Analysis of ion and X-ray time series measurements of electron beam welding for development of online monitoring

Time series analysis results show the singular value decomposition is a candidate of online monitoring of welding penetration in a case that the covariance matrix of a full penetration is used as a mapping function. The mapped time series lie on a hyper-ellipsoid in which the lengths of semi-axes are the squared eigenvalues of the covariance matrix. Furthermore, this algorithm is fast compared with others since only the multiplication with the covariance matrix is used. A depth of welding is closely related with the volume of hyper-ellipsoid.