Reduced Order Models for Systems with Disparate Spatial and Temporal Scales

Ilbeigi, Shahab; Chelidze, David

doi:10.1007/978-3-319-30084-9_41

Cited by 10 publications

(7 citation statements)

References 34 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%

“…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%

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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“…The similitude laws were defined by applying the classical modal approach and quantifying the inequalities in the structural dynamic response. Ilbeigi and Chelidze (2016a) developed a method to design reduced scale models for an euler-bernoulli beam and later they extended their approach to study reduced scale models for systems with disparate spatial and temporal scales (Ilbeigi and Chelidze, 2016b).…”

Section: Introductionmentioning

confidence: 99%

Similitude analysis of thin-walled composite I-beams for subcomponent testing of wind turbine blades

et al. 2017

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In this study, the I-beam structure of a utility-scale blade is used as the basis for the design of a small-scale subcomponent emulating the same type of structural element of a utility-scale wind turbine blade. Governing equations for the bending of a shear deformable thin-walled composite I-beam are considered. Similitude theory is applied to derive the corresponding scaling laws. Accuracy of the derived scaling laws in predicting the strain and displacement fields of the full-scale I-beam is considered as a design criterion for small-scale I-beams. Both complete and partial similarity cases are discussed. A novel approach is proposed to design partially similar scaled I-beams with totally different layups from those of the full-scale I-beam. Using the proposed technique, scaled-down composite I-beams are designed that predict the strain and displacement fields of their full-scale parent I-beam with very good accuracy.

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Reduced Order Models for Systems with Disparate Spatial and Temporal Scales

Cited by 10 publications

References 34 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

Similitude analysis of thin-walled composite I-beams for subcomponent testing of wind turbine blades

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