Optimal Measurement Methods for Distributed Parameter System Identification

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.

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