Mini-Workshop: Entropy, Information and Control

This mini-workshop was motivated by the emerging field of networked control, which combines concepts from the disciplines of control theory, information theory and dynamical systems. Many current approaches to networked control simplify one or more of these three aspects, for instance by assuming no dynamical disturbances, or noiseless communication channels, or linear dynamics. The aim of this meeting was to approach a common understanding of the relevant results and techniques from each discipline in order to study the major, multi-disciplinary problems in networked control

Self-Evaluation Applied Mathematics 2003-2008 University of Twente

This report contains the self-study for the research assessment of the Department of Applied Mathematics (AM) of the Faculty of Electrical Engineering, Mathematics and Computer Science (EEMCS) at the University of Twente (UT). The report provides the information for the Research Assessment Committee for Applied Mathematics, dealing with mathematical sciences at the three universities of technology in the Netherlands. It describes the state of affairs pertaining to the period 1 January 2003 to 31 December 2008

Directed Data-Processing Inequalities for Systems with Feedback

We present novel data-processing inequalities relating the mutual information and the directed information in systems with feedback. The internal blocks within such systems are restricted only to be causal mappings, but are allowed to be non-linear, stochastic and time varying. These blocks can for example represent source encoders, decoders or even communication channels. Moreover, the involved signals can be arbitrarily distributed. Our first main result relates mutual and directed informations and can be interpreted as a law of conservation of information flow. Our second main result is a pair of data-processing inequalities (one the conditional version of the other) between nested pairs of random sequences entirely within the closed loop. Our third main result is introducing and characterizing the notion of in-the-loop (ITL) transmission rate for channel coding scenarios in which the messages are internal to the loop. Interestingly, in this case the conventional notions of transmission rate associated with the entropy of the messages and of channel capacity based on maximizing the mutual information between the messages and the output turn out to be inadequate. Instead, as we show, the ITL transmission rate is the unique notion of rate for which a channel code attains zero error probability if and only if such ITL rate does not exceed the corresponding directed information rate from messages to decoded messages. We apply our data-processing inequalities to show that the supremum of achievable (in the usual channel coding sense) ITL transmission rates is upper bounded by the supremum of the directed information rate across the communication channel. Moreover, we present an example in which this upper bound is attained. Finally, ...Comment: Submitted to Entropy. arXiv admin note: substantial text overlap with arXiv:1301.642

Hybrid structural health monitoring using data-driven modal analysis and model-based Bayesian inference.

Civil infrastructures that are valuable assets for the public and owners must be adequately and periodically maintained to guarantee safety, continuous service, and avoid economic losses. Vibration-based structural health monitoring (VBSHM) has been a significant tool to assess the structural performance of civil infrastructures over the last decades. Challenges in VBSHM exist in two aspects: operational modal analysis (OMA) and Finite element model updating (FEMU). The former aims to extract natural frequency, damping ratio, and mode shapes using vibrational data under normal operation; the latter focuses on minimizing the discrepancies between measurements and model prediction. The main impediments to real-world application of VBSHM include 1) uncertainties are inevitably involved due to measurement noise and modeling error; 2) computational burden in analyzing massive data and high-fidelity model; 3) updating structural coupled parameters, e.g., mass and stiffness. Bayesian model updating approach (BMUA) is an advanced FEMU technique to update structural parameters using modal data and account for underlying uncertainties. However, traditional BMUA generally assumes mass is precisely known and only updating stiffness to circumvent the coupling effect of mass and stiffness. Simultaneously updating mass and stiffness is necessary to fully understand the structural integrity, especially when the mass has a relatively large variation. To tackle these challenges, this dissertation proposed a hybrid framework using data-driven and model-based approaches in two sequential phases: automated OMA and a BMUA with added mass/stiffness. Automated stochastic subspace identification (SSI) and Bayesian modal identification are firstly developed to acquire modal properties. Following by a novel BMUA, new eigen-equations based on two sets of modal data from the original and modified system with added mass or stiffness are derived to address the coupling effect of structural parameters, e.g., mass and stiffness. To avoid multi-dimensional integrals, an asymptotic optimization method and Differential Evolutionary Adaptive Metropolis (DREAM) sampling algorithm are employed for Bayesian inference. To alleviate computational burden, variance-based global sensitivity analysis to reduce model dimensionality and Kriging model to substitute time-consuming FEM are integrated into BMUA. The proposed VBSHM are verified and illustrated using numerical, laboratory and field test data, achieving following goals: 1) properly treating parameter uncertainties; 2) substantially reducing the computational cost; 3) simultaneously updating structural parameters with addressing the coupling effect; 4) performing the probabilistic damage identification at an accurate level