7 Composite Fuselage Impact Testing and Simulation: A Model Calibration Exercise 69 Fig. 7.2 LS-DYNA model of fuselage section Table 7.1 Parameter uncertainty definitions Parameter. No. Properties Nominal Lower bound Upper bound 1 Ea (lbs/in2) 1.00EC07 5.00EC06 2.50EC07 2 Eb (lbs/in2) 1.00EC07 3.00EC05 2.50EC07 3 GAB, GBC, GCA (lbs/in2) 7.40EC05 1.90EC05 1.05EC06 4 ERODS 0.15 0.02 0.60 5 ™x roll (deg) 0.00 0.50 0.00 6 ™y pitch (deg) 0.00 0.00 0.50 7 Velocity (in/s) 249.00 255.00 243.00 function. Statistical sampling is used to create a family of N equally probable parameter vectors with their corresponding responses, where Nis user selected. For calibration it is important to estimate the probability of being able to reconcile test with predictions, assuming that both the model and parameter uncertainty are appropriate. To this end, let Q(t,p)Dkv(t,p)k2 be a scalar time varying function in which the response vector v is used to compute the 2-norm at time t as a function of the parameter vector p. Furthermore, let N D min8pQ.t;p/ be the minimum value over all parameter variations, and let Dmin8pQ.t;p/ be the maximum value. Using these definitions and N LS-DYNA solutions corresponding to equally probable parameter vectors, a calibration metric is established to bound the probability of predicting different values of Q(t,p) as: M1.t/ DProb. < Q.t/ < / D N 1 N (7.1) This probability simply states that after N observations, the next observation has a probability better than (N 1)/N of being within the computed bounds. Conversely, the probability that the model is capable of predicting experimental observations Qe(t) (in terms of 2-norm of responses) outside the analysis bounds is that less than 1/N. Note that N controls the tightness of the bounds and also the number of LS-DYNA solutions required. 7.3.2 Metric 2: Orthogonality Data from either test or analysis are often collected at fixed time intervals from multiple sensors. It is convenient to assess the validity of models using time invariant quantities. For example, in traditional vibration analysis, structures are tested and models are verified using vibration modes and frequencies. Analogously, impact data can also be assessed using time
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