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Robust learning is an important issue in Scientific Machine Learning (SciML). There are several works in the literature addressing this topic. However, there is an increasing demand for methods that can simultaneously consider all the different uncertainty components involved in SciML model identification. Hence, this work proposes a comprehensive methodology for uncertainty evaluation of the SciML that also considers several possible sources of uncertainties involved in the identification process. The uncertainties considered in the proposed method are the absence of theory and causal models, the sensitiveness to data corruption or imperfection, and the computational effort. Therefore, it was possible to provide an overall strategy for the uncertainty-aware models in the SciML field. The methodology is validated through a case study, developing a Soft Sensor for a polymerization reactor. The results demonstrated that the identified Soft Sensor are robust for uncertainties, corroborating with the consistency of the proposed approach., 23 pages

Data-driven sensors are techniques capable of providing real-time information of unmeasured variables based on instrument measurements. They are valuable tools in several engineering fields, from car automation to chemical processes. However, they are subject to several sources of uncertainty, and in this way, they need to be able to deal with uncertainties. A way to deal with this problem is by using soft sensors and evaluating their uncertainties. On the other hand, the advent of deep learning (DL) has been providing a powerful tool for the field of data-driven modeling. The DL presents a potential to improve the soft sensor reliability. However, the uncertainty identification of the soft sensors model is a known issue in the literature. In this scenario, this work presents a strategy to identify the uncertainty of DL models prediction based on a novel Monte Carlo uncertainties training strategy. The proposed methodology is applied to identify a Soft Sensor to provide a real-time prediction of the productivity of a chemical process. The results demonstrate that the proposed methodology can yield a soft sensor based on DL that provides reliable predictions, with precision being proven by its corresponding coverage region.

n-Propyl Propionate (ProPro) is a harmless biodegradable product employed in several fields for the production of drugs, inks, coating, food, and perfume. ProPro is synthesized in an equilibrium reaction for which its yield can be enhanced by constant withdraw of the products as the reaction takes place. Simulated Moving Bed Reactor (SMBR) is a candidate for the production of ProPro with high efficiency as it is a multifunction unit able to simultaneously run reaction and separation, hence shifting the equilibrium reaction toward products. This paper proposes a complete phenomenological model for the ProPro synthesis in a Simulated Moving Bed Reactor (SMBR) packed with the heterogeneous catalyst Amberlyst 46 resin. The operating conditions are defined by the Triangle Theory to design an SMBR unit to produce ProPro efficiently and a comprehensive parameter estimation procedure is employed to obtain more representative parameters. The validated phenomenological model was applied to design an SMBR unit to produce high purity (99.28%) ProPro.

A misusage of machine learning (ML) strategies is usually observed in the process systems engineering literature. This issue is even more evident when dynamic identification is performed. The root of this problem is the gradient explode and vanishing issue related to the recurrent neural networks training. However, after the advent of deep learning, these issues were mitigated. Furthermore, the problem of data structuration is often overlooked during the machine learning model identification in this field. In this scenario, this work proposes a guideline for identifying ML models for the different applications in process systems engineering, which are usually for simulation or prediction purposes. While using the proposed guideline, the work also identifies a virtual analyzer for a pressure swing adsorption unit. In these types of adsorption separations, it is usual that the measurement of the main properties is not done online. Therefore, the virtual analyzer is another contribution of this manuscript. The overall results demonstrate that even though the test provides good performance during the ML model identification, its quality might degenerate over the application domain if the model application is overlooked.