4 C.-H. Loh and C.-K. Chan Fig. 1.2 Comparison on the identified dominant frequencies from two test specimen; (a) Specimen 1, (b) Specimen 2 Since the coefficients for recent time lags of AR model are most informative about different modes of vibration [14], therefore, the damage feature is defined as ŒDFi 2 M D " 1 ii;1 1 ii;2 2 ii;1 2 ii;2 k ii;1 k ii;2 Mii;1 Mii;2 # (1.6) The reason for selecting the previous two step of AR model coefficients is because that other coefficient in the parameter matrix contains mixed information about sensor locations so that they do not capture vibration changes at a single location, where ‘m’ is the m-th dataset collected from sensor node ‘i’ and a total of Mdata set is collected from a particular test case. Each column vector in ŒDFm 2 M represents the two coefficients identified from a specific time window data using MV-AR model. Data fromŒDFm 2 M matrix can be plotted into a Cartesian coordinate system with k ii,1 and k ii,2 as two perpendicular coordinates. The distribution of each coefficient pair represents the variation of the identified coefficients from a specific sensing node with dataset from ‘k-th’ time window of the specific test. Combine all the distribution of each coefficient pair from a specific test data indicated the uncertainty of the subsystem system near the sensing node. This approach can be applied to all the recorded sensing nodes and extended to all the test cases. Based on the calculated damage feature matrix, ŒDFi 2 M , a covariance matrix can be defined: ŒCi 2 2 DŒDFi ŒDFi T (1.7) Through eigen-value analysis on the covariance matrix ŒCi 2 2 , two eigen-vectors and the corresponding eigen-values can be calculated. As a result, the error ellipse by considering two eigen-values as major and minor axes and two eigen-vectors as the orientation of the ellipse is developed to get a clearer result for observation. One can observe the migration of the ellipse error among all the test cases to see the change of feature. If the migration of ellipse calculated from each test case becomes diverse, it indicated the structural properties near the sensing node are changed from event to event. Through such an observation one can detect the damage location. Based on the white noise test data the damage feature matrix of each sensing node for each test case can be constructed using MV-AR coefficients. From which the error ellipse at each sensing node for all test cases can be generated. Significant migration of error ellipse at any particular sensing node through all the test cases indicated the dynamic characteristics of local structure near that sensing node were changed. From the observation of the migration of error ellipse of all sensing nodes one can identify the damage location. Consider the test case of specimen 2 the migration of AR-coefficient ellipse error from each sensing node is calculated. The ellipse error index calculated from the top floor and the first floor was shown in Fig. 1.2. The three identified fundamental modes of specimen 2 is also shown in this figure. To detect the damage location of the specimen 2, the migration of elliptic error index in cooperated with the identified mode shapes of specimen 2 are used. The following observation were pointed out: 1. Location of sensing node with significant migration of elliptic error index shows good correlation with the large nodal modal response of the identified torsion mode (i.e. AX11 node and AY6 node). Besides, location of sensing node with
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