7,342 research outputs found
Predictive Reduced Order Modeling of Chaotic Multi-scale Problems Using Adaptively Sampled Projections
An adaptive projection-based reduced-order model (ROM) formulation is
presented for model-order reduction of problems featuring chaotic and
convection-dominant physics. An efficient method is formulated to adapt the
basis at every time-step of the on-line execution to account for the unresolved
dynamics. The adaptive ROM is formulated in a Least-Squares setting using a
variable transformation to promote stability and robustness. An efficient
strategy is developed to incorporate non-local information in the basis
adaptation, significantly enhancing the predictive capabilities of the
resulting ROMs. A detailed analysis of the computational complexity is
presented, and validated. The adaptive ROM formulation is shown to require
negligible offline training and naturally enables both future-state and
parametric predictions. The formulation is evaluated on representative reacting
flow benchmark problems, demonstrating that the ROMs are capable of providing
efficient and accurate predictions including those involving significant
changes in dynamics due to parametric variations, and transient phenomena. A
key contribution of this work is the development and demonstration of a
comprehensive ROM formulation that targets predictive capability in chaotic,
multi-scale, and transport-dominated problems
Gradient-preserving hyper-reduction of nonlinear dynamical systems via discrete empirical interpolation
This work proposes a hyper-reduction method for nonlinear parametric
dynamical systems characterized by gradient fields such as Hamiltonian systems
and gradient flows. The gradient structure is associated with conservation of
invariants or with dissipation and hence plays a crucial role in the
description of the physical properties of the system. Traditional
hyper-reduction of nonlinear gradient fields yields efficient approximations
that, however, lack the gradient structure. We focus on Hamiltonian gradients
and we propose to first decompose the nonlinear part of the Hamiltonian, mapped
into a suitable reduced space, into the sum of d terms, each characterized by a
sparse dependence on the system state. Then, the hyper-reduced approximation is
obtained via discrete empirical interpolation (DEIM) of the Jacobian of the
derived d-valued nonlinear function. The resulting hyper-reduced model retains
the gradient structure and its computationally complexity is independent of the
size of the full model. Moreover, a priori error estimates show that the
hyper-reduced model converges to the reduced model and the Hamiltonian is
asymptotically preserved. Whenever the nonlinear Hamiltonian gradient is not
globally reducible, i.e. its evolution requires high-dimensional DEIM
approximation spaces, an adaptive strategy is performed. This consists in
updating the hyper-reduced Hamiltonian via a low-rank correction of the DEIM
basis. Numerical tests demonstrate the applicability of the proposed approach
to general nonlinear operators and runtime speedups compared to the full and
the reduced models
A local basis approximation approach for nonlinear parametric model order reduction
The efficient condition assessment of engineered systems requires the
coupling of high fidelity models with data extracted from the state of the
system `as-is'. In enabling this task, this paper implements a parametric Model
Order Reduction (pMOR) scheme for nonlinear structural dynamics, and the
particular case of material nonlinearity. A physics-based parametric
representation is developed, incorporating dependencies on system properties
and/or excitation characteristics. The pMOR formulation relies on use of a
Proper Orthogonal Decomposition applied to a series of snapshots of the
nonlinear dynamic response. A new approach to manifold interpolation is
proposed, with interpolation taking place on the reduced coefficient matrix
mapping local bases to a global one. We demonstrate the performance of this
approach firstly on the simple example of a shear-frame structure, and secondly
on the more complex 3D numerical case study of an earthquake-excited wind
turbine tower. Parametric dependence pertains to structural properties, as well
as the temporal and spectral characteristics of the applied excitation. The
developed parametric Reduced Order Model (pROM) can be exploited for a number
of tasks including monitoring and diagnostics, control of vibrating structures,
and residual life estimation of critical components.Comment: 23 pages, 28 figure
An error indicator-based adaptive reduced order model for nonlinear structural mechanics -- application to high-pressure turbine blades
The industrial application motivating this work is the fatigue computation of
aircraft engines' high-pressure turbine blades. The material model involves
nonlinear elastoviscoplastic behavior laws, for which the parameters depend on
the temperature. For this application, the temperature loading is not
accurately known and can reach values relatively close to the creep
temperature: important nonlinear effects occur and the solution strongly
depends on the used thermal loading. We consider a nonlinear reduced order
model able to compute, in the exploitation phase, the behavior of the blade for
a new temperature field loading. The sensitivity of the solution to the
temperature makes {the classical unenriched proper orthogonal decomposition
method} fail. In this work, we propose a new error indicator, quantifying the
error made by the reduced order model in computational complexity independent
of the size of the high-fidelity reference model. In our framework, when the
{error indicator} becomes larger than a given tolerance, the reduced order
model is updated using one time step solution of the high-fidelity reference
model. The approach is illustrated on a series of academic test cases and
applied on a setting of industrial complexity involving 5 million degrees of
freedom, where the whole procedure is computed in parallel with distributed
memory
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