Design of Multi-Model Linear Inferential Sensors with SVM-based Switching Logic ⋆ Martin Mojto ∗Karol Ľubušký ∗∗Miroslav Fikar ∗ Radoslav Paulen ∗ ∗Faculty of Chemical and Food Technology, Slovak University of Technology in Bratislava, Bratislava, Slovakia ∗∗Slovnaft, a.s., Bratislava, Slovakia Abstract: The data-based design of multi-model linear inferential (soft) sensors (MIS) is studied. These promise increased prediction accuracy yet simplicity of the model structure and training. The state-of-the-art approach to the MIS design consists of three steps: 1) data labeling (establishing training subsets for individual models), 2) data classiﬁcation (creating a switching logic for the models), and 3) training of individual models. There are two main issues with this concept as steps 2) & 3) are separate: (i) discontinuities can occur when switching between the models; (ii) data labeling disregards the quality of the resulting model. Our contribution aims at both the mentioned problems, where, for the problem (i), we introduce a novel support vector method (SVM)-based model training coupled with switching logic identiﬁcation and, for the problem (ii), we propose a direct optimization of data labeling. The proposed methodology and its beneﬁts are illustrated on an example from the chemical engineering domain. Keywords: Machine learning and data analytics in process control, Monitoring and performance assessment, Monitoring of product quality and control performance 1. INTRODUCTION The use potential of advanced inference solutions is rising in many industrial ﬁelds. Frequent and accurate estimation of key variables already plays a major role in monitoring and control in various real-world use cases (Li et al., 2021; Qi et al., 2021). One way of dealing with the key- variables estimation is represented by inferential (soft) sen- sors (ISs) (Joseph and Brosilow, 1978). The principle is to infer the hard-to-measure variables from easy-to-measure variables (e.g., temperatures, pressures), e.g., see (Qin et al., 1997; Zhu et al., 2020). The designed inferential sensor thus usually yields less expensive yet more frequent estimation of the key variable than a physical sensor. The main IS-design trade-oﬀis that the higher accuracy is provided at the cost of the higher complexity of the model structure and model training. Industrial processes are usually nonlinear, which often prohibits a use of sim- ple (linear) inferential sensors due to their inaccuracy (i.e., poor extrapolation performance). This aspect can be easily compensated by the design of more complex ISs, e.g., nonlinear IS (Park and Han, 2000) or dynamic IS (Wang et al., 2019). However, the design of complex ISs usually involves much greater eﬀort (model selection, ⋆This research is funded by the Slovak Research and Development Agency (projects APVV-21-0019 and APVV SK-FR-2019-0004), by the Scientiﬁc Grant Agency of the Slovak Republic (grants VEGA 1/0691/21 and VEGA 1/0297/22), and by the European Commission under the grant no. 101079342 (Fostering Opportunities Towards Slovak Excellence in Advanced Control for Smart Industries). The authors acknowledge discussions with M. Klaučo and K. Kiš from Slovak University of Technology in Bratislava. Corresponding author: R. Paulen (e-mail: radoslav.paulen@stuba.sk) data treatment, model validation, etc.) and there are even situations when only a linear IS can be implemented along the actual plant automation solution. In such situations, it is possible to approximate the nonlinear behavior of pro- cess by designing a so-called multi-model inferential sensor (MIS) (Khatibisepehr et al., 2012). The MISs found their use, e.g., in the petrochemical industry (Khatibisepehr et al., 2012), in manufacturing (Zhongda et al., 2016), and in the process industry (Hou et al., 2020). The state-of-the-art approach for the MIS design usually involves three consecutive steps (on the training dataset): a priori labeling, classiﬁcation, and training of