Bilinear system model of the action potential of a single neuron

Neurons are characterized by an electric potential which is established between their inside and outside media. They exhibit specific voltage fluctuations, in response to strong enough current impulses, called action potentials. In this work, a bang-bang controlled bilinear system (BLS) is derived to approximate the generation of a simple neuron's action potential. The shape of the response, as well as the timing seem to be useful for experimental planning and interpretation to neural physiologists. The BLS-model has the potential to aid the design and fabrication of commercial neural networks for communication, control and computing. In this manner, a variable-structure membrane impedance, such as exhibited by a stable focus and a saddle point in state space, and/or other modes, arises naturally. Added positive and negative stimuli, such as from other neurons, have the capability to alter the voltage across the inside and the outside media of the neuron and elicit an advanced or delayed response in the action potential. Such latency is significant as noted above, and is an active area of experimental research. The response shape and the timing with respect to some other event(latency} are related to experimental data. This simple model is compared to the complex and highly celebrated Hodgkin-Huxley model for the squid giant axon. The bang-bang feedback control is given a biological interpretation of sodium and potassium ion channels in this axon, that yields a variable-structure membrane impedance

SMP: A solid modeling program version 2.0

The Solid Modeling Program (SMP) provides the capability to model complex solid objects through the composition of primitive geometric entities. In addition to the construction of solid models, SMP has extensive facilities for model editing, display, and analysis. The geometric model produced by the software system can be output in a format compatible with existing analysis programs such as PATRAN-G. The present version of the SMP software supports six primitives: boxes, cones, spheres, paraboloids, tori, and trusses. The details for creating each of the major primitive types is presented. The analysis capabilities of SMP, including interfaces to existing analysis programs, are discussed

Multi-Rate Observers for Model-Based Process Monitoring

Very often, critical quantities related to safety, product quality and economic performance of a chemical process cannot be measured on line. In an attempt to overcome the challenges caused by inadequate on-line measurements, state estimation provides an alternative approach to reconstruct the unmeasured state variables by utilizing available on-line measurements and a process model. Chemical processes usually possess strong nonlinearities, and involve different types of measurements. It remains a challenging task to incorporate multiple measurements with different sampling rates and different measurement delays into a unified estimation algorithmic framework. This dissertation seeks to present developments in the field of state estimation by providing the theoretical advances in multi-rate multi-delay observer design. A delay-free multi-rate observer is first designed in linear systems under asynchronous sampling. Sufficient and explicit conditions in terms of maximum sampling period are derived to guarantee exponential stability of the observer, using Lyapunov’s second method. A dead time compensation approach is developed to compensate for the effect of measurement delay. Based on the multi-rate formulation, optimal multi-rate observer design is studied in two classes of linear systems where optimal gain selection is performed by formulating and solving an optimization problem. Then a multi-rate observer is developed in nonlinear systems with asynchronous sampling. The input-to-output stability is established for the estimation errors with respect to measurement errors using the Karafyllis-Jiang vector small-gain theorem. Measurement delay is also accounted for in the observer design using dead time compensation. Both the multi-rate designs in linear and nonlinear systems provide robustness with respect to perturbations in the sampling schedule. Multi-rate multi-delay observer is shown to be effective for process monitoring in polymerization reactors. A series of three polycondensation reactors and an industrial gas-phase polyethylene reactor are used to evaluate the observer performance. Reliable on-line estimates are obtained from the multi-rate multi-delay observer through simulation

Data-Driven Forecasting of High-Dimensional Chaotic Systems with Long Short-Term Memory Networks

We introduce a data-driven forecasting method for high-dimensional chaotic systems using long short-term memory (LSTM) recurrent neural networks. The proposed LSTM neural networks perform inference of high-dimensional dynamical systems in their reduced order space and are shown to be an effective set of nonlinear approximators of their attractor. We demonstrate the forecasting performance of the LSTM and compare it with Gaussian processes (GPs) in time series obtained from the Lorenz 96 system, the Kuramoto-Sivashinsky equation and a prototype climate model. The LSTM networks outperform the GPs in short-term forecasting accuracy in all applications considered. A hybrid architecture, extending the LSTM with a mean stochastic model (MSM-LSTM), is proposed to ensure convergence to the invariant measure. This novel hybrid method is fully data-driven and extends the forecasting capabilities of LSTM networks.Comment: 31 page

Population balance modeling of crystallization for monitoring and optimal control

The Population Balance Equation (PBE) describe the change in the particle size distribution occasioned by a variety of mechanisms. This study evaluate the PBE with nucleation, growth and dissolution. The nucleation with growth process is known to be problematic due to the sharp profiles that it causes. The dissolution process requires the knowledge of the number of particles at the minimal stable size, such that unstable particles are removed from the particulate phase. These conditions require the use of specialized numerical method for mathematical modeling. In this thesis, an emphasis is given in the Moving Sectional Method, which combines the method of classes with the method of characteristics to mitigate numerical diffusion errors. The work focused on the PBE application for the enantioselective crystallization of racemic compounding forming systems. Initially, the conservation of the moments of the distribution was analyzed for the MSM with growth and nucleation mechanisms and methods were proposed for the addition of new elements of the particle size mesh. The estimation of kinetic parameters was approached for the dissolution of NaCl in solutions of monoethyleneglycol (MEG) from data of color patterns (RGB), which can be obtained by experimental apparatus of low cost. A method for determining the operating conditions for the batch crystallizer based on the ternary diagram is described. Subsequently, it is shown that the information obtained in the ternary diagram, such as the maximum yield obtained by the process due to thermodynamics, can be used to formulate constraints for a control method based on non-linear optimization to obtain the desired characteristics of the product.A Equação do Balanço da População (PBE) descreve a mudança na distribuição do tamanho de partícula. Este estudo avalia a PBE com nucleação, crescimento e dissolução. Processos com nucleação e crescimento são conhecidos por serem problemáticos devido aos perfis descontínuos que causam. A dissolução requer o conhecimento do número de partículas no tamanho estável mínimo, de modo que as partículas instáveis sejam removidas da fase particulada. Essas condições requerem o uso de métodos numéricos especializados para sua modelagem matemática. Nesta tese, é dada ênfase ao Moving Section Method (MSM) que combina o método das classes com o método das características para mitigar erros de difusão numérica. O trabalho concentrou-se na aplicação do PBE para a cristalização enantiosseletiva de sistemas formadores de compostos racêmicos. Inicialmente, a conservação dos momentos da distribuição foi analisada para o MSM com mecanismos de crescimento e nucleação e propôs-se métodos para a adição de novos elementos da malha do tamanho de partículas. A estimação de parâmetros cinéticos foi abordada para a dissolução de NaCl em soluções de monoetilenoglicol (MEG) a partir de dados de padrões de cores (RGB), o que pode ser obtido por aparato experimental de baixo custo. Um método para determinar as condições de operação para o cristalizador em batelada com base no diagrama ternário é descrito. Posteriormente, mostram-se que as informações obtidas no diagrama ternário, como o rendimento máximo obtido pelo processo devido à termodinâmica, podem ser usadas para formular restrições para um método de controle baseado em otimização não linear para obter as características desejadas do produto

Optimal input design and parameter estimation for continuous-time dynamical systems

Diese Arbeit behandelt die Themengebiete Design of Experiments (DoE) und Parameterschätzung für zeitkontinuierliche Systeme, welche in der modernen Regelungstheorie eine wichtige Rolle spielen. Im gewählten Kontext untersucht DoE die Auswirkungen von verschiedenen Rahmenbedingungen von Simulations- bzw. Messexperimenten auf die Qualität der Parameterschätzung, wobei der Fokus auf der Anwendung der Theorie auf praxisrelevante Problemstellungen liegt. Dafür wird die weithin bekannte Fisher-Matrix eingeführt und die resultierende nicht lineare Optimierungsaufgabe angeschrieben. An einem PT1-System wird der Informationsgehalt von Signalen und dessen Auswirkungen auf die Parameterschätzung gezeigt. Danach konzentriert sich die Arbeit auf ein Teilgebiet von DoE, nämlich Optimal Input Design (OID), und wird am Beispiel eines 1D-Positioniersystems im Detail untersucht. Ein Vergleich mit häufig verwendeten Anregungssignalen zeigt, dass generierte Anregungssignale (OID) oft einen höheren Informationsgehalt aufweisen und mit genaueren Schätzwerten einhergeht. Zusätzlicher Benefit ist, dass Beschränkungen an Eingangs-, Ausgangs- und Zustandsgrößen einfach in die Optimierungsaufgabe integriert werden können. Der zweite Teil der Arbeit behandelt Methoden zur Parameterschätzung von zeitkontinuierlichen Modellen mit dem Fokus auf der Verwendung von Modulationsfunktionen (MF) bzw. Poisson-Moment Functionals (PMF) zur Vermeidung der zeitlichen Ableitungen und Least-Squares zur Lösung des resultierenden überbestimmten Gleichungssystems. Bei verrauschten Messsignalen ergibt sich daraus sofort die Problematik von nicht erwartungstreuen Schätzergebnissen (Bias). Aus diesem Grund werden Methoden zur Schätzung und Kompensation von Bias Termen diskutiert. Beitrag dieser Arbeit ist vor allem die detaillierte Aufarbeitung eines Ansatzes zur Biaskompensation bei Verwendung von PMF und Least-Squares für lineare Systeme und dessen Erweiterung auf (leicht) nicht lineare Systeme. Der vorgestellte Ansatz zur Biaskompensation (BC-OLS) wird am nicht linearen 1D-Servo in der Simulation und mit Messdaten validiert und in der Simulation mit anderen Methoden, z.B., Total-Least-Squares verglichen. Zusätzlich wird der Ansatz von PMF auf die weiter gefasste Systemklasse der Modulationsfunktionen (MF) erweitert. Des Weiteren wird ein praxisrelevantes Problem der Parameteridentifikation diskutiert, welches auftritt, wenn das Systemverhalten nicht gänzlich von der Identifikationsgleichung beschrieben wird. Am 1D-Servo wird gezeigt, dass ein Deaktivieren und Reaktivieren der PMF Filter mit geeigneter Initialisierung diese Problematik einfach löst.This thesis addresses two topics that play a significant role in modern control theory: design of experiments (DoE) and parameter estimation methods for continuous-time (CT) models. In this context, DoE focuses on the impact of experimental design regarding the accuracy of a subsequent estimation of unknown model parameters and applying the theory to real-world applications and its detailed analysis. We introduce the Fisher-information matrix (FIM), consisting of the parameter sensitivities and the resulting highly nonlinear optimization task. By a first-order system, we demonstrate the computation of the information content, its visualization, and an illustration of the effects of higher Fisher information on parameter estimation quality. After that, the topic optimal input design (OID), a subarea of DoE, will be thoroughly explored on the practice-relevant linear and nonlinear model of a 1D-position servo system. Comparison with standard excitation signals shows that the OID signals generally provide higher information content and lead to more accurate parameter estimates using least-squares methods. Besides, this approach allows taking into account constraints on input, output, and state variables. In the second major topic of this thesis, we treat parameter estimation methods for CT systems, which provide several advantages to identify discrete-time (DT) systems, e.g., allows physical insight into model parameters. We focus on modulating function method (MFM) or Poisson moment functionals (PMF) and least-squares to estimate unknown model parameters. In the case of noisy measurement data, the problem of biased parameter estimation arises immediately. That is why we discuss the computation and compensation of the so-called estimation bias in detail. Besides the detailed elaboration of a bias compensating estimation method, this work’s main contribution is, based on PMF and least squares for linear systems, the extension to at least slightly nonlinear systems. The derived bias-compensated ordinary least-squares (BCOLS) approach for obtaining asymptotically unbiased parameter estimates is tested on a nonlinear 1D-servo model in the simulation and measurement. A comparison with other methods for bias compensation or avoidance, e.g., total least-squares (TLS), is performed. Additionally, the BC-OLS method is applied to the more general MFM. Furthermore, a practical issue of parameter estimation is discussed, which occurs when the system behavior leaves and re-enters the space covered by the identification equation. Using the 1D-servo system, one can show that disabling and re-enabling the PMF filters with appropriate initialization can solve this problem

Left Ventricle Myocardium Segmentation from 3D Cardiac MR Images using Combined Probabilistic Atlas and Graph Cut-based Approaches

Medical imaging modalities, including Computed Tomography (CT) Magnetic Resonance Imaging (MRI) and Ultrasound (US) are critical for the diagnosis and progress monitoring of many cardiac conditions, planning, visualization and delivery of therapy via minimally invasive intervention procedures, as well as for teaching, training and simulation applications. Image segmentation is a processing technique that allows the user to extract the necessary information from an image dataset, in the form of a surface model of the region of interest from the anatomy. A wide variety of segmentation techniques have been developed and implemented for cardiac MR images. Despite their complexity and performance, many of them are intended for specific image datasets or are too specific to be employed for segmenting classical clinical quality Magnetic Resonance (MR) images. Graph Cut based segmentation algorithms have been shown to work well in regards to medical image segmentation. In addition, they are computationally efficient, which scales well to real time applications. While the basic graph cuts algorithms use lower-order statistics, combining this segmentation approach with atlas-based methods may help improve segmentation accuracy at a lower computational cost. The proposed technique will be tested at each step during the development by assessing the segmentation results against the available ground truth segmentation. Several metrics will be used to quantify the performance of the proposed technique, including computational performance, segmentation accuracy and fidelity assessed via the Sørensen-Dice Coefficient (DSC), Mean Absolute Distance (MAD) and Hausdorff Distance (HD) metrics

Probabilistic Framework for Behavior Characterization of Traffic Participants Enabling Long Term Prediction

This research aims at developing new methods that predict the behaviors of the human driven traffic participants to enable safe operation of autonomous vehicles in complex traffic environments. Autonomous vehicles are expected to operate amongst human driven conventional vehicles in the traffic at least for the next few decades. For safe navigation they will need to infer the intents as well as the behaviors of the human traffic participants using extrinsically observable information, so that their trajectories can be predicted for a time horizon long enough to do a predictive risk analysis and gracefully avert any risky situation. This research approaches this challenge by recognizing that any maneuver performed by a human driver can be divided into four stages that depend on the surrounding context: intent determination, maneuver preparation, gap acceptance and maneuver execution. It builds on the hypothesis that for a given driver, the behavior not only spans across these four maneuver stages, but across multiple maneuvers. As a result, identifying the driver behavior in any of these stages can help characterize the nature of all the subsequent maneuvers that the driver is likely to perform, thus resulting in a more accurate prediction for a longer time horizon. To enable this, a novel probabilistic framework is proposed that couples the different maneuver stages of the observed traffic participant together and associates them to a driving style. To realize this framework two candidate Multiple Model Adaptive Estimation approaches were compared: Autonomous Multiple Model (AMM) and Interacting Multiple Model(IMM) filtering approach. The IMM approach proved superior to the AMM approach and was eventually validated using a trajectory extracted from a real world dataset for efficacy. The proposed framework was then implemented by extending the validated IMM approach with contextual information of the observed traffic participant. The classification of the driving style of the traffic participant (behavior characterization) was then demonstrated for two use case scenarios. The proposed contextual IMM (CIMM) framework also showed improvements in the performance of the behavior classification of the traffic participants compared to the IMM for the identified use case scenarios. This outcome warrants further exploration of this framework for different traffic scenarios. Further, it contributes towards the ongoing endeavors for safe deployment of autonomous vehicles on public roads