48 research outputs found
Structure-Preserving Model Reduction of Physical Network Systems
This paper considers physical network systems where the energy storage is naturally associated to the nodes of the graph, while the edges of the graph correspond to static couplings. The first sections deal with the linear case, covering examples such as mass-damper and hydraulic systems, which have a structure that is similar to symmetric consensus dynamics. The last section is concerned with a specific class of nonlinear physical network systems; namely detailed-balanced chemical reaction networks governed by mass action kinetics. In both cases, linear and nonlinear, the structure of the dynamics is similar, and is based on a weighted Laplacian matrix, together with an energy function capturing the energy storage at the nodes. We discuss two methods for structure-preserving model reduction. The first one is clustering; aggregating the nodes of the underlying graph to obtain a reduced graph. The second approach is based on neglecting the energy storage at some of the nodes, and subsequently eliminating those nodes (called Kron reduction).</p
Approximating a flexible beam model in the Loewner framework
The paper develops the Loewner approach for data-based modeling of a linear
distributed-parameter system. This approach is applied to a controlled flexible
beam model coupled with a spring-mass system. The original dynamical system is
described by the Euler-Bernoulli partial differential equation with the
interface conditions due to the oscillations of the lumped part. The transfer
function of this model is computed analytically, and its sampled values are
then used for the data-driven design of a reduced model. A family of
approximate realizations of the corresponding input-output map is constructed
within the Loewner framework. It is shown that the proposed finite-dimensional
approximations are able to capture the key properties of the original dynamics
over a given range of observed frequencies. The robustness of the method to
noisy data is also investigated.Comment: This is a preprint version of the paper submitted to the 2023
European Control Conference (ECC
Data-Driven Reduced Model Construction with Time-Domain Loewner Models
This work presents a data-driven nonintrusive model reduction approach for large-scale time-dependent systems with linear state dependence. Traditionally, model reduction is performed in an intrusive projection-based framework, where the operators of the full model are required either explicitly in an assembled form or implicitly through a routine that returns the action of the operators on a vector. Our nonintrusive approach constructs reduced models directly from trajectories of the inputs and outputs of the full model, without requiring the full-model operators. These trajectories are generated by running a simulation of the full model; our method then infers frequency-response data from these simulated time-domain trajectories and uses the data-driven Loewner framework to derive a reduced model. Only a single time-domain simulation is required to derive a reduced model with the new data-driven nonintrusive approach. We demonstrate our model reduction method on several benchmark examples and a finite element model of a cantilever beam; our approach recovers the classical Loewner reduced models and, for these problems, yields high-quality reduced models despite treating the full model as a black box. Key words: data-driven model reduction, nonintrusive model reduction, projection-based
reduced models, Loewner framework, black-box models, dynamical systems, partial differential equationsNational Science Foundation (U.S.) (Award 1507488