Neurofuzzy modelling examples.- 4.5.1 Thermistor modelling.- 4.5.2 Time series modelling.- 5. Parsimonious neurofuzzy modelling.- 5.1 Iterative construction modelling.- 5.2 Additive neurofuzzy modelling algorithms.- 5.3 Adaptive spline modelling algorithm (ASMOD).- 5.3.1 ASMOD refinements.- 5.3.2 Illustrative examples of.- 5.4 Extended additive neurofuzzy models.- 5.4.1 Weight identification.- 5.4.2 Extended additive model structure identification.- 5.5 Hierarchical neurofuzzy models.- 5.6 Regularised neurofuzzy models.- 5.6.1 Bayesian regularisation.- 5.6.2 Error bars.- 5.6.3 Priors for neurofuzzy models.- 5.6.4 Local regularised neurofuzzy models.- 5.7 Complexity reduction through orthogonal least squares.- 5.8 A-optimality neurofuzzy model construction (NeuDec).- 6. Local neurofuzzy modelling.- 6.1 Introduction.- 6.2 Local orthogonal partitioning algorithms.- 6.2.1 k-d Trees.- 6.2.2 Quad-trees.- 6.3 Operating point dependent neurofuzzy models.- 6.4 State space representations of operating point dependent neurofuzzy models.- 6.5 Mixture of experts modelling.- 6.6 Multi-input-Multi-output (MIMO) modelling via input variable selection.- 6.6.1 MIMO NARX neurofuzzy model decomposition.- 6.6.2 Feedforward Gram-Schmidt OLS procedure for linear systems.- 6.6.3 Input variable selection via the modified Gram-Schmidt OLS for piecewise linear submodels.- 7. Delaunay input space partitioning modelling.- 7.1 Introduction.- 7.2 Delaunay triangulation of the input space.- 7.3 Delaunay input space partitioning for locally linear models.- 7.4 The Bézier-Bernstein modelling network.- 7.4.1 Neurofuzzy modelling using Bézier-Bernstein function for univariate term fi(xi) and bivariate term fi1, j1(xi1, xj1).- 7.4.2 The complete Bézier-Bernstein model construction algorithm.- 7.4.3 Numerical examples.- 8. Neurofuzzy linearisation modelling for nonlinear state estimation.- 8.1 Introduction to linearisation modelling.- 8.2 Neurofuzzy local linearisation and the MASMOD algorithm.- 8.3 A hybrid learning scheme combining MASMOD and EM algorithms for neurofuzzy local linearisation.- 8.4 Neurofuzzy feedback linearisation (NFFL).- 8.5 Formulation of neurofuzzy state estimators.- 8.6 An example of nonlinear trajectory estimation.- 9. Multisensor data fusion using Kaiman filters based on neurofuzzy linearisation.- 9.1 Introduction.- 9.2 Measurement fusion.- 9.2.1 Outputs augmented fusion (OAF).- 9.2.2 Optimal weighting measurement fusion (OWMF).- 9.2.3 On functional equivalence of OAF and.- 9.2.4 On the decentralised architecture.- 9.3 State-vector fusion.- 9.3.1 State-vector assimilation fusion (SVAF).- 9.3.2 Track-to-track fusion (TTF).- 9.3.3 On the decentralised architecture.- 9.4 Hierarchical multisensor data fusion — trade-off between centralised and decentralised Architectures.- 9.5 Simulation examples.- 9.5.1 On functional equivalence of two measurement fusion methods.- 9.5.2 On hierarchical multisensor data fusion.- 10. Support vector neurofuzzy models.- 10.1 Introduction.- 10.2 Support vector machines.- 10.2.1 Loss functions.- 10.2.2 Feature space and kernel functions.- 10.3 Support vector regression.- 10.4 Support vector neurofuzzy networks.- 10.5 SUPANOVA.- 10.6 A comparison among neural network models.- 10.7 Conclusions.- References.

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