11 Characteristic Analysis of Modified Dolly Test: A Sensitivity Study of Initial Conditions on Rollover Outcomes 111 M: The net torque I: Moments of inertia in roll direction around COG A: Angular acceleration To define time and orientation of the bus at maximum impact force, the position of the bus at the maximum angular acceleration was determined. As a result, depending on the orientation of the bus, the maximum impact force applied to either roof or tires. Based on Eq. (11.1), in some cases, the value of the denominator reaches zero which can significantly influence the final value of the calculated force. This is because friction value assumed to be coulomb friction with no relative velocity between vehicle’s body and ground whereas in some cases it would be less than coulomb friction. To prevent this situation, these cases were removed from sample points. The LHS method was used to generate optimal sample points. This sampling method creates a uniform distribution of optimal points which can minimize the bias part of the mean square error. In the present study, a uniform distribution for five input parameters was selected with a certain range (Table 11.2). The range of each input parameter was chosen based on different experimental values that were used in rollover tests. For example, the lowest value for friction represents the flat wet concrete where the upper bound represent the racked concrete surface [17]. The maximum 23◦ are currently used for the initial slope of the passenger cars and 0◦ for the rollover sled test. For heavy vehicles, due to the high amount of crash energy that dolly test produced, usually the vehicle placed on the flat cart without tilting. The maximum height 0.8 m was chosen from the tilt table test procedure to show the effects of height on output parameters. For each set of input parameters, the output parameters from PC-Crash simulation was extracted and considered as “training” points for Kriging model formation. We used R Squared to evaluate the accuracies of the metamodels (see [11]). The results of the accuracy evaluation are shown in Fig. 11.7. It should be noted that for certain initial conditions, the number of quarter turns was equal to zero which indicates that the rollover did not happen (see Fig. 11.7). Here, the global sensitivity analysis was performed using the constructed surrogate model for each output parameters in MATLAB. The sensitivity analysis investigated in this study include Standardized Regression Coefficient (SRC). SRC gives the strength of the correlation between output and input variables [18]. In Fig. 11.8, the output parameters for 400 sample points were plotted with respect to all variables. The results were then used to compute the SRC and reveal the correlation between initial conditions and corresponded rollover outcomes (Fig. 11.5). Table 11.2 Selected input parameters to build the Kriging model Item Range Distribution Initial velocity (m/s) [0–30] Uniform Height (m) [0–0.8] Uniform Orientation (degree) [0–23] Uniform Initial roll rate (deg/s) [0–200] Uniform Friction [0.2–0.9] Uniform Fig. 11.5 The SRC results for each output parameter
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