Synergetics of Measurement, Prediction and Control

ISBN-13: 9783642643590 / Angielski / Miękka / 2011 / 458 str.

Igor Grabec;Wolfgang Sachse

Opis

In this monograph, a statistical description of natural phenomena is used to develop an information processing system capable of modeling non-linear relationships between sensory data. The system, based on self-organized, optimal preservation of empirical information, applies these relationships for prediction and adaptive control.
This monograph is written for students, scientists and engineers in academia and industry who are interested in experimental work related to the adaptive modeling of natural laws, the development of sensory-neural networks, intelligent control, synergetics and informatics. No specific knowledge of advanced mathematics is presupposed. Examples taken from physics, engineering, medicine and economics demonstrate the applicability of such intelligent systems.

Spis treści

1. Introduction.- 1.1 Goal.- 1.2 Relation to Other Scientific Fields.- 1.3 Plan of the Monograph.- 2. A Quantitative Description of Nature.- 2.1 Synergetics of Natural Phenomena.- 2.2 A Description of Nature.- 2.3 Fundamentals of Quantitative Description.- 2.4 Fundamentals of Physical Laws.- 2.5 The Random Character of Physical Variables.- 2.6 Expression of Natural Laws by Differential Equations.- 2.7 Methods of Empirical Modeling.- 2.7.1 The Role of Models.- 2.7.2 Piecewise Linear Models of Empirical Natural Laws.- 2.8 Introduction to Modeling by Neural Networks.- 2.8.1 Functional Properties of a Neuron.- 2.8.2 Empirical Modeling by a Perceptron.- 3. Transducers.- 3.1 The Role of Sensors and Actuators.- 3.2 Sensors and Actuators of Biological Systems.- 3.2.1 Performance Characteristics of Biological Sensors.- 3.2.2 Structure of Biological Sensors.- 3.2.3 Transduction Characteristics of Biological Sensors.- 3.3 Operational Characteristics of Transducers.- 3.3.1 Transducer Classification.- 3.3.2 Transduction Characteristics.- 3.3.3 Sensor Loading Effects.- 3.3.4 Transducer Field Characteristics.- 3.4 Fabricated Transducers.- 3.4.1 Microsensors and Integrated Sensors.- 3.4.2 Synthetic Bio-sensors and Neurobiology.- 3.5 Transducers in Intelligent Measurement Systems.- 3.6 Future Directions in Transducer Evolution.- 4. Probability Densities.- 4.1 Estimation of Probability Density.- 4.1.1 Parzen Window Approach.- 4.1.2 An Optimal Selection of the Window Function.- 4.1.3 Nearest Neighbor and Maximal Self-Consistency Approach.- 4.1.4 The Self-Consistent Method in the Multivariate Case..- 4.1.5 Numerical Examples.- 4.1.6 Conclusions About Filtering of the Empirical PDF.- 5. Information.- 5.1 Some Basic Ideas.- 5.2 Entropy of Information.- 5.3 Properties of Information Entropy.- 5.4 Relative Information.- 5.4.1 Information of Continuous Distributions.- 5.4.2 Information Gain from Experiments.- 5.5 Information Measure of Distance Between Distributions.- 6. Maximum Entropy Principles.- 6.1 Gibbs Maximum Entropy Principle.- 6.2 The Absolute Maximum Entropy Principle.- 6.3 Quantization of Continuous Probability Distributions.- 6.3.1 Quadratic Measure of Discrepancy Between Distributions.- 6.3.2 Information Divergence as a Measure of Discrepancy.- 6.3.3 Vector Quantization and Reconstruction Measure of Discrepancy.- 7. Adaptive Modeling of Natural Laws.- 7.1 Probabilistic Modeler of Natural Laws.- 7.2 Optimization of Adaptive Modeler Performance.- 7.3 Stochastic Approach to Adaptation Laws.- 7.4 Stochastic Adaptation of a Vector Quantizer.- 7.5 Perturbation Method of Adaptation.- 7.6 Evolution of an Optimal Modeler and Perturbation Method.- 7.7 Parametric Versus Non-Parametric Modeling.- 8. Self-Organization and Formal Neurons.- 8.1 Optimal Storage of Empirical Information in Discrete Systems.- 8.2 Adaptive Vector Quantization and Topological Mappings.- 8.3 Self-Organization Based on the Absolute Maximum-Entropy Principle.- 8.4 Derivation of a Generalized Self-Organization Rule.- 8.5 Numerical Examples of Self-Organized Adaptation.- 8.6 Formal Neurons and the Self-Organization Process.- 9. Modeling by Non-Parametric Regression.- 9.1 The Problem of an Optimal Prediction.- 9.2 Parzen’s Window Approach to General Regression.- 9.3 General Regression Modeler, Feedback and Recognition.- 9.4 Application of the General Regression Modeler.- 9.4.1 Empirical Modeling of Acoustic Phenomena.- 9.4.2 Prediction of the Seismic Capacity of Walls.- 9.4.3 Modeling of a Periodontal Disease Healing Process.- 10. Linear Modeling and Invariances.- 10.1 Relation Between Parametric Modeling and Invariances.- 10.2 Generalized Linear Regression Model.- 10.2.1 An Example of Iterative Determination of a Linear Regression Model.- 10.3 Sequential Adaptation of Linear Regression Model.- 10.4 Transition from the Cross- to Auto-Associator.- 10.4.1 Application of the Auto-Associator to Analysis of Ultrasonic Signals.- 11. Modeling and Forecasting of Chaotic Processes.- 11.1 Modeling of Chaotic Processes.- 11.2 Examples of Chaotic Process Forecasting.- 11.3 Forecasting of Chaotic Acoustic Emission Signals.- 11.4 Empirical Modeling of Non-Autonomous Chaotic Systems.- 11.4.1 Example of Economic Time-Series Forecasting.- 11.5 Cascade Modeling of Chaos Generators.- 11.5.1 Numerical Experiments.- 11.5.2 Concluding Remarks.- 12. Modeling by Neural Networks.- 12.1 From Biological to Artificial Neural Networks.- 12.1.1 Basic Blocks of Neural Networks and Their Dynamics.- 12.2 A Linear Associator.- 12.3 Multi-layer Perceptrons and Back-Propagation Learning.- 12.4 Radial Basis Function Neural Networks.- 12.5 Equivalence of a Radial Basis Function NN and Perceptrons.- 13. Fundamentals of Intelligent Control.- 13.1 Introduction.- 13.2 Basic Tasks of Intelligent Control.- 13.2.1 Empirical Description of a Controlled System.- 13.2.2 General Identification by Non-Parametric Modeling.- 13.3 The Tracking Problem.- 13.4 Cloning.- 13.5 An Empirical Approach to Optimal Control.- 13.5.1 The Theoretical Problem of Optimal Control.- 13.5.2 Experimental Description of Plant Performance and Optimal Control.- 13.5.3 Design of an Intelligent Optimal Controller.- 13.5.4 The Influence of the Environment on Optimal Control.- 13.5.5 The Problem of Phase Space Exploration.- 13.5.6 Numerical Simulations of Optimal Control.- 13.5.7 Summary and Conclusions.- 14. Self-Control and Biological Evolution.- 14.1 Modeling of Natural Phenomena by Biological Systems.- 14.2 Joint Modeling of Organism and Environment.- 14.3 An Operational Description of Consciousness.- 14.4 The Fundamental Problem of Evolution.- A. Fundamentals of Probability and Statistics.- A.1 Sample Points, Sample Space, Events and Relations.- A.2 Probability.- A.3 Random Variables and Probability Distributions.- A.4 Averages and Moments.- A.5 Random Processes.- A.6 Sampling, Estimation and Statistics.- B. Fundamentals of Deterministic Chaos.- B.1 Instability of Chaotic Systems.- B.2 Characterization of Strange Attractors.- B.3 Experimental Characterization of Chaotic Phenomena.- References.

Blurb

The electronic processing of information permits the construction of intelligent systems capable of carrying out a synergy of autonomous measurement, the modeling of natural laws, the control of processes, and the prediction or forecasting of a large variety of natural phenomena. In this monograph, a statistical description of natural phenomena is used to develop an information processing system capable of modeling non-linear relationships between sensory data. The system, based on self-organized, optimal preservation of empirical information, applies these relationships for prediction and adaptive control.
This monograph is written for students, scientists and engineers in academia and industry who are interested in experimental work related to the adaptive modeling of natural laws, the development of sensory-neural networks, intelligent control, synergetics and informatics. No specific knowledge of advanced mathematics is presupposed. Examples taken from physics, engineering, medicine and economics demonstrate the applicability of such intelligent systems.