Karhunen-Loeve Decomposition for Reducing the Order and Monitoring the Dynamics of Coupled Oscillators

2001 ◽  
Author(s):  
Xianghong Ma ◽  
Alexander F. Vakakis ◽  
Lawrence A. Bergman
Keyword(s):  
Coupled Oscillators ◽  
Large Scale ◽  
Order Reduction ◽  
Mode Shapes ◽  
Flexible Systems ◽  
Higher Order Modes ◽  
Orthogonality Relations ◽  
Series Of Experiments ◽  
Theory And Experiment ◽  
Low Order

Abstract Karhunen-Loeve - KL modes are used to discretize the dynamics of a four-bay linear truss. This is achieved by defining global KL modal amplitudes and employing the orthogonality relations between KL modes that are inherent in the KL decomposition. It is found that the KL-based low-order models can capture satisfactory the transient dynamics of the truss, even when only a limited number of them is used for the order reduction. A comparison between the exact and low-order dynamics in the frequency domain reveals that the low-order models capture the leading resonances of the truss. A series of experiments with a practical three-bay truss is then performed to validate the theoretical KL decomposition. A comparison between theory and experiment indicates agreement between the predicted and realized dominant KL mode shapes, but less so in the higher order modes. The reasons for this discrepancy between theory and experiment are discussed, and possible applications of the KL-based order reduction to passive and active control of practical large-scale flexible systems are outlined.

Order Reduction of Nonsmooth Structural Systems With Multiple Surfaces of Discontinuity

2003 ◽  
Author(s):  
Eric A. Butcher ◽  
Rongdong Lu
Keyword(s):  
Large Scale ◽  
Arbitrary Dimension ◽  
Linear Part ◽  
Order Reduction ◽  
Mode Shapes ◽  
Full Model ◽  
Linear Transformations ◽  
Reduced Order ◽  
Reduced Models ◽  
Nonlinear Normal

A technique for order reduction of nonsmooth vibrating systems in structural form of arbitrary dimension with multiple surfaces of discontinuity is presented. By utilizing methods based on the bilinear frequency relation which approximates the nonlinear normal mode (NNM) frequencies and mode shapes, reduced order models are constructed which retain the form of the nonsmooth nonlinearity of the full model and more accurately represent the NNM dynamics in the full model than do reduced models obtained via linear transformations. The technique is applied to multi-degree-of-freedom systems with nonsmooth nonlinearities of deadzone and saturation type in which the full and reduced models are compared by direct numerical simulation. The advantages of the present technique include obtaining a reduced order model which uses a subset of the original physical coordinates and can easily accommodate large order systems and multiple nonsmooth nonlinearities with several surfaces of discontinuity. These characteristics make the method practical for use in large-scale structural dynamics applications in which the linear part of the model dominates the dynamics.

scholarly journals Effect of Mechanical Ventilation on Accidental Hydrogen Releases—Large-Scale Experiments

Energies ◽  
2021 ◽  
Vol 14 (11) ◽  
pp. 3008
Author(s):  
Agnieszka W. Lach ◽  
André V. Gaathaug
Keyword(s):  
Mechanical Ventilation ◽  
Mass Flow ◽  
Large Scale ◽  
Ventilation System ◽  
Hydrogen Gas ◽  
Forced Ventilation ◽  
British Standard ◽  
Confined Spaces ◽  
Series Of Experiments ◽  
Rate Limit

This paper presents a series of experiments on the effectiveness of existing mechanical ventilation systems during accidental hydrogen releases in confined spaces, such as underground garages. The purpose was to find the mass flow rate limit, hence the TPRD diameter limit, that will not require a change in the ventilation system. The experiments were performed in a 40 ft ISO container in Norway, and hydrogen gas was used in all experiments. The forced ventilation system was installed with a standard 315 mm diameter outlet. The ventilation parameters during the investigation were British Standard with 10 ACH and British Standard with 6 ACH. The hydrogen releases were obtained through 0.5 mm and 1 mm nozzles from different hydrogen reservoir pressures. Both types of mass flow, constant and blowdown, were included in the experimental matrix. The analysis of the hydrogen concentration of the created hydrogen cloud in the container shows the influence of the forced ventilation on hydrogen releases, together with TPRD diameter and reservoir pressure. The generated experimental data will be used to validate a CFD model in the next step.

Capacity of prestressed concrete bridge decks under fatigue loading

2021 ◽  
Author(s):  
Eva O. L. Lantsoght ◽  
Cor van der Veen ◽  
Rutger Koekkoek ◽  
Henk Sliedrecht
Keyword(s):  
Prestressed Concrete ◽  
Large Scale ◽  
Fatigue Loading ◽  
Membrane Action ◽  
Variable Amplitude ◽  
Girder Bridges ◽  
Prestressed Girders ◽  
Series Of Experiments ◽  
Prestressed Concrete Bridge ◽  
Compressive Membrane Action

<p>In The Netherlands, existing slab-between-girder bridges with prestressed girders and thin transversely prestressed concrete decks require assessment. The punching capacity was studied in a previous series of experiments, showing a higher capacity thanks to compressive membrane action in the deck. Then, concerns were raised with regard to fatigue loading. To address this, two series of large-scale experiments were carried out, varying the number of loads (single wheel print versus double wheel print), the loading sequence (constant amplitude versus variable amplitude, and different loading sequences for variable amplitude), and the distance between the prestressing ducts. An S-N curve is developed for the assessment of slab-between-girder bridges. The experiments showed that compressive membrane actions enhances the capacity of thin transversely prestressed decks subjected to fatigue loading.</p>

scholarly journals Order Reduction based on Coulomb’s and Franklin’s laws Algorithm

2021 ◽  
Author(s):  
Ram Kumar ◽  
Afzal Sikander
Keyword(s):  
Large Scale ◽  
Linear Time ◽  
Order Reduction ◽  
Absolute Error ◽  
Search Space ◽  
Engineering Problem ◽  
Reduced Order Model ◽  
Order Model ◽  
Reduced Order ◽  
Linear Time Invariant

Abstract The Coulomb and Franklin laws (CFL) algorithm is used to construct a lower order model of higher-order continuous time linear time-invariant (LTI) systems in this study. CFL is quite easy to implement in obtaining reduced order model of large scale system in control engineering problem as it employs the combined effect of Coulomb’s and Franklin’s laws to find the best values in search space. The unknown coefficients are obtained using the CFLA methodology, which minimises the integral square error (ISE) between the original and proposed ROMs. To achieve the reduced order model, five practical systems of different orders are considered. Finally, multiple performance indicators such as the ISE, integral of absolute error (IAE), and integral of time multiplied by absolute error were calculated to determine the efficacy of the proposed methodology. The simulation results were compared to previously published well-known research.

A Hybrid Approach for Model Order Reduction and Controller Design of Large-Scale Power Systems

2021 ◽  
pp. 211-226
Author(s):  
Rishabh Singhal ◽  
Yashonidhi Srivastava ◽  
Shini Agarwal ◽  
Abhimanyu Kumar ◽  
Souvik Ganguli
Keyword(s):  
Power Systems ◽  
Model Order Reduction ◽  
Large Scale ◽  
Controller Design ◽  
Hybrid Approach ◽  
Order Reduction ◽  
Model Order
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