*5.4. Sensor Calibration*

Squared conducting plates of length 40 mm to 200 mm are used to calibrate the single and the matrix sensors. The plates are pressed against the sensors and voltage drop is measured. Figure 9 shows an exemplary single sensor voltage drop for 200 mm square plate. The maximum voltage drop for the single sensor is 3.1 V. A mean reference voltage is calculated by averaging the first 300 samples. After many threshold iterations, a 4% threshold is applied to identify the touch. Suppose there is a touch, the voltage drops and reaches a minimum. A 20% threshold is used for the lower voltage because of the high noise. The mean value within a 20% voltage band (yellow curve in Figure 9) is calculated. The difference between mean reference and lower mean is Δ*V*, which gives contact time and the area.

**Figure 9.** Voltage drop calculation method.

The voltage drops for different plates are obtained (Figure 10a). A non-linear 4th-order polynomial (in a least-square sense) equation is applied to the voltage drop data to fit the curve. The values of the contact areas are centered at zero and scaled to have a unit standard deviation, which improves the numerical properties of the polynomial. The fitted curve is interpolated using Piecewise Cubic Hermite Interpolating Polynomial (PCHIP) method to calculate the area from the voltage drop (Figure 10b). The curve's behavior matches the theoretical voltage drop calculation shown in Figure 5b. From the theoretical simulation model, the maximum voltage drop is close to 4.2 V. During the calibration, the maximum observed drop is 3.1 V. Cable effects, stray capacitances and environmental parameters contribute to the deviation.

**Figure 10.** Calibrated voltage drop curve for single sensor: (**a**) sensor voltage drop; (**b**) calibrated and interpolated voltage drop.

Similar to single sensor, individual sensors in the matrix are calibrated (Figures 11 and 12). The maximum voltage drop for all the sensors is between 2 V and 2.4 V, whereas the simulated voltage drop is close to 2.5 V.

**Figure 11.** Calibrated voltage drop curve for L1 and R1: (**a**) L1 sensor; (**b**) R1 sensor.

**Figure 12.** Calibrated voltage drop curve for L2 and R2: (**a**) L2 sensor; (**b**) R2 sensor.

### *5.5. Hypothesis*

It is hypothesized that the sensor voltage decreases with contact progression. At constant pressure and increasing velocity, the voltage drop increases with less contact time due to increased area. Further, the magnitude and peak time depend on the airbag pressure and the impact velocity. The hypothesis is tested by comparing the contact sensor results with the high-speed videos.

#### *5.6. Experimental Design*

Airbag pressure, occupant's impact velocity and the sensor position are the variables that decide the restraint effect in real crash situations. Therefore, we choose these parameters to design the experiments. Changing the pendulum position for out-of-position cases is a challenge to the test results' reproducibility; hence, the sensor's position is varied. The head's velocity is chosen based on the occupant's motion modeling during crashes [29]. Pressure values are chosen such that there is a perfect contact between the airbag and the sensor (Table 2).


**Table 2.** Single-sensor test matrix.

The single sensor is tested by varying airbag pressure and impact velocity (Table 2) while keeping the sensor position and the impact point constant. The matrix sensor is tested with an approximately constant pressure (1.2 bar) and velocity (3.41 m/s) by varying the sensor's position to identify the position additionally. The matrix sensor has four individual sensors, which are geometrically symmetric on the airbag surface; hence, three experiments are carried out. Two experiments involve L1- and R1-centered impacts, which simulate out-of-position impact with respect to sensors' configuration and one in the middle of all sensors to simulate in-position impact.

#### *5.7. Sensor Benchmark and Data Analysis Method*

#### 5.7.1. Head Depth Calculation from the Contact Sensor

The contact sensors are benchmarked with high-speed videos. Figure 13 shows an exemplary contact event for the single sensor. Since contact occurs before the trigger, the times before 0 s are negative. From the camera, the first touch is at −4.8 ms and peak displacement occurs at 56.4 ms. The total contact time is 61.2 ms. The contact time from the sensor is 64.3 ms. There is a 3.1 ms difference with a reasonable agreement between camera and contact sensor time.

**Figure 13.** Sensor benchmarking.

Further, the contact sensor voltage drop at the peak displacement is 2.96 V. From the calibration curve (Figure 10) the area at 2.96 V is 0.0249 m2. Since the head is a hemispherical form, the area obtained is the curved surface area of the hemisphere. The head depth (*Dc* in Figure 14) is calculated from the curved surface area, which is 0.063 m (63 mm).

#### 5.7.2. Head Depth Calculation from the High-Speed Videos

The calculated depth from the contact sensor (Section 5.7.1) is compared with the depth obtained from the high-speed test video analysis. An open-source software (Tracker) is used for kinematic analysis. Initially, the pendulum's arm width (0.03 m) is calibrated in the video and the impact velocity is calculated. The impact velocities calculated from the swing angle and the video for an exemplary test are 5.11 m/s and 5.089 m/s, respectively. Then the peak head displacement is calculated. At the beginning of the contact, head depth (*X*) from the reference is 92.5 mm (Figure 14a). When the head is at peak displacement, the depth (*X*1) from the reference is 36.7 mm (Figure 14b). The depth *Dc* is the head depth inside the airbag during the restraint phase, which is 55.8 mm. There is a 7.2 mm difference between the depth calculated from the contact sensor (63 mm from Section 5.7.1) and the video.

**Figure 14.** Depth calculation from high-speed video: (**a**) first contact; (**b**) peak displacement.

#### **6. Results**

*6.1. Single Sensor*

The sensor's voltage is a function of velocity and bag pressure. In the first set of experiments (tests 1 to 4), we observe that when the velocity is increased from a minimum of 2.30 m/s to 4.46 m/s, there is a major difference in voltage drop and contact time. From Figure 15a and Table 3 it can be seen that the voltage drop increases from 2.64 V (test 1) to 3.01 V (test 3) indicating an increase in the contact area. On the other hand, from Figure 15b, it can be noted that the contact time from the first touch to peak displacement decreases

from 114 ms to 69.2 ms from the test 1 to 3. When the velocity is increased beyond 4.46 m/s, we observe no further drop in the voltage because the pendulum head covers the sensor completely at 4.46 m/s. Similar behaviour is observed for tests 5 to 8.

Further, Figure 15b shows the contact time comparison for the contact sensor and the camera for different tests. The contact time (first contact to peak depth) decreases with the increase in impact velocity. The maximum and minimum deviations from the camera are 17.76% (test 1) and 2.97% (test 3), respectively.

In the second set of experiments (tests 5 to 8), we reduced the bag's pressure from 1.4 bar to 1.2 bar. The bag pressure variation changes the impact positions dramatically due to its thickness in the inflated condition. The pendulum hits the bag even before achieving maximum velocity, which is a challenge to the reproducibility of the tests. Hence, we varied pressure such that impact always occurs at peak pendulum velocity. We observed similar behavior as in tests 1 to 4. There is no major deviation in the voltage drop values and contact times. From Figure 15a, we observe that the voltage drop for tests 1 and 5 (same velocity and different pressures) are approximately the same (highlighted in black box). Further, the drop behavior for 3.41 m/s (test 2 and 6) is also similar. After 4.46 m/s all the tests have the same behavior due to full contact between the pendulum and the sensor.

The contact area is calculated at the peak depth as the kinetic energy and sensor variations are low. Firstly, the depth (*Dc* in Figure 14) is calculated from the high-speed video. The voltage drop (Δ*Vcap*) from the sensor is compared with the calibration curve and the contact area, A, is calculated. Then the depth (*Ds*) is calculated. *Dd* is the difference between the depths obtained from the camera and the contact sensor. The deviation is calculated, keeping camera values as the reference (Table 3). The sensor has a minimum and maximum deviation of 13.32% and 16.41%, respectively.

**Figure 15.** Single sensor results: (**a**) sensor voltage drop; (**b**) contact time comparison for sensor and high-speed camera.


**Table 3.** Single sensor results.

### *6.2. Matrix Sensor*

Figure 16 illustrates matrix sensor results for L1, R1 and middle impacts.

**Impact at L1 sensor**: The voltage drops for L1 and L2 are 2.56 V and 1.22 V, respectively. The pendulum does not touch R1 and R2.

**Impact at R1 sensor**: In this test, the sensor is moved to make R1-centered impact. R1 and R2 sensors record 2.40 V and 0.68 V, respectively. R1 has full contact while R2 has partial contact. L1 and L2 record no touch.

**Impact in the middle of all the sensors**: The sensors' voltage drop varies from 0.9 V to 1.4 V. The voltage drops are identical since the impact and the sensors are symmetrical.

First contact point estimation is crucial for the in-position and out-of-position decision. The first contact is detected when the voltage drops below 4% of the mean reference value. Table 4 shows the estimated first contact time from the tests. The first column is the impact position. During the L1 impact test, the head first touches the L1 sensor, detecting early touch at −3.9 ms. Once the airbag starts to deform, the head touches the L2 sensor at 21.8 ms, followed by R1 touch at 73.7 ms.

**Figure 16.** Matrix sensor tests with different impact points by changing sensor position. **Table 4.** First touch identification for matrix sensor using threshold.


NA = not available.

The contact area is calculated similarly to the single sensor (Table 5). The voltage drops of L1, L2, R1 and R2 for the L1 impact are 2.56 V, 1.22 V, 0.20 V and 0.07 V, respectively. These voltage drops are compared with the calibration curves and the corresponding contact area is calculated. A is the total contact area obtained by adding the gap area

between sensors. The depth *Ds* is then determined and deviation from the camera is calculated. The deviation is close to 22%.

**Table 5.** Matrix sensor depth calculation for head-form impact tests.


#### **7. Discussion**

Airbag performance is assessed through various test stages. Firstly, static deployment is performed to analyze the unfolding and filling behaviour, followed by linear impactor or pendulum impact tests. These tests are performed to analyze free-form body motion without vehicle deformation to assess airbag performance only. Further, sled tests are carried out on a rigid sled where vehicle motion and seatbelt restraint effects are considered. Finally, full-vehicle crash tests are performed to consider vehicle structural deformation, airbag displacement, and restraint effects. We have chosen pendulum tests in our work while it is practically feasible to change the parameters and provide scaled-down occupant free-form head kinematics and restraint effect. The experiments are cost and time-effective, hence better suited for first performance evaluation and hypothesis testing of the sensors. However, there are certain limitations of the test bench and experiments. The arm length limits the pendulum's impact velocity and, vibrations in the pendulum increase with arm length. Hence in our study, we have restricted the velocity to 5.11 m/s. Airbag pressure also has limitations. Pressure change increases the bag thickness, making pendulum impact before maximum kinetic energy, resulting in lower voltage drop and higher contact times. These limitations can be overcome by testing the airbag in a drop tower facility. The results of single and matrix sensors are further discussed in the following subsections.

#### *7.1. Single Sensor*

As hypothesized, the sensor voltage drops with contact progression and reaches a minimum when the head reaches peak depth. When the impact velocity is increased, the voltage drop increases due to the larger contact surface.

The deviation (Table 3) for low velocities is less as the sensor makes perfect contact with the head. When the velocity is high, the sensor flies and contacts different parts of the pendulum assembly, contributing to the deviation. This problem can be overcome by knitting the sensor on the airbag. On the other hand, the contact area is smaller when the head slides on the airbag beyond the sensor area. The drop increases when the velocity is increased. The deviations (Table 3) for the single sensor are reasonably acceptable due to dynamic irregular complex deployment. They can be further reduced by adequately integrating the sensor with the airbag. From the single sensor results (Table 3), it can be concluded that as the impact velocity increases, the area deviation also increases. In real-time moderate speed vehicle collisions, the deviation is acceptable.

Further, the contact times obtained from the sensor are in good agreement with the high-speed video times (Figure 15). With the increase in impact velocity, contact time decreases with a higher drop.

#### *7.2. Matrix Sensor*

The minimum deviation for the matrix sensor (from the camera depth) as a whole is 21.44% (Table 5), which means the measured area is smaller than the area obtained from the camera. There are several possible reasons. Firstly, the shape of the head is circular. When the head makes contact, the airbag wraps around the head, making contact with other parts at different time stamps. One solution to this problem is to provide a flat contact. This can be achieved by using a square plate. Although the square plate is not a

real condition, it can ease the testing and analysis. The second reason is mutual capacitance and contact capacitance induced between the sensors when the object makes contact. A correction parameter can be incorporated in the occupant detection algorithm by testing individual sensors in the matrix. Mutual capacitance can be reduced by increasing the distance between the sensors.

Further, the experimental results answer the questions in Section 2.

• What are the first and total contact times?

The contact time from the first contact to the peak can be estimated from both sensors (Figures 15 and 16). Irrespective of the contact position, the single sensor provides first contact time, total contact time, whereas the matrix sensor is position-specific. It gives contact parameters on different regions on the airbag. If there is a single-chambered airbag and out-of-position is not of interest, the single sensor can be preferred over the matrix. If region-specific times are required, the matrix is a choice of application.


When the impact position is the parameter of interest, then the matrix sensor plays a significant role. The position can be identified from the matrix sensor based on the threshold crossing time for different sensors in the matrix (Table 4). Early position estimation helps decide in-position and out-of-position, which is crucial information to control the individual chamber pressure.

Three main results—first contact point, time and position—significantly impact the vehicle's passive safety system (airbag or seat belt) during in-crash and post-crash phases. Each parameter can be used to tune the restraint system. Curtain airbags are usually multichambered with optional gas flow control between the chambers [30]. The integration of matrix sensors with such airbags enables inflation and exhaust pressure control of each chamber to define an optimal control strategy, which minimizes the occupant's rebound velocity.

Furthermore, sensor data also play a significant role in injury monitoring and rescue strategies. The vehicle can be used as a diagnostic space by installing accelerometers to monitor the respiration [31,32]. The head depth obtained (Table 3) can be combined with respiration data to correlate injuries and respiration. The detailed injury estimation analysis is beyond the scope of this paper. Finally, there is an eCall system in the vehicles which communicates the accident with vehicle data [33]. The diagnostic data and injury data can be integrated with the eCall system.

#### **8. Conclusions**

Airbag–occupant contact detection was an open research opportunity due to the short deployment time, sensor material and complex airbag shape during deployment. In this research, we have successfully developed tactile occupant detection sensors capable of estimating contact time with position and the area. The single sensor can be used when there is less probability of OOP occurrence, whereas the matrix sensor is suitable for bigger multi-chambered airbags with pressure control. The passive safety systems can be fully controlled and tuned from the sensor feedback. Injuries can also be estimated and communicated, which makes airbags smarter and adaptive to various crash scenarios.

**Author Contributions:** Conceptualization, N.S. and C.B.; methodology, N.S., C.B., T.M.D., R.H.; software, N.S.; validation, N.S. and C.B.; formal analysis, N.S., C.B., T.M.D., R.H.; investigation, N.S.; resources, N.S.; data curation, N.S.; writing—original draft preparation, N.S.; writing—review and editing, N.S., C.B., T.M.D., R.H.; visualization, N.S., C.B., T.M.D., R.H.; supervision, C.B., T.M.D., R.H.; project administration, C.B.; funding acquisition, C.B. All authors have read and agreed to the published version of the manuscript.

**Funding:** This work was financially supported by *Bayerisches Staatsministerium für Wirtschaft, Landesentwicklung und Energie* under the grant *IUK-1902-0007//DIK0102/01* and APC was funded by Technische Hochschule Ingolstadt.

**Institutional Review Board Statement:** Not applicable.

**Informed Consent Statement:** Not applicable.

**Data Availability Statement:** Data is contained within the article.

**Conflicts of Interest:** The authors declare no conflict of interest.
