Flaw identification is an important inverse problem that underlies techniques for nondestructive evaluation (NDE). In this study, a known steady state thermal field is used to identify multiple flaws in a material. The problem is to determine locations and sizes of the multiple flaws if the number of flaws and the temperature at certain probe locations on the boundary are known. The boundary element method (BEM) is used as a computational tool in this task;Earlier work in this area has dealt with the case of a single flaw, while we address the case of multiple flaws. The identification of the multiple flaws is difficult because it is impossible to identify the disturbances caused by each individual fLaw; As a result, the iterative methods, used in the single flaw identification, typically fail to converge unless approximate locations of the multiple flaws are known;In our method, the characterization of flaws is performed in two stages. First, the specimen probe data is compared with a set of known cases of probe data (training set) to predict the approximate locations and sizes of the multiple flaws. Second, the final prediction of flaws is determined using a nonlinear optimization method;To prepare the training set, we need only the information of a single flaw of fixed size at various locations. The superposition principle and a special scaling are used to create the multiple flaws information. This procedure is developed as an extension of the theory of potential flows in fluid mechanics. The distinguishing feature of this technique is that only a small training set is stored in the memory;In this study, the final characterizations are made by two different methods. One of them is an iteration method, which minimizes an error functional. The other is called the multivariate adaptive regression splines (MARS). Various test cases yielded excellent solutions. The tolerance of both methods to experimental errors is also discussed. It is found that the iterative method performs better than MARS.

The direct boundary element method is proposed in this thesis to solve acoustic radiation problems as well as to achieve regional noise cancellation in half space with uniform finite impedance over the surface. The boundary integral equation and half space Green's function were derived to accomplish these goals. Those formulations were verified by comparing numerical simulations with theoretical solutions as well as experimental results. In addition, the above formulations were extended to achieve regional noise cancellation in half space by applying the boundary element method;Two methods were investigated to obtain noise cancellation in desired regions. They are the iterative control method and the coupled equation method. A set of Fortran programs including discretizing of geometries, incorporating boundary integral equations, and accommodating the noise cancellation technique were developed. Various problems concerning ill-conditioned matrices in numerical simulation and practical application of noise cancellation technique were discussed as well. Finally, data banks for various configurations of sound sources were set up for quick reference of the locations and driving functions of secondary sources. Thus, noise reduction in a designated area is shown to be feasible;A 6" speaker was used to simulate a noise source with uniform surface velocity. In addition, a ribbed aluminum plate with the dimension 71.12cm x 60cm was used to simulate a noise source with variable surface velocity. Four 10" speakers were used as secondary sources to achieve noise reduction in desired regions at certain frequencies. A multi-channel digital/analog converter was used in order to control desired driving functions for each individual secondary sources. The computer-controlled scanning system including a 2-channel controller, 2-D scanner, and stepping motors was used to place a quarter-inch microphone at certain locations. The acoustic pressure on a 120cm by 120cm plane at various distances above the source plane was measured. A Bruel and Kjaer model 2032 FFT analyzer was used to acquire and process signals from the microphone. The experimental results agreed well with numerical simulations. This indicated that the proposed noise cancellation technique attenuated the acoustic noise level successfully.