# Ship's Digital Twin--A Review of Modelling Challenges and Applications
## 2 SDT Concept Development and Methods Used
### Modelling and Modelling Methods  
Processed data are then used for modelling, which can be identified as the third step. Traditional physical-based mathematical modelling has often been used; however, it would be expected for a DT concept to benefit from the application of data-based modelling tools such as time series models, artificial neural network algorithms, fuzzy logic, and genetic algorithms. Modelling methods used for DT development in the reviewed literature vary based on scope of application, starting from conventional mathematical modelling and statistical analysis used in [13; 17; 18; 17; 19; 21], the finite elements method (FEM) used in [11; 12; 16; 20; 21; 26], data-driven modelling (DDM) used in [8; 12; 13; 14], artificial neural networks (ANN) used in [8; 9; 10; 11], grey-box modelling (GBM) in [27; 10], cycle mean value (CMV) in [15; 19], boundary element method (BEM) used in [24], model based systems engineering (MBSE) used in [23], and model-based design (MBD) as used in [25]. BBM represents the input-output relation based on acquired data, thus being based entirely on empirical data, while WBM represents purely theoretical modelling based on system equations, as stated in [27]. In between the two, GBM combines acquired data with the theoretical model, and its use has been proposed in [10] to develop a DT predicting fuel consumption and ship speed. Moreover, a GBM method has been proposed in [27] to develop a DT model of a boost converter as part of a shipboard power system. In [27] also, an artificial neural network (ANN) and the available data were used to develop GBM, which was validated to successfully predict fuel consumption and ship speed. The use of an ANN and regression analysis was proposed in [8] to estimate the effect of fouling on ship speed and hence on fuel consumption, operating costs, and emissions, requiring only operational data as input. In addition, changes in the speed loss distribution were calculated with robust regression. The combined use of the ANN and statistical analysis was proposed in [9] by implementing two algorithms on data collected through a step-input test on the electric propulsion motors in a four-corner manoeuvre scenario. The first algorithm calculates the mean value and standard deviation of an electrical current and propeller speed, measured at different set-points of a propulsion motor power. The acceptable range of electrical current for each set-point was set to three standard deviations below and above mean value, indicating a normally operating motor. The case of values going out of rangefor more than two seconds was considered as a fault of the propulsion motor. The second algorithm is the ANN algorithm, where the input nodes are set-points of propulsion motor power, motor speed, and current, and the output node represents the state of the propulsion motor, where 0 represents a normally functioning motor, while 1 represents a faulty motor. If the output node value is at 0.8 for more than 0.5 s, an alarm is triggered. CMV is a mathematical modelling method for the transient response of machinery working in iterative cycles such as a marine diesel engine, and its use was proposed in [15], thus developing a cycle mean value (CMV) model of a marine diesel engine that was further compared with a model developed using the Runge-Kutta method. A statistical analysis method was proposed in [21], where data acquired from DT and the real system (physical twin) were analysed, thus forming a basis for data correction and error detection such as detecting outliers or stuck values caused by malfunctioned sensors. DDM represents modelling based on the acquired data, and it was proposed in [14] to develop a DT of a ship and ship crane system. MBSE represents the formalised application of models throughout the lifecycle of a physical twin, as described in [37; 38], and it was proposed in [23] to develop a DT of a cruise ship.