The response of the spine acceleration to rib and pelvis
acceleration input of the side impact dummy (SID) is modeled using
system identification methods. The basis for the modeling is a
simplified representation of the SID by a 3-mass, 2-spring system.
Based on this spring-mass representation, two types of response
models are established. The first is a "gray-box" type
with rib/pelvis-spine relationship modeled by Auto Regression with
eXogeneous (or eXtra) input (ARX) type system models. The structure
of these models is partially based on the spring-mass simplified
representation, hence the notion "gray- box." The
parameters of these models are identified through linear regression
from test data. The second type of models is noted "physical
model" here, since it is strictly a state- space form of the
equation of motion of the simple spring-mass representation. The
parameters of the model, which have clear physical meanings, are
identified through nonlinear parameter identification with
minimization of the prediction error of the state-space model. Data
for parameter estimation of all these models come from three groups
of tests: a sled impact, a dummy local impact, and full-vehicle
test group. With any one test from the groups, a parameter estimate
can be obtained for any given model. The quality of a model such
established is then assessed by studying the prediction by this
model of the spine acceleration responses of the rest of the tests
in the group against the actual test data. It is found that the
models are able to predict the trend with tests with impact
conditions similar to that of the test on which the estimate is
based; however, when the condition deviates significantly, the
estimate does not predict the behavior of the SID
satisfactorily.
Results from the parameter identification of the gray-box ARX
type models strongly suggest that the simple spring-mass system
reflects the fundamental characteristics of the SID response
studied. Results also show that the ARX type models generally
better describe the response than the physical model, due to the
flexibility provided by the additional number of parameters.
It has been observed from test data that under certain
conditions, the spine acceleration may decrease as a result of the
change in relative timing and magnitude of the accelerations of the
rib and pelvis. To study this, the models in this work are further
used to predict the change in spine response when either the rib or
the pelvis response is changed externally. Such information is
useful in understanding the responses of the SID in full-vehicle
side impact tests. The result of this study also implies that the
lower spine acceleration, and consequently the thoracic trauma
index (TTI), is not solely a function of the external thoracic
loading, and does not represent the external loading to the dummy
exclusively. As a result, under certain conditions, it is possible
to increase the severity of the loading while reducing the
assessment value of TTI.