Improved iterative regularization for vibration-based damage detection
Bibliographic record
Abstract
A vibration-based damage detection method is presented, which updates a finite element model from measured eigenfrequencies and mode shapes. Changes in stiffness of individual elements are interpreted as damage. The update problem is ill-posed and needs therefore regularization. Tikhonov regularization is a well known regularization method for linear problems. However, the update problem is nonlinear and there are different ways to use Tikhonov regularization in the nonlinear case. The usual way is to linearize the update problem with the sensitivity matrix and then apply regularization in each iteration. This approach has the disadvantage that the regularization effect depends on the number of iterations and may get lost as the number of iterations increases. The problem has been discussed in the mathematical literature but is not widely recognized in the engineering community. The alternative way is to regularize the nonlinear problem and then linearize it. This results in an additional term in the update equation that guarantees that regularization is independent of the number of iterations. Both ways are applied to a two-story frame with simulated measurements. Generalized cross-validation, L-curves, and errors of the update parameters are compared. The simulations confirm that the algorithm characterized by "regularize, then linearize" gives superior results. This algorithm is finally applied to a real frame recently tested in the lab. The frame is part of a full-size structure that has been damaged by pseudo-dynamic tests simulating different earthquake levels.
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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 | 0.002 |
| Meta-epidemiology (narrow) | 0.001 | 0.000 |
| 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 | 0.001 | 0.001 |
| Research integrity | 0.001 | 0.001 |
| Insufficient payload (model declined to judge) | 0.001 | 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".