## 3 Experimental Results, Analysis and Discussion
### Detection of Failing Joint  
As explained in Section 2.2, the testing protocol involved using the waveform generator to create a suitably selected signal (triangular with amplitude of 600 Vpp and frequency equal to 80 Hz) and driving the mini-exciter with it. Then, following vibration of structure-A or -B for the configurations described in Section 2.2, the output signal created in the reception coil circuit was recorded by means of an oscilloscope. Past experience with similar testing setups [19] suggested that there should be no visible differences between signal time histories from structures with normally fastened or failing joints. This proved again true and may be noted for structure-A in Figure 3a. The main reason for this characteristic is that, in such passive setups (i.e., without excitation of the reception coil) with signal transmission carried out in a contactless manner, the external mechanical loading cannot generate significant electrical power via the magnetoelastic phenomenon. Accordingly, it is difficult to produce response signals with variance visibly larger than that of the noise. Furthermore, due to the principle of contactless reception/ recording of data, it is difficult to avoid noise in data, or issues such as significant total harmonic distortion (THD) values or spectrum intermodulation. This last issue can also be traced to specific magnetic properties (hysteresis loop) of materials such as MetGlas(r) used in the current case for contactless transmission/reception purposes. Thus, one should be assessing specific qualitative rather than quantitative changes in the recorded signals. This means that only changes in their spectral characteristics could point to the original structure being affected by some kind of failure, which in the current case is a failing joint. The case of test data from structure-A is presented in Figure 3b, with the inset showing the three largest peaks (modes). The previous comments on noise and significant total harmonic distortion values (estimated between 18.66% and 35.25% for 50 harmonics with data from all test cases in Table 1) seem valid. There is a clear shift in frequency values of modes around 1200, 1400 and 1600 Hz. The exact values of frequencies and the associated damping factors estimated by means of the second-order approximation (see Section 2.3)  
Figure 3: Output signals from test runs with structure-A for the configurations in Section 2.2: (**a**) Typical time histories of NJ-A versus FJ1-A showing no visible differences; (**b**) Spectra of NJ-A versus FJ1-A showing clear frequency shifts for the three largest modes due to failing joint. Dashed lines indicate confidence intervals at 95% level. may be found in Table 1. Clearly, structure-A with normally fastened joints shows peaks at lower frequencies than those produced when joint J1 is failing. This behavior is probably due to the fact that failing joints cause low static friction between two contacting slab surfaces, thus allowing for relative displacement (rubbing) between them. Hence, the initial system with two firmly connected slabs becomes a group of two loosely connected slabs and this leads to frequency shifting phenomena at some frequencies. Another characteristic may be noted by examining the damping factor values in Table 1. Damping values resulting from structure-A with failing joints are generally lower than those from structures with normally secured joints, and this is particularly true for Modes II and III. Note that the second-order approximation procedure yields results in about 6 min for each considered mode. This time interval is significantly shorter than that required for identifying a system model equivalent, for instance, to that in [19]. An indication of the second order approximation's accuracy is provided by the quantity \(\surd{r(k)}/q\) (see Section 2.3--step 3), which essentially shows the mean distance between the spectrum of the second order system and that from test data for the monitored mode.