کد مقاله کد نشریه سال انتشار مقاله انگلیسی نسخه تمام متن
755593 895973 2006 20 صفحه PDF دانلود رایگان
عنوان انگلیسی مقاله ISI
A threshold for the use of Tikhonov regularization in inverse force determination
موضوعات مرتبط
مهندسی و علوم پایه سایر رشته های مهندسی مهندسی مکانیک
پیش نمایش صفحه اول مقاله
A threshold for the use of Tikhonov regularization in inverse force determination
چکیده انگلیسی

In the analysis of structure-borne sound from installed machinery, it is important to be able to estimate the operational forces. Assuming that their location is known, indirect approaches based on matrix inversion can be used to reconstruct the operational forces from a set of measured operational responses and corresponding matrix of frequency response functions. In common with many such inverse problems, matrix ill-conditioning can affect the reliability of the results. Methods such as pseudo-inversion of over-determined matrices, singular value rejection, and Tikhonov regularization have been used previously to overcome this and it has been found that Tikhonov regularization generally performs well in reducing the errors in the reconstructed forces. However, full-rank pseudo-inversion (unregularized solution) gives better results than Tikhonov regularization in some cases, particularly with low condition numbers. Since the need for regularization is greatest when the matrix is ill-conditioned, this suggests the introduction of a threshold above which Tikhonov regularization is used and below which pseudo-inversion is used. In this study, the extent to which response errors are amplified in the force estimates is considered and plotted against the matrix condition number. This allows a threshold condition number to be identified above which Tikhonov regularization gives improved results. It is found that the threshold is related not only to the condition number but also to the matrix dimensions including the extent of over-determination. A simple empirical formula is obtained for this threshold that is usable for matrices in a wide range of matrix dimensions.

ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Applied Acoustics - Volume 67, Issue 7, July 2006, Pages 700–719
نویسندگان
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