Diagnosis through bilateral membership functions and pattern recognition

International audienceOn real processes many junctional states are usually observed. However some of them may represent different significant levels (or rates) of the same functional node. They do not represent by themselves a functional mode, they are only sub-modes of the same functional mode (e.g. one of the functional mode of my car is tank empty; some functional states observed may be 10% empty tank, 50% empty tank, 96% empty tank). Thus the interest is not only to diagnose the functional mode (e.g. tank empty, sleeping driver) but also to highlight the gravity level of this functional mode (e.g. the reaction in the middle of desert, confronted to a 4% empty tank is not the same as confronted to a 98% empty tank). The aim of this paper is to present a diagnosis method based on fuzzy pattern recognition. Such a method allows the diagnosis of the current functional mode of a process and its gravity level. Usually in pattern recognition area, a membership function is a monotonic decreasing function of a Euclidean distance between two objects. Those objects represent two states of the process and a distance here is a dissimilarity measure between those states. Such a distance is defined in all the fuzzy subset associated with this membership function. So that function is monotonic decreasing in all subset directions. In this paper directional membership functions are proposed. In this case the distance is defined only by reference to a path describing the evolution from one functional state to another one. Then the obtained membership function is oriented according to this path and do not decrease identically within all directions in the subset. Such membership functions are then suitable in order to diagnose the state associated with data evoluting between known functional modes. An application to the French telephone network illustrates this method