Proceedings of the Thirty-second (2022) International Ocean and Polar Engineering ConferenceShanghai, China, June 5–10, 2022
Copyright © 2022 by the International Society of Offshore and Polar Engineers (ISOPE)
ISBN 978-1-880653-81-4; ISSN 1098-6189

www.isope.org

Uncertainty Quantification of Motor Efficiency Map for All-electric Ships
Fengxiang GUO1,2, Li CHEN1,2
1 Institute of Marine Power Plant and Automation, Shanghai Jiao Tong University, Shanghai, China
2 State Key Laboratory of Ocean Engineering, Shanghai Jiao Tong University, Shanghai, China.

ABSTRACT

important to accurately model motor efficiency and quantify its
uncertainty when modeling the marine power system.

The analysis of data acquired by the dynamometer bench indicates thatmotor efficiency at each operating point appears basically normal
distribution. Consequently, Gaussian Process Regression (GPR) isemployed to estimate the motor efficiency mean map and efficiency
standard deviation map for quantifying efficiency uncertainty caused byfactors 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 forstudy on motor efficiency uncertainty.

Several attempts have been made to study the uncertainty of motor
efficiency. The uncertainty of the measured motor efficiency wasanalyzed with IEC 60034-2-1 measurement standard method in(Aarniovuori et al., 2014). It is noted that the total uncertainty of motor
efficiency was summarized as the comprehensive influence of electricalsensors, instrument ranges, reading, self-generated heat and power factor
error. Study of (Kärkkäinen et al., 2019) has analyzed the uncertainty of
motor loss measurement from the perspectives of electrical power andmechanical power, by considering the influence of voltage and current
amplitude, frequency, power, speed, and torque comprehensively.
Moreover, the factors, such as temperature and correction factors, noload loss, friction loss, wind loss, iron loss and stator winding loss, weretaken into account, and the total refine mathematical models for
uncertainties in the measuring process of direct and indirect efficiency
were established (Bucci et al., 2016). However, in (Kärkkäinen et al.,2019), the authors have pointed out that the refined numerical models ofmotor uncertainty are too ideal to a certain extent. And the concerning
factors are not comprehensive enough, where there is a contradiction
between model complexity and computational cost. Hence, it seems that,the motor efficiency under real operating could be quite different fromthe value from calibrated efficiency map or the refined numerical model.

KEY WORDS: Gaussian Process Regression; motor efficiency map;
efficiency uncertainty
INTRODUCTION
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 andemissions 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 ofelectrical machine when constructing energy consumption model forvessel and tug ship (Zhu et al., 2018; Zhu et al., 2019).

The aim of this research project has therefore been to establish the motor
efficiency map with data-driven method, and meanwhile quantify
efficiency uncertainty. With the development of machine learningtechnology, numerous studies are based on data-driven methods toevaluate uncertainty from the perspective of mathematical statistics.
Among them, the Gaussian Process Regression (GPR) model isdeveloped on the Bayesian framework and can evaluate prediction
uncertainty with probabilistic inference (Williams and Rasmussen,2006). Recently, GPR has been widely applied for uncertainty prediction
in many domains. A GPR model was trained to quantify the uncertaintyof the ship's lateral navigation, and predict the probability of a real-timeship deviating from the preset route relying on the historical ship
trajectory data between two ports in Portugal (Rong et al., 2019). GPRwas also applied to the long-term power load probability prediction, andexperimental results showed that the proposed interval estimation
method accurately describes the true data distribution (Guan et al., 2021).
Apart from that, GPR was introduced to the real-time prediction anduncertainty quantification of fatigue failure under stochastic loading(Farid, 2022). To the best of the author's knowledge, the literature on theHowever, the actual operating conditions of motor are complex andchangeable, which is quite different from the calibration test forefficiency 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 longterm 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 aconsiderable disagreement between the expected and the actual energy
consumption. Consequently, the design parameters of power systemcomponents, such as capacity and endurance of battery, are tooconservative or radical. Hence one can see that it is particularly

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