CASES STUDIED The comparison between reference solution and expansion solution is made in this section. Several different analytical cases have been studied to evaluate the effectiveness of the proposed expansion algorithm. The cases studied are based on some important factors that affect the implementation of the technique. The cases studied in this section are based on three important factors that need to be considered for successful implementation of proposed approach: 1. Number of modes used in expansion process. 2. Effect of different noise levels on solution obtained through proposed technique. 3. Different sensor configurations used for obtaining full-field expanded data set. Foremost among the prominent factors affecting the expansion solution is the number of modes used in the expansion algorithm. Theoretically, there is no upper limit for the number of modes to be used for expansion, but from a practical standpoint only a limited number of modes can be used for expansion. The Case 1 deals with the study of the number of modes used for expansion. Different noise levels have been studied in Case 2 to gage the performance of the expansion algorithm in the presence of noise. Noise is another important issue that has been shown to have an affect on the successful implementation of the expansion algorithm. Case 3 discusses the different sensor configurations and their effect on the solution obtained through expansion algorithm. The sensors used for obtaining the real-time data (adof measurements), invariably plays an important role in accuracy of the solution. CASE 1 For obtaining full-field displacement response from limited sets of displacement data, using real-time operating data expansion technique, the formulation of the expansion transformation matrix is known to be an important factor. The transformation matrix for SEREP expansion technique is formulated using mode shape information. The expansion transformation matrix should contain at least those structure modes which are primarily excited. For reference, the displacement response solution obtained using limited sets of displacement data is shown for typical response locations (tip and interior of the box-beam) in Figure 6. Note that the full-field displacement solution obtained from limited sets of displacement data has been discussed in detail in [1]. The first six modes were used in formulation of expansion transformation matrix. As observed in Figure 6, the expansion solution matches well with the reference solution with TRAC values of 99.9+% showing that the prediction of full-field displacement response through the expansion process is very accurate. 193
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