Model Order Reduction of Nonlinear Euler-Bernoulli Beam

Ilbeigi, Shahab; Chelidze, David

doi:10.1007/978-3-319-15221-9_34

Cited by 12 publications

(11 citation statements)

References 22 publications

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“…This concept was further used in Refs. [31] and [32]. The common theme noted earlier is that SOD-based ROM produces more robust and lower dimensional models than PODbased ROM.…”

Section: Introductionmentioning

confidence: 94%

On the Inclusion of Time Derivatives of State Variables for Parametric Model Order Reduction for a Beam on a Nonlinear Foundation

Segala

2017

Journal of Dynamic Systems, Measurement, and Control

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The computational burden of parameter exploration of nonlinear dynamical systems can become a costly exercise. A computationally efficient lower dimensional representation of a higher dimensional dynamical system is achieved by developing a reduced order model (ROM). Proper orthogonal decomposition (POD) is usually the preferred method in projection-based nonlinear model reduction. POD seeks to find a set of projection modes that maximize the variance between the full-scale state variables and its reduced representation through a constrained optimization problem. Here, we investigate the benefits of an ROM, both qualitatively and quantitatively, by the inclusion of time derivatives of the state variables. In one formulation, time derivatives are introduced as a constraint in the optimization formulation—smooth orthogonal decomposition (SOD). In another formulation, time derivatives are concatenated with the state variables to increase the size of the state space in the optimization formulation—extended state proper orthogonal decomposition (ESPOD). The three methods (POD, SOD, and ESPOD) are compared using a periodically, periodically forced with measurement noise, and a randomly forced beam on a nonlinear foundation. For both the periodically and randomly forced cases, SOD yields a robust subspace for model reduction that is insensitive to changes in forcing amplitudes and input energy. In addition, SOD offers continual improvement as the size of the dimension of the subspace increases. In the periodically forced case where the ROM is developed with noisy data, ESPOD outperforms both SOD and POD and captures the dynamics of the desired system using a lower dimensional model.

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“…This concept was further used in Refs. [31] and [32]. The common theme noted earlier is that SOD-based ROM produces more robust and lower dimensional models than PODbased ROM.…”

Section: Introductionmentioning

confidence: 94%

On the Inclusion of Time Derivatives of State Variables for Parametric Model Order Reduction for a Beam on a Nonlinear Foundation

Segala

2017

Journal of Dynamic Systems, Measurement, and Control

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“…In this paper, we use smooth orthogonal decomposition (SOD) as a new tool for model order reduction (MOR) for nonlinear control systems. Our method is categorized under Galerkin projection–based reduced order modeling, which projects a high‐dimensional nonlinear system onto an appropriate linear subspace to yield a lower‐dimensional system.…”

Section: Introductionmentioning

confidence: 99%

“…Within the realm of complex dynamical systems, reduced order modeling is being extensively used to reduce the redundant computations and data storage requirements . We place the majority of reduced order modeling methods for a dynamical system into two main categories.…”

Section: Introductionmentioning

confidence: 99%

“…The methodologies for obtaining low‐dimensional subspaces are, although not limited to, linear normal modes (LNMs), proper orthogonal decomposition (POD) (also known as singular value decomposition, principal component analysis, or Karhunen‐Loève expansion), and SOD . In addition, Krylov subspace projections, Hankel norm approximations, truncated balance realizations, and a recently developed Bayesian approach are to be mentioned.…”

Section: Introductionmentioning

confidence: 99%

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Persistent model order reduction for complex dynamical systems using smooth orthogonal decomposition

Ilbeigi

Chelidze

2017

Mechanical Systems and Signal Processing

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A new approach to model order reduction of nonlinear control systems is aimed at developing persistent reduced order models (ROMs) that are robust to the changes in system's energy level. A multivariate analysis method called smooth orthogonal decomposition (SOD) is used to identify the dynamically relevant modal structures of the control system. The identified SOD subspaces are used to develop persistent ROMs. Performance of the resultant SOD-based ROM is compared with proper orthogonal decomposition (POD)-based ROM by evaluating their robustness to the changes in system's energy level. Results show that SOD-based ROMs are valid for a relatively wider range of the nonlinear control system's energy when compared with POD-based models. In addition, the SOD-based ROMs show considerably faster computations compared to the POD-based ROMs of same order. For the considered dynamic system, SOD provides more effective reduction in dimension and complexity compared to POD. KEYWORDS nonlinear control systems, nonlinear model reduction, proper orthogonal decomposition, smooth orthogonal decomposition, subspace robustness Int J Robust Nonlinear Control. 2018;28:4367-4381.wileyonlinelibrary.com/journal/rnc

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“…Hence, model order reduction is only meaningful in terms of repetitive simulations. In the past, both methods were applied to dynamical systems by several authors, and the interested reader is referred to [3,5,6,10,11,13,17] and references therein.…”

Section: Introductionmentioning

confidence: 99%

A generalized constraint reduction method for reduced order MBS models

2016

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In this paper we deal with the problem of ill-conditioned reduced order models in the context of redundant formulated nonlinear multibody system dynamics. Proper Orthogonal Decomposition is applied to reduce the physical coordinates, resulting in an overdetermined system. As the original set of algebraic constraint equations becomes, at least partially, redundant, we propose a generalized constraint reduction method, based on the ideas of Principal Component Analysis, to identify a unique and well-conditioned set of reduced constraint equations. Finally, a combination of reduced physical coordinates and reduced constraint coordinates are applied to one purely rigid and one partly flexible largescale model, pointing out method strengths but also applicability limitations.

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Model Order Reduction of Nonlinear Euler-Bernoulli Beam

Cited by 12 publications

References 22 publications

On the Inclusion of Time Derivatives of State Variables for Parametric Model Order Reduction for a Beam on a Nonlinear Foundation

On the Inclusion of Time Derivatives of State Variables for Parametric Model Order Reduction for a Beam on a Nonlinear Foundation

Persistent model order reduction for complex dynamical systems using smooth orthogonal decomposition

A generalized constraint reduction method for reduced order MBS models

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