Sparse POD modal subsets for reduced‐order nonlinear explicit dynamics

Phalippou, Pierre; Bouabdallah, Salim; Breitkopf, Piotr; Villon, Pierre; Zarroug, Malek

doi:10.1002/nme.6243

Cited by 10 publications

(5 citation statements)

References 18 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…The selection of basis vectors, that is, POD modes, is based on the magnitude of the corresponding singular value. Dealing with temporal snapshots, however, it is noteworthy that this common selection of basis vectors is not always the best choice and other selection criteria may be beneficial 31 …”

Section: Methodsmentioning

confidence: 99%

A nonintrusive nonlinear model reduction method for structural dynamical problems based on machine learning

Kneifl

Grunert

Fehr

2021

Numerical Meth Engineering

View full text Add to dashboard Cite

Model order reduction (MOR) has become one of the most widely used tools to create efficient surrogate models for time-critical applications. For nonlinear models, however, linear MOR approaches are only practicable to a limited extent. Nonlinear approaches, on the contrary, often require intrusive manipulations of the used simulation code. Hence, non-intrusive MOR approaches using classic model order reduction along with machine learning (ML) algorithms can provide remedy. Such approaches have drawn a lot of attention in the recent years. They rely on the idea to learn the dynamics not in a high-dimensional but in a reduced space, i.e., they predict the discrete sequence of reduced system states successively. Open questions are the suitability of such methods in the field of structural dynamics and the best choice of the used ML algorithm. Both are addressed in this paper in addition to the integration of the methodology into a modular and flexible framework that can effortless be adapted to various requirements. By applying the methodology to a dynamic mechanical system, accurate surrogate models are received, which can speed up the simulation time significantly, while still providing high-quality state approximations.

show abstract

Section: Methodsmentioning

confidence: 99%

A nonintrusive nonlinear model reduction method for structural dynamical problems based on machine learning

Kneifl

Grunert

Fehr

2021

Numerical Meth Engineering

View full text Add to dashboard Cite

show abstract

“…where q(t) is the response in the reduced n r -dimensional space; x(t) is the response vector in the original n-dimensional space; Φ T n r is the n r × n coordinate transformation matrix with n r n;. The transformation matrix can be obtained by singular value decomposition (SVD) [24,25]. For the n s samples of the simulation results for the MDOF dynamic system under uncertainties, a snapshot matrix can be formulated as follows:…”

Section: Model Order Reductionmentioning

confidence: 99%

A Comparative Study of Meta-Modeling for Response Estimation of Stochastic Nonlinear MDOF Systems Using MIMO-NARX Models

et al. 2022

View full text Add to dashboard Cite

Complex dynamic behavior of nonlinear structures makes it challenging for uncertainty analysis through Monte Carlo simulations (MCS). Surrogate modeling presents an efficient and accurate computational alternative for a large number of MCS. The previous study has demonstrated that the multi-input multi-output nonlinear autoregressive with exogenous input (MIMO-NARX) model provides good discrete-time representations of deterministic nonlinear multi-degree-of-freedom (MDOF) structural dynamic systems. Model order reduction (MOR) is executed to eliminate insignificant modes to reduce the computational burden due to too many degrees of freedom. In this study, the MIMO-NARX strategy is integrated with different meta-modeling techniques for uncertainty analysis. Different meta-models including Kriging, polynomial chaos expansion (PCE), and arbitrary polynomial chaos (APC) are used to surrogate the NARX coefficients for system uncertainties. A nine-DOF structure is used as an MDOF dynamic system to evaluate different meta-models for the MIMO-NARX. Good fitness of statistical responses is observed between the MCS results of the original system and all surrogated MIMO-NARX predictions. It is demonstrated that the APC-NARX model with the advantage of being data-driven is the most efficient and accurate tool for uncertainty quantification of nonlinear structural dynamics.

show abstract

“…Other approaches suggest an efficient snapshot selection to reduce the dimension of the snapshot matrix e.g. (Phalippou et al 2020). Moreover, in the field of structural topology optimisation first principal component based surrogate models have been developed by (Alaimo et al 2018;Xiao et al 2020).…”

Section: Introductionmentioning

confidence: 99%

Data-driven models for crashworthiness optimisation: intrusive and non-intrusive model order reduction techniques

Czech

Lesjak

Bach

et al. 2022

Struct Multidisc Optim

View full text Add to dashboard Cite

To enable multi-query analyses, such as optimisations of large-scale crashworthiness problems, a numerically efficient model is crucial for the development process. Therefore, data-driven Model Order Reduction (MOR) aims at generating low-fidelity models that approximate the solution while strongly reducing the computational cost. MOR methods for crashworthiness became only available in recent years; a detailed and comparative assessment of their potential is still lacking. Hence, this work evaluates the advantages and drawbacks of intrusive and non-intrusive projection based MOR methods in the framework of non-linear structural transient analysis. Both schemes rely on the collection of full-order training simulations and a subsequent subspace construction via Singular Value Decomposition. The intrusive MOR is based on a Galerkin projection and a consecutive hyper-reduction step. In this work, its inter-and extrapolation abilities are compared to the non-intrusive technique, which combines the subspace approach with machine learning methods. Moreover, an optimisation analysis incorporating the MOR methods is proposed and discussed for a crashworthiness example.

show abstract

Sparse POD modal subsets for reduced‐order nonlinear explicit dynamics

Cited by 10 publications

References 18 publications

A nonintrusive nonlinear model reduction method for structural dynamical problems based on machine learning

A nonintrusive nonlinear model reduction method for structural dynamical problems based on machine learning

A Comparative Study of Meta-Modeling for Response Estimation of Stochastic Nonlinear MDOF Systems Using MIMO-NARX Models

Data-driven models for crashworthiness optimisation: intrusive and non-intrusive model order reduction techniques

Contact Info

Product

Resources

About