An adaptive sampling procedure for parametric model order reduction by matrix interpolation

Ying Liu,Guang Meng,Ningke Tong,Hongguang Li,Huanyu Du

doi:10.1177/1461348419851595

Abstract

An adaptive sampling approach for parametric model order reduction by matrix interpolation is developed. This approach is based on an efficient exploration of the candidate parameter sets and identification of the points with maximum errors. An error indicator is defined and used for fast evaluation of the parameter points in the configuration space. Furthermore, the exact error of the model with maximum error indicator is calculated to determine whether the adaptive sampling procedure reaches a desired error tolerance. To improve the accuracy, the orthogonal eigenvectors are utilized as the reduced-order basis. The proposed adaptive sampling procedure is then illustrated by application in the moving coil of electrical-dynamic shaker. It is shown that the new method can sample the parameter space adaptively and efficiently with the assurance of the resulting reduced-order models’ accuracy.

Highlights

Finite element method (FEM) has become a common approach to simulate the behavior of complex physical systems
Model order reduction (MOR) methods have been employed to obtain a low-dimensional but accurate approximation of the large-scale dynamic system by projecting the high-dimensional model (HDM) onto a low-dimensional subspace described by an ROB
It is inefficient and impractical to reduce the model order repeatedly at different parameter values. This has promoted the study of parametric model order reduction (PMOR) technique, which aims to generate a parametric ROM approximating the original full-order dynamical system with high fidelity over the range of parameters

Summary

Introduction

Finite element method (FEM) has become a common approach to simulate the behavior of complex physical systems. (16) just cost little time and can be solved more In this way, we can obtain the reduced matrices and basis vectors and calculate the order-reduced response xÃr ðpÞ and eigenvector UÃr ðpÞ by the use of KÃr ðpÞ; MÃr ðpÞ; DÃr ðpÞ; FÃr ðpÞ at this specific parameter value. We can obtain the reduced matrices and basis vectors and calculate the order-reduced response xÃr ðpÞ and eigenvector UÃr ðpÞ by the use of KÃr ðpÞ; MÃr ðpÞ; DÃr ðpÞ; FÃr ðpÞ at this specific parameter value They are projected back to the original space to get the results expressed in real physical coordinate by the formula xðpÞ 1⁄4 VÃðpÞ Á xÃr ðpÞ (17). Input: Parameter domain X, sampling points numbers N Output: Compatible ROMs (HKi ; HMi ; HDi ; FÃri; VÃi )

Uniformly select a set of N candidate parameters

Choose the ROB V1 as the reference basis

19. Compute the exact error of modal shape vectors e3ðumaxÞ

Findings

Conclusions