292 L. A. Bull et al. Fig. 32.3 FRF data across a population of twenty 8DOF systems, 19 members are simulated and the 20th member is the experimental rig. For the simulated and experimental systems, normal-condition data are shown by black markers and magenta markers, while the damaged data are shown by red markers that could relate to damage (although such features will also be sensitive to confounding influences [8]. Therefore, the frequency response function (FRF) (denoted by H(ω)) is selected as a frequency-domain observation; this also matches the experimental data recorded at LANL. Specifically, the FRF here is the ratio of the output acceleration at mass eight ¨z8(t), to the spectrum of the input forcing time series at mass one u1(t). As with the experimental data, the input is a white-noise excitation over 8s, with a sample-rate of 400.25 Hz. A Hanning window is applied to the 8s input and output time series, and the empirical FRF is calculated. The resulting FRF is truncated, such that there are 1040 bins in the frequency domain, ranging from 0–130 Hz. Measurement noise is added to the outputs to represent the experimental measurements recorded at LANL; the noise assumed to be zero-mean normally-distributed, with variance leading to a signal-to-noise ratio of 40 dB. Each FRF is considered to be an observation of the system in terms of the SHM strategy, and these observations are used to inform damage detection. Following the same procedure as the practical experiments [8], the stiffness of k5 is reduced to imitate damage. Reductions are 7%, 14% and 24% for the simulated members, and a single reduction of 24% for data recorded from the test rig. The FRF is widely used as a functional feature in the conventional SHM literature [8]; as discussed, such methods should apply to the population-based approach, in the restricted strongly-homogeneous case. Dataset Summary The dataset represents a population of twenty8-DOF systems, 19 are simulated, while the 20th member is the LANL test-rig. Each system is observed over time, through the FRFs estimated from 8s time-windows. Each FRF in the dataset has 1040 frequency bins. Measurements from the simulated members are defined such that: • For the normal-condition data, there are 20 FRFs from each structure. These data are shown by black markers in Fig. 32.3. • 20 additional normal-condition FRFs are simulated to validate the form. These data are shown by magenta markers in Fig.32.3. • 20 FRFs are generated for each of the three states of damage (7%, 14% and 24%), shown by red markers in Fig. 32.3. The experimental data, recorded from the test-rig, includes: • 8 FRFs — four correspond to the undamaged state, and four were recorded following the introduction of damage (24% only). In Fig. 32.3, the normal and damaged test-data are also shown by magenta and red markers respectively.
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