Generation of Tri-Directional Spectra-Compatible Time Histories Coupling the Influence Matrix Method and Gram–Schmidt Orthogonalization
Bibliographic record
Abstract
This study presents a new approach for obtaining a set of tri-directional time histories compatible with target design spectra by modifying real recorded earthquake ground motions. The influence matrix method (IMM) based on eigenfunction expansion is improved for typical design response spectra with different shapes and employed in order to achieve accurate matching with the target design spectra. By applying the Gram–Schmidt orthogonalization in each iteration of the IMM procedure, the correlation coefficient between any two components can be guaranteed to be strictly zero. Hence, the generated three components in the orthogonal directions are statistically independent. The generated time histories satisfy the requirements of current codes and standards. Two examples are presented to illustrate the procedure and the superiority of the proposed method, with the maximum relative error between the generated time histories and target design spectra being less than 0.2% in [0.6, 100] Hz, and the code requirements being satisfied strictly.
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How this classification was reachedexpand
Full frame distilled prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. Learned from the 10,348 direct Codex labels and 10,348 direct Gemma labels. Candidate is the union of thresholded teacher heads; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels or direct frontier model labels.
Codex and Gemma teacher scores by category
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.000 | 0.000 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.000 | 0.000 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.000 | 0.000 |
| Research integrity | 0.000 | 0.000 |
| Insufficient payload (model declined to judge) | 0.000 | 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 teacher head, 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".