27 Evaluating Initial Model for Dynamic Model Updating: Criteria and Application 283 the deviations between the experimental and the computational modal frequencies given the model configuration. According to criterion 2, with these given ranges for the selected parameters, this model is updatable. 27.4 Numerical Simulation: Model Updating 27.4.1 Updating of Initial Model with Erroneous Boundary Condition In this case, ten elements are divided into five groups. Each group consists of two adjacent elements. Two elements of the same group have the same EI. Then five EI are taken as updating objects in sensitivity based model updating [1]. Modal frequencies of the first four modes are employed in the updating. The fifth and sixth frequencies are not used in updating but in quality assessment of updated model [16]. MACs of the first four modes are also used because the number of updating objects exceeds the number of modal frequencies. The following figures (Fig. 27.4) show the convergence of modal frequencies and MAC. From the figures, it’s could be seen that though modal frequency errors converge between forty to sixty iterations, MAC converge till ninety iterations. More importantly, it’s obvious that MAC of two modes are less than 0.7, one of them even less than 0.1. Tables 27.4 and 27.5 list the Modal frequencies, parameters and corresponding errors. Comparing the fourth and sixth column of Table 27.4, it could be seen that all six modal frequencies are greatly improved. But, from the sixth column, it could be seen that though modal frequencies of the first four modes which are used in the updating are accurate after updating, modal frequencies of the fifth and the sixth mode which are not used in the updating remain significant errors. This means the updated model is capable of reproducing but not predicting [16]. From the sixth column of Table 27.5, it could be seen that values are greatly changed. Five EI differ much from each other. This is not possible in practice. The updated model is more like a mathematically equivalent model than a practical finite element model for a beam. All these results support the judgment byCriterion 1 that the initial model is not updatable. 0 20 40 60 80 100 120 140 160 -2 0 2 4 6 8 10 12 14 16 Iteration Step Modal Frequency Errors (%) 0 20 40 60 80 100 120 140 160 180 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 Iteration Step MAC Fig. 27.4 Convergence curves for erroneous boundary case Table 27.4 Comparison of modal frequencies: Incorrect initial model Mode order Experimental modal frequency (Hz) Initial modal frequency (Hz) Initial frequency errors (%) Updated modal frequency (Hz) Updated frequency errors (%) 1 37:5 41:9 11.7 37:5 0 2 236:8 262:4 10.8 236:5 0:1 3 657:6 734:8 11.7 654:6 0:5 4 1;256:3 1;441:0 14.7 1;262:8 0:5 5 1;996:6 2;385:8 19.5 2;112:9 5:8 6 2;889:7 3;574:2 23.7 3;223:0 11:5
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