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.

scholarly journals Reduced Order Models for Nonlinear Dynamic Analysis With Application to a Fan Blade

2019 ◽  
Author(s):  
Mikel Balmaseda ◽  
G. Jacquet-Richardet ◽  
A. Placzek ◽  
D.-M. Tran
Keyword(s):  
Normal Modes ◽  
Nonlinear Dynamic Analysis ◽  
Evaluation Procedure ◽  
Reduced Order Models ◽  
Reduced Basis ◽  
Reduced Order ◽  
Stiffness Evaluation ◽  
Fan Blade ◽  
Proper Orthogonal ◽  
Good Agreement

Abstract In the present work reduced order models (ROM) that are independent from the full order finite element models (FOM) considering geometrical non linearities are developed and applied to the dynamic study of a fan. The structure is considered to present nonlinear vibrations around the pre-stressed equilibrium induced by rotation enhancing the classical linearised approach. The reduced nonlinear forces are represented by a polynomial expansion obtained by the Stiffness Evaluation Procedure (STEP) and then corrected by means of a Proper Orthogonal Decomposition (POD) that filters the full order nonlinear forces (StepC ROM). The Linear Normal Modes (LNM) and Craig-Bampton (C-B) type reduced basis are considered here. The latter are parametrised with respect to the rotating velocity. The periodic solutions obtained with the StepC ROM are in good agreement with the solutions of the FOM and are more accurate than the linearised ROM solutions and the STEP ROM. The proposed StepC ROM provides the best compromise between accuracy and time consumption of the ROM.

scholarly journals Reduced Order Models for Nonlinear Dynamic Analysis With Application to a Fan Blade

2020 ◽  
Vol 142 (4) ◽  
Author(s):  
Mikel Balmaseda ◽  
G. Jacquet-Richardet ◽  
A. Placzek ◽  
D.-M. Tran
Keyword(s):  
Normal Modes ◽  
Nonlinear Dynamic Analysis ◽  
Evaluation Procedure ◽  
Reduced Order Models ◽  
Reduced Basis ◽  
Reduced Order ◽  
Stiffness Evaluation ◽  
Fan Blade ◽  
Proper Orthogonal ◽  
Good Agreement

Abstract In this work, reduced order models (ROM) that are independent from the full order finite element models (FOM) considering geometrical nonlinearities are developed and applied to the dynamic study of a fan. The structure is considered to present nonlinear vibrations around the prestressed equilibrium induced by rotation enhancing the classical linearized approach. The reduced nonlinear forces are represented by a polynomial expansion obtained by the stiffness evaluation procedure (STEP) and then corrected by means of a proper orthogonal decomposition (POD) that filters the full order nonlinear forces (StepC ROM). The linear normal modes (LNM) and Craig-Bampton (C-B) type reduced basis are considered here. The latter are parameterized with respect to the rotating velocity. The periodic solutions obtained with the StepC ROM are in good agreement with the solutions of the FOM and are more accurate than the linearized ROM solutions and the STEP ROM. The proposed StepC ROM provides the best compromise between accuracy and time consumption of the ROM.

A method for interpolating on manifolds structural dynamics reduced-order models

2009 ◽  
Vol 80 (9) ◽  
pp. 1241-1258 ◽  
Author(s):  
David Amsallem ◽  
Julien Cortial ◽  
Kevin Carlberg ◽  
Charbel Farhat
Keyword(s):  
Structural Dynamics ◽  
Reduced Order Models ◽  
Reduced Order

scholarly journals Progress on the Development of a Holistic Coupled Model of Dynamics for Offshore Wind Farms: Phase II — Study on a Data-Driven Based Reduced-Order Model for a Single Wind Turbine

2019 ◽  
Author(s):  
Z. Lin ◽  
A. Stetco ◽  
J. Carmona-Sanchez ◽  
D. Cevasco ◽  
M. Collu ◽  
...  
Keyword(s):  
Wind Turbine ◽  
Wind Farm ◽  
Coupled Model ◽  
Operating Conditions ◽  
Offshore Wind ◽  
Coupled Analysis ◽  
Offshore Wind Turbine ◽  
Reduced Order Models ◽  
Reduced Order ◽  
Good Agreement

Abstract At present, over 1500 offshore wind turbines (OWTs) are operating in the UK with a capacity of 5.4GW. Until now, the research has mainly focused on how to minimise the CAPEX, but Operation and Maintenance (O&M) can represent up to 39% of the lifetime costs of an offshore wind farm, mainly due to the assets’ high cost and the harsh environment in which they operate. Focusing on O&M, the HOME Offshore research project (www.homeoffshore.org) aims to derive an advanced interpretation of the fault mechanisms through holistic multiphysics modelling of the wind farm. With the present work, an advanced model of dynamics for a single wind turbine is developed, able to identify the couplings between aero-hydro-servo-elastic (AHSE) dynamics and drive train dynamics. The wind turbine mechanical components, modelled using an AHSE dynamic model, are coupled with a detailed representation of a variable-speed direct-drive 5MW permanent magnet synchronous generator (PMSG) and its fully rated voltage source converters (VSCs). Using the developed model for the wind turbine, several case studies are carried out for above and below rated operating conditions. Firstly, the response time histories of wind turbine degrees of freedom (DOFs) are modelled using a full-order coupled analysis. Subsequently, regression analysis is applied in order to correlate DOFs and generated rotor torque (target degree of freedom for the failure mode in analysis), quantifying the level of inherent coupling effects. Finally, the reduced-order multiphysics models for a single offshore wind turbine are derived based on the strength of the correlation coefficients. The accuracy of the proposed reduced-order models is discussed, comparing it against the full-order coupled model in terms of statistical data and spectrum. In terms of statistical results, all the reduced-order models have a good agreement with the full-order results. In terms of spectrum, all the reduced-order models have a good agreement with the full-order results if the frequencies of interest are below 0.75Hz.

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 Design of sensor networks for instantaneous inversion of modally reduced order models in structural dynamics

2015 ◽  
Vol 52-53 ◽  
pp. 628-644 ◽  
Author(s):  
K. Maes ◽  
E. Lourens ◽  
K. Van Nimmen ◽  
E. Reynders ◽  
G. De Roeck ◽  
...  
Keyword(s):  
Sensor Networks ◽  
Structural Dynamics ◽  
Reduced Order Models ◽  
Reduced Order
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