System- and Data-Driven Methods and Algorithms

An increasing complexity of models used to predict real-world systems leads to the need for algorithms to replace complex models with far simpler ones, while preserving the accuracy of the predictions. This two-volume handbook covers methods as well as applications. This first volume focuses on real-time control theory, data assimilation, real-time visualization, high-dimensional state spaces and interaction of different reduction techniques

Structure-Preserving Model Reduction of Physical Network Systems

This paper considers physical network systems where the energy storage is naturally associated to the nodes of the graph, while the edges of the graph correspond to static couplings. The first sections deal with the linear case, covering examples such as mass-damper and hydraulic systems, which have a structure that is similar to symmetric consensus dynamics. The last section is concerned with a specific class of nonlinear physical network systems; namely detailed-balanced chemical reaction networks governed by mass action kinetics. In both cases, linear and nonlinear, the structure of the dynamics is similar, and is based on a weighted Laplacian matrix, together with an energy function capturing the energy storage at the nodes. We discuss two methods for structure-preserving model reduction. The first one is clustering; aggregating the nodes of the underlying graph to obtain a reduced graph. The second approach is based on neglecting the energy storage at some of the nodes, and subsequently eliminating those nodes (called Kron reduction).</p

Benelux meeting on systems and control, 23rd, March 17-19, 2004, Helvoirt, The Netherlands

Book of abstract

OBSERVABILITY-BASED SAMPLING AND ESTIMATION OF FLOWFIELDS USING MULTI-SENSOR SYSTEMS

The long-term goal of this research is to optimize estimation of an unknown flowfield using an autonomous multi-vehicle or multi-sensor system. The specific research objective is to provide theoretically justified, nonlinear control, estimation, and optimization techniques enabling a group of sensors to coordinate their motion to target measurements that improve observability of the surrounding environment, even when the environment is unknown. Measures of observability provide an optimization metric for multi-agent control algorithms that avoid spatial regions of the domain prone to degraded or ill-conditioned estimation performance, thereby improving closed-loop control performance when estimated quantities are used in feedback control. The control, estimation, and optimization framework is applied to three applications of multi-agent flowfield sensing including (1) environmental sampling of strong flowfields using multiple autonomous unmanned vehicles, (2) wake sensing and observability-based optimal control for two-aircraft formation flight, and (3) bio-inspired flow sensing and control of an autonomous unmanned underwater vehicle. For environmental sampling, this dissertation presents an adaptive sampling algorithm steering a multi-vehicle system to sampling formations that improve flowfield observability while simultaneously estimating the flow for use in feedback control, even in strong flows where vehicle motion is hindered. The resulting closed-loop trajectories provide more informative measurements, improving estimation performance. For formation flight, this dissertation uses lifting-line theory to represent a two-aircraft formation and derives optimal control strategies steering the follower aircraft to a desired position relative to the leader while simultaneously optimizing the observability of the leader's relative position. The control algorithms guide the follower aircraft to a desired final position along trajectories that maintain adequate observability and avoid areas prone to estimator divergence. Toward bio-inspired flow sensing, this dissertation presents an observability-based sensor placement strategy optimizing measures of flowfield observability and derives dynamic output-feedback control algorithms autonomously steering an underwater vehicle to bio-inspired behavior using a multi-modal artificial lateral line. Beyond these applications, the broader impact of this research is a general framework for using observability to assess and optimize experimental design and nonlinear control and estimation performance

Efficient uncertainty propagation schemes for dynamical systems with stochastic finite element analysis.

Efficient uncertainty propagation schemes for dynamical systems are investigated here within the framework of stochastic finite element analysis. Uncertainty in the mathematical models arises from the incomplete knowledge or inherent variability of the various parametric and geometric properties of the physical system. These input uncertainties necessitate the use of stochastic mathematical models to accurately capture their behavior. The resolution of such stochastic models is computationally quite expensive. This work is concerned with development of model order reduction techniques for obtaining the dynamical response statistics of stochastic finite element systems. Efficient numerical methods have been proposed to propagate the input uncertainty of dynamical systems to the response variables. Response statistics of randomly parametrized structural dynamic systems have been investigated with a reduced spectral function approach. The frequency domain response and the transient evolution of the response of randomly parametrized structural dynamic systems have been studied with this approach. An efficient discrete representation of the input random field in a finite dimensional stochastic space is proposed here which has been integrated into the generic framework of the stochastic finite element weak formulation. This framework has been utilized to study the problem of random perturbation of the boundary surface of physical domains. Truncated reduced order representation of the complex mathematical quantities which are associated with the stochastic isoparametric mapping of the random domain to a deterministic master domain within the stochastic Galerkin framework have been provided. Lastly, an a-priori model reduction scheme for the resolution of the response statistics of stochastic dynamical systems has also been studied here which is based on the concept of balanced truncation. The performance and numerical accuracy of the methods proposed in this work have been exemplified with numerical simulations of stochastic dynamical systems and the convergence behavior of various error indicators

Spatio-Temporal Optimization for Control of Infinite Dimensional Systems in Robotics, Fluid Mechanics, and Quantum Mechanics

The majority of systems in nature have a spatio-temporal dependence and can be described by Partial Differential Equations (PDEs). They are ubiquitous in science and engineering, and are of rising interest among the control, robotics, and machine learning communities. Related methods usually treat these infinite dimensional problems in finite dimensions with reduced order models. This leads to committing to specific approximation schemes and the subsequent control laws cannot generalize outside of the approximation schemes. Additionally, related work does not consider spatio-temporal descriptions of noise that realistically represent the stochastic nature of physical systems. This thesis develops a variety of approaches for control optimization and co-design optimization for PDE and stochastic PDE (SPDE) systems from a unified perspective that can be applied to macroscopic systems in robotics and fluid dynamics, as well as microscopic systems in quantum mechanics. These approaches are each developed completely in the infinite dimensional Hilbert spaces where the systems are mathematically described, enabling the frameworks to be agnostic to the discretization scheme used to implement them. The first three developed approaches are applied in simulation to classical systems in fluid dynamics such as the Heat and Burgers equation. The fourth approach is developed for second-order SPDEs that arise in robotic systems, and is applied in simulation to systems in soft-robotics such as the Euler-Bernoulli equation and a biological model of a soft-robotic limb. Finally, several approaches are developed in the context of quantum feedback control of open quantum systems with non-demolition measurement, and one such approach is applied in simulation to perform explicit feedback control of the two qubit open quantum system.Ph.D

Damage localization in data-driven vibration-based structural health monitoring using linear quadratic estimation theory

Vibration-based Structural Health Monitoring (SHM) is classically approached from two different directions; both involve the acquisition and processing of vibration signals. The first and most popular strategy, which is also followed in the present thesis, relies entirely on the measurements. In contrast, the second approach employs physical models such as finite element (FE) models that are designed based on mechanical principles. In times in which the real-time processing of digital twins for engineering structures becomes more and more realistic, model-based approaches for vibration-based SHM receive increasing attention. Data-driven strategies are still primarily used in vibration-based SHM, and they will remain appealing in situations where precise physical modeling appears cumbersome. Hence, the need for efficient, robust, and reliable data-driven techniques concerning all stages and hurdles of SHM that can prove themselves in practice will never vanish. In this regard, after over 25 years of research, the number of real-life validation studies is still surprisingly low. As for all SHM strategies, the difficulty concerning damage analysis increases with higher levels of realization. Beginning with the goal of detecting damage, SHM finally seeks to predict the remaining lifetime of a structure. The intermediate steps comprise the localization, classification, and assessment of damage. Without the existence of adequately calibrated physics-based models, the successful implementation of methods tackling the objectives beyond damage localization in an unsupervised data-driven scheme is questionable. The term ‘unsupervised’ refers to the fact that knowledge about the manifestation of damage is not available. Especially in civil engineering, this situation pertains in general and is considered in the present thesis. In data-driven SHM, where the area of structural alterations is narrowed down to adjacent sensors, damage localization suffers from the coarse spatial resolution of parsimonious data acquisition systems. Classical modal approaches that hold potential for damage localization require a dense sensor network or significant damage. Originating from the field of fault detection and isolation, estimator- and filter-based methods have proven to be applicable for damage identification of mechanical and civil engineering structures. Notably, they feature an enormous sensitivity towards structural changes when properly designed. Although it remains advantageous for the sake of precise damage localization, these tools such as Kalman or H-infinity filters do not exhibit the inherent demand for a dense sensor network. Consequently, they promise to be viable techniques for the application in vibration-based SHM. A central challenge of this discipline is the discrimination between the natural variability of the structure’s dynamics and the one caused by damage. The former results from varying environmental and operational conditions (EOCs). Especially highly sensitive methods for damage identification are affected by these natural changes, and thus, rely on an efficient data normalization strategy, which can prove itself in practice. In light of these challenges, this thesis provides a real-life validation for the application of quadratic estimators in data-driven vibration-based SHM. To this end, an elaborate technique for estimator-based damage localization is adapted and included in an SHM framework comprising the necessary steps of data normalization and statistical testing. The damage analysis methodology was originally designed for H-infinity filters, which seem well-suited for use in SHM, as they do not assume specific properties of the excitation acting on the structure nor of the involved disturbances. However, previous studies have shown that, in some cases, the filter performance required to achieve high levels of sensitivity towards localized damage cannot be obtained. This issue can be circumvented by employing well-tuned Kalman filters. Therefore, a novel approach for noise covariance estimation is established at first. The associated estimation scheme constitutes a parametric extension of the popular autocovariance least-squares (ALS) technique. The effectiveness of this estimation technique in the context of Kalman filter-based damage localization is studied first using simulations and laboratory experiments. The second part is dedicated to the problem of handling EOCs. This body of work proposes an identification scheme for linear parameter-varying systems based on the interpolation of linear time-invariant systems for different operating points. A simulation study demonstrates the applicability for the purpose of data normalization. Finally, real-life validation of the proposed methods for SHM is conducted. Therefore, a steel lattice mast located outdoors functions as the test object. It is naturally affected by ambient sources of excitation, variability, and uncertainty. The mast, explicitly designed for this validation purpose, is equipped with reversible damage mechanisms that may be activated or removed to reduce the stiffness at multiple locations of the structure. The investigations conducted in this part of the thesis demonstrate proper damage detection of all considered damages as well as localization for the highest degree of severity. These promising results suggest the applicability of the presented methods for Kalman filter tuning, damage localization, and data-normalization in the context of vibration-based SHM