This document precisely defines the mathematical meaning of every value produced by the Aethelix inference engine. Read this before interpreting any result, before integrating any output into a downstream system, and before extending the engine with new features.
Aethelix currently solves a single, well-defined problem:
Given a set of observed telemetry anomalies and a manually curated causal DAG, rank the root-cause hypotheses from most to least consistent with the evidence.
That is the full scope of the current output. Nothing more, nothing less. Understanding what this implies - and what it does not imply - is the foundation of correct interpretation.
The engine computes a raw score for each independent root-cause hypothesis r as:
score(r) = coverage(r) × (1 − β × inconsistency(r)) × severity_weighted(r) × depth_prior(r)
where:
coverage(r): The fraction of active anomalous observables reachable fromrin the DAG.inconsistency(r): The fraction of inactive (quiet) observables thatrpredicts should be anomalous.β: The consistency softening penalty weight (set to0.5in the v2 engine to avoid over-penalising secondary hypotheses).severity_weighted(r): Weighted sum of observed anomaly severities that are causally explained byr.depth_prior(r): Structural prior based on topological depth from root causes in the DAG. Rewarding true root cause nodes (depth 0:1.0,depth 1:0.7,depth 2:0.5,depth 3+:0.35) and penalising intermediate nodes to resolve cascading ambiguity.
To handle multi-fault scenarios, the engine also evaluates candidate pairs of root causes (r1, r2) and scores their combined explanatory power:
joint_score(r1, r2) = union_coverage(r1, r2) × (1 − β × joint_inconsistency) × severity_factor × mean_prior
where:
union_coverage(r1, r2): Fraction of active anomalies explained by eitherr1orr2.joint_inconsistency: Softened penalty for quiet channels predicted anomalous by either cause.severity_factor: Fraction of total anomaly severity explained by the pair.mean_prior: The average of the individual depth priors ofr1andr2(depth_prior(r1) + depth_prior(r2)) / 2.0.
Single hypotheses probabilities are normalized to sum to 1.0:
P(h | evidence) = raw_score(h) / Σ raw_score(h_i)
Joint hypotheses probabilities are normalized among candidate pairs:
P(r1, r2 | evidence) = joint_score(r1, r2) / Σ joint_score(a, b)
A joint hypothesis r1 + r2 is exposed in the unified ranked list if its joint probability is at least 5% higher than the top single candidate's probability.
The Confidence value reported alongside each hypothesis is:
confidence(h) = 0.4 × posterior_factor + 0.2 × consistency_factor + 0.2 × saturation_factor + 0.2 × margin_factor
For joint hypotheses, the confidence is the maximum of individual confidences multiplied by a joint probability bonus (1.0 + 0.1 × joint_prob). It reflects how strongly the evidence supports the hypothesis independent of other candidates.
This is the most important section of this document.
The values produced after normalization look like posterior probabilities —
they are positive, they sum to 1.0, and they are labeled with P=. They are
not calibrated Bayesian posteriors in the formal sense.
A calibrated posterior P(h | e) requires:
- A prior
P(h)over hypotheses, derived from historical base rates or engineering priors, - A likelihood
P(e | h)that models how likely each observation is given that hypothesis h is the true cause, - Bayes' rule applied over a normalized hypothesis space.
Aethelix does not implement any of these steps. There are no priors. There are
no likelihoods. The normalization step is a rescaling operation applied to
heuristic scores, not an application of Bayes' theorem. Calling the output
P=46.3%is shorthand for "this hypothesis holds 46.3% of the total score mass." It is a proportion, not a probability.
Concretely: you cannot say "there is a 46.3% chance that solar degradation is the root cause." You can say "solar degradation is the strongest-scoring hypothesis, accounting for roughly 46% of the total evidence weight."
Although Aethelix now explicitly scores pairs of faults via joint scoring, the output values do not represent independent marginal probabilities like P(A is active) and P(B is active). The probability values are rescaled heuristic scores, meaning that increasing one candidate's score mechanically decreases the others in the normalised list.
Aethelix now implements a targeted joint two-hypothesis scoring pass to diagnose double-fault scenarios. It evaluates pairs of root causes and ranks their combined explanatory power. While this successfully solves the two-fault co-occurrence problem (raising two-fault accuracy significantly), it does not search for higher-order subsets (3+ simultaneous faults) or solve the general multi-fault partition search.
| Use Case | Appropriate? | Notes |
|---|---|---|
| Identifying the single most likely dominant root cause | Yes | Core design intent |
| Ordering hypotheses for manual investigation | Yes | Ranking is reliable |
| Eliminating clearly unsupported hypotheses | Yes | Low-scoring hypotheses are weak candidates |
| Detecting that something is anomalous | Yes | Severity scores are directly useful |
| Estimating the probability that a specific fault is active | No | Values are not calibrated |
| Concluding that two faults are both present simultaneously | Yes | Supported via joint two-hypothesis scoring when joint probability significantly exceeds single probability |
| Computing a probability threshold for automatic action | No | Requires calibration first |
| Formal certification or safety-critical automated decisions | No | Requires a full probabilistic model |
1. solar_degradation P=46.3% Confidence=93.3%
2. battery_aging P=18.8% Confidence=71.7%
3. battery_thermal P=18.7% Confidence=75.0%
4. sensor_bias P=16.3% Confidence=75.0%
Correct interpretation:
Solar degradation is by far the strongest-scoring hypothesis. It accounts for nearly half the total evidence weight and is supported with very high consistency. Battery aging and battery thermal effects are secondary candidates of roughly equal relative weight. Sensor bias is the weakest candidate. The engine's primary output is that solar degradation should be investigated first.
Incorrect interpretations to avoid:
"There is a 46.3% probability that solar degradation is the cause.""There is a 54% probability that solar degradation is NOT the cause.""Battery aging and battery thermal are equally likely to be co-occurring.""Since scores sum to 1.0, only one fault is present."
The high confidence values (93.3%, 75%) are separately meaningful: they say that the evidence strongly engages with these hypotheses, not just that they scored higher in the ranking.
To be fully explicit, the Aethelix engine implements a dual-pass objective:
- Single Hypothesis Pass: Find the candidate
rthat maximizes:score(r) = coverage(r) × (1 − β × inconsistency(r)) × severity_weighted(r) × depth_prior(r) - Joint Hypothesis Pass: Evaluate all combinations of top candidates
(r1, r2)and rank them using:joint_score(r1, r2) = union_coverage(r1, r2) × (1 − β × joint_inconsistency) × severity_factor × mean_prior
This objective is appropriate when:
- The operator wants to identify the dominant single fault or pair of faults quickly.
- The cascading failure path is well-represented in the Causal DAG. This objective is insufficient when:
- Three or more independent faults occur simultaneously.
- Downstream systems require safety-certified, mathematically calibrated marginal probabilities.
For reference, here is what each stronger semantic would require. These are directions for future work, not current claims.
Would require: empirical prior probabilities over faults (e.g., from historical
satellite failure records), a likelihood model P(telemetry deviation | fault active) per node, and validation against held-out cases to confirm that a
stated P=40% is correct in approximately 40% of similar cases.
Would require: scoring all 2ⁿ subsets of hypotheses (or a smarter search), a joint likelihood that accounts for fault interactions, and a criterion such as MAP subset selection or a credible interval over the fault set.
Aethelix now implements a formal Structural Causal Model (SCM) layer, providing syntactic validity for do-calculus operations and counterfactual queries via do() and ate() operations.
CRITICAL CALIBRATION WARNING:
While the truncated factorization P(effect | do(cause)) is mathematically legitimate within the engine, the structural coefficients in the default GSAT-6A model are NOT empirically validated. They are derived from hand-tuned edge weights originally built for heuristic anomaly scoring.
The SCM layer effectively operates as a structured hypothesis generator, not a factual causal oracle. An ATE number from the formal causal-inference API invites trust, but until you calibrate the structural equations with real interventional or sufficient observational data, the numerical results remain guesses.
Use these outputs for hypothesis generation and what-if exploration. Do not use them for automated decision-making without empirical calibration.
To avoid ambiguity in code, comments, and documentation, use the following terms consistently:
| Term | Correct Usage |
|---|---|
| normalized score | The value printed as P=xx% in output |
| ranking score | The raw pre-normalization score for a hypothesis |
| consistency | The evidence-quality × consistency scalar |
| dominant root cause | The highest-ranking hypothesis output by the engine |
| causal path | A directed path in the DAG from a root cause to an observable |
| Do not use for the current output | |
| Do not use for the current output | |
| Do not use for the current output |
This document describes the semantics of Aethelix as of the current master
branch. If the scoring formula, normalization method, or output structure
changes, this document must be updated before the change is merged.
Any feature that would change the semantic category of the output values - for example, introduction of calibrated priors, a likelihood model, or joint multi-fault scoring - must be accompanied by a corresponding update to this document and to the output labels in the code.
Precision about what a model proves is not a limitation - it is what makes the model trustworthy.
This documentation page includes updates from the v2.0 evaluation suite, incorporating empirical validation on European Space Agency (ESA) flight telemetry and improved hierarchical network rendering:
-
ESA OPS-SAT (OPSSAT-AD): Evaluated on ADCS reaction wheel magnetic interference and magnetometer attitude anomalies. By applying subsystem-aware persistence filtering (
$N=15$ consecutive samples for noisy magnetometer channels,$N=3$ for clean optical sensors), Aethelix achieves a 78.3% F1 score, comparable to deep LSTM autoencoder baselines (78.0% F1) without requiring historical model training. -
ESA-ADB Multi-Mission: Evaluated on satellite telemetry subject to periodic orbital thermal variation. To prevent false alarms caused by 90-minute day/night baseline oscillations, the engine evaluates innovation residuals (
$\Delta x_t = x_t - x_{t-1}$ ). Decoupling slow orbital dynamics from step-change fault signatures isolates transient subsystem anomalies.
-
Bounded Functional Corridors: The visualization script (
scripts/generate_dag_visuals.py) enforces strict vertical coordinate bounding (maximum node altitude$y=0.68$ ), ensuring clean separation from structural layer labels ($y=0.87$ ). -
Normalized Ranking Score Visualization: In accordance with project semantics, node color intensity maps directly to normalized ranking scores (e.g., 0.94 normalized score weight for
PCDU Regulator Failureon GSAT-6A; 0.89 normalized score weight forReaction Wheel Magnetic Interferenceon OPS-SAT). Active causal propagation paths connecting dominant root causes to observed telemetry deviations are highlighted along directed edges.
Benchmark datasets and diagnostic charts can be generated locally using the standalone scripts:
# Render hierarchical causal DAGs with normalized score weighting
python3 scripts/generate_dag_visuals.py
# Generate empirical validation charts across ESA datasets
python3 scripts/generate_validation_plots.py
# Execute benchmark suite evaluation
python3 scripts/esa_benchmark.py --dataset allGenerated diagnostic charts in docs/:
causal_dag_intensity_gsat6a.png— Multi-subsystem causal DAG mapping normalized ranking scores.causal_dag_intensity_opssat.png— ADCS magnetometer interference DAG structure.validation_signal_overlay.png— Telemetry Z-score deviations and persistence window thresholds.validation_confusion_matrix.png— Detection performance comparison against sequence-level baselines.validation_subsystem_metrics.png— Subsystem-level precision, recall, and F1 evaluation.validation_causal_attribution.png— Normalized root-cause score distribution across benchmark scenarios.