A new model order reduction strategy adapted to nonlinear problems in earthquake engineering

Purpose A novel technique for control of complex physical processes based on the solution of their sufficiently accurate models is presented. The technique works with the model order reduction (MOR), which significantly accelerates the solution at a still acceptable uncertainty. Its advantages are illustrated with an example of induction brazing. Design/methodology/approach The complete mathematical model of the above heat treatment process is presented. Considering all relevant nonlinearities, the numerical model is reduced using the orthogonal decomposition and solved by the finite element method (FEM). It is cheap compared with classical FEM. Findings The proposed technique is applicable in a wide variety of linear and weakly nonlinear problems and exhibits a good degree of robustness and reliability. Research limitations/implications The quality of obtained results strongly depends on the temperature dependencies of material properties and degree of nonlinearities involved. In case of multiphysics problems characterized by low nonlinearities, the results of solved problems differ only negligibly from those solved on the full model, but the computation time is lower by two and more orders. Yet, however, application of the technique in problems with stronger nonlinearities was not fully evaluated. Practical implications The presented model and methodology of its solution may represent a basis for design of complex technologies connected with induction-based heat treatment of metal materials. Originality/value Proposal of a sophisticated methodology for solution of complex multiphysics problems established the MOR technology that significantly accelerates their solution at still acceptable errors.

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Model Order Reduction of Nonlinear Magnetodynamics with Manifold Interpolation

10.14293/p2199-8442.1.sop-eng.pjqna9.v1 ◽

2015 ◽

Author(s):

Y. Paquay ◽

O. Brüls ◽

C. Geuzaine

Keyword(s):

Model Order Reduction ◽

Interpolation Method ◽

Order Reduction ◽

Nonlinear Problems ◽

Single Shot ◽

Reduced Basis ◽

Model Order ◽

Core System ◽

Input Parameters ◽

Speed Up

In the model order reduction community, linear systems have been widely studied and reduced thanks to various techniques. Proper Orthogonal Decomposition (POD) in particular has been very successful, and has recently been gaining popularity in computational electromagnetics. However, the efficiency of POD degrades considerably for nonlinear problems, in particular for nonlinear magnetodynamic models---necessary for designing most of today's electrical machines and drives. We propose to investigate an algorithm which first applies the POD to construct reduced order models of nonlinear magnetodynamic problems for discrete sets of values of the input parameters. Then, for a new set of values of the input parameters, a nonlinear interpolation on manifolds is performed to determine the reduced basis. This interpolation method is based on the theory previously studied for aerodynamic problems. The goal here is not to speed up single shot calculations, but to be able to determine efficiently reduced models for nonlinear problems based on previous offline computations. As a simple application, we apply the procedure to a nonlinear inductor-core system, solved using a classical finite element method. In order to gauge the interest of manifold interpolation we compare the proposed approach to the direct use of a precomputed reduced basis, as well as with the use of standard Lagrange interpolation.

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Local/global model order reduction strategy for the simulation of quasi-brittle fracture

International Journal for Numerical Methods in Engineering ◽

10.1002/nme.3234 ◽

2011 ◽

Vol 89 (2) ◽

pp. 154-179 ◽

Cited By ~ 43

Author(s):

P. Kerfriden ◽

J. C. Passieux ◽

S. P. A. Bordas

Keyword(s):

Brittle Fracture ◽

Model Order Reduction ◽

Order Reduction ◽

Global Model ◽

Model Order ◽

Reduction Strategy

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Using backward elimination with a new model order reduction algorithm to select best double mixture model for document clustering

Expert Systems with Applications ◽

10.1016/j.eswa.2009.01.068 ◽

2009 ◽

Vol 36 (7) ◽

pp. 10485-10493 ◽

Cited By ~ 4

Author(s):

Tahereh Emami Azadi ◽

Farshad Almasganj

Keyword(s):

Mixture Model ◽

Model Order Reduction ◽

Document Clustering ◽

Order Reduction ◽

Reduction Algorithm ◽

Model Order ◽

New Model ◽

Backward Elimination

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Model order reduction for nonlinear problems in circuit simulation

PAMM ◽

10.1002/pamm.200700537 ◽

2007 ◽

Vol 7 (1) ◽

pp. 1021603-1021604 ◽

Cited By ~ 6

Author(s):

A. Verhoeven ◽

T. Voss ◽

P. Astrid ◽

E.J.W. ter Maten ◽

T. Bechtold

Keyword(s):

Model Order Reduction ◽

Circuit Simulation ◽

Order Reduction ◽

Nonlinear Problems ◽

Model Order

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Information Theoretic Tools for Parameter Estimation and Model Order Reduction for Mechanical Systems

Volume 4A: Dynamics, Vibration, and Control ◽

10.1115/imece2017-70744 ◽

2017 ◽

Author(s):

Jared D. Elinger ◽

Jonathan D. Rogers

Keyword(s):

Parameter Estimation ◽

Nonlinear Systems ◽

Model Order Reduction ◽

Multivariate Time Series ◽

A Priori ◽

Order Reduction ◽

Nonlinear Problems ◽

Continuous Systems ◽

Time Model ◽

Model Order

Parameter estimation and model order reduction (MOR) are important techniques used in the development of mechanical system models. A variety of classical parameter estimation and MOR methods are available for nonlinear systems but performance generally suffers when little is known about the system model a priori. Recent advancements in information theory have yielded a quantity called causation entropy, which is a measure of the influence between multivariate time series. In parameter estimation problems involving dynamic systems, causation entropy can be used to identify which functions in a discrete-time model are important in driving the subsequent state values. This paper extends on previous works’ use of a Causation Entropy Matrix to nonlinear systems modeled from the real world. This work explores the conversion of continuous systems to a discrete model and applies the causation entropy matrix to the system. Results show that model structure can be estimated by the causation entropy matrix. This work extends the previous work by showing that the method can be applied to general nonlinear systems. Previously shown examples were toy, additively separable nonlinear problems. This work shows that the methodology can be extended to any nonlinear system, including time varying systems, which provides a framework to examine parameter estimation for general nonlinear systems.

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