We present a novel Explainable methodology for Condition Monitoring, relying on healthy data only. Since faults are rare events, we propose to focus on learning the probability distribution of healthy observations only, and detect Anomalies at runtime. This objective is achieved via the definition of probabilistic measures of deviation from nominality, which allow to detect and anticipate faults. The Bayesian perspective underpinning our approach allows us to perform Uncertainty Quantification to inform decisions. At the same time, we provide descriptive tools to enhance the interpretability of the results, supporting the deployment of the proposed strategy also in safety-critical applications. The methodology is validated experimentally on two use cases: a publicly available benchmark for Predictive Maintenance, and a real-world Helicopter Transmission dataset collected over multiple years. In both applications, the method achieves competitive detection performance with respect to state-of-the-art anomaly detection methods.
Figures & tables
Strategy
G
I
F
H
Ad-Hoc Indicators (e.g., Soo Lon Wah et al. [22] )
✗
✓
✗
✗
Multi-class Learning (e.g., Yessoufou and Zhu [31] )
✓
✗
✓
✗
Single-class Learning (e.g., Jung et al. [11] )
✓
✗
✓
✓
Table 1: Condition Monitoring (CM) Strategies and their typical Advantages ( G : General applicability; I : Interpretability; F : Flexibility; H : requiring a Healthy sample only).
Term
Definition
Failure
A window of consecutive samples in which the machinery failed.
Alert
A window of consecutive samples for which the detection algorithm raised a warning.
Validity Window
All observations within a given number of days ( w ) prior to a fault; depending on the observed data, gaps may be present.
True Positive ( TP )
Number of failure instances for which at least an alert was active in the related validity window.
False Negative ( FN )
Number of failure instances for which no alert was raised in the related validity window
False Positive ( FP )
Number of recorded days outside validity windows, for which at least one alert was active.
Table 2: Glossary of Definitions Relating to Failure Detection Metrics.
Figure 1: Illustrative example of Failure Detection-related concepts.
Figure 2: Predictive Inference for the Vibration Index of the Azure Train Dataset.
Figure 3: Predictive Inference Results for the Pressure (First Row), Rotate (Second Row), Vibration (Third Row), and Volt (Last Row) Indices of the Azure Test Dataset.
Train
Test
1 Day to Event
↑↓ 95% CIC
↑↓ 95% CIC
↑ Prec. [%]
↑ Rec. [%]
↑ F1 [%]
pressure
0.96±0.01
0.95±0.01
0.00
0.00
0.00
rotate
0.96±0.01
0.93±0.01
100.00
25.00
40.00
vibration
0.94±0.02
0.87±0.01
100.00
75.00
85.71
volt
0.95±0.02
0.96±0.01
0.00
0.00
0.00
Table 3: Train and Test Metrics for each Index of the Azure Dataset.
Figure 4: Anomaly Scores and Alerts on Pooled Indices of the Azure Dataset (Test Set).
Days to Event
Samples in Range
↑ Prec. [%]
↑ Rec. [%]
↑ F1 [%]
4-1
384
100.00
100.00
100.00
Table 4: Fault Detection Metrics for the Azure Test Dataset.
Variable
Details
[ Alphanumeric Identifier ]
Health Index, e.g., “ENHKUR”, “S1R”
Engine 1 Torque
Engine 2 Torque
MGB 1 Oil Temperature
MGB: Main Gearbox Bearing
MGB 2 Oil Temperature
Main Rotor Torque
Table 5: List of flight parameters in the datasets
Figure 5: Predictive Inference for the ENHKUR Health Index of First Helicopter on the Train (top), Validation (middle), and Test (bottom) Sets.
Train
Test
60 Days to Event
↑↓ 95% CIC
↑↓ 95% CIC
↑ Prec. [%]
↑ Rec. [%]
↑ F1 [%]
ENHKUR
0.96±0.01
0.94±0.03
100.00
100.00
100.00
ENHM6
0.96±0.02
0.94±0.03
0.00
0.00
0.00
ENHP2P
0.95±0.02
1.00±0.00
0.00
0.00
0.00
ENHSTD
0.98±0.01
0.99±0.01
0.00
0.00
0.00
Table 6: Train and Test Metrics for each Health Index of the First Helicopter.
Figure 6: CoCoAFusE Anomaly Scores and Alerts on Pooled Health Indices of the First Helicopter (Test Set).
Days to Event
Samples in Range
↑ Prec. [%]
↑ Rec. [%]
↑ F1 [%]
1
2
0.00
0.00
0.00
89-17
46
100.00
100.00
100.00
Table 7: Fault Detection Metrics for the First Helicopter (CoCoAFusE).
Days to Event
Samples in Range
↑ Prec. [%]
↑ Rec. [%]
↑ F1 [%]
89-1
48
100.00
100.00
100.00
Table 8: Fault Detection Metrics for the First Helicopter (from Leoni et al. [14] ).
Figure 7: Predictive Inference for the OREB1A Health Index of the Second Helicopter on the Train (top), Validation (middle), and Test (bottom) Sets.
Train
Test
60 Days to Event
↑↓ 95% CIC
↑↓ 95% CIC
↑ Prec. [%]
↑ Rec. [%]
↑ F1 [%]
BPEB1A
0.96±0.01
0.87±0.03
50.00
100.00
66.67
BPEB1B
0.98±0.01
0.86±0.03
0.00
0.00
0.00
FTEB1A
1.00±0.00
0.99±0.01
0.00
0.00
0.00
FTEB1B
0.98±0.01
0.97±0.01
0.00
0.00
0.00
Table 9: Train and Test Metrics for each Health Index of the Second Helicopter.
Days to Event
Samples in Range
↑ Prec. [%]
↑ Rec. [%]
↑ F1 [%]
89-4
68
100.00
100.00
100.00
Table 10: Fault Detection Metrics for the Second Helicopter (CoCoAFusE).
Days to Event
Samples in Range
↑ Prec. [%]
↑ Rec. [%]
↑ F1 [%]
70-4
49
50.00
100.00
66.67
89-71
19
100.00
100.00
100.00
Table 11: Fault Detection Metrics for the Second Helicopter (from Leoni et al. [14] ).
Figure 8: Test Anomaly Scores and Alerts on Pooled Indices of the Second Helicopter.
Figure 9: Explanatory Analysis on the ENHKUR Model for the First Helicopter.
Figure 10: Explanatory Analysis on the OREB1A Model for the Second Helicopter.
Independent Researcher. · College of Engineering, Biochemical Engineering. University of Georgia. · College of Engineering, EETI. University of Georgia.