Process/model mismatch diagnosis by latent variable modeling

First-principles (FP) models are often preferred to data-based (DB) ones because they rely on a physical understanding of the mechanisms that govern the physical behavior of the system under investigation and allow for some extrapolation. The development of an FP model usually takes longer than that of a DB model, and the resulting model may be unreliable if the knowledge about the underlying mechanisms of the process is limited, or if the complexity of the physical phenomena involved forces one to simplify the model structure. In these cases, the FP model results does not match the experimental evidence to a desired accuracy, and process/model mismatch (PMM) therefore occurs. PMM may be a critical issue if the model is used within a design, optimization or control activity. For this reason, when PMM is detected, the FP model should be adjusted (in terms of parameters or equations) in order to match the available experimental data. Adjusting an FP model requires diagnosing the PMM, i.e. being able to assess whether the mismatch is a parametric or a structural one, and which model parameters or model equations need improving. Model-based design of experiments (MBDoE) techniques (Franceschini and Macchietto, 2008) can be used both for model discrimination among alternative set of equations, and for parameter identification from a given set of equations. However, these techniques may be very demanding if one does not know in advance which equations or parameters are most responsible for the observed mismatch. Ideally, one would like to diagnose the PMM without carrying out any additional experiment, i.e. using only an available historical database. After this preliminary diagnosis, MBDoE can indeed be used as an effective method to enhance the FP model performance. In this study, we propose a two-step methodology to diagnose an observed PMM. First, an historical dataset is used to design a DB model (namely, a latent-variable multivariate statistical model). Then, this model is used to diagnose the observed PMM, and this is achieved by assessing the consistency between the correlation structure of the historical dataset and that of a similar dataset generated using the FP model. The proposed methodology is tested on two simulated systems: a jacket-cooled chemical reactor and a solids milling unit. In the latter case study, gSOLIDS 3.0 (2013) is used to provide the historical simulated data and the first principles model to be analyzed. It is shown that, considering different sources of PMM, the proposed model diagnosis methodology can reduce the iterations needed to identify the FP model sections that need improving.