Modal Dominancy Analysis Based on Modal Contribution to Frequency Response Function -Norm

Rahrovani, Sadegh; Vakilzadeh, Majid Khorsand; Abrahamsson, Thomas

doi:10.1016/j.ymssp.2014.03.003

Cited by 9 publications

(7 citation statements)

References 17 publications

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“…For this purpose, several methods have been proposed in the literature which have been comprehensively reviewed in Antoulas et al (2001). One of these approaches is modal dominancy analysis based on modal contributions Rahrovani et al (2014) which is discussed more in Section 4.2. In this case, the reduced model…”

Section: Problem Formulationmentioning

confidence: 99%

“…be the transfer function of the error system resulting from deflation of the i th modal coordinate fromΣ. Then, the contribution of the i th modal coordinate to the input-output relation of the system in the H 2 sense can be defined as Rahrovani et al (2014),…”

Section: Modal Dominancy Analysis Based On Modal Contribution Into Symentioning

confidence: 99%

“…The main contribution of this paper is developing a reduced-order PCE-based surrogate model for linear dynamic systems when they are presented in SS form. For this purpose, the PCE-based surrogate model is developed in conjunction with modal dominancy analysis Rahrovani et al (2014) in order to reduce the model order, if required, while preserving the model structure. Computational efficiency is another beneficial feature of the modal dominancy analysis which is of our special interest in this work.…”

Section: Introductionmentioning

confidence: 99%

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Reduced order surrogate modeling technique for linear dynamic systems

Yaghoubi

Rahrovani

Nahvi

et al. 2018

Mechanical Systems and Signal Processing

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The availability of reduced order models can greatly decrease the computational costs needed for modeling, identification and design of real-world structural systems. However, since these systems are usually employed with some uncertain parameters, the approximant must provide a good accuracy for a range of stochastic parameters variations. The derivation of such reduced order models are addressed in this paper. The proposed method consists of a polynomial chaos expansion (PCE)-based state-space model together with a PCE-based modal dominancy analysis to reduce the model order. To solve the issue of spatial aliasing during mode tracking step, a new correlation metric is utilized. The performance of the presented method is validated through four illustrative benchmarks: a simple mass-spring system with four Degrees Of Freedom (DOF), a 2-DOF system exhibiting a mode veering phenomenon, a 6-DOF system with large parameter space and a cantilever Timoshenko beam resembling large-scale systems.

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Section: Problem Formulationmentioning

confidence: 99%

Section: Modal Dominancy Analysis Based On Modal Contribution Into Symentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Reduced order surrogate modeling technique for linear dynamic systems

Yaghoubi

Rahrovani

Nahvi

et al. 2018

Mechanical Systems and Signal Processing

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“…A selection criteria was proposed for the truncation of eigenmodes which minimizes the H 2norm of the error associated to modal truncation method [23].…”

Section: Introductionmentioning

confidence: 99%

An Error Bound for Low Order Approximation of Dynamical Systems Subjected to Initial Conditions

Maciel

Barbosa

2018

Tend. Mat. Apl. Comput.

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In recent years, a great effort has been taken focused on the development of reduced order modeling techniques of dynamical systems. This necessity is pushed by the requirement for efficient numerical techniques for simulations of dynamical systems arising from structural dynamics, controller design, circuit simulation, fluid dynamics and micro electromechanical systems.We introduce a method to calculate the minimum upper $\mathcal{L}_2$ error bound of a linear time invaritant reduced order model considering any possible unitary initial conditions (IC). As a consequence, the proposed method calculates the unitary IC vector which leads to the maximum $\mathcal{L}_2$ norm of the error. Based on this error bound, it is discussed the capacity of a reduced order system to approximate the free transient response in the worst case scenario.

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“…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. The reader may also refer to the works of Kerfriden et al for discussion on the link between POD and Newton‐Krylov algorithm, and other works for discussion on error estimation of projection‐based MOR.…”

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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Modal Dominancy Analysis Based on Modal Contribution to Frequency Response Function -Norm

Cited by 9 publications

References 17 publications

Reduced order surrogate modeling technique for linear dynamic systems

Reduced order surrogate modeling technique for linear dynamic systems

An Error Bound for Low Order Approximation of Dynamical Systems Subjected to Initial Conditions

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

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