## 1 Introduction  
Hybrid electric vehicles adopt multiple power sources to drive vehicles to improve fuel economy and reduce pollutant emissions. The energy management strategy (EMS) greatly impacts the fuel economy by controlling the power distribution among the power sources [1; 2]. Global optimization methods such as dynamic programming (DP), genetic algorithm (GA), and simulated annealing (SA) are widely used to solve the optimal energy management problem over a finite horizon [3; 4; 5]. Major disadvantages of these numerical methods are the computational burden and the need to know the driving cycle in advance in order to calculate the required power at the wheels. Therefore, it is not applicable in an actual controller. To tackle this problem, based on [PERSON]'s minimum principle, [PERSON] et al. [6] first proposed the equivalent consumption minimization strategy (ECMS). The equivalent factor has a great influence on the results of ECMS and the constraint on the battery state of charge (SOC), and it varies with different driving cycles. In order to enhance robustness to varying driving cycles, [PERSON] et al. [7] proposed a method by adding an on-the-fly algorithm for the estimation of the equivalent factor to the original ECMS framework, so that the SOC is maintained within the boundaries and the fuel consumption is minimized. [PERSON] et al. [8]employed a penalty function, and the equivalent factor was continuously estimated as a function of SOC deviations. In some studies, total fuel consumption was regarded as a function of the equivalent factor, and the control parameters under optimal fuel economy could be calculated by using systematic methods for given driving cycles [9; 10]. In [11], the piecewise correction coefficient was used to penalize SOC variations, which was updated by a period of historical driving data. The abovementioned methods usually adopted fixed initial conditions while neglecting the influence of complex driving conditions on the performance of the EMS, thus often leading to suboptimal results. In order to improve the flexibility of the controller, it is necessary to periodically recognize the driving pattern and update the control parameters accordingly [12]. Typically, a learning vector quantization (LVQ) neural network model can be well suited for realizing the on-line driving pattern recognition (DPR) through calculating the Euclidean distances [13]. In [14], based on the sample database of several standard driving cycles, the representative feature parameters were obtained by principal component analysis (PCA), and a real-time DPR algorithm was established by using an LVQ neural network model. The optimized control parameters were then periodically updated according to the driving pattern. A comprehensive review of DPR-based control algorithms can be found in [15]. In addition, the DPR algorithm can be incorporated into an adaptive-ECMS (A-ECMS) controller for on-line estimation of the equivalent factor. In [16], an A-ECMS based on DPR was proposed, and a reasonable time window of historical driving data for the DPR algorithm was determined. In [17], the standard driving cycles were classified by K-means clustering, and the nominal equivalent factor was periodically updated by a mean equivalent factor of the selected driving class. A similar method can be found in [18], in which fuzzy rules were adopted for driving cycle classification, and each driving pattern was represented by the optimal equivalent factor of a typical standard cycle in the driving class. These methods have shown promising results for on-line implementation of the ECMS; however, they ignore the influence of the SOC on the estimation of the equivalent factor. In fact, the initial SOC and the subtle change of the equivalent factor are very sensitive to the SOC balance [19]. In this paper, a novel adaptation method of the equivalent factor is proposed by considering the type of driving pattern and the battery SOC to improve fuel economy.