1,571 research outputs found
Termolecular Association of Ions in Gases
Issued as Technical reports [nos. 1-4], and Final report, Project no. G-41-61
Deep Burst Denoising
Noise is an inherent issue of low-light image capture, one which is
exacerbated on mobile devices due to their narrow apertures and small sensors.
One strategy for mitigating noise in a low-light situation is to increase the
shutter time of the camera, thus allowing each photosite to integrate more
light and decrease noise variance. However, there are two downsides of long
exposures: (a) bright regions can exceed the sensor range, and (b) camera and
scene motion will result in blurred images. Another way of gathering more light
is to capture multiple short (thus noisy) frames in a "burst" and intelligently
integrate the content, thus avoiding the above downsides. In this paper, we use
the burst-capture strategy and implement the intelligent integration via a
recurrent fully convolutional deep neural net (CNN). We build our novel,
multiframe architecture to be a simple addition to any single frame denoising
model, and design to handle an arbitrary number of noisy input frames. We show
that it achieves state of the art denoising results on our burst dataset,
improving on the best published multi-frame techniques, such as VBM4D and
FlexISP. Finally, we explore other applications of image enhancement by
integrating content from multiple frames and demonstrate that our DNN
architecture generalizes well to image super-resolution
State estimation for coupled reaction-diffusion PDE systems using modulating functions
Many systems with distributed dynamics are described by partial differential equations (PDEs). Coupled reaction-diffusion equations are a particular type of these systems. The measurement of the state over the entire spatial domain is usually required for their control. However, it is often impossible to obtain full state information with physical sensors only. For this problem, observers are developed to estimate the state based on boundary measurements. The method presented applies the so-called modulating function method, relying on an orthonormal function basis representation. Auxiliary systems are generated from the original system by applying modulating functions and formulating annihilation conditions. It is extended by a decoupling matrix step. The calculated kernels are utilized for modulating the input and output signals over a receding time window to obtain the coefficients for the basis expansion for the desired state estimation. The developed algorithm and its real-time functionality are verified via simulation of an example system related to the dynamics of chemical tubular reactors and compared to the conventional backstepping observer. The method achieves a successful state reconstruction of the system while mitigating white noise induced by the sensor. Ultimately, the modulating function approach represents a solution for the distributed state estimation problem without solving a PDE online
Stability and synchronization of discrete-time Markovian jumping neural networks with mixed mode-dependent time delays
Copyright [2009] IEEE. This material is posted here with permission of the IEEE. Such permission of the IEEE does not in any way imply IEEE endorsement of any of Brunel University's products or services. Internal or personal use of this material is permitted. However, permission to reprint/republish this material for advertising or promotional purposes or for creating new collective works for resale or redistribution must be obtained from the IEEE by writing to [email protected]. By choosing to view this document, you agree to all provisions of the copyright laws protecting it.In this paper, we introduce a new class of discrete-time neural networks (DNNs) with Markovian jumping parameters as well as mode-dependent mixed time delays (both discrete and distributed time delays). Specifically, the parameters of the DNNs are subject to the switching from one to another at different times according to a Markov chain, and the mixed time delays consist of both discrete and distributed delays that are dependent on the Markovian jumping mode. We first deal with the stability analysis problem of the addressed neural networks. A special inequality is developed to account for the mixed time delays in the discrete-time setting, and a novel Lyapunov-Krasovskii functional is put forward to reflect the mode-dependent time delays. Sufficient conditions are established in terms of linear matrix inequalities (LMIs) that guarantee the stochastic stability. We then turn to the synchronization problem among an array of identical coupled Markovian jumping neural networks with mixed mode-dependent time delays. By utilizing the Lyapunov stability theory and the Kronecker product, it is shown that the addressed synchronization problem is solvable if several LMIs are feasible. Hence, different from the commonly used matrix norm theories (such as the M-matrix method), a unified LMI approach is developed to solve the stability analysis and synchronization problems of the class of neural networks under investigation, where the LMIs can be easily solved by using the available Matlab LMI toolbox. Two numerical examples are presented to illustrate the usefulness and effectiveness of the main results obtained
State estimation for coupled PDE systems using Modulation Functions
This master thesis is devoted to the state estimation of a particular form of PDE systems, coupled parabolic PDEs with spatial dependent coefficients. This form of PDEs represent some dynamic systems such as Tubular Reactors, Diffusion in lithium-ion cells and Diffusive Gradient in Thin Films sensor. Other methods for this problem use "Backstepping" observers, in which the estimation error system is transformed into another system that is stable, reducing the problem to calculate the Kernel functions making the transformation possible. In some cases this calculation is not simple, also the simulation in real time of the observer system, that is also a PDE, can be difficult. The method presented in this thesis uses the properties of the so-called Modulating Functions in order to estimate the states. The procedure con- sists of generating an orthonormal basis of functions that can represent the state as a combination of them. Then auxiliary systems are formed from the original systems with boundary conditions that help in the simplification of the problem. Resolving these auxiliary systems, result in the calculation of the Modulating kernels. All of these steps can be made offline and do not have to be repeated. The functions are used together with the orthonormal basis in the online part, that consists of an inte- gration of a combination of the kernel functions, inputs and outputs of the system in a time window. Finally, with a matrix multiplication the coefficients for the ba- sis expansion of the state can be obtained, resulting in the desired state estimation. The present method is tested in systems that resemble the forms of the dynamics of Tubular Reactors and the performance is compared to other methods.Diese Masterarbeit widmet sich der Zustandsschätzung einer bestimmten Art von Systemen, gekoppelten partiellen Differenzialgleichungen mit raumabhängigen Ko- effizienten. Diese besondere Form von PDEs repräsentiert einige dynamische Sys- teme wie Röhrenreaktoren, Diffusion in Lithium-Ionen-Batterien und Gradienten in dünnen Schichten. Andere Methoden für dieses Problem benutzen "Backstep- ping" Beobachter, bei denen das Schätzfehlersystem in ein anderes stabiles System transformiert wird, wodurch das Problem reduziert wird, um die Kernfunktionen zu berechnen, die die Transformation ermöglichen. In manchen Fällen ist diese Berech- nung nicht einfach. Auch die Simulation in Echtzeit des Beobachters System, das auch eine PDE ist, kann sehr schwierig sein. Die in dieser Arbeit vorgestellte Meth- ode verwendet die Eigenschaften der sogenannten Modulationsfunktionen, um die Zustände zu schätzen. Das Verfahren besteht darin, eine Orthonormalbasis von Funktionen zu erzeugen können, die den Zustand als Kombination von ihnen repräsen- tieren, dann werden Hilfssysteme gebildet von dem ursprünglichen Systemen mit Randbedingungen, die bei der Vereinfachung helfen, von dem Problem. Das Au- flösen dieser Hilfssysteme ergibt die Berechnung der modulierende Kerne. Alle diese Schritte können offline durchgeführt und müssen nicht wiederholt werden. Die Funktionen werden zusammen mit der Orthonormalbasis im Online-Teil ver- wendet. Dieser Teil besteht aus einer Integration einer Kombination der Kernfunk- tionen, Eingaben und Ausgaben des Systems in einem Zeitfenster. Schließlich kön- nen die Koeffizienten zur Basiserweiterung mit einer Matrixmultiplikation berech- net werden, was zu der gewünschte Zustandsschätzung führt. Das Verfahren wird am Beispiel der Dynamik eines Rohreaktors getestet und die Ergebnisse werden mit anderen Methoden verglichen
Neural Operators for Delay-Compensating Control of Hyperbolic PIDEs
The recently introduced DeepONet operator-learning framework for PDE control
is extended from the results for basic hyperbolic and parabolic PDEs to an
advanced hyperbolic class that involves delays on both the state and the system
output or input. The PDE backstepping design produces gain functions that are
outputs of a nonlinear operator, mapping functions on a spatial domain into
functions on a spatial domain, and where this gain-generating operator's inputs
are the PDE's coefficients. The operator is approximated with a DeepONet neural
network to a degree of accuracy that is provably arbitrarily tight. Once we
produce this approximation-theoretic result in infinite dimension, with it we
establish stability in closed loop under feedback that employs approximate
gains. In addition to supplying such results under full-state feedback, we also
develop DeepONet-approximated observers and output-feedback laws and prove
their own stabilizing properties under neural operator approximations. With
numerical simulations we illustrate the theoretical results and quantify the
numerical effort savings, which are of two orders of magnitude, thanks to
replacing the numerical PDE solving with the DeepONet
Deep Learning of Delay-Compensated Backstepping for Reaction-Diffusion PDEs
Deep neural networks that approximate nonlinear function-to-function
mappings, i.e., operators, which are called DeepONet, have been demonstrated in
recent articles to be capable of encoding entire PDE control methodologies,
such as backstepping, so that, for each new functional coefficient of a PDE
plant, the backstepping gains are obtained through a simple function
evaluation. These initial results have been limited to single PDEs from a given
class, approximating the solutions of only single-PDE operators for the gain
kernels. In this paper we expand this framework to the approximation of
multiple (cascaded) nonlinear operators. Multiple operators arise in the
control of PDE systems from distinct PDE classes, such as the system in this
paper: a reaction-diffusion plant, which is a parabolic PDE, with input delay,
which is a hyperbolic PDE. The DeepONet-approximated nonlinear operator is a
cascade/composition of the operators defined by one hyperbolic PDE of the
Goursat form and one parabolic PDE on a rectangle, both of which are bilinear
in their input functions and not explicitly solvable. For the delay-compensated
PDE backstepping controller, which employs the learned control operator,
namely, the approximated gain kernel, we guarantee exponential stability in the
norm of the plant state and the norm of the input delay state.
Simulations illustrate the contributed theory
Optimization of niobium oxide-based threshold switches for oscillator-based applications
In niobium oxide-based capacitors non-linear switching characteristics can be observed if the oxide properties are adjusted accordingly. Such non-linear threshold switching characteristics can be utilized in various non-linear circuit applications, which have the potential to pave the way for the application of new computing paradigms. Furthermore, the non-linearity also makes them an interesting candidate for the application as selector devices e.g. for non-volatile memory devices. To satisfy the requirements for those two areas of application, the threshold switching characteristics need to be adjusted to either obtain a maximized voltage extension of the negative differential resistance region in the quasi-static I-V characteristics, which enhances the non-linearity of the devices and results in improved robustness to device-to-device variability or to adapt the threshold voltage to a specific non-volatile memory cell. Those adaptations of the threshold switching characteristics were successfully achieved by deliberate modifications of the niobium oxide stack. Furthermore, the impact of the material stack on the dynamic behavior of the threshold switches in non-linear circuits as well as the impact of the electroforming routine on the threshold switching characteristics were analyzed. The optimized device stack was transferred from the micrometer-sized test structures to submicrometer-sized devices, which were packaged to enable easy integration in complex circuits. Based on those packaged threshold switching devices the behavior of single as well as of coupled relaxation oscillators was analyzed. Subsequently, the obtained results in combination with the measurement results for the statistic device-to-device variability were used as a basis to simulate the pattern formation in coupled relaxation oscillator networks as well as their performance in solving graph coloring problems. Furthermore, strategies to adapt the threshold voltage to the switching characteristics of a tantalum oxide-based non-volatile resistive switch and a non-volatile phase change cell, to enable their application as selector devices for the respective cells, were discussed.:Abstract I
Zusammenfassung II
List of Abbrevations VI
List of Symbols VII
1 Motivation 1
2 Basics 5
2.1 Negative differential resistance and local activity in memristor devices 5
2.2 Threshold switches as selector devices 8
2.3 Switching effects observed in NbOx 13
2.3.1 Threshold switching caused by metal-insulator transition 13
2.3.2 Threshold switching caused by Frenkel-Poole conduction 18
2.3.3 Non-volatile resistive switching 32
3 Sample preparation 35
3.1 Deposition techniques 35
3.1.1 Evaporation 35
3.1.2 Sputtering 36
3.2 Micrometer-sized devices 36
3.3 Submicrometer-sized devices 37
3.3.1 Process flow 37
3.3.2 Reduction of the electrode resistance 39
3.3.3 Transfer from structuring via electron beam lithography to structuring via
laser lithography 48
3.3.4 Packaging procedure 50
4 Investigation and optimization of the electrical device characteristic 51
4.1 Introduction 51
4.2 Measurement setup 52
4.3 Electroforming 53
4.3.1 Optimization of the electroforming process 53
4.3.2 Characterization of the formed filament 62
4.4 Dynamic device characteristics 67
4.4.1 Emergence and measurement of dynamic behavior 67
4.4.2 Impact of the dynamic device characteristics on quasi-static I-V
characteristics 70
5 Optimization of the material stack 81
5.1 Introduction 81
5.2 Adjustment of the oxygen content in the bottom layer 82
5.3 Influence of the thickness of the oxygen-rich niobium oxide layer 92
5.4 Multilayer stacks 96
5.5 Device-to-device and Sample-to-sample variability 110
6 Applications of NbOx-based threshold switching devices 117
6.1 Introduction 117
6.2 Non-linear circuits 117
6.2.1 Coupled relaxation oscillators 117
6.2.2 Memristor Cellular Neural Network 121
6.2.3 Graph Coloring 127
6.3 Selector devices 132
7 Summary and Outlook 138
8 References 141
9 List of publications 154
10 Appendix 155
10.1 Parameter used for the LT Spice simulation of I-V curves for threshold
switches with varying oxide thicknesses 155
10.2 Dependence of the oscillation frequency of the relaxation oscillator circuit
on the capacitance and the applied source voltage 156
10.3 Calculation of the oscillation frequency of the relaxation oscillator circuit 157
10.4 Characteristics of the memristors and the cells utilized in the simulation of
the memristor cellular neural network 164
10.5 Calculation of the impedance of the cell in the memristor cellular network 166
10.6 Example graphs from the 2nd DIMACS series 179
11 List of Figures 182
12 List of Tables 19
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