Related papers: Data-driven Nonlinear Model Reduction to Spectral …
To fully understand, analyze, and determine the behavior of dynamical systems, it is crucial to identify their intrinsic modal coordinates. In nonlinear dynamical systems, this task is challenging as the modal transformation based on the…
Multiple time scale stochastic dynamical systems are ubiquitous in science and engineering, and the reduction of such systems and their models to only their slow components is often essential for scientific computation and further analysis.…
The theory of spectral submanifolds (SSMs) has emerged as a powerful tool for constructing rigorous, low-dimensional reduced-order models (ROMs) of high-dimensional nonlinear mechanical systems. A direct computation of SSMs requires…
Dynamical systems are often subject to algebraic constraints in conjunction to their governing ordinary differential equations. In particular, multibody systems are commonly subject to configuration constraints that define kinematic…
We present a data-driven approach to efficiently approximate nonlinear transient dynamics in solid-state systems. Our proposed machine-learning model combines a dimensionality reduction stage with a nonlinear vector autoregression scheme.…
We propose a unified approach to nonlinear modal analysis in dissipative oscillatory systems. This approach eliminates conflicting definitions, covers both autonomous and time-dependent systems, and provides exact mathematical existence,…
We present a novel method for learning reduced-order models of dynamical systems using nonlinear manifolds. First, we learn the manifold by identifying nonlinear structure in the data through a general representation learning problem. The…
In this paper, we present a data-driven controller design method for continuous-time nonlinear systems, using no model knowledge but only measured data affected by noise. While most existing approaches focus on systems with polynomial…
Delay embedding is a commonly employed technique in a wide range of data-driven model reduction methods for dynamical systems, including the Dynamic mode decomposition (DMD), the Hankel alternative view of the Koopman decomposition (HAVOK),…
We introduce a nonlinear stochastic model reduction technique for high-dimensional stochastic dynamical systems that have a low-dimensional invariant effective manifold with slow dynamics, and high-dimensional, large fast modes. Given only…
This paper presents a new data-driven control for multi-input, multi-output nonlinear systems with partially unknown dynamics and bounded disturbances. Since exact nonlinearity cancellation is not feasible with unknown disturbances, we…
Bolted joints can exhibit nonsmooth and significantly nonlinear dynamics. Finite Element Models (FEMs) of this phenomenon require fine spatial discretizations, inclusion of nonlinear contact and friction laws, as well as geometric…
This paper presents an indirect data-driven output feedback controller synthesis for nonlinear systems, leveraging Structured State-space Models (SSMs) as surrogate models. SSMs have emerged as a compelling alternative in modelling…
Artificial muscles are essential for compliant musculoskeletal robotics but complicate control due to nonlinear multiphysics dynamics. Hydraulically amplified electrostatic (HASEL) actuators, a class of soft artificial muscles, offer high…
We show how spectral submanifold theory can be used to provide analytic predictions for the response of periodically forced multi-degree-of-freedom mechanical systems. These predictions include an explicit criterion for the existence of…
This paper presents a novel non-linear model reduction method: Probabilistic Manifold Decomposition (PMD), which provides a powerful framework for constructing non-intrusive reduced-order models (ROMs) by embedding a high-dimensional system…
Data-Driven Computational Mechanics is a novel computing paradigm that enables the transition from standard data-starved approaches to modern data-rich approaches. At this early stage of development, one can distinguish two mainstream…
For general nonlinear mechanical systems, we derive closed-form, reduced-order models up to cubic order based on rigorous invariant manifold results. For conservative systems, the reduction is based on Lyapunov Subcenter Manifold (LSM)…
This paper aims at reviewing nonlinear methods for model order reduction of structures with geometric nonlinearity, with a special emphasis on the techniques based on invariant manifold theory. Nonlinear methods differ from linear based…
Model reduction of high-dimensional dynamical systems alleviates computational burdens faced in various tasks from design optimization to model predictive control. One popular model reduction approach is based on projecting the governing…