TY - JOUR

T1 - Robust model updating in structural dynamics using a new non-implausibility-motivated optimisation approach

AU - Hübler, Clemens

AU - Gardner, Paul

AU - Wolniak, Marlene

N1 - Funding Information: We gratefully acknowledge the financial support of the Deutsche Forschungsgemeinschaft (DFG, German Research Foundation) – SFB-1463 – 434502799 and ENERGIZE – 436547100 . Dr Gardner would like to acknowledge the support of the UK Engineering and Physical Sciences Research Council (EPSRC) via Grant No. EP/R006768/1 .

PY - 2023/9/1

Y1 - 2023/9/1

N2 - Over the last few decades, model updating has become popular in structural dynamics, as it can be used to calibrate (finite element) models, with applications in assessing whether damage has occurred in a structural health monitoring context. Early approaches focused on determining the “best” fitting model in a deterministic manner. For example, mathematical optimisation was employed to minimise the discrepancy between measured and simulated modal parameters. More up-to-date approaches take uncertainties, e.g., due to measurement errors or model discrepancy, into account. In this context, Bayesian model updating has become increasingly popular. Recently, “likelihood-free” approaches have been proposed as an alternative to (exact) Bayesian model updating, with Bayesian history matching (BHM) being a promising “likelihood-free” technique. However, since BHM is based on an approximation of the simulation model using a Gaussian process regression (GPR), it can become inaccurate for highly non-linear and especially for (quasi-)discontinuous problems. Therefore, in this work, a new non-implausibility-motivated optimisation (NIMO) approach is proposed, which overcomes the non-linear space problem. The method is a combination of global optimisation and GPR. Global optimisation is used to accurately determine a non-implausible region in the design space, even for discontinuous problems. Subsequently, a GPR is fitted within the non-implausible region to efficiently approximate a posterior distribution. First, the NIMO approach is verified using test functions. Second, a validation is conducted by localising damage on a laboratory beam structure. It is demonstrated that the NIMO approach yields more robust results compared to BHM, while its computing times are manageable and – depending on the objective function – even smaller compared to BHM.

AB - Over the last few decades, model updating has become popular in structural dynamics, as it can be used to calibrate (finite element) models, with applications in assessing whether damage has occurred in a structural health monitoring context. Early approaches focused on determining the “best” fitting model in a deterministic manner. For example, mathematical optimisation was employed to minimise the discrepancy between measured and simulated modal parameters. More up-to-date approaches take uncertainties, e.g., due to measurement errors or model discrepancy, into account. In this context, Bayesian model updating has become increasingly popular. Recently, “likelihood-free” approaches have been proposed as an alternative to (exact) Bayesian model updating, with Bayesian history matching (BHM) being a promising “likelihood-free” technique. However, since BHM is based on an approximation of the simulation model using a Gaussian process regression (GPR), it can become inaccurate for highly non-linear and especially for (quasi-)discontinuous problems. Therefore, in this work, a new non-implausibility-motivated optimisation (NIMO) approach is proposed, which overcomes the non-linear space problem. The method is a combination of global optimisation and GPR. Global optimisation is used to accurately determine a non-implausible region in the design space, even for discontinuous problems. Subsequently, a GPR is fitted within the non-implausible region to efficiently approximate a posterior distribution. First, the NIMO approach is verified using test functions. Second, a validation is conducted by localising damage on a laboratory beam structure. It is demonstrated that the NIMO approach yields more robust results compared to BHM, while its computing times are manageable and – depending on the objective function – even smaller compared to BHM.

KW - Bayesian history matching

KW - Damage localisation

KW - FE model updating

KW - Global optimisation

KW - Uncertainty quantification

UR - http://www.scopus.com/inward/record.url?scp=85158817310&partnerID=8YFLogxK

U2 - 10.1016/j.ymssp.2023.110401

DO - 10.1016/j.ymssp.2023.110401

M3 - Article

VL - 198

JO - Mechanical Systems and Signal Processing

JF - Mechanical Systems and Signal Processing

SN - 0888-3270

M1 - 110401

ER -