Data Reconciliation-Based Hierarchical Fusion of Machine Learning Models

In the context of hierarchical system modeling, ensuring constraints between different hierarchy levels are met, so, for instance, ensuring the aggregation constraints are satisfied, is essential. However, modelling and forecasting each element of the hierarchy independently introduce errors. To mitigate this balance error, it is recommended to employ an optimal data reconciliation technique with an emphasis on measurement and modeling errors. In this study, three different machine learning methods for development were investigated. The first method involves no data reconciliation, relying solely on machine learning models built independently at each hierarchical level. The second approach incorporates measurement errors by adjusting the measured data to satisfy each constraint, and the machine learning model is developed based on this dataset. The third method is based on directly fine-tuning the machine learning predictions based on the prediction errors of each model. The three methods were compared using three case studies with different complexities, namely mineral composition estimation with 9 elements, forecasting of retail sales with 14 elements, and waste deposition forecasting with more than 3000 elements. From the results of this study, the conclusion can be drawn that the third method performs the best, and reliable machine learning models can be developed.