Fault diagnosis and fault tolerant control using set-membership approaches: Application to real case studies: This paper reviews the use ofset-membership methodsinfault diagnosis(FD) andfault tolerant control(FTC). Setmembership methods use a deterministic unknown-but-bounded description of noise and parametric uncertainty (interval models). These methods aims at checking the consistency between observed and predicted behaviour by using simple sets to approximate the exact set of possible behaviour (in theparameteror thestate space). When an inconsistency is detected between the measured and predicted behaviours obtained using a faultless system model, a fault can be indicated. Otherwise, nothing can be stated. The same principle can be used to identify interval models for fault detection and to develop methods for fault tolerance evaluation. Finally, some real applications will be used to illustrate the usefulness and performance of set-membership methods for FD and FTC.

The efficient distribution of water is a subject of major concern for water utilities and authorities [1]. While some leaks in water distribution networks (WDNs) are unavoidable, one of the main challenges in improving the efficiency of drinking water networks is to minimize leaks. Leaks can cause significant economic losses in fluid transportation and extra costs for the final consumer due to the waste of energy and chemicals in water treatment plants. Leaks may also damage infrastructure and cause third-party damage and health risks. In many WDNs, losses due to leakage are estimated to account up to 30% of the total amount of extracted water [2]; a very important issue in a world struggling to satisfy water demands of a growing population.

This paper proposes a new sensor placement approach for leak location in water distribution networks (WDNs). The sensor placement problem is formulated as an integer optimization problem. The optimization criterion consists in minimizing the number of non-isolable leaks according to the isolability criteria introduced. Because of the large size and non-linear integer nature of the resulting optimization problem, genetic algorithms (GAs) are used as the solution approach. The obtained results are compared with a semi-exhaustive search method with higher computational effort, proving that GA allows one to find near-optimal solutions with less computational load. Moreover, three ways of increasing the robustness of the GA-based sensor placement method have been proposed using a time horizon analysis, a distance-based scoring and considering different leaks sizes. A great advantage of the proposed methodology is that it does not depend on the isolation method chosen by the user, as long as it is based on leak sensitivity analysis. Experiments in two networks allow us to evaluate the performance of the proposed approach.