TY - JOUR

T1 - Optimization or Bayesian Strategy? Performance of the Bhattacharyya Distance in Different Algorithms of Stochastic Model Updating

AU - Bi, Sifeng

AU - Beer, Michael

AU - Zhang, Jingrui

AU - Yang, Lechang

AU - He, Kui

N1 - Funding Information: This work was supported by the Alexander von Humboldt Foundation in Germany (Award No. 1193706) and the Beijing Institute of Technology Research Fund Program for Young Scholars in China, which are greatly appreciated. Dr. Lechang Yang acknowledges the support of the National Natural Science Foundation of China under Grant No. 52005032, the Aeronautical Science Foundation of China under Grant No. 2018ZC74001.

PY - 2021/6

Y1 - 2021/6

N2 - The Bhattacharyya distance has been developed as a comprehensive uncertainty quantification metric by capturing multiple uncertainty sources from both numerical predictions and experimental measurements. This work pursues a further investigation of the performance of the Bhattacharyya distance in different methodologies for stochastic model updating, and thus to prove the universality of the Bhattacharyya distance in various currently popular updating procedures. The first procedure is the Bayesian model updating where the Bhattacharyya distance is utilized to define an approximate likelihood function and the transitional Markov chain Monte Carlo algorithm is employed to obtain the posterior distribution of the parameters. In the second updating procedure, the Bhattacharyya distance is utilized to construct the objective function of an optimization problem. The objective function is defined as the Bhattacharyya distance between the samples of numerical prediction and the samples of the target data. The comparison study is performed on a four degrees-of-freedom mass-spring system. A challenging task is raised in this example by assigning different distributions to the parameters with imprecise distribution coefficients. This requires the stochastic updating procedure to calibrate not the parameters themselves, but their distribution properties. The second example employs the GARTEUR SM-AG19 benchmark structure to demonstrate the feasibility of the Bhattacharyya distance in the presence of practical experiment uncertainty raising from measuring techniques, equipment, and subjective randomness. The results demonstrate the Bhattacharyya distance as a comprehensive and universal uncertainty quantification metric in stochastic model updating.

AB - The Bhattacharyya distance has been developed as a comprehensive uncertainty quantification metric by capturing multiple uncertainty sources from both numerical predictions and experimental measurements. This work pursues a further investigation of the performance of the Bhattacharyya distance in different methodologies for stochastic model updating, and thus to prove the universality of the Bhattacharyya distance in various currently popular updating procedures. The first procedure is the Bayesian model updating where the Bhattacharyya distance is utilized to define an approximate likelihood function and the transitional Markov chain Monte Carlo algorithm is employed to obtain the posterior distribution of the parameters. In the second updating procedure, the Bhattacharyya distance is utilized to construct the objective function of an optimization problem. The objective function is defined as the Bhattacharyya distance between the samples of numerical prediction and the samples of the target data. The comparison study is performed on a four degrees-of-freedom mass-spring system. A challenging task is raised in this example by assigning different distributions to the parameters with imprecise distribution coefficients. This requires the stochastic updating procedure to calibrate not the parameters themselves, but their distribution properties. The second example employs the GARTEUR SM-AG19 benchmark structure to demonstrate the feasibility of the Bhattacharyya distance in the presence of practical experiment uncertainty raising from measuring techniques, equipment, and subjective randomness. The results demonstrate the Bhattacharyya distance as a comprehensive and universal uncertainty quantification metric in stochastic model updating.

KW - Bayesian model updating

KW - Bhattacharyya distance

KW - Markov chain Monte Carlo

KW - Optimization model updating

KW - Uncertainty quantification

UR - http://www.scopus.com/inward/record.url?scp=85126909447&partnerID=8YFLogxK

U2 - 10.1115/1.4050168

DO - 10.1115/1.4050168

M3 - Article

VL - 7

JO - ASCE-ASME Journal of Risk and Uncertainty in Engineering Systems, Part B: Mechanical Engineering

JF - ASCE-ASME Journal of Risk and Uncertainty in Engineering Systems, Part B: Mechanical Engineering

SN - 2332-9017

IS - 2

M1 - 020903

ER -