Model Reduction for Nonlinear Structural Systems Using Balanced Realization Theory

2013 ◽  
Author(s):  
Al Ferri
Keyword(s):  
Model Reduction ◽  
Dry Friction ◽  
Numerical Models ◽  
Contact Stiffness ◽  
Reduced Order Models ◽  
Joint Models ◽  
Reduced Order ◽  
Truncation Techniques ◽  
Modal Truncation

The development of accurate and efficient numerical models for jointed structures is an important and challenging problem. Due to nonlinearities in the joints, notably dry friction, contact stiffness, and impact, joint models are often complicated and computer-intensive. To create practical models, engineers typically combine “lumped joint models” with reduced-order models for the structural members that they connect. However, the model reduction often distorts how the joint behaves and sometimes destroys important qualitative traits. Simple modal truncation is often inadequate to produce reduced-order models because nonlinearities within the joints such as impact and dry friction can depend critically on the high-frequency characteristics of the mating structural elements. This paper examines the issues surrounding the development of accurate, reduced-order models for nonlinear, jointed structures. The concept of “balanced realizations” from control theory are used to create reduced-order models that best capture the input-output characterization of the linear substructures with the smallest model order. The balanced-realizations are seen to produce very favorable results when compared with standard modal truncation techniques.

A Physics-Based Dynamic Model for Boilers: Part 2 — Model Reduction in a Cogeneration Application

2017 ◽  
Author(s):  
Matthew J. Blom ◽  
Michael J. Brear ◽  
Chris G. Manzie ◽  
Ashley P. Wiese
Keyword(s):  
Model Reduction ◽  
Gas Turbine ◽  
Dynamic Model ◽  
Reduction Process ◽  
Singular Perturbation Theory ◽  
Reduced Order Models ◽  
Reduced Order ◽  
One Dimensional ◽  
Time Scale Separation ◽  
Modelling Framework

This paper is the second part of a two part study that develops, validates and integrates a one-dimensional, physics-based, dynamic boiler model. Part 1 of this study [1] extended and validated a particular modelling framework to boilers. This paper uses this framework to first present a higher order model of a gas turbine based cogeneration plant. The significant dynamics of the cogeneration system are then identified, corresponding to states in the gas path, the steam path, the gas turbine shaft, gas turbine wall temperatures and boiler wall temperatures. A model reduction process based on time scale separation and singular perturbation theory is then demonstrated. Three candidate reduced order models are identified using this model reduction process, and the simplest, acceptable dynamic model of this integrated plant is found to require retention of both the gas turbine and boiler wall temperature dynamics. Subsequent analysis of computation times for the original physics-based one-dimensional model and the candidate, reduced order models demonstrates that significantly faster than real time simulation is possible in all cases. Furthermore, with systematic replacement of the algebraic states with feedforward maps in the reduced order models, further computational savings of up to one order of magnitude can be achieved. This combination of model fidelity and computational tractability suggest suggests that the resulting reduced order models may be suitable for use in model based control of cogeneration plants.

Nonlinear Reduced-Order Models for the Structural Dynamics of Combustor Systems With Pre-Stress and Friction

2013 ◽  
Author(s):  
Chulwoo Jung ◽  
Bogdan I. Epureanu ◽  
Sanghum Baik ◽  
Marcus B. Huffman
Keyword(s):  
Coulomb Friction ◽  
Convex Surface ◽  
Contact Stiffness ◽  
Reduced Order Models ◽  
Order Model ◽  
Transient Dynamic Analysis ◽  
Reduced Order ◽  
Require Time ◽  
Flow Induced Vibrations ◽  
Transition Piece

An efficient methodology to capture the nonlinear responses of combustor systems with pre-stress and Coulomb friction is developed. The combustor systems experience wear at the interfaces between components due to flow-induced vibrations. In particular, wear has been observed at the interface between the transition piece and the hula seal, and at the interface between the hula seal and the liner. These interfaces are pre-stressed, and their vibratory response has a softening nonlinearity caused by Coulomb friction combined with micro-slip. In addition, the contact between the hula seal and the transition piece is that between a convex surface and a concave surface. Hence, geometric nonlinearity of the contact stiffness in the normal direction is present also. These phenomena are hard to capture by full order finite element approaches because they require time marching or harmonic balancing of very large models. To address this issue, we develop reduced order models (ROMs) which are specifically designed to capture Coulomb friction (combined with micro-slip and macro-slip). To demonstrate the proposed approach, a simplified hula seal is placed between two very rigid plates (which relate to the transition piece and the liner). For validation, contact elements are used to model the interface between the plates and the hula seal. Transient dynamic analysis (TDA) in ANSYS is applied to the full order model. The model is shown to exhibit softening nonlinearity and micro-slip at all levels of pre-stress. To show that ROMs for this system are possible (i.e., they exist), we use proper orthogonal decomposition to show that the dynamics is dominated by a low number of spatial coherences. For a variety of frequency ranges and pre-stress levels, we show that a single such coherence is dominant. Next, low order models are proposed and their parameters are identified. A systematic method to identify these parameters is developed. Particular attention is paid to the amount of calculations needed for obtaining these parameters. Finally, the ROMs are validated by comparing their predictions with results from TDA for the full-order model. We show that these ROMs can accurately predict the nonlinear response of the system.

Nonlinear Reduced Order Models for the Structural Dynamics of Combustor Systems With Prestress and Friction

2014 ◽  
Vol 10 (1) ◽  
Author(s):  
Chulwoo Jung ◽  
Bogdan I. Epureanu ◽  
Sanghum Baik ◽  
Marcus B. Huffman
Keyword(s):  
Coulomb Friction ◽  
Convex Surface ◽  
Contact Stiffness ◽  
Reduced Order Models ◽  
Order Model ◽  
Transient Dynamic Analysis ◽  
Reduced Order ◽  
Require Time ◽  
Flow Induced Vibrations ◽  
Transition Piece

An efficient methodology to capture the nonlinear responses of combustor systems with prestress and Coulomb friction is developed. The combustor systems experience wear at the interfaces between components due to flow-induced vibrations. In particular, wear has been observed at the interface between the transition piece and the hula seal, and at the interface between the hula seal and the liner. These interfaces are prestressed, and their vibratory response has a softening nonlinearity caused by Coulomb friction combined with microslip. In addition, the contact between the hula seal and the transition piece is that between a convex surface and a concave surface. Hence, geometric nonlinearity of the contact stiffness in the normal direction is present also. These phenomena are hard to capture by full-order finite element (FE) approaches because they require time marching or harmonic balancing of very large models. To address this issue, we develop reduced order models (ROMs) which are specifically designed to capture Coulomb friction (combined with micro- and macroslip). To demonstrate the proposed approach, a simplified hula seal is placed between two very rigid plates (which relate to the transition piece and the liner). For validation, contact elements are used to model the interface between the plates and the hula seal. Transient dynamic analysis (TDA) in ansys is applied to the full-order model. The model is shown to exhibit softening nonlinearity and microslip at all levels of prestress. To show that ROMs for this system are possible (i.e., they exist), we use proper orthogonal decomposition (POD) to show that the dynamics is dominated by a low number of spatial coherences. For a variety of frequency ranges and prestress levels, we show that a single such coherence is dominant. Next, low order models are proposed and their parameters are identified. A systematic method to identify these parameters is developed. Particular attention is paid to the amount of calculations needed for obtaining these parameters. Finally, the ROMs are validated by comparing their predictions with results from TDA for the full-order model. We show that these ROMs can accurately predict the nonlinear response of the system.

scholarly journals Frequency Weighted Model Order Reduction Technique and Error Bounds for Discrete Time Systems

2014 ◽  
Vol 2014 ◽  
pp. 1-8 ◽  
Author(s):  
Muhammad Imran ◽  
Abdul Ghafoor ◽  
Victor Sreeram
Keyword(s):  
Frequency Response ◽  
Model Reduction ◽  
Discrete Time ◽  
Error Bounds ◽  
Reduced Order Models ◽  
Reduced Order ◽  
Reduction Techniques ◽  
Discrete Time Systems ◽  
Weighted Model ◽  
Time Systems

Model reduction is a process of approximating higher order original models by comparatively lower order models with reasonable accuracy in order to provide ease in design, modeling and simulation for large complex systems. Generally, model reduction techniques approximate the higher order systems for whole frequency range. However, certain applications (like controller reduction) require frequency weighted approximation, which introduce the concept of using frequency weights in model reduction techniques. Limitations of some existing frequency weighted model reduction techniques include lack of stability of reduced order models (for two sided weighting case) and frequency response error bounds. A new frequency weighted technique for balanced model reduction for discrete time systems is proposed. The proposed technique guarantees stable reduced order models even for the case when two sided weightings are present. Efficient technique for frequency weighted Gramians is also proposed. Results are compared with other existing frequency weighted model reduction techniques for discrete time systems. Moreover, the proposed technique yields frequency response error bounds.

scholarly journals Model reduction for a power grid model

2021 ◽  
Vol 0 (0) ◽  
pp. 0
Author(s):  
Jing Li ◽  
Panos Stinis
Keyword(s):  
Model Reduction ◽  
Long Memory ◽  
Power Grid ◽  
The State ◽  
Reduced Order Models ◽  
Reduced Order ◽  
Grid Model ◽  
Reduction Techniques ◽  
Short Memory ◽  
Better Than

<p style='text-indent:20px;'>We examine the complexity of constructing reduced order models for subsets of the variables needed to represent the state of the power grid. In particular, we apply model reduction techniques to the DeMarco-Zheng power grid model. We show that due to the oscillating nature of the solutions and the absence of timescale separation between resolved and unresolved variables, the construction of accurate reduced models becomes highly non-trivial because one has to account for long memory effects. In addition, we show that a reduced model that includes even a short memory is drastically better than a memoryless model.</p>

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