arXiv subjects

Yevgeniya Filanova

Publications and source records attributed to Yevgeniya Filanova.

4 recordsLinked to original sources

arXiv2025

Reduced-Order Inference with Structure-Preserving Parametrization for Bending and Rotating Systems

Mechanical systems are often characterized only by their response to certain loads known from experiments or simulations. The obtained data can be used for various purposes: system analysis, design of mathematical models, or construction of reduced-order models for further simulations under different loading conditions. The use of data for reduced-order modeling is an important developing research direction, especially when the high-dimensional system operators are unknown and their low-dimensional approximation is required for accurate but fast simulations. Our goal is to obtain the low-dimensional surrogate model from the available input signal and deformation trajectory data, capturing the correct system behavior for the basic deformation cases, namely bending and rotation, which are present in almost every complex mechanical system. In this work, we propose a methodology to infer the system operators by solving a nonlinear unconstrained optimization problem. The methodology is based on the operator inference approach for second-order systems and includes a parametrization of the unknown operators that preserves their symmetric positive definite or skew-symmetric structure. We demonstrate the performance of the novel approach for three numerical examples that are used to simulate basic bending and rotating.

math.DS↗

arXiv2025

Application of operator inference to reduced-order modeling of constrained mechanical systems

Constrained mechanical systems occur in many applications, such as modeling of robots and other multibody systems. In this case, the motion is governed by a system of differential-algebraic equations (DAE), often with large and sparse system matrices. The problem dimension strongly influences the effectiveness of simulations for system analysis, optimization, and control, given limited computational resources. Therefore, we aim to obtain a simplified surrogate model with a few degrees of freedom that is able to accurately represent the motion and other important properties of the original high-dimensional DAE model. Classical model reduction methods intrusively exploit the system matrices to construct the projection of the high-fidelity model onto a low-dimensional subspace. In practice, the dynamical equations are frequently an inaccessible part of proprietary software products. In this work, we show an application of the non-intrusive operator inference (OpInf) method to DAE systems of index 2 and 3. Considering the fact that for proper DAEs there exists an ODE realization on the so-called hidden manifold, the OpInf optimization problem directly provides the underlying ODE representation of the given DAE system in the reduced subspace. A significant advantage is that only the DAE solution snapshots in a compressed form are required for identification of the reduced system matrices. Stability and interpretability of the reduced-order model is guaranteed by enforcing the symmetric positive definite structure of the system operators using semidefinite programming. The numerical results demonstrate the implementation of the proposed methodology for different examples of constrained mechanical systems, tested for various loading conditions.

math.DS↗

arXiv2025

Inference of Substructured Reduced-Order Models for Dynamic Contact from Contact-free Simulations

In this paper, we propose an operator-inference-based reduction approach for contact problems, leveraging snapshots from simulations without active contact. Contact problems are solved using adjoint methods, by switching to the dual system, where the corresponding Lagrange multipliers represent the contact pressure. The Craig-Bampton-like substructuring method is incorporated into the inference process to provide the reduced system matrices and the coupling of the contact and interior nodes. The maximum possible set of contact nodes must be known a priori. Characteristic properties of the inferred matrices, such as symmetry and positive definiteness, are enforced by appending additional constraints to the underlying least-squares problem. The resulting dual system, which forms a linear complementarity problem, is well-defined and can be effectively solved using methods such as Lemke's algorithm. The performance of the proposed method is validated on three-dimensional finite element models.

math.NA↗

arXiv2022

An Operator Inference Oriented Approach for Mechanical Systems

Model-order reduction techniques allow the construction of low-dimensional surrogate models that can accelerate engineering design processes. Often, these techniques are intrusive, meaning that they require direct access to underlying high-fidelity models. Accessing these models is laborious or may not even be possible in some cases. Therefore, there is an interest in developing non-intrusive model reduction techniques to construct low-dimensional models directly from simulated or experimental data. In this work, we focus on a recent data-driven methodology, namely operator inference, that aims at inferring the reduced operators using only trajectories of high-fidelity models. We present an extension of operator inference for mechanical systems, preserving the second-order structure. We also study a particular case in which complete information about the external forces is available. In this formulation, the reduced operators having certain properties inspired by the original system matrices are enforced by adding constraints to the optimization problem. We illustrate the presented methodology using three numerical examples.

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