Fault-Tolerant Soft Sensor Modeling Based on a Two-Dimensional Group Distributionally Robust Optimization Framework
Bibliographic record
Abstract
In industrial automation and intelligence, fault tolerance mechanisms have always been an attractive topic. To develop soft sensors with fault tolerance for different types of faults and unforeseen new faults, this article proposes a two-dimensional group distributionally robust optimization (2D-GDRO) framework for fault-tolerant soft sensor modeling. We propose to describe the potential distributions of new fault conditions with an uncertainty set and optimize the soft sensor model by minimizing the worst-case risk over the uncertainty set. Considering the restricted representation range of the uncertainty set constructed directly from a mixture distribution of a limited number of existing fault conditions in the training set, a two-dimensional uncertainty set is designed at the group dimension and the sample dimension. To efficiently train a fault-tolerant soft sensor within the 2D-GDRO framework, we introduce a triple-interleaved optimization algorithm. This algorithm integrates mini-batch stochastic gradient descent, exponentiated gradient ascent, and group-wise SoftMax techniques. Finally, the fault tolerance of the 2D-GDRO framework based soft sensor is verified using the Tennessee-Eastman process and the real three-phase flow facility. The experimental results show that 2D-GDRO outperforms other training frameworks in average soft sensing accuracy under new fault conditions.
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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 | 0.001 | 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".