Karlsruhe Series on Intelligent Sensor - Actuator - Systems

This work was performed within the DFG Research Training Group 1194 “Self-organizing Sensor-Actuator Networks” in the subproject I1 “Decentralized Reconstruction of Continuous Phenomena based on Space-Time Discrete Measurements”. One of the main applications for sensor networks is the observation, monitoring, and exploration of space-time continuous physical phenomena, such as temperature distributions or biochemical concentrations. In practical implementations, the individual miniaturized sensor nodes are widely deployed either inside the phenomenon or very close to it, and are gathering measurements. The main goal of this research work is the reconstruction and identification of the complete continuous phenomena using space-time discrete measurements. For the exploration by a sensor network, a trade-off between accuracy and cost needs to be found, where the number of used sensor nodes and their respective measurement rate can be regarded as deciding measures. The framework developed in this work is characterized by the rigorous exploitation of physical background knowledge in terms of a system model. This approach leads to more accurate interpolation results with justifiable measurement costs. The uncertainties inherently arising during the modelling process and existing in the measurements are systematically considered in an integrated fashion. This research work is devoted to the development of probabilistic model-based interpolation techniques for the reconstruction of space-time continuous phenomena using discrete measurements. In general, space-time continuous phenomena, which are also called distributed-parameter systems, can be modelled by stochastic partial differential equations that describe not only the dynamic, but in particular the distributed properties. The derivation of reconstruction techniques that is directly based on such system description is a challenging task. For that reason, the model description including its uncertainty representation is converted into a corresponding lumped-parameter system. Based on this system description, an appropriate Bayesian estimator can be derived. Thanks to the probabilistic and model-based approach, the space-time continuous state vector describing the system in the entire area of interest can be reconstructed in a systematic and physically correct fashion. Due to the fact that the system is reconstructed even at non-measurement points, a lower number of sensor nodes is required for a given reconstruction accuracy. The results of the reconstruction can be used for several additional tasks concerning the observation of physical phenomena. For example, optimal placements and measurement time sequences for the individual measuring nodes can be derived. In many cases, the underlying true physical phenomenon deviates from the nominal mathematical model, basically caused by neglecting particular physical effects or external disturbances. Hence, one of the main challenges for a model-based approach is that parameters of both the physical phenomenon being observed and the spatially distributed measurement system are usually imprecisely known or can be identified only with complex and expensive methods. In addition, these model parameters usually need to be regarded as varying over space and time. This research work is devoted to the development of efficient methods not only for reconstructing the space-time continuous system state, but also for identifying specific model parameters.