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

Advances in geometrical parametrization and reduced order models and methods for computational fluid dynamics problems in applied sciences and engineering: Overview and perspectives

Several problems in applied sciences and engineering require reduction techniques in order to allow computational tools to be employed in the daily practice, especially in iterative procedures such as optimization or sensitivity analysis. Reduced order methods need to face increasingly complex problems in computational mechanics, especially into a multiphysics setting. Several issues should be faced: stability of the approximation, efficient treatment of nonlinearities, uniqueness or possible bifurcations of the state solutions, proper coupling between fields, as well as offline-online computing, computational savings and certification of errors as measure of accuracy. Moreover, efficient geometrical parametrization techniques should be devised to efficiently face shape optimization problems, as well as shape reconstruction and shape assimilation problems. A related aspect deals with the management of parametrized interfaces in multiphysics problems, such as fluid-structure interaction problems, and also a domain decomposition based approach for complex parametrized networks. We present some illustrative industrial and biomedical problems as examples of recent advances on methodological developments

Automating the Reconstruction of Neuron Morphological Models: the Rivulet Algorithm Suite

The automatic reconstruction of single neuron cells is essential to enable large-scale data-driven investigations in computational neuroscience. The problem remains an open challenge due to various imaging artefacts that are caused by the fundamental limits of light microscopic imaging. Few previous methods were able to generate satisfactory neuron reconstruction models automatically without human intervention. The manual tracing of neuron models is labour heavy and time-consuming, making the collection of large-scale neuron morphology database one of the major bottlenecks in morphological neuroscience. This thesis presents a suite of algorithms that are developed to target the challenge of automatically reconstructing neuron morphological models with minimum human intervention. We first propose the Rivulet algorithm that iteratively backtracks the neuron fibres from the termini points back to the soma centre. By refining many details of the Rivulet algorithm, we later propose the Rivulet2 algorithm which not only eliminates a few hyper-parameters but also improves the robustness against noisy images. A soma surface reconstruction method was also proposed to make the neuron models biologically plausible around the soma body. The tracing algorithms, including Rivulet and Rivulet2, normally need one or more hyper-parameters for segmenting the neuron body out of the noisy background. To make this pipeline fully automatic, we propose to use 2.5D neural network to train a model to enhance the curvilinear structures of the neuron fibres. The trained neural networks can quickly highlight the fibres of interests and suppress the noise points in the background for the neuron tracing algorithms. We evaluated the proposed methods in the data released by both the DIADEM and the BigNeuron challenge. The experimental results show that our proposed tracing algorithms achieve the state-of-the-art results

SOLID-SHELL FINITE ELEMENT MODELS FOR EXPLICIT SIMULATIONS OF CRACK PROPAGATION IN THIN STRUCTURES

Crack propagation in thin shell structures due to cutting is conveniently simulated using explicit finite element approaches, in view of the high nonlinearity of the problem. Solidshell elements are usually preferred for the discretization in the presence of complex material behavior and degradation phenomena such as delamination, since they allow for a correct representation of the thickness geometry. However, in solid-shell elements the small thickness leads to a very high maximum eigenfrequency, which imply very small stable time-steps. A new selective mass scaling technique is proposed to increase the time-step size without affecting accuracy. New ”directional” cohesive interface elements are used in conjunction with selective mass scaling to account for the interaction with a sharp blade in cutting processes of thin ductile shells

Methods of system identification, parameter estimation and optimisation applied to problems of modelling and control in engineering and physiology

Mathematical and computer-based models provide the foundation of most methods of engineering design. They are recognised as being especially important in the development of integrated dynamic systems, such as “control-configured” aircraft or in complex robotics applications. These models usually involve combinations of linear or nonlinear ordinary differential equations or difference equations, partial differential equations and algebraic equations. In some cases models may be based on differential algebraic equations. Dynamic models are also important in many other fields of research, including physiology where the highly integrated nature of biological control systems is starting to be more fully understood. Although many models may be developed using physical, chemical, or biological principles in the initial stages, the use of experimentation is important for checking the significance of underlying assumptions or simplifications and also for estimating appropriate sets of parameters. This experimental approach to modelling is also of central importance in establishing the suitability, or otherwise, of a given model for an intended application – the so-called “model validation” problem. System identification, which is the broad term used to describe the processes of experimental modelling, is generally considered to be a mature field and classical methods of identification involve linear discrete-time models within a stochastic framework. The aspects of the research described in this thesis that relate to applications of identification, parameter estimation and optimisation techniques for model development and model validation mainly involve nonlinear continuous time models Experimentally-based models of this kind have been used very successfully in the course of the research described in this thesis very in two areas of physiological research and in a number of different engineering applications. In terms of optimisation problems, the design, experimental tuning and performance evaluation of nonlinear control systems has much in common with the use of optimisation techniques within the model development process and it is therefore helpful to consider these two areas together. The work described in the thesis is strongly applications oriented. Many similarities have been found in applying modelling and control techniques to problems arising in fields that appear very different. For example, the areas of neurophysiology, respiratory gas exchange processes, electro-optic sensor systems, helicopter flight-control, hydro-electric power generation and surface ship or underwater vehicles appear to have little in common. However, closer examination shows that they have many similarities in terms of the types of problem that are presented, both in modelling and in system design. In addition to nonlinear behaviour; most models of these systems involve significant uncertainties or require important simplifications if the model is to be used in a real-time application such as automatic control. One recurring theme, that is important both in the modelling work described and for control applications, is the additional insight that can be gained through the dual use of time-domain and frequency-domain information. One example of this is the importance of coherence information in establishing the existence of linear or nonlinear relationships between variables and this has proved to be valuable in the experimental investigation of neuromuscular systems and in the identification of helicopter models from flight test data. Frequency-domain techniques have also proved useful for the reduction of high-order multi-input multi-output models. Another important theme that has appeared both within the modelling applications and in research on nonlinear control system design methods, relates to the problems of optimisation in cases where the associated response surface has many local optima. Finding the global optimum in practical applications presents major difficulties and much emphasis has been placed on evolutionary methods of optimisation (both genetic algorithms and genetic programming) in providing usable methods for optimisation in design and in complex nonlinear modelling applications that do not involve real-time problems. Another topic, considered both in the context of system modelling and control, is parameter sensitivity analysis and it has been found that insight gained from sensitivity information can be of value not only in the development of system models (e.g. through investigation of model robustness and the design of appropriate test inputs), but also in feedback system design and in controller tuning. A technique has been developed based on sensitivity analysis for the semi-automatic tuning of cascade and feedback controllers for multi-input multi-output feedback control systems. This tuning technique has been applied successfully to several problems. Inverse systems also receive significant attention in the thesis. These systems have provided a basis for theoretical research in the control systems field over the past two decades and some significant applications have been reported, despite the inherent difficulties in the mathematical methods needed for the nonlinear case. Inverse simulation methods, developed initially by others for use in handling-qualities studies for fixed-wing aircraft and helicopters, are shown in the thesis to provide some important potential benefits in control applications compared with classical methods of inversion. New developments in terms of methodology are presented in terms of a novel sensitivity based approach to inverse simulation that has advantages in terms of numerical accuracy and a new search-based optimisation technique based on the Nelder-Mead algorithm that can handle inverse simulation problems involving hard nonlinearities. Engineering applications of inverse simulation are presented, some of which involve helicopter flight control applications while others are concerned with feed-forward controllers for ship steering systems. The methods of search-based optimisation show some important advantages over conventional gradient-based methods, especially in cases where saturation and other nonlinearities are significant. The final discussion section takes the form of a critical evaluation of results obtained using the chosen methods of system identification, parameter estimation and optimisation for the modelling and control applications considered. Areas of success are highlighted and situations are identified where currently available techniques have important limitations. The benefits of an inter-disciplinary and applications-oriented approach to problems of modelling and control are also discussed and the value in terms of cross-fertilisation of ideas resulting from involvement in a wide range of applications is emphasised. Areas for further research are discussed

Robust de-centralized control and estimation for inter-connected systems

The thesis is concerned with the theoretical development of the control of inter-connected systems to achieve the whole overall stability and specific performance. A special included feature is the Fault-Tolerant Control (FTC) problem for the inter-connected system in terms of local subsystem actuator fault estimation. Hence, the thesis describes the main FTC challenges of distributed control of uncertain non-linear inter-connected systems. The basic principle adopted throughout the work is that the controller has two components, one involving the nominal control with unmatched components including uncertainties and disturbances. The second controller dealing with matched components including uncertainties and actuator faults.The main contributions of the thesis are summarised as follows:- The non-linear inter-connected systems are controlled by two controllers. The linear part via a linear matrix inequality (LMI) technique and the discontinuous part by using Integral Sliding Mode Control (ISMC) based on state feedback control.- The development of a new observer-based state estimate control strategy for non-linear inter-connected systems. The technique is applied either to every individual subsystem or to the whole as one shot system.- A new proposal of Adaptive Output Integral Sliding Mode Control (AOISMC) based only on output information plus static output feedback control is designed via an LMI formulation to control non-linear inter-connected systems. The new method is verified by application to a mathematical example representing an electrical power generator.- The development of a new method to design a dynamic control based on an LMI framework with Output Integral Sliding Mode Control (OISMC) to improve the stability and performance.- Using the above framework, making use of LMI tools and ISMC, a method of on-line actuator fault estimation has been proposed using the Proportional Multiple Integral Observer (PMIO) for fault estimation applicable to non-linear inter-connected systems