Identifying the presence of structural damage: A statistical hypothesis testing approach combined with residual strain energy

A statistical hypothesis testing scheme is presented for damage detection considering environmental variations, in which the presence of damage is identified via Welch's t-test by comparing the means of two groups of residual strain energy (RSE) samples from healthy and inspected structures. The RSE, as a damage indication feature, is determined from the mode shape residual (MSR), and the corresponding effects of environmental variations are eliminated via the PCA method. To further improve the damage sensitivity of RSE samples, an MSR selection strategy is proposed to examine the sensitivity of the available MSR matrices to damage and select the most effective MSR matrix. The sensitivity formula of the test statistic with respect to damage is derived and defined as the sensitivity index. Moreover, the mode shape expansion process is not required because an MSR that only includes x- or y-translational degrees of freedom (DoFs) at the measured points is sufficient for detecting damage. The effects of the location and extent of damage, incomplete measurements, and the critical value of the t-test on the performance of the proposed scheme are discussed by numerically analyzing an offshore platform. The results indicate that the scheme can simultaneously limit the probability of committing Type I and Type II errors under temperature variations and noise contamination. An analysis of field test data for a real-world wind turbine also indicates that this approach can avoid Type I error in a real marine environment. (C) 2020 Elsevier Ltd. All rights reserved. A statistical hypothesis testing scheme is presented for damage detection considering environmental variations, in which the presence of damage is identified via Welch's t-test by comparing the means of two groups of residual strain energy (RSE) samples from healthy and inspected structures. The RSE, as a damage indication feature, is determined from the mode shape residual (MSR), and the corresponding effects of environmental variations are eliminated via the PCA method. To further improve the damage sensitivity of RSE samples, an MSR selection strategy is proposed to examine the sensitivity of the available MSR matrices to damage and select the most effective MSR matrix. The sensitivity formula of the test statistic with respect to damage is derived and defined as the sensitivity index. Moreover, the mode shape expansion process is not required because an MSR that only includes x- or y-translational degrees of freedom (DoFs) at the measured points is sufficient for detecting damage. The effects of the location and extent of damage, incomplete measurements, and the critical value of the t-test on the performance of the proposed scheme are discussed by numerically analyzing an offshore platform. The results indicate that the scheme can simultaneously limit the probability of committing Type I and Type II errors under temperature variations and noise contamination. An analysis of field test data for a real-world wind turbine also indicates that this approach can avoid Type I error in a real marine environment. (C) 2020 Elsevier Ltd. All rights reserved.