A linear time-invariant filtering approach for ultrasonic transducer normalization

The increased use of automatic defect detection and characterization systems of the self-learning type has created a demand for means capable of normalizing signals from ultrasonic transducers. Measurements obtained using different measurement setups should be normalized with reference to a standard transducer. It is usually an unfeasible task to optimize characterization procedures for all combinations of measurement parameters that are usually available in a modem complex measurement system. For instance, a change of transducer or only a change in cable length may result in substantial differences in measured data. We propose a linear filtering approach for normalizing ultrasonic pulse-echo measurements as a preprocessing step before presenting the data to a characterization system. The approach requires two data sets: one for the reference transducer and one for the transducer to normalize. We formulate the normalization problem as a general linear approximation problem and derive an optimal linear transformation for an ideal situation with known transducer and noise characteristics. Due to the properties of the optimal linear transformation, a close approximation of this transformation can be implemented using a linear time-invariant filter. We verify by simulations that the filter approximation is valid, and we also examine some properties concerning the accuracy of the estimates obtained using the filter approximation. The filter is obtained using the output error method, one of the standard system identification methods. The proposed method is tested on real ultrasonic data obtained from carbon-fiber-reinforced epoxy composites. The results of experiments with real data, illustrating one of the possible applications, are used to point out some practical considerations that have to be taken into account when implementing the proposed method.