An Efficient Methodology to Predict the Dynamic Instabilities of a Frictional System
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Bibliographic record
Abstract
<div class="section abstract"><div class="htmlview paragraph">Stochastic Finite Elements Method (SFEM) is applied in many fields. For instance, in frictional systems, it helps quantify uncertainties about the parameters controlling the involved process and thus, provides a more reliable prediction of the dynamic instabilities. Usually, SFEM is coupled with sensitivity theory to investigate the effect of a given input on the output. However, the available methods which often couple Monte-Carlo (MC) algorithm with the Finite Element (FE) method have a computational cost that scales linearly as a number of stochastic iteration N and input parameters k (i.e., t ~ N x k). To achieve convergence, the magnitude of N must be on the order of thousands or even millions. Hence, for a frictional system with 5 random variables and requiring 15 min of CPU time per run, the computational cost will exceed 52 days (!). Such a method cannot be applied in an industrial design framework with a high number of random variables since its CPU time becomes prohibitive. In this paper, an efficient SFEM is presented, and its performances demonstrated on a simplified disc brake system. The goal is to predict the most likely dynamic instabilities. The method is formulated to (i) reduce the computational cost while ensuring convergence and (ii) provide a reliable input-output mapping of the model which allows in turn a better prediction and investigation of the friction-induced vibration problem. The approach is based on the Fourier Sensitivity Amplitude Test (FAST) algorithm coupled with FE method through a Complex Eigenvalues Analysis (CEA). First, the uncertainties propagation is carried out using the periodic sampling approach by considering a variety of random variables (e.g., friction coefficient, Young modulus, etc.). Secondly, the random generated data are evaluated in an iterative way by mean of the CEA solver. Lastly, Fourier expansion is introduced to derive the partial variances and the variance of the model output. Based on the last decomposition, a 2D design map is used to visualize the effect of each random variable on the predicted instabilities. The obtained FAST-FE results are systematically compared with the reference approach, namely MC-FE. It is found that the inherent assumption of using a large number of samples is not more needed for reaching the stochastic convergence and thus, the estimation of the moments (i.e., the expected value, the variance and so forth). The periodic properties, carried by FAST research curve function, made it possible to propagate efficiently and within a reasonable computational cost the uncertainties upstream of the FE model. In comparison with the MC-FE, the proposed solver provides good results even when a coarser sample is used. The inefficiency of MC-FE solver is discussed.</div></div>
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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 | 0.002 | 0.000 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.000 |
| Bibliometrics | 0.000 | 0.001 |
| Science and technology studies | 0.001 | 0.000 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.001 | 0.000 |
| Research integrity | 0.000 | 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 it