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.