Probabilistic Models to Approximate Highly Repetitive Linear and Nonlinear Finite Element Analyses of Nuclear Components
Bibliographic record
Abstract
In the development and technical support of nuclear plants, Engineers have to deal with highly repetitive finite element analyses that involve modeling of local variations of the initial design, local flaws due to corrosion-erosion effects, material properties degradation, and modifications of the loading conditions. This paper presents the development of generic models that emulate the behavior of a complex finite element model in a simplified form, with the statistical representation based on a sampling of base-model data for a variety of test cases. An improved Latin Hypercube algorithm is employed to generate the sampling points based on the number and the range of the variables that are considered in the design space. Four filling methods of the approximation models are discussed in this study: response surface, nonlinear, neural networks, and piecewise polynomial model. Furthermore, a bootstrapping procedure is employed to improve the confidence intervals of the original coefficients, and the single-factor or double-factor analysis of variance is applied to determine whether a significant influence exists between the investigated factors. Two numerical examples highlight the accuracy and efficiency of the methods. The first example is the linear elastic analysis of a pipe bend under pressure loading. The objective of the probabilistic assessment is to determine the relation between the loading conditions as well as the geometrical aspects of this elbow (pipe wall thickness, outside diameter, elbow radius, and maximum ovality tolerance) and the maximum stress in the elbow. The second example is an axisymmetric nozzle under primary and secondary cycling loads. Variations of the geometrical dimensions, nonlinear material properties, and cycling loading are taken as the input parameters, whereas the response variable is defined in terms of Melan’s theorem translated into the Nonlinear Superposition 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 | 0.002 | 0.005 |
| 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 | 0.001 |
| Insufficient payload (model declined to judge) | 0.002 | 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".