scholarly journals A Construction of Thermal Basis Functions for Coupled Structural - Thermal Reduced Order Models

2017 ◽  
Author(s):  
Raghavendra Murthy ◽  
X.Q. Wang ◽  
Andrew Matney ◽  
Marc P. Mignolet
Keyword(s):  
Basis Functions ◽  
Reduced Order Models ◽  
Reduced Order

scholarly journals Model Reduction of Systems With Localized Nonlinearities

2007 ◽  
Vol 2 (3) ◽  
pp. 249-266 ◽  
Author(s):  
Daniel J. Segalman
Keyword(s):  
Linear System ◽  
Structural Dynamics ◽  
Small Amplitude ◽  
Basis Functions ◽  
Basis Sets ◽  
Reduced Order Models ◽  
Linear Combinations ◽  
Reduced Order ◽  
Galerkin Solution ◽  
Good Agreement

An approach to development of reduced order models for systems with local nonlinearities is presented. The key of this approach is the augmentation of conventional basis functions with others having appropriate discontinuities at the locations of nonlinearity. A Galerkin solution using the above combination of basis functions appears to capture the dynamics of the system very efficiently—employing small basis sets. This method is particularly useful for problems of structural dynamics, but may have application in other fields as well. For problems involving small amplitude dynamics, when one employs as a basis the eigenmodes of a reference linear system plus the discontinuous (joint) modes, the resulting predictions, though still nonlinear, are approximated well as linear combinations of the eigenmodes. This is in good agreement with the experimental observation that jointed structures, though demonstrably nonlinear, manifest kinematics that are well described using eigenmodes of a corresponding system where the joints are replaced by linear springs.

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

2019 ◽  
Vol 233 (14) ◽  
pp. 5107-5121 ◽  
Author(s):  
Xu Wang ◽  
Jiaqing Kou ◽  
Weiwei Zhang
Keyword(s):  
Neural Network ◽  
Radial Basis Function ◽  
Basis Function ◽  
Unsteady Aerodynamics ◽  
Basis Functions ◽  
Reduced Order Models ◽  
Generalization Capability ◽  
Reduced Order ◽  
Radial Basis ◽  
Input Variables

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.

scholarly journals Reduced Order Models for Distributed Adaptive Monitoring of Atmospheric Dispersion Processes

2016 ◽  
Author(s):  
Tobias Ritter ◽  
Stefan Ulbrich ◽  
Oskar von Stryk
Keyword(s):  
Parameter Estimation ◽  
Radial Basis Functions ◽  
Atmospheric Dispersion ◽  
Estimation Procedure ◽  
Basis Functions ◽  
Initial Condition ◽  
Reduced Order Models ◽  
Reduced Order ◽  
Advection Diffusion Equation ◽  
Radial Basis

Atmospheric dispersion of hazardous materials due to chemical leaks can highly affect human health and well-being. For this reason, online state and parameter estimation of these processes is an important step for disaster response to enable the assessment of future impacts. The estimation procedure relies on a combination of the forecasts of a process PDE-model and on measurements obtained by multiple mobile sensor platforms, which are adaptively guided to locations where additional measurements are most useful. The latter challenge can be solved by a cooperative vehicle controller maximizing the quality of the estimates based on the current error covariance matrix. The described approach can be made more flexible and less prone to error if the required calculations (model forecast, estimation procedure, vehicle control) are performed locally on-board of the sensor vehicles instead of using a central supercomputer. While the on-board computing power is limited and results have to be obtained in real-time, complex PDE-models are required to describe the dynamics and to compute accurate forecasts. This highly motivates the use of model order reduction in this context and demonstrates at the same time that the described problem scenario is a paradigmatic application area for reduced order models. A reduced dual state parameter estimation approach is developed for the advection-diffusion equation. The initial condition as well as possible source functions, shapes and locations are unknown. However, it is assumed that the initial condition can be approximated by several radial basis functions with height parameter to be determined. Furthermore, source effects can be represented by the convolution of the same radial basis functions with their height. In the offline phase, multiple simulations with the different radial basis function as initial conditions are performed and snapshots are taken. With the aid of Proper Orthogonal Decomposition, the reduced order model is constructed out of the snapshot matrix and reduced model forecasts are performed locally to repeatedly estimate process state and parameters of the radial basis functions with the Kalman Filter. As a first step, a basic two-dimensional test-case, in which the true state is simulated along with the estimation, is set up and promising results are obtained.

scholarly journals REDUCED ORDER MODELS BASED ON POD METHOD FOR SCHRÖDINGER EQUATIONS

2013 ◽  
Vol 18 (5) ◽  
pp. 694-707 ◽  
Author(s):  
Gerda Jankevičiutė ◽  
Teresė Leonavičienė ◽  
Raimondas Čiegis ◽  
Andrej Bugajev
Keyword(s):  
Numerical Experiments ◽  
Approximate Solutions ◽  
Basis Functions ◽  
Schrodinger Equations ◽  
Reduced Order Models ◽  
Schrödinger Equations ◽  
Optimal Basis ◽  
Reduced Order ◽  
One Dimensional ◽  
Proper Orthogonal

Reduced-order models (ROM) are developed using the proper orthogonal decomposition (POD) for one dimensional linear and nonlinear Schrödinger equations. The main aim of this paper is to study the accuracy and robustness of the ROM approximations. The sensitivity of generated optimal basis functions on various parameters of the algorithms is discussed. Errors between POD approximate solutions and exact problem solutions are calculated. Results of numerical experiments are presented.

Reduced-order models of structures with viscoelastic components

AIAA Journal ◽  
1999 ◽  
Vol 37 ◽  
pp. 1318-1325 ◽  
Author(s):  
Michael I. Friswell ◽  
Daniel J. Inman
Keyword(s):  
Reduced Order Models ◽  
Reduced Order
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