Integrating physical knowledge with machine learning is critical to developing industrially-focused digital twins for monitoring and optimisation of biomanufacturing systems. However, identifying the correct model structure to quantify kinetic mechanisms poses a challenge for the construction of mechanistic and data-driven models. This study proposes a hybrid modelling strategy comprising of a simple kinetic model to describe the overall process trajectory and a data-driven model to estimate the mismatch between the kinetic equations and real process. An automatic model structure identification algorithm is used to identify the most probable kinetic model structure and minimum number of data-driven model parameters that can well represent different bioprocess behaviours over broad operating conditions. Through this approach, a hybrid model was constructed to simulate biomass growth, nutrient consumption, and product synthesis in an algal photo-production process. Performance of this model for predictive modelling, optimisation, and online self-calibration is demonstrated, indicating its advantages for industrial application.