Confidence Limits Analysis (CLA)


Introduction

Modelling and simulation of real-life systems relies on having a sufficiently good knowledge of the plant and its environment, so that the simulated behaviour can match the real one. Unfortunately, it is frequently the case that the knowledge of system components and the system environment is limited, which makes it impossible to produce simulated results that reflect the behaviour of the physical system.

This research has developed a novel methodological approach to modelling uncertain systems. Rather than trying to optimise scalar estimates of individual system states we have developed interval estimation which explicitly captures the uncertainty inherent in the system. The interval estimates are in effect sets of all feasible states corresponding to a given level of uncertainty in the system. The sets are presented in the form of lower and upper bounds on individual state variables, and hence provide limits on the potential error of each variable. We refer to this state estimation as the Confidence Limits Analysis (CLA). In what follows we present the derivation of the CLA using a water distribution system as a reference.

The system model





Confidence Limit Analysis




Monte Carlo method




Linearised confidence limit analysis











Linear programming method








Sensitivity matrix method











Ellipsoid method













Real-life application
















Conclusions



Publications

  • Bargiela A., Hainsworth G., Pressure and flow uncertainty in water systems, ASCE Journal of Water Resources Planning and Management, Vol 115, 2, March 1989, pp. 212-229, PDF
  • Bargiela A., Hainsworth G., Pressure and flow uncertainty in water systems, Water Resources Journal, Sept., 1990, pp. 40-48. This paper was selected for a reprint from the ASCE Journal, Vol.115, 2
  • Bargiela A., A graphical interactive software tool for confidence limit analysis, AWWA Conference on Computers and Automation in the Water Industry, Denver, CO, 2-4 April 1989.
  • Bargiela A., Hainsworth G., Confidence limit analysis in water systems, pp. 43-58, in Computer Applications in Water Supply, Vol 2. Systems Optimisation, Coulbeck B., Orr C.H. (Eds.), Research Studies Press U.K., John Wiley and Sons, 1988, ISBN: 0 471917842, PDF
  • Bargiela A., Hainsworth G., Telemetry design with TCLAS software, pp. 1-11, in Computer Applications in Water Supply, Vol 2. Systems Optimisation, Coulbeck B., Orr C.H. (Eds.), Research Studies Press U.K., John Wiley and Sons, 1988, ISBN: 0 471917842, PDF
  • Bargiela A., Managing uncertainty in operational control of water distribution systems", in Integrated Computer Applications, Vol 2, (Ed.) B Coulbeck, J Wiley, 1993, ISBN: 0 471 94232 2, pp 353-363.
  • Bargiela, A., 1985, An algorithm for observability determination in water systems state estimation, Proc. IEE, Vol. 132, Pt. D, No. 6, pp. 245-249
  • Bargiela, A., 1994, Ellipsoid method for quantifying the uncertainty in water system state estimation, Proc. IEE Colloquium on Modelling Uncertain Systems, Vol. 1994/105, pp.10/1-10/3.
  • Bargiela A., Nonlinear network tearing algorithm for transputer system implementation, Proc. of Int. Conf. TAPA-92, Melbourne, November 1992, ISBN 905199115 0, pp. 19-24
  • Bargiela A., Hosseinzaman A., Parallel simulation of nonlinear networks using diakoptics, in Parallel Computing and Transputer Applications, M. Valero (ed.), IOS Press/CIMNE, Barcelona, 1992, ISBN 84 87867 138, pp. 1463-1473.
  • Belforte, G., Bona, B., 1985, An improved parameter identification algorithm for signals with unknown-but-bounded errors, Proc. IFAC/IFORS., York.
  • Cichocki, A., Bargiela, A., 1997, Neural networks for solving linear inequality systems, Parallel Computing, Vol. 22, No. 11, pp. 1455-1475
  • Fogel, E., Huang, Y.F., 1982, On the value of information system identification – bounded noise case, Automatica, Vol. 18, No. 2,
  • Gabrys, B., Bargiela, A., 1999, Neural networks based decision support in presence of uncertainties, ASCE J. of Water Res. Planning and Management, Vol. 125. No. 5, pp.272-280
  • Hainsworth G., Bargiela A., Optimal telemetry system for water networks, Int. Symposium on Optimal Modeling of Water Distribution Systems, Lexington, K.Y., May 1988.
  • Hartley J., Bargiela A., TPML: Parallel meta-language for scientific and engineering computations using transputersProceedings of 2nd Int. Conference on Software for Supercomputers and Multiprocessors. SMS-94, Moscow 1994, PDF
  • Hartley J., Bargiela A., XTPML - Simplifying the Development of Parallel Programs for Implementation on Various Transputer Architectures, Proc. European Simulation Symposium ESS-98, Oct. 1998, ISBN 1-56555-147-8, pp.119-123, PDF
  • Hartley J., Bargiela A., Probabilistic Simulation of Large-scale Water Distribution Systems, Proceedings of European Simulation Symposium ES-96, Genoa, October 1996, ISBN 1-565555-099-4 (Vol.2), pp.403-407, PDF
  • Hartley J., Bargiela A., Cant R., Parallel simulation of large scale water distribution systems, Proceedings of Modelling and Simulation Conference ESM-95, Prague, June 1995, ISBN 1-56555-080-3, pp. 723-727, PDF
  • Hartley J., Bargiela A., Parallel State Estimation with Confidence Limit Analysis, Parallel Algorithms and Applications , Vol. 11, No.1-2, 1997, pp. 155-167, PDF
  • Jaulin, L., Walter, E., 1996, Guaranteed nonlinear set estimation via interval analysis, in: Bounding approaches to system identification (Milanese et al., eds.), Plenum Press
  • Mo, S.H., Norton, J.P., 1988, Parameter bounding identification algorithms for boundednoise records, Proc. IEE, Vol. 135, Pt D, No. 2
  • Moore, R.E., 1966, Interval analysis, Prentice-Hall, Englewood Cliffs, NJ.
  • Pedrycz, W., Vukovich, G., !999, Data-based design of fuzzy sets, Journal of Fuzzy Logic and Intelligent Systems, Vol. 9, No. 3.
  • Pedrycz, W., Smith M.H., Bargiela, A., 2000, A Granular Signature of Data, Proc. NAFIPS’2000
  • Ratschek, A., Rokne, J., 1988, New computer methods for global optimization, Ellis Horwood Ltd., John Wiley & Sons, New York
  • Rokne, J.G., Interval arythmetic and interval analysis: An introduction, in: Granular Computing (Pedrycz ed.), Elsevier
  • Sterling, M.J.H., Bargiela, A., 1984, Minimum-norm state estimation for computer control of water distribution systems, Proc. IEE, Part D, Vol. 131
  • Warmus, M., 1956, Calculus of approximations, Bull. Acad. Polon. Sci., Cl III 4, pp. 253-259.


Last update: 7/05/96