A hierarchical framework for statistical model calibration in engineering product development

Youn, Byeng D.; Jung, Byung C.; Xi, Zhimin; Kim, Sang Bum; Lee, W.R.

doi:10.1016/j.cma.2010.12.012

Cited by 66 publications

(19 citation statements)

References 21 publications

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“…remeshing the FE model and/or redefining the mathematical model can be conducted as demonstrated in Ref. [12].…”

Section: Calibration Framework For the Fe Modelmentioning

confidence: 99%

“…To appropriately assess the performance of the numerical model, the uncertainties and errors should be statistically quantified and a proper metric that represents the agreement between the numerical model and experimental data should be introduced. The statistical calibration or updating of the numerical model can also be defined as the refining the prior distributions of a set of input parameters for the numerical model in order to maximize the agreement between the results of the numerical model and a chosen set of experimental data [12,13]. The validation and calibration of a numerical model under data and model uncertainties are ongoing issues in many areas [14,15].…”

Section: Introductionmentioning

confidence: 99%

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Statistical calibration of a finite element model for human middle ear

Lee

Ahn²

2015

J Mech Sci Technol

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A Finite element (FE) model of a human middle ear is developed, assessed, and updated using a statistical approach. The model consists of three ossicles (malleus, incus, and stapes), a tympanic membrane, tendons, and ligaments. The uncertainty of the model input parameters associated with the material properties and boundary conditions are considered in order to assess the validity of the model. The variation of the umbo displacement transfer function (UDTF) as a result of the uncertainty of the model input parameters is estimated and compared with those from experiments. Using the analysis of variance (ANOVA) with a three-level orthogonal array, the most important calibration parameters, which are composed of stiffness-related and density variables, are selected. Furthermore, a metric for statistical calibration is introduced. Through minimizing the calibration metric, the calibration parameters are updated in order to enhance the performance of the middle ear FE model. The proposed statistical calibration framework effectively improves the middle ear FE model performance.

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“…remeshing the FE model and/or redefining the mathematical model can be conducted as demonstrated in Ref. [12].…”

Section: Calibration Framework For the Fe Modelmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Statistical calibration of a finite element model for human middle ear

Lee

Ahn²

2015

J Mech Sci Technol

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“…In addition, the material property is commonly used as a tuning parameter in the calibration process because of its uncertainty. 21,22 The MOO for calibration is formulated as follows:…”

Section: Calibration Of Fe Modelmentioning

confidence: 99%

Design Optimization of PZT-Based Piezoelectric Cantilever Beam by Using Computational Experiments

Kim

Park

Lim

et al. 2016

Journal of Elec Materi

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Piezoelectric energy harvesting is gaining huge research interest since it provides high power density and has real-life applicability. However, investigative research for the mechanical-electrical coupling phenomenon remains challenging. Many researchers depend on physical experiments to choose devices with the best performance which meet design objectives through case analysis; this involves high design costs. This study aims to develop a practical model using computer simulations and to propose an optimized design for a lead zirconate titanate (PZT)-based piezoelectric cantilever beam which is widely used in energy harvesting. In this study, the commercial finite element (FE) software is used to predict the voltage generated from vibrations of the PZT-based piezoelectric cantilever beam. Because the initial FE model differs from physical experiments, the model is calibrated by multi-objective optimization to increase the accuracy of the predictions. We collect data from physical experiments using the cantilever beam and use these experimental results in the calibration process. Since dynamic analysis in the FE analysis of the piezoelectric cantilever beam with a dense step size is considerably time-consuming, a surrogate model is employed for efficient optimization. Through the design optimization of the PZT-based piezoelectric cantilever beam, a high-performance piezoelectric device was developed. The sensitivity of the variables at the optimum design is analyzed to suggest a further improved device.

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“…This situation can be prevented as long as statistical model calibration is performed. The authors developed a statistical calibration technique which employs uncertainty propagation, optimization and likelihood function as calibration metric 25 . The technique is used to increase accuracy of the computer model of EH skin in next subsection.…”

Section: A Overview Of Statistical Model Calibrationmentioning

confidence: 99%

Statistical Model Calibration for Energy Harvesting Skin Analysis and Design

Jung¹,

Cho²,

Yoon

et al. 2012

53rd AIAA/ASME/ASCE/AHS/ASC Structures, Structural Dynamics and Materials Conference

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The modern advances in wireless technology and low-power electronics has brought a variety of wireless sensors in market recently; however, the limited lifespan and high replacement cost of batteries make it difficult to fully utilize performance of wireless sensors. Energy harvesting (EH) technology that harvests electrical energy from the ambient vibration energy has been emerged as an ultimate solution to prolong the battery life or eliminate the need of batteries for wireless sensors. Energy harvesting (EH) skin is one of the EH devices that generates electrical energy from the vibrating skin structure with an additional thin piezoelectric layer as one embodiment. As long as the power level of EH skin does not far exceed required one of wireless sensors, the key design consideration must be reliable power generation through the life of wireless sensors regardless of uncertainty and/or variation in material property, boundary condition, excitation etc. This paper presents a framework of statistical model calibration to develop a stochastic computer model for robust and reliable EH skin design. The framework consists of two different hierarchical levels: (1) bottom-level calibration with mechanical response and (2) top-level calibration with electrical response. Cantilever-type energy harvesters are used to demonstrate the statistical calibration framework. The statistical calibration employs uncertainty propagation analysis, optimization and likelihood metric to obtain unknown model variables such as compliance (s 11 ), piezoelectric strain coefficient (d 31 ) and permittivity (ε 33 ). With a computer model after model calibration, the EH skin was designed to generate maximum power and the probability density function (PDF) of predicted power is calculated and verified by experiments. Finally, a prototype of the EH skin was manufactured and demonstrated to operate wireless temperature sensors for structural health monitoring and/or building automation. It is conclude that the EH skin can generates enough power to operate many wireless sensors for building automation, smart plant and/or structural health monitoring. Nomenclatures 11 = compliance d 31 = piezoelectric strain constant ε 33 = permittivity θ = unknown model variable vectors 1 Senior researcher, The 1 st R&D Institute, bcjung79@gmail.com. 2 Master student, School of Mechanical and Aerospace Engineering, odyssey44@naver.com, AIAA student member. 3 Master student, School of Mechanical and Aerospace Engineering, heonjun@snu.ac.kr, AIAA student member. 4

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A hierarchical framework for statistical model calibration in engineering product development

Cited by 66 publications

References 21 publications

Statistical calibration of a finite element model for human middle ear

Statistical calibration of a finite element model for human middle ear

Design Optimization of PZT-Based Piezoelectric Cantilever Beam by Using Computational Experiments

Statistical Model Calibration for Energy Harvesting Skin Analysis and Design

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