Multiple Model Adaptive Estimation Coupled With Nonlinear Function Approximation and Gaussian Mixture Models for Predicting Fuel Consumption in Marine Engines

Abstract

Digital twin type models can be developed for physical systems that are complex nonlinear a system of systems (SoS). However, such models are usually difficult to represent by linear equations. Therefore, an adequate linearization technique should be introduced. Therefore, linear models as digital twins can be interpreted easily and need much less computational power when applied to various industrial applications. On the other hand, a linearization approach can increase the respective system-model errors and impose significant constraints on the models of SoS, i.e., since linear models can be applicable only in limited operating regions. This research study aims to combine positive characteristics of both linear and nonlinear modelling into a digital twin development framework by having the properties of linear digital twin models locally while the model framework is covering the whole operating region of the SoS. An industrial application of marine engines as an SoS is considered for this study, where the respective models have been used to predict engine fuel consumption. For this purpose, firstly, a dataset is selected from a marine engine of a selected ocean-going vessel. Then, several localized linear operational regions of the respective data set are identified using an unsupervised data-driven technique, i.e., on the engine propeller combinator diagram. For developing the localized models: firstly, the Gaussian Mixture Models method is used to cluster the data points into different operational regions of the engine propeller combinator diagram. Then, a nonlinear model of the relationship between features is developed in each cluster using the polynomial regression approach. Then, these models are combined using the Multiple Model Adaptive Estimation (MMAE) method to create an overall model for the marine engine as an SoS. The same model is utilized to predict the respective fuel consumption based on engine operational conditions.