8 Noise Sensitivity Evaluation of Autoregressive Features Extracted from Structure Vibration 85 Fig. 8.4 Plots of the Mahalanobis distance and Cosh distance damage feature values as noise level increases. Plots (a, b): simulation results from one experiment; (c, d): the average simulation results from 50 runs (confidence intervals are constructed based on average values) Spatially and chronologically uncorrelated random excitation is applied at each node of the system. Acceleration signals are simulated from the system using Newmark’s method, and both feature values are extracted from the signals during multiple runs of simulation. These simulation results regarding effects of measurement noise on feature values are compared with theoretical analysis results and sensitivity analysis results. Here theoretical results refer to that computed directly from the theoretical ACF for each measurement noise case. For all simulations and computations, the AR model order is set at 20. During each run of simulation, 88 signal segments, each containing 5,400 data points sampled at a frequency of 50 Hz, are used to calculate the Mahalanobis distance and Cosh distance features. Figure 8.4 shows the trends of Mahalanobis distance and Cosh distance as the noise level increases. All data are collected at node 4. Signals with 2 % noise level are used as baseline and another case with 2 % noise level is included for false positive testing. It can be seen that the 3 lines have relatively close values in comparison to the 95 % confidence interval from one simulation, thereby demonstrating the validity and effectiveness of the tangent sensitivity analysis for evaluation of the
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