Engineering Performance

To begin, it is necessary to understand how design changes affect the safety perfor- mance of a vehicle, as well as how those design changes impact the other components of the market systems model in engineering performance and cost. From the list of safety-related design variables used in the study of Chapter V, summarized in Ta- ble 5.1, it is evident that there are no common variables shared by the market systems model in Table 7.1 and those of the safety optimization formulation. This indicates that adding a safety model similar to those previously discussed in this dissertation will not influence the existing engineering performance calculations that contribute to consumer demand or the existing constraints.

However, manufacturing costs may change when modifying the restraint system and structural variables from Table 5.1. Little is known about these material-specific design variables for vehicles in the existing market, and so a top-down cost estimate for the impact of these variables would require extensive testing or insider knowledge on

the engineering characteristics of every firm’s vehicle structures and restraint systems. It is also possible that the small changes in material properties or tuning of the airbag flow rates would not incur significant costs, seeing that the material quantities and manufacturing processes would remain largely unchanged. For these reasons, the cost model from Frischknecht described in Equation (7.2) is used without modification for the safety considerations, assuming that any adjustments to the safety design variables have a negligible effect on manufacturing costs.

Since previous research suggests that crash test ratings have no significant effect on consumer demand (Pruitt and Hoffer , 2004), safety must be quantified in a new way to enter the demand formulation and therefore the profit-maximization objective. The safety study of Chapter V assumed fixed vehicle mass, and while mass may not be a design decision that is commonly tuned for a vehicle’s crash test performance, it does influence on-road safety in multiple-vehicle collisions as shown in Figure 5.8. The injury probability function considering societal uncertainty developed in Section 5.2.3 provides an overall probability of driver injury given a frontal crash, which can be a suitable attribute to consider for estimating consumer choice. This is an appropriate consumer demand attribute under either of the following conditions:

1. Consumers internally recognize the safety benefits of high vehicle mass, and they consider weight when purchasing a new vehicle in a manner that accurately predicts the safety benefits of high vehicle mass.

2. Crash test ratings that are posted on new vehicle stickers are modified to account for vehicle weight and distributions of crash speed, driver size, and seat position as described in Section 5.2.3.

Both of these conditions would follow the same engineering and choice modeling framework as discussed in the present section.

as a fixed design parameter along with the five design variables of Table 5.1. Here, the objective is to develop an explicit formula that relates vehicle mass (m) to probability of driver injury (PAIS3+), accounting for variability in crash speed, driver stature, and

driver-specific seat position. Since an additional design factor (m) is considered, new computational DOE studies are conducted and new surrogate models are fit to the data in the manner outlined in Figure 7.1.

As in Chapter V, compliance requirements of the FMVSS are included as con- straints in the design optimization formulation. The additional variable m necessi- tates new computational DOE studies for both the 30-mph frontal crash with a belted occupant and the 25-mph frontal crash with an unbelted occupant, whereas the static out-of-position simulation results, which are not a function of structural variables, are re-used from the previous study. The results of the three DOE studies were fit with polynomial surrogate models and used as constraints for optimization.

Following the results of the prior sensitivity analysis, the formulation is narrowed to two structural quantities (m and s) and four restraint system variables (b, r, a, and d). The structural quantities are first sampled across the two-dimensional design space and parameterized using POD methods into five parameters. These five POD parameters are fit with kriging surrogate models (Lophaven et al., 2002) to estimate a full crash pulse as a function of m and s, and then a six-variable DOE study of the restraint system is conducted and fit with polynomial surrogate models. These surrogates are then optimized parametrically across a range of vehicle masses, subject to the constraints from the three FMVSS regulatory standards. In each of the studies described in the next section, all three constraints were inactive at the optima.

From the optimization results, regression models are made for the optimal design variables s, b, r, a, and d as a function of m, and then the random societal variables v, h, and p are sampled along with m and the respectively-optimized design variables. Finally, polynomial surrogate models are fit to these four variables, and an integral

calculation of expected injury probability in a frontal crash is made for a range of vehicle masses as in Equation (5.14), with the results depicted in Figure 7.2.

Figure 7.2: Expected probability of serious injury varying vehicle mass

A power regression on these data yields the driver’s probability of injury as a function of vehicle mass (m) in kilograms, and for the case of optimizing the vehicle to the 35-mph NCAP standard it is given as Equation (7.3):

PAIS3+= 18.39m−0.7483. (7.3)