A Structural Dynamic Model Inversion-Based Technique to Characterize Impacts to a Full-Scale and Operational Helicopter Rotor Blade

The structural integrity of the rotor blades is critical to the performance and safe operation of a rotorcraft system. Over the course of normal operations, the blades are exposed to a number of potential impact events from a variety of sources, such as rotor wash debris, bird strikes, dropped tools, and, in military applications, ballistic impacts, each of which carries a potential to produce damage to the blade [1]. Each event must be followed by a thorough inspection and informed maintenance decision as to the health of the blade. The most common inspection approach in use today is a regular, manual inspection of the blades. Current inspection techniques, such as visual inspection, coin-tap, and ultrasonic testing, are time consuming and subjective. With the increasing use of advanced composite materials in blade manufacturing, the challenges of identifying and repairing blade damage are exacerbated further. Damage mechanisms are more often subsurface, such as material disbonds or core crushing, and difficult to detect visually. More targeted methods, such as thermographic imaging, are emerging but the severity of damages is difficult to quantify using inspection results. The implementation of real-time structural health monitoring, to support the existing inspection methods, has the potential to substantially reduce the inspection burden and increase the rate of impact identification [1–5].

From a health and usage monitoring (HUMs) perspective, the characterization of impacts in the operational setting, especially if conducted in real-time, is particularly critical in successfully monitoring the health of the aircraft. Thus, the implementation of onboard sensors to automatically detect and characterize the impact events would enable improved maintenance decision making and allow for more targeted and cost effective inspection routines. The development of sensor-based damage detection methods is a large and wide ranging field of study, and one set of methods is focused on the use of vibration data. These methods identify system parameters, using a technique known as modal parameter estimation (MPE), in order to detect and identify damage. Allemang and Brown and others provide reviews of the technique [6–9].

In a survey of such methods, Doebling discussed several approaches including methods based on tracking changes in modal parameters and iterative models which update modal parameters and compare to a baseline model [10]. Inverse methods, which rely on a physics-based model of the structure dynamics and are the foundation of this work, are included in the former group under the subgrouping of frequency-based techniques.

Inverse-based techniques most commonly use a frequency response function (FRF) as the foundational model, relating impulsive forces applied to the structure to the vibratory response captured through accelerometers or strain gauges. These methods use the resulting model to produce estimates of the location and magnitude of an impact force. Similar techniques for impact identification have been applied by Yoder and Adams [11,12], Chang and Seydel [13], and Zwink et al. [14], the last of which applied inverse methods to a stationary helicopter blade. Pawar provides an overview of structural health monitoring techniques applied to helicopter blades, including inverse techniques for both damage detection and impact identification [15].

Such methods require the development of an inverse model which accurately captures the operational blade behavior. Unfortunately, frequency responses are not easily obtained in the operational environment and models developed in a nonrotating setting do not accurately describe the behavior of the blades in flight. This deviation may be attributed to three key factors: the change in root boundary condition due to the repositioning of the droop stop,¹ the presence of centrifugal and Coriolis forces acting on the blade during flight, and the presence of aerodynamic forces affecting the stiffness and damping of the system. These errors in turn may lead to errors in the location and force estimation.

Some of these factors may be compensated for using purely experimental techniques. The HUMs application will often require repair, replacement, or recalibration of blades, thus, requiring the collection of new FRF models. Most experimental methods are not practical for such an application or introduce additional sources of error. For example, suspending a blade vertically may simulate some degree of centrifugal forces and remove the droop stop effects, but such an approach would leave other complex boundary conditions, such as the lag dampers, unaccounted for and thereby introduce an additional source of error. Similarly, the blades may be mounted on the hub and suspended with a bungee, again removing the droop stop effects. This approach is feasible but not practical for the field practitioner. An approach which will allow HUMs technicians to complete the retraining in the field and without the need for a complex experimental apparatus is necessary.

Looking at the data-processing approaches present in the literature, Budde et al. [16] utilized inverse methods for locating impacts to spinning-cantilevered beams in a laboratory setting. However, Budde's approach was developed for simple beams operating at low speed, eliminating many of the dynamics present in a full-scale helicopter blade operational setting. Because these factors were not present in the subscale experimental system, Budde's approach does not account for the previously discussed discrepancies and would thus be inadequate in an operational rotorcraft environment.

This paper analyzes the first steps toward an approach for compensating hub-mounted, nonrotating FRF data for application in the operational environment, specifically compensating for the effects of the droop stop boundary condition. Importantly, compensation methods for the centrifugal force and aerodynamic effects will be left for future work. The derivation of a preliminary approach upon which this work builds is given in [17]. The work in this paper will present the complete droop stop compensation approach and the results of a series of nonrotating bench tests which validate the proposed procedure.

Additionally, the methods identified in the literature limit the scope of impact characterization to the impact location and force magnitude. While useful, an expanded set of information is necessary to perform useful damage modeling and make the subsequent maintenance decisions. The stationary tests are leveraged further to provide supplemental impact characteristics beyond the impact location and force magnitude. In particular, the impact identification techniques are enhanced to provide information regarding the two-dimensional planar impact area as well as insight into the stiffness of the impacting object. Bench testing results validating these two new procedures are also discussed.

The approach utilized in this work builds on a well-known inverse method, which is adapted for use with a recently developed entropy-based approach in the final impact localization stage and incorporates a novel model manipulation methodology to account for changes in the root boundary condition of the blades. This particular work uses accelerance FRFs to construct the blade model. In the inverse FRF approach, a matrix of FRFs are experimentally obtained using a discretization of the structure and used to construct the structural model. The data are collected using an instrumented modal hammer, which records the time history of the impact force, and a single triaxial accelerometer on each blade, which records the vibratory response. Once the model has been acquired, it is manipulated, inverted, and stored for later use. The details of this manipulation are discussed later. With the model in place, the sensor outputs are monitored for a threshold crossing, which indicate an impact event. For the purposes of this work, an impact event is defined broadly as a short-duration impact such as a hammer strike or ballistic impact. When an event is detected, the acceleration time history is captured, and the inverse FRF model is multiplied by the Fourier transform of the recorded response data. The result of this multiplication is an estimate of the force time history which in turn is used to obtain an estimate of the impact location, as discussed below.

It should be noted that this approach operates on a discrete representation of the blade, with a finite number of measurement locations and potential impact positions, namely those locations used in creation of the blade model. Except in the rare case when the number of measurement degrees-of-freedom meets or exceeds the number of potential impact locations, the inverse problem will be underdetermined. To overcome this challenge, it is assumed that any given impact may occur only at a single location. Operating on this assumption, the inverse problem is solved iteratively, once for each potential impact location, and a location and force estimate is obtained for each case. Identifying which among these estimates is the true impact location has been the matter of significant study throughout the literature. While a number of approaches have been proposed, such as the curve-fitting approach of Budde et al. [16] and the technique of comparing measured and estimated FRF models applied by Yoder and Adams [11,12], this work follows a novel entropy-based approach as proposed by Bond [18,19]. In brief, this approach estimates the signal entropy, or randomness, of the estimated force time history. For a true impact event, which is presumed to be impulsive in nature, the entropy value will be low. This metric is estimated for each possible impact location and the results are ranked. The location corresponding to the lowest entropy value is identified yielding the most impulsive force history and therefore the most likely impact location. This approach is heavily reliant on the accuracy and viability of the FRF matrix to be used as the model. For the reasons discussed previously, it is therefore critical that a corrective approach be developed by which to account for the various sources of error present in the operational environment. This work provides such an approach only for one aspect of this error, the droop stop effects. Further improvements to the technique accuracy and applicability may be enabled by the incorporation of additional compensation steps.

A key source of error in the operational environment is the repositioning of the droop stop and the resulting change in blade root boundary condition. At low rotor speeds and when the rotor is stationary, the root of the each blade rests on a droop stop to prevent contact with the fuselage. At higher speeds the blade is lifted off of the droop stop, producing a shift in the blade structural dynamics. The former case will be referred to as constrained and the later as unconstrained. In a laboratory setting, the change in FRFs due to this change in boundary condition can be accounted for by suspending the blade from a sufficiently compliant bungee and directly collecting the unconstrained FRFs. More practically however, the means to suspend a blade for FRF collection is not readily available in the field. Thus, to accurately compensate for the change in boundary conditions at the root of the blade, the effects of the droop stop must be removed from the constrained FRFs.

The study of boundary condition effects is not a new one to the modal analysis community. The impedance modeling technique was popularized in the late 1970s as a means by which to analytically evaluate the effects of various boundary conditions on structural dynamics [20]. Alternatively known as structural dynamic modification, the technique has since been applied to a number of applications, including computer components [21], machine tools [22], and helicopter munitions mounting [23]. The same approach will be used here to account for the change in boundary condition at the root of the blade. A thorough derivation of the relevant equations and an in depth discussion of the impedance modeling technique as applied to this work has been previously presented [24]. A similar derivation and discussion is repeated here, extending the previous work with new alterations and experimental considerations conducted for validation and refinement purposes.

The impedance modeling approach allows an unknown frequency response of a constrained system to be analytically derived from that of an unconstrained system, or vice versa. A foundational example is commonly used throughout the literature and will serve here as a starting point for derivation. Consider a cantilevered beam, shown in Fig. 1, with three points of interest—a, b, and c. Using this convention, the FRF relating an input at location b to the response measured at location a may be denoted as $Hab(jω)$⁠, where ω denotes frequency. Consider a second case of the same beam, shown in Fig. 2, introducing the additional constraint of a pin joint at point c. In this new case, the FRF relating points a and b may instead be denoted as $Hab+(jω)$⁠, where the superscript denotes the constrained condition.

Notice in particular that this expression describes a constrained FRF entirely in terms of unconstrained FRF data. Also, the effect of the constraint, $−HacHcc−1Hcb$⁠, is clearly identifiable.

Consider next the case of a helicopter blade with a sensor (position p), an impact (position q), and a droop stop, shown in Fig. 3. Note that the positions b and d are the blade and droop stop sides of the contact point, respectively.

Note that this equation, unlike the cantilevered beam case, contains both constrained and unconstrained FRF measurements. Similarly, however, the effects of the droop stop are clearly identifiable in the form of the ratio term. This additional term includes information which is location specific, relating response at b to an input at an arbitrary location q, as well as information about the mechanics of the droop stop which is independent of impact location.

This final point is key to the correction strategy, in that the ratio term need only be collected once but may be applied to the entire set of possible impact locations, q. From an experimental standpoint, this term is of even greater interest. While the constituent data may be collected directly, collecting data on the droop stop itself is a significant challenge. The droop stop is a small, sprung plate which retracts when exposed to centripetal forces. Without those forces present, the contact point is difficult to reach without removing one or more components of the surrounding assembly and thereby altering the structural dynamics of the system. This attribute makes impacts to the droop stop difficult to apply in a controllable manner. Because of the likelihood of an improperly applied forcing impact, there is a high risk of collecting erroneous response data which, by extension, will introduce errors into the force and location estimates. Instead, by collecting $Hpq$⁠, $Hpq+$⁠, and $Hbq+$ data for a limited subset of locations, q, the $Hpb/Hdd$ term of Eq. (10) may be estimated without actually collecting the driving point FRFs. Once obtained, this term may then be propagated through a full set of constrained FRFs to produce the complete unconstrained data set.

Additionally, because the terms encompassed in the ratio only involve locations on or around the droop stop and because the root of the blade is typically robust to damage, the measurements needed to calculate the corrective term would not need to be updated after damaging impacts or other effects that might require the collection of a new blade model had occurred. From a practical viewpoint, this implies that, once calculated, the ratio term may be reused to correct subsequent training data sets without the need to collect any additional unconstrained data.

where x and y are the spanwise and chordwise dimensions of the blade. The selection of these measures as the metrics for success was informed by the fact that, in a HUMs application, critical variables are the location of an impact—enabling the targeting of supplementary inspection and maintenance actions—and the force of the impact—allowing the use of damage modeling algorithms to make maintenance decisions. Thus, minimizing the error in these two metrics was identified as critical for the success of the impact characterization technique.

To validate the methods proposed in this work, a full-scale helicopter blade was overlaid with a modal test grid using 12 in. spanwise spacing and chordwise positioning of 0 in., 2.5 in., 5 in., 13 in., and 20 in. from the leading edge, as depicted in Fig. 4. A single tri-axial accelerometer was mounted near the root of the blade (p) and another near the contact point between the blade and droop stop (b).

An instrumented modal hammer was used to apply impacts to each grid location and FRFs recorded, which related the applied impact to the corresponding response as measured at the sensor positions. To validate the proposed method, data were collected in an at-rest condition, supported by the droop stop, as well as an in-flight condition, lifted off of the droop stop. To simulate the effect of the blade disengaging from the droop stop during flight, a compliant bungee was used to lift the blade off of the droop stop. As shown in Fig. 5, the blade was lifted at 2/3 the total length, at a balance point. The lift position and bungee stiffness were selected such that the effects of the bungee on the blade response were minimal, as discussed by Crandall [25].

Training data were collected in each of these configurations, recording all of the frequency response components described in Eqs. (8) and (9). From this data, four blade models were generated—resting on the droop stop (on-stop), lifted off of the droop stop (off-stop), and two modified cases. The first of the modified models utilized the driving point measurements, $Hbb$ and $Hdd$⁠, directly and applied Eq. (9) to obtain the simulated off-stop data set. This data set will be referred to as the measured driving points data. The second-modified model instead followed the approach discussed previously, estimating the ratio term in Eq. (10) by using a subset of off-stop data. In this case, the modal grid locations of the two inboard-most chords were used to estimate the ratio term, which was then used to correct the entire data set. This data will be referred to as the calculated ratio data set.

For each of the four cases, the FRF model was inverted and a set of validation data, collected in the lifted configuration, was processed. The accuracy of the technique was assessed for each impact location, averaging the results for the three impacts applied to that position. Figures 6 and 7 depict the resulting accuracy metrics for each of the four cases. Figure 6 depicts the location error, measured in inches, as calculated using Eq. (13). Figure 7 depicts the error in force magnitude, measured as a percentage in decimal form, as calculated using Eq. (12).

Looking first at the uncorrected on-stop case, the large location and force errors indicate that some corrective approach is necessary for useful deployment of this technology. Both location and force errors are severe in several regions, especially so along the trailing edge of the blade. By contrast, the off-stop data represents the ideal case and results show near perfect accuracy.

The two cases using the corrected data sets offer significant improvement over the uncorrected case. In terms of location estimation, 87% and 94% of impacts were located correctly for the measured and calculated cases, respectively. For the calculated ratio approach, 98.3% of impacts were identified within 1 ft of the actual location and 99.2% within 2.5 ft. In fact, only a single data point fell outside of those bounds. It should be noted that it is not uncommon for human error to produce faulty training data for at least one point over the course of such a large grid as was used in this test. With that in mind, it is hypothesized that the outlier data point may have been produced by such an error—a mistake that can be screened for and corrected in any real-world application. Overall, the ratio estimation approach produced slightly better results than the measured driving points approach. The improvement is attributable to the difficulties discussed previously with accurately obtaining FRF data on and around the droop stop, data which is made unnecessary by the ratio estimation procedure (Table 1).

Closer investigation of the force error present in the estimated ratio case indicates that the errors are still significant but are also clearly biased. Figure 8 depicts the force error for each point in the modal grid. As can be seen, there is an average over-estimation bias of nearly 40%. The sawtooth pattern may be attributed to increased error along the trailing edge. Because the grid positions are numbered such that 1–5 represent one chord line, 6–10 the next, and so on, patterns of increased error at particular chord-wise positions produce a sawtooth pattern when plotted in this fashion. Correcting the estimates for this overestimation, results in a significantly improved result (Fig. 9). The cases of most egregious error correspond to those positions for which the location estimation had the highest errors and, as a result of that error, are using an invalid training data point for the force estimation.

Finally, a study was conducted to determine the most useful configuration of data points to use in obtaining the estimated corrective ratio term. As discussed previously, the initial validation testing utilized the inboard-most ten grid locations, corresponding to the first two chord positions, to estimate the ratio term for Eq. (10). Using the same on- and off-stop training data as collected previously, various alternative cases were applied, a new set of FRF models generated, and the accuracy assessed for each new case. The first three cases investigated using only the first chord (5 points), the first two chords (10 points), and the first three chords (15 points). The last three cases involved using the first four chords (20 points), the middle three chords (15 points positioned at midspan), and a scattered set of 15 points capturing the first, middle, and last chords. The results of these three cases are depicted in Table 2.

The case of the three midspan chords produces the most accurate force estimates, both in terms of mean absolute error and maximum error, while the inboard four chord case produces the best location estimation results. The preference between the two methods is largely dependent on the target application of the approach and the needs of the user, prioritizing either force or location estimates.

Based on the results of the above studies, this work will proceed using the calculated ratio case utilizing the three inboard most chords for the ratio estimation. While other configurations may provide slight improvement in terms of accuracy, practical considerations make this approach a more desirable option.

With the modified FRF model in place, the approach as discussed is capable of estimating impact position and force magnitude. However, in addition to these metrics, it was desired that the information pertaining to impactor stiffness and planar impact area will be characterized. This section will present formulation of methods for both additions as well as the results of experimental testing to verify the efficacy of the proposed approaches.

The proposed approach for planar impact area estimation makes use of the same FRF inverse calculations as used in the force and location estimation. As discussed in the “Method Context and Overview” section, an estimated force time history is identified for each possible impact location. The most likely impact location is selected by calculating the signal entropy, or impulsiveness, of each force history. In the base technique, those force histories not identified as corresponding to the most likely impact location are discarded. In the proposed approach to identify impact area, they are instead repurposed to provide information about the region surrounding the impact.

It was observed during validation testing of the core technique that the entropy metric appeared correlated to the distance of the grid point from the impact location. A preliminary study of phenomenon was undertaken to determine the validity of this observed feature. A subset of nine modal grid points arranged in a 3 × 3 grid was used for testing, with impacts applied to the center point using 0.25 in., 1 in., and 2 in. diameter modal hammers. The impacts were applied with a PCB 086C03 impact hammer with 084C05 tip, PCB 086D05 impact hammer with 084A50 tip, and PCB 086D20 minisledge with 084A62 tip, respectively. The hammers and associated hammer tips are depicted in Fig. 10. The FRF model for the selected region was interpolated from the base 2 in. grid spacing to a resolution of 0.25 in. using a cubic-spline interpolation approach. The data from the impacts from the variably sized hammers were processed, and the estimated entropy values for each estimated force history were extracted. These outputs were normalized to the maximum entropy estimate for effective comparison between the impacts and plotted. The results are depicted in Fig. 11, where a clear distinction between impact areas may be observed.

Based on these promising preliminary results, it was desired that a more controlled experiment be undertaken to investigate the limits of the proposed approach. It was noted that the factors such as hammer mass or tip stiffness may have played a role in differentiating the results of the preliminary study. A new set of strikers was fabricated to be used with the PCB 086C03 type modal hammer. The strikers, of diameters 0.25 in., 0.5 in., 1 in., and 2 in., were all of the same rubber material and are depicted in Fig. 12.

The following test procedure was then applied:

1. (1)

   Collect FRF data using a PCB 086C03 hammer and custom-fabricated striker for a selected blade region of five chords, spaced at 5 in. intervals, each containing 11 grid points spaced at 2.5 in. intervals, as depicted in Fig. 4.

2. (2)

   Apply ten impacts each with 0.25 in., 0.5 in., 1 in., and 2 in. diameter strikers, with all the impacts to the same point in the pocket region.

3. (3)

   Extract a 5 × 5 grid of FRF data surrounding the impact point and interpolate to 0.5 in. spacing.

4. (4)

   Count the number of pixels, or grid positions, which produced an entropy value within 5% of the maximum entropy for that impact.

5. (5)

   Repeat steps 2–4 for a spar location.

6. (6)

   It should be noted that scaling the metric to the impact-specific maximum entropy in step four, by utilizing a percentage threshold rather than an absolute difference, allowed the method to be unaffected by changes in impact magnitude.

The results of this analysis are depicted in Figs. 13 and 14. In both cases, the x-axis corresponds to the striker diameter used in that test, while the y-axis denotes the number of pixels flagged by the 5% metric. As can be seen, there is a clear differentiation between the larger 2 in. diameter impacts and the smaller sizes.

Given that the grid was interpolated to a 0.5in. spacing, any impacts sized smaller than this were within the grid resolution and thus should not be distinguishable without increasing the grid resolution, either through alteration of the data collection grid or through finer interpolation. Unfortunately, due to computational limitations, a finer resolution interpolation was not able to be analyzed. A finer initial resolution could be considered for additional testing of the technique, but increasing the number of grid locations needed directly opposes the initial motivation for this work. Requiring a greater number of grid locations to be included in the system model greatly increases the data collection time needed for deployment of the technology in a nonlaboratory setting.

The proposed approach for the estimation of impactor stiffness is based on the bandwidth of the estimated force. It is known that the bandwidth of an impact force, defined as an order of magnitude drop in the first lobe of the force spectrum, is related to the stiffness of the two impacting bodies. In this case, the bandwidth will be related to the stiffness of the blade region being impacted and the object striking the blade.

In order to test this approach, a similar set-up was used as for the impact area testing. A second set of custom strikers was fabricated using aluminum, to supplement the rubber set deployed previously. The full set of sizes (0.25 in., 0.5 in., 1 in., and 2 in.) was used to ensure that the approach is resilient to changes in impactor size. The full set is depicted in Fig. 14.

Impacts were applied to the same point with each striker over a range of force magnitudes, to evaluate the efficacy of the estimation approach in the presence of varying impact conditions. Due to concern over the damage potential of the metal strikers when impacting the pocket, impacts were constrained to the spar region of the blade. For each impact, the force history was estimated and the bandwidth calculated.

The results of this test are depicted in Fig. 15. As can be observed, the different material types may be clearly differentiated. The one exception is the 2 in. metal striker, depicted in Fig. 15 as the largest diamond marker. It was noted that producing a clean impact with the large rigid disk was difficult. Such attempts often resulted in rolling the disk or otherwise impacting with one edge prior to the rest of the disk. It is believed that these inconsistencies produced longer contact time during the impact and therefore a less impulsive impact event and lower force bandwidth. The approach appears to be resilient to both changes in impactor size and impact magnitude.

To investigate the effects of spatial variation, a second series of impacts was applied at various locations on both the spar and the pocket regions of the blade. A secondary blade was obtained which, due to pre-existing damage to unrelated sections of the blade, made pocket impacts possible. Impacts were applied at points inboard, midspan, and outboard along the blade. The 2 in. metal impactor was not used in this study because of the difficulty in performing a clean impact (Figs. 16 and 17).

As can be seen, the spar region results are well differentiated. The pocket region, by nature of the blade structure and material, is much more compliant and, as a result, there is less bandwidth within which to differentiate the impactor materials. However, while the result is less clear than in the spar case, there is still a marked distinction between the rubber and metal strikers which holds for all sizes and impact magnitudes. Note also that the pocket region forces were applied across a much more limited range of magnitudes out of concern for damaging the blade.

Application of inverse techniques for impact identification and characterization on a helicopter rotor blade in an operational environment faces two key challenges—the change in root boundary condition due to the removal of the droop stop and the presence of centripetal forcing during operation. The objective of this research was to present an approach by which to solve the first of these challenges.

A method for correcting the blade frequency response model for changes in root boundary condition has been developed. This approach is founded on the principles of impedance modeling, by which the effects of the droop stop may be accounted for and removed. While the uncorrected model provides a location estimation accuracy of only 52% of impacts, the two proposed correction strategies achieved accuracies of 87.5% and 94%, respectively. While the average error in the force magnitude estimates was not greatly reduced without further compensation, the spread of those errors was improved. The force error was reduced from 200% to 80% and 90% for the two presented correction approaches, respectively.

Through further investigation of these results, it was demonstrated that the remaining force errors were biased toward over estimation and, by extension, largely correctable. In the results presented, the unbiased error was reduced to within ±10%.

A modification to the impedance modeling technique was proposed by which the driving point measurements on and around the droop stop, which are inherently difficult to collect, may be calculated rather than measured. Further study of this method determined that, of the cases studied, a ratio estimated using three midspan chords produces the most accurate force estimates, both in terms of mean absolute error and maximum error, while the inboard four chord case produces the best location estimation results.

Building on the entropy-based methods used for impact location and force estimation, a method by which to estimate the planar impact area was also presented. Preliminary results clearly indicated that the entropy values of the region surrounding the point of impact were related to the size of the impact. Interpolating the model in the vicinity of the impact and estimating a series of entropy values produced a metric by which various sizes of impact could be differentiated. The technique was evaluated in a bench test environment for both the pocket and spar regions of a blade and proven to be effective.

Additionally, a method was presented by which the stiffness of the impacting object may be estimated, leveraging information about the bandwidth of the estimated force. This approach was evaluated in a bench test environment, and it was successfully demonstrated that varying impactor materials could be differentiated and that the technique was resilient to changes in impact size, location, and force magnitude.

While the methods presented here are encouraging, there remains much work to be done in this area. In particular, an approach by which to account for the remaining challenges of deployment in an operational environment, such as the centripetal forcing and aerodynamic loading effects, must be developed. Additional study of the impact area estimation technique may further validate the approach utilizing a finer resolution interpolation grid, thereby allowing the differentiation of smaller impactors. Finally, additional study of the impactor stiffness estimation approach is needed, especially with regards to other materials besides those presented in this work.

This research was partially funded by the Government under Agreement No. W911W6-10-2-0006. The U.S. Government is authorized to reproduce and distribute reprints for Government purposes notwithstanding any copyright notation thereon. The views and conclusions contained in this document are those of the authors and should not be interpreted as representing the official policies, either expressed or implied, of the Aviation Applied Technology Directorate or the U.S. Government. Distribution Statement A: Approved for public release; distribution is unlimited.

H =

frequency response function

F =

input force

x =

spanwise dimension of the helicopter blade

X =

measured Response

y =

chordwise dimension of the helicopter blade

ω =

excitation frequency

Subscripts

b =

contact point, blade side

d =

contact point, droop stop side

p =

input/impact location

q =

output/sensor location

Superscripts

+ =

constrained frequency response function

* =

complex conjugate

Acronym

FRF =

frequency response function