Data-Assisted Non-Intrusive Model Reduction for Forced Nonlinear Finite Elements Models

Spectral submanifolds (SSMs) have emerged as accurate and predictive model reduction tools for dynamical systems defined either by equations or data sets. While finite-elements (FE) models belong to the equation-based class of problems, their implementations in commercial solvers do not generally provide information on the nonlinearities required for the analytical construction of SSMs. Here, we overcome this limitation by developing a data-driven construction of SSM-reduced models from a small number of unforced FE simulations. We then use these models to predict the forced response of the FE model without performing any costly forced simulation. This approach yields accurate forced response predictions even in the presence of internal resonances or quasi-periodic forcing, as we illustrate on several FE models. Our examples range from simple structures, such as beams and shells, to more complex geometries, such as a micro-resonator model containing more than a million degrees of freedom. In the latter case, our algorithm predicts accurate forced response curves in a small fraction of the time it takes to verify just a few points on those curves by simulating the full forced-response

Data-Driven Spectral Submanifold Reduction for Nonlinear Optimal Control of High-Dimensional Robots

Modeling and control of high-dimensional, nonlinear robotic systems remains a challenging task. While various model- and learning-based approaches have been proposed to address these challenges, they broadly lack generalizability to different control tasks and rarely preserve the structure of the dynamics. In this work, we propose a new, data-driven approach for extracting low-dimensional models from data using Spectral Submanifold Reduction (SSMR). In contrast to other data-driven methods which fit dynamical models to training trajectories, we identify the dynamics on generic, low-dimensional attractors embedded in the full phase space of the robotic system. This allows us to obtain computationally-tractable models for control which preserve the system's dominant dynamics and better track trajectories radically different from the training data. We demonstrate the superior performance and generalizability of SSMR in dynamic trajectory tracking tasks vis-a-vis the state of the art, including Koopman operator-based approaches.Comment: 9 pages, 4 figures, 1 table, Submission to International Conference for Robotics and Automation 202

LPDs – «Linked to penumbra» discharges or EEG correlate of excitotoxicity: A review based hypothesis

Periodic lateralized epileptiform discharges (PLEDs) or lateralized periodic discharges (LPDs) are a well-known variant of pathological EEG activity. However, the mechanisms underpinning the appearance of this pattern are not completely understood. The heterogeneity of the features derived from LPDs patterns, and the wide range of pathological conditions in which they occur, raise a question about the unifying mechanisms underlying these phenomena. This paper reassesses the current opinion surrounding LPDs which considers glutamate excitotoxicity to be the primary pathophysiological basis, and the penumbral region to be the main morphological substrate. Arguments in favour of this hypothesis are presented, with interpretations supported by evidence from recent literature involving clinical and experimental data. Presently, no single hypothesis places considerable emphasis on the pathochemical properties of LPDs, which are implicitly meaningful towards better understanding of the clinical significance of this pattern. © 2020 Elsevier B.V.This work was supported by the Russian Science Foundation [grant number 16-18-10371 ]

A Geometric Approach to Nonlinear Mechanical Vibrations: from Analytic to Data-driven Methods

This doctoral thesis devises analytical and data-driven methods for the analysis of nonlinear vibrations in mechanical systems, potentially with a large number of degrees of freedom. Modern challenges in engineering require deeper understanding of nonlinear oscillations in mechanical systems, as well as extracting data-driven models for their predictions. In the first part of this thesis, the focus is set on analytical models, with forced-damped nonlinear mechanical systems viewed as small perturbations from their energy-preserving counterpart. Indeed, weakly damped mechanical systems under small periodic forcing tend to showcase periodic response in a close vicinity of some periodic orbits of their conservative limit. Specifically, amplitude frequency plots for the conservative limit have frequently been observed, both numerically and experimentally, to serve as backbone curves for the near-resonance peaks of the forced response. A systematic mathematical analysis is then derived, allowing to predict which members of conservative periodic orbit families will survive in the forced-damped response. Moreover, the method is not limited to predicting existence, but can also forecast stability type of vibrations in the forced response. Not only does this method provide a rigorous analytical tool, but it also finds precise mathematical conditions under which approximate numerical and experimental approaches, such as energy balance and force appropriation, are justified. The second part of this thesis looks at oscillatory dynamics from a data-driven perspective. The objective is to determine reduced-order models from trajectory data of dynamical systems. Based on the theory of spectral submanifolds, a method is developed for simultaneous dimensionality reduction and identification of the dynamics in normal form. In contrast with other data-driven modeling techniques, the normal form of the dynamics offers valuable insights and is capable of predictions when small perturbations, such as external forcing, are added to systems. Moreover, there are, in principle, no restrictions of dimensionality or constraints on the states observed in the trajectory data. The algorithm based on this approach automatically detects the appropriate normal form for a given set of trajectories, thereby providing an intelligent, unsupervised learning strategy for dynamical systems. The accuracy and the validity of the method is demonstrated on different examples, featuring data from numerical simulations and physical experiments

A real-time, MPC-based Motion Cueing Algorithm with Look-Ahead and driver characterization

The use of dynamic driving simulators is nowadays common practice in the automotive industry. The effectiveness of such devices is strongly related to their capabilities of well reproducing the driving sensations, hence it is crucial that the motion control strategies generate both realistic and feasible inputs to the platform. Such strategies are called Motion Cueing Algorithms (MCAs). Model Predictive Control (MPC) has been successfully applied to MCAs, being well suited to solve constrained optimal control problems. However, the predictive aspect of the algorithm has not been exploited effectively yet, mainly due to the hard real-time requirement when using a significantly long prediction window. In this paper, a real time implementation of the so called Look-Ahead (LA) strat- egy is presented, that is based on an effective manipulation of the reference along the pre- diction horizon, and on an on-line switching policy to a Non-Look-Ahead strategy when the expected driver behavior is not reliable. An optimal tuning of the MCA is computed by means of a multi-objective optimization, where both performance improvement due to the prediction exploitation, and robustness to varying driver behavior are taken into account. Finally, a characterization of the driver skill level is proposed and validated in experimental environment

Dynamics-based machine learning for nonlinearizable phenomena. Data-driven reduced models on spectral submanifolds

ISSN:1557-9573ISSN:0036-143

Fast data-driven model reduction for nonlinear dynamical systems

We present a fast method for nonlinear data-driven model reduction of dynamical systems onto their slowest nonresonant spectral submanifolds (SSMs). While the recently proposed reduced-order modeling method SSMLearn uses implicit optimization to fit a spectral submanifold to data and reduce the dynamics to a normal form, here, we reformulate these tasks as explicit problems under certain simplifying assumptions. In addition, we provide a novel method for timelag selection when delay-embedding signals from multimodal systems. We show that our alternative approach to data-driven SSM construction yields accurate and sparse rigorous models for essentially nonlinear (or non-linearizable) dynamics on both numerical and experimental datasets. Aside from a major reduction in complexity, our new method allows an increase in the training data dimensionality by several orders of magnitude. This promises to extend data-driven, SSM-based modeling to problems with hundreds of thousands of degrees of freedom.ISSN:0924-090XISSN:1573-269

A motion cueing algorithm with look-Ahead and driver characterization: Application to vertical car dynamics

Driving simulators are nowadays a widely used tool in the automotive industry. In particular, the need for safe and repeatable conditions in automated driving testing is now defining a new challenge: to extend the use of the tool to nonprofessional drivers. Quality of the motion control strategies in generating both realistic and feasible inputs to the driver is therefore, more than ever, a crucial aspect. The motion strategies are implemented in the so-called motion cueing algorithms (MCAs). A recently proposed effective approach to MCA is based on model predictive control (MPC), as it is well suited to solve constrained optimal control problems and to take advantage of models of the human sensing system. However, the predictive aspect of the algorithm has not been exploited yet, due to the hard real-time requirement when using long prediction windows. In this paper, a real-time implementation of an MPC-based MCA with predictive feature is presented, endowed with an on-line switching policy to a nonpredictive algorithm when the expected driver behavior is considered unreliable. The motion action based on the actual driver behavior and the expected one are considered in the same procedure, thus fully exploiting the availability of a perceptive model. An optimal tuning procedure is also proposed, based on a multiobjective optimization, where both performance improvement due to the prediction exploitation, and robustness to varying driver behaviour are considered. Finally, a characterization of the driver skill level is proposed and validated in an experimental environment for the specific case of the vertical DOF