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

Jiajie Chen; Jinfeng Li

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

Jiajie Chen, Jinfeng Li

arXiv:2608.14756v1Aug 14, 2026eess.SPcs.LGcs.SD

TL;DR

Reliable causal insight from EV charging data is hindered by hardware fragmentation, physical violations, and collider bias. The Note–Chord–Voice framework addresses these problems with axiom-validated data repair, source separation, and causal analysis, finding Voice 3 to be the primary actionable causal result and discount targeting to recover 52.8% of expenditures.

Problem
Reliable causal inference from EV charging data is limited by hardware fragmentation, physical violations, and collider bias from conditioning on post-treatment outcomes.
Method
The framework uses axiom-based falsification gates, modular data repair, NMF voice separation, and per-voice causal regression to analyze charging behavior.
Results
Voice 3 is the primary actionable causal finding with β = −14.16 minutes, while targeting discounts to price-sensitive voices recovers 52.8% of discount expenditures.
Takeaways & Limitations
Causal claims should be restricted to stable voices, with treatment-driven voices used only descriptively.
Takeaways & Limitations
Treatment-driven voices violate the stable pre-treatment baseline assumption, restricting causal interpretation to stable voices.

Abstract

from arXiv · show

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.

1. Introduction

Reliable causal insight from EV charging data is constrained by hardware fragmentation, physical violations, and collider bias. The Note–Chord–Voice framework addresses these interlocking problems through structured representations, falsification gates, constrained NMF, instrument isolation, and per-voice OLS.

Motivation: Three interlocking pathologies—hardware fragmentation, physical violations, and collider bias—restrict reliable causal inference from EV charging data.These problems span data integrity, physical consistency, and treatment-outcome conditioning.
Data pathologies: A single continuous charging attempt can be split into truncated micro-sessions by network timeouts, grid fluctuations, or billing resets, inflating counts and distorting baselines.One 60-minute session may be recorded as three 20-minute transactions.
Data pathologies: Independent energy and duration models can predict physically impossible states, such as 50 kWh in 10 minutes at a 7 kW charger, implying 300 kW average power.The implied average power exceeds the charger’s physical limit by more than 40-fold.
Data pathologies: Clustering on post-treatment outcomes such as energy or duration can create collider bias by opening backdoor paths and systematically biasing price-elasticity estimates.Discounts can affect the outcomes used to form behavioral segments.
Proposed framework: The framework maps charging analysis to Notes, Repair Chords, Harmonic Chords, Voices, Measures, and Movements, then adds falsification gates, Γ-initialized NMF, instrument isolation, and per-voice OLS.These components represent validated transactions, repaired sessions, recurring patterns, latent behavioral streams, temporal baselines, regime shifts, and the stated methodological contributions.

2. The Note—Chord—Voice (NCV) Framework Architecture · 2.1. Topological Ontology

The NCV framework organizes EV charging observations into six topological concepts and formalizes them through physically constrained notes, repair operations, harmonic pattern discovery, source factorization, and movement detection. Its architecture separates these operators by explicit mathematical definitions and implementation rules.

2.1. Topological Ontology: Table 1 defines six core Note–Chord–Voice concepts that structure the framework’s topological ontology.
2.1.1. Mathematical Formulations: A note ni = (ti, Ei, ∆ti, pi, ci) records time, energy, physical duration, unit energy price, and coupon discount, and is valid only within the physical manifold M.The manifold uses rated peak power Pmax,i and tolerance factor ηphys = 1.2 to account for transient grid fluctuations.
2.1.1. Mathematical Formulations: Repair Chord contraction merges adjacent notes into one note when the MDL change ∆MDL is positive.The merged note preserves total energy and combines both durations with the intervening gap τi; MDL compares one-session and two-session Gamma models with complexity penalties.
2.1.1. Mathematical Formulations: Harmonic Chords identify recurring subsequence pairs using Matrix Profile distances among sliding windows of length m.The implementation selects the top-k smallest distances with k = 5 and applies a 0.25 m exclusion zone to prevent trivial overlap while allowing nearby recurrences.
2.1.1. Mathematical Formulations: The source-separation stage factorizes the station-by-hour-of-week energy load matrix X into station responsibilities W and basis patterns H using multiplicative updates.Gamma-initialized NMF derives 168-hour seasonal profiles via STL, clusters them into K groups, initializes H with cluster centroids, and min-max normalizes inputs to [0, 1].
2.1.1. Mathematical Formulations: Foote novelty detects movements from daily load matrices by convolving a checkerboard Gaussian kernel along the diagonal of a cosine-similarity self-similarity matrix.Movements are local maxima of the globally normalized novelty curve N*(t) that exceed a relative prominence threshold and satisfy a minimum inter-peak distance.

2.2. Axiomatic Falsification Gates and Graceful Degradation

The framework tests data and structural assumptions through falsification gates before downstream modeling, then reduces assumptions and interpretation conservatively when gates fail. On Jiangmen data, physical validity and coupon relevance are supported, while failed gates constrain causal and harmonic modeling.

Design Philosophy: Falsification tests precede downstream routines, and failed axioms trigger reduced modeling assumptions rather than pipeline abortion.This design prevents downstream errors and requires more conservative interpretation of estimates.
G3 – Multi-periodicity FFT Gate: G3 failure restricts the harmonic basis to daily cycles, preventing spurious 168-hour structures from biasing downstream results.The framework therefore degrades gracefully instead of propagating an unsupported weekly periodicity assumption.
A1 – Physical Manifold Validation: 0.03% observed violation rate yields p ≈0, decisively rejecting the high-contamination null and permitting reconstruction under A1.The null posits that at least 95% of sessions violate the physical manifold.
A5 – Interaction and Stability Gate: Only stable voices support causal identification; treatment-driven voices remain descriptive, and Jiangmen had no unstable voices.When stable and treatment-driven voices coexist, causal inference is qualified and restricted exclusively to stable components.
G10 – Coupon Relevance Gate: R2 = 0.773 far exceeds the G10 threshold, confirming that discount rate accounts for substantial price variance.G10 evaluates the first-stage instrument equation linking discount rate to price discount percentage.

2.3. Pipeline Execution Strategy and Key Design Decisions

The pipeline executes seven gated stages, from preprocessing and axiom-based suitability checks through repair, motif discovery, voice separation, structural-shift detection, and causal pricing analysis. Design choices enforce physical plausibility, stable decomposition, interpretable voice models, and decision thresholds for revenue simulation.

Step 0: Preprocessing: 495,707 cleaned sessions remain after removing physically impossible records, encoding holidays, structuring promotion tags, and auditing the physical manifold.Preprocessing removes sessions with start ≥ end or E ≤0.
Step 0.5: Axiom Gate: K = 5 latent voices are selected after falsification tests A1–A5, G3, and G10, with voices classified as stable {0, 2, 3} or treatment-driven {1, 4}.The axiom gate tests data suitability before complex modeling.
Step 1: MDL Repair Chord Contraction: 5,345 successful merges reduce 495,707 sessions to 490,362 notes through physically constrained, likelihood-prefiltered, MDL-gated contraction.MDL is bounded to gaps ≤2 minutes because positive log-likelihood evidence concentrates in the (0, 2] minute bracket.
Step 2: STL Decomposition & Harmonic Motif Discovery: 210 motifs successfully pass the MDL gate after STL decomposition extracts per-station seasonal baselines Γ(t) and Matrix Profile analysis evaluates residual series.STL uses seasonal and trend decomposition with LOESS.
Step 3: Voice Separation & Duration Model: NMF R2 = 0.9921 after Γ-initialization and input normalization, while the duration model combines a CC-CV lower bound, softplus overhead, and idle components.The CC-CV bound assumes charging efficiency ηcharge = 0.90.
Step 4: Movement Inference & Load Forecasting: 96 changepoints detected, including 15 major structural shifts, while WMAPE improved by 15.5% using globally normalized Foote novelty scores.The method uses L = 14 days, a 30% prominence threshold, and a minimum inter-peak distance of 28 days.

2.4. Causal Decoupling Formulation

Grouping EV charging sessions by post-treatment energy or duration can make price-elasticity estimates unreliable through collider bias. The framework instead uses pre-treatment station-level load profiles to define soft latent Voices and estimates voice-specific treatment interactions with independent regressions.

2.4.1. The Collider Bias Problem: Post-treatment clustering on energy delivery or connection duration can make cluster-wise EV price-elasticity estimates unreliable.The formulation defines treatment as coupon discount, outcome as connection duration, unobserved preference as U, and cluster assignment as C.
2.4.1. The Collider Bias Problem: Because cluster assignment C is constructed from post-treatment outcomes, conditioning on C opens T →Y ←U and induces endogenous selection bias.The framework replaces this structural artifact with soft, pre-treatment behavioral dimensions based on station-level aggregate load profiles W.
2.4.2. Per-Voice Interaction Model: NMF responsibilities rik represent each session’s membership in voice k and lie on the probability simplex.These responsibilities provide the voice-membership terms used in the interaction model.
2.4.2. Per-Voice Interaction Model: The simplex constraint creates perfect multicollinearity with the intercept because Σ_k rik = 1.This makes a pooled interaction regression unsuitable without addressing the dependence among voice-membership variables.
2.4.2. Per-Voice Interaction Model: Independent OLS regressions are fit for each voice k using the full sample of treated and control sessions.The model includes voice membership, treatment, their interaction, energy demand, and an error term.
2.4.2. Per-Voice Interaction Model: The interaction coefficient β3k identifies voice-specific heterogeneous treatment effects while avoiding simplex collinearity and controlling for membership, treatment, and energy demand.Robust causal identification additionally requires a quasi-random instrument orthogonal to unobserved confounders such as time-of-day preferences or user urgency.

3. Experimental Setup and Case Study Design

The study validates the NCV framework on 495,707 charging sessions from 20 Jiangmen stations over nine months, using graded promotions to isolate quasi-random price variation. It benchmarks core components against minimalist reference models and evaluates load, duration, clustering, and causal performance with complementary metrics.

Case study dataset: 495,707 charging sessions across 20 public stations in Jiangmen cover July 2024–March 2025 and record energy, connection duration, price, and promotional discounts.The dataset spans nine months after initial cleaning.
Coupon-based causal design: Grade A coupons are issued platform-wide without conditioning on time, location, or user history, making them the primary treatment against unpromoted controls.Night-session shares are nearly identical for Grade A and None, while prices differ significantly: 18.1% vs. 17.4% and 0.962 vs. 1.214 CNY/kWh, respectively.
Reference models: The framework is benchmarked against minimalist reference models to isolate the structural contributions of its components rather than compare against SOTA architectures.The benchmarks include a historical station-mean load predictor and an unconstrained time-only log-duration model.
Evaluation metrics: Performance is evaluated using WMAPE for load forecasting, session- and aggregate-level R^2 for duration modeling, ARI for clustering stability, and β3k for causal effects.ARI is computed across 50 bootstrap resamples, while β3k uses heteroskedasticity-robust standard errors at the 5% significance level.

4. Empirical Validation and Results

The empirical validation finds that the data largely satisfy physical and structural suitability checks, while the framework separates robust behavioral voices from treatment-driven patterns. Voice 3 provides the primary causal result, and voice-targeted discounts improve simulated expenditure recovery.

Voice decomposition: R2 = 0.9921 versus a station-mean baseline of R2 = 0.8475 (+0.1446), with row-normalized refits preserving temporal bases and downstream causal metrics.K = 5 was selected as the smallest number of voices passing both reconstruction-error and treatment-inclusion stability gates.
Physical duration modeling: R2 = 0.5409 for the physically constrained duration model at the station-hour-of-week aggregate level, versus R2 = 0.0334 for the time-only session-level baseline.The aggregate and session-level values are not directly comparable because they use different granularities; approximately 60% of voice-hour cells contain meaningful post-charge idle components (¯π = 0.597).
Structural validation and forecasting: WMAPE = 0.3257 versus the station-mean baseline WMAPE = 0.3855, an improvement of 15.5%, showing that NMF voice reconstruction captures temporal structure beyond historical averages.Foote novelty detection found 96 changepoints across 20 stations, including 15 major changes; Station 2 rose from 390 to 544 kWh/day (+40%).
Causal price sensitivity: β = −14.16 minutes, p < 0.001 for stable Voice 3, which supports causal claims; treatment-driven Voice 1 is descriptive only, while Voices 0, 2, and 4 are not significantly price-sensitive.Grade A matches control night-session shares closely (18.1% vs. 17.4%), while its price difference reflects the coupon treatment rather than an underlying confounder.
Counterfactual targeting: 52.8% of discount expenditures are recovered by targeting sessions dominated by Voices 3 and 1, annualizing to approximately 0.85 million CNY/year.Restricting targeting to stable Voice 3 yields a more conservative, causally cleaner estimate; movement-conditional effects remain preliminary because movement boundaries are endogenous to discount-influenced load data.

5. Discussion: Theoretical Elegance and Empirical Imperfection

The Jiangmen pilot exposes empirical limits behind the framework’s conceptual elegance, including weak weekly periodicity, treatment-driven latent voices, and potential aggregation bias. Despite these constraints, the modular NCV design may extend to other IoT domains with fragmented logs, physical violations, and collider bias.

The Jiangmen pilot reveals vulnerabilities that require critical appraisal despite the framework’s conceptual elegance.
Weekly-cycle limitation: The weak 168-hour periodicity leads the framework to restrict Γ to daily cycles, avoiding spurious weekly patterns but limiting harmonic discovery.Public chargers appear predominantly daily, with blurred weekend/weekday distinctions caused by on-demand operational urgency.
Aggregation-bias robustness: Row-normalized ablation produced virtually identical temporal bases and causal metrics, indicating voices are volume-invariant city-wide chronotypes rather than station-scale artifacts.
Treatment-driven latent structures: Voices 1 and 4 are treatment-driven, so causal claims must be restricted to stable voices 0, 2, and 3.Promotional sessions significantly shift the treatment-driven profiles, violating the assumption of a stable pre-treatment behavioral baseline.
Broader applicability: The framework’s modular separation of data cleaning, source separation, and causal inference can extend beyond EV charging to IoT domains with fragmented logs, physical violations, and collider bias.Shared micro-mobility systems are given as an example involving GPS-related trip splitting, impossible speeds or energy consumption, and duration-based biased usage segments.

6. Conclusion and Future Work

The framework provides an axiom-validated, modular pipeline for EV charging data, producing interpretable voice-specific price elasticities despite moderate duration fit, G3 failure, and treatment-driven voices. Voice 3 is the primary actionable causal finding, while future work targets more realistic electrochemical modeling.

Conclusion: Voice 3’s stable elasticity is the primary actionable causal finding, with β = −14.16 minutes.The framework describes this result as causally plausible despite two treatment-driven voices.
Conclusion: The framework passes all critical falsification gates despite moderate duration fit, G3 failure, and two treatment-driven voices.Its modular structure separates data analysis stages while retaining interpretable voice-specific price elasticities.
Future Work: Future work will replace the linear softplus overhead with a differentiable constant-current constant-voltage charging model to better capture battery dynamics.CC-CV parameters can be estimated from sessions spanning two price tiers, using energy delivery across thresholds to fit the model.