Journal of the Computational Structural Engineering Institute of Korea (한국전산구조공학회논문집)

Computational Structural Engineering Institute of Korea (한국전산구조공학회)
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Markov Chain Monte Carlo Simulation to Estimate Material Properties of a Layered Half-space

층상 반무한 지반의 물성치 추정을 위한 마르코프 연쇄 몬테카를로 모사 기법

  • Jin Ho Lee (Department of Ocean Engineering, Pukyong National University) ;
  • Hieu Van Nguyen (Department of Ocean Engineering, Pukyong National University) ;
  • Se Hyeok Lee (Department of Structural Engineering Research, Korea Institute of Civil Engineering and Building Technology)
  • 이진호 (부경대학교 해양공학과) ;
  • ;
  • 이세혁 (한국건설기술연구원 구조연구본부 )
  • Received : 2023.05.03
  • Accepted : 2023.06.12
  • Published : 2023.06.30
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Abstract

A Markov chain Monte Carlo (MCMC) simulation is proposed for probabilistic full waveform inversion (FWI) in a layered half-space. Dynamic responses on the half-space surface are estimated using the thin-layer method when a harmonic vertical force is applied. Subsequently, a posterior probability distribution function and the corresponding objective function are formulated to minimize the difference between estimations and observed data as well as that of model parameters from prior information. Based on the gradient of the objective function, a proposal distribution and an acceptance probability for MCMC samples are proposed. The proposed MCMC simulation is applied to several layered half-space examples. It is demonstrated that the proposed MCMC simulation for probabilistic FWI can estimate probabilistic material properties such as the shear-wave velocities of a layered half-space.

층상 반무한체에서의 확률론적 완전파형역산을 위한 Markov chain Monte Carlo (MCMC) 모사 기법을 정식화한다. Thin-layer method를 사용하여 조화 수직 하중이 작용하는 층상 반무한체의 지표면에서 추정된 동적 응답과 관측 데이터와의 차이 및 모델 변수의 사전 정보와의 차이를 최소화하도록 목적함수와 모델 변수의 사후 확률밀도함수를 정의한다. 목적함수의 기울기에 기반하여 MCMC 표본을 제안하기 위한 분포함수와 이를 수락 또는 거절할지 결정하는 수락함수를 결정한다. 기본 진동모드 뿐만이 아니라 고차 진동모드가 우세한 경우를 포함하여 다양한 층상 반무한체의 전단파 속도 추정에 제안된 MCMC 모사 기법을 적용하고 그 정확성을 검증한다. 제안된 확률론적 완전파형역산을 위한 MCMC 모사 기법은 층상 반무한체의 전단파 속도와 같은 재료 특성의 확률적 특성을 추정하는 데 적합함을 확인할 수 있다.

Keywords

Acknowledgement

이 논문(또는 저서)은 부경대학교 자율창의학술연구비(2021년)에 의하여 연구되었음.

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