The Note-Chord-Voice Framework: Structured Source Separation and Causal Inference for EV Charging Data

Jiajie Chen; Jinfeng Li

eess.SPAug 14, 2026

The Note-Chord-Voice Framework: Structured Source Separation and Causal Inference for EV Charging Data

Authors: Jiajie Chen, Jinfeng Li

Organizations: Xuteli School, Beijing Institute of Technology, No 8 and 9 Yards, Liangxiang East Road, Fangshan District, Beijing, 102488, China · School of Integrated Circuits and Electronics, Beijing Institute of Technology, No. 5 South Zhongguancun Street, Haidian District, Beijing, 100081, China

Abstract

Real-world EV charging data exhibit three interlocking pathologies: hardware fragmentation (network timeouts and billing resets split sessions), physical violations (independent energy/duration models produce impossible states like 50 kWh in 10 min on a 7 kW charger), and collider bias (clustering on post-treatment outcomes opens backdoor paths for price elasticity). We propose the Note-Chord-Voice framework, a music-inspired, axiom-driven pipeline that separates data cleaning (Repair Chords), structural pattern discovery (Harmonic Chords), descriptive source separation (NMF Voices), and causal inference into distinct, falsifiable stages. Key innovations: (i) falsification gates (A1-A5, G3, G10) that test data suitability before modeling; (ii) Gamma-initialized NMF with input rescaling for convergence stability from STL decomposition; (iii) tag-based coupon grading (A/B/C/D) to isolate quasi-random treatment from night-time confounders and targeted promotions; (iv) separate per-voice OLS to avoid simplex collinearity; (v) Foote novelty curves for structural regime detection. Applied to the Jiangmen dataset (495,707 sessions, 20 stations, from July 2024 to March 2025), all core axioms pass except G3 (no strong 168 h cycle). NMF achieves R^2=0.9921; the physically constrained duration model yields aggregate R^2=0.5409. Two voices are price-sensitive (beta = -11 to -14 min, p<0.001), of which one is stable (Voice 3, beta=-14.16) and one treatment-driven (Voice 1, beta=-11.10); only the stable voice supports causal claims. Counterfactual simulation shows targeting discounts to price-sensitive voices recovers 52.8% of discount expenditures (~0.85M CNY/year); restricting to the single stable price-sensitive voice yields a more conservative estimate.

Figures & tables

Concept	Symbol	Definition	Role
Note	$n_{i}$	$(t_{i},E_{i},\Delta t_{i},p_{i},c_{i})$ subject to physical manifold $\mathcal{M}$	Atomic validated event
Repair Chord	$C^{r}$	Information-theoretic reconstruction operator merging fragmented notes when $\Delta\text{MDL}>0$	Data reconstruction
Harmonic Chord	$C^{h}$	Recurrent local tensor motif discovered via Matrix Profile on residuals	Residual pattern discovery
Voice	$V_{k}$	Horizontal latent stream operationalized as non-negative basis vector in NMF factorization	Source separation
Measure	$\Gamma(t)$	Hierarchical metrical field (e.g. $24\text{ h}$ , $168\text{ h}$ , and holidays) via STL decomposition	Baseline intensity
Movement	$M_{j}$	Structural regime change in station load, detected by Foote novelty method	Regime segmentation

Table 1: Topological definitions for the Note–Chord–Voice framework.

Axiom	Statement	Test	Pass Cond.	Result
A1 Physical Manifold	A non-trivial fraction of sessions obey $E/\Delta t\leq 1.2P_{\max}$	Binomial proportion: $H_{0}$ : $>$ 95% violate	$p<0.05$	PASS (0.03% violations, $p\approx 0$ )
A2 Topological Contractibility	Short-gap sessions show MDL compression when merged	Wilcoxon on $\Delta\text{MDL}$ for gap $\in(0,2]$	med $>0$ , $p<0.01$	PASS (median log-likelihood ratio $=+0.43$ , $p=2.3\times 10^{-25}$ )
A3 Motif Recurrence	Residuals after $\Gamma(t)$ contain recurring patterns	Permutation test on MP distance vs. phase-randomized surrogate	$p<0.05$	PASS (best $p=0.000$ over 9 tests)
G3 Multi-periodicity	Load exhibits both 24 h and 168 h periodicity	FFT: rank of 24 h and 168 h frequency bins $\leq 3$	both	FAIL (only 24 h strong; 168 h rank $\geq 7$ )
A4 Source Separability	NMF outperforms station-mean baseline	Bootstrap error + ARI stability	err $<$ base, ARI $>0.7$	PASS ( $R^{2}=0.9921$ , stable $K=5$ )
A5 Interaction Structure	(a) Station–hour interaction $>5\%$ (b) NMF stable to treatment inclusion	(a) Two-way ANOVA (b) Control–full NMF alignment $r\geq 0.7$	both	PASS (partial) (16.9% interaction; 3/5 stable, 2 td)

Table 2: Axiom falsification gates: statement, test, pass condition, and result on the Jiangmen dataset.

Panel of Figure 1 — Figure 1: Note–Chord–Voice pipeline overview. The Axiom Gate (Step 0.5) tests data suitability before any complex model is built, ensuring graceful degradation if assumptions fail.

Grade	Description	Identification rationale	Role
Grade A	Generic platform-wide coupons, no targeting, available to all users	Exogenous: orthogonal to session timing and user characteristics	Primary instrument
Grade B	Night-time specific coupons (e.g., “off-peak discount”)	Endogenous: severely confounded by circadian timing	Excluded from main analysis
Grade C	Targeted promotions (user-specific, post-purchase, station-specific)	Correlated with user behavior and station characteristics	Excluded
Grade D	Other/unknown promotional tags	Ambiguous; excluded to maintain instrument purity	Excluded
None	No discount applied	Natural control group	Control

Table 3: Coupon grading taxonomy for Jiangmen promotions.

Figure 2: Physical manifold: energy vs. duration on log–log axes, colored by charger type. Diagonal lines show power limits ( $E/\Delta t=P_{\max}$ ) for 7 kW, 30 kW, 120 kW, and 480 kW chargers. The $\Gamma$ -initialized NMF is fitted to data within these boundaries, while unconstrained models might produce impossible states.

Figure 3: A2 axiom test results by gap bracket. Left: Median log-likelihood ratio (negative for back-to-back sessions, positive for short gaps). Right: Fraction of session pairs where merging is statistically beneficial. The fragmentation signal concentrates in the

(0,2]

minute gap bracket, contradicting the assumption that back-to-back sessions are the primary fragmentation source.

Figure 4: NMF voice selection: reconstruction error (left axis) and stability (ARI, right axis) vs. number of voices

K

K=5

is selected as the smallest

K

passing both A4 and A5(b).

K=3

achieves higher ARI but fails A5(b) (only 1/3 voices stable).

Figure 5: NMF voice temporal profiles (rows of

\mathbf{H}

). Each panel shows one voice’s normalized energy intensity across 168 hours of the week. Solid lines = stable voices (support causal claims); dashed lines = treatment-driven voices (descriptive only).

Figure 6: Station voice composition (normalized NMF responsibilities). Each bar shows how a station’s load is distributed across the 5 voices. Stations dominated by a single voice have clear behavioural signatures; mixed stations reflect overlapping user populations.

Figure 7: Movement detection for a representative station. Top: cosine self-similarity matrix of daily load profiles. Middle: Foote novelty curve (globally normalized) with detected changepoints. Bottom: daily energy load with Major (solid lines) and Minor (dashed lines) Movement boundaries.

Figure 8: Confounder check by coupon grade. Left axis: average price per kWh (blue); right axis: percentage of night-time sessions (orange). Grade B has an 86% night-time session concentration and average price 0.575 CNY/kWh, confirming that night-time electricity pricing—not coupons—drives its low price.

Figure 9: Voice-specific heterogeneous treatment effects (Grade A vs. None). Circles = stable voices (support causal claims); diamonds = treatment-driven voices (descriptive only). Red = price-sensitive (

\beta<-5

minutes,

p<0.1

); blue = price-insensitive. Voice 3 (stable,

\beta=-14.16

minutes) is the clean causal finding.

Figure 10: Revenue counterfactuals under alternative discount strategies. Comparison of baseline expenditure, targeted allocation to price-sensitive voices (Voices 1 and 3), and the new-targeted expansion scenario, illustrating net expenditure recovery and revenue impacts.

Limitation	Root Cause	Mitigation Strategy
G3 failure (no 168 h cycle)	Limited 9-month observation window; weak aggregate weekly periodicity	Framework adaptation: restrict $\Gamma$ to daily cycles; validate with multi-year data
Aggregate duration $R^{2}=0.54$	Linear approximation ( $\alpha\cdot E+\beta$ ) oversimplifies the CC-CV charging taper	Adopt physics-informed neural networks (PINNs) or differentiable CC-CV layers to bound electrochemical dynamics Wang et al. [2024] .
Treatment-driven voices (1, 4)	NMF responsibility distributions shift upon treatment inclusion	Classify as descriptive only and strictly exclude from causal effect estimation
Quasi-random instrument assumption (Grade A)	Active user coupon-claiming behavior may introduce self-selection bias	Deploy instrumental variable frameworks incorporating user fixed effects or propensity score matching
Static revenue counterfactuals	Assumption that removing discounts leaves user demand behavior invariant	Incorporate estimated demand elasticities into dynamic revenue optimization models
Movement endogeneity	Changepoints are detected from load data that is endogenously influenced by promotional pricing	Instrument structural movement timing using exogenous policy or grid events

Table 4: Known limitations, their root causes, and corresponding mitigation strategies.

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