Optimization of approximating networks for optimal fault diagnosis

Abstract

An optimization-based approach to fault diagnosis for nonlinear stochastic dynamic models is developed. An optimal diagnosis problem is formulated according to a receding-horizon strategy. This approach leads to a functional optimization problem (also called ‘infinite optimization problem’), whose admissible solutions belong to a function space. As in such a context, the tools from mathematical programing are either inapplicable or inefficient, a methodology of approximate solution is proposed that exploits diagnosis strategies made up of combinations of a certain number of simple basis functions, easy to implement and dependent on some parameters to be optimized. The optimization of the parameters is performed in two phases. In the first, ‘a-priori’ knowledge of the statistics of the stochastic variables is used to initialize (off-line) the parameter values. In the second phase, the optimization continues on-line. Both off-line and on-line phases rely upon stochastic approximation algorithms. The overall procedure turns out to be effective in high-dimensional settings such as those characterized by a large dimension of the state space and a large diagnosis window. This favorable behavior results from certain properties of the proposed methodology of approximate optimization, such as polynomial bounds on the rate of growth of the number of parameterized basis functions, which guarantees the desired accuracy of approximate optimization. The effectiveness of the approach is confirmed by simulations in the context of a complex instance of the fault-diagnosis problem. The advantages over classical approaches to fault diagnosis are discussed and pointed out by numerical results.

Keywords:

• Model-based fault diagnosis
• Functional optimization
• Polynomially complex approximators
• High-dimensional admissible solutions
• Nonlinear programing
• Stochastic approximation
• Optimal estimation

Acknowledgements

This work was supported by the CNR-Agenzia 2000 Project ‘New Algorithms and Methodo-logies for the Approximate Solution of Nonlinear Optimization Problems in a Stochastic Environment’.

Notes

The term ‘sufficiently smooth’ means that the mappings have to be continuous together with their partial derivatives up to the order required by the proof of Proposition 1 (see Appendix A).