Hardware-benchmarked uncertainty-aware virtual NOx sensor for onboard emission monitoring of off-highway diesel machinery

Onboard nitrogen oxides (NOx) monitoring of non-road mobile machinery (NRMM) is constrained by the cost and limited fleet coverage of physical sensing: hardware NOx sensors degrade over time, and portable emissions measurement system (PEMS) campaigns can sample only a small fraction of in-service machines. A virtual soft sensor that infers NOx from routinely available engine parameters offers a scalable alternative for continuous fleet-level monitoring and supervisory decision-support applications. This study presents an uncertainty-aware virtual NOx soft sensor for European Union (EU) Stage V NRMM, validated against both field measurements and published hardware sensor specifications. A transfer-learning long short-term memory (LSTM) ensemble, trained on laboratory cycle data and fine-tuned with field PEMS measurements, achieves R ² of 0.932 and 0.958 on a wheel loader and an excavator. Split conformal prediction provides prediction intervals with finite-sample coverage guarantees under the exchangeability assumption; on the evaluated datasets, the resulting intervals achieved high marginal coverage (98.6%–100%) at the 80%–90% nominal levels, although independent high-NOx regime coverage could not be assessed for the 6 L platform. A structured multi-dimensional benchmarking against commercial hardware NOx sensors reveals complementary roles, and fleet-scale cost analysis shows 63% lower total cost for 1000-unit fleets over a 5-year horizon against a conservative portable-analyzer baseline. Literature-based onboard deployment assessment on embedded platforms suggests real-time feasibility, though on-device benchmarking remains a necessary validation step. The results indicate that a software-based virtual soft sensor, grounded in conformal prediction-based uncertainty quantification and hardware-benchmarked validation, can support onboard NOx monitoring and screening-oriented decision support for NRMM using only Controller Area Network (CAN) bus signals.