Batch processes are inherently more difficult to model than continuous processes due to their complex dynamics

non-steady-state operation and batch-to-batch variation

especially under new operation condition and with small samples.To improve the generalization performance of the global learning based modeling methods

such as least squares support vector regression (LSSVR)

a local LSSVR (LLSSVR) was proposed for modeling batch processes.By combining the optimized parameters of LSSVR from previous batches off-line

an online LLSSVR built a model for each set of new data to be predicted in a new batch by considering only the neighbors of this query.The proposed LLSSVR algorithm was applied to the online prediction of biomass concentration in the penicillin fed-batch process.The simulations showed that LLSSVR could predict the biomass concentration online just from the second batch

which was more accurate and robust to batch-to-batch variation than LSSVR.