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Source-tree mirror of EVOLV.wiki.git refactor (27a42ee on wiki.git): - 7 master pages rewritten with clean design (Home, Architecture, Topology-Patterns, Topic-Conventions, Telemetry, Getting-Started, Glossary). Tables and Mermaid for visuals, gitea alert callouts for warnings, shields badges for metadata only. No emoji as decoration. - Archive.md becomes a removal-changelog pointing readers to git history and to the successor pages. - _Sidebar.md updated to navigate the new flat-name layout. - Concept / finding / manual pages: uniform mini-header (badges + "reference page" callout) added without rewriting domain content. - Every internal link now uses the flat naming that resolves on the live gitea wiki (Concept-ASM-Models, Finding-BEP-..., etc.). On wiki.git: 29 Archive-* pages hard-deleted (the git history preserves them; Archive.md documents the removal). Co-Authored-By: Claude Opus 4.7 (1M context) <noreply@anthropic.com>
40 lines
1.7 KiB
Markdown
40 lines
1.7 KiB
Markdown
---
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title: Pump Curve Non-Convexity
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created: 2026-04-07
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updated: 2026-04-07
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status: proven
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tags: [curves, interpolation, C5, non-convex]
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sources: [nodes/generalFunctions/datasets/assetData/curves/hidrostal-C5-D03R-SHN1.json]
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---
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> [!NOTE]
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> Reference page. Maintained for context; not regenerated by code. See [Home](Home) for current top-level navigation.
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# Pump Curve Non-Convexity from Sparse Data
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## Finding
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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:
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```
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C5 dP/dQ across flow range @ ΔP=2000 mbar:
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6.4 m3/h → 1,316,610 (high)
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10.2 m3/h → 2,199,349 (spikes UP)
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17.7 m3/h → 1,114,700 (dropping)
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21.5 m3/h → 453,316 (valley — cheapest)
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29.0 m3/h → 1,048,375 (rising again)
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44.1 m3/h → 1,107,708 (high)
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```
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## Root Cause
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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.
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## Impact
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- The equal-marginal-cost theorem (KKT conditions) does not apply — it requires convexity
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- The BEP-Gravitation slope estimate at a single point can be misleading in non-convex regions
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- The marginal-cost refinement loop fixes this by using actual power evaluations instead of slope assumptions
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## Recommendation
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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.
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