scholarly journals A technique for non-intrusive greedy piecewise-rational model reduction of frequency response problems over wide frequency bands

2022 ◽  
Vol 12 (1) ◽  
Author(s):  
Davide Pradovera ◽  
Fabio Nobile
Keyword(s):  
Frequency Response ◽  
Order Reduction ◽  
Rational Interpolation ◽  
Frequency Range ◽  
Model Order ◽  
Adaptive Selection ◽  
Rational Models ◽  
Numerical Instabilities ◽  
Large Frequency ◽  
Selection Of

AbstractIn the field of model order reduction for frequency response problems, the minimal rational interpolation (MRI) method has been shown to be quite effective. However, in some cases, numerical instabilities may arise when applying MRI to build a surrogate model over a large frequency range, spanning several orders of magnitude. We propose a strategy to overcome these instabilities, replacing an unstable global MRI surrogate with a union of stable local rational models. The partitioning of the frequency range into local frequency sub-ranges is performed automatically and adaptively, and is complemented by a (greedy) adaptive selection of the sampled frequencies over each sub-range. We verify the effectiveness of our proposed method with two numerical examples.

Effective Modal Derivatives Based Reduction Method for Geometrically Nonlinear Structures

2011 ◽  
Author(s):  
Paolo Tiso
Keyword(s):  
Reduction Method ◽  
Order Reduction ◽  
Second Order ◽  
Geometrically Nonlinear ◽  
Vibration Modes ◽  
Model Order ◽  
Modal Derivatives ◽  
Dynamics Problems ◽  
Modal Truncation ◽  
Selection Of

Effective Model Order Reduction (MOR) for geometrically nonlinear structural dynamics problems can be achieved by projecting the Finite Element (FE) equations on a basis constituted by a set of vibration modes and associated second order modal derivatives. However, the number of modal derivatives generated by such approach is quadratic with respect to the number of chosen vibration modes, thus quickly making the dimension of the reduction basis large. We show that the selection of the most important second order modes can be based on the convergence of the underlying linear modal truncation approximation. Given a certain time dependency of the load, this method allows to select the most significant modal derivatives set before computing it.

scholarly journals Model order reduction of thermo-mechanical models with parametric convective boundary conditions: focus on machine tools

2020 ◽  
Author(s):  
Pablo Hernández-Becerro ◽  
Daniel Spescha ◽  
Konrad Wegener
Keyword(s):  
Boundary Conditions ◽  
Machine Tools ◽  
Model Order Reduction ◽  
Order Reduction ◽  
Convective Boundary Conditions ◽  
Frequency Range ◽  
Order Model ◽  
Convective Boundary ◽  
Model Order ◽  
Reduced Order

Abstract Thermo-mechanical finite element (FE) models predict the thermal behavior of machine tools and the associated mechanical deviations. However, one disadvantage is their high computational expense, linked to the evaluation of the large systems of differential equations. Therefore, projection-based model order reduction (MOR) methods are required in order to create efficient surrogate models. This paper presents a parametric MOR method for weakly coupled thermo-mechanical FE models of machine tools and other similar mechatronic systems. This work proposes a reduction method, Krylov Modal Subspace (KMS), and a theoretical bound of the reduction error. The developed method addresses the parametric dependency of the convective boundary conditions using the concept of system bilinearization. The reduced-order model reproduces the thermal response of the original FE model in the frequency range of interest for any value of the parameters describing the convective boundary conditions. Additionally, this paper investigates the coupling between the reduced-order thermal system and the mechanical response. A numerical example shows that the reduced-order model captures the response of the original system in the frequency range of interest.

scholarly journals Non-intrusive double-greedy parametric model reduction by interpolation of frequency-domain rational surrogates

2021 ◽  
Author(s):  
Fabio Nobile ◽  
Davide Pradovera
Keyword(s):  
Parameter Space ◽  
Model Order Reduction ◽  
Optimization Problem ◽  
Order Reduction ◽  
Rational Interpolation ◽  
Sparse Grids ◽  
Parametric Model ◽  
High Dimensional ◽  
Model Order ◽  
Interpolation Strategy

We propose a model order reduction approach for non-intrusive surrogate modeling of parametric dynamical systems. The reduced model over the whole parameter space is built by combining surrogates in frequency only, built at few selected values of the parameters. This, in particular, requires matching the respective poles by solving an optimization problem. If the frequency surrogates are constructed by a suitable rational interpolation strategy, frequency and parameters can both be sampled in an adaptive fashion. This, in general, yields frequency surrogates with different numbers of poles, a situation addressed by our proposed algorithm. Moreover, we explain how our method can be applied even in high-dimensional settings, by employing locally-refined sparse grids in parameter space to weaken the curse of dimensionality. Numerical examples are used to showcase the effectiveness of the method, and to highlight some of its limitations in dealing with unbalanced pole matching, as well as with a large number of parameters.

scholarly journals Implementation of MOIDS Algorithm for Optimal Parameter Selection of SFPT for Modern Radars

2020 ◽  
Vol 8 (5) ◽  
pp. 4093-4099
Keyword(s):  
Optimal Parameter ◽  
Three Dimensional ◽  
Frequency Range ◽  
Range Resolution ◽  
Narrowband Signal ◽  
Stepped Frequency ◽  
Pareto Fronts ◽  
Large Frequency ◽  
Selection Of ◽  
Frequency Pulse

Modern radars require signals of the large frequency range to attain relatively greater range resolution. Frequency stepping is the technique to convert the narrowband signal, i.e., a train of pulses into a wideband signal to achieve high accuracy in range resolution measurements. Due to the cause of constant step in frequency of successive pulses, grating lobes appeared when the period of pulse multiplied by step in frequency exceeds unity as is needed in modern radars. Hence to achieve the best resolution, grating lobes height, sidelobes level, and mainlobe width have to be minimum. In this paper an attempt has been made to diminish grating lobes, minimize sidelobes and reduce mainlobe width using MOIDSA to find the parameters of Stepped Frequency Pulse Train (SFPT) mechanism. The compromise between various lobes is obtained by using three dimensional Pareto fronts for different ranges of SFPT parameters.

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