Local modal participation analysis of nonlinear systems using Poincaré linearization

Hamzi, Boumediene; Abed, Eyad H.

doi:10.1007/s11071-019-05363-1

Cited by 16 publications

(7 citation statements)

References 27 publications

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“…Within the same context, some studies have utilized the same definition to determine the eigenvector matrix [33,34], whereas, in other instances, researchers defined a more convenient mathematical form and made an indistinct use of the term [35][36][37][38][39][40]. However, it is to be noted that the definition of modal participation has an associated dichotomy [17] with it, especially in time-invariant linear systems, where it is observed that there is interchangeability between the measurement of participation of the state in modes [41] and that of participation of modes in states. This is solved using an averaging technique of the initial conditions [17] with a symmetric uncertainty.…”

Section: Introductionmentioning

confidence: 99%

A Comparative Analysis of the Response-Tracking Techniques in Aerospace Dynamic Systems Using Modal Participation Factors

Nieto,

Babu,

ElSayed

et al. 2023

Applied Mechanics

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Mechanical structural systems are subject to multiple dynamic disturbances during service. While several possible scenarios can be examined to determine their design loading conditions, only a relatively small set of such scenarios is considered critical. Therefore, only such particular deterministic set of critical load cases is commonly employed for the structural design and optimization. Nevertheless, during the design and optimization stages, the mass and stiffness distributions of such assemblies vary, and, in consequence, their dynamic response also varies. Thus, it is important to consider the variations in the dynamic loading conditions during the design-and-optimization cycles. This paper studies the modal participation factors at length and proposes an alternative to the current point-wise treatment of the dynamic equations of motion of flexible bodies during design optimization. First, the most relevant-to-structural-dynamics definitions available in the literature are reviewed in depth. Second, the analysis of those definitions that have the potential to be adopted as point-wise constraint equations during structural optimization is extended. Finally, a proof of concept is presented to demonstrate the usability of each definition, followed by a case study in which the potential advantages of the proposed extended analysis are shown.

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Section: Introductionmentioning

confidence: 99%

A Comparative Analysis of the Response-Tracking Techniques in Aerospace Dynamic Systems Using Modal Participation Factors

Nieto,

Babu,

ElSayed

et al. 2023

Applied Mechanics

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“…Therefore, cheaper numerical approximations using "adequate-fidelity" models are usually acceptable [2]. In this regard, reduced order modeling offers a viable technique to address systems characterized by underlying patterns [3][4][5][6][7][8][9][10][11][12]. This is especially true for fluid flows dominated by coherent structures (e.g., atmospheric and oceanic flows) [13][14][15][16][17][18][19][20][21].…”

Section: Introductionmentioning

confidence: 99%

A long short-term memory embedding for hybrid uplifted reduced order models

Ahmed

San

Rasheed

et al. 2020

Physica D: Nonlinear Phenomena

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In this paper, we introduce an uplifted reduced order modeling (UROM) approach through the integration of standard projection based methods with long short-term memory (LSTM) embedding. Our approach has three modeling layers or components. In the first layer, we utilize an intrusive projection approach to model dynamics represented by the largest modes. The second layer consists of an LSTM model to account for residuals beyond this truncation. This closure layer refers to the process of including the residual effect of the discarded modes into the dynamics of the largest scales. However, the feasibility of generating a low rank approximation tails off for higher Kolmogorov n-width systems due to the underlying nonlinear processes. The third uplifting layer, called superresolution, addresses this limited representation issue by expanding the span into a larger number of modes utilizing the versatility of LSTM. Therefore, our model integrates a physics-based projection model with a memory embedded LSTM closure and an LSTM based super-resolution model. In several applications, we exploit the use of Grassmann manifold to construct UROM for unseen conditions. We performed numerical experiments by using the Burgers and Navier-Stokes equations with quadratic nonlinearity. Our results show robustness of the proposed approach in building reduced order models for parameterized systems and confirm the improved trade-off between accuracy and efficiency.Keywords Hybrid analysis and modeling · Supervised machine learning · Long short-term memory · Model reduction · Galerkin projection · Grassmann manifold.Reduced order models (ROMs) have shown great success for prototypical problems in different fields. In particular, Galerkin projection (GP) coupled with proper orthogonal decomposition (POD) capability to extract the most energetic modes has been used to build ROMs for linear and nonlinear systems [22][23][24][25][26][27][28][29]. These ROMs preserve sufficient arXiv:1912.06756v1 [physics.flu-dyn]

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“…However, ROMs are limited in how they handle nonlinear dependence and perform poorly for complex physical phenomena, which are inherently multiscale in space and time [16,17,18,19]. Researchers continue to search for efficient and reliable ROM techniques for such transient nonlinear systems [20,21,22,23,24,6]. The identification of a reduced basis to ensure a compressed representation that is minimally lossy is a core component of most ROM development strategies (some examples include [25,26,27]).…”

Section: Introductionmentioning

confidence: 99%

Reduced-order modeling of advection-dominated systems with recurrent neural networks and convolutional autoencoders

Maulik,

Lusch,

Balaprakash

2020

Preprint

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A common strategy for the dimensionality reduction of nonlinear partial differential equations relies on the use of the proper orthogonal decomposition (POD) to identify a reduced subspace and the Galerkin projection for evolving dynamics in this reduced space. However, advection-dominated PDEs are represented poorly by this methodology since the process of truncation discards important interactions between higher-order modes during time evolution. In this study, we demonstrate that an encoding using convolutional autoencoders (CAEs) followed by a reduced-space time evolution by recurrent neural networks overcomes this limitation effectively. We demonstrate that a truncated system of only two latent-space dimensions can reproduce a sharp advecting shock profile for the viscous Burgers equation with very low viscosities, and a twelve-dimensional latent space can recreate the evolution of the inviscid shallow water equations. Additionally, the proposed framework is extended to a parametric reduced-order model by directly embedding parametric information into the latent space to detect trends in system evolution. Our results show that these advection-dominated systems are more amenable to low-dimensional encoding and time evolution by a CAE and recurrent neural network combination than the POD Galerkin technique.

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Local modal participation analysis of nonlinear systems using Poincaré linearization

Cited by 16 publications

References 27 publications

A Comparative Analysis of the Response-Tracking Techniques in Aerospace Dynamic Systems Using Modal Participation Factors

A Comparative Analysis of the Response-Tracking Techniques in Aerospace Dynamic Systems Using Modal Participation Factors

A long short-term memory embedding for hybrid uplifted reduced order models

Reduced-order modeling of advection-dominated systems with recurrent neural networks and convolutional autoencoders

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