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

Nonparametric Stochastic Discount Factor Decomposition

Stochastic discount factor (SDF) processes in dynamic economies admit a permanent-transitory decomposition in which the permanent component characterizes pricing over long investment horizons. This paper introduces an empirical framework to analyze the permanent-transitory decomposition of SDF processes. Specifically, we show how to estimate nonparametrically the solution to the Perron-Frobenius eigenfunction problem of Hansen and Scheinkman (2009). Our empirical framework allows researchers to (i) recover the time series of the estimated permanent and transitory components and (ii) estimate the yield and the change of measure which characterize pricing over long investment horizons. We also introduce nonparametric estimators of the continuation value function in a class of models with recursive preferences by reinterpreting the value function recursion as a nonlinear Perron-Frobenius problem. We establish consistency and convergence rates of the eigenfunction estimators and asymptotic normality of the eigenvalue estimator and estimators of related functionals. As an application, we study an economy where the representative agent is endowed with recursive preferences, allowing for general (nonlinear) consumption and earnings growth dynamics

Multi‐decadal Stochastic Streamflow Projections and Application to Water Resources Decision Making in the Colorado River Basin

Effective water resources planning and management requires skillful decisions on multiyear or decadal timeframes. In basins such as the Colorado River Basin (CRB), streamflow is not stationary but exhibits variability that reflects teleconnections with large scale climate indices such as Atlantic Multi-decadal Oscillation (AMO) and Pacific Decadal Oscillation (PDO). This research addresses this problem with four main contributions: It develops a stochastic streamflow simulation model and decadal scale streamflow projections based on these climate indices, compares this with other models recently developed, identifies and quantifies periods of unpredictability, and demonstrates the value of adding decadal scale projections to existing decision criteria in the CRB Supply and Demand Study (Basin Study). The novel WKNN model identifies and reconstructs dominant signals in the AMO and PDO using wavelet analysis, simulates each using block K-nearest neighbor (K-NN) bootstrap, then simulates the streamflow using a K-NN bootstrap conditioned on the simulated climate forcings. Traditional methods develop similar models on the flow timeseries and have limited skill in projections. Here, the climate indices are modeled and streamflow generated conditionally, exploiting the skill in climate indices. Our WKNN model is compared with other recently developed methods – Conditional Hidden Markov Model and the enhanced wavelet autoregressive model – with respect to skill of projections over a range of lead times. To understand and quantify the time-varying predictability of streamflow, we recover the underlying dynamics using a nonlinear dynamical system based approach. Time varying iv predictability is assessed by quantifying the divergence of trajectories in the phase space with time, using Local Lyapunov Exponents (LLE). Ensembles of projections from a current time are generated by block resampling trajectories from the K-nearest neighbors of the current vector in the phase space. Decadal scale WKNN projections and time varying predictabilities indicated by LLE are demonstrated to enhance existing decision criteria in the CRB Study that identify system vulnerability and invoke options and strategies to increase water availability or reduce demand through conservation or efficiency. Based on projections being wet, dry or unpredictable, improved decisions may reduce cost or reduce shortage and are illustrated by tradeoff curves of risk of shortage vs. cost

Diagnostics of machines and structures: dynamic identification and damage detection

This research work deals with damage detection of engineering machines and structures. This topic, developed in particular for bearing diagnostics in the first part of the work, is strictly related to dynamic identification when structures are considered. Thus, subspace-based methods are investigated in the second part of the work, with particular attention to nonlinear system identification. Changes in operational and environmental conditions for structures (such as air temperature, temperature gradients, humidity, wind, etc.) or machines (such as oil temperature, loads, rotating regimes, etc.) are known to have considerable effects on signal features and, consequently, on the reliability of diagnostics. Useful tools for eliminating this influence are provided by a Principal Component Analysis (PCA)-based method for damage detection. The same way as many published works applied PCA-based diagnostics of structures, in this research work a bearing diagnostic application is considered. After a detailed description of the test rig, the huge amount of acquired data, on several different damaged bearings, is investigated. Results are useful for giving an overview on how the PCA-based method for damage detection can be applied on a complicated real-life machine. In general cases of real structures, the application of efficient identification techniques is crucial for correctly exploiting the capabilities of the PCA-based method for damage detection. Moreover, in many cases damage causes a structure that initially behaves in a predominantly linear manner to exhibit nonlinear response: the application of nonlinear system identification methods to the feature-extraction process can also be used as a direct detection of damage. For these reasons, a detailed study of the nonlinear subspace-based identification methods is presented in the second part of this work. Since the classical data-driven subspace method can in some cases be affected by memory limitation problems, two alternative techniques are developed and demonstrated on numerical and experimental applications. Moreover, a modal counterpart of the nonlinear subspace identification method is introduced, to extend its relevance also to realistic large engineering structures. In a conclusive application, two of the main sources of non-stationary dynamics, namely the time-variability and the presence of nonlinearity, are analysed through the analytical and experimental study of a time-varying inertia pendulum, having a nonlinear equation of motion due to its large swinging amplitude

Neural Networks: Training and Application to Nonlinear System Identification and Control

This dissertation investigates training neural networks for system identification and classification. The research contains two main contributions as follow:1. Reducing number of hidden layer nodes using a feedforward componentThis research reduces the number of hidden layer nodes and training time of neural networks to make them more suited to online identification and control applications by adding a parallel feedforward component. Implementing the feedforward component with a wavelet neural network and an echo state network provides good models for nonlinear systems.The wavelet neural network with feedforward component along with model predictive controller can reliably identify and control a seismically isolated structure during earthquake. The network model provides the predictions for model predictive control. Simulations of a 5-story seismically isolated structure with conventional lead-rubber bearings showed significant reductions of all response amplitudes for both near-field (pulse) and far-field ground motions, including reduced deformations along with corresponding reduction in acceleration response. The controller effectively regulated the apparent stiffness at the isolation level. The approach is also applied to the online identification and control of an unmanned vehicle. Lyapunov theory is used to prove the stability of the wavelet neural network and the model predictive controller. 2. Training neural networks using trajectory based optimization approachesTraining neural networks is a nonlinear non-convex optimization problem to determine the weights of the neural network. Traditional training algorithms can be inefficient and can get trapped in local minima. Two global optimization approaches are adapted to train neural networks and avoid the local minima problem. Lyapunov theory is used to prove the stability of the proposed methodology and its convergence in the presence of measurement errors. The first approach transforms the constraint satisfaction problem into unconstrained optimization. The constraints define a quotient gradient system (QGS) whose stable equilibrium points are local minima of the unconstrained optimization. The QGS is integrated to determine local minima and the local minimum with the best generalization performance is chosen as the optimal solution. The second approach uses the QGS together with a projected gradient system (PGS). The PGS is a nonlinear dynamical system, defined based on the optimization problem that searches the components of the feasible region for solutions. Lyapunov theory is used to prove the stability of PGS and QGS and their stability under presence of measurement noise

Control of chaos in nonlinear circuits and systems

Nonlinear circuits and systems, such as electronic circuits (Chapter 5), power converters (Chapter 6), human brains (Chapter 7), phase lock loops (Chapter 8), sigma delta modulators (Chapter 9), etc, are found almost everywhere. Understanding nonlinear behaviours as well as control of these circuits and systems are important for real practical engineering applications. Control theories for linear circuits and systems are well developed and almost complete. However, different nonlinear circuits and systems could exhibit very different behaviours. Hence, it is difficult to unify a general control theory for general nonlinear circuits and systems. Up to now, control theories for nonlinear circuits and systems are still very limited. The objective of this book is to review the state of the art chaos control methods for some common nonlinear circuits and systems, such as those listed in the above, and stimulate further research and development in chaos control for nonlinear circuits and systems. This book consists of three parts. The first part of the book consists of reviews on general chaos control methods. In particular, a time-delayed approach written by H. Huang and G. Feng is reviewed in Chapter 1. A master slave synchronization problem for chaotic Lur’e systems is considered. A delay independent and delay dependent synchronization criteria are derived based on the H performance. The design of the time delayed feedback controller can be accomplished by means of the feasibility of linear matrix inequalities. In Chapter 2, a fuzzy model based approach written by H.K. Lam and F.H.F. Leung is reviewed. The synchronization of chaotic systems subject to parameter uncertainties is considered. A chaotic system is first represented by the fuzzy model. A switching controller is then employed to synchronize the systems. The stability conditions in terms of linear matrix inequalities are derived based on the Lyapunov stability theory. The tracking performance and parameter design of the controller are formulated as a generalized eigenvalue minimization problem which is solved numerically via some convex programming techniques. In Chapter 3, a sliding mode control approach written by Y. Feng and X. Yu is reviewed. Three kinds of sliding mode control methods, traditional sliding mode control, terminal sliding mode control and non-singular terminal sliding mode control, are employed for the control of a chaotic system to realize two different control objectives, namely to force the system states to converge to zero or to track desired trajectories. Observer based chaos synchronizations for chaotic systems with single nonlinearity and multi-nonlinearities are also presented. In Chapter 4, an optimal control approach written by C.Z. Wu, C.M. Liu, K.L. Teo and Q.X. Shao is reviewed. Systems with nonparametric regression with jump points are considered. The rough locations of all the possible jump points are identified using existing kernel methods. A smooth spline function is used to approximate each segment of the regression function. A time scaling transformation is derived so as to map the undecided jump points to fixed points. The approximation problem is formulated as an optimization problem and solved via existing optimization tools. The second part of the book consists of reviews on general chaos controls for continuous-time systems. In particular, chaos controls for Chua’s circuits written by L.A.B. Tôrres, L.A. Aguirre, R.M. Palhares and E.M.A.M. Mendes are discussed in Chapter 5. An inductorless Chua’s circuit realization is presented, as well as some practical issues, such as data analysis, mathematical modelling and dynamical characterization, are discussed. The tradeoff among the control objective, the control energy and the model complexity is derived. In Chapter 6, chaos controls for pulse width modulation current mode single phase H-bridge inverters written by B. Robert, M. Feki and H.H.C. Iu are discussed. A time delayed feedback controller is used in conjunction with the proportional controller in its simple form as well as in its extended form to stabilize the desired periodic orbit for larger values of the proportional controller gain. This method is very robust and easy to implement. In Chapter 7, chaos controls for epileptiform bursting in the brain written by M.W. Slutzky, P. Cvitanovic and D.J. Mogul are discussed. Chaos analysis and chaos control algorithms for manipulating the seizure like behaviour in a brain slice model are discussed. The techniques provide a nonlinear control pathway for terminating or potentially preventing epileptic seizures in the whole brain. The third part of the book consists of reviews on general chaos controls for discrete-time systems. In particular, chaos controls for phase lock loops written by A.M. Harb and B.A. Harb are discussed in Chapter 8. A nonlinear controller based on the theory of backstepping is designed so that the phase lock loops will not be out of lock. Also, the phase lock loops will not exhibit Hopf bifurcation and chaotic behaviours. In Chapter 9, chaos controls for sigma delta modulators written by B.W.K. Ling, C.Y.F. Ho and J.D. Reiss are discussed. A fuzzy impulsive control approach is employed for the control of the sigma delta modulators. The local stability criterion and the condition for the occurrence of limit cycle behaviours are derived. Based on the derived conditions, a fuzzy impulsive control law is formulated so that the occurrence of the limit cycle behaviours, the effect of the audio clicks and the distance between the state vectors and an invariant set are minimized supposing that the invariant set is nonempty. The state vectors can be bounded within any arbitrary nonempty region no matter what the input step size, the initial condition and the filter parameters are. The editors are much indebted to the editor of the World Scientific Series on Nonlinear Science, Prof. Leon Chua, and to Senior Editor Miss Lakshmi Narayan for their help and congenial processing of the edition