Stochastic control of reservoir systems using indicator functions: New enhancements
Bibliographic record
Abstract
In our previous works, deterministic release policies were considered for the development of approximations of the two lower moments of the storage volume defined by the dynamic equation of the reservoir in discrete time but in continuous state space. Important innovation in that work was the incorporation of the lower and upper bounds of reservoir systems into the dynamic equation for the storage volume using indicator functions. The current work, which also does not use discretization, looks at an extension of previous developments that incorporates standard operating policies, and also a new randomized release policy, both of which make the moments calculations exact under the assumptions that (1) the sum of current random inflow and the previous storage volume can be described by just the two lower moments and (2) only the means and variances of the inflows are known. First‐ and second‐moment expressions are derived for the stochastic storage state variable and include terms for the failure probabilities (probabilities of spills or deficits). Expected values of the storage state, variances of storage, release policies, and failure probabilities are obtained by solving the optimal reservoir operations problem using nonlinear programming. The various statistics thus obtained from this optimization compare extremely well with those obtained from simulation for the single‐reservoir monthly operations problem studied. The exact characterization of the mean and variance of the storage state variable is derived, which is a difficulty in existing formulations based on linear quadratic Gaussian methods. For example, the latter methods have been unable to estimate these moments reasonably accurately, especially for long‐term operations, whereas the traditional storage theory based on discretization brings on the “curse of dimensionality.” The presentation herein is directed to both traditional reservoir storage theorists who are interested in the design of a reservoir where estimating the probabilities of spills and deficits is important and modern reservoir analysts who are interested in multiperiod optimal release decisions in the operations of reservoirs.
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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 | 0.004 | 0.007 |
| 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 | 0.002 | 0.003 |
| Open science | 0.001 | 0.002 |
| Research integrity | 0.001 | 0.003 |
| Insufficient payload (model declined to judge) | 0.002 | 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 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".