Fig. 6.1 Layout of the PM with all relevant components and state variables in which the instantaneous cylinder volume can be expressed as a function of crank- angle @ according to the kinematics of the crankshaft as (Merker et al. 2005; Heywood 1988) Finally, the energy conservation equations for each combustion zone can be expressed as WUMDeT OF CYNNAETS IN Me CngimMe, The combustion products are evaluated exploiting the method of Rakopoulos et il. (1994), due to its minimal computational time requirements and reasonable agree- nent with experiments. For the burning zone, given its volume, temperature, mass of uel burnt and mass of air entrained, the concentration of each species can be evalu- ited by solving a 11 x 11 non-linear system obtained from 7 non-linear equilibrium >quations and 4 linear atom balance equations. This system is converted to a 4 x 4 Fig. 6.3. Input and output variables of the DDMs where p = [p},.--, Pn]’. The solution of this problem is again equivalent to solving a linear system Table 6.2. Main characteristics of the MAN 12 V28-33D engine Fig. 6.4 Propulsion system layout for the holland class oceangoing patrol vessels Table 6.6 Performance metrics on PM-SO dataset Table 6.7 Subset of data source from Table 6.3 exploited as inputs and outputs of the DDM and HM Fig. 6.7 Scatter plot (measured vs. predicted) and trend in time for the Nic (rpm) output feature using the different models (PMs, DDMs, and HMs) with A = 0 Table 6.8 Indexes of performances (MAE, MAPE, and PPMCC) of the different models (PMs DDMs, and HMs) for different A € {0, 10, 20, 30} for the different quantities to predict Note that A = 0 means that the authors do not exploit time series information from the past, fot A > O there is no PM result It should be noted that, although DDMs are computationally demanding in the training phase, they are characterised by lower computational complexity in the feed- forward phase, as they just require matrix manipulation methods, in contrast with the solution of a system of first order differential equations that the PM requires (see Sect. 6.3.1). The combination of both accurate and fast predictions, makes DDMs an ideal candidate for real-time performance and condition estimation. How- ever, the necessary data to reach this level of performance is rather high as reported in (Cipollini et al. 2018a,b), which makes this type of models applicable only after extensive measurement campaigns have been undertaken. In addition, another disad- vantage of DDMs is the lack of interpretability as it is not supported by any physical interpretation (Shawe-Taylor and Cristianini 2004). Ts Ansara thane: HsitAhnAe <oe BeAeNGAH the woe Af TYAMe ‘Thea alla tha Fig. 6.13 Scatter plot (measured vs. predicted) and trend in time for T,, (°C) output feature using the different models (DDMs and HMs) with A = 20
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