Optimal Measurement Methods for Distributed Parameter System Identification
Features
Summary
For dynamic distributed systems modeled by partial differential equations, existing methods of sensor location in parameter estimation experiments are either limited to one-dimensional spatial domains or require large investments in software systems. With the expense of scanning and moving sensors, optimal placement presents a critical problem.
Optimal Measurement Methods for Distributed Parameter System Identification discusses the characteristic features of the sensor placement problem, analyzes classical and recent approaches, and proposes a wide range of original solutions, culminating in the most comprehensive and timely treatment of the issue available. By presenting a step-by-step guide to theoretical aspects and to practical design methods, this book provides a sound understanding of sensor location techniques.
Both researchers and practitioners will find the case studies, the proposed algorithms, and the numerical examples to be invaluable. This text also offers results that translate easily to MATLAB and to Maple. Assuming only a basic familiarity with partial differential equations, vector spaces, and probability and statistics, and avoiding too many technicalities, this is a superb resource for researchers and practitioners in the fields of applied mathematics, electrical, civil, geotechnical, mechanical, chemical, and environmental engineering.
Table of Contents
INTRODUCTION
The Optimum Experimental Design Problem in Context
A General Overview of Literature
KEY IDEAS OF IDENTIFICATION AND EXPERIMENTAL DESIGN
System Description
Parameter Identification
Measurement Location Problem
Main Impediments
Deterministic Interpretation of the FIM
Calculation of Sensitivity Coefficients
A Final Introductory Note
LOCALLY OPTIMAL DESIGNS FOR STATIONARY SENSORS
Linear-in-Parameters Lumped Models
Construction of Minimax Designs
Continuous Designs in Measurement Optimization
Clusterization-Free Designs
Nonlinear Programming Approach
A Critical Note on Some Deterministic Approach
Modifications Required by Other Settings
Summary
LOCALLY OPTIMAL STRATEGIES FOR SCANNING AND MOVING OBSERVATIONS
Optimal Activation Policies for Scanning Sensors
Adapting the Idea of Continuous Designs for Moving Sensors
Optimization of Sensor Trajectories Based on Optimal-Control Techniques
Concluding Remarks
MEASUREMENT STRATEGIES WITH ALTERNATIVE DESIGN OBJECTIVES
Optimal Sensor Location for Prediction
Sensor Location for Model Discrimination
Conclusions
ROBUST DESIGNS FOR SENSOR LOCATION
Sequential Designs
Optimal Designs in the Average Sense
Optimal Designs in the Minimax Sense
Robust Sensor Location Using Randomized Algorithms
Concluding Remarks
TOWARDS EVEN MORE CHALLENGING PROBLEMS
Measurement Strategies in the Presence of Correlated Observations
Maximization of an Observability Measure
Summary
APPLICATIONS FROM ENGINEERING
Electrolytic Reactor
Calibration of Smog Prediction Models
Monitoring of Groundwater Resources Quality
Diffusion Process With Correlated Observational Errors
Vibrating H-Shaped Membrane
CONCLUSIONS AND FUTURE RESEARCH DIRECTIONS
APPENDICES
List of Symbols
Mathematical Background
On Statistical Properties of Estimators
Analysis of the Largest Eigenvalue
Differentiation of Nonlinear Operators
Accessory Results for PDE's
Interpolation of Tabulated Sensitivity Coefficients
Differentials of Section 4.3.3
Solving Sensor Location Problems Using Maple and MATLAB
