128 Z. Wang and Y.-J. Cha 1. Calculate the local density ¡i for point i. For the case studies in this paper, the Gaussian kernel function of radius is introduced to calculate the local density [13]. Its expression is as follows: i D N XjD1 exp - dij-dc 2 (13.7) where N is the number of points for clustering in a space, dc is a predefined cut-off distance, and dij is the distance between point i and j. 2. Calculate •i for point i. In this algorithm, •i is defined as the minimum distance between the point i and any other points with higher local density: ıi DminjW j> i dij (13.8) For the point with the highest local density, take •i Dmax j dij . 3. Select the points with a relatively high ¡i and anomalously large •i as cluster centers. This choice makes the selected cluster centers surrounded by sufficient points. At the same time, these cluster centers are relatively far apart from each other. 4. Assign each remaining point to the same cluster as its nearest point of higher local density. 5. Identify halo points in the formed clusters. Halo points are defined as the set of points in one cluster having shorter distances than dc to any points in the other clusters. Then, the halo point with the highest density in this cluster is found, and set its local density as threshold of this cluster for novelty detection, denoted by¡b. Compute the average value of ¡b of all clusters, and set this value as a threshold of local density¡c. 6. Increase the value of dc if the halo points cannot be detected in step 5. Introduce a weight for dc to increase the updated cutoff distance wdc until the halo points can be detected. 7. Add the testing points separately to the well-trained normal clusters formed in step 5. Calculate their local densities ¡t and compare them with¡c. The testing points with lower local densities than ¡c can be identified as novelty points. 13.4 Damage-Sensitive Features In structural damage detection, the ideal features should be those that are sensitive to the presence of damage, but which are insensitive to operational and environmental variability in the normal range [1]. In Sect. 13.6, the acceleration histories a(tn) of structural joints are measured for feature extraction. 13.4.1 Crest Factor The crest factor of the a(tn) is one feature that is verified as a sensitive quantity to the structural response before and after damage [1], and it can be calculated by: CFD j ajmax arms (13.9) where jajmax Dmaxja(tn)j; arms Dq 1 nPn.a.tn// 2.
RkJQdWJsaXNoZXIy MTMzNzEzMQ==