Modeling of driveline dynamic efficiency and application to mass estimation

The inherent uncertainty in driveline dynamic efficiency constrains the mass sensing capability of model-driven approaches for heavy vehicles, such as wheel loaders (WLs). To overcome these limitations, this study develops a data model-driven framework for predicting dynamic efficiency without relying on torque transducers, aiming to improve both mass estimation accuracy and convergence speed. First, the dynamics of the planetary gear driveline are derived by simplifying the Lagrange equations through the principle of virtual work. Subsequently, a longitudinal dynamics model is established that incorporates the efficiency parameters of the drivetrain, including the gearbox and drive shaft. This modeling procedure effectively captures the dynamic efficiency patterns of the WL during start-up and acceleration phases. Building on this foundation, a hybrid WOA-TCN-BiGRU architecture is proposed, integrating a whale optimization algorithm-enhanced temporal convolutional network with a bidirectional gated recurrent unit. This neural network architecture enables accurate prediction of driveline dynamic efficiency without the need for torque sensors, while remaining compatible with classical recursive least squares algorithms. The dynamic efficiency prediction model was validated using a specialized test bench, demonstrating that the least squares method, empowered by dynamic efficiency parameters, achieves mass estimation convergence within 2 s, significantly faster than previously reported methods, and maintains a persistent error below 3 %. By integrating neural networks with physics-based modeling, this approach offers novel insights and a fast, reliable method for WL mass estimation.