A linear time-invariant filtering approach for ultrasonic transducer normalization

The increased use of automatic defect detection and characterization system s of the self-learning type has created a demand for means capable of norma lizing signals from ultrasonic transducers. Measurements obtained using dif ferent 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 diffe rences in measured data. We propose a linear filtering approach for normali zing ultrasonic pulse-echo measurements as a preprocessing step before pres enting the data to a characterization system. The approach requires two dat a sets: one for the reference transducer and one for the transducer to norm alize. We formulate the normalization problem as a general linear approxima tion problem and derive an optimal linear transformation for an ideal situa tion with known transducer and noise characteristics. Due to the properties of the optimal linear transformation, a close approximation of this transf ormation 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 th e filter approximation. The filter is obtained using the output error metho d, one of the standard system identification methods. The proposed method i s tested on real ultrasonic data obtained from carbon-fiber-reinforced epox y composites. The results of experiments with real data, illustrating one o f the possible applications, are used to point out some practical considera tions that have to be taken into account when implementing the proposed met hod.