Second-Moment-Based Design of Dynamic Systems with Both Uncertain Excitations and Parameters Via Differentiable Meta-Models
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Bibliographic record
Abstract
Design using second-moments is readily understood by engineers. The output means (first-moments) and covariances (second-moments) are expressed through the means and covariances of the inputs. Further, various performance indexes can be formulated in terms of the second-moments and used to measure the “goodness” of the system’s performance. This paper addresses the design of nonlinear dynamic systems with uncertainty in both the component parameters and the excitations. In order to reduce the computational effort needed for design iterations on the mechanistic model, meta-models are introduced as computationally efficient surrogates. Herein, a novel, differentiable, meta-model that finds the response of dynamic systems with simultaneous component and excitation uncertainty is presented. Operationally, a family of training excitations and sets of training parameters are chosen and stored in respective matrices. Both types of inputs must have some realistic bounds. The corresponding responses, produced by the mechanistic model, make use of all of the training parameter sets interleafed with the training excitations: the time-sampled results are stored in the response matrix. An application of singular value decomposition on the response matrix reveals a repeating pattern of sub-vectors in the left singular vectors. Each sub-vector (viewed as the output) is replaced by a least-squares meta-model that links in the parameter matrix. The result is a parameter-response matrix with the same number of rows as the excitation matrix. Finally, to complete the meta-model, another application of the least-squares paradigm links the excitation matrix to the columns of the parameter-response matrix. Performance indexes, and approximations of their means and covariances through Taylor series, provide cogent optimization measures. The required derivatives are easily obtained from the explicit form of the meta-model. The efficacy of the meta-model is shown through the design of a nonlinear, quarter automobile, system. The accuracy, increased computation speed and robustness of the methodology provide the impact of the work herein. The sources of errors are identified and ways to mitigate them are discussed.
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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 | 0.005 | 0.001 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 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 it