Fig.1

Digital twin framework of rudder loop system

Fig.2

Electrical and control model of rudder loop in closed-loop control system

Fig.3

Principle diagram of electromechanical and control model of rudder loop system based on AMESim

Fig.4

Control closed-loop and inverter direction determination logic model based on AMESim

Table 1

Power-driver-circuit’s 3-phase on-off logic

Fig.5

Model of power switch and brushless DC motor based on AMESim

Fig.6

Illustration of vehicle’s X-rudder layout

Fig.7

Flowchart of hinge moment modelling process

Fig.8

Illustration of rudder defect model and rotation model

Table 2

Boundary conditions and values for simulations

Fig.9

Illustration of lift and hinge moment trends

Fig.10

Logic diagram of rudder dynamic moment fitting and modelling

Table 3

Fifth-order polynomial fit coefficients

Fig.11

Results of dynamic moment fitting

Fig.12

Framework diagram of virtual-physical consistency perception and twin dynamic adjustment mechanism

Fig.13

Illustration of current and rudder angle indicators before and after faults

Fig.14

Illustration of dimensionality reduction and clustering results of virtual-physical consistency features

Fig.15

Illustration of threshold model based on convex hull

Table 4

Results of threshold test

Fig.16

Illustration of entity’s fault indicators under normal and faulty conditions

Fig.17

Illustration of current-factor and rudder-factor’s frequency and cumulative frequency

Fig.18

Illustration of normalized current’s frequency and cumulative frequency

Fig.19

Illustration of the fitting result between normalized current and rudder defect rate

Fig.20

Illustration of rudder system’s physical-entity and platform for simulation， loading and measurement

Fig.21

Illustration of fault current tracking results of digital twin

Fig.22

Illustration of virtual-physical consistency for time-domain current metrics in normal segment

Fig.23

Illustration of virtual-physical consistency for time-domain current metrics in fault segment

Fig.24

Illustration of fault rudder tracking results of digital twin

Fig.25

Illustration of virtual-physical consistency for time-domain rudder metrics in normal segment

Fig.26

Illustration of virtual-physical consistency for time-domain rudder metrics in fault segment

Table 5

Comparison of virtual and actual current rudder angle metrics under normal and fault conditions

Table 6

Comparison of fidelity results of different rudder modelling methods

Fig.27

Illustration of digital-twin’s extended parameter variation with fault