The ideal design of an airplane should include built-in sensors that are pre-blended in the perfect aerodynamic shape. Each built-in sensor is expensive to blend in and requires continuous maintenance and data processing, so we would like to use as few sensors as possible. The ideal formulation of the corresponding optimization problem is, e.g., to minimize the average detection error for fault locations. However, there are two obstacles to this ideal formulation:
--First, this ideal formulation requires that we know the probabilities of different fault locations etc., and there are usually not enough statistics to determine these probabilities.
--Second, even for a known distribution, finding the best locations is a very difficult computational problem.
To solve these problems, geometric symmetries are used; these symmetries enable to choose several possible sets of sensor locations; the best location is then found by using a neural network to test all these (few) selected locations.