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.

One of the significant problems in our society is the handling and processing of the vast amount of waste produced by households and industrial processes. Nowadays, packaging material regulations are constantly changing, which can significantly impact the quality of municipal waste, requiring the continuous development and redesign of waste processing plants. Since only a few uncertain measurements (composition, mass, etc.) are available for this task, analysing and redesigning waste processing technologies is challenging. This research aims to develop a modelling and simulation concept that can integrate all the available information and can also handle the uncertainty of the measurements. The proposed modular modelling framework can serve as a basis for designing and redesigning the technologies needed to process ever-changing municipal waste. The most important steps of the framework are as follows: identifying the typical equipment, these are the elements; building models of the elements; determining the characteristic parameters of the equipment; exploring the possible relationships between the elements. For example, the information needed to define the model parameters can be gathered from measurements, industrial experience, and expert knowledge. In many cases, the data obtained represent ranges. The stationary model framework applies efficiency factors and divides the solids into substreams based on expert knowledge. Furthermore, a modular simulator framework was developed to simulate the technological schemes with various connections. The specifications for all widely used waste industrial equipment (shredders, air separators, sieves, magnetic-, eddy current-, optical-, and ballistic separators) were used to construct the developed simulator. This simulator can open new opportunities for the design of waste sorting technological networks. The model was calibrated based on expertise gained from operating the studied technology. The changes in the material parameters can be considered, and the modular simulator can lead to flexible waste sorting technologies capable of adapting to governmental and environmental regulations changes. The main result of the work is that a methodology for designing a modular simulator, model development, and a validation method has been proposed, which provides the possibility to deal with uncertainty. All this is successfully presented through the analysis of an operating waste separation system.

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.