Several approaches can be employed to tackle source and path identification problems via multiple-input/single-output modeling. When the inputs are not correlated to each other, contribution of each input can be obtained easily by using the ordinary coherence function between the input and output. However, the independence among the measured inputs is not always warranted in real situations. Partial coherence function approach is one of them especially when the measured inputs are correlated to each other, in which conditioning of the inputs is performed before calculating the contribution of each input. On the other hand, virtual coherence function approach decompose simply the real correlated inputs into virtual independent inputs. The physical meanings, general advantages and limitations of several techniques via multiple-input/single-output modeling were discussed with an acoustical system.
It is impractical or impossible to directly measure the physical sources in many experiments. From this difficulty, responses in the vicinities of the real sources are usually employed as inputs for the multiple-inpt/single-output modeling. The measured inputs therefore can be correlated to each other for the reason that physical sources are inherently correlated to each other or input measurements are contaminated by other sources. The linear relationships among the measured inputs can be explained in two ways. One possibility of the input correlation is the case where the inputs cause each other partially and another is the case where the measured inputs do not cause each other although they are correlated. In real situations, it may not be clear whether the linear relationship among the inputs is related with the causality or not. In order to make the conditioning analysis successful, first of all, priorities of the correlated inputs should be correctly decide corresponding to the physical situations in a given model. This problem can be resolved based on the property of transfer function between any pair of correlated inputs.
Since the causalities among the inputs are frequency dependent and the conditioning analysis of the correlated inputs is more frequently performed in the frequency domain, Hilbert transform approach is introduced in this thesis to determine such priorities in frequency domain. Theoretical background of the proposed method was introduced and the procedure was illustrated through an application to measurements from an acoustical system. The feasibility of causality checking method and source identification methods have been demonstrated through practical applications.
