Hybrid Modelling Strategies for Development of Digital Twins

Chemical and biochemical industries are continuously exploring and adapting technologies to transition into more sustainable productions. Two of the current greatest trends are the transition towards biomanufacturing and the use of continuous processing. This has however brought its own challenges, since it comes with an increased number of potential process disturbances and a greater complexity. Meanwhile, over the past two decades, the industry has undergone a significant digital transformation, which opens a wide range of new business opportunities. One of the greatest opportunities is product customisation, which makes it possible to accommodate niche markets, enabling economic growth
without necessarily increasing consumption of raw materials and utilities.

To transition into continuous processing and biomanufacturing,and at the same time allow for greater product customisation, the concept of digital twinning has gained significantindustrial attention. A digital model of a physical object or process is here constructed that is continuously updated to reflect the physical domain using sensing devices and actuators.It comes with promises of reduced time-to-market, enabling optimisation of manufacturing processes, and is furthermore considered a potential key enabler of continuous processing. However, digital twins are today very costly and time consuming to develop. Especially the time requirement is a significant challenge when it comes to reducing the
time-to-market.
The development of a sufficiently accurate model is one of the costliest and time consuming  tasks of constructing a digital twin. This is especially the case for bio manufacturing  processes. To solve this challenge, hybrid modelling approaches have been widely examined  in literature over the past two decades. Traditional parametric modelling (e.g., mass  and energy balances) is here combined with machine learning. In many earlier studies,  this has been shown to provide more robust models compared to fully data-driven  models  and at the same time require less first principles knowledge compared to a traditional  parametric model. However, most of the previously applied hybrid modelling strategies
lead to static models, which is not optimal for digital twin applications.

In this PhD thesis, hybrid modelling strategies are explored and developed, to evaluate whether they can be used within the frame of facilitating a rapid and cost-effective development of digital twins in the chemical and biochemical industries. This is done by developing a modelling framework that can be used to systematically construct, validate, and test hybrid semi-parametric models of dynamic chemical and biochemical processes, that also will allow for continuous learning. Both deterministic and probabilistic hybrid modelling strategies are here studied and compared in terms of their predictive capabilities and suitability for integration into a digital twin. Finally, it is discussed how the presented hybrid models can be integrated into a digital twin, and what challenges that must be solved going forward.
To evaluate the performance of the presented modelling framework, three solidliquid separation processes are considered, all operated in batch mode. This includes both laboratory scale and industrial scale crystallisation processes and a   laboratory scale flocculation process. For each of the case studies, factors such as data quantity, data variability and the experimentally available sensing technology impact the overall predictive performance of the constructed hybrid models are evaluated. Furthermore, the computational requirements are addressed. Finally, it is analysed how accounting for various sources of uncertainties during model training can be used to construct increasingly robust hybrid models, which furthermore allow for quantifying the uncertainty of the model predictions .Based on the case studies, it is concluded that proposed hybrid modelling strategies in deed can offer a costeffective  model development, which is suitable for the development  of digital twins. It does however require the availability of online/at line  sensors that  are capable of measuring most of the critical process parameters and critical quality attributes  at a sufficient frequency. It is furthermore concluded that with the proposed modelling  strategy, methods such as automatic differentiation must be applied to make model  development computationally feasible. If not, only very simplified hybrid models will be  feasible to construct, which will in the end will offer little to no advantages over traditional  parametric modelling. With that said, even by applying these computationally efficient  methods, the computational time needed for training might limit the feasibility of hyper-parameter  optimisation of the machine learning models. This means that to ensure that  the constructed hybrid models can leverage from increasing quantities of training data, the  machine learning models may have to be designed more complex than otherwise would  be desirable.

Following this it is found that the risk of overfitting  for hybrid semiparametric  models is a  legitimate concern and must be addressed during the construction of the model and whenever  the model is trained using new data. However, by accounting for uncertainties during  the model training, and applying simple regularisation techniques such as early stopping,  it is possible to mitigate overfitting  to a considerable extent. Furthermore, by accounting  for uncertainties during model construction, it also becomes possible to estimate the uncertainty  of the hybrid model predictions, which is essential for the construction of digital  twins to be used for critical decisionmaking.  Overall, this PhD thesis forms a basis from which hybrid models can be constructed and evaluated, which are computationally feasible to integrate into a digital twin. Going forward,  this makes it possible to quantify the potential benefits of using a digital twin for both theoretical and experimental case studies. This includes rapid testing and application of  advanced model-based  control strategies, such as model predictive control, which previously  were not economically feasible due to the cost of model development.  Furthermore,  due to its flexible nature, it also has an immense potential of enabling the use of digital  twins at the early stages of process development.