An alternative method to study cross-flow instabilities based on high order dynamic mode decomposition

Clainche, Soledad Le; Han, Zhonghua; Ferrer, Esteban

doi:10.1063/1.5110697

Cited by 26 publications

(6 citation statements)

References 47 publications

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“…HODMD is an extension of the well known technique, in the field of fluid dynamics, dynamic mode decomposition (DMD) [34], generally used for the analysis of complex data modeling non-linear dynamical systems, solving different applications (e.g, [42], [43], [44]). Similarly to DMD, HODMD decomposes spatio-temporal data into a number of modes, each mode related to a frequency, growth rate and amplitude, as presented in the following DMD expansion…”

Section: Methodsmentioning

confidence: 99%

“…( 11), then the method is applied iteratively over this data reconstruction until the number of HOSVD modes is the same between two consecutive iterations. The algorithm has been validated and successfully tested in several applications (see [42], [43], [44]). More details about the algorithm can be found in [41].…”

Section: Multidimensional Higher Order Dynamic Mode Decompositionmentioning

confidence: 99%

“…In this work, we explore a new method that, to the authors knowledge has not yet been used in the field of medical imaging before: the Higher Order Dynamic Mode Decomposition (HODMD) technique [40]. As has been demonstrated in ( [41], [42], [43], [44]), the HODMD method is a more robust and accurate version of classical DMD, suitable for the analysis of complex signals and non-linear dynamical systems. The enhanced performance of HODMD, solidly grounded on mathematics and computer science principles, justifies our interest in its application for the analysis of medical images.…”

Section: Introductionmentioning

confidence: 99%

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Higher Order Dynamic Mode Decomposition: from Fluid Dynamics to Heart Disease Analysis

Groun¹,

Villalba-Orero²,

Lara‐Pezzi³

et al. 2022

Preprint

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In this work, we study in detail the performance of Higher Order Dynamic Mode Decomposition (HODMD) technique when applied to echocardiography images. HODMD is a data-driven method generally used in fluid dynamics and in the analysis of complex non-linear dynamical systems modeling several complex industrial applications. In this paper we apply HODMD, for the first time to the authors knowledge, for patterns recognition in echocardiography, specifically, echocardiography data taken from several mice, either in healthy conditions or afflicted by different cardiac diseases. We exploit the HODMD advantageous properties in dynamics identification and noise cleaning to identify the relevant frequencies and coherent patterns for each one of the diseases. The echocardiography datasets consist of video loops taken with respect to a long axis view (LAX) and a short axis view (SAX), where each video loop covers at least three cardiac cycles, formed by (at most) 300 frames each (called snapshots). The proposed algorithm, using only a maximum quantity of 200 snapshots, was able to capture two branches of frequencies, representing the heart rate and respiratory rate. Additionally, the algorithm provided a number of modes, which represent the dominant features and patterns in the different echocardiography images, also related to the heart and the lung. Six datasets were analyzed: one echocardiography taken from a healthy subject and five different sets of echocardiography taken from subjects with either Diabetic Cardiomyopathy, Obesity, SFSR4 Hypertrophy, TAC Hypertrophy or Myocardial Infarction. The results show that HODMD is robust and a suitable tool to identify characteristic patterns able to classify the different pathologies studied.

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Section: Methodsmentioning

confidence: 99%

Section: Multidimensional Higher Order Dynamic Mode Decompositionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Higher Order Dynamic Mode Decomposition: from Fluid Dynamics to Heart Disease Analysis

Groun¹,

Villalba-Orero²,

Lara‐Pezzi³

et al. 2022

Preprint

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show abstract

“…Higher Order Dynamic Mode Decomposition (HODMD) [23] is a data driven method used in fluid dynamics to identify flow patterns. The latter represents an extension of Dynamic Mode Decomposition (DMD) [17] used for the analysis of complex flow [29], noisy experiments [30] or turbulent flows [31]. HODMD decomposes data equispaced in time as an expansion of Fourier-like DMD modes as…”

Section: Higher Order Dynamic Mode Decompositionmentioning

confidence: 99%

Hierarchical Higher-Order Dynamic Mode Decomposition for Clustering and Feature Selection

Corrochano¹,

D’Alessio²,

Parente³

et al. 2023

Preprint

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In this work, a new algorithm based on the application of higher-order dynamic mode decomposition (HODMD) is proposed for feature selection and variables clustering in reacting flow simulations. The hierarchical HODMD (h-HODMD) performs a reduction of the model order, followed by the iterative selection of the best reconstructed variables thus creating clusters of features which can eventually be associated with distinct dynamical phenomena. Firstly, h-HODMD is combined with different data pre-processing techniques to assess their influence on the algorithm in terms of reconstruction error. Afterwards, the proposed algorithm is applied to analyze three different databases obtained from numerical simulations of a non-premixed co-flow methane flame, and its performance are compared with the standard HODMD in terms of the achievable degree of reduction as well as in terms of reconstruction error. Two detailed kinetic mechanisms are used for the simulations, and different time horizons are considered to assess the influence of the number of considered cycles on the accuracy of the reduced model. Results show that h-HODMD improves the reconstruction for all the variables when compared to the standard HODMD algorithm. This condition is achieved thanks to the iterative variables' clustering: finding dedicated modes for a specific group of features does in fact lead to a better reconstruction of the dynamics with respect to the case when the same (global) modes are used to reconstruct the entire set of variables.Finally, the clusters of variables found by means of h-HODMD are analyzed, and it is observed that the algorithm can group, in an unsupervised fashion, chemical species whose behavior is also consistent from a kinetic point of view. In fact, radicals responsible for fast chemistry processes (such as propagation and branching reactions) are grouped together, and the same happens for nitrogen oxides (whose chemical timescales are instead order of magnitudes slower). The possibility to identify and to describe correctly the main dynamics with reduced order models for these two classes of chemical species is extremely important for practical applications in combustion. In fact, it allows for the possibility to formulate inexpensive reduced dynamical models for predicting flames liftoff, as well as for identifying the formation of local extinction and blowout conditions, to formulate accurate reduced models to describe the formation of pollutants in aviation, and for control purposes.

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“…DMD has been used to study various fluid flow problems [33][34][35][36][37][38]. However, there are very few studies that have used DMD in complex cardiovascular flows.…”

Section: Introductionmentioning

confidence: 99%

Data-Driven Pulsatile Blood Flow Physics with Dynamic Mode Decomposition

Habibi

Dawson

Arzani

2020

Fluids

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Dynamic mode decomposition (DMD) is a purely data-driven and equation-free technique for reduced-order modeling of dynamical systems and fluid flow. DMD finds a best fit linear reduced-order model that represents any given spatiotemporal data. In DMD, each mode evolves with a fixed frequency and therefore DMD modes represent physically meaningful structures that are ranked based on their dynamics. The application of DMD to patient-specific cardiovascular flow data is challenging. First, the input flow rate is unsteady and pulsatile. Second, the flow topology can change significantly in different phases of the cardiac cycle. Finally, blood flow in patient-specific diseased arteries is complex and often chaotic. The objective of this study was to overcome these challenges using our proposed multistage dynamic mode decomposition with control (mDMDc) method and use this technique to study patient-specific blood flow physics. The inlet flow rate was considered as the controller input to the systems. Blood flow data were divided into different stages based on the inlet flow waveform and DMD with control was applied to each stage. The system was augmented to consider both velocity and wall shear stress (WSS) vector data, and therefore study the interaction between the coherent structures in velocity and near-wall coherent structures in WSS. First, it was shown that DMD modes can exactly represent the analytical Womersley solution for incompressible pulsatile flow in tubes. Next, our method was applied to image-based coronary artery stenosis and cerebral aneurysm models where complex blood flow patterns are anticipated. The flow patterns were studied using the mDMDc modes and the reconstruction errors were reported. Our augmented mDMDc framework could capture coherent structures in velocity and WSS with a fewer number of modes compared to the traditional DMD approach and demonstrated a close connection between the velocity and WSS modes.

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An alternative method to study cross-flow instabilities based on high order dynamic mode decomposition

Cited by 26 publications

References 47 publications

Higher Order Dynamic Mode Decomposition: from Fluid Dynamics to Heart Disease Analysis

Higher Order Dynamic Mode Decomposition: from Fluid Dynamics to Heart Disease Analysis

Hierarchical Higher-Order Dynamic Mode Decomposition for Clustering and Feature Selection

Data-Driven Pulsatile Blood Flow Physics with Dynamic Mode Decomposition

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