Efficient frequency response and its direct sensitivity analyses for large-size finite element models using Krylov subspace-based model order reduction

Han, Jeong Sam

doi:10.1007/s12206-012-0227-8

Cited by 22 publications

(6 citation statements)

References 23 publications

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“…2.1 프리스트레스 주파수응답해석 주파수응답해석(harmonic response analysis)을 위한 구조 시스템의 운동방정식은 다음과 같다 (Han, 2010;2012;Kang et al, 2021).…”

Section: 모델차수축소법 기반 프리스트레스 주파수응답해석unclassified

Convolutional Neural Network-based Prediction of Bolt Clamping Force in Initial Bolt Loosening State Using Frequency Response Similarity

Lee,

Han

2023

J. Comput. Struct. Eng. Inst. Korea

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This paper presents a novel convolutional neural network (CNN)-based approach for predicting bolt clamping force in the early bolt loosening state of bolted structures. The approach entails tightening eight bolts with different clamping forces and generating frequency responses, which are then used to create a similarity map. This map quantifies the magnitude and shape similarity between the frequency responses and the initial model in a fully fastened state. Krylov subspace-based model order reduction is employed to efficiently handle the large amount of frequency response data. The CNN model incorporates a regression output layer to predict the clamping forces of the bolts. Its performance is evaluated by training the network by using various amounts of training data and convolutional layers. The input data for the model are derived from the magnitude and shape similarity map obtained from the frequency responses. The results demonstrate the diagnostic potential and effectiveness of the proposed approach in detecting early bolt loosening. Accurate bolt clamping force predictions in the early loosening state can thus be achieved by utilizing the frequency response data and CNN model. The findings afford valuable insights into the application of CNNs for assessing the integrity of bolted structures.

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Section: 모델차수축소법 기반 프리스트레스 주파수응답해석unclassified

Convolutional Neural Network-based Prediction of Bolt Clamping Force in Initial Bolt Loosening State Using Frequency Response Similarity

Lee,

Han

2023

J. Comput. Struct. Eng. Inst. Korea

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“…This section briefly reviews the finite element model of the heat equation and the time integration scheme. We then introduce a model order reduction technique based on the Krylov subspace techniques [19], [22] for real-time sensing.…”

Section: Thermal Modelingmentioning

confidence: 99%

“…However, unlike structural problems, thermal modes do not exhibit resonance and hence, the behavior of a thermal system at a frequency is generally not dominated by a few number of eigenvectors. Therefore, for thermal problems, it is recommended to use a Krylov basis [19]- [22] rather than the eigenvector. The Krylov subspace technique is the moment-matching method.…”

Section: Introductionmentioning

confidence: 99%

Virtual Thermal Sensor for Real-Time Monitoring of Electronic Packages in a Totally Enclosed System

Ahn

Kim

et al. 2022

IEEE Access

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A monitoring system is essential for controlling temperatures under safe levels of operation. It is often challenging to attach temperature sensors directly to drive chips owing to the operating environment or geometric challenges. Based on this motivation, we present a model-based virtual thermal sensing technique for the real-time temperature monitoring of the electronics package. A few real sensors located far from the target position are utilized in this virtual sensing system. These are then connected to a well-tuned finite element model for data augmentation utilizing an inverse heat conduction framework. Therefore, the virtual sensor allows us to estimate the temperature without the aid of a sensor installed inside. However, this technique has a stability issue because it is classified into an inverse problem (i.e., an ill-posed problem). We propose a Tikhonov regularization method to address this challenge, including an efficient ridge estimator. The ridge estimator is used to select an optimal regularization parameter so that we can obtain the stable and reliable inverse solution. Since conventional ridge estimators rely on total transient errors, they require a significant computation. The proposed estimator is based on the bias and variance errors, not the total errors, which allow us to efficiently find the optimal parameter. In this paper, the thermal model is modeled using the finite element method, and the Krylov subspace-based model order reduction is employed to reduce the computational burden. Finally, the proposed virtual thermal sensor was experimentally validated utilizing a sealed cylindrical structure in which the commercial servo drive operated.INDEX TERMS Electronic packages, finite element method, inverse heat conduction problem, ridge estimator, Tikhonov regularization, virtual thermal sensor.

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“…A possible reduction in computational cost can be achieved by neglecting the sensitivities of the reduction basis. Using such approximate sensitivities, Han (2012) investigates frequency response sensitivities for a Krylov-based reduced-order model and concludes that the sensitivities are still usable although some degree of accuracy is lost. Furthermore, Yoon (2010) reports the approximate sensitivities hamper the optimization process due to their inaccuracy in non-self-adjoint problems.…”

Section: Introductionmentioning

confidence: 99%

Efficient limitation of resonant peaks by topology optimization including modal truncation augmentation

Delissen

Keulen

Langelaar

2020

Struct Multidisc Optim

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In many engineering applications, the dynamic frequency response of systems is of high importance. In this paper, we focus on limiting the extreme values in frequency response functions, which occur at the eigenfrequencies of the system, better known as resonant peaks. Within an optimization, merely sampling the frequency range and limiting the maximum values result in high computational effort. Additionally, the sensitivities of this method are not complete, since only information about the resonance peak amplitude is included. The design dependence with respect to the frequency of the extreme value is missed, thus hampering the convergence. To overcome these difficulties, we propose a constraint which can efficiently and accurately limit resonant peaks in a frequency response function. It has a close relation with eigenfrequency maximization; however, in that case, the amplitudes of the frequency response are unconstrained. In order to keep the computational time low, efficient implementation of this constraint is studied using reduced-order models based on modal truncation and modal truncation augmentation. Furthermore, approximated sensitivities are investigated, resulting in a large computational gain, while still yielding very accurate sensitivities and designs with almost equivalent performance compared with the non-approximated case. Conditions are established for the accuracy and computational efficiency of the proposed methods, depending on the number of peaks to be limited, numbers of inputs and outputs, and whether or not the system input and output are collocated.

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Efficient frequency response and its direct sensitivity analyses for large-size finite element models using Krylov subspace-based model order reduction

Cited by 22 publications

References 23 publications

Convolutional Neural Network-based Prediction of Bolt Clamping Force in Initial Bolt Loosening State Using Frequency Response Similarity

Convolutional Neural Network-based Prediction of Bolt Clamping Force in Initial Bolt Loosening State Using Frequency Response Similarity

Virtual Thermal Sensor for Real-Time Monitoring of Electronic Packages in a Totally Enclosed System

Efficient limitation of resonant peaks by topology optimization including modal truncation augmentation

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