Anton Sodja

Supervised Hierarchical Clustering in Fuzzy Model Identification

This paper presents a new, supervised, hierarchical clustering algorithm (SUHICLUST) for fuzzy model identification. The presented algorithm solves the problem of global model accuracy, together with the interpretability of local models as valid linearizations of the modeled nonlinear system. The algorithm combines the advantages of supervised, hierarchical algorithms, which are based on heuristic tree-construction algorithms, together with the advantages of fuzzy product space clustering. The high flexibility of the validity functions that is obtained by fuzzy clustering combined with supervised learning results in an efficient partitioning algorithm, which is independent of initialization and results in a parsimonious fuzzy model. Furthermore, the usability of SUHICLUST is very undemanding, because it delivers, in contrast with many other methods, reproducible results. In order to get reasonable results, the user only has to set either a threshold for the maximum number of local models or a value for the maximum allowed global model error as a termination criterion. For fine-tuning, the interpolation smoothness controls the degree of regularization. The performance is illustrated on both analytical examples and benchmark problems from the literature.

Modelling thermal processes in buildings using an object-oriented approach and Modelica

Abstract Most of today’s modelling and simulation concepts originate from the times and methods of analog computers. Usually, it is assumed that the model must be expressed in an explicit state-space form. Consequently, the topology of the system gets lost and any future extension and reuse of the model is tedious and error-prone. In other words, it is the modeller’s task to consider the computational order of the operations during a simulation. In this paper we discuss the re-implementation of a passive-solar- building simulator in an object-oriented environment; it was originally built in the non-object-oriented simulation environment of Matlab–Simulink. The former simulator was designed to resemble a real physical test chamber with regard to the thermal and solar radiation flows. However, due to the lack of object orientation in Matlab–Simulink it was very difficult to apply any configuration modifications and extensions. We start with a brief description of the mathematical modelling which includes thermal dynamics and solar radiation. Then the implementation in Modelica is presented. So, a much superior environment in comparison with Matlab-Simulink was obtained, giving us the possibility of high-level modular and object-oriented modelling. The model is also extremely efficient in multidisciplinary projects in which control-engineering specialists (our group) cooperate with specialists from civil engineering, because civil engineers can more easily understand graphical and textual models in Modelica than schemes in Simulink. We expect that such a model will fulfil and significantly improve several model properties in comparison to the Matlab–Simulink implementation, i.e., a better understanding of the influences of thermal and radiation flows on comfortable living conditions, a model-based control-system design, which will enable the harmonization of active and passive energy resources, important energy savings, and a very suitable environment for education in modelling, simulation and control.

Computer-aided physical multi-domain modelling: Some experiences from education and industrial applications

Abstract For the purposes of this paper, computer-aided physical modelling means a type of modelling in which a computer-aided approach is used, with the basic aim being to maintain the physical structure of a real system or its topology as much as possible in the model. Bond graphs represent a very efficient and traditional approach. However, new, object-oriented and multi-domain tools based on the Modelica language are more appropriate for industrial staff or for the people who do not have a deep insight into modelling and simulation. In this paper we describe several educational and industrial application projects in the Dymola–Modelica environment: a process-systems library, two mechanical systems (an inverted pendulum and a laboratory helicopter), a model of thermal and radiation flows in buildings and two models of processes in mineral-wool production, i.e., a pendulum system and a recuperator system. We describe some experiences from these projects, but also from a more general use of the Matlab–Simulink and Dymola–Modelica environments over many years. One simple conclusion is that we need to educate with two approaches: a more physical and advanced acausal Modelica-like approach, but also a more traditional causal or block-oriented approach according to the historical CSSL standard. The important advantages and disadvantages of both approaches are described. The Modelica-based approach enables true ‘physical’ modelling with fully reusable components. However, there is a particular danger, i.e., users occasionally forget some basic modelling principles when using sophisticated libraries. The result is a very complex modelling structure that is relatively inefficient for the simulation and sometimes has many numerical problems. It is usually very difficult to detect the real reasons for that.

Advanced Multi-Domain Modelling: Advantages and Dangers

Multi-domain modelling becomes a very modern expression for approaches which support so called physical modelling when combining components from different application areas. Physical modelling means in this contest a modelling when a computer aided approach is used with the basic aim to keep the physical structure of a real system or its topology as much as possible in the model. Bond graphs represent a very efficient and traditional approach. However new object-oriented and multi-domain tools based on Modelica language are more appropriate for industrial staff or for the people who do not have a deep insight into modelling and simulation. In the paper we describe some experiences obtained with several education and industrial application projects using Dymola-Modelica environment. Mostly advantages obtained with object oriented approach and a special connection implementation will be presented. However such advanced tools bring also potential dangers: namely when users can develop complex models with powerful libraries they often forget that validation is still the most important part of a modelling cycle. The second problem appears from the complexity which is usually obtained. These problems directed our research activities and will be briefly presented at the end of the paper.

Some Aspects of Thermal and Radiation Flows Modelling in Buildings Using Modelica

Efficient use of energy in buildings is very important. Special attention is given to the use of passive energy resources as the costs for heating and cooling can be significantly reduced and living conditions at the same time improved. Modelling of thermal and radiant flows and illumination is very important in this area and so many models with different aims and complexity were developed in the past. Traditional models have a significant lack of object orientation which represents an important disadvantage, because it is difficult or sometimes even impossible to reuse model components. This paper deals with some activities about a simulator which models thermal and radiation flows in buildings. It was originally developed in Matlab/Simulink environment. With the reimplementation in object-oriented Dymola Modelica environment the quality of simulator was significantly improved in different aspects. However, since distribution of radiation flows is mostly geometrical problem, the reusability is not gained implicitly by using Modelica as it is when using models described by DAE. Additional efforts were needed to make components fully reusable. The proposed solutions significantly increased the possibilities for more complicated building structures modelling.

SUpervised HIerarchical CLUSTering (SUHICLUST) for nonlinear system identification

In this paper the new algorithm SUHICLUST (SUpervised HIerarchical CLUSTering) is presented. It unifies the strengths of the supervised, incremental construction scheme LOLIMOT with the advantages of product space clustering. The result of this fusion is a powerful structure identification algorithm that enables approximation of processes with axes-oblique partitioning, high flexible validity functions and local polynomial models. The theoretical comparison with LOLIMOT and product space clustering and a demonstration example underline the usefulness of SUHICLUST.

Global Supervised and Local Unsupervised Learning in Local Model Networks

Abstract In this paper a new algorithm for nonlinear system identification with local linear models is proposed. The algorithm utilizes product space clustering inherently in a heuristic tree-construction algorithm. The high flexible validity functions obtained by fuzzy clustering combined with supervised learning in the framework of a local model network result in an efficient partitioning algorithm. Its properties are illustrated by a demonstration example.