A fault in an aerospace structure can lead to catastrophic consequences; therefore, it is extremely important to test these structures regularly. Thorough testing of a huge aerospace structures results in a large amount of data, and processing this data takes a lot of time. To decrease the processing time, we use a "multi-resolution" technique, in which we first separate the data into data corresponding to different vibration modes, and then combine these data together. There are many possible ways to transform each mode's data into the probability of a fault, and many possible way of combining these mode-based probabilities; different approaches lead to different results. In this paper, we show how a general methodology for choosing the optimal uncertainty representation can be used to find the optimal uncertainty representations for this particular problem. Namely, we we show that the problem of finding the best approximation to the probability of detection (POD) curve (describing the dependence of probability p(a) of detection on the size a of the fault) can be solved similarly to the problem of finding the best activation function in neural networks. A similar approach can be used in detecting faults in medical images (e.g., in mammography).