The analysis of data acquired by the dynamometer bench indicates that motor efficiency at each operating point appears basically normal distribution. Consequently, Gaussian Process Regression (GPR) is employed to estimate the motor efficiency mean map and efficiency standard deviation map for quantifying efficiency uncertainty caused by factors such as temperature, control tracking error and measurement noise. The results show that maximum absolute error (MAE) between the efficiency mean maps established by GPR and the measured data does not exceed 0.2270%, and MAE between the predicted efficiency standard deviation and the actual value is below 0.0792. It demonstrates that GPR can be introduced to quantify efficiency uncertainty effectively when modeling motor efficiency map, which provides a reference for study on motor efficiency uncertainty.


Electric ships are currently the most promising method to reduce the air pollution and tackle excessive fossil energy crisis (Inal et al., 2022). Accurately evaluating the energy consumption, battery capacity and emissions based on the ship dynamics model is essential for design purpose (Nuchturee et al., 2020). As the critical component in the drive configuration of all-electric ships, previous studies have reported that efficiency map is currently one of the main application forms of electrical machine when constructing energy consumption model for vessel and tug ship (Zhu et al., 2018; Zhu et al., 2019).

However, the actual operating conditions of motor are complex and changeable, which is quite different from the calibration test for efficiency map, resulting in a notable gap between the actual motor efficiency and the efficiency from the map (Li et al., 2015). Additionally, factors such as ambient temperature, control tracking error, and long-term aging bring greater uncertainty to motor efficiency (Bucci et al., 2016; Kärkkäinen et al., 2019; Ostroverkhov and Buryk, 2019). Therefore, in design stage, only utilizing the calibrated motor efficiency map to set up ship energy consumption model would generate a considerable disagreement between the expected and the actual energy consumption. Consequently, the design parameters of power system components, such as capacity and endurance of battery, are too conservative or radical. Hence one can see that it is particularly important to accurately model motor efficiency and quantify its uncertainty when modeling the marine power system.

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