13 Probabilistic Model Updating of Controller Models for Groups of People in a Standing Position 133 G(s) H1(s) H2(s) R(s) E(S) C(s) B(S) Fig. 13.2 Human-structure interaction controller model for a group of three people Table 13.1 Properties of the individuals involved in tests Height Weight Person ID [lbs] [ft, in] P1 161 5’8” P2 148 5’6” P3 159 5’10” 13.2.3 Model Updating The parameters of the structural and human models were updated in a probabilistic fashion using Bayesian inference [9]. This process estimates the probability density function of the model parameters given a set of experimental data and any prior knowledge that the analyst might have about the parameters. Bayes’ theorem is usually expressed as: P.‚jD/ /P.Dj‚/P.‚/ (13.3) Where the prior knowledge of the parameters ‚is expressed in P.‚/, the termP.‚jD/ is the posterior PDF of the parameters, D denotes the experimental observations, and P.Dj‚/ is the likelihood. A more detailed description of the model updating process within the context of HSI can be found in [6]. Interested readers are encouraged to read [9, 10] for a full discussion in Bayesian model updating. 13.3 Experimental Setup A steel structure with additional concrete blocks to simulating dead loads was build in the structures’ lab at the University of South Carolina [6, 7, 11]. For this specific paper, the supports of the structure and the mass were set to produce a vertical natural frequency of 3.9 Hz. Experimental tests involved impulse hammer testing to determine transfer function estimates. Three sets of tests were performed. The first set was for the empty structure. The second set involved three single occupants. Weight and height the people involved in tests are presented in Table 13.1. The last test involved three groups of two people. The last set of tests were used to validate the methodology proposed in this paper. The test names indicates who were on each test. For example P1P2 means that the person 1 (P1) and the person 2 (P2) are at standing on the structure. The Impact Hammer used during testing was a PCB 096D50 with a maximum load of ˙ 22240 N peak. A PCB accelerometer with a sensitivity of 100 mV/g was placed in the middle of the structure, below the persons and close to the hammer hit location. Force (input) and accelerations (output) where read using a NI CompactDAQ data acquisition system with a NI9234 module. Data was acquired using a sampling frequency of 1652 Hz. Three records of 20 s where done for each single test.
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