Subscribe to the gold package and get unlimited access to Shamra Academy
Register a new userReduced-Order Modeling of Large-Scale Network Systems
350
0
0.0
(
0
)
Ask ChatGPT about the research
No Arabic abstract
Large-scale network systems describe a wide class of complex dynamical systems composed of many interacting subsystems. A large number of subsystems and their high-dimensional dynamics often result in highly complex topology and dynamics, which pose challenges to network management and operation. This chapter provides an overview of reduced-order modeling techniques that are developed recently for simplifying complex dynamical networks. In the first part, clustering-based approaches are reviewed, which aim to reduce the network scale, i.e., find a simplified network with a fewer number of nodes. The second part presents structure-preserving methods based on generalized balanced truncation, which can reduce the dynamics of each subsystem.
rate research
Read More
This paper studies reduced-order modeling of dynamic networks with strongly connected topology. Given a graph clustering of an original complex network, we construct a quotient graph with less number of vertices, where the edge weights are parameters to be determined. The model of the reduced network is thereby obtained with parameterized system matrices, and then an edge weighting procedure is devised, aiming to select an optimal set of edge weights that minimizes the approximation error between the original and the reduced-order network models in terms of H2-norm. The effectiveness of the proposed method is illustrated by a numerical example.
We consider the classic School Bus Routing Problem (SBRP) with a multi modal generalization, where students are either picked up by a fleet of school buses or transported by an alternate transportation mode, subject to a set of constraints. The constraints that are typically imposed for school buses are a maximum fleet size, a maximum walking distance to a pickup point and a maximum commute time for each student. This is a special case of the Vehicle Routing Problem (VRP) with a common destination. We propose a decomposition approach for solving this problem based on the existing notion of a shareability network, which has been used recently in the context of dynamic ridepooling problems. Moreover, we simplify the problem by introducing the connection between the SBRP and the weighted set covering problem (WSCP). To scale this method to large-scale problem instances, we propose i) a node compression method for the shareability network based decomposition approach, and ii) heuristic-based edge compression techniques that perform well in practice. We show that the compressed problem leads to an Integer Linear Programming (ILP) of reduced dimensionality that can be solved efficiently using off-the-shelf ILP solvers. Numerical experiments on small-scale, large-scale and benchmark networks are used to evaluate the performance of our approach and compare it to existing large-scale SBRP solving techniques.
Considering the use of dynamical systems in practical applications, often only limited regions in the time or frequency domain are of interest. Therefor, it usually pays off to compute local approximations of the used dynamical systems in the frequency and time domain. In this paper, we consider a structure-preserving extension of the frequency- and time-limited balanced truncation methods to second-order dynamical systems. We give a full overview about the first-order limited balanced truncation methods and extend those methods to second-order systems by using the different second-order balanced truncation formulas from the literature. Also, we present numerical methods for solving the arising large-scale sparse matrix equations and give numerical modifications to deal with the problematic case of second-order systems. The results are then illustrated on three numerical examples.
There exist many ways to stabilize an infinite-dimensional linear autonomous control systems when it is possible. Anyway, finding an exponentially stabilizing feedback control that is as simple as possible may be a challenge. The Riccati theory provides a nice feedback control but may be computationally demanding when considering a discretization scheme. Proper Orthogonal Decomposition (POD) offers a popular way to reduce large-dimensional systems. In the present paper, we establish that, under appropriate spectral assumptions, an exponentially stabilizing feedback Riccati control designed from a POD finite-dimensional approximation of the system stabilizes as well the infinite-dimensional control system.
In the construction of reduced-order models for dynamical systems, linear projection methods, such as proper orthogonal decompositions, are commonly employed. However, for many dynamical systems, the lower dimensional representation of the state space can most accurately be described by a textit{nonlinear} manifold. Previous research has shown that deep learning can provide an efficient method for performing nonlinear dimension reduction, though they are dependent on the availability of training data and are often problem-specific citep[see][]{carlberg_ca}. Here, we utilize randomized training data to create and train convolutional autoencoders that perform nonlinear dimension reduction for the wave and Kuramoto-Shivasinsky equations. Moreover, we present training methods that are independent of full-order model samples and use the manifold least-squares Petrov-Galerkin projection method to define a reduced-order model for the heat, wave, and Kuramoto-Shivasinsky equations using the same autoencoder.
Log in to be able to interact and post comments
comments
Fetching comments
Sign in to be able to follow your search criteria
