Article
Engineering, Multidisciplinary
Stefania Fresca, Andrea Manzoni
Summary: DL-ROMs are proposed to overcome limitations of conventional ROMs, but require expensive training. The proposed method combines POD and multi-fidelity pretraining to avoid the costly training stage of DL-ROMs.
COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING
(2022)
Article
Engineering, Aerospace
Daitong Wei, Hongkun Li, Yugang Chen, Xinwei Zhao, Jiannan Dong, Zhenfang Fan
Summary: This study proposes a frequency domain-based model reduction method for the dynamic model reduction problem of mistuned blisks, which improves calculation efficiency while ensuring accuracy. The results show that the method outperforms other reduction methods in terms of modal characteristics and response characteristics.
AEROSPACE SCIENCE AND TECHNOLOGY
(2022)
Article
Mathematics, Interdisciplinary Applications
Orestis Friderikos, Marc Olive, Emmanuel Baranger, Dimitris Sagris, Constantine David
Summary: This work introduces a novel non-intrusive space-time POD basis interpolation scheme, defining ROM spatial and temporal basis curves on compact Stiefel manifolds and incorporating oriented SVD to avoid the bottleneck associated with standard POD interpolation. By applying the proposed method to a specific metal forming process, correlations between the ST POD models and high-fidelity FEM counterpart simulations are demonstrated, showcasing the potential for near real-time parametric simulations using offline computed ROM POD databases.
COMPUTATIONAL MECHANICS
(2021)
Article
Automation & Control Systems
Yu Kawano, Jacquelien M. A. Scherpen
Summary: This paper introduces an empirical balanced truncation method for nonlinear systems with constant input vector fields. By defining differential reachability and observability Gramians, it demonstrates the possibility of computing these values along a fixed state trajectory without solving nonlinear partial differential equations. The development of an approximation method based on trajectories of the original nonlinear systems is also presented.
Article
Mechanics
Jie Hou, Alfa Heryudono, Wenzhen Huang, Jun Li
Summary: This article presents the use of the proper generalized decomposition (PGD) method for parametric solutions of full stress fields in heterogeneous materials. PGD enables accurate prediction of the full stress fields including all localized stress concentration patterns.
Article
Engineering, Mechanical
Giorgio Gobat, Andrea Opreni, Stefania Fresca, Andrea Manzoni, Attilio Frangi
Summary: In this study, the Proper Orthogonal Decomposition (POD) method is applied to efficiently simulate the nonlinear behavior of Micro-Electro-Mechanical-Systems (MEMS) in various scenarios involving geometric and electrostatic nonlinearities. The POD method reduces the polynomial terms up to cubic order associated with large displacements through exact projection onto a low-dimensional subspace spanned by the Proper Orthogonal Modes (POMs). Electrostatic nonlinearities are modeled using precomputed manifolds based on the amplitudes of the electrically active POMs. The reliability of the assumed linear trial space is extensively tested in challenging applications such as resonators, micromirrors, and arches with internal resonances. Comparisons are made between the periodic orbits computed with POD and the invariant manifold approximated with Direct Normal Form approaches, highlighting the reliability and remarkable predictive capabilities of the technique, particularly in terms of estimating the frequency response function of selected output quantities of interest.
MECHANICAL SYSTEMS AND SIGNAL PROCESSING
(2022)
Article
Mathematics, Applied
Li Wang, Zhen Miao, Yao-Lin Jiang
Summary: This paper studies and analyzes new fast computing methods for partial differential equations with variable coefficients, including two kinds of two-sided Krylov enhanced proper orthogonal decomposition (KPOD) methods. The spatial discrete scheme of an advection-diffusion equation is obtained by Galerkin approximation. Then, algorithms based on two-sided KPOD approaches involving block Arnoldi and block Lanczos processes are proposed for the obtained time-varying equations. Moreover, another type of two-sided KPOD algorithm based on Laguerre orthogonal polynomials in frequency domain is provided. The feasibility of four two-sided KPOD algorithms is verified by numerical results with different inputs and setting parameters.
NUMERICAL METHODS FOR PARTIAL DIFFERENTIAL EQUATIONS
(2023)
Article
Multidisciplinary Sciences
Davide Lengani, Daniele Petronio, Daniele Simoni, Marina Ubaldi
Summary: A POD-based procedure is developed to identify the necessary tests/experiments for modeling a complex system. By reducing data dimensionality and learning parsimonious efficiency trends, significant time reduction in test execution can be achieved.
PROCEEDINGS OF THE ROYAL SOCIETY A-MATHEMATICAL PHYSICAL AND ENGINEERING SCIENCES
(2022)
Article
Engineering, Mechanical
Haijun Peng, Ningning Song, Ziyun Kan
Summary: This paper introduces a novel model order reduction strategy for simulating flexible multibody systems based on the idea of data-driven models, known as the symplectic model order reduction. By obtaining snapshot matrices and converting them to symplectic matrices using cotangent lift, as well as conducting a systematic study on model order reduction at both system and component levels, the proposed method is validated to have better numerical accuracy and computational efficiency compared to classic POD-based models.
NONLINEAR DYNAMICS
(2022)
Article
Engineering, Multidisciplinary
Peter Benner, Jan Heiland
Summary: In this work, a multidimensional Galerkin proper orthogonal decomposition method is proposed to reduce the complexity of quantifying multivariate uncertainties in partial differential equations. The analytical framework and results are provided to define and quantify the low-dimensional approximation. An application for uncertainty modeling using polynomial chaos expansions is illustrated, showing the efficiency of the proposed method.
INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING
(2023)
Article
Engineering, Civil
Ning Zhao, Yan Jiang, Liuliu Peng, Xiaowei Chen
Summary: This study proposes a POD interpolation-enhanced approach to expedite the simulation of nonstationary wind fields by reducing computational cost and speeding up the summing of cosine functions.
JOURNAL OF WIND ENGINEERING AND INDUSTRIAL AERODYNAMICS
(2021)
Article
Engineering, Multidisciplinary
Francesco A. B. Silva, Stefano Lorenzi, Antonio Cammi
Summary: This article presents two extensions of the empirical interpolation method (EIM) designed to deal with vector interpolation problems: EIM-roto and EIM-orto. Testing on a benchmark case shows that EIM-roto interpolation allows reconstruction performances close to the POD ones, while EIM-orto interpolation does not provide reliable reconstructions.
INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING
(2021)
Article
Mathematics, Applied
K. Chikhaoui, R. Mosquera, Y. Guevel, J. M. Cadou, E. Liberge
Summary: This paper proposes a model order reduction procedure that uses Proper Orthogonal Decomposition (POD) and Grassmann manifold-based Interpolation (GI) to accurately approximate the dynamic behavior of mechanical structures with reduced computational cost. The approach involves building reduced bases using POD in an offline phase and using GI to interpolate subspaces in an online phase. The results demonstrate the efficiency of this approach in terms of accuracy and computing time reduction.
FINITE ELEMENTS IN ANALYSIS AND DESIGN
(2023)
Article
Thermodynamics
Jiacheng Ma, Donghun Kim, James E. Braun
Summary: This paper presents a computationally efficient and accurate dynamic modeling approach for vapor compression systems using model order reduction techniques. By reformulating the heat exchanger model and applying POD, reduced order models for evaporator and condenser are constructed with system stability and numerical efficiency in mind. Transient simulations conducted under various operating conditions show that the reduced order model can execute faster with negligible prediction errors compared to the high-fidelity finite volume model.
INTERNATIONAL JOURNAL OF REFRIGERATION
(2021)
Article
Mathematics, Applied
M. Salvador, L. Dede, A. Manzoni
Summary: The proposed nonlinear reduced basis method combines kernel proper orthogonal decomposition (KPOD) and neural networks to efficiently approximate parametrized partial differential equations. By utilizing KPOD on high-fidelity solutions to extract a more accurate reduced basis with lower dimension, and using a neural network to learn the coefficients, the method achieves precise approximation of high-fidelity snapshots while reducing computational cost.
COMPUTERS & MATHEMATICS WITH APPLICATIONS
(2021)