The effect of surface roughness on extrapolation from thickness C-scan data using extreme value theory

Ultrasonic thickness C-scans are a key tool in the assessment of the condition of engineering components. C-scans provide information of the wall thickness over the entire inspected area. Full inspection of a component is time consuming, costly and sometimes impossible due to obstacles. Therefore, the condition of the whole structure is often estimated by extrapolation of data from a small sample where C-scan information is available. Extreme value theory (EVT) provides a framework by which one can extrapolate to the size of the worst case defect from a small inspected sample area of a component. The framework and assumptions of EVT are discussed, with experimental and simulated examples. The influence of both the surface roughness and the timing algorithm, used to extract thickness measurements from the collected ultrasonic signals, is also analyzed. It can be shown that for uniformly rough surfaces the C-scan data can lead to conservative estimates of the size of the worst case defect.