Hybrid MB-DEIM approach for parametrized nonlinear dynamics of a verticalaxis rotating machine
Bibliographic record
Abstract
Abstract: Rotating machinery is involved in many industrial systems, such as aircraft, vehicles, machine centers, and turbines. Assessing their functioning conditions is very important to ensure safe operations and to schedule maintenance. Most of the shafts in such machines are horizontal. In this case, the bearing reaction forces can be calculated based on the static radial load caused by the dead weight of the rotor. However, if the rotating shaft is installed vertically, the clearance between the shaft and the bearing causes the bearing reaction forces to be nonlinear and difficult to quantify. Our objective is to create a parametrized model of a vertical axis rotating machine that can reproduce the response for a wide range of problem parameters, allowing us to adjust those parameters in real-time. As high-fidelity numerical models usually become computationally expensive when considering high-dimensional systems, or systems with multiple parameters, reduced-order models (ROMs) approximate the solution in a way that simplifies the calculation without compromising accuracy. They also allow parameter tuning in real-time. Towards developing a parametrized model of the aforementioned machine, we developed a nonlinear global space-frequency solver that iteratively constructs a lowrank representation of the solution based on the use of Modal Basis (MB) analysis and the Discrete Empirical Interpolation Method (DEIM). The DEIM builds an approximating reduced basis of the nonlinear force(s) using calculated (if available) or experimental values, which helps to accelerate computations compared to classical time-incremental numerical solvers such as Newton-Raphson. To create the parametrized model, we run this solver several times, where in each iteration it solves for a random set of problem parameters creating a set of sparse data. The sparse data is then fed into a sparse Proper Generalized Decomposition (s-PGD) algorithm that generates a library of solutions to the parametrized problem. This will allow to extract the solution corresponding to any set of problem parameters quickly and efficiently. The VARM's behavior can be predicted in a variety of scenarios using this library of solutions. Using this information, we can choose optimal operating conditions, predict failures, and plan maintenance. We can also identify actual values of parameters that are approximated or challenging to quantify by choosing a solution from this library that matches real-time measured data. Future developments can extend this method to the full Francis turbine. This method can also be used for other systems represented by a similar mathematical model.
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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 | 0.001 |
| 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".