A Moving Least Squares Methodology for Dynamic Systems with Parameter and Excitation Inputs
Bibliographic record
Abstract
Meta-models have a valuable place in the efficient design and optimization of many probabilistic engineering systems wherein numerous iterations are required. Meta-models are simple to form, typically much faster, and usually as accurate as the original mechanistic model. The least squares (LS) approach is one of the oldest means of forming meta-models. Further, a modification of the original model, called the moving least squares (MLS) method, permits a larger design space, needs fewer training sets, and usually produces a more accurate model since it uses only the data local to the query point. Herein, we expand the one- or two-parameter MLS method to accommodate systems with both multiple parameters, multiple excitations and multiple responses. The novelty of this paper is the simple and effective distance measure proposed to select the training sets nearest to the query set. Herein, the training sets comprise a mixture of time-dependent excitations and scalar component parameters. The excitations in the training sets are compared to the query set using standard performance indexes. These excitations and the component parameters typically have different magnitudes and units, and scaling to a common range is necessary. Finally, the individual measures are combined into a single system distance metric for each training set via an unbiased 2-Norm computation. Only the training sets within a critical distance are retained for the reduced meta-model. The impact of the work herein is the considerable reduction in the standard number of training sets needed to build the meta-model, while at the same time, maintaining a broad design space and acceptable accuracy. Examples with dynamic systems show the accuracy and efficiency of the novel MLS method.
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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 | 0.001 |
| 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 | 0.001 | 0.001 |
| Research integrity | 0.001 | 0.002 |
| Insufficient payload (model declined to judge) | 0.004 | 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".