Mathematical Warning Model · v2 Technical Documentation

Version: v2 (second release) Algorithm name: Sensor-calibrated + fast sliding baseline warning model Date: 2026-08-14

1. Changes from v1

Item	v1	v2	Reason
Level naming	1 = Level-3 / 3 = Level-1 (Level-1 most severe)	0 = Normal / 1 = Level 1 / 2 = Level 2 / 3 = Level 3 (Level 3 most severe)	Standardized level system: larger number = more severe, maximum is Level 3
Debris-flow weights	0.40S+0.30Q+0.20dQ+0.10ΔS	0.30S+0.35Q+0.20dQ+0.15ΔS	Soil saturates easily and used to dominate the score, weight lowered; flow (flash-flood signal) raised to the highest weight
Q_MAX (full-channel flow)	30 L/min	3 L/min	Aligned with YF-S401 measured range (measured max ~1.7)
DQ_MAX (change-rate cap)	5 L/min/s	0.5 L/min/s	Measured per-second jumps ~0.3
Spike fallback threshold	2.0	0.5	Same as above; lets flow data truly participate in inference
Sliding-baseline cold start	2 hours	15 minutes	Adapts to local climate faster
Flash-flood independent path F	0.6Q̄+0.4dQ̄	Retained	Flow surge triggers independently, not gated by soil threshold
LCD display	None	Wind / soil moisture / flow / warning level	On-site visualization
Flow pulse diagnostics	Single-edge counting	Rising/falling edges counted separately + D8 level	Quickly locate wiring/edge-direction problems

Final level = max(Debris flow D, Flash flood F, Wind, Flow spike, Surge, Soil saturation)   ← 0~3

Level definitions (larger number = more severe):

Level	Meaning	Example trigger
0	Normal	All factors below thresholds
1	Level-1 warning (mildest)	D/F ≥ 0.45, or wind ≥ 25 km/h, or surge
2	Level-2 warning	D/F ≥ 0.55, or wind ≥ 40 km/h, or spike ≥ P95
3	Level-3 warning (most severe)	D/F ≥ 0.75, or wind ≥ 60 km/h

D = 0.30 × S̄ + 0.35 × Q̄ + 0.20 × dQ̄ + 0.15 × ΔS̄

Path skipped while soil < 60% (unsaturated) — flash flood / wind paths are not gated
Special rules: soil above local P90 + rising flow + 5-min continuous rise → Level 3 directly; soil above local P90 + flow ≥ 70% of channel capacity → Level 2; soil 10-min rise ≥ 20% → at least Level 1

F = 0.60 × Q̄ + 0.40 × dQ̄

Not gated by the soil threshold — triggers on flow surge alone
Acts as a flow-based approximation of the 70% Manning component (this scheme does not use an ultrasonic water-level sensor — water level overlaps with flow rate functionally, flow is the core)

Per-second flow change rate above local historical P95 → Level 2; ≥ 0.8 normalized → Level 1

Surge	Trigger
Soil rises ≥ 20% within 5 s	Level 1 immediately
Wind rises ≥ 12 km/h within 60 s	Level 1 immediately

Soil ≥ 85% or above local P90 → at least Level 1 (saturated soil is itself a hazard, independent of flow; persists until soil drops)

Upgrade: takes effect immediately and is held
Downgrade: only after the hold time — Level 1: 10 s / Level 2: 15 s / Level 3: 20 s
Prevents level flickering from single-point jitter / momentary drops

Window: 24 h, sampled once per minute; current value mapped to the local [P10, P95] range → 0~1 relative position
Cold start shortened to 15 minutes: baseline activates after 15 min of data; the previous 2-hour wait is removed
Fallback when data insufficient (absolute values, aligned to sensor range): Qn = flow/3, dQn = change-rate/0.5

W12.3 S45% F0.50     ← wind km/h · soil moisture % · flow L/min
ALARM:3 L3           ← warning level 0~3 (0=normal, 3=most severe)

Wind and warning level are pushed from the server (server.py) over serial (protocol D<wind>,<level>); soil moisture and flow are read locally by the Arduino

Flow data truly participates in inference: after calibration parameters are aligned with the sensor range, Q̄/dQ̄ change from "squashed mosquito legs" into effective factors; the flash-flood path responds to real flow changes
Sliding baseline activates quickly: 15-min cold start — self-adapts to local climate a quarter hour after power-on
Standardized level system: 0~3, larger number = more severe; LCD/web/docs use a consistent convention (Level 3 = highest)
On-site visualization: LCD shows the four core data streams in real time, observable without a computer/web page
Diagnostics: dual-edge pulse counting + level output — wiring/signal problems located within 30 s
Retains all v1 advantages: independent multi-paths, simple and explainable, cold-start capable

Flow sensor range still narrow: YF-S401 measured 0.05~3 L/min; real flood flows far exceed this — calibration parameters serve the current test environment (pump + pipe) and must be recalibrated when the environment changes
Wind data depends on an external computer (192.168.1.200:8001): when that service is offline the wind path is disabled (LCD wind shows 0)
15-min sliding baseline may still be unstable: under sudden weather, the first 15 minutes of baseline are low quality; absolute fallback precision is limited
Surge thresholds remain empirical (soil +20%/5 s, wind +12 km/h/60 s), not statistically calibrated
LCD is ASCII-only: cannot display Chinese; field staff must learn the 0~3 number meanings
Hard level thresholds: 0.45/0.55/0.75 step jumps with no confidence/persistence check (single-point jitter may cause false alarms)

Real-time: recomputed every second + LCD refreshed every second + web page refreshed every 0.5 s
Dual-end display: web page (full metrics) + LCD (core on-site metrics)
Calibratable parameters: Q_MAX/DQ_MAX/spike threshold come from measurements, not guesses
Modular: 5 independent paths, each can be iterated separately later

v2.x candidates: calibrate surge thresholds from historical distribution (replacing empirical values); ~~add persistence check (trigger only after N consecutive seconds above threshold, debounce)~~ — implemented: hysteresis hold (Level 1: 10 s / Level 2: 15 s / Level 3: 20 s)
v3 candidates: wind sensor onboard (sensor migrated to the integrated board, removing external-computer dependency); LCD shows flash-flood F / debris-flow D values