Details
| Original language | English |
|---|---|
| Article number | 117490 |
| Journal | Computer Methods in Applied Mechanics and Engineering |
| Volume | 433 |
| Issue number | Part A |
| Early online date | 7 Nov 2024 |
| Publication status | E-pub ahead of print - 7 Nov 2024 |
Abstract
Non-probabilistic convex models are powerful tools for structural model updating with uncertain‑but-bounded parameters. However, existing non-probabilistic model updating (NPMU) methods often struggle with detecting parameter correlation due to limited prior information. Worth still, the unique core steps of NPMU, involving nested inner layer forward uncertainty propagation and outer layer inverse parameter updating, present challenges in efficiency and convergence. In response to these challenges, a novel and flexible NPMU scheme is introduced, integrating analytical correlation propagation and parallel interval bounds prediction to enable automatic detection of parameter correlations. In the forward uncertainty propagation phase, a linear coordinate transformation is applied to map the original parameter space to a standard hypercube space, simplifying correlation-involved bounds prediction into conventional interval bounds prediction. Moreover, an analytical correlation propagation formula is derived using a second-order response approximation to sidestep the complexities of geometry-based correlation calculations. To expedite forward propagation, a derivative-aware neural network model is employed to replace the physical solver, facilitating improved fitting capabilities and automatic differentiation, including the calculation of Jacobian and Hessian matrices essential for correlation propagation. The neural network's inherent parallelism accelerates interval bounds prediction through parallel computation of samples. In the inverse parameter updating phase, the block coordinate descent algorithm is embraced to narrow the search space and boost convergence capabilities, while the perturbation method is utilized to determine the optimal starting point for optimization. Two numerical examples illustrate the efficacy of the proposed method in updating structural models while considering correlations.
Keywords
- Block coordinate descent, Correlation propagation, Derivative-aware metamodel, Model updating, Neural network, Non-probabilistic uncertainty
ASJC Scopus subject areas
- Engineering(all)
- Computational Mechanics
- Engineering(all)
- Mechanics of Materials
- Engineering(all)
- Mechanical Engineering
- Physics and Astronomy(all)
- General Physics and Astronomy
- Computer Science(all)
- Computer Science Applications
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In: Computer Methods in Applied Mechanics and Engineering, Vol. 433, No. Part A, 117490, 01.01.2025.
Research output: Contribution to journal › Article › Research › peer review
}
TY - JOUR
T1 - Efficient non-probabilistic parallel model updating based on analytical correlation propagation formula and derivative-aware deep neural network metamodel
AU - Mo, Jiang
AU - Yan, Wang Ji
AU - Yuen, Ka Veng
AU - Beer, Michael
N1 - Publisher Copyright: © 2024 Elsevier B.V.
PY - 2024/11/7
Y1 - 2024/11/7
N2 - Non-probabilistic convex models are powerful tools for structural model updating with uncertain‑but-bounded parameters. However, existing non-probabilistic model updating (NPMU) methods often struggle with detecting parameter correlation due to limited prior information. Worth still, the unique core steps of NPMU, involving nested inner layer forward uncertainty propagation and outer layer inverse parameter updating, present challenges in efficiency and convergence. In response to these challenges, a novel and flexible NPMU scheme is introduced, integrating analytical correlation propagation and parallel interval bounds prediction to enable automatic detection of parameter correlations. In the forward uncertainty propagation phase, a linear coordinate transformation is applied to map the original parameter space to a standard hypercube space, simplifying correlation-involved bounds prediction into conventional interval bounds prediction. Moreover, an analytical correlation propagation formula is derived using a second-order response approximation to sidestep the complexities of geometry-based correlation calculations. To expedite forward propagation, a derivative-aware neural network model is employed to replace the physical solver, facilitating improved fitting capabilities and automatic differentiation, including the calculation of Jacobian and Hessian matrices essential for correlation propagation. The neural network's inherent parallelism accelerates interval bounds prediction through parallel computation of samples. In the inverse parameter updating phase, the block coordinate descent algorithm is embraced to narrow the search space and boost convergence capabilities, while the perturbation method is utilized to determine the optimal starting point for optimization. Two numerical examples illustrate the efficacy of the proposed method in updating structural models while considering correlations.
AB - Non-probabilistic convex models are powerful tools for structural model updating with uncertain‑but-bounded parameters. However, existing non-probabilistic model updating (NPMU) methods often struggle with detecting parameter correlation due to limited prior information. Worth still, the unique core steps of NPMU, involving nested inner layer forward uncertainty propagation and outer layer inverse parameter updating, present challenges in efficiency and convergence. In response to these challenges, a novel and flexible NPMU scheme is introduced, integrating analytical correlation propagation and parallel interval bounds prediction to enable automatic detection of parameter correlations. In the forward uncertainty propagation phase, a linear coordinate transformation is applied to map the original parameter space to a standard hypercube space, simplifying correlation-involved bounds prediction into conventional interval bounds prediction. Moreover, an analytical correlation propagation formula is derived using a second-order response approximation to sidestep the complexities of geometry-based correlation calculations. To expedite forward propagation, a derivative-aware neural network model is employed to replace the physical solver, facilitating improved fitting capabilities and automatic differentiation, including the calculation of Jacobian and Hessian matrices essential for correlation propagation. The neural network's inherent parallelism accelerates interval bounds prediction through parallel computation of samples. In the inverse parameter updating phase, the block coordinate descent algorithm is embraced to narrow the search space and boost convergence capabilities, while the perturbation method is utilized to determine the optimal starting point for optimization. Two numerical examples illustrate the efficacy of the proposed method in updating structural models while considering correlations.
KW - Block coordinate descent
KW - Correlation propagation
KW - Derivative-aware metamodel
KW - Model updating
KW - Neural network
KW - Non-probabilistic uncertainty
UR - http://www.scopus.com/inward/record.url?scp=85208230839&partnerID=8YFLogxK
U2 - 10.1016/j.cma.2024.117490
DO - 10.1016/j.cma.2024.117490
M3 - Article
AN - SCOPUS:85208230839
VL - 433
JO - Computer Methods in Applied Mechanics and Engineering
JF - Computer Methods in Applied Mechanics and Engineering
SN - 0045-7825
IS - Part A
M1 - 117490
ER -