cs.LGOct 15, 2026

Sensor Diagnosis for Fuel and Emissions Monitoring in Heavy-Duty Diesel Vehicles

Authors: Tejas Dahiya, Saurabh Kumar Gupta

Organizations: University of Chicago · University of Wisconsin–Madison

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Abstract

Faulty sensor readings can distort estimates of fuel use and carbon dioxide emissions from diesel engines. We evaluate two procedures that use relationships learned from healthy measurements to diagnose faults and guide fuel correction. The diagnosis procedure tests whether replacing a suspected faulty reading with an estimated healthy value helps a model predict another sensor's recorded reading more accurately. It then predicts the fault type and decides whether to report the diagnosis. We evaluate five synthetic fault types on 217 steady-state operating points from a heavy-duty diesel engine, excluding all measurements at selected engine speeds from training. Across 31,500 fault-injected groups of 20 operating points, it issues diagnoses for 77.3% of groups, with 92.1% of diagnoses issued on these groups correct. The fuel correction procedure uses a different sensor-selection rule at individual operating points, testing how each replacement changes the largest prediction error across all six sensors. Fuel correction requires a fault alarm and engine speed and torque close to the training conditions. A fuel reading is replaced only when its replacement reduces the largest prediction error sufficiently more than replacements for the other sensors. Assuming faults in 1% of one-hour scenarios, equally likely sensors and fault types, and equal time at each measured condition, selected fuel corrections reduce mean absolute error in calculated combustion CO2 by 83.8%. On this engine map, learned relationships support complete sensor diagnoses and fuel corrections that improve emissions accounting while preserving unaffected readings.

Figures & tables

Figure 1: Diagnosis combines 20 operating points, while fuel correction evaluates each point.
Evaluated groupsAlarm raisedDiagnosis issuedDiagnosis correct
All generated injections80.0%77.3%92.1%
Equally likely fault types72.6%70.4%90.5%
Injections that change a reading82.3%79.6%92.3%
Table 1: Diagnosis on fault-injected groups at engine speeds excluded from training. Correctness is measured among diagnoses issued on those groups; healthy groups are evaluated separately.
Figure 2: Alarm frequency, diagnosis frequency, and correctness among issued diagnoses as fault magnitude changes, pooling five sensors, three seeds, and seven test splits. Offsets are expressed in training standard deviations and clipping limits in training percentiles. Models and thresholds remain fixed, so the curves show their responses to changing fault magnitude.
Sensor-identification methodDiagnosis issuedDiagnosis correctHealthy groups diagnosed
Test estimated replacements77.3%92.1%6.7%
Largest adjusted prediction error78.0%91.8%6.8%
Account for correlated errors63.4%87.1%0.2%
Principal-component reconstruction74.6%88.8%11.5%
Autoencoder reconstruction63.1%91.8%3.0%
Table 2: Identification methods with the same alarms and newly fitted fault-type and reporting models. Reporting and correctness concern fault-injected groups; the final column gives diagnoses on healthy groups.
Figure 3: Mean absolute error in calculated combustion CO 2 as the assumed fraction of faulty one-hour scenarios increases. The vertical markers identify the 1% assumption used for the headline result. Panels consider fuel flow, the other five sensors, or all six sensors with equal fault probability. Curves average three seeds with equal operating time and fixed correction rules. Correcting readings known to be faulty uses the same estimated replacements. Panel-specific vertical ranges show the different error levels; Appendix I specifies the weights.
Appendix figures & tables23 assets

Supplementary material from the paper’s appendix.

Appendix

Data columnMeasurementUnit
Engine SpeedEngine speedRevolutions per minute
TorqueEngine torqueNewton-metres
T_IMIntake-manifold temperatureDegrees Celsius
P_IMIntake-manifold pressureBar
EGR_RateExhaust-gas-recirculation ratePercent
MF_IAIntake-air mass flowKilograms per hour
Appendix
Table 3: Measurement columns in the engine map used for these experiments. Speed and torque describe the operating condition, the next five measurements are monitored in the primary diagnosis, and fuel flow is added for accounting.
Fault typeDevelopmentTest
Offset0.5, 1.0, 2.00.5,\ 1.0,\ 2.00.75, 1.5, 3.00.75,\ 1.5,\ 3.0
Scaling error5, 12, 20%5,\ 12,\ 20\%8, 16%8,\ 16\%
Added noise1.0, 2.01.0,\ 2.01.5, 3.01.5,\ 3.0
Clipping80th, 88th84th, 92nd
Intermittent zeros15, 30%15,\ 30\%10, 40%10,\ 40\%
Appendix
Table 4: Fault strengths used in development and testing. Offset and noise sizes are multiples of the sensor’s training standard deviation. Clipping limits are training percentiles.
Figure 4: The dark cells mark speeds at which all measurements are reserved for testing in each split. Each of the 21 speeds appears in one test split, and all three seeds use these assignments.
QuantityCalculation
Mean absolute errorMean of ∣ri∣|r_{i}|
Mean signed errorMean of rir_{i}
Standard deviation of errorsStandard deviation of rir_{i}
Consistency of directionAbsolute mean of rir_{i} divided by its standard deviation plus 10−910^{-9}
Error dependence on valueCorrelation of ∣ri∣|r_{i}| with yiy_{i}
Distinct-value fractionNumber of distinct yiy_{i} , rounded to six decimal places, divided by group size
Appendix
Table 5: Twelve summaries of the sensor selected by the diagnostic procedure. Means, standard deviations, and percentiles are calculated within the group.
Sensor-identification methodCorrect sensor given alarmDiagnoses issuedCorrect among issuedHealthy groups diagnosed
Test estimated replacements96.7%77.3%92.1%6.7%
Largest adjusted prediction error97.4%78.0%91.8%6.8%
Account for correlation between errors82.3%63.4%87.1%0.2%
Principal-component reconstruction91.8%74.6%88.8%11.5%
Autoencoder reconstruction85.7%63.1%91.8%3.0%
Appendix
Table 6: Comparison of sensor-identification methods using 20 randomly sampled operating points per group. Each row evaluates 31,500 fault groups and 2,520 healthy groups. Sensor identification is measured among fault groups that produce an alarm.
Figure 5: Diagnosis as the reporting threshold changes, calculated from saved predictions for 31,500 fault groups and 2,520 healthy groups. The highlighted points show the thresholds selected during training, placing the reported results on these curves.
Fault typeGroupsAlarm raisedDiagnoses issuedCorrect issuedCorrect among issued
Added offset9,45099.9%9,1238,79996.4%
Scaling error6,30057.1%2,9311,84963.1%
Added noise6,300100.0%6,2876,28699.98%
Intermittent zero readings6,30080.1%5,1554,94896.0%
Clipping3,15025.7%86856665.2%
All generated groups31,50080.0%24,36422,44892.1%
Appendix
Table 7: Results by fault type for 20 randomly sampled operating points. Correct issued diagnoses require a changed reading, an alarm, an accepted operating point, and correct identification of both the sensor and fault type.
PointsConstructionFault alarmsDiagnoses issuedCorrect among issuedHealthy alarmsHealthy groups diagnosed
5Random68.8%62.7%94.2%1.6%0.0%
5Nearby62.4%54.9%94.0%1.5%0.0%
10Random75.1%70.9%93.0%3.1%0.2%
10Nearby71.3%64.8%92.1%3.6%0.3%
20Random80.0%77.3%92.1%6.8%6.7%
20Nearby78.6%73.5%92.7%5.1%5.1%
Appendix
Table 8: Group-size experiment. Each row contains 31,500 fault groups and 2,520 healthy groups. The two healthy columns distinguish alarms from issued diagnoses.
Faulty sensorOffset 0.25 issued / correctOffset 3.0 issued / correctScaling 8% issued / correct
Intake-manifold temperature25.9 / 29.4100.0 / 100.063.8 / 37.8
Intake-manifold pressure60.0 / 38.4100.0 / 100.030.5 / 77.1
Exhaust-gas-recirculation rate14.6 / 17.4100.0 / 100.017.9 / 27.4
Intake-air mass flow36.5 / 10.4100.0 / 100.016.3 / 0.0
Engine-out nitrogen oxide10.6 / 29.996.8 / 98.54.6 / 79.3
Appendix
Table 9: Fraction of groups receiving diagnoses and correctness among those diagnoses in selected magnitude tests. Each cell gives the two percentages in that order. Offset magnitudes are in healthy training standard deviations.
Figure 6: Intake-manifold temperature diagnosis as fault magnitude changes, pooling three seeds and seven test splits with fixed models and thresholds. The curves give alarm frequency, diagnosis frequency, and correctness among issued diagnoses, using the units in Figure 2 .
Figure 7: Intake-manifold pressure diagnosis as fault magnitude changes, pooling three seeds and seven test splits with fixed models and thresholds. The curves give alarm frequency, diagnosis frequency, and correctness among issued diagnoses, using the units in Figure 2 .
Figure 8: Exhaust-gas-recirculation rate diagnosis as fault magnitude changes, pooling three seeds and seven test splits with fixed models and thresholds. The curves give alarm frequency, diagnosis frequency, and correctness among issued diagnoses, using the units in Figure 2 .
Figure 9: Intake-air mass flow diagnosis as fault magnitude changes, pooling three seeds and seven test splits with fixed models and thresholds. The curves give alarm frequency, diagnosis frequency, and correctness among issued diagnoses, using the units in Figure 2 .
Figure 10: Engine-out nitrogen oxide concentration diagnosis as fault magnitude changes, pooling three seeds and seven test splits with fixed models and thresholds. The curves give alarm frequency, diagnosis frequency, and correctness among issued diagnoses, using the units in Figure 2 .
ModelCoefficient of determinationCorrect sensor
Linear ridge regression0.929180.6%
Second-order polynomial ridge regression0.991092.6%
Partial least squares regression0.908668.7%
Extremely randomized trees0.992478.2%
Random forest0.980764.7%
Five-neighbour regression0.976975.4%
Appendix
Table 10: Healthy-model component comparison, averaged across sensors and folds. Sensor identification uses one positive-offset setting.
AdjustmentRandom point splitHeld-out speeds
Global healthy error scale8.7%20.7%
Speed-and-load region scale6.9%17.5%
Disagreement between randomized trees1.4%3.7%
Nearby-point error scale5.5%19.4%
Appendix
Table 11: Alarm rates on healthy operating points under different adjustments of prediction error.
Design and reporting ruleSplitHealthy alarmsFault alarmsDiagnoses issuedCorrect among issued
Regional adjustmentRandom0.0%78.1%0.0%Undefined
Regional adjustmentHeld-out speed14.3%77.6%0.0%Undefined
Tree adjustment Fault-type probabilityRandom0.0%82.1%70.8%97.9%
Tree adjustment Fault-type probabilityHeld-out speed10.7%79.5%62.6%97.5%
Tree adjustment Diagnosis correctnessRandom0.0%82.1%75.3%96.7%
Tree adjustment Diagnosis correctnessHeld-out speed10.7%79.5%72.5%94.6%
Appendix
Table 12: Single-seed 20-point component comparison. Random point splits contain 7,500 fault groups, and held-out-speed splits contain 10,500. The reporting rule requires a training Wilson interval lower endpoint of 90% for correctness among issued diagnoses.
Fault typeGroupsAlarm raisedCorrect sensor given alarmDiagnoses issuedCorrect among issued
Added offset3,15099.7%99.9%93.9%96.5%
Scaling error2,10056.3%84.6%31.4%72.1%
Added noise2,100100.0%100.0%99.5%99.9%
Intermittent zero readings2,10078.9%99.5%79.7%96.8%
Clipping1,05025.3%65.8%21.6%70.0%
Appendix
Table 13: Single-seed held-out-speed results by fault type for 20-point groups. These results use 10,500 generated groups and different reporting training and correctness definitions from the three-seed results in Table 7 .
Figure 11: The curves show how often individual operating points raise alarms as offset magnitude increases, using prediction errors scaled within regions of the engine map. Each sensor and magnitude includes 434 positive and negative offset injections across five shuffled folds with seed 42, with the dashed line marking 90% detection.
Measure5-point estimate5-point interval20-point estimate20-point interval
Fault alarms67.8%61.6–74.1%79.5%55.5–100.0%
Correct sensor among alarms97.1%94.3–100.0%96.6%82.8–100.0%
Diagnoses issued59.0%53.4–64.7%72.5%52.5–92.4%
Correct among issued diagnoses96.3%95.0–97.7%94.6%86.0–100.0%
Appendix
Table 14: Single-seed held-out-speed results and delete-one-point sensitivity intervals. These intervals apply to the single-seed generated groups and are not uncertainty intervals for the three-seed results.
Fuel-reading treatmentEqual timeLow-load weightingHigh-load weighting
Use recorded readings0.0529080.0503420.056073
Correct selected readings0.0085520.0084370.009058
Replace every reading0.3488380.4230680.260979
Correct readings known to be faulty0.0003250.0003990.000237
Appendix
Table 15: Mean absolute error in calculated combustion carbon dioxide, in kilograms per engine-hour. Results assign 1% of scenario weight to faulty hours, with equal weights for six sensors and five fault types, and average across three seeds.
SplitChanged pointsFault alarmsSelection reportedFuel correct among reportsError removedError removed known faults
Random2,76570.2%66.3%100.0%89.7%98.2%
Held-out speed2,77871.2%63.2%99.9%83.8%98.0%
Appendix
Table 16: Fuel-only experiment at individual operating points, restricted to changed fuel readings. Error removal measures summed absolute fuel-reading error.
Actual corruption sizeActive-fault rowsDetected
Below 0.51,7524.5%
0.5 to 11,3814.8%
1 to 22,2398.8%
2 to 31,5139.6%
3 to 51,49175.7%
5 to 81,550100.0%
Appendix
Table 17: Turbofan detection by actual corruption size in units of healthy prediction-error standard deviation. Active drift labels include small changes near fault onset.
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