53,103 research outputs found
Model reduction of network systems with structure preservation:Graph clustering and balanced truncation
A framework of complex networks can adequately describe a wide class of complex systems composing of many interacting subsystems. A large number of subsystems and their high-dimensional dynamics often result in the high complexity of a network system, which poses intense challenges to system management and operation. The main motivation of this research is to establish suitable model reduction techniques that generate simplified models to capture the essential features of the complex network systems. Two approaches are developed in this thesis to reduce the complexity of a network system with structure preservation. The first one is based on graph clustering, which aims to partition a network into several nonoverlapping clusters and merges all the vertices in each cluster into a single vertex. A reduced-order model is then formulated via the framework of the Petrov-Galerkin projection. This thesis discusses the applications of the clustering-based model reduction methods for second-order networks, controlled power networks, multi-agent systems and directed networks in Part I. The second approach in Part II extends the balanced truncation method for control systems to the simplification of dynamical networks. For networked linear passive systems, the proposed method reduces interconnection structures of a network and the dynamics of each subsystem via a unified framework. Additionally, an approach is developed for the reduction of nonlinear Lur’e networks, showing that the dimension of each nonlinear subsystem can be reduced while preserving the robust synchronization property of the overall network
Machine Learning for Fluid Mechanics
The field of fluid mechanics is rapidly advancing, driven by unprecedented
volumes of data from field measurements, experiments and large-scale
simulations at multiple spatiotemporal scales. Machine learning offers a wealth
of techniques to extract information from data that could be translated into
knowledge about the underlying fluid mechanics. Moreover, machine learning
algorithms can augment domain knowledge and automate tasks related to flow
control and optimization. This article presents an overview of past history,
current developments, and emerging opportunities of machine learning for fluid
mechanics. It outlines fundamental machine learning methodologies and discusses
their uses for understanding, modeling, optimizing, and controlling fluid
flows. The strengths and limitations of these methods are addressed from the
perspective of scientific inquiry that considers data as an inherent part of
modeling, experimentation, and simulation. Machine learning provides a powerful
information processing framework that can enrich, and possibly even transform,
current lines of fluid mechanics research and industrial applications.Comment: To appear in the Annual Reviews of Fluid Mechanics, 202
Reduction of Second-Order Network Systems with Structure Preservation
This paper proposes a general framework for structure-preserving model
reduction of a secondorder network system based on graph clustering. In this
approach, vertex dynamics are captured by the transfer functions from inputs to
individual states, and the dissimilarities of vertices are quantified by the
H2-norms of the transfer function discrepancies. A greedy hierarchical
clustering algorithm is proposed to place those vertices with similar dynamics
into same clusters. Then, the reduced-order model is generated by the
Petrov-Galerkin method, where the projection is formed by the characteristic
matrix of the resulting network clustering. It is shown that the simplified
system preserves an interconnection structure, i.e., it can be again
interpreted as a second-order system evolving over a reduced graph.
Furthermore, this paper generalizes the definition of network controllability
Gramian to second-order network systems. Based on it, we develop an efficient
method to compute H2-norms and derive the approximation error between the
full-order and reduced-order models. Finally, the approach is illustrated by
the example of a small-world network
Cluster-based feedback control of turbulent post-stall separated flows
We propose a novel model-free self-learning cluster-based control strategy
for general nonlinear feedback flow control technique, benchmarked for
high-fidelity simulations of post-stall separated flows over an airfoil. The
present approach partitions the flow trajectories (force measurements) into
clusters, which correspond to characteristic coarse-grained phases in a
low-dimensional feature space. A feedback control law is then sought for each
cluster state through iterative evaluation and downhill simplex search to
minimize power consumption in flight. Unsupervised clustering of the flow
trajectories for in-situ learning and optimization of coarse-grained control
laws are implemented in an automated manner as key enablers. Re-routing the
flow trajectories, the optimized control laws shift the cluster populations to
the aerodynamically favorable states. Utilizing limited number of sensor
measurements for both clustering and optimization, these feedback laws were
determined in only iterations. The objective of the present work is not
necessarily to suppress flow separation but to minimize the desired cost
function to achieve enhanced aerodynamic performance. The present control
approach is applied to the control of two and three-dimensional separated flows
over a NACA 0012 airfoil with large-eddy simulations at an angle of attack of
, Reynolds number and free-stream Mach number . The optimized control laws effectively minimize the flight power
consumption enabling the flows to reach a low-drag state. The present work aims
to address the challenges associated with adaptive feedback control design for
turbulent separated flows at moderate Reynolds number.Comment: 32 pages, 18 figure
Structure-preserving model reduction of physical network systems by clustering
In this paper, we establish a method for model order reduction of a certain
class of physical network systems. The proposed method is based on clustering
of the vertices of the underlying graph, and yields a reduced order model
within the same class. To capture the physical properties of the network, we
allow for weights associated to both the edges as well as the vertices of the
graph. We extend the notion of almost equitable partitions to this class of
graphs. Consequently, an explicit model reduction error expression in the sense
of H2-norm is provided for clustering arising from almost equitable partitions.
Finally the method is extended to second-order systems
- …