Recent advancements in Structural Health Monitoring (SHM) have focused on developing efficient methods to detect and localize structural damage by analysing dynamic parameters before and after significant events or as structures age. SHM systems frequently rely on the correlation between structural damage and changes in eigenfrequencies. However, minor frequency variations do not always indicate damage, emphasizing the need to reduce false positives to improve SHM reliability. This study addresses this issue by identifying conditions in which frequency shifts are caused by non-stationary factors, such as wind, traffic, or stochastic changes in mass, damping, and stiffness due to environmental effects, rather than structural damage. To separate these non-damage-related fluctuations from true nonlinear damage responses, statistical thresholds are proposed to distinguish linear non-stationary behaviour from that associated with actual damage. The methodology is validated using the Duffing oscillator and Monte Carlo simulations to enable comprehensive nonlinear analysis. This research contributes to SHM by enhancing the detection of real structural changes, reducing false positives, and improving damage identification. By focusing on effective thresholding and response differentiation, the study advances SHM practices across various applications, from critical infrastructure to buildings, supporting more reliable monitoring and early warning of potential structural issues.