Proposal of a stable solution of inverse problem with a larger number of unknowns

Abstract

Moment of inertia is an important factor for rating a performance of mechanical products with rotational motion. Inertia moment can be designed, but the wooden products of it may vary due to the individual difference between timbers. Moreover, mass moment of inertia may change over time due to factors such as spoilage, corrosion, and drying. Nondestructive evaluations of mass distribution are important to improve the inertia moment of the actual product. The author have proposed a non-destructive method to estimate mass distribution and internal shape in solids. In this method, mass distribution is estimated by an inverse analysis of inertia moments which are measured at several rotational axes. It is possible to detect internal voids using this method because estimated masses become zero there. The material densities can be also calculated from the estimated masses and the shape. In the previous study, numerical simulations for buttcylindrical rods were carried out to prove the effectiveness of this method. Relatively high estimation accuracy of this method was obtained by an inverse analysis when there are two unknown parameters. In this study, I tried to apply new approaches for the problem including relatively large number of unknowns, however it was difficult to improve the estimation accuracy.