Time‐varying reliability analysis based on hybrid Kalman filtering and probability density evolution
Bibliographic record
Abstract
Abstract The study introduces a novel approach for time‐varying reliability analysis of structures called “hybrid UKF‐PDEM” by integrating the unscented Kalman filter (UKF) and the probability density evolution method (PDEM). The UKF estimates the displacement, velocity, stiffness, and damping parameters of a structure at each time step subjected to dynamic loading for structural damage quantification. The estimated parameters at each time step are then input into the PDEM to calculate the time‐varying probability density function (PDF) of the estimated states. The estimated PDF is used to update the uncertainty matrix of the estimated states in each iteration and to determine the time‐varying reliability curves of the structure. To demonstrate the effectiveness of the proposed method, we applied it to a numerical model of a three‐degree‐of‐freedom system and a full‐scale seven‐story building with different damage scenarios. The method is used to estimate the level of damage and calculate the corresponding reliability curve of the system over time for each damage scenario, utilizing the estimated structural responses and stiffness values. The extracted reliability values for each damage scenario follow the level of damage over time. This study shows that the newly developed method is computationally efficient for building a digital twin and enables real‐time damage identification and reliability analysis in various structural systems. The method's applicability to different types of structures highlights its versatility and potential for widespread use in assessing the integrity of buildings and infrastructure.
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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 | 0.001 | 0.003 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.001 | 0.000 |
| Science and technology studies | 0.000 | 0.001 |
| Scholarly communication | 0.001 | 0.001 |
| Open science | 0.001 | 0.001 |
| Research integrity | 0.001 | 0.001 |
| Insufficient payload (model declined to judge) | 0.001 | 0.000 |
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".