An FBG-Based Hard Landing Monitoring System: Assessment for Drops on Different Soils

Abstract

This study aims to develop an integrated monitoring system using a fiber Bragg grating sensor network to record the structural response of a landing gear system under operational loads to detect hard landing conditions on soils with different absorbing characteristics and to differentiate between soil types during landings. This paper refers to drop tests carried out at a drop tower of the test article, an integrated leaf spring landing gear with fiber Bragg grating sensors, measuring strain to evaluate landings from different heights on different soil types: hard soil, sand, and gravel. Cross-correlation and fast Fourier transform analyses can help to assess the repeatability of the impact tests, to assess the developed system as very reliable in detecting landing conditions and ensure very low error in the accuracy of the sensor placement, or to assess whether different impacts under different conditions produce consistent responses.

1. Introduction

Landing gear, a vital component in aircraft and helicopters, traditionally employs safe-life design methods [1]. This approach ensures structural integrity throughout the component’s expected lifespan but limits the potential for advanced health monitoring techniques [2]. Unlike fail-safe systems, where continuous monitoring is crucial, landing gear monitoring primarily focuses on verifying actual loads against oversized design loads to assess the remaining lifespan [3]. This approach offers several advantages [4]; in fact, by accurately determining actual loads, operators can increase the operational lifespan of landing gear components. Improved monitoring can identify potential issues early, reducing the risk of unexpected failures, and by extending service life and reducing maintenance costs, operators can achieve substantial economic benefits [5,6,7].

To achieve these goals, various monitoring techniques have been explored, such as sensor integration into the structure. Incorporating sensors or sensor networks into landing gear systems can provide valuable data for tasks, such as hard landing (HL) detection, flight management, weight distribution, and vibration analysis. Researchers have developed specialized methods to accurately measure loads experienced during landing gear operation. Overcoming technical challenges, engineers have created practical and reliable hardware solutions for implementing monitoring systems in real-world aircraft. By combining these approaches, the aviation industry aims to optimize landing gear performance, improve safety, and reduce operational costs.

This work is part of the “More Electric Aircraft—Smart Landing Gear (MELA-SLG)” project, which aims to develop a Smart Landing Gear (SLG) system. This system would integrate a sensory network of fiber Bragg grating (FBG) optical sensors to monitor the structural response of the “Intelligent Gear” under operational loads, with the ultimate aim of assisting the pilot during flight operations. The SLG system is designed to provide information on weight on wheel, hard lading detection, and weight and balance of the aircraft.

A useful application of the SLG is the weight on wheel (WoW). Historically, WoW systems have primarily relied on the shock absorbers’ stroke movement to determine whether an aircraft’s wheels are loaded. Inductive sensors, capable of detecting displacement, are commonly used in these systems.

In [8], a novel WoW system architecture based on strain gauges was introduced. This approach offers several advantages over traditional methods. Strain gauges can detect smaller changes in stress, potentially providing a more accurate and timely indication of wheel loading. Moreover, this system demonstrated the ability to detect wheel contact at a lower threshold compared to traditional systems. By measuring shear stresses, strain gauges can potentially provide valuable insights into the distribution of loads on the landing gear. Another useful application is the weight and balance (W&B) system that can estimate the total weight and the position of the center of gravity of an aircraft after the loading phase, including passengers, baggage, and so on, and before taking off. A solution was proposed in [9].

A wheel dynamometer is a specialized device used to measure the forces acting on an aircraft’s wheels during ground testing. This information is essential for understanding the performance and safety of the landing gear system [10].

Modern wheel dynamometers often incorporate strain gauges, which can accurately measure the forces exerted on the wheel. Wireless communication technologies enable these systems to transmit data to both on-board and ground-based systems [11].

Wheel dynamometers have various applications in aircraft testing, including HL detection, operational loads monitoring (OLM), and vibration analysis. Identifying excessive forces during landing can help assess the structural integrity of the aircraft.

OLM systems use data from wheel dynamometers to evaluate the remaining useful life of critical components [12]. Analysing vibrations during taxiing can provide insights into the dynamic behaviour of the landing gear.

Wheel dynamometers, equipped with advanced technologies like strain gauges and wireless communication, play a crucial role in ensuring the safety and performance of aircraft. By accurately measuring wheel loads, these devices provide valuable data for assessing structural integrity, optimizing maintenance schedules, and improving overall aircraft safety.

An HL occurs when an aircraft makes abnormal contact with the runway. This can be caused by various factors, including adverse weather conditions, mechanical failures, excessive weight, pilot errors, and other unforeseen circumstances.

Currently, there is no definitive, in-flight method for directly determining whether a landing gear has been overloaded during landing or ground maneuvers. Airlines and aircraft manufacturers rely on a combination of pilot assessment and recorded data to evaluate potential HL events [13].

To address this challenge, researchers and engineers have explored various approaches for direct load measurement in landing gear structures. Battery-powered strain gauge data logger: This system integrates strain gauges into the landing gear structure to collect data without requiring external power sources [14].

Laser deflection measurement: This method uses laser-based sensors to measure the deflection of the landing gear structure, providing insights into the loads experienced [15].

Instrumented load pin: Incorporating load pins equipped with sensors allows for direct measurement of the forces acting on the landing gear [5,14].

A recent study proposed a capacitive transducer-based HL recorder for helicopters. This device can be used to monitor the condition of the helicopter’s landing gear and detect potential damage or overloading [16]. While current methods for HL detection have limitations, emerging technologies offer promising solutions. By implementing direct load measurement systems, the aviation industry can improve safety, reduce maintenance costs, and enhance our understanding of landing gear behavior during critical events.

Several early attempts at HL detection focused on monitoring the shock absorber’s behavior. Stroke displacement: Measuring the displacement of the shock absorber proved to be unreliable, as it was not directly correlated with the severity of an HL [17]. Fluid pressure: Monitoring the fluid pressure within the shock absorber provided a more promising approach. However, this method requires significant modifications to the shock absorber’s architecture, making it expensive and sometimes inaccessible. Piezoelectric accelerometer: While sensitive to accelerations, this approach could lead to false alarms, particularly for fighters that experience high vertical accelerations during flight. Pilot’s physiological detection: Relying on the pilot’s subjective perception of accelerations was deemed unreliable due to its subjective nature and limited time frame. More recent approaches have explored the use of heuristic algorithms that analyze flight parameters and sensor data to estimate impact loads. These algorithms offer a more data-driven and objective approach to HL detection [18].

The development of reliable hard-landing detection systems has been challenging due to the complexity of the phenomenon and the limitations of existing technologies. While various methods have been proposed, none have proven to be entirely satisfactory. Future research may focus on combining multiple approaches and leveraging advanced data analysis techniques to improve the accuracy and reliability of HL detection systems.

Traditional load cells have faced limitations in size, weight, and calibration issues when used for monitoring landing gear loads. Additionally, transmitting large volumes of data from the aircraft to the ground for analysis presents significant challenges. Integrating a sensor network into a landing gear requires careful consideration of several factors [19,20]. These are the following: Limited space: the available space within a landing gear is constrained, necessitating compact and lightweight sensor designs; harsh operating conditions: landing gears are subjected to severe conditions, including shock loads, vibrations, temperature extremes, and environmental factors; maintainability and reliability: the sensor network should not compromise the landing gear’s overall maintainability and reliability. Fiber Bragg grating sensors have emerged as a promising solution for structural health monitoring (SHM) applications [21,22]. Their small size, resistance to harsh environments, and ability to measure strain and deformation make them well-suited for landing gear monitoring [23,24] by overcoming the limitations of traditional methods. The proposed approach demonstrates the potential of FBG technology in this critical application area.

FBG sensors have been successfully applied in a variety of engineering fields, including railway infrastructure monitoring, where they are used to measure mechanical stress in overhead contact wires [25], and in automotive modal testing, where they provide insights into strain distribution and vibrational analysis of composite materials [26]. These applications demonstrate the versatility of FBG sensors for real-time strain monitoring in dynamic environments.

A key challenge in impact strain measurement is the ability to capture high-frequency dynamic events. Hard landings induce rapid strain variations, requiring a high-speed interrogation system capable of resolving short-duration impact loads. Studies on ultrasonically embedded FBG sensors have demonstrated that FBGs can measure strain at frequencies up to 10 kHz, making them well-suited for impact and vibration analysis in aerospace applications [27]. Furthermore, modal analysis in automotive structures has validated the feasibility of FBG-based strain sensors for high-impact mechanical loads, providing a strong foundation for their use in landing gear SHM [26].

FBG-based monitoring systems have also been implemented in railway applications, where sensors were embedded into overhead contact wire clamps to track strain variations due to mechanical loading and environmental factors [25]. Additionally, impact testing using FBG sensors in composite and metallic structures has demonstrated their effectiveness in detecting structural responses to mechanical stress [28]. Numerical models analyzing strain values in composite materials with embedded FBGs further validate the use of FBG sensors in complex structural applications, particularly in cases where uniaxial stress assumptions affect sensor accuracy [29]. These applications highlight the potential of FBG sensors in assessing transient impact loads and structural integrity in high-risk environments.

Accurate data processing techniques are also essential for FBG-based monitoring systems. The interrogation of FBG signals can be affected by signal noise and spectral distortions, reducing measurement accuracy. To address this, advanced signal processing methods, such as center-of-mass algorithms, have been developed to improve wavelength resolution and strain sensitivity [28]. Additionally, finite element analysis (FEA) has been widely used to validate FBG sensor measurements under simulated loading conditions, enhancing confidence in their real-world application [27].

This paper presents drop tests conducted on a test article (TA), an integrated leaf spring landing gear with strain sensors, using a drop tower. The experiments validate a methodology for measuring the dynamic strain field upon ground impact using FBG sensors embedded along an optical fiber. This study aims to detect HL conditions, defined by the exceedance of specific vertical velocities.

Preliminary results from previous experiments on the same TA and drop tower have been presented by the authors in prior research [30].

The objective of the previous campaign was to verify the potential of a landing gear monitoring system based on FBG technology to distinguish an HL or to operate as an active weight-on-wheel system [31]. The present study further investigates the capability of the FBG array installed on the TA to detect HL conditions on soils with different absorbing characteristics and differentiate between soil types during landing.

This objective is pursued through the results of a test campaign in which different types of soil were arranged at the base of the drop tower. The effects of soil type on the deformation of the TA were then compared. To evaluate the feasibility of detecting HL events on different terrains, the system underwent a series of drop tests on surfaces of varying consistencies, including hard (steel plate), intermediate (gravel), and soft (sand).

The present study provides additional empirical validation of the proposed methodology; in this paper, cross-correlation analysis can help quantify the repeatability of the impact test or assess whether different impacts under different conditions produce consistent responses and fast Fourier analysis confirms the repeatability of the experiments.

The remainder of this paper is organized as follows: Section 2 describes the methodology and experimental setup, including sensor configuration and data acquisition procedures. Section 3 presents the results of impact strain measurements, followed by a discussion in Section 4 on the implications of numerical validation techniques for improving FBG sensor performance. Finally, Section 5 concludes the study with recommendations for future applications of SHM in aviation.

2. Materials and Methods

2.1. The FBG Sensor Network

FBGs are a well-established technology for measuring structural deformations [14,21] and offer several advantages for integrating into landing gear structures such as high sensitivity, electromagnetic immunity, minimal harness, and minimum weight. In fact, they can accurately measure small strains and deformations, are not affected by electromagnetic interference, have a small diameter, reducing the need for bulky cabling, and are lightweight, making them suitable for aircraft applications. Moreover, FBGs can be embedded into structures with minimal impact on their integrity, and multiple FBG sensors can be connected to a single interrogation unit, reducing the number of required cables. They operate as optical filters that reflect light at a specific wavelength, known as the Bragg wavelength. This wavelength is determined by the grating period and the effective refractive index of the fiber core.

The Bragg condition describes the relationship between the Bragg wavelength (λ_B), the grating period Λ, and the effective refractive index n_eff [21], λ_B = 2n_effΛ. The strain dependence of an FBG can be calculated by differentiating the Bragg condition:

(1)${\displaystyle \frac{{\Delta \lambda }_B}{{\lambda }_B}}=\left(1+{\displaystyle \frac{1}{n_{eff}}}{\displaystyle \frac{\mathsf{\partial }{n}_{eff}}{\mathsf{\partial }\epsilon }}\right)\Delta \epsilon =\left(1+p_e\right)\Delta \epsilon ={\beta }_{\epsilon }\Delta \epsilon$

This equation shows that the change in Bragg wavelength is directly related to the strain (ε) applied to the FBG. By monitoring the shift in Bragg wavelength, it is possible to accurately measure the strain variation (Δε) experienced by the landing gear structure.

In this equation, β_ε represents the strain sensitivity of the Bragg grating at a given temperature, and p_e is the photo-elastic constant (variation of the core refraction index vs. the axial stress). For most silica optical fibers, the effect of core doping (typically, germanium) can be neglected. Theoretical mechanical strain sensitivity at a given temperature may be expressed as

(2)$S_{theor}={\displaystyle \frac{{\Delta \lambda }_B}{\Delta \epsilon }}={\beta }_{\epsilon }{\lambda }_B$

2.2. The Test Article: Leaf Spring Landing Gear

The TA is a 1:3 replica of a Piper PA-18 Super Cub leaf-spring landing gear (Figure 1), a single-engine high-wing tourism light aircraft. The TA’s max dimensions are 770 (width) by 325 mm (height), and the weight is 2.97 kg. The elastic architecture is particularly prone to absorbing dynamic loads at the impact.

On each leg of the TA, an FBG strain sensor is integrated as shown in Figure 2. Additionally, in Figure 2 are shown two conventional strain gauges (designated as SG3 and SG4, with the numerical value referring to the reference FBG), which were employed to substantiate the data collected by the FBGs, as detailed in Section 3.2.

2.3. The Test Set-Up (The Tower and the Soils)

Impact tests were executed utilizing a small drop tower (Figure 3a). Two metal containers were then deployed at ground level in the region where the wheels were expected to make contact with the ground (Figure 3b). The dimensions of the containers were 380 by 400 by 70 mm. These containers were used to lay out the three different impact grounds: soft with sand, intermediate with gravel, and hard, i.e., the free surface of the bottom of the containers. Within each container, an FBG was installed to detect the impact time (Figure 3c). It is imperative to note that both FBGs were placed at a safe distance from the impact area (Figure 3c), as their sole function is to detect impacts. The objective is not to quantify the level of strain recorded by the sensors on the plates during impacts; rather, it is to ascertain the moment at which the TA wheels make contact with the ground (i.e., the bottom of the container) or even the instant of the detachment of the wheels during the lift phase. This is done to facilitate a comparison with the recorded signals.

Two measurement chains, each consisting of two gratings, were prepared and integrated into the TA and the test rig. Two of the gratings (FBG1 and FBG2, Figure 3c) were attached to the containers deployed at the base of the drop tower to detect the instant of impact, while the other two (FBG3 and FBG4, Figure 2) were attached to the legs of the TA to monitor the structure’s deformation. The sensors were bonded to the outer surfaces of the steel containers and the legs of the TA using HBM Z70 cyanoacrylate adhesive. The two chains were connected to two separate channels of the Micron Optics’ SM130 Acquisition System, with an acquisition rate of 1000 Hz for the entire test campaign. Table 1 summarises the wavelengths and positions of each FBG.

To facilitate a more effective comparison of the data, the recorded wavelength shifts were converted to microstrain (με, dimensionless) using a set of equations (based on Equations (1) and (2)) embedded in the ENLIGHT measurement analysis software included with the Micron Optics sensing instruments.

3. Experimental Tests

3.1. Test Description

The tests performed consisted of a series of drops of the TA from different heights at the drop tower on different types of soils.

Three different impact heights (0.10, 0.15, and 0.20 m) (Figure 4) were considered, corresponding to three different impact velocities, as reported in Table 2.

Impacts occurred on three soil types: rigid soil (a steel plate fixed on a concrete floor), sand, and gravel, as shown in Figure 5.

The tests are performed by adopting the following procedure: For each soil, drop tests are carried out at three different heights. The first set of drops is carried out on the rigid soil, followed by the drop tests on the sand and gravel. For each set of tests, drops are performed from increasing heights, starting from 0.1 m. At each drop, the landing gear is placed at a height h from the soil, as shown in Figure 4. The height is measured to the lowest point of the TA, i.e., the bottom point of the wheel. The single experiment is then conducted by letting the landing gear drop freely, after having activated the release system; the mechanical guidance system allows the TA to follow a pure vertical descent, up to hitting the ground. When the landing gear is placed at a certain height, it is suspended. FBG sensors on the landing gear legs and the ground containers are zeroed. In other words, the reference is set as the rest condition. Indeed, weight force and thermal effects could lead the strain sensors to some deviations.

3.2. Support Data

During each test, two accelerations were measured on the drop tower slide and two strains on the test article by classical instrumentation (accelerometers and strain gauges, respectively), for a total of two acquisition channels. The acquisition frequency band was set at 1650 Hz, while the sampling frequency was set at 10 kHz, according to the applicable SAE standards. Such data were essential to give a prompt validation of the measures retrieved by the fiber optic system. In Figure 6, Figure 7 and Figure 8, as an example case, the time history of the signals representative of each cited sensor is reported, regarding the test featuring the test article dropped by 0.20 m on the three available surfaces (rigid, sand, and gravel).

These simple diagrams evidence some peculiar properties. First of all, it can be seen that the two pieces of information are strictly correlated to each other. Impact times, max excursion, rebound and free air movement, and so on are distinguishable among the couples of signals. Accelerations are instead characterized by two more features at the very beginning of the test. After the first rest segment (acceleration, a = 0), it gradually moves to the value of 1 g free-fall. The regular growth is related to the characteristic nature of the release system, which is not capable of releasing the test article immediately, but after a few seconds. Then, the free-fall follows, up to the touchdown, where a sharp variation of the acceleration does occur. The rest of the tracks are very similar; among the three drop tests, it is also easy to distinguish among the different impact surfaces, providing more (sand, gravel in sequence) or less damping (rigid plate), intended as energy dissipation capability.

4. Results

4.1. Test Results: Strain Measurements

The strain measurements retrieved by the FBG sensors placed on the soil and the falling TA show a behavior that is repeated for different drops from different heights and on different soils. The image in Figure 9 shows the strain measurements retrieved by the FBG sensors placed on the containers (indicated as 1 and 2) and on the legs of the TA (indicated as 3 and 4) vs. time. The signals are taken during the drop and the impact of the TA from a 0.10 m height on rigid soil.

As the landing gear is released, a shortfall occurs, followed by the impact to the ground, a first rebound leading to a short ascent, and so on, until the relaxation of the whole structural system. In the drop phase, the two FBGs placed on the containers do not record any signal, while the other two deployed on the landing gear start feeling the inertial force and, above all, the vibration field associated with the free fall and the sliding movement over the guides. At the impact, the sensors on the containers are dynamically excited by the impulse caused by the landing gear hitting the base, while the sensors on the landing gear retrieve the dynamic deformations generated by the same impact forces on its legs. As the landing gear rebounds and detaches from the soil, the sensors continue to record a dynamic motion, associated with the landing gear vibrations. It is relevant to say that both these oscillations refer mainly to the first eigenmode of the landing gear structure featuring two different constraints: the first, at the impact, referring to a 2-point simple supported structure, and the second, to a free structure. At the second impact, the signal resembles the first path again. The sequence is finally interrupted as the landing gear does not rebound anymore and slowly loses its energy until rest. Such a sequence is illustrated in the diagram reported in Figure 9.

In the first phase, the TA is hung on the test rig at rest, and the 4 FBG sensors record no signal coherently to the zeroing set at the start. At the impact with the ground, the sensors on the containers record the event with a sharp peak deformation, while the sensors on the trolley record the compression progress, occurring on the two legs of the landing gear with negative strain, following the way they were deployed. Since the containers are much more rigid than the TA, the strains therein measured are significantly lower. In this frame, the time history of the deformation of the containers is significantly regular, since no other relevant phenomenon occurs. Instead, the strain recorded over the landing gear shows another history: first, there is a regular compression, describing the typical movement of something elastic touching the ground and continuing its movement downwards, until the elastic forces exhaust the inertial ones. Then, the elastic forces recall the mass upwards, causing its detachment from the ground. This process occurs at a frequency about the first resonance of the object, simply supported on its wheels. As the TA loses contact with the soil, its free movement in the air starts, and it is possible to detect an insurgent vibration at a higher frequency than before. This is very close to the first frequency of the free object (i.e., without constraints to the ground). This phase is visible in the diagrams and terminates with its new contact with the ground (complete rebound). At that point, the cycle is repeated, with the difference that in this latter case, the structure does not leave the ground anymore but continues its oscillations until rest. Such oscillations occur at the same frequency as before, featuring again the landing gear simply supported on its wheels. It can be remarked that the resting phase concludes with a perceptible displacement from the zero line for all the FBG strain sensors, since the weight affects both the TA, imposing its deformation, and the containers, where the landing gear weight is transferred. A discernible discrepancy in the strain information between the two legs and the two containers is evident, attributable to variations in position for the left and right leg of the TA, as well as an imperfectly even distribution of the masses. The container exhibited discrepancies in its position, the distribution of the applied load (as the TA did not strike the ground at the same relative location as the two containers), minor variations in its structural design, and its asymmetrical deployment on the ground. Nevertheless, the retrieved data are sufficient for the aims of this investigation. The images in Figure 10 show the results of the deformation measurements for the case of drops on rigid soil from the impact heights of 0.15 and 0.20 m, respectively. The result of the drop from 0.10 m on the same ground has already been shown in Figure 9. The trend documented by the same sensor in the case of drops from three distinct heights exhibits a high degree of similarity. As might be expected, the magnitude of the peaks increases in proportion to the height of the drops. In instances of impacts at 0.15 and 0.20 m, as well as at 0.10 m, two complete rebounds are observed. That is to say, following the initial drop, the system rebounds to the ground. Before reaching a state of complete rest, during which dynamic energy is fully dissipated, the system undergoes a subsequent, shorter detachment from the ground. This phenomenon can be discerned by the presence of the two densest peaks between the largest and widest peaks, which are indicative of on-ground oscillations.

In the images reported in Figure 11, the deformation measures by the FBG sensors for drops from 0.10, 0.15, and 0.20 m on sand (right) and gravel (left) are shown, respectively. The behaviors are similar to the previous ones on rigid soil but the signals result damped significantly. For instance, it retrieved just one bounce in all the cases, but also one (0.10 m, sand) when the TA never leaves the ground after the impact. It should be observed that such an energy dissipation process mainly affects the signal coming from the sensors deployed on the containers and not the landing gear response. Sand and gravel are distributed over the surface of the containers to directly influence their vibration, but they have a minimal role in the TA dynamics. The ground materials have a poor influence on the nominal constraints of the structure under investigation. This is trivial in the case of the free movement in the air, where there is not even a minimal contact between the two items (sand or gravel vs. the landing gear legs). Instead, when the TA touches the ground, the only interface between the two elements is at the level of the wheels. Therefore, the only way for the materials deployed in the containers to contribute to the damping is to intervene in the wheels’ movement during the oscillation; this is a very small, almost negligible, contribution. While the strains measured at rest result in the same magnitude, some difference in the absolute values may be perceived. This means that the landing gear does not assume the same configuration after the different drops; this is very important as the system is intended to detect the HL condition, i.e., quantify the overall energy entering the TA at the touchdown. It follows that a suitable dense sensor network shall be sized to ensure coherent information for those aims. The design of such a map is one of the arguments that shall be faced in the next stages of the activities.

4.2. Test Results: Signal Correlation

It may be of certain interest to compare the different responses of the proposed architecture, the sensor network integrated into the TA, for a series of drops, to verify the repeatability of the tests, in case of drops with the same characteristics, or the coherence of the whole system in case of drops under different conditions, such as different heights or different soils. In this paper, cross-correlation (CC) analysis can help quantify the repeatability of the impact test or assess whether different impacts under different conditions produce consistent responses.

A high value of the CC coefficient indicates that the signals are similar. Figure 12 shows the plots of the signals from the two FBGs, sensor S3 on the left leg and sensor S4 on the right leg of the TA, recorded during three consecutive drops from 0.10 m on hard soil. The figures show the signals of the first drop (S3.1) with the blue dashed curve, of the second drop (S3.2) with the red continuous curve, and of the third drop (S3.3) with the black dashed curve. Table 3 and Table 4 show the correlation coefficient matrices of the signals for these drops. A strong similarity between repeated drops of the same height appears as a high CC coefficient. The maximum value is 1, which means that the two signals are identical, as is the case on the matrix diagonal where the signals of each sensor are correlated with themselves. Variability between impacts with the same height and on the same soil can indicate possible internal or external noise, such as changes in the structure during the impacts or environmental factors. Moreover, the sensors integrated into the TA may have errors in the positions or orientations; hence, variations in the strain wave propagation paths and arrival times at each sensor could result in low correlation coefficient values.

The reported CC of the signals related to different drops from the same height and on the same soil is generally very high, indicating a high correlation between repeated events in the same conditions, hence assessing the developed system as very reliable in detecting landings and assuring very low error in the accuracy of the sensor placement. Nonetheless, the signal of the sensor S3, particularly in the third drop, shows a trend slightly different from the two previous drops (see Figure 12a). This deviation occurs mostly in the latter part of the test, after 7 s, and is most evident when the TA is stationary on the ground, after 11 s. The third drop was expected to stabilize around the same equilibrium value, but instead, it is slightly more compressed. When the TA was checked after the last drop, it was observed that the left leg was slightly deformed at the constraint between the TA and the wheel, resulting in a difference in height of approximately 5 mm between the right and left legs and consequently a different pressure on the two wheels. The TA load weighed more on the left leg. A slight deformation of the structure resulted in a slight lowering of the CC value.

A second CC analysis was executed by comparing the drop signals of a sensor for any given height on three distinct surfaces. The ensuing results are displayed in Figure 13. Figure 13a illustrates the signals of sensor S3 from the given height of 0.10 m on the three different soils; Figure 13b is from 0.15 m, and Figure 13c is from 0.20 m. The corresponding CC matrices are provided in Table 5, Table 6 and Table 7.

The CC matrices in Table 5, Table 6 and Table 7 show a low correlation between signals related to different soils, suggesting that the strain waveforms captured by the FBGs, although similar in general appearance, are different. Impacts on different soils, which absorb the impact energy differently, generate different strain magnitudes, frequencies, and temporal patterns. The material and surface properties of the ground significantly influence the distribution and propagation of the impact forces. Some soils may exhibit nonlinear behavior, such as soft soils like sand that compress more on higher impacts, or uneven soils like gravel that compress unevenly, displace on impact, or resist more, to the same or greater extent than rigid soils. This can result in distinct deformation patterns that are less correlated between different elevations or soils. In addition, soil materials with different damping properties may dissipate energy at different rates, resulting in different characteristics of signal variation.

A third CC analysis compared the signals of a sensor for impacts on any given type of soil from three different heights.

The results are shown in Figure 14a for the drop on hard ground, Figure 14b for the drop on sand, and finally Figure 14c for the drop on gravel. The corresponding CC matrices are given in Table 8, Table 9 and Table 10. The CC matrices in Table 8, Table 9 and Table 10 show a low correlation between signals related to different heights of the drops. Impacts from different heights produce mainly different strain magnitudes and temporal patterns. This could be due to different energy levels associated with each height.

The findings from the two most recent correlation analyses demonstrate that the developed system can discern impacts from varying heights, resulting in deformations of differing magnitude, frequency, and time course, particularly on different terrains. Additionally, they underscore the significant influence that the characteristics of diverse impact surfaces exert on the distribution and propagation of impact forces.

4.3. Test Results: Fast Fourier Transform Analysis

Without loss of generality, a study was carried out on three specific signals to extrapolate what kind of detailed information can be extracted from a fast Fourier transform (FFT) analysis and to what extent. The three signals refer to three consecutive drops, recorded by sensor S3 from a height of 0.10 m on hard ground. The three signals clearly show a drop at 0.9 s, an impact at 2.3 s, a rebound at 2.8 s, and free flight until 5.0 s. During this time, the signal displays three large amplitude oscillations. There is a second impact at 5.1 s, followed by a series of rebounds until the dynamics come to a complete stop at 11 s, as shown in Figure 15. As in the previous cases, the sampling rate is 1.0 kHz. An obvious consideration is that the timing of the phenomenon is very narrow. Therefore, an acquisition aimed at one of the different phases would lead to a very coarse discretization in the frequency domain, regardless of the time resolution. The elementary relations may be recalled:

(3)$\Delta f=1/T$

where Δf is the frequency resolution, and T is the observation time, while

(4)$F=1/\Delta t$

where Δt is the temporal resolution, and F is the observable frequency range. A series of graphically synthesized analyses was then carried out in the upper figure. Details are given in Table 11.

Figure 16 and Figure 17 show the FFT results in the two examined windows. Four distinct peaks are confirmed in the various representations at the frequencies reported in Table 12, which also shows the range of variation in each analysis.

In this phase of the study, the FFT is not meant to verify the modal analysis characteristics; such an investigation deserves its own devoted publication. In this case, a further complication is associated with the co-existence of two different constraints in the observation period (namely, free–free (during floating) and simply supported (during the landing moments)). Instead, the FFT was intended as a check to verify the repeatability of the experiments. To avoid any influence on the elaboration process, it was chosen to identify two different time windows, where the contribution of the different boundary conditions could have influenced the transformed time signals in the frequency domain differently. Unfortunately, as already cited in the text, it was not possible to reduce the time window too much, otherwise the frequency resolution would have been very poor (several Hz), attaining the same magnitude of the characteristic structural system eigenvalues. Though these precautions were taken, the high decay of the signal made the peaks little discernible from the background noise, making the analysis difficult but not impossible to perform. A look at Figure 16 and Figure 17 permits easy highlighting of four different peaks, repeated all along the different analyses at the same levels. As can be observed, the background noise (the line outside the marked circles) appears much more irregular in itself and somehow different in the various FFTs.

The results are consistent: the identified eigenmodes are repeated in the three drops from the same height on the same soil, characterizing the TA both in the ground contact and in the rebound flight phase.

5. Conclusions

The objective of the activity presented here is to develop a Smart Landing Gear system capable of recording the structural response when subjected to operational loads during landings and to detect hard landing conditions on various soils with different absorbing characteristics. The SLG is an integrated system with a sensory network based on the use of fiber Bragg grating optical sensors. The focus of the experimental activities described here concerned the landings from different impact heights on different types of soils: hard soil, sand, and gravel.

This paper refers to drop tests carried out at a drop tower with the test article, an integrated leaf spring landing gear with strain sensors. The experiments aimed to validate a methodology to measure the dynamic strain field during the impact on the ground and to assess the repeatability and consistency of the acquired signals of the SLG when undergoing landings on different soils.

The strain measurements retrieved by the FBG sensors placed on the soil and the falling TA show a behavior that is repeated for different drops from different heights and on different soils.

Cross-correlation analysis is used to assess the correlation between signals for a series of the same drops, all with the same characteristics, to verify the repeatability of the tests or assess whether different impacts under different conditions produce consistent responses and to test the coherence of the whole system.

The reported CC of the signals related to different drops from the same height and on the same soil is generally very high, indicating a high correlation between repeated events in the same conditions, hence assessing the developed system as very reliable in detecting landings and assuring very low error in the accuracy of the sensor placement. Impacts from different heights produce mainly different strain magnitudes and temporal patterns. This could be due to different energy levels associated with each height. Impacts on different soils, which absorb the impact energy differently, generate different strain magnitudes, frequencies, and temporal patterns. Correlation analyses demonstrate that impacts from varying heights result in deformations of differing magnitude, frequency, and time course, particularly on different terrains. Additionally, they underscore the significant influence that the characteristics of diverse impact surfaces exert on the distribution and propagation of impact forces.

Finally, a study was carried out on three specific signals, a series of the same drops with the same characteristics, to extrapolate what kind of detailed information can be extracted from a fast Fourier transform analysis and to what extent. The identified eigenmodes from the FFT analysis are repeated in the signals related to the three drops from the same height on the same soil, showing the consistency of the results.

Author Contributions

Conceptualization, A.B.; methodology, C.V. and A.B.; software, C.V.; validation, A.B. and C.V.; formal analysis, A.C. and C.V.; investigation, M.I. and V.F.; resources, L.T. and M.I.; data curation, C.V., A.B. and V.F.; writing—original draft preparation, A.B. and C.V.; writing—review and editing, A.C.; visualization, A.B. and C.V.; supervision, L.T.; project administration, M.B.; funding acquisition, A.C. All authors have read and agreed to the published version of the manuscript.

Institutional Review Board Statement

Not applicable.

Informed Consent Statement

Not applicable.

Data Availability Statement

The data are not publicly available due to confidentiality reasons.

Conflicts of Interest

The authors declare no conflicts of interest.

Footnotes

Disclaimer/Publisher’s Note: The statements, opinions and data contained in all publications are solely those of the individual author(s) and contributor(s) and not of MDPI and/or the editor(s). MDPI and/or the editor(s) disclaim responsibility for any injury to people or property resulting from any ideas, methods, instructions or products referred to in the content.

Figures and Tables

Figure 1. The Test Article.

Figure 2. The test article: the two legs of the LG are integrated with strain sensors.

Figure 3. The test article. Installation details: (a) the test rig and the TA installed on the slit at a suitable drop height; (b) the drop tower with two containers deployed at its base; (c) detail over the two containers deployed at the drop tower base, with an FBG sensor installed in each of them. In the two containers, the impact areas of the wheels of the TA are highlighted in yellow.

Figure 4. Free-fall height, h.

Figure 5. The three different impact soils: rigid (left), sand (center), and gravel (right).

Figure 6. Time histories of the reference sensors during a 0.20 m drop test over a rigid surface: accelerations (left) and deformations (right).

Figure 7. Time histories of the reference sensors during a 0.20 m drop test over sand: accelerations (left) and deformations (right).

Figure 8. Time histories of the reference sensors during a 0.20 m drop test over gravel: accelerations (left) and deformations (right).

Figure 9. Deformation measurements of the FBG sensors for a drop test from 0.10 m on a rigid impact surface: in the first phase, the test article is suspended; then, there is the free-fall frame, up to the impact; a rebound then occurs, followed by an ascent and descent phase, up to the second impact, and finally a smooth oscillation until rest.

Figure 10. Outcome of drop tests from (a) 0. 15 and (b) 0.20 m, featuring an impact on a rigid surface.

Figure 11. On the left column, from top to bottom, are the 0.10, 0.15, and 0.20 drops on sand; on the right column are the 0.10, 0.15, and 0.20 drops on gravel.

Figure 12. Correlation graphs between three consecutive drops from 0.10 m on rigid soil related to (a) sensor S3 and (b) sensor S4. The first drop is indicated with the blue dashed curve, the second drop with the red continuous curve, and the third drop with the black dashed curve.

Figure 13. Correlation graphs between signals of sensor S3 for drops from a given height on the three different soils. From top to bottom: (a) drops from 0.10 m, (b) drops from 0.15 m, and (c) drops from 0.20 m.

Figure 14. Correlation graphs between signals of sensor S3 for drops on the same soil from three heights. From top to bottom: (a) drops on rigid soil, (b) drops on sand, and (c) drops on gravel.

Figure 15. Detailed analysis schematic and an indication of the two different analysis windows, whose description is reported in Table 11. An1 (0–16,384 ms) and An2 (2500–6596 ms).

Figure 16. Analysis no 1. FFT analyses of the signal frames are defined in Table 11. The repeated peaks are evident, even though it is not possible to distinguish among the system responses in the supported (grounded) and floating (free) conditions. The FFT analyses are related to three drops from a height of 0.10 m on a rigid soil recorded by sensor no. 3. On the left, (a–c) are the complete frequency range from 0 to 500 Hz; on the right, (a′–c′) are zoomed in from 0 to 50 Hz.

Figure 17. Analysis no 2. The FFT analyses are related to three drops from a height of 0.10 m on a rigid soil recorded by sensor no. 3. On the left, (a–c) are the complete frequency range from 0 to 500 Hz; on the right, (a′–c′) are zoomed in from 0 to 50 Hz.

Table 1

Measurement chain configuration.

Sensor Reference Number	WL (nm)	Position	Chain/Channel
FBG 1	1,530,254	Left Container	Ch1
FBG 2	1,540,333	Right Container	Ch1
FBG 3	1,549,921	Left Leg	Ch2
FBG 4	1,570,187	Right Leg	Ch2

Table 2

Drop height (h) and related impact velocity (v).

Drop Height, h (m)	Impact Velocity, v (m/s)
0.10	1.40
0.15	1.71
0.20	1.98

Table 3

Matrix of correlation coefficients for three consecutive drops from h 0.10 m on rigid soil, related to sensor 3.

	S3.1	S3.2	S3.3
S3.1	1.000	0.995	0.986
S3.2	0.995	1.000	0.996
S3.3	0.986	0.996	1.000

Table 4

Matrix of correlation coefficients for three consecutive drops from h 0.10 m on rigid soil, related to sensor 4.

	S4.1	S4.2	S4.3
S4.1	1.000	0.995	0.989
S4.2	0.995	1.000	0.997
S4.3	0.989	0.997	1.000

Table 5

Matrix of correlation coefficient signals of sensor S3 for drops from the same height of 0.10 m for three different soils: rigid soil, sand, and gravel.

	Rigid Soil	Sand	Gravel
Rigid Soil	1.000	0.437	0.477
Sand	0.437	1.000	0.989
Gravel	0.477	0.989	1.000

Table 6

Matrix of correlation coefficient signals of sensor S3 for drops from the same height of 0.15 m for three different soils: rigid soil, sand, and gravel.

	Rigid Soil	Sand	Gravel
Rigid Soil	1.000	0.695	0.721
Sand	0.695	1.000	0.987
Gravel	0.721	0.987	1.000

Table 7

Matrix of correlation coefficient signals of sensor S3 for drops from the same height of 0.20 m for three different soils: rigid soil, sand, and gravel.

	Rigid Soil	Sand	Gravel
Rigid Soil	1.000	0.696	0.743
Sand	0.696	1.000	0.977
Gravel	0.743	0.977	1.000

Table 8

Matrix of correlation coefficients for three drops on rigid soil from three different heights: h 0.10 m, 0.15, and 0.20.

	h0.10	h0.15	h0.20
h0.10	1.000	0.253	−0.033
h0.15	0.253	1.000	0.527
h0.20	−0.033	0.527	1.000

Table 9

Matrix of correlation coefficients for three drops on gravel from three different heights: h 0.10 m, 0.15, and 0.20.

	h0.10	h0.15	h0.20
h0.10	1.000	0.839	0.502
h0.15	0.839	1.000	0.765
h0.20	0.502	0.765	1.000

Table 10

Matrix of correlation coefficients for three drops on the same soil (sand) from three different heights (h 0.10 m, 0.15, and 0.20).

	h0.10	h0.15	h0.20
h0.10	1.000	0.853	0.568
h0.15	0.853	1.000	0.811
h0.20	0.568	0.811	1.000

Table 11

Description of the FFT analysis carried out on the signal reported in Figure 15.

ID	t Start(s)	t End(s)	Samples	Δf (Hz)	n → (2n)	Description
1.1	0.000	16.384	16384	0.061	14	The analysis is carried out from the first acquisition (t = 0), aiming at covering the whole phenomenon and extending the observation time at the furthest n exponent (2n)
1.2	2.500	6.596	4096	0.24	12	The focus of the analysis is on the three in-flight oscillations between the first and second impacts, extending the observation period at the furthest n exponent (2n)

Table 12

Main frequencies (eigenfrequencies): the outcome of the FFT of the signal reported in Figure 15.

Freq ID	Freq (Hz)
F1	0.2–0.9
F2	6.5–7.5
F3	16.0–17.5
F4	21.5–22.5

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