The application of white box models in digital twins is often hindered by missing knowledge, uncertain information and computational difficulties. Our aim was to overview the difficulties and challenges regarding the modelling aspects of digital twin applications and to explore the fields where surrogate models can be utilised advantageously. In this sense, the paper discusses what types of surrogate models are suitable for different practical problems as well as introduces the appropriate techniques for building and using these models. A number of examples of digital twin applications from both continuous processes and discrete manufacturing are presented to underline the potentials of utilising surrogate models. The surrogate models and model-building methods are categorised according to the area of applications. The importance of keeping these models up to date through their whole model life cycle is also highlighted. An industrial case study is also presented to demonstrate the applicability of the concept.

In this article, the authors focus on the introduction of a hybrid method for risk-based fault detection (FD) using dynamic principal component analysis (DPCA) and failure method and effect analysis (FMEA) based Bayesian networks (BNs). The FD problem has garnered great interest in industrial application, yet methods for integrating process risk into the detection procedure are still scarce. It is, however, critical to assess the risk each possible process fault holds to differentiate between non-safety-critical and safety-critical abnormalities and thus minimize alarm rates. The proposed method utilizes a BN established through FMEA analysis of the supervised process and the results of dynamical principal component analysis to estimate a modified risk priority number (RPN) of different process states. The RPN is used parallel to the FD procedure, incorporating the results of both to differentiate between process abnormalities and highlight critical issues. The method is showcased using an industrial benchmark problem as well as the model of a reactor utilized in the emerging liquid organic hydrogen carrier (LOHC) technology.

Fault Detection and Isolation (FDI) methodology focuses on maintaining safe and reliable operating conditions within industrial practices which is of crucial importance for the profitability of technologies. In this work, the development of an FDI algorithm based on the use of dynamic principal component analysis (DPCA) and the Fréchet distance $\left({\delta }_{dF}\right)$ metric is explored. The three-tank benchmark problem is studied and utilized to demonstrate the performance of the FDI method for six fault types. A DPCA transformation for the system was established, and fault detection was conducted based on the Q statistic. Fault isolation is also of critical importance for proper intervention to mitigate fault effects. To identify the type of detected faults, the fault responses within the PC subspace were analyzed using the ${\delta }_{dF}$ metric. The use of the Fréchet distance metric for the isolation of faults combined with DPCA for feature extraction is a novel technique to the best of the authors’ knowledge that provides a robust computational tool with low computational cost for FDI purposes that fits well into the Industry 4.0 framework.The robustness and sensitivity of the method was validated for a wide variety of signal-to-noise ratio (SNR) conditions, with findings indicating a possible average false and missed alarm rate of 0.1 and a macro-averaged F-score above 0.8 in all cases.

Fossil materials are widely used raw materials in polymerization processes; hence, in many cases, the primary goal of green and sustainable technologies is to replace them with renewables. An exciting and promising technology from this aspect is the isocyanate-free polyurethane production using vegetable oil as a raw material. Functional compounds can be formed by the epoxidation of vegetable oils in three reaction steps: epoxidation, carbonation, and aminolysis. In the case of vegetable oil carbonation, the material properties vary strongly, with the composition affecting the solubility of CO₂ in the reaction mixture. Many attempts have been made to model these interactions, but they generally do not account for the changes in the material properties in terms of spatial coordinates. A 2D CFD model based on the combination of the k-ε turbulence model and component mass balances considering the spatial inhomogeneities on the performance of the reactor was created. After the evaluation of the mesh independence study, the simulator was used to calculate the carbonation reaction in a transient analysis with spatial coordinate-dependent density and viscosity changes. The model parameters (height-dependent mass transfer parameters and boundary flux parameters) were identified based on one physical experiment, and a set of 15 experiments were used for model validation. With the validated model, the optimal operating temperature, pressure, and catalyst concentration was proposed.