This section demonstrates the benefits of using a modeling environment for HEMS missions in vibration rating estimation, and presents how to achieve an optimal HEMS cabin interior layout adaptation of an existing rotary-wing platform.

#### 4.1. Configuration Optimization

To demonstrate the optimization of HEMS cabin interior design, eight possible structural locations for mounting seats, a stretcher, and a piece of medical equipment are defined, as illustrated in

Figure 9. The objective is to find the optimal configuration of those eight locations. The constraints reported below are considered:

each seat shall be mounted on a single point, two for the pilot and co-pilot, and two for the crew;

the seats of pilot and co-pilot are fixed at 1L and 1R; both are always considered occupied and included in the optimization;

the stretcher is aligned laterally (which is safer in case of crash [

52]), and shall be mounted on the floor at its two ends;

the equipment shall be aligned longitudinally, and mounted on two points, one of which adjacent to the head of the patient;

The crew shall sit adjacent to the equipment and to each other.

These constraints result in the possible configurations reported in

Figure 10. The baseline helicopter is assumed to carry only pilot and co-pilot.

It is assumed that there are two pilots, two medical and rescue crew, one patient lying on a stretcher, and one piece of medical equipment. The output vector includes the variables and consists of frequency-weighted vertical accelerations of these subjects:

where

${a}_{pi,1}$ and

${a}_{pi,2}$ is the acceleration of each pilot at the seat surface;

${a}_{cr,1}$ and

${a}_{cr,2}$ is the acceleration of each crew at the seat surface;

${a}_{pt}$ is the average of the sum of the acceleration at the cushion surface under the head, upper body, and lower body segments;

${a}_{e}$ is the acceleration of the center of gravity of the equipment. The objective function of the optimization is referred to as vibration index (VI):

where:

To illustrate the sensitivity of the relative weights on the vibration performance, four values of the cost matrix

$\mathit{W}$ are used. The pilots are present in all optimization cases and always included in the cost matrix. However, an independent pilot-focused optimization is not included since the pilot seat locations cannot be modified. Consequently, the cost matrices that affect the other elements are reported in

Table 6. They respectively give equal cost to all elements (1), or focus on patient (2), crew (3), or equipment (4). An on–off approach is used by setting the weights either to 1 or 0, while those weights can take any value. The first cost matrix is used for a comparative study of the eight mentioned HEMS configurations of

Figure 10. The other ones are used to show how the choice of the cost matrix changes the least vibratory solution.

The proposed approach is suitable for a broad variety of optimization techniques, since it can handle arbitrary parametric and topological modifications to a baseline plant. However, in the present case, the total number of configurations is limited. Therefore, brute-force optimization is preferred, which guarantees an absolute minimum. In other words, the objective function in Equation (

16) is simply calculated for all the possible configurations of

Figure 10, and the resulting values are compared to find the optimum solution.

Finally, it should be noted that additional constraints can be applied on individual accelerations, for example setting a limit to pilot seat acceleration, or, instead of using a single VI, a multi-objective optimization can be formulated. Such improvements are possible and should be used when necessary, since they can significantly change the optimum layout. However, within the scope of this work, we preferred an overall VI formula without any individual constraints on subjects.

#### 4.2. Results and Discussion

Figure 11 presents the vibration index (

$\mathrm{VI}$) and the acceleration of each subject for the eight possible configurations defined in

Figure 10 for equally weighted subjects of: (i) the baseline helicopter, referred to as “nominal”, and (ii) one modified by adding the vibration absorber of

Section 3.6, referred to as “modified”. All results are normalized with those of the nominal one. Since an increased

$\mathrm{VI}$ means a higher overall vibratory level, for both the nominal and the modified plant, configuration 7 shows the smallest VI for the defined HEMS mission, whereas configuration 4 is the least successful.

The effect of the vibration alleviation device is remarkable. The vibration index in the modified helicopter is always significantly less than in the nominal design for the same cabin layout. However, an interesting conclusion can be drawn in favor of cabin layout design: optimizing the cabin layout without the cost (design, weight, maintenance, etc.) of adding a vibration alleviation device can lead to lower overall vibrational level than simply applying vibration alleviation devices with a prescribed cabin layout. For example, configuration No. 7 of the nominal helicopter has $21\%$ lower vibrational level than configuration No. 4 of the modified helicopter, and similar considerations apply to all configurations from No. 1 to No. 4 of the modified helicopter. Moving the patient one row aft is at least as effective as adding a vibration alleviation device on a prescribed HEMS configuration. This shows that the proposed method can either save the cost associated with adding a vibration alleviation device, or lead to lower vibration when simultaneously designing cabin interior and vibration alleviation devices.

Figure 12 shows the best configurations when an alternative use is made of the subject weights: when the different costs of

Table 6 are applied in the evaluation of the vibration index of the nominal and modified helicopters, the optimal HEMS layout changes. The baseline and best (“Equal weights”) configurations of

Figure 11 are repeated for comparison. For the nominal plant, there appears a tendency to place the subject under consideration in the last row. However, as can be seen in the “Two crew” case, this does not happen for the modified plant. Moreover, one subject can dominate the others, as can be inferred from the identical layouts that resulted for “Equal weights” and “Patient” optimizations in the nominal plant.

The presence of a vibration absorber changes the optimal configurations achieved using different objectives. However, the modified plant with an absorber has a lower overall VI as compared to the nominal one regardless of the objective. The optimal layouts obtained for nominal and modified plants are not necessarily the same, as can be seen for the two-crew only case shown in

Figure 12. This shows how, if both layout optimization and the inclusion of vibration devices are planned for HEMS, it would be better to optimize the layout in the presence of the vibration device to achieve the least possible VI.

The accelerations of the individual points are not included in the results, since the scope is to achieve an overall reduction in vibration. However, it should be emphasized that an overall objective, such as the VI of Equation (

16), can result in an increase of the acceleration for individual subjects. This aspect needs attention if there are prescribed limits for any of the subjects, which can be a requirement set by HEMS operators in case of human patients or operators of medical equipment. In case such limits have to be considered, constraints on individual responses can be defined or a multi-objective optimization problem should be considered instead of a single VI.