## 1 Introduction  
The wheel loader, as a kind of off-highway vehicle, has complicated working conditions and drastic changes in load. Hence, the vehicle's transmission plays a vital role in improving its efficiency and performance. The conventional transmission applied to the wheel loader is the mechanical transmission with torque converter. Therefore, many scholars have studied the traditional transmission with torque converter [1; 2; 3]. However, the efficiency of the torque converter has a greater impact on the efficiency of the transmission system, which results in no significant increase in efficiency, whatever structure is adopted. Therefore, the hydro-mechanical continuously variable transmission (HMCVT) has received widespread attention. Hydro-mechanical continuously variable transmission (HMCVT) is a kind of power split transmission. Composition of the HMCVT is as displayed in Figure 1. The input power is divided into two paths (mechanical transmission and hydrostatic CVT) through the power split device, and the power of the two paths will be combined through the power junction device (PJD). It can achieve high-efficiency power transmission through mechanical transmission and CVT through hydrostatic transmission. The efficiency of the hydrostatic transmission is higher than the hydrodynamic transmission. The hydrostatic transmission not only has high efficiency compared to the hydrodynamic transmission, but also can achieve CVT and has the adaptability to the load. Many companies like Dana Rexroth, ZF, and Liebherr, have developed and produced HMCVT, and the efficiency has generally improved by about 25% [4; 5; 6; 7]. Many scholars have studied hydrostatic mechanical power split transmission. [PERSON] et al. developed a novel power-split-input-coupled infinitely variable transmission (IVT) system and carried out kinematic analysis of the new system [8]. [PERSON] et al. designed and analyzed comparatively the directly coupled HST and the output-coupled power split transmission (PST) for a 10 ton wheel loader for improving the fuel economy of a wheel loader [9]. [PERSON] et al. introduced and analyzed a kind of multi-range hydro-mechanical transmission (HMT) based on dual stage input-coupled layout, which had a mean efficiency of about 83% in a wide speed range through the simulation [10]. [PERSON] et al., through a \"direct search\" algorithm based on the swarm method, defined the design of a hydro-mechanical transmission as an optimization problem in which the objective function is the average efficiency of transmission [11]. [PERSON] et al. investigated the efficiency characteristic of the hydro-mechanical continuous variable transmission (HMCVT) in tractors and proposed a method for building the HMCVT efficiency model based on an improved simulated annealing (SA) algorithm according to a small amount of test data [12]. [PERSON] et al. set the design of a hydro-mechanical transmission as a multi-objective optimization problem, where the goal is not only the best efficiency but also the smallest size of the transmission [13]. [PERSON] et al. provided a new model for the preliminary design of compound power-split CVTs, which allowed the engineers to prioritize functionality and efficiency of the transmission, while delaying the choice of the involved gear sets' layout as long as possible [14]. [PERSON] et al. provided a fast kinematic analysis method for compound power-split CVTs, which consented to identify their functional parameters [15; 16]. [PERSON] et al. presented an analytical formulation of the layouts of three-shaft hydro-mechanical transmissions and obtained the formulation starting from the Willis equation for the planetary gears [17]. [PERSON] et al. presented a comparison between the different architectures of power-split transmissions utilizing hydraulic units as the variators, with a focus on efficiency, control effort, and system complexity [18]. [PERSON] et al.