RA: MATLAB Toolbox for Qualitative Modeling and Simulation of Ill-defined Systems by Means of Reconstruction Analysis

Introduction

Given a set of n variables spanning an n-dimensional search space. The elimination of one of these variables corresponds to the projection of the n-dimensional search space onto an (n-1)-dimensional search space. RA analyzes, if the original n-dimensional search space can be reconstructed from any subset of the available (n-1)-dimensional search spaces. If this can be done, the (n-1)-dimensional subspaces that are being used in the reconstruction can be considered as equivalent to the original n-dimensional space.

In this way, it is possible to determine a suitable hypothesis for the internal structure of a system under study, a hypothesis that suggests, which variables should best be used in the identification of behavioral models of the subsystems.

Just like FIR, also RA methodology is derived from the concepts of general system theory. Unfortunately, the RA algorithms are characterized by a very high computational complexity. There is still much work to do, until RA can be applied successfully to large-scale systems in a fully automated fashion. In particular, suboptimal search techniques need to be defined that would keep the computational burden within acceptable limits.

Historical Development

• In 1979, Hugo Uyttenhove designed and developed a first version of the software SAPS (System Approach Problem Solver) as part of his PhD dissertation that he wrote under the guidance of George Klir at the State University of New York at Binghamton. SAPS was a closed software system. It implemented some of Klir's concepts of general system theory, but it could only be used for a fixed set of previously determined problem structures.

• In 1986, David Yandell developed a new version of this software, called SAPS-II, in his Senior Project. This version was developed as a library for CTRL-C, a predecessor of the MATLAB software in use today. The SAPS modules were coded in Fortran. Yandell recognized that the data structures needed in SAPS can be elegantly represented in the form of matrices. For this reason, CTRL-C was well suited for implementing SAPS in it. Contrary to the original version of SAPS, SAPS-II was very flexible. The individual SAPS modules were invoked as subprograms (functions). They could be combined in an arbitrary fashion. Both the original version of SAPS and the newer SAPS-II version offered algorithms for discrete reconstruction analysis [1].

• This is the version of RA that was presented in chapter 13 of the book Continuous System Modeling.

• In 1993, Adelinde (Lin) Uhrmacher developed a fuzzy extension of the RA methodology while she worked as a postdoctoral fellow at the University of Arizona [3]. Lin's research was sponsored by the Humboldt Foundation.

• In 1996, the RA methodology was used by Álvaro de Albornoz in his PhD dissertation. Álvaro applied this technique to the selection of variables in the qualitative monitoring of large-scale systems. When an alarm goes off in a nuclear power station, the operators have exactly 15 minutes time to discover the cause of the alarm. After 15 minutes have passed, the power station must be shut down, which causes a loss of millions of dollars. When an alarm occurs, the operators don't have time to look at all measurement signals. They don't have time either to study in detail the 5000 pages thick emergency procedures manual (EPM). They should be told almost immediately, which of the measurement signals to look at, and what pages in the EPM might contain information relevant to the problem at hand. The results of Álvaro's dissertation shall be concentrated into three articles that are supposed to be published in the International Journal of General Systems. However, these articles have not yet been submitted to date. The only published article concerns some results that show that the fuzzy extension of RA leads to a distortion free reconstruction, whereas the same is not necessarily true when using the discrete reconstruction algorithms [4].

• In 2001, Josep Maria Mirats once again made use of RA techniques in his PhD dissertation. He developed interesting new algorithms for the hierarchical decomposition of systems into subsystemes, using both RA and FIR techniques [5]. The version of the RA toolbox that is being made available through this web page () was developed by Josep Maria. Both Álvaro and Josep Maria worked on projects that were sponsored by the Consejo Interministerial de Ciencia y Tecnología (CICYT). Álvaro was furthermore also directly sponsored by the Mexican Consejo Nacional de Ciencia y Tecnología (CONACYT). My own research activities during my frequent visits in Barcelona were financially supported by the Consejo Interministerial de Ciencia y Tecnología (CICYT) and by the Generalitat de Catalunya in several projects.

Most Important Publications

1. Cellier, F.E., and D.W. Yandell (1987), SAPS-II: A New Implementation of the Systems Approach Problem Solver, Intl. J. General Systems, 13(4), pp.307-322.

2. Cellier, F.E. (1991), Continuous System Modeling, Springer-Verlag, New York.

3. Uhrmacher, A.M., F.E. Cellier, and R.J. Frye (1997), Applying Fuzzy-Based Inductive Reasoning to Analyze Qualitatively the Dynamic Behavior of an Ecological System, International Journal on Applied Artificial Intelligence in Natural Resource Management, 11(2), pp.1-10.

4. Cellier, F.E., and A. de Albornoz (1998), The Problem of Distortions in Reconstruction Analysis, Systems Analysis, Modelling, Simulation, 33(1), pp.1-19.

5. Mirats, J.M., F.E. Cellier, and R.M. Huber (2004), Reconstruction Analysis Based Algorithm to Decompose a Complex System into Subsystems, Intl. J. General Systems, 33(5), pp.527-551.

Sponsors

• Consejo Interministerial de Ciencia y Tecnología (CICYT)
• Consejo Nacional de Ciencia y Tecnología (CONACYT)
• Generalitat de Catalunya
• Humboldt Foundation

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