Zhang, H., Sanchez, L., Spears, M., Sarlashkar, J. et al., "Cycle-Average Heavy-Duty Engine Test Procedure for Full Vehicle Certification - Numerical Algorithms for Interpreting Cycle-Average Fuel Maps," SAE Int. J. Commer. Veh. 9(2):105-119, 2016, https://doi.org/10.4271/2016-01-8018.
In June of 2015, the Environmental Protection Agency and the National Highway Traffic Safety Administration issued a Notice of Proposed Rulemaking to further reduce greenhouse gas emissions and improve the fuel efficiency of medium- and heavy-duty vehicles. The agencies proposed that vehicle manufacturers would certify vehicles to the standards by using the agencies’ Greenhouse Gas Emission Model (GEM). The agencies also proposed a steady-state engine test procedure for generating GEM inputs to represent the vehicle’s engine performance. In the proposal the agencies also requested comment on an alternative engine test procedure, the details of which were published in two separate 2015 SAE Technical Papers [1, 2]. As an alternative to the proposed steady-state engine test procedure, these papers presented a cycle-average test procedure. The papers also explored how a range of vehicle configurations could be defined and selected for generating the engine duty cycles for this test procedure. In addition, these papers described and used a simple interpolation-based numerical algorithm for determining the fuel consumption of a vehicle configuration based on a cycle-average engine “fuel map” that was generated via the cycle-average engine test procedure.This paper is a continuation of this earlier work , and this particular paper presents a more comprehensive evaluation of a range of numerical algorithms for determining fuel consumption values from a cycle-average engine fuel map. These numerical algorithms include interpolation and extrapolation schemes as well as different linear and non-linear equations, where the equations’ coefficients were fitted via least-squares regression. The selection of independent and dependent variables for all of these numerical methods was explored in detail. It is shown that the most robust numerical algorithm that we explored specifies fuel mass as the dependent variable, and a linear combination of the ratio of average engine speed to average vehicle speed and cycle work as the two independent variables. It is demonstrated that the cycle-average test procedure, combined with a robust numerical algorithm for interpreting the cycle-average fuel map, can effectively predict the fuel consumption of an engine in different vehicle configurations, including configurations with different parent and child engine ratings and a wide range of transmissions. It is also shown that the cycle-average test procedure represents transient engine performance more accurately than the agencies’ proposed steady-state test procedure.