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In vibration-based structural health monitoring damage in structure is tried to detect from damage-sensitive features. Because neither prior information nor data about expected damage are normally available, damage detection problem must be solved by using a novelty detection approach. Features, which are sensitive to damage, are often sensitive to environmental and operational variations. Therefore elimination of these variations is essential for reliable damage detection. At present many of the damage detection methods are linear, though it has been shown that many of the vibration changes in structures are bilinear or nonlinear. This paper proposes to use nonlinear factor analysis to detect damage via elimination of external effects from damage features. The effectiveness of the proposed method is demonstrated by analyzing the experimental Z24 Bridge data with a comparison to a linear method. It is shown that elimination of adverse effects and damage detection are feasible.