On the use of the theory of dynamical systems for transient problems

This paper is a preliminary work to address the problem of dynamical systems with parameters varying in time. An idea to predict their behaviour is proposed. These systems are called \emph{transient systems}, and are distinguished from \emph{steady systems}, in which parameters are constant. In particular, in steady systems the excitation is either constant (e.g. nought) or periodic with amplitude, frequency and phase angle which do not vary in time. We apply our method to systems which are subjected to a transient excitation, which is neither constant nor periodic. The effect of switching-off and full-transient forces is investigated. The former can be representative of switching-off procedures in machines; the latter can represent earthquake vibrations, wind gusts, etc. acting on a mechanical system. This class of transient systems can be seen as the evolution of an ordinary steady system into another ordinary steady system, for both of which the classical theory of dynamical systems holds. The evolution from a steady system to the other is driven by a transient force, which is regarded as a map between the two steady systems.Comment: 7 pages, 9 figure

On deformation of Poisson manifolds of hydrodynamic type

We study a class of deformations of infinite-dimensional Poisson manifolds of hydrodynamic type which are of interest in the theory of Frobenius manifolds. We prove two results. First, we show that the second cohomology group of these manifolds, in the Poisson-Lichnerowicz cohomology, is ``essentially'' trivial. Then, we prove a conjecture of B. Dubrovin about the triviality of homogeneous formal deformations of the above manifolds.Comment: LaTeX file, 24 page

Multiple structure recovery with T-linkage

reserved2noThis work addresses the problem of robust fitting of geometric structures to noisy data corrupted by outliers. An extension of J-linkage (called T-linkage) is presented and elaborated. T-linkage improves the preference analysis implemented by J-linkage in term of performances and robustness, considering both the representation and the segmentation steps. A strategy to reject outliers and to estimate the inlier threshold is proposed, resulting in a versatile tool, suitable for multi-model fitting “in the wild”. Experiments demonstrate that our methods perform better than J-linkage on simulated data, and compare favorably with state-of-the-art methods on public domain real datasets.mixedMagri L.; Fusiello A.Magri, L.; Fusiello, A

Multiple structure recovery with maximum coverage

We present a general framework for geometric model fitting based on a set coverage formulation that caters for intersecting structures and outliers in a simple and principled manner. The multi-model fitting problem is formulated in terms of the optimization of a consensus-based global cost function, which allows to sidestep the pitfalls of preference approaches based on clustering and to avoid the difficult trade-off between data fidelity and complexity of other optimization formulations. Two especially appealing characteristics of this method are the ease with which it can be implemented and its modularity with respect to the solver and to the sampling strategy. Few intelligible parameters need to be set and tuned, namely the inlier threshold and the number of desired models. The summary of the experiments is that our method compares favourably with its competitors overall, and it is always either the best performer or almost on par with the best performer in specific scenarios

Multiple structure recovery via robust preference analysis

2noThis paper address the extraction of multiple models from outlier-contaminated data by exploiting preference analysis and low rank approximation. First points are represented in the preference space, then Robust PCA (Principal Component Analysis) and Symmetric NMF (Non negative Matrix Factorization) are used to break the multi-model fitting problem into many single-model problems, which in turn are tackled with an approach inspired to MSAC (M-estimator SAmple Consensus) coupled with a model-specific scale estimate. Experimental validation on public, real data-sets demonstrates that our method compares favorably with the state of the art.openopenMagri, Luca; Fusiello, AndreaMagri, Luca; Fusiello, Andre

Stability, sensitivity and optimisation of chaotic acoustic oscillations

In an acoustic cavity with a heat source, such as a flame in a gas turbine, the thermal energy of the heat source can be converted into acoustic energy, which may generate a loud oscillation. If uncontrolled, these nonlinear acoustic oscillations, also known as thermoacoustic instabilities, can cause large vibrations up to structural failure. Numerical and experimental studies showed that thermoacoustic oscillations can be chaotic. It is not yet known, however, how to minimise such chaotic oscillations. We propose a strategy to analyse and minimise chaotic acoustic oscillations, for which traditional stability and sensitivity methods break down. We investigate the acoustics of a nonlinear heat source in an acoustic resonator. First, we propose covariant Lyapunov analysis as a tool to calculate the stability of chaotic acoustics making connections with eigenvalue and Floquet analyses. We show that covariant Lyapunov analysis is the most general flow stability tool. Second, covariant Lyapunov vector analysis is applied to a chaotic system. The time-averaged acoustic energy is investigated by varying the heat-source parameters. Thermoacoustic systems can display both hyperbolic and non-hyperbolic chaos, as well as discontinuities in the time-averaged acoustic energy. Third, we embed sensitivities of the time-averaged acoustic energy in an optimisation routine. This procedure achieves a significant reduction in acoustic energy and identifies the bifurcations to chaos. The analysis and methods proposed enable the reduction of chaotic oscillations in thermoacoustic systems by optimal passive control. The techniques presented can be used in other unsteady fluid-dynamics problems with virtually no modification