A comparative study on global wavelet and polynomial models for nonlinear regime-switching systems

A comparative study of wavelet and polynomial models for non-linear Regime-Switching (RS) systems is carried out. RS systems, considered in this study, are a class of severely non-linear systems, which exhibit abrupt changes or dramatic breaks in behaviour, due to RS caused by associated events. Both wavelet and polynomial models are used to describe discontinuous dynamical systems, where it is assumed that no a priori information about the inherent model structure and the relative regime switches of the underlying dynamics is known, but only observed input-output data are available. An Orthogonal Least Squares (OLS) algorithm interfered with by an Error Reduction Ratio (ERR) index and regularised by an Approximate Minimum Description Length (AMDL) criterion, is used to construct parsimonious wavelet and polynomial models. The performance of the resultant wavelet models is compared with that of the relative polynomial models, by inspecting the predictive capability of the associated representations. It is shown from numerical results that wavelet models are superior to polynomial models, in respect of generalisation properties, for describing severely non-linear RS systems

Hierarchical Decomposition of Nonlinear Dynamics and Control for System Identification and Policy Distillation

The control of nonlinear dynamical systems remains a major challenge for autonomous agents. Current trends in reinforcement learning (RL) focus on complex representations of dynamics and policies, which have yielded impressive results in solving a variety of hard control tasks. However, this new sophistication and extremely over-parameterized models have come with the cost of an overall reduction in our ability to interpret the resulting policies. In this paper, we take inspiration from the control community and apply the principles of hybrid switching systems in order to break down complex dynamics into simpler components. We exploit the rich representational power of probabilistic graphical models and derive an expectation-maximization (EM) algorithm for learning a sequence model to capture the temporal structure of the data and automatically decompose nonlinear dynamics into stochastic switching linear dynamical systems. Moreover, we show how this framework of switching models enables extracting hierarchies of Markovian and auto-regressive locally linear controllers from nonlinear experts in an imitation learning scenario.Comment: 2nd Annual Conference on Learning for Dynamics and Contro

Operational modal analysis with non stationnary inputs

Operational modal analysis (OMA) techniques enable the use of in-situ and uncontrolled vibrations to be used to lead modal analysis of structures. In reality operational vibrations are a combination of numerous excitations sources that are much more complex than a random white noise or a harmonic. Numerous OMA techniques exist like SSI, NExT, FDD and BSS. All these methods are based on the fundamental hypothesis that the input or force applied to the structure to be analyzed is a stationary white noise. For some applications this hypothesis is reasonable. However in numerous situations, the analyzed structure is subject to harmonic and transient forces. Numerous methods and research has enabled to develop methods that are robust to such harmonic contributions. To enable OMA during pressure oscillations in solid rocket boosters, the authors propose to consider transient and harmonic inputs no longer as parasites but as the main force applied to the structure that must be analyzed. This is the case during pressure oscillations in rocket boosters. We propose the use of phase analysis adapted to a transient context to conduct operational modal analysis under a harmonic transient input. This time-based novel OMA method will be exposed. The theoretical developments and algorithmic implementations are exposed. First tests have been conducted on laboratory single degree of freedom setup to validate this new OMA technique and are reported here

A steady-state approach to trend/cycle decomposition of regime-switching processes

In this paper, we present a new approach to trend/cycle decomposition under the assumption that the trend is the permanent component and the cycle is the transitory component of an integrated time series. The permanent component is defined as the steady-state level of the series, a definition that has exploitable forecasting implications useful for identification. We operationalize the steady-state approach for regime-switching processes and we use generated data from such processes to demonstrate the advantages of the steady-state approach over alternative approaches to trend/cycle decomposition. We then apply the steady-state approach to estimate the trend and cycle of U.S. real GDP implied by a regime-switching forecasting model. Our findings portray a very different picture of the business cycle than implied by more traditional methods.Time-series analysis ; Business cycles

Correlation regimes in fluctuations of fatigue crack growth

This paper investigates correlation properties of fluctuations in fatigue crack growth of polycrystalline materials, such as ductile alloys, that are commonly encountered in structures and machinery components of complex electromechanical systems. The model of crack damage measure indicates that the fluctuations of fatigue crack growth are characterized by strong correlation patterns within short time scales and are uncorrelated for larger time scales. The two correlation regimes suggest that the 7075-T6 aluminum alloy, analyzed in this paper, is characterized by a micro-structure which is responsible for an intermittent correlated dynamics of fatigue crack growth within a certain scale. The constitutive equations of the damage measure are built upon the physics of fracture mechanics and are substantiated by Karhunen-Lo\`{e}ve decomposition of fatigue test data. Statistical orthogonality of the estimated damage measure and the resulting estimation error is demonstrated in a Hilbert space setting.Comment: 30 pages, 8 figures, to appear in Physica

Identification of vortexes obstructing the dynamo mechanism in laboratory experiments

The magnetohydrodynamic dynamo effect explains the generation of self-sustained magnetic fields in electrically conducting flows, especially in geo- and astrophysical environments. Yet the details of this mechanism are still unknown, e.g., how and to which extent the geometry, the fluid topology, the forcing mechanism and the turbulence can have a negative effect on this process. We report on numerical simulations carried out in spherical geometry, analyzing the predicted velocity flow with the so-called Singular Value Decomposition, a powerful technique that allows us to precisely identify vortexes in the flow which would be difficult to characterize with conventional spectral methods. We then quantify the contribution of these vortexes to the growth rate of the magnetic energy in the system. We identify an axisymmetric vortex, whose rotational direction changes periodically in time, and whose dynamics are decoupled from those of the large scale background flow, is detrimental for the dynamo effect. A comparison with experiments is carried out, showing that similar dynamics were observed in cylindrical geometry. These previously unexpected eddies, which impede the dynamo effect, offer an explanation for the experimental difficulties in attaining a dynamo in spherical geometry.Comment: 25 pages, 12 figures, submitted to Physics of Fluid