12 D.-S. Li and X.-H. Li -20 1.9 1.95 2 2.05 2.1 2.15 -10 0 10 temperature( ˚C ) elastic modulus (1011pa) 20 30 40 50 Fig. 2.1 Elastic modulus variation with temperature. (a) Temperature variation with time. (b) First natural frequency of the beam 0 -20 -10 10 20 30 40 a time ( h ) temperature (˚C) 0 1000 2000 3000 4000 5000 33 33.5 34 34.5 35 35.5 b frequency (Hz) time ( h ) 0 1000 2000 3000 4000 5000 Fig. 2.2 Temperature variation and the first natural frequency of the beam both by environmental temperature and damage. The frequency variation with time is shown in Fig. 2.2b. Compared with Fig. 2.2a, it is found that in Fig. 2.2b there is a strong correlation between the frequency and the temperature, and that the structural damage is completely submerged in the temperature’s influence. 2.3.3 Damage Identification of the Simply Supported Beam First, the temperature data is decomposed by SGSA with the embedding dimension set to five. The decomposed five components are shown in Fig. 2.3. Figure 2.3a shows the original temperature signal, whereas Fig. 2.3b–f shows the five components of the original temperature decomposed by the SGSA. As illustrated in Fig. 2.3, the first component shown in Fig. 2.3b represents temperature seasonal trend, whereas the second component shown in Fig. 2.3c is the daily temperature fluctuation which is an approximately simple harmonic signal as shown in the enlarged picture of Fig. 2.4. The daily temperature fluctuates within around 10ı. The amplitude of the components shown in Fig. 2.3d–f are very small compared with the first two components and they can be neglected as noise. Second, decomposing the first natural frequency of the beam by SGSA and the embedding dimension also set to five. The decomposed five components are shown in Fig. 2.5. Figure 2.5a shows the original frequency, whereas Fig. 2.5b–f
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