biology, and engineering. They are particularly valuable in situations where empirical data is limited or unreliable or where a deep understanding of the underlying physical processes is necessary for accurate predictions. First prin- ciples models offer several advantages, including the ability to extrapolate beyond the range of observed data, provide insights into underlying mechanisms, and make predictions in novel or complex situations. However, they can also be computationally intensive and require detailed knowledge of the system’s physical properties and behaviour. Hybrid modelling is a promising approach to leveraging the combined strengths of the first principles and machine learning methods. The first principles model is well-suited to capture high-level trends and extrapolate beyond the historically known data points. At the same time, ML meth- ods are good at capturing dependencies that analytic mod- els cannot precisely express. Another benefit of the hybrid model is its explainability, as the crucial part of the dependency has an analytical formulation, with the ML part accounting for the minor adjustment part. These benefits of hybrid modelling explain the interest in their application for technological process modelling. Hybrid models applied in this domain can be classified into two main groups: ML models improving the science-driven ones and scientific principles improving the the ML models. An example of the latter kind is incorporating scientific principles in the loss function formulation of a neural net- works model. For example, a loss function of a neural net- work predicting two material streams can include a term penalising for material balance violation. An example of the former is employing an ML model to predict the residual error, which the first principles model of the process does not cover. In formulating a hybrid modelling approach to blend model formulation, we draw inspiration from the residual hybrid model approach to technological process modelling. The DuPont blend model is the analytic part of the hybrid model. The ML learning part of the model is responsible for the residual or bias prediction, which takes as parameters blended components’ ratios, the octane number properties of these components, and the regressed DuPont model biases. The diagram of the model is presented in Figure 1 . Minimising giveaway While a precise blending model is intrinsically valuable, its primary function is to support the model-based optimisa- tion problem of finding the blend’s recipe under the defined criteria. The optimisation problem is generally devoted to finding the recipe that allows the production of the desired quantity of the blended product at the lowest cost. This is a constrained optimisation problem. The typical constraints are the quantities of the available blending components, the desired blend amount, and the specified minimum or maximum allowed properties’ values of the blend. This imposes an additional requirement on the hybrid model. The model must be smooth to support major non-linear optimisation algorithms, such as Interior Point OPTimizer (IPOPT), allowing a derivative calculation.
Blended components ratios Blended component property values DuPont interaction coe cients
DuPont model prediction
DuPont model
+
Residual AI model
Residual prediction
Figure 1 Hybrid model architecture
One must be mindful that some machine learning algo- rithms, such as artificial neural networks (ANNs) and pol - ynomial regression, are smooth and support derivative calculation. At the same time, the efficient and widespread family of tree-based machine learning algorithms, such as Random Forest and Gradient Boost, generally are not smooth functions. A consideration should therefore be given to this nuance when choosing an algorithm for the machine learning component of the hybrid model. As the blended streams’ properties slightly deviate from their values assumed during batch planning, recipe cor- rections are necessary during the execution of the blend- ing batch. The ability to do this adjustment in real time is directly tied to the giveaway minimisation objective. Its implementation requires online measuring of the blended streams’ and the blending station’s products’ properties. Near-infrared (NIR) analysers commonly perform this function. They execute spectrometric analysis of the fluids passing through them. As with batch planning, stream ratio adjustment during batch execution also depends on model- ling the dependency between the property of the blending components and the products of the blend. Figure 2 shows the real-time blend optimisation system. The same blend model can be used for both online and offline optimisation tasks. However, the calculation time constraints are much tighter for the optimisation done. There is a difference in formulating online and offline blend optimisation problems. The real-time problem is responsi- ble for adjusting the blended stream rates pre-calculated in advance.
Online blend optimiser
Distributed control system (DCS)
Static mixer
NIR analyser
Figure 2 Online blending system
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