6 Vibration-Based Occupant Detection Using a Multiple-Model Approach 53 −1 −0.5 0 0.5 1 Sensor 3 Sensor 4 −2 0 2 Sensor 1 19.5 19.8 20.1 20.4 −2 0 2 Sensor 2 19.5 19.8 20.1 20.4 −1 −0.5 0 0.5 1 Acceleration (mg) Acceleration (mg) Acceleration (mg) Acceleration (mg) Time (s) Time (s) 19.5 19.8 20.1 20.4 19.5 19.8 20.1 20.4 Time (s) Time (s) Fig. 6.3 Signals induced by one footstep (see Fig. 6.1) recorded on the 4 sensors Table 6.1 Uncertainty sources and distribution Source Distribution Min/Mean Max/Std dev Measurement uncertainty (%) Gaussian 0 3 Modelling uncertainty (%) Uniform 35 85 Sensor 1 location uncertainty (mm) Uniform 0.0006 0.0006 Sensor 2 location uncertainty (mm) Uniform 0.0006 0.0005 Sensor 3 location uncertainty (mm) Uniform 0.0010 0.0010 Sensor 4 location uncertainty (mm) Uniform 0.0004 0.0004 of structural response due to this loading. These uncertainty sources are synthesized as modelling uncertainty. In addition, measurement uncertainty that is provided by the sensor manufacturer is taken into account. Finally, the uncertainty related to the exact position of sensors on the slab are derived from a parametric analysis using the finite element model, by changing the sensor location by ˙250 mm. The estimated distribution of these three uncertainty sources is shown in Table 6.1. The uncertainties are subsequently combined using a Monte Carlo simulation to obtain the combined uncertainty distribution. Once the combined uncertainty distribution is obtained, the thresholds of the error-domain are computed using Eq. (6.2) for a target reliability of identification of 0.95. In EDMF, a model instance is falsified if the residual between model prediction and measurement lies outside the threshold bounds. In this application, the model prediction is the vertical displacement at sensor locations for a unit load applied at various locations on the grid multiplied by the weight of the occupant and a dynamic amplification value that is taken equal to 1.3. For measurement response, a single step of a human being detected (see Fig. 6.3) is considered. The maximum displacement experienced for a step, obtained through numerical integration using the trapezoidal integration scheme, is considered to be the measurement response. The difference between measured and predicted vertical displacement response is then calculated for all possible occupant locations. Figure 6.4 shows the residuals calculated for sensor location 1. Falsified location instances that fall between thresholds for sensor 1 are falsified by another sensor.
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