41 research outputs found
Nonlinear Systems
Open Mathematics is a challenging notion for theoretical modeling, technical analysis, and numerical simulation in physics and mathematics, as well as in many other fields, as highly correlated nonlinear phenomena, evolving over a large range of time scales and length scales, control the underlying systems and processes in their spatiotemporal evolution. Indeed, available data, be they physical, biological, or financial, and technologically complex systems and stochastic systems, such as mechanical or electronic devices, can be managed from the same conceptual approach, both analytically and through computer simulation, using effective nonlinear dynamics methods. The aim of this Special Issue is to highlight papers that show the dynamics, control, optimization and applications of nonlinear systems. This has recently become an increasingly popular subject, with impressive growth concerning applications in engineering, economics, biology, and medicine, and can be considered a veritable contribution to the literature. Original papers relating to the objective presented above are especially welcome subjects. Potential topics include, but are not limited to: Stability analysis of discrete and continuous dynamical systems; Nonlinear dynamics in biological complex systems; Stability and stabilization of stochastic systems; Mathematical models in statistics and probability; Synchronization of oscillators and chaotic systems; Optimization methods of complex systems; Reliability modeling and system optimization; Computation and control over networked systems
Study of the best linear approximation of nonlinear systems with arbitrary inputs
System identification is the art of modelling of a process (physical, biological,
etc.) or to predict its behaviour or output when the environment condition
or parameter changes. One is modelling the input-output relationship of a system,
for example, linking temperature of a greenhouse (output) to the sunlight intensity
(input), power of a car engine (output) with fuel injection rate (input). In linear
systems, changing an input parameter will result in a proportional increase in the
system output. This is not the case in a nonlinear system. Linear system identification
has been extensively studied, more so than nonlinear system identification.
Since most systems are nonlinear to some extent, there is significant interest in this
topic as industrial processes become more and more complex.
In a linear dynamical system, knowing the impulse response function of a
system will allow one to predict the output given any input. For nonlinear systems
this is not the case. If advanced theory is not available, it is possible to approximate
a nonlinear system by a linear one. One tool is the Best Linear Approximation
(Bla), which is an impulse response function of a linear system that minimises the
output differences between its nonlinear counterparts for a given class of input. The
Bla is often the starting point for modelling a nonlinear system. There is extensive
literature on the Bla obtained from input signals with a Gaussian probability
density function (p.d.f.), but there has been very little for other kinds of inputs.
A Bla estimated from Gaussian inputs is useful in decoupling the linear dynamics
from the nonlinearity, and in initialisation of parameterised models. As Gaussian
inputs are not always practical to be introduced as excitations, it is important to
investigate the dependence of the Bla on the amplitude distribution in more detail.
This thesis studies the behaviour of the Bla with regards to other types of signals,
and in particular, binary sequences where a signal takes only two levels. Such an
input is valuable in many practical situations, for example where the input actuator
is a switch or a valve and hence can only be turned either on or off.
While it is known in the literature that the Bla depends on the amplitude
distribution of the input, as far as the author is aware, there is a lack of comprehensive
theoretical study on this topic. In this thesis, the Blas of discrete-time
time-invariant nonlinear systems are studied theoretically for white inputs with an arbitrary amplitude distribution, including Gaussian and binary sequences. In doing
so, the thesis offers answers to fundamental questions of interest to system engineers,
for example: 1) How the amplitude distribution of the input and the system
dynamics affect the Bla? 2) How does one quantify the difference between the
Bla obtained from a Gaussian input and that obtained from an arbitrary input?
3) Is the difference (if any) negligible? 4) What can be done in terms of experiment
design to minimise such difference?
To answer these questions, the theoretical expressions for the Bla have been
developed for both Wiener-Hammerstein (Wh) systems and the more general Volterra
systems. The theory for the Wh case has been verified by simulation and physical
experiments in Chapter 3 and Chapter 6 respectively. It is shown in Chapter 3
that the difference between the Gaussian and non-Gaussian Bla’s depends on the
system memory as well as the higher order moments of the non-Gaussian input.
To quantify this difference, a measure called the Discrepancy Factor—a measure of
relative error, was developed. It has been shown that when the system memory is
short, the discrepancy can be as high as 44.4%, which is not negligible. This justifies
the need for a method to decrease such discrepancy. One method is to design a random
multilevel sequence for Gaussianity with respect to its higher order moments,
and this is discussed in Chapter 5.
When estimating the Bla even in the absence of environment and measurement
noise, the nonlinearity inevitably introduces nonlinear distortions—deviations
from the Bla specific to the realisation of input used. This also explains why more
than one realisation of input and averaging is required to obtain a good estimate of
the Bla. It is observed that with a specific class of pseudorandom binary sequence
(Prbs), called the maximum length binary sequence (Mlbs or the m-sequence), the
nonlinear distortions appear structured in the time domain. Chapter 4 illustrates
a simple and computationally inexpensive method to take advantage this structure
to obtain better estimates of the Bla—by replacing mean averaging by median
averaging.
Lastly, Chapters 7 and 8 document two independent benchmark studies separate
from the main theoretical work of the thesis. The benchmark in Chapter 7 is
concerned with the modelling of an electrical Wh system proposed in a special session
of the 15th International Federation of Automatic Control (Ifac) Symposium on
System Identification (Sysid) 2009 (Schoukens, Suykens & Ljung, 2009). Chapter 8
is concerned with the modelling of a ‘hyperfast’ Peltier cooling system first proposed
in the U.K. Automatic Control Council (Ukacc) International Conference
on Control, 2010 (Control 2010)
Dirty RF Signal Processing for Mitigation of Receiver Front-end Non-linearity
Moderne drahtlose Kommunikationssysteme stellen hohe und teilweise
gegensätzliche Anforderungen an die Hardware der Funkmodule, wie z.B.
niedriger Energieverbrauch, große Bandbreite und hohe Linearität. Die
Gewährleistung einer ausreichenden Linearität ist, neben anderen analogen
Parametern, eine Herausforderung im praktischen Design der Funkmodule. Der
Fokus der Dissertation liegt auf breitbandigen HF-Frontends für
Software-konfigurierbare Funkmodule, die seit einigen Jahren kommerziell
verfügbar sind. Die praktischen Herausforderungen und Grenzen solcher
flexiblen Funkmodule offenbaren sich vor allem im realen Experiment. Eines
der Hauptprobleme ist die Sicherstellung einer ausreichenden analogen
Performanz über einen weiten Frequenzbereich. Aus einer Vielzahl an
analogen Störeffekten behandelt die Arbeit die Analyse und Minderung von
Nichtlinearitäten in Empfängern mit direkt-umsetzender Architektur. Im
Vordergrund stehen dabei Signalverarbeitungsstrategien zur Minderung
nichtlinear verursachter Interferenz - ein Algorithmus, der besser unter
"Dirty RF"-Techniken bekannt ist. Ein digitales Verfahren nach der
Vorwärtskopplung wird durch intensive Simulationen, Messungen und
Implementierung in realer Hardware verifiziert. Um die Lücken zwischen
Theorie und praktischer Anwendbarkeit zu schließen und das Verfahren in
reale Funkmodule zu integrieren, werden verschiedene Untersuchungen
durchgeführt. Hierzu wird ein erweitertes Verhaltensmodell entwickelt, das
die Struktur direkt-umsetzender Empfänger am besten nachbildet und damit
alle Verzerrungen im HF- und Basisband erfasst. Darüber hinaus wird die
Leistungsfähigkeit des Algorithmus unter realen Funkkanal-Bedingungen
untersucht. Zusätzlich folgt die Vorstellung einer ressourceneffizienten
Echtzeit-Implementierung des Verfahrens auf einem FPGA. Abschließend
diskutiert die Arbeit verschiedene Anwendungsfelder, darunter spektrales
Sensing, robuster GSM-Empfang und GSM-basiertes Passivradar. Es wird
gezeigt, dass nichtlineare Verzerrungen erfolgreich in der digitalen
Domäne gemindert werden können, wodurch die Bitfehlerrate gestörter
modulierter Signale sinkt und der Anteil nichtlinear verursachter
Interferenz minimiert wird. Schließlich kann durch das Verfahren die
effektive Linearität des HF-Frontends stark erhöht werden. Damit wird der
zuverlässige Betrieb eines einfachen Funkmoduls unter dem Einfluss der
Empfängernichtlinearität möglich. Aufgrund des flexiblen Designs ist der
Algorithmus für breitbandige Empfänger universal einsetzbar und ist nicht
auf Software-konfigurierbare Funkmodule beschränkt.Today's wireless communication systems place high requirements on the
radio's hardware that are largely mutually exclusive, such as low power
consumption, wide bandwidth, and high linearity. Achieving a sufficient
linearity, among other analogue characteristics, is a challenging issue in
practical transceiver design. The focus of this thesis is on wideband
receiver RF front-ends for software defined radio technology, which became
commercially available in the recent years. Practical challenges and
limitations are being revealed in real-world experiments with these radios.
One of the main problems is to ensure a sufficient RF performance of the
front-end over a wide bandwidth. The thesis covers the analysis and
mitigation of receiver non-linearity of typical direct-conversion receiver
architectures, among other RF impairments. The main focus is on DSP-based
algorithms for mitigating non-linearly induced interference, an approach
also known as "Dirty RF" signal processing techniques. The conceived
digital feedforward mitigation algorithm is verified through extensive
simulations, RF measurements, and implementation in real hardware. Various
studies are carried out that bridge the gap between theory and practical
applicability of this approach, especially with the aim of integrating that
technique into real devices. To this end, an advanced baseband behavioural
model is developed that matches to direct-conversion receiver architectures
as close as possible, and thus considers all generated distortions at RF
and baseband. In addition, the algorithm's performance is verified under
challenging fading conditions. Moreover, the thesis presents a
resource-efficient real-time implementation of the proposed solution on an
FPGA. Finally, different use cases are covered in the thesis that includes
spectrum monitoring or sensing, GSM downlink reception, and GSM-based
passive radar. It is shown that non-linear distortions can be successfully
mitigated at system level in the digital domain, thereby decreasing the bit
error rate of distorted modulated signals and reducing the amount of
non-linearly induced interference. Finally, the effective linearity of the
front-end is increased substantially. Thus, the proper operation of a
low-cost radio under presence of receiver non-linearity is possible. Due to
the flexible design, the algorithm is generally applicable for wideband
receivers and is not restricted to software defined radios
System Engineering Applied to Fuenmayor Karst Aquifer (San Julián de Banzo, Huesca) and Collins Glacier (King George Island, Antarctica)
La ingeniería de sistemas, definida generalmente como arte y ciencia de crear soluciones integrales a problemas complejos, se aplica en el presente documento a dos sistemas naturales, a saber, un sistema acuífero kárstico y un sistema glaciar, desde una perspectiva hidrológica. Las técnicas de identificación, desarrolladas típicamente en ingeniería para representar sistemas artificiales por medio de modelos lineales y no lineales, pueden aplicarse en el estudio de los sistemas naturales donde se producen fenómenos de acoplamiento entre el clima y la hidrosfera. Los métodos evolucionan para afrontar nuevos campos de identificación donde se requieren estrategias para encontrar el modelo idóneo adaptado a las peculiaridades del sistema. En este sentido, se han considerado especialmente las herramientas basadas en la transformada wavelet utilizadas en la preparación de series temporales, suavizado de señales, análisis espectral, correlación cruzada y predicción, entre otros. Bajo este enfoque, una aplicación a mencionar entre las tratadas en esta tesis, es la determinación analítica del núcleo efectivo estacional (SEC) a través del estudio de la coherencia wavelet entre temperatura del aire y la descarga del glaciar, que establece un conjunto de períodos de muestreo aceptablemente coherentes, a partir del cual se crearán los modelos del sistema glacial. El estudio está dirigido específicamente a estimar la influencia de la precipitación sobre la descarga del acuífero kárstico de Fuenmayor, en San Julián de Banzo, Huesca, España. De la misma manera, se ocupa de las consecuencias de la temperatura del aire en la fusión del hielo glaciar, que se manifiesta en la corriente de drenaje del glaciar Collins, isla King George, Antártida. En el proceso de identificación paramétrica y no paramétrica se buscan los modelos que mejor representen la dinámica interna del sistema. Eso conduce a pruebas iterativas, donde se van creando modelos que se verifican sistemáticamente con los datos reales del muestreo, de acuerdo a un criterio de eficiencia dado. La solución mejor valorada según los resultados obtenidos en los casos tratados apuntan a estructuras de modelos en bloques. Esta tesis significa una exposición formal de la metodología de identificación de sistemas propios de la ingeniería en el contexto de los sistemas naturales, que mejoran los resultados obtenidos en muchos casos de la hidrología kárstica que comúnmente usaban métodos ad hoc ocasionales de carácter estadístico; así mismo, los enfoques propuestos en los casos de glaciología con el análisis wavelet y los modelos orientados a datos raramente considerados en la literatura, revelan información esencial ante la imposibilidad de precisar la totalidad de la física que rige el sistema. Notables resultados se derivan en la caracterización de la respuesta del manantial de Fuenmayor y su correlación con la precipitación, desde la perspectiva de un sistema lineal, que se complementa con los métodos de identificación basados en técnicas no lineales. Así mismo, la implementación del modelo para el glaciar Collins, obtenido también mediante métodos de identificación de caja negra, puede revelar una inestabilidad de los límites de los periodos activos de la descarga, y consecuentemente la variabilidad en la tendencia actual en el cambio climático global
Regularized System Identification
This open access book provides a comprehensive treatment of recent developments in kernel-based identification that are of interest to anyone engaged in learning dynamic systems from data. The reader is led step by step into understanding of a novel paradigm that leverages the power of machine learning without losing sight of the system-theoretical principles of black-box identification. The authors’ reformulation of the identification problem in the light of regularization theory not only offers new insight on classical questions, but paves the way to new and powerful algorithms for a variety of linear and nonlinear problems. Regression methods such as regularization networks and support vector machines are the basis of techniques that extend the function-estimation problem to the estimation of dynamic models. Many examples, also from real-world applications, illustrate the comparative advantages of the new nonparametric approach with respect to classic parametric prediction error methods. The challenges it addresses lie at the intersection of several disciplines so Regularized System Identification will be of interest to a variety of researchers and practitioners in the areas of control systems, machine learning, statistics, and data science. This is an open access book