A new model as a damage index in an eigen value problem with application in health monitoring of offshore jacket platform

A set of second-order differential equations (the initial value problem) is used to analyze the vibrations of structures. This method is based on changing the second-order differential equations to the eigenvalue problem, which is usually used for modal analysis of structures. This problem involves a matrix equation with mass and stiffness as coefficient matrices. Changes in some stiffness matrix arrays change eigenvalues ​​and eigenvectors, and changes in stiffness matrices indicate damage to one or more structural members. Therefore, identifying modified arrays is very useful for monitoring the health of structures. Modified stiffness array arrays can be obtained by comparing new eigenvalues ​​and eigenvectors with old ones. The Stubbs Index (Modal Strain Energy) Stubbs (MSE) uses only special vectors to identify injuries. In the improved modal strain energy method (IMSE) proposed by Lee et al., In addition to special vectors, special values ​​are also entered in relation to the damage index. In this research, a new injury index is presented with the development of the above two indicators, which show more accurate results than them. In this study, the health monitoring of a template platform structure of Forouzan Persian Gulf oil field is compared to compare the accuracy of these three indicators. The results show that the new method is more accurate than the Stubbs and IMSE indices, especially in the presence of multiple injuries.