Chemical Engineering Science 59 (2004) 2801–2810 www.elsevier.com/locate/ces A new data-based methodology for nonlinear process modeling Cheng Cheng, Min-Sen Chiu * Department of Chemical and Biomolecular Engineering, National University of Singapore, 10 Kent Ridge Crescent, Singapore 119260, Singapore Received 17 March 2003; received in revised form 24 June 2003; accepted 18 April 2004 Abstract A new data-based method for nonlinear process modeling is developed in this paper. In the proposed method, both distance measure and angle measure are used to evaluate the similarity between data, which is not exploited in the previous work. In addition, parametric stability constraints are incorporated into the proposed method to address the stability of local models. Furthermore, a new procedure of selecting the relevant data set is proposed. Literature examples are presented to illustrate the modeling capability of the proposed method. The adaptive capability of the proposed method is also evaluated. ? 2004 Elsevier Ltd. All rights reserved. Keywords: Process modeling; Just-in-time learning; Distance measure; Angle measure; Stability 1. Introduction Mathematical models are often required for purposes of process modeling, control, and fault detection and isola- tion. However, because most chemical processes are mul- tivariate and nonlinear in nature, and their dynamics can be time-varying, rst-principle models are often unavailable due to the lack of complete physicochemical knowledge of chemical processes. An alternative approach is to develop data-based methods to build model from process data mea- sured in industrial processes. Traditional treatments of the data-based modeling meth- ods focus on global approaches, such as neural networks, fuzzy set, and other kinds of nonlinear parametric mod- els (Nelles, 2001). However, when dealing with large sets of data, this approach becomes less attractive because of the diculties in specifying model structure and the com- plexity of the associated optimization problem, which is usually highly non-convex. Another fundamental limitation of these methods is that it is dicult for them to be updated online when the process dynamics are moved away from the nominal operating space. On the other hand, the idea of local modeling is to approximate a nonlinear system with a set of relatively simple local models valid in a certain oper- ating regimes. The T–S fuzzy model (Takagi and Sugeno, ∗ Corresponding author. Tel.: +65+6874-2223, fax: +65+6779-1936. E-mail address: checms@nus.edu.sg (M.-S. Chiu). 1985)andneuro-fuzzynetwork(JangandSun,1995; Nelles, 2001) are well-known examples of local modeling approach. However, most local modeling approaches suer from the drawback of requiring a priori knowledge to determine the partition of operating space and when this information is lacking, complicated training strategy needs to be resorted to determine both optimal model structure and parameters of the local models. To alleviate the aforementioned problems, just-in-time learning (JITL) (Cybenko, 1996) was recently developed as an attractive alternative for modeling the nonlinear sys- tems. It is also known as instance-based learning (Aha et al., 1991), locally weighted model (Atkeson et al., 1997; Rhodes and Morari, 1997), lazy learning (Bontempi et al., 2001), or model-on-demand (Braun et al., 2001; Hur et al., 2003) in the literature. This approach is inspired by ideas from lo- cal modeling and database technology. JITL assumes that all available observations are stored in a database, and the models are built dynamically upon query. Compared with the traditional modeling methods, JITL exhibits three main characteristics. First, the model building is postponed un- til an output for a given query data is requested. Next, the predicted output for the query data is computed by exploit- ing the stored data in the database. Finally, the constructed answer and any intermediate results are discarded after the predicted output is obtained (Atkeson et al., 1997; Bontempi et al., 2001; Nelles, 2001). Fig. 1 illustrates the dierence between the traditional methods and JITL. Standard methods like neural networks and neuro-fuzzy network are typically 0009-2509/$ - see front matter ? 2004 Elsevier Ltd. All rights reserved. doi:10.1016/j.ces.2004.04.020