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Ultrasonic equivalent flaw sizing methods have been recently used to size a flaw in a material by obtaining a best-fit simple equivalent shape that matches the ultrasonic scattering data. However, current ultrasonic equivalent flaw sizing methods have a number of important limitations: ( 1 ) they are both iterative and highly nonlinear in nature, and (2) they require the availability of flaw classification information. Here, a series of approaches are outlined that address both of the above problems. Both numerical and experimental results that validate these new approaches are also given. First, when the flaw shape is determined in terms of a best-fit equivalent ellipsoid, a new linear least-squares/eigenvalue method is described that can replace existing nonliner routines and provide a computationally fast and robust sizing procedure. Second, it is shown that if the shape is determined instead in terms of an expansion in spherical harmonics, the sizing problem again reduces tO a simpler linear leastsquares/differentiation process. Third, a way to do equivalent flaw sizing even when flaw classification information is not present is demonstrated. When such classification information is available, however, one can see how it can be used to improve sizing estimates for cracks, by the elimination of systematic measurement errors due to finite transducer bandwidth effects.

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The ultrasonic signals observed in inspection processes can often be accurately predicted by suitable measurement models. These model predictions can be used to provide important information to guide the development of subsequent signal processing algorithms. Here such a hybrid use of ultrasonic modeling and signal processing is demonstrated in the context of the problem of detecting ultrasonic flaw signals in noise. In particular, we wish to apply this hybrid methodology as an initial approach to solving the problem of detecting hard-alpha inclusions in titanium alloys.The "hard-alpha" inclusions are known to be brittle regions of microstructure caused by oxygen or nitrogen contaminations. During high-stressed manufacturing process or inservice operations, they are likely to initiate cracking, which may subsequently leads to catastrophic failure of aircraft components [1]. Hence, early detection is desired. However, the inherently weak strength of signals from hard-alpha inclusions, complicated further by the presence of high-level correlated grain noise, have long rendered this a particularly serious inspection problem. Furthermore, the lack of appropriate test specimens has made the development and evaluation of detection techniques even more challenging.In our engineering approach toward this problem, we first utilize a measurement model to simulate signals for specific inclusions and superimpose on these noise traces obtained on real samples. We then show that it is feasible to construct matched fIlters to achieve significant signal-to-noise ratio (SNR) enhancement. Based on simulation studies of largescale data sets, we can then assess the matched filter performance and the detectability in terms of the receiver operating characteristics estimates. Examples of detection of different inclusion impedances and sizes are presented in combination with various experimental setups. The results of using split-spectrum technique are also included. A parallel effort of applying neural networks and statistical analysis to the hard-alpha problem can be found in these proceedings [2]. SIGNAL SIMULATIONThe manufacture of test specimens containing seeded hard-alpha inclusions is currently underway in a separate work [3]. Presently, it is believed that these hard-alpha inclusions have similar ultrasonic characteristics as those of weakly scattering inclusions, and can be simulated from models [4]. Here the Thompson-Gray measurement model [5] is employed to simulate the hard-alpha inclusion signals. This model simulates flaw signals through modeling of the entire ultrasound propagation process using theoretical calculations of flaw