1. **Fuzzy rules may be extracted from expert knowledge and used to create an initial** 
model. The parameters of the model can then be fine tuned using data collected from the operational system being modelled. 

2. **The number of rules can be determined from collected numerical data using a** 
model selection technique. The parameters of the model are also optimised using the existing data. 

The second approach is used in this study as there is no expert knowledge which will allow us to create an adequate initial model. 

## Experimental Setup Data Gathering And Pre-Processing

The data in this work is obtained by performing an experiment on a population of cylinders, which are supported by inserting a sponge rested on a bubble-wrap, to simulate a 'free-free' environment. This setup is illustrated in figure 1 below. The sponge is inserted inside the cylinders to control boundary conditions. This will be further discussed below. Conventionally, a 'free-free' environment is achieved by suspending a structure usually with light elastic bands. A 'free-free' environment is implemented so that rigid body modes, which do not exhibit bending or flexing, can be identified. These modes occur at frequency of 0Hz and they can be used to calculate the mass and inertia properties. In the present study, we are not interested in the rigid body modes. Testing the cylinders suspended is approximately the same as testing it while resting on a bubble-wrap, because the frequency of cylinder-on-wrap is below 100Hz. The first natural frequency of cylinders being analysed is over 300Hz and this value is several order of magnitudes above the natural frequency of a cylinder on a bubble-wrap. Therefore the cylinder on the wrap is effectively decoupled from the ground. It should be noted that the use of a bubble-wrap adds some damping to the structure but the damping added is found to be small enough for the modes to be easily identified. The impulse hammer test is then performed on each of the 20 steel seam-welded cylindrical shells. The impulse is applied at 19 different locations as indicated in Figure 1: 9 on the upper half of the cylinder and 10 on the lower half of the cylinder. The sponge is inserted inside the cylinder to control boundary conditions by rotating it every time a measurement is taken. The top impulse positions are located 25mm from the top edge and the bottom impulse positions are located 25mm from the bottom edge of the cylinder. The angle between two adjacent impulse positions is 36o. 

For one cylinder the first type of fault is a zero-fault scenario. This type of fault is given the identity [0 0 0], indicating that there are no faults in any of the three substructures. The second type of fault is a one-fault-scenario, where a hole may be located in any of the three substructures. Three possible one-fault-scenarios are [1 0 0], [0 1 0], and [0 0 1] indicating one hole in substructures 1, 2 or 3 respectively. The third type of fault is a two-fault scenario, where one hole is located in two of the three substructures. Three possible two-fault-scenarios are [1 1 0], [1 0 1], and [0 1 1]. The final type of fault is a three-fault-scenario, where a hole is located in all three substructures, and the identity of this fault is [1 1 1]. There are 8 different types of fault-cases considered (including [0 0 0]). 