Data assimilation in the low noise regime with application to the Kuroshio

On-line data assimilation techniques such as ensemble Kalman filters and particle filters lose accuracy dramatically when presented with an unlikely observation. Such an observation may be caused by an unusually large measurement error or reflect a rare fluctuation in the dynamics of the system. Over a long enough span of time it becomes likely that one or several of these events will occur. Often they are signatures of the most interesting features of the underlying system and their prediction becomes the primary focus of the data assimilation procedure. The Kuroshio or Black Current that runs along the eastern coast of Japan is an example of such a system. It undergoes infrequent but dramatic changes of state between a small meander during which the current remains close to the coast of Japan, and a large meander during which it bulges away from the coast. Because of the important role that the Kuroshio plays in distributing heat and salinity in the surrounding region, prediction of these transitions is of acute interest. Here we focus on a regime in which both the stochastic forcing on the system and the observational noise are small. In this setting large deviation theory can be used to understand why standard filtering methods fail and guide the design of the more effective data assimilation techniques. Motivated by our analysis we propose several data assimilation strategies capable of efficiently handling rare events such as the transitions of the Kuroshio. These techniques are tested on a model of the Kuroshio and shown to perform much better than standard filtering methods.Comment: 43 pages, 12 figure

Urban and extra-urban hybrid vehicles: a technological review

Pollution derived from transportation systems is a worldwide, timelier issue than ever. The abatement actions of harmful substances in the air are on the agenda and they are necessary today to safeguard our welfare and that of the planet. Environmental pollution in large cities is approximately 20% due to the transportation system. In addition, private traffic contributes greatly to city pollution. Further, “vehicle operating life” is most often exceeded and vehicle emissions do not comply with European antipollution standards. It becomes mandatory to find a solution that respects the environment and, realize an appropriate transportation service to the customers. New technologies related to hybrid –electric engines are making great strides in reducing emissions, and the funds allocated by public authorities should be addressed. In addition, the use (implementation) of new technologies is also convenient from an economic point of view. In fact, by implementing the use of hybrid vehicles, fuel consumption can be reduced. The different hybrid configurations presented refer to such a series architecture, developed by the researchers and Research and Development groups. Regarding energy flows, different strategy logic or vehicle management units have been illustrated. Various configurations and vehicles were studied by simulating different driving cycles, both European approval and homologation and customer ones (typically municipal and university). The simulations have provided guidance on the optimal proposed configuration and information on the component to be used

Optimal Control and Estimation Strategies for Nonlinear and Switched Systems

This dissertation includes two main parts. In the first part, the main contribution is to use an inverse optimality approach to analytically solve the Hamilton-Jacobi-Bellman equation of a third order nonlinear optimal control problem for which the dynamics are affine and the cost is quadratic in the input. One special advantage of this work is that the solution is directly obtained for the control input without finding a value function first. However, the value function can be obtained after one solves for the control input and it is shown to be at least a local Lyapunov function. Furthermore, the developed controller is combined with a Continuous-Discrete Extended Kalman Filter (CDEKF) as an approach to deal with noisy measurements and provide an estimate of the states for feedback. The proposed technique is illustrated by its application to a path following problem of a Wheeled Mobile Robot (WMR). The main contribution of the second part of this thesis is the development of two recursive state estimation algorithms for discrete-time piecewise affine (PWA) singular systems with simulation evidence that the idea works for both uncorrelated and correlated process and measurement noise. The proposed algorithms are derived based on successive QR decompositions and Maximum Likelihood (ML) estimation theory. Numerical examples are presented for the case of a PWA system with an unknown input, transformed to a PWA singular system

Switching Costs in Network Industries

In network industries, switching costs have two opposite effects on the tendency towards market tipping. First, the fat-cat effect makes the larger firm price less aggressively and lose consumers to the smaller firm. This effect tends to prevent tipping. Second, the network-solidifying effect reinforces network effects by making a network size advantage longer-lasting and hence more valuable, thus intensifying price competition when networks are of comparable size. This effect tends to cause tipping. I find that when switching costs are high, the fat-cat effect dominates and an increase in switching costs can change the market from a tipping equilibrium to a sharing equilibrium. When switching costs are low, the network-solidifying effect dominates and an increase in switching costs can change the market from a sharing equilibrium to a tipping equilibrium. Policy intervention to remove switching costs in network industries may substantially reduce the likelihood of market tipping

Stochastic and deterministic models for age-structured populations with genetically variable traits

Understanding how stochastic and non-linear deterministic processes interact is a major challenge in population dynamics theory. After a short review, we introduce a stochastic individual-centered particle model to describe the evolution in continuous time of a population with (continuous) age and trait structures. The individuals reproduce asexually, age, interact and die. The 'trait' is an individual heritable property (d-dimensional vector) that may influence birth and death rates and interactions between individuals, and vary by mutation. In a large population limit, the random process converges to the solution of a Gurtin-McCamy type PDE. We show that the random model has a long time behavior that differs from its deterministic limit. However, the results on the limiting PDE and large deviation techniques \textit{\`a la} Freidlin-Wentzell provide estimates of the extinction time and a better understanding of the long time behavior of the stochastic process. This has applications to the theory of adaptive dynamics used in evolutionary biology. We present simulations for two biological problems involving life-history trait evolution when body size is plastic and individual growth is taken into account.Comment: This work is a proceeding of the CANUM 2008 conferenc

1D elastic full-waveform inversion and uncertainty estimation by means of a hybrid genetic algorithm-Gibbs sampler approach

Stochastic optimization methods, such as genetic algorithms, search for the global minimum of the misfit function within a given parameter range and do not require any calculation of the gradients of the misfit surfaces. More importantly, these methods collect a series of models and associated likelihoods that can be used to estimate the posterior probability distribution. However, because genetic algorithms are not a Markov chain Monte Carlo method, the direct use of the genetic-algorithm-sampled models and their associated likelihoods produce a biased estimation of the posterior probability distribution. In contrast, Markov chain Monte Carlo methods, such as the Metropolis-Hastings and Gibbs sampler, provide accurate posterior probability distributions but at considerable computational cost. In this paper, we use a hybrid method that combines the speed of a genetic algorithm to find an optimal solution and the accuracy of a Gibbs sampler to obtain a reliable estimation of the posterior probability distributions. First, we test this method on an analytical function and show that the genetic algorithm method cannot recover the true probability distributions and that it tends to underestimate the true uncertainties. Conversely, combining the genetic algorithm optimization with a Gibbs sampler step enables us to recover the true posterior probability distributions. Then, we demonstrate the applicability of this hybrid method by performing one-dimensional elastic full-waveform inversions on synthetic and field data. We also discuss how an appropriate genetic algorithm implementation is essential to attenuate the "genetic drift" effect and to maximize the exploration of the model space. In fact, a wide and efficient exploration of the model space is important not only to avoid entrapment in local minima during the genetic algorithm optimization but also to ensure a reliable estimation of the posterior probability distributions in the subsequent Gibbs sampler step