6 Vibration-Based Occupant Detection Using a Multiple-Model Approach 51 where, * is the vector of model parameter values and gi( *) is the predicted structural response at measurement location i. By rearranging Eq. (6.1), the residual between the model prediction and measurements is equal to the combined uncertainty at a measurement location, "c,i. In a probabilistic approach, these errors "mod,i, "meas,i and "c,i are represented as random variables Umod,i, Umeas,i and Uc,i, respectively. Thresholds are defined using the combined uncertainty Uc,i. For a target reliability of identification 2 f0,1g, the falsification thresholds, Thigh,i and Tlow,i, are computed as shown in Eq. (6.2) 1=m D Thigh;i Z Tlow;i fUc;i ."c;i/ d"c;i (6.2) where, fUc;i is the PDF of the combined uncertainty and is the target reliability of identification. Due to small number of measurements available, the target reliability of identification is corrected using the term 1/m, called as Šidák correction for multiple hypotheses testing [15]. In EDMF, the user generates model response for multiple values of model parameters . Then the residual at each measurement location is calculated as the difference between model prediction and measurement. For all measurement locations, model instances whose residuals lie outside the thresholds are falsified, as represented by Eq. (6.3). 8i 2 f1; ::; mg Tlow;i gi . / yi Thigh;i (6.3) All model instances not falsified using Eq. (6.3) are accepted into the candidate model set [16–18]. Due to the lack of information of the true uncertainty distributions, all candidate models are treated as equally probable. The localization challenge is treated as an inverse problem where the primary parameter to be identified is the location of the load. 6.3 Test Setup The application of human detection and localization has been performed on a continuous reinforced concrete slab that forms the entrance hall of a building on the EPFL campus. The slab is 24 cm thick, which is typical for buildings in Northern Europe. In addition to the high stiffness of the slab, a dense network of structural and non-structural walls underneath the slab results in relatively short spans of the slab (see Fig. 6.1). Most structural walls are in reinforced concrete, while nonstructural walls are built in unreinforced masonry. In combination with the rigid slab, the coarse sensor network makes the tested setup an unconventionally complex one. Therefore, the results obtained demonstrate a lower limit of the efficiency of human detection and localization with a multiple model approach. Roctest Actimon-X1 sensors are used to record accelerations in all three directions. The sensors have a measurement range of 1.5 g and a resolution of 0.05 mg. The frequency response of the sensor ranges from 0 to 200 Hz and the maximum sampling rate is 2000 Hz. The sensors are attached underneath the slab using screws. 6.4 Results Prior information of the vibration characteristics of the building are obtained from ambient-vibration measurements performed on 4 days. As described above, the most important features that are obtained are the fundamental frequency of the structure and the baseline level of ambient vibrations. The fundamental frequency of the slab is 18 Hz, while at sensor location 4, more energy is present around 24 Hz. Based on the mean level of measured ambient vibrations, thresholds are calculated for detection of occupants. In order to increase the signal-to-noise ratio, and accounting for the measured fundamental frequencies, the measured signal is bandpass-filtered using a sixth order Butterworth filter between 16 and 25 Hz. Best results are obtained if thresholds for human detection are set to six standard deviations of the filtered ambient signals. Comparison with raw signal, wavelet transforms (Mexican hat wavelet) and short-term average over long-term average (STA/LTA) ratios showed that for this application, a comparatively simple technique such as bandpass filtering provides the best results for human detection.
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