The research team at the University of Arizona proposed several novel structural health assessment (SHA) algorithms. Structures are represented by finite elements (FE) and the health is assessed by identifying the stiffness parameters of all the elements and comparing them with expected values or with previous values, or by observing differences between similar elements. They can identify the location and severity of defect and exact location within a defective element. These algorithms use several system identification- (SI-) based concepts with different levels of sophistications. They do not require excitation information and can assess the health of large structural systems using only limited noise-contaminated acceleration time-histories measured at a small part of a structure. They are widely available in the literature. However, algorithmic and computational rigors of them are generally not presented in technical papers due to severe page limitation. Some of them are briefly presented in this paper without discussing the specific algorithms.