Environmental and operational variability due to changes in the excitation or any other variable can mimic or altogether obscure evidence of structural defects in measured data leading to false positive/negative diagnoses of damage and conservative/tolerant predictions of remaining useful life in structural health monitoring system. Diagnostic and prognostic errors like these in many types of commercial and defense-related applications must be eliminated if health monitoring is to be widely implemented in these applications. A theoretical framework of "dynamic similiarity" in which two sets of mathematical operators are utilized in one system/data model to distinguish damage from nonlinear, time-varying and stochastic events in the measured data is discussed in this paper. Because structural damage initiation, evolution and accumulation are nonlinear processes, the challenge here is to distinguish damage from nonlinear, time-varying and stochastic events in the measured data is discussed in this paper. Because structural damage initiation, evolution and accumulation are nonlinear processes, the challenge here is to distinguish abnormal from normal nonlinear dynamics, which are accentuated by physically or statistically non-stationary events in the operating environment. After discussing several examples of structural diagnosis and prognosis involving dynamic similarity, a simplifeid numerical finite element model of a helicopter blade with time-varying flexural stiffness on a nonlinear aerodynamic elastic foundation that is subjected to a stochastic base excitation is utilized to introduce and examine the effects of dynamic similarity on health monitoring systems. It is shown that environmental variability can be distinguished from structural damage using a physics-based model in conjunction with the dynamic similarity operators to develop more robust damage detection algorithms, which may prove to be more accurate and precise when operating conditions fluctuate.