• Smart Structures and Systems
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• v.13 no.1
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• pp.99-109
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• 2014

The goal of any Model Order Reduction (MOR) technique is to build a model of order lower than the one of the real model, so that the computational effort is reduced, and the ability to estimate the input-output mapping of the original system is preserved in an important region of the input space. Actually, since only a subset of the input space is of interest, the matching is required only in this subset of the input space. In this contribution, the consequences on the achieved accuracy of adopting different reduction technique patterns is discussed mainly with reference to a linear case study.

• Transactions of the Korean Society of Mechanical Engineers A
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• v.30 no.3 s.246
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• pp.310-317
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• 2006

Currently most practical vibration and structural problems in automotive suspensions require the use of the finite element method to obtain their structural responses. When the finite element model has a very large number of degrees of freedom the harmonic and dynamic analyses are computationally too expensive to repeat within a feasible design process time. To alleviate the computational difficulty, this paper presents a moment-matching based model order reduction (MOR) which reduces the number of degrees of freedom of the original finite element model and speeds up the necessary simulations with the reduced-size models. The moment-matching model reduction via the Arnoldi process is performed directly to ANSYS finite element models by software mor4ansys. Among automotive suspension components, a knuckle is taken as an example to demonstrate the advantages of this approach for vibration simulation. The frequency and transient dynamic responses by the MOR are compared with those by the mode superposition method.

• Smart Structures and Systems
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• v.18 no.1
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• pp.1-16
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• 2016

Model Order Reduction (MOR) denotes the theory by which one tries to catch a model of order lower than that of the real model. This is conveniently pursued in view of the design of an efficient structural control scheme, just passive within this paper. When the nonlinear response of the reference structural system affects the nature of the reduced model, making it dependent on the visited subset of the input-output space, standard MOR techniques do not apply. The mathematical theory offers some specific alternatives, which however involve a degree of sophistication unjustified in the presence of a few localized nonlinearities. This paper suggests applying standard MOR to the linear parts of the structural system, the interface remaining the original unreduced nonlinear components. A case study focused on the effects of a helicopter land crash is used to exemplify the proposal.

• Structural Engineering and Mechanics
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• v.81 no.4
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• pp.411-428
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• 2022

This paper presents the Campbell diagram analysis of the rotordynamic system using the full order model (FOM) and the reduced order model (ROM) techniques to determine the critical speeds, identify the stability and reduce the computational time. Due to the spin-speed-dependent matrices (e.g., centrifugal stiffening matrix), several model order reduction (MOR) techniques may be considered, such as the modal superposition (MS) method and the Krylov subspace-based MOR techniques (e.g., Ritz vector (RV), quasi-static Ritz vector (QSRV), multifrequency quasi-static Ritz vector (MQSRV), multifrequency/ multi-spin-speed quasi-static Ritz vector (MMQSRV) and the combined Ritz vector & modal superposition (RV+MS) methods). The proposed MMQSRV method in this study is extended from the MQSRV method by incorporating the rotational-speed-dependent stiffness matrices into the Krylov subspace during the MOR process. Thus, the objective of this note is to respond to the question of whether to use the MS method or the Krylov subspace-based MOR technique in establishing the Campbell diagram of the shaft-disc-blade assembly systems in three-dimensional (3D) finite element analysis (FEA). The Campbell diagrams produced by the FOM and various MOR methods are presented and discussed thoroughly by computing the norm of relative errors (ER). It is found that the RV and the MS methods are dominant at low and high rotating speeds, respectively. More precisely, as the spinning velocity becomes large, the calculated ER produced by the RV method is significantly increased; in contrast, the ER produced by the MS method is smaller and more consistent. From a computational point of view, the MORs have substantially reduced the time computing considerably compared to the FOM. Additionally, the verification of the 3D FE rotordynamic model is also provided and found to be in close agreement with the existing solutions.

• JSTS:Journal of Semiconductor Technology and Science
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• v.9 no.4
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• pp.216-224
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• 2009

The endless scaling down of the semiconductor process made the impact of the power network noise on the performance of the state-of-the-art chip a serious design problem. This paper compares the performances of two popular circuit reduction approaches used to improve the efficiency of power network noise analysis: moment matching-based model order reduction (MOR) and node elimination-based MOR. As the benchmarks, we chose PRIMA and R2Power as the matching-based MOR and the node elimination-based MOR. Experimental results indicate that the accuracy, efficiency, and memory requirement of both methods very strongly depend on the structure of the given circuit, i.e., numbers of the nodes and sources, and the number of moments to preserve for PRIMA. PRIMA has higher accuracy in general, while the error of R2Power is also in the acceptable range. On the other hand, PRIMA has the higher efficiency than R2Power, only when the numbers of nodes and sources are small enough. Otherwise, R2Power clearly outperforms PRIMA in efficiency. In the memory requirement, the memory size of PRIMA increases very quickly as the numbers of nodes, sources, and preserved moments increase.

• Structural Engineering and Mechanics
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• v.50 no.1
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• pp.19-36
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• 2014

This paper focuses on a model order reduction (MOR) for large-scale rotordynamic systems by using finite element discretization. Typical rotor-bearing systems consist of a rotor, built-on parts, and a support system. These systems require careful consideration in their dynamic analysis modeling because they include unsymmetrical stiffness, localized nonproportional damping, and frequency-dependent gyroscopic effects. Because of this complex geometry, the finite element model under consideration may have a very large number of degrees of freedom. Thus, the repeated dynamic analyses used to investigate the critical speeds, stability, and unbalanced response are computationally very expensive to complete within a practical design cycle. In this study, we demonstrate that a Krylov subspace-based MOR via moment matching significantly speeds up the rotordynamic analyses needed to check the whirling frequencies and critical speeds of large rotor systems. This approach is very efficient, because it is possible to repeat the dynamic simulation with the help of a reduced system by changing the operating rotational speed, which can be preserved as a parameter in the process of model reduction. Two examples of rotordynamic systems show that the suggested MOR provides a significant reduction in computational cost for a Campbell diagram analysis, while maintaining accuracy comparable to that of the original systems.

• Smart Structures and Systems
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• v.13 no.3
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• pp.343-352
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• 2014

Given a body undergoing a stress-strain status as consequence of external excitations, sensors can be deployed on the accessible lateral surface of the body. The sensor readings are regarded as input of a numerical model of reduced order (i.e., the number of sensors is lower than the number of the state variables the full model would require). The goal is to locate the sensors in such a way to minimize the deviations from the response of the true (full) model. One adopts either accelerometers as sensors or devices reading relative displacements. Two applications are studied: a plane frame is first investigated; the focus is eventually on a 3D body.

• Proceedings of the Korean Society for Noise and Vibration Engineering Conference
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• 2011.10a
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• pp.764-765
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• 2011

In this paper, rotordynamic analyses of the Campbell diagram, critical speeds, and harmonic responses for a TMP rotor system are performed. Since the finite element model of the TMP rotor system has a very large number of degrees of freedom because of its complex geometry, and dynamic analyses for investigating the critical speeds, stability, and harmonic response are repeated for various design parameters, model order reduction (MOR) is necessary to reduce the computational cost. The Krylov-based model order reduction via moment matching significantly speeds up the rotordynamic analyses for the TMP rotor system.

• Structural Engineering and Mechanics
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• v.76 no.5
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• pp.643-651
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• 2020

Generally, it is necessary to perform transient structural analysis in order to verify and improve the seismic performance of high-rise buildings and bridges against earthquake loads. In this paper, we propose the model order reduction (MOR) method using the Krylov vectors to perform seismic analysis for linear and elastic systems in an efficient way. We then compared the proposed method with the mode superposition method (MSM) by using the limited numbers of modal vectors (or eigenvectors) calculated from the modal analysis. In the calculation, the data of the El Centro earthquake in 1940 were adopted for the seismic loading in the transient analysis. The numerical accuracy and efficiency of the two methods were compared in detail in the case of a simplified high-rise building.

• Proceedings of the Korean Society of Precision Engineering Conference
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• 2006.05a
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• pp.121-122
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• 2006

In the case of mechanical control systems, it is highly useful to be able to provide a compact model of the mechanical system to control engineers using the smallest number of variables, while still providing an accurate model. The reduced mechanical model can then be inserted into the complete mechanical control system models and used for system-level dynamic simulation. In this paper, a moment-matching based model order reduction (MOR) which reduces the number of degrees of freedom of an original finite element model via the Arnoldi process is considered to study the dynamic responses of a HDD actuator and suspension system.