3.3 Online calibration for state estimation
In practice, new measurement of state variables can be collected through regular sampling and offline analysis during an ongoing process. However, it is not easy to directly use this data to effectively calibrate a kinetic model or a machine learning model. For instance, although parameters of a kinetic model can be rapidly re-estimated, its prediction will always suffer from model-plant mismatch due to the fixed model structure. Although a data-driven model may eliminate model-plant mismatch, it requires substantial amount of data to frequently update its large number of parameters. However, new data collected from an ongoing process is usually limited, hence not able to satisfy this prerequisite. Nonetheless, both of these issues can be resolved by a hybrid model. The kinetic part of a hybrid model does not have to be frequently calibrated as its mismatch has been included in the data-driven part. The data-driven part of a hybrid model has a simple structure with a minimal amount of parameters (e.g. 5 parameters in this case), thus new data (usually sampled once per 4 hours in a large scale process, hence 6 data points per day) collected from an ongoing process can be used to effectively update the model’s accuracy. As a result, online calibrating a hybrid model is straightforward.
To illustrate this advantage, another case study was conducted. Since the current hybrid model is accurate for long-term offline optimisation, it was decided to first add errors in its parameter values so that a large initial model-plant mismatch is observed. Therefore, a 15% random error was assigned to all the parameters, and the new model’s prediction is shown in Fig. 6 when only the initial operating conditions and pre-determined control actions are given. It is seen that large mismatch exists at a later stage of the process. However, after model re-calibration at the end of day 1 (using 6 new data points), it is found that the model’s prediction is improved significantly, particularly for biomass and lutein concentrations. Daily calibration of the data-driven part of the model leads to moderate improvement until day 3, beyond which this effect becomes negligible. Nonetheless, it is also observed that the hybrid model still contains an error for online state estimation and long-term prediction, particularly for nitrate concentration. This is because the kinetic part of the model comprises a 15% error in its parameters and has never been calibrated. As a result, once enough new data points are accumulated from the ongoing process, they should be used to re-estimate values of all the parameters in the hybrid model to further improve model accuracy.