13th International Conference on Fracture June 16–21, 2013, Beijing, China -7- The experimental modal frequency is firstly identified by the LMS modal analysis software using the acceleration signal. Here the results of State 1 (health state), State 2 (damage state 1), State 3 (damage state 2), and State 4 (damage state 3) are shown in Table 2. Table 2. Modal frequency of the healthy and damage states Mode State 1 (Hz) State 2 (Hz) State 3 (Hz) State 4 (Hz) 1 40.9330 42.4120 42.3030 41.9960 2 137.4630 135.9660 135.6860 134.9330 3 307.7550 304.8220 305.3790 301.6580 4 436.2560 436.2100 432.7160 430.4220 5 690.2900 683.8950 674.1470 679.2060 6 806.7520 803.8900 802.2440 808.0970 The geometric parameters of the plate are accurately measured as 515 mm by 515 mm and 2.95 mm thick. The density of the 304 stainless steel is 8150 kg/m3, the Modulus of Elasticity is 189 GPa, and the Poissons ratio is 0.285. The four-node rectangular element is used in the FE model, and the size of the grid element is 51.5 mm by 51.5 mm. The nodes of the elements located in four corners are fully constrained to simulate the bolt constraint. The comparison of the modal frequency between the FE model and the actual undamaged plate is shown in Table 3. Table 3. Comparison of the modal frequency between FE model and actual plate Mode Test(Hz) FEM(Hz)Diff(%) 1 40.9330 40.9361 0.0076 2 137.4630 140.5776 2.2658 3 307.7550 315.8144 2.6188 4 436.2560 427.5859 -1.9874 5 690.2900 703.1238 1.8592 6 806.7520 809.1443 0.2965 Although the refined FE model is close to the actual structure, the model error is modelled a Gaussian process. Then the post PDF is constructed according to the Bayesian theorem. The posterior samples of the damage parameters θi are generated using the stochastic simulation method based on TMCMC-slice sampling. 3.3.2. Damage Identification The damage identification results of the TMCMC-slice algorithm are checked. The statistics of the sample are shown in Table 4, where column 1 is the actual values of the parameters, column 2 shows the identified sample mean, column 3 shows the sample standard deviation (s.d.), and column 4 displays the coefficient of variance (c.o.v.). Table 4. Results of damage identification for plate structure based on TMCMC-slice Actual Identified s.d. c.o.v. θ1 1.0000 0.9950 0.77420.7781 θ2 0.5000 0.5181 0.21000.4053 θ3 1.0000 2.6051 1.56470.6006
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