###### Abstract
Furthermore, they established that more aggressive driving conditions could increase this range due to increased transient contribution. Certainly, this difference depends not only on the driving cycle but also on the vehicle parameters and the engine type. Various engines with 3.8 Lto 8 L displacement were studied in [7], demonstrating that on different drive cycles, the fuel enrichment due to transient phenomena varied by 2-8%. A relatively wide range of literature describes different approaches to model the engine transient behavior that estimates precisely the fuel consumption under different operating conditions and for different applications [6; 7; 8; 9; 10; 11; 12]. The authors of [6] considered four transient events, such as powertrain torque management (during the gear upshift phase for shafts synchronization), tip-in demand, deceleration fuel cutoff, and cylinder deactivation. The influence of each event on the transient fuel rate has been analyzed using experimental data. The corresponding adjustments have been applied to the steady-state fuel consumption to obtain the transient one. In [8], to produce an engine map that includes transient behavior, the engine torque and speed range was divided into equal bins. Then, the experimentally measured fuel consumption data was allocated to the bins to determine a representative value for each bin. The probability distribution function was analyzed and based on this data, the corresponding engine map was created. Fuel consumption prediction was improved relative to steady-state calculation in [9] by applying the correction factor, which is function of torque, speed, and power change rates. In [10], the vehicle fuel consumption was separated into two modes: cruising at a constant speed and acceleration operating modes. In each of these modes, the fuel consumption was calculated based on the instantaneous engine efficiency, approximated using an analytical function rather than the fuel consumption map. In [11], a real-time prediction of the fuel consumption was evaluated as first order linear function that varies with VSP (vehicle specific power). The analysis in [12] used vehicle speed (v) and acceleration (a) as dynamic variables to provide the transient correction to be added to the steady-state predicted value. The sign of VSP was used to choose a form of the correction factor. The model proposed by [12] was used as a reference in [13] and further improved taking into account the computational time and accuracy of the model. In [14], engine torque and rotation speed are used as dynamic variables. Four different cases were considered, depending on the sign of engine torque and rotation speed change rate. A correction factor was then applied to multiply the steady-state fuel consumption. The approach was convenient to compute the fuel consumption of a vehicle in transient conditions using a backward model. The abovementioned transient corrections were performed on a vehicle with conventional powertrains to improve the accuracy of fuel consumption computation using steady-state maps. As to the authors' knowledge, no attempt was made to study the improvement of the control strategy of the HEVs by integrating the transient correction of the engine fuel consumption. In HEV applications, the improved accuracy of fuel consumption computation allows for further optimization of the torque split between EM and ICE. Equivalent fuel consumption minimization strategy (ECMS) is an online optimization-based strategy. Due to its online feature, the ECMS controller can define an optimal ratio of torque split at each instant of time, hence acting as a real-time controller. The ECMS was first applied by [PERSON] et al. to HEV [15], where a concept of conversion of the battery energy to equivalent fuel consumption was introduced. The equivalence factor had a substantial effect on the overall efficiency of the HEV. A genetic algorithm was used in [16] for optimal selection of the equivalence factor.