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In this book, various approaches have been investigated to improve the force identification process of TPA. The study has been completed in two parts. First part presents a comparison of response predictions as a result of performing Transfer Path Analysis using the matrix inversion technique with different matrix arrangements, all of which are based on coherence knowledge and cross coupling omission. The second part describes a new method of improving the quality of the matrix inversion procedure and lowering the condition number of the matrix by selective omission of the cross-coupling terms. In addition to comparing the predicted results with the measured experimental values, they will be also compared with those obtained through the Moore-Penrose pseudo-inverse technique to verify the validity of the selective omission technique.