Related papers: The spatiotemporal coupling in delay-coordinates d…
Dynamic mode decomposition (DMD) is a data-driven method for estimating the dynamics of a discrete dynamical system. This paper proposes a tensor-based approach to DMD for applications in which the states can be viewed as tensors.…
The conventional modal analysis techniques face difficulties in handling nonstationary phenomena, such as transient, nonperiodic, or intermittent phenomena. This paper presents a variational mode decomposition--based nonstationary coherent…
Delay-coordinate mapping is an effective and widely used technique for reconstructing and analyzing the dynamics of a nonlinear system based on time-series outputs. The efficacy of delay-coordinate mapping has long been supported by Takens'…
Modern time series are usually composed of multiple oscillatory components, with time-varying frequency and amplitude contaminated by noise. The signal processing mission is further challenged if each component has an oscillatory pattern,…
Recently there has been significant interest in measuring time-varying functional connectivity (TVC) between different brain regions using resting-state functional magnetic resonance imaging (rs-fMRI) data. One way to assess the…
A data-driven analysis method known as dynamic mode decomposition (DMD) approximates the linear Koopman operator on projected space. In the spirit of Johnson-Lindenstrauss Lemma, we will use random projection to estimate the DMD modes in…
The correlation and extraction of coherent structures from a turbulent flow is a principle objective of data-driven modal decomposition techniques. The Conditional space-time Proper Orthogonal Decomposition (CPOD) offers insight into…
Experimental Modal Analysis (EMA) has been widely used to identify structural dynamic properties, including natural frequencies, damping ratios, and mode shapes, for structural integrity assessment. The Poly-reference Least Squares Complex…
Time-delay embeddings and dimensionality reduction are powerful techniques for discovering effective coordinate systems to represent the dynamics of physical systems. Recently, it has been shown that models identified by dynamic mode…
This paper presents unifying results for subspace identification (SID) and dynamic mode decomposition (DMD) for autonomous dynamical systems. We observe that SID seeks to solve an optimization problem to estimate an extended observability…
We introduce the map representation of a time-delayed system in the presence of delay time modulation. Based on this representation, we find the method by which to analyze the stability of that kind of a system. We apply this method to a…
Making accurate forecasts for a complex system is a challenge in various practical applications. The major difficulty in solving such a problem concerns nonlinear spatiotemporal dynamics with time-varying characteristics. Takens' delay…
Understanding nonlinear dynamical systems (NLDSs) is challenging in a variety of engineering and scientific fields. Dynamic mode decomposition (DMD), which is a numerical algorithm for the spectral analysis of Koopman operators, has been…
Koopman operator theory shows how nonlinear dynamical systems can be represented as an infinite-dimensional, linear operator acting on a Hilbert space of observables of the system. However, determining the relevant modes and eigenvalues of…
We study the convergence of Hermitian Dynamic Mode Decomposition (DMD) to the spectral properties of self-adjoint Koopman operators. Hermitian DMD is a data-driven method that approximates the Koopman operator associated with an unknown…
In order to guarantee the safety of payload, crew, and structures, ships must exhibit good seakeeping, maneuverability, and structural-response performance, also when they operate in adverse weather conditions. In this context, the…
Compared to real-valued signals, complex-valued signals provide a unique and intuitive representation of the phase of real physical systems and processes, which holds fundamental significance and is widely applied across many fields of…
With numerous distributed energy resources (DERs) integrated into the distribution networks (DNs), the coordinated economic dispatch (C-ED) is essential for the integrated transmission and distribution grids. For large scale power grids,…
Real-world systems can be strongly influenced by time delays occurring in self-coupling interactions, due to unavoidable finite signal propagation velocities. When the delays become significantly long, complicated high-dimensional phenomena…
Time-delay embedding is an increasingly popular starting point for data-driven reduced-order modeling efforts. In particular, the singular value decomposition (SVD) of a block Hankel matrix formed from successive delay embeddings of the…