title, created, updated, status, tags, sources
| title | created | updated | status | tags | sources | |||||
|---|---|---|---|---|---|---|---|---|---|---|
| BEP-Gravitation Optimality Proof | 2026-04-07 | 2026-04-07 | proven |
|
|
Note
Reference page. Maintained for context; not regenerated by code. See Home for current top-level navigation.
BEP-Gravitation vs Brute-Force Global Optimum
Claim
The machineGroupControl BEP-Gravitation algorithm (with marginal-cost refinement) produces near-optimal flow distribution across a pump group.
Method
Brute-force exhaustive search: 1000 steps per pump, all 2^n combinations, 0.05% flow tolerance. Station: 2x H05K-S03R + 1x C5-D03R-SHN1 @ ΔP=2000 mbar.
Results
| Demand | Brute force | machineGroupControl | Gap |
|---|---|---|---|
| 10% (71 m3/h) | 17.65 kW | 17.63 kW | -0.10% (MGC wins) |
| 25% (136 m3/h) | 34.33 kW | 34.33 kW | +0.01% |
| 50% (243 m3/h) | 61.62 kW | 61.62 kW | -0.00% |
| 75% (351 m3/h) | 96.01 kW | 96.10 kW | +0.08% |
| 90% (415 m3/h) | 122.17 kW | 122.26 kW | +0.07% |
Maximum deviation: 0.1% from proven global optimum.
Why the Refinement Matters
Before the marginal-cost refinement loop, the gap at 50% demand was 2.12%. The BEP-Gravitation slope estimate pushed 14.6 m3/h to C5 (costing 5.0 kW) when the optimum was 6.5 m3/h (0.59 kW). The refinement loop corrects this by shifting flow from highest actual dP/dQ to lowest until no improvement is possible.
Stability
Sweep 5-95% in 2% steps: 1 switch (rising), 1 switch (falling), same transition point. No hysteresis. See Pump Switching Stability.
Computational Cost
0.027-0.153ms median per optimization call (3 pumps, 6 combinations). Uses 0.015% of the 1000ms tick budget.