FIR: MATLAB Toolbox for Qualitative Modeling and Simulation of Ill-defined Systems by Means of Fuzzy Inductive Reasoning

Introduction

Every inductive model identification problem in the final analysis reduces to an optimization problem. As ill-defined systems must be assumed highly non-linear and with a totally or at least almost unknown internal structure, most optimization algorithms fail, as they get stuck in local optima. In contrast to such tools, FIR offers a global optimization strategy. Consequently, FIR will never get stuck in a local optimum.

Optimization algorithms with global convergence are notoriously inefficient computationally. In order to keep the amount of computations needed within bounds, the search space of FIR is discretized. Fuzzy logic is being used to interpolate between neighboring discrete solutions. Use of fuzzy logic permits setting up a discrete search space with a course granularity.

Most of the inductive model identification techniques assume a fixed (although often arbitrary) structure and map the knowledge contained in the training data set onto a set of parameter values. The training data are only used during the model identification phase, i.e., the modeling phase. Once the model has been identified, simulation runs are based solely upon the previously optimized parameter values. Such techniques suffer from the problem that they normally are unable to recognize, when the testing data lie outside the range, for which the model has been validated.

In contrast, FIR is a non-parametric technique. The training data are characterized and classified during the model identification phase, but they are not mapped onto parameter sets. Therefore, FIR refers back to the classified training data set also during the simulation phase. This property makes it impossible for FIR to extrapolate "generously" during simulation.

It is always very easy to make predictions. What is less easy is to know how good these predictions are. FIR methodology offers an intrinsic error estimation algorithm. FIR thus always provides an estimate of the confidence in a prediction together with the prediction itself. This property distinguishes FIR from most other non-linear model identification techniques, such as e.g. artificial neural networks (ANNs). Statistical approaches do offer confidence intervals as well. However, those techniques are essentially linear.

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 to implement 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 [1-3].

• In 1988, Pentti Vesanterä developed a first practical application of this new technology in his MS Thesis. He developed a qualitative model of a Boeing 707 airplane in high altitude horizontal flight [4]. It should be remarked though that SAPS at that moment was still a purely discrete modeling technique.

• In 1990, Donghui Li enhanced the software by fuzzy logic modules [5]. The name FIR was created to reflect upon the fuzzy nature of the enhanced methodology. This is the version of FIR that I introduced in chapter 13 of the book Continuous System Modeling. FIR is also regularly taught in my classes ().

• In 1993, an interface to the continuous system simulation language ACSL was developed. This interface enabled us for the first time to simulate mixed quantitative and qualitative models [9]. This was made possible, because FIR, contrary to most other qualitative approaches, treats the time variable as quantitative, i.e., real-valued.

• In 1994, Àngela Nebot showed in her PhD dissertation, how FIR can be applied to biomedical systems [ 10, 13]. In the same year, Àngela developed additional algorithms for FIR that enabled the software to deal correctly with data sets characterized by missing or wrong values (outliers), as they occur frequently in biomedical applications [7].

• In 1995, Francisco (Paco) Mugica demonstrated in his PhD dissertation, how FIR methodology can be applied to the systematic design of fuzzy controllers [8]. He applied his new techniques to the control of a large oil tanker ship.

• In 1996, Álvaro de Albornoz showed in his PhD dissertation, how FIR methodology can be employed in the design of watchdog monitors of large-scale technical systems. He demonstrated the suitability of his methods by means of the development of a watchdog monitor for a nuclear power station. Álvaro made use of FIR as well as the structuring technique of reconstruction analysis (RA). The research projects of Àngela, Paco, and Álvaro, as well as my own research efforts during my frequent visits to Barcelona were generously supported by the Consejo Interministerial de Ciencia y Tecnología (CICYT) as well as the Generalitat de Catalunya under a number of research grants. Paco and Álvaro were also directly supported by the Mexican Consejo Nacional de Ciencia y Tecnología (CONACYT).

• In 1998, Mukund Moorthy illustrated in his MS Thesis, how FIR models can be structured hierarchically and applied in this fashion to the analysis of macro-economic processes [14]. This research project was financially supported by the U.S. Department of Defense under a research grant.

• In 1999, Josefina (Fina) López enhanced the FIR set of tools by modules for the estimation of the prediction error. To this end, she introduced two separate confidence criteria [11,15]. She showed in her PhD dissertation, how these criteria can help in improving the accuracy of predictions of univariant and multivariant time series [12]. The version of FIR that is being made available on this web page () reflects the state-of-the-art of the software development after completion of Fina's PhD dissertation. This version of the FIR software is coded in C. The ZIP file contains only the already compiled software modules (DLLs) that can be called directly by MATLAB. Appended are two sample programs for the estimation of the depth of anesthesia during a surgical intervention [10].

• In 2001, Josep Maria Mirats developed methods for selecting and grouping variables for the qualitative modeling of large-scale systems in his PhD dissertation [16,17]. He made use of FIR as well as reconstruction analysis techniques in his research.

• In 2004, Ántoni (Toni) Escobet designed and developed a new software layer on top of FIR that should simplify the use of FIR techniques. He called his software VisualFIR [18]. Whereas FIR is command-driven, VisualFIR is menu-driven software. MATLAB functions must always be written by the user when FIR is used directly. In contrast, VisualFIR allows to select FIR algorithms from a list of available tools from a menu. Consequently, VisualFIR is somewhat less general than FIR, but it enables the user to compare much more rapidly and easily different FIR algorithms with each other. Those interested in receiving a copy of VisualFIR are requested to contact Àngela Nebot. The development of VisualFIR forms part of Toni's still incomplete PhD dissertation. Toni is expected to defend his dissertation in 2006. Àngela and I are jointly supervising this project. Currently, Toni is working on yet another software layer, one that shall enable the user to embed FIR modules graphically within SimuLink programs.

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. (1987), Prisoner's Dilemma Revisited - A New Strategy Based on the General System Problem Solving Framework, Intl. J. General Systems, 13(4), pp.323-332.

3. Cellier, F.E. (1987), Qualitative Simulation of Technical Systems by Means of the General System Problem Solving Framework, Intl. J. General Systems, 13(4), pp.333-344.

4. Vesanterä, P.J., and F.E. Cellier (1989), Building Intelligence into an Autopilot Using Qualitative Simulation to Support Global Decision Making, Simulation, 52(3), pp.111-121.

5. Li, D., and F.E. Cellier (1990), Fuzzy Measures in Inductive Reasoning, Proc. Winter Simulation Conference, New Orleans, LA, pp.527-538.

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

7. Nebot A., and F.E. Cellier (1994), Dealing With Incomplete Data Records in Qualitative Modeling and Simulation of Biomedical Systems, Proc. CISS'94, First Joint Conf. of Intl. Simulation Societies, Zurich, Switzerland, pp.605-610.

8. Cellier, F.E., and F. Mugica (1995), Inductive Reasoning Supports the Design of Fuzzy Controllers, J. Intelligent & Fuzzy Systems, 3(1), pp.71-85.

9. Cellier, F.E., A. Nebot, F. Mugica and A. de Albornoz (1996), Combined Qualitative/Quantitative Simulation Models of Continuous-Time Processes Using Fuzzy Inductive Reasoning Techniques, Intl. J. General Systems, 24(1-2), pp.95-116.

10. Nebot, A., F.E. Cellier, and D.A. Linkens (1996), Synthesis of an Anaesthetic Agent Administration System Using Fuzzy Inductive Reasoning, Artificial Intelligence in Medicine, 8(3), pp.147-166.

11. Cellier, F.E., J. López, A. Nebot, and G. Cembrano (1996), Means for Estimating the Forecasting Error in Fuzzy Inductive Reasoning, Proc. ESM'96, European Simulation MultiConference, Budapest, Hungary, pp.654-660.

12. López, J., G. Cembrano, and F.E. Cellier (1996), Time Series Prediction Using Fuzzy Inductive Reasoning: A Case Study, Proc. ESM'96, European Simulation MultiConference, Budapest, Hungary, pp.765-770.

13. Nebot, A., F.E. Cellier, and M. Vallverdú (1998), Mixed Quantitative/Qualitative Modeling and Simulation of the Cardiovascular System, Computer Methods and Programs in Biomedicine, 55(2), pp.127-155.

14. Moorthy. M., F.E. Cellier, and J.T. LaFrance (1998), Predicting U.S. Food Demand in the 20th Century: A New Look at System Dynamics, Proc. SPIE Conference 3369: "Enabling Technology for Simulation Science II", part of AeroSense'98, Orlando, Florida, PP.343-354.

15. López, J., and F.E. Cellier (1999), Improving the Forecasting Capability of Fuzzy Inductive Reasoning by Means of Dynamic Mask Allocation, Proc. ESM'99, European Simulation MultiConference, Warsaw, Poland, pp.355-362.

16. Mirats, J.M., F.E. Cellier, R.M. Huber, and S.J. Qin (2002), On the Selection of Variables for Qualitative Modelling of Dynamical Systems, Intl. J. General Systems, 31(5), pp.435-467.

17. Mirats, J.M., F.E. Cellier, and R.M. Huber (2002), Variable Selection Procedures and Efficient Suboptimal Mask Search Algorithms in Fuzzy Inductive Reasoning, Intl. J. General Systems, 31(5), pp.469-498.

18. Escobet, A., A. Nebot, and F.E. Cellier (2004), Visual-FIR: A New Platform for Modeling and Prediction of Dynamical Systems, Proc. SCSC’04, Summer Computer Simulation Conference, San Jose, California, pp.229-234.

Sponsors

• Consejo Interministerial de Ciencia y Tecnología (CICYT)
• Consejo Nacional de Ciencia y Tecnología (CONACYT)
• Generalitat de Catalunya
• U.S. Department of Defense (DoD)

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