LUB: A Novel Adaptive Kriging Framework Incorporating Lower and Upper Bound Analysis for Enhanced Structural Reliability-Based Design Optimization
Bibliographic record
Abstract
Reliability-based design optimization (RBDO) is increasingly recognized for its potential to enhance the performance of structural engineering systems. Despite its potential, traditional RBDO methods are often hampered by significant computational challenges, especially when applied to nonlinear structures where simultaneous execution of structural optimization and reliability analysis increases the complexity of analysis. This computational burden presents a significant barrier for broader application of RBDO in complex systems, which therefore highlights the need for more efficient approaches. To address this challenge, we introduce an adaptive Kriging-assisted RBDO framework that leverages lower and upper bounds (LUB) analysis to improve its computational efficiency and robustness. In this proposed framework, regions delineated by varying confidence bounds are used for identifying design points close to the limit state. Convergence is rigorously assessed by comparing design and reliability predictions across upper and lower bound interfaces, thereby ensuring both interpretability and robustness. The framework allows for flexibility through its seamless integration with various adaptive sampling processes, evolutionary optimization algorithms, and reliability assessment techniques. The proposed framework is evaluated for four benchmark examples and two engineering cases, demonstrating superior accuracy and efficiency with fewer model evaluations compared with existing approaches. Through iterative optimization, the framework consistently maintains cost and errors of reliability estimation within predefined thresholds, offering robust and computationally efficient solutions.
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How this classification was reachedexpand
Full frame machine prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. The Gemma side is a direct model label for every work in the frame, read from the title-only record. The Codex side is a classifier learned from the 10,348 direct Codex labels and calibrated to design-weighted sample rates; fields without enough sample support carry no Codex call. Candidate is the union of the two sides; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels.
Distilled classifier scores by category (both heads)
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.002 | 0.003 |
| Meta-epidemiology (narrow) | 0.001 | 0.001 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.000 | 0.001 |
| Scholarly communication | 0.001 | 0.001 |
| Open science | 0.002 | 0.002 |
| Research integrity | 0.001 | 0.001 |
| Insufficient payload (model declined to judge) | 0.002 | 0.001 |
Machine scores (provisional)
The two teacher heads of the student model, read on this work. A score orders the frame for review; it never asserts a category, and the validation status ships verbatim with every row.
Baseline scores from an immature model (maturity gate not passed, 7 training rounds). Scores rank; they never assert a category.
score_only:v0-immature-baseline · verbatim from the scoring run: score_only means the number may rank works, and no category label ships from itClassification
machine, unvalidatedMachine predicted; a candidate call from one source (direct Gemma or distilled Codex), not a consensus.
How this classification was reached, model by model and score by score, is at the end of the page under "How this classification was reached".