A Bi-level Optimization Approach for Historical Data-Driven System Identification

System identification is the field of systems mathematical modeling from experimental data. In the modeling chain, experiments realization, model structure selection and parameter estimation are essential steps. However, performing tests for system identification is time-consuming and not always possible. Also, while in most modeling workflows model parameters are optimized, model structure is generally selected manually, and if optimized, data informativity is not considered. For these reasons, an approach using historical data with optimized selection of model’s structure and parameters, considering data informativity, is proposed. Therefore, historical data is collected and data around the process operating point is selected. Then, data is prefiltered, resampled, cleaned, and normalized. Then, for modeling, a vector autoregressive with exogenous variables model structure is considered. To estimate the model’s structural parameters and coefficients, a bi-level optimization algorithm is proposed. For the outer optimization, genetic algorithm, fireworks algorithm, particle swarm optimization, and simulated annealing algorithm are simulated and compared to conventional methods. Also, as normal operation data is used, a data informativity step is integrated to discard non-informative model structures. To estimate the model coefficients, ridge regression is used. In a case study, the approach is applied to model an industrial thickener. The obtained results show that the proposed approach outperforms conventional ones.