This article addresses the problem of optimal vehicle sampling for fleet-wide
in-use emissions monitoring, a necessity driven by the absence of direct
emissions sensors in modern production vehicles and the variable impact of
in-use changes and operational factors (mileage, time-in-service, workload) on
emissions performance across a fleet. Recognizing that comprehensive fleet
testing is impractical due to significant downtime and cost, we propose a novel
approach to identify a small, yet optimally informative subset of vehicles for
sampling. The proposed approach leverages submodular function maximization, a
technique rooted in optimal experimental design, specifically D-optimal design,
to maximize the determinant of the information matrix (e.g., of
XTX, where X is the
regressor/design matrix in the case of a linear in parameters model). This
approach ensures that the collected data yields maximum information for refining
and building accurate models for emissions changes. We compare the submodular
maximization strategy with conventional uniform and extreme sampling methods.
Our simulation results demonstrate the potential for the submodular approach to
outperform both alternatives by achieving lower variance (as measured by
standard deviation and coefficient of variation) in estimating parameters for
the assumed linear, quadratic, and simplified quadratic models for emission
changes. The application of submodular function maximization is thus shown to be
beneficial in vehicle fleet management for data collection in
resource-constrained environments and leading to more accurate in-use emissions
prediction. The envisioned process, in which a limited number of vehicles
selected by our methodology are tested and the data are utilized to improve
emissions models, can support the implementation of model-based strategies for
engine emissions management.