CASE 2 Experimental noise is a very common phenomenon which corrupts the data. While collecting experimental data, the noise component is always inevitable. To study the expansion technique realistically, some random noise is added to the base-line measurements using ^ ` ^ ` ^ ` of measurment amplitude t r maximum Measuremen Original t Measuremen Noise Induced (8) where, r is random set of numbers ranging from -1% to +1% of the maximum amplitude of measurement. Figure 10 shows the noise induced in the model to simulate experimental conditions. Figure 10: Effect of different noise levels (5% and 10%) on displacement-time response. Case 1 showed the expansion algorithm to be an accurate tool when appropriate number of modes are used for expansion. However, the expansion algorithm could also be affected by noise as shown in Figure 10. A varying percentage of noise was added on the model used in Case 1 to simulate the experimental conditions of real-time data acquisition; noise levels ranging from typical levels of noise (5%) and higher levels of noise (10%) were studied. The full-field displacement solution was obtained from the noisy adof measurements through expansion. The full-field displacements thus obtained were then back-substituted into the finite element process to recover the stress-strain solution. The dynamic strain solution for 5% noise on adof measurements is shown in Figure 11 and the strain solution for 10% noise case is shown in Figure 12. Comparison is made between the predicted strain solution with reference solution at two typical response locations (at the tip and at an interior location in the rib of the box beam). As seen from Case 1, more than 6 modes are needed for accurate expansion results for predicting strain. Hence first ten modes of the structure were used in expansion process for obtaining the full-field displacement solution. As seen from Figure 11, addition of low levels of noise (up to 5%) did not significantly 196
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