Model-reduction techniques for reliability-based design problems of complex structural systems

Jensen, Héctor A.; Muñoz, A.; Papadimitriou, Costas; Millas, E.

doi:10.1016/j.ress.2016.01.003

Cited by 36 publications

(10 citation statements)

References 32 publications

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“…Furthermore, a quadratic manifold [22] and a non-intrusive [23] approach were proposed for MOR of nonlinear structural systems. MOR techniques have also been used for Bayesian finite element model updating [24] and for reliability-based design problems [25].…”

Section: Introductionmentioning

confidence: 99%

Model order reduction for real-time hybrid simulation: Comparing polynomial chaos expansion and neural network methods

Tsokanas

Simpson²,

Pastorino³

et al. 2022

Mechanism and Machine Theory

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Section: Introductionmentioning

confidence: 99%

Model order reduction for real-time hybrid simulation: Comparing polynomial chaos expansion and neural network methods

Tsokanas

Simpson²,

Pastorino³

et al. 2022

Mechanism and Machine Theory

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“…Reduced basis (RB) methods belong to this family of metamodeling techniques and are widely applied as surrogates for parametrized large scale systems [1,2,3,4]. The idea behind RB methods is to find a suitable low-dimensional subspace of the system's high-dimensional solution space and project the governing equations onto this reduced space, where they can be solved more efficiently.…”

Section: Introductionmentioning

confidence: 99%

Non-intrusive Surrogate Modeling for Parametrized Time-dependent PDEs using Convolutional Autoencoders

Nikolopoulos,

Kalogeris,

Papadopoulos

2021

Preprint

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This work presents a non-intrusive surrogate modeling scheme based on machine learning technology for predictive modeling of complex systems, described by parametrized time-dependent PDEs. For this type of problems, typical finite element solution approaches involve the spatiotemporal discretization of the PDE and the solution of the corresponding linear system of equations at each time step. Instead, the proposed method utilizes a convolutional autoencoder in conjunction with a feed forward neural network to establish a low-cost and accurate mapping from the problem's parametric space to its solution space. The aim is to evaluate directly the entire time history solution matrix through these interpolation schemes. For this purpose, time history response data are collected by solving the high-fidelity model via FEM for a reduced set of parameter values. Then, by applying the convolutional autoencoder to this data set, a low-dimensional representation of the high-dimensional solution matrices is provided by the encoder, while the reconstruction map is obtained by the decoder. Using the latent representation given by the encoder, a feed-forward neural network is efficiently trained to map points from the problem's parametric space to the compressed version of the respective solution matrices. This way, the encoded time-history response of the system at new parameter values is given by the neural network, while the entire high-dimensional system's response is delivered by the decoder. This approach effectively bypasses the need to serially formulate and solve the governing equations of the system at each time increment, thus resulting in a significant computational cost reduction and rendering the method ideal for problems requiring repeated model evaluations or 'real-time' computations. The elaborated methodology is demonstrated on the stochastic analysis of time-dependent PDEs solved with the Monte Carlo method, however, it can be straightforwardly applied to other similartype problems, such as sensitivity analysis, design optimization, etc.

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Section: Introductionmentioning

confidence: 99%

Model Order Reduction for Real-Time Hybrid Simulation: Comparing Polynomial Chaos Expansion and Neural Network methods

Tsokanas¹,

Simpson²,

Pastorino³

et al. 2021

Preprint

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Hybrid simulation is a method used to investigate the dynamic response of a system subjected to a realistic loading scenario by combining numerical and physical substructures. To ensure high fidelity of the simulation results, it is often necessary to conduct hybrid simulation in real-time. One of the challenges arising in real-time hybrid simulation originates from high-dimensional nonlinear numerical substructures and, in particular, from the computational cost linked to the computation of their dynamic responses with sufficient accuracy. It is often the case that the simulation time-step must be decreased to capture the dynamic behavior of numerical substructures, thus resulting in longer computation. When such computation takes longer than the actual simulation time, time delays are introduced and the simulation timescale becomes distorted. In such a case, the only viable solution for doing hybrid simulation in real-time is to reduce the order of such complex numerical substructures.In this study, a model order reduction framework is proposed for real-time hybrid simulation, based on polynomial chaos expansion and feedforward neural networks. A parametric case study encompassing a virtual hybrid model is used to validate the framework. Selected numerical substructures are substituted with their respective reduced-order models. To determine the robustness of the framework, parameter sets are defined to cover the design space of interest. A comparison between the full- and reduced-order hybrid model response is delivered. The attained results demonstrate the performance of the proposed framework.

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Model-reduction techniques for reliability-based design problems of complex structural systems

Cited by 36 publications

References 32 publications

Model order reduction for real-time hybrid simulation: Comparing polynomial chaos expansion and neural network methods

Model order reduction for real-time hybrid simulation: Comparing polynomial chaos expansion and neural network methods

Non-intrusive Surrogate Modeling for Parametrized Time-dependent PDEs using Convolutional Autoencoders

Model Order Reduction for Real-Time Hybrid Simulation: Comparing Polynomial Chaos Expansion and Neural Network methods

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