NONLINEAR SCALING IN SMART ADAPTIVE MODELLING Esko K. Juuso Control Engineering, Faculty of Technology, University of Oulu, Finland esko.juuso@oulu.fi ABSTRACT Modelling methodologies provide a good basis for the integration of intelligent systems. Small, specialised systems have a large number of feasible solutions, but developing truly adaptive, and still understandable, systems for highly complex systems require domain expertise and more compact approaches at the basic level. The nonlinear scaling approach extends the application areas of linear methodologies to nonlinear modelling and reduces the need for decomposition with local models. The close connection to the fuzzy set systems provides a good basis for understandable models. Data-based methodologies are suitable for developing smart adaptive applications. Complex problems are solved level by level to keep the domain expertise as an essential part of the solution. Keywords: nonlinear systems, linguistic equations, smart adaptive systems, statistical analysis 1. INTRODUCTION Models are understood as relationships between variables and used to predict of properties or behaviours of the system. Variable interactions and nonlinearities are important in extending the operation areas (Juuso 2014). Phenomenological models based on physics, chemistry and mathematics require domain expertise (Figure 1). Linear methodologies extended with principal components (Jolliffe 2002; Gerlach et al. 1979) and semi-physical models (Ljung 1999) provide a feasible solution for many applications. Nonlinearities have been handled commonly with interaction and quadratic terms (Box and Wilson 1951). Artificial neural networks (ANNs) starting from (Rummelhart et al. 1986) continue this by using more complex architectures. Knowledge-based information can be handled with fuzzy set systems introduced by Zadeh (1965): numerous methodologies have been developed, see (Takagi and Sugeno 1985; Driankov et al. 1993; Dubois et al. 1999), and combined with neural networks (Fullér 2000). Different fuzzy approaches can be efficiently combined (Juuso 2014). First order ordinary differential equations are solved by numerical integration and special solutions have been developed for identification (Ljung 1999). These approaches, which are also used in ANNs and fuzzy set systems (Babuška and Verbruggen 2003), define structures for hybrid dynamic models (Figure 1). Local models need to be combined in complex systems (Sontag 1981; Ljung 2008; Jardine et al. 2006). The linguistic equation (LE) approach originates from fuzzy set systems (Juuso and Leiviskä 1992): rule sets are replaced with equations, and meanings of the variables are handled with scaling functions which have close connections to membership functions (Juuso 1999a). The nonlinear scaling technique is needed in constructing nonlinear models with linear equations (Juuso 2004c). Constraints handling (Juuso 2009) and data-based analysis (Juuso and Lahdelma 2010), improve possibilities to update the scaling functions recursively (Juuso 2011; Juuso and Lahdelma 2011). The LE approach together with knowledge-based systems, neural networks and evolutionary computation form the computational intelligence part (Figure 1). Three levels of smart adaptive systems (SAS) identified in (Anguita 2001): 1. adaptation to a changing environment; 2. adaptation to a similar setting without explicitly being ported to it; 3. adaptation to a new or unknown application. Smart use of intelligence by integrating specific intelligent systems is essential in development of complex adaptive applications. Figure 1: Methodologies and application types of modelling and simulation, modified from (Juuso 2004b) Technically, an automatic black box modelling could be possible in various Big Data problems by using combinations of these methodologies. The domain expertise is an essential part in integrated solutions to understand and assess the applicability. This paper classifies modelling methodologies and focuses on the nonlinear scaling and integrates the LE approach in developing modelling applications for complex systems. Various applications are shortly discussed. Proceedings of the European Modeling and Simulation Symposium, 2015 978-88-97999-57-7; Affenzeller, Bruzzone, Jiménez, Longo, Merkuryev, Zhang Eds. 457