One of the crucial steps in structural health monitoring (SHM) is damage diagnosis based on features extracted from highdimension response signals, which are often under uncertain conditions. These uncertainties occur due to noisy ambient excitations, environmental and operational variation (EOV), and measurement conditions. To address this issue, a new feature extraction method is proposed by generalizing the correlation relationship in the frequency domain. In this manner, the characteristic function of the response is achieved using time-series analysis and calculating model parameters. Then, by generalizing the correlation relationship in the frequency domain, a new damage sensitive feature (DSF) as a complex value is extracted. Through the investigation of the new DSF, damage can be detected and localized. In addition, the severity of damage is estimated with higher accuracy. To validate the abilities of the new feature extraction and damage diagnosis methods, a well-known laboratory structure, a three-story frame, and a real-world full-scale bridge known as S101 Bridge, are examined. The accomplishments of this study indicate that through the calculation of haracteristic function, the highdimensional structural response is transferred to a space with a lower dimension. Furthermore, the negative effects of noisy ambient excitations are eliminated from the extracted DSF by utilizing the characteristic function. The new feature can identify conditions governing damaged structure, and through this, the negative effects of EOVs and measurement conditions are removed from estimated severities of damage. The achievements of the S101 Bridge illustrate high-quality performances of the proposed algorithms in damage diagnosis of real structures, which are often exposed to real challenging conditions. Further to these achievements, the results i ndicate that the new feature can identify the type of damages and distinguish between low-frequency damages and high-frequency ones

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