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Finding Curve Non Convexity
znetsixe edited this page 2026-05-11 22:24:29 +02:00
title, created, updated, status, tags, sources
| title | created | updated | status | tags | sources | |||||
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| Pump Curve Non-Convexity | 2026-04-07 | 2026-04-07 | proven |
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Note
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Pump Curve Non-Convexity from Sparse Data
Finding
The C5-D03R-SHN1 pump's power curve is non-convex after spline interpolation. The marginal cost (dP/dQ) shows a spike-then-valley pattern:
C5 dP/dQ across flow range @ ΔP=2000 mbar:
6.4 m3/h → 1,316,610 (high)
10.2 m3/h → 2,199,349 (spikes UP)
17.7 m3/h → 1,114,700 (dropping)
21.5 m3/h → 453,316 (valley — cheapest)
29.0 m3/h → 1,048,375 (rising again)
44.1 m3/h → 1,107,708 (high)
Root Cause
The C5 curve has only 5 raw data points per pressure level. The monotonic cubic spline (Fritsch-Carlson) creates a smooth curve through all 5 points, but with such sparse data it introduces non-convex regions that don't match the physical convexity of a real pump.
Impact
- The equal-marginal-cost theorem (KKT conditions) does not apply — it requires convexity
- The BEP-Gravitation slope estimate at a single point can be misleading in non-convex regions
- The marginal-cost refinement loop fixes this by using actual power evaluations instead of slope assumptions
Recommendation
Add more data points (15-20 per pressure level) to the C5 curve. This would make the spline track the real convex physics more closely, eliminating the non-convex artifacts.