A POD-Based Center Selection for RBF Neural Network in Time Series Prediction Problems

Zhang, Wenbo; Guo, Xuexin; Wang, Chaoyong; Wu, Chunguo

doi:10.1007/978-3-540-71629-7_22

Cited by 9 publications

(6 citation statements)

References 23 publications

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“…Zhang et al [26] developed radial basis function-based neural network ROM to predict aerodynamic responses subjected to nonlinear flow caused by large-scale shock motion, and the ROM is then used to investigate limited cycle oscillation behavior in the transonic flow regime. The approach was later improved by the width determination technique [27] and the center selection via the proper orthogonal decomposition (POD) technique [28], and their combinations [29]. Ghoreyshi, Jirasek, and Cummings [30] developed a radial basis function NN and extended the approach to multifidelity recurrent surrogate modeling to incorporate secondary data (Euler simulation) that is cheaper to obtain relative to the primary data (Reynolds-averaged Navier-Stokes simulation).…”

Section: Introductionmentioning

confidence: 99%

State consistence of data-driven reduced order models for parametric aeroelastic analysis

et al. 2021

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This paper investigates the state consistence of parametric data-driven reduced order models (ROMs) in a state-space form obtained by various system identification methods, including autoregressive exogenous (ARX) and subspace identification (N4SID), for aeroelastic analysis in varying flight conditions. The target flight envelop is first partitioned into discrete grid points, on each of which an aerodynamic ROM is constructed using system identification to capture the dependence of the generalized aerodynamic force on the generalized displacement of structural modes. High-fidelity aeroelastic modal perturbation simulations are used to generate the ROM training and verification data. Aerodynamic ROMs not on the grid point are obtained by interpolating those at neighboring grid points. Through a thorough analysis of the model coefficients and pole migration, it is found that only the ARX-based aerodynamic ROM preserves the state consistence, and hence, allowing direct interpolation of system matrices at the non-grid point and rapid aerodynamic ROM database development in the entire flight parameter space. In contrast, N4SID-based ROM destroys the state consistence and yields physically meaningless results when ROMs are interpolated. The origin of the difference in the state consistence caused by both methods is also discussed. The interpolated ARX aerodynamic ROMs coupled with the structural ROM for parametric aeroelastic analysis exhibit excellent agreement with the high fidelity full order model (mostly <5% relative error) and salient computational efficiency.

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Section: Introductionmentioning

confidence: 99%

State consistence of data-driven reduced order models for parametric aeroelastic analysis

et al. 2021

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“…The center vector selection via the POD technique was proposed in Ref. [30] and was extended to nonlinear aerodynamic ROM in Ref. [34].…”

Section: Introductionmentioning

confidence: 99%

Constructing reduced model for complex physical systems via interpolation and neural networks*

Lai¹,

Wang²,

Nie³

2021

Chinese Phys. B

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The work studies model reduction method for nonlinear systems based on proper orthogonal decomposition (POD) and discrete empirical interpolation method (DEIM). Instead of using the classical DEIM to directly approximate the nonlinear term of a system, our approach extracts the main part of the nonlinear term with a linear approximation before approximating the residual with the DEIM. We construct the linear term by Taylor series expansion and dynamic mode decomposition (DMD), respectively, so as to obtain a more accurate reconstruction of the nonlinear term. In addition, a novel error prediction model is devised for the POD-DEIM reduced systems by employing neural networks with the aid of error data. The error model is cheaply computable and can be adopted as a remedy model to enhance the reduction accuracy. Finally, numerical experiments are performed on two nonlinear problems to show the performance of the proposed method.

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“…37 This method avoids the model from failing into overfitting and makes the model take into account the training and prediction performance; Mannarino and Mantegazza 8 used standard and automatic differentiation integration techniques in the training of network synaptic weights, and compared the differences of their generalization capabilities. Zhang et al 38 proposed an effective center selection algorithm based on the proper orthogonal decomposition (POD), which extracts features in samples before model training. These methods all enhanced the model's generalization capability without changing the model structure.…”

Section: Introductionmentioning

confidence: 99%

Unsteady aerodynamic modeling based on fuzzy scalar radial basis function neural networks

Wang

Kou

Zhang

2019

Proceedings of the Institution of Mechanical Engineers, Part G:

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In this paper, a fuzzy scalar radial basis function neural network is proposed, in order to overcome the limitation of traditional aerodynamic reduced-order models having difficulty in adapting to input variables with different orders of magnitude. This network is a combination of fuzzy rules and standard radial basis function neural network, and all the basis functions are defined as scalar basis functions. The use of scalar basis function will increase the flexibility of the model, thus enhancing the generalization capability on complex dynamic behaviors. Particle swarm optimization algorithm is used to find the optimal width of the scalar basis function. The constructed reduced-order models are used to model the unsteady aerodynamics of an airfoil in transonic flow. Results indicate that the proposed reduced-order models can capture the dynamic characteristics of lift coefficients at different reduced frequencies and amplitudes very accurately. Compared with the conventional reduced-order model based on recursive radial basis function neural network, the fuzzy scalar radial basis function neural network shows better generalization capability for different test cases with multiple normalization methods.

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A POD-Based Center Selection for RBF Neural Network in Time Series Prediction Problems

Cited by 9 publications

References 23 publications

State consistence of data-driven reduced order models for parametric aeroelastic analysis

State consistence of data-driven reduced order models for parametric aeroelastic analysis

Constructing reduced model for complex physical systems via interpolation and neural networks*

Unsteady aerodynamic modeling based on fuzzy scalar radial basis function neural networks

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