Comparative Analysis of the Load Spectra Recorded During Photogrammetric Missions of Lightweight Uavs in Tailless and Conventional Configurations

A significant increase in the use of unmanned aerial vehicles (UAVs) is observed in various fields of the civil economy; see: (Everaerts, 2008; Norasma et al., 2019; Giordan et al., 2020; Goetzendorf-Grabowski et al., 2021; Zmarz et al., 2018, as well as in the military field (Slack, 2013; Kozera, 2018). The joint use of airspace by manned and unmanned aviation makes the safety issues of the UAV operations a major problem. One of the important aspects is reliability, especially in terms of structural strength and fatigue life (Jin et al., 2013; Rodzewicz, 2012). To estimate the fatigue life, it is necessary to know the load spectra. For this reason, it is important to investigate the load spectra of various types of UAVs. It is well known that the loads in flight depend on the dynamic characteristics of aircraft, the type of maneuvers performed, and air turbulence (Leishman, 2022; Rodzewicz and Glowacki, 2020). The dynamic characteristics of the plane mainly depend on the adopted aerodynamic configuration and airframe geometry, mass characteristics, and characteristics of the installed propulsion systems. However, the behavior of the UAV in the air is the result of the entire system operation, including the aircraft and the autopilot. Both of them must be mutually integrated (in the sense of adjusting the dynamic characteristics of both subsystems), and this applies to an automatic flight in particular. It has already been investigated that the load spectrum (LS) in automatic flight differs from that of remote manual control (Glowacki and Rodzewicz, 2014). This is due to the fact that the UAV operator is deprived of stimuli in the form of feeling the acceleration, so the operator reacts mainly by observing the change in the aircraft’s position in space (i.e., the effect of integration of these accelerations over the time). Due to the lack of acceleration sensing by the UAV operator, the spectrum of loads with manual control is therefore more aggressive and causes a greater fatigue effect.

The mild spectrum of loads is associated with a calm flight and a smooth flight path. This is very important when a UAV performs a photogrammetric mission. This is both about the quality of the photos, which must not be blurred, and about keeping the axis of the camera vertical with a very small tolerance for deviations. This is especially important when the aircraft is not equipped with stabilization systems for the optical axis of the camera (Rodzewicz et al., 2017). In small planes, this is not always possible because the photogrammetry camera itself is a large load that exhausts the loading capacity of the plane. This was the case with the UAVs described in this article.

The purpose of this work is to study the differences between the load spectra of two lightweight unmanned vehicles of different aerodynamic designs (flying wing vs conventional configuration) that were used by the authors for photogrammetry missions (Zmarz et al.,· 2018). One of them is the popular flying wing X-8, for which kits are available on the market (Gryte et al. 2018). The other UAV is the PW-ZOOM – the plane designed and used for monitoring Antarctic areas (Goetzenderf-Grabowski and Rodzewicz, 2017). Although both aircraft differ from each other in terms of aerodynamics and structure, they belong to the same UAV class (having MTOM 25 kg).The data of both planes are shown in Figs. 1 and 2.

Figure 1.

Figure 2.

The differences between these two aircraft are easy to see, but what they have in common is the same photogrammetry equipment (i.e., Canon 700D camera with the GPS) and the same type of autopilot (i.e., Micropilot MP2128g). Due to the different performance levels of the two aircraft, the X-8 aircraft is used for short-range photogrammetric missions (up to 30 km), while the PW-ZOOM aircraft is used for the missions up to 330 km.

The presence on board of the MP2118g autopilot allows us to record several dozen flight parameters, including servos positions, airspeed, GPS speed, GPS position, altitude, heading, current pitch and roll, 3-axis data concerning linear and angle accelerations. All these data are stored in the autopilot memory as a log-file with the specific sampling frequency (here it was 5 Hz). This source of data allows many analyses, especially those concerning the dynamic behavior of planes and the LS, which is the focus of this study.

The signal that is necessary for the LS analysis is a_z (i.e., acceleration along the z design axis, which is oriented vertically during a normal horizontal flight). On this basis, the load factor n_z is calculated, as shown in Eq. (1): 1 nz(t)=az(t)g,wheregistheEarthaccelerationandtistime \[{{n}_{z}}\left( t \right)=\frac{{{a}_{z}}\left( t \right)}{g},\,\,\text{where}\,g\,\text{is}\,\text{the}\,\text{Earth}\,\text{acceleration}\,\text{and}\,t\,\text{is}\,\text{time}\]

The load signal n_z(t) representing a string of real numbers is then transformed into a string of discrete load levels LL(t). As a standard, 32 load levels are applied, following a standardization formula similar to that used for composite gliders or light composite airplanes (Kossira and Reinke, 1986): 2 LL=3fornz_maxandLL=31fornz_min; \[\text{LL}=3\,\text{for}\,{{\text{n}}_{\text{z }\!\!\_\!\!\text{ max}}}\,\text{and}\,\text{LL}=31\,\text{for}\,{{\text{n}}_{\text{z }\!\!\_\!\!\text{ min}}};\]

The interval LL = 3 up to LL = 31 represents the operational load range, and the n_{z_max} and n_{z_min} are extreme operating load limits. The LL = 1, 2, and 32 are reserved for the cases of incidental overloading of the aircraft beyond the operational limit.

The 3rd step of load signal elaboration consists in filtering the signal to the form local extremes chain (see Figure 3). The chain of local extremes becomes an input to the process based on the rainflow counting algorithm. The output of this process is a transfer array named the half cycle array (HC array) or full cycle array (depending on an applied algorithm (Rodzewicz, 2023).

Figure 3.

With the HC array, it is possible to derive the incremental load spectrum in the form of a chart with the values of load increments ΔLL on the horizontal axis and a cumulated number of load cycles n_C on the vertical axis (Fig. 4). The expression “cumulated” means that it is a sum of load cycles for ΔLL equal to or higher than a concerned value; for example, the number of load cycles for ΔLL = 1 is a sum of load cycles of all possible load increments. According to the standardization formula, the maximum value of ΔLL within the operational load limit is theoretically equal to 28, but usually during photogrammetry flights (which have to be very stable), the load increments are not so high.

Figure 4.

The entire signal processing process was carried out by the authors through a program written in the LabView environment.

The example of the result concerning X-8 flight data recorded as a file log20151010_125213 is shown in Figs. 5 and 6. Figure 5 contains the GPS trajectory of the flight. The green path denotes automatic control, while the blue path denotes the manual control during the take-off and landing. The chart shows the load signal and the altitude (which is added for better illustration of the course of the flight).

Figure 5.

Figure 6.

Figure 6 shows the cumulated number of load cycles n_C and the level number of load cycles n_L (representing the absolute data of load cycles for the current ΔLL value), as well as the same data but related to 1 h of flight: n_1hC and n_1hL. The chart in Fig. 6 presents the incremental load spectra (ILSs): n_C and n_L vs ΔLL.

Several analyses of the load spectra which occurred during photogrammetry flights of both UAVs: X-8 and PW-ZOOM – are described in this section. As the authors had 10 logs of X-8 flights and 23 logs of PW-ZOOM flights at their disposal – it was decided to use two approaches for PW-ZOOM logs analysis: at first, dealing only with 10 logs from the selected flights, and then dealing with all the 23 logs. The selected 10 logs concern PW-ZOOM flights performed in conditions similar to the X-8 operation conditions (good weather with stable wind up to 5 m/s without thermal gusts, conducive to generating a moderate LS).

Another aspect that was taken into account was a way of UAV control because automated control and manual control produce different LSs (Glowacki and Rodzewicz, 2013). Therefore, all analyses were conducted twice: for entire flights (covering manual control during the take-off and landing) and the part of the flights controlled by autopilot while flying along the programmed photogrammetric route using only the automated mode. All analyses are listed in Table 1.

To be able to compare the load spectra of both UAVs, the following parameters for the standardization formula were considered: 2a LL=3fornz=5andLL=31fornz=-3; \[\text{LL}=3\,\text{for}\,{{\text{n}}_{\text{z}}}=5\,\text{and}\,\text{LL}=31\,\text{for}\,{{\text{n}}_{\text{z}}}=\text{-}3;\]

It was checked before that this range of n_z variation is sufficient enough for both the X-8 and the PW-ZOOM load spectra regardless of the control mode and flight conditions.

The process of LS analysis will be explained using as an example 10 logs covering the entire flights of X-8. All the 10 flights were made at 300 m AGL over the same flat terrain in the aforementioned non-turbulent weather conditions. In the case of the analyzed logs for the entire 10 flights of X-8, the range of maximum ΔLL value variation was 6 ≤ ΔLL 19.

Basing on Eq. (2a), the incremental load spectra were derived for all the 10 flights and presented in the form of tables and charts (n_1hC and n_1hL vs ΔLL) in the same manner as the one described in Fig. 6. Next, two arrays were created in Excel. The 1st array was the n_1hL array, which contains 19 rows (each for a certain value of ΔLL) and 10 columns with the LS data (each for a certain flight). An element of this array was labeled as n_1hL_j,f, where j is the number of rows (i.e., ΔLL values) and f is an index of the flight (i.e., column number).

The 2nd array was the 1-row t array, which contains all the flight times. An element of this array was labeled as t_f. This array is of an auxiliary nature in performed calculations.

B/ LS envelope

To create the LS envelope, it is necessary to find maxima in each column of the n_1hL array (i.e., to find the maxima of n_1hL_j,f for each particular j-value). This process for ΔLL = j is described by Eqs (5) and (6). 5 n_1hL_envj=MAXf=1F(n_1hLj,f); \[n\_1hL\_en{{v}_{j}}=MAX_{f=1}^{F}\left( n\_1h{{L}_{j,f}} \right);\] 6 n_1hC_envj=∑j=Jj(n_1hL_envj); \[n\_1hC\_en{{v}_{j}}=\sum\nolimits_{j=J}^{j}{\left( n\_1hL\_en{{v}_{j}} \right);}\]

The results of calculation for the aggregated LS and the LS envelope (together with 10 ILSs from the X-8 flights) are presented in Fig. 7. The aggregated LS represents the values averaged for the whole flight session. Such LS is non-conservative because almost half of flights indicate a higher number of load cycles for particular ΔLL values in comparison with the aggregated LS. Using the aggregated LS for fatigue life calculations will result in a high risk of overestimating the result. On the other hand, the LS envelope gives conservative results because it represents the extreme values of n_1hL that occurred during the whole flight session. The chart shows that number of load cycles per 1 h differs for both curves of about 1 order for the most ΔLL values.

Figure 7.

All curves in Fig. 7 refer to the entire flights from the take-off to landing without distinguishing between the manual and automatic controlled flight fragments.

C/ Load spectra statistical analysis – equal or weighted influence of the flights

To assess the conservatism of the LS represented by the LS envelope, the load spectra based on the mean value plus 1, 2, or 3 standard deviations were examined. They were created by calculating the mean value and standard deviation (function symbols in the text: MEAN and STD) for each row of the n_1hL array.

The following example shows the procedure for the case “mean value plus 1 standard deviation” (indexed as “m+1s”). The operations are described by formulas (7) and (8):

For each ΔLL = j, 7 n_1hL_m+1sj=MEAN(n_1hLj,f)+STD(n_1hLj,f); \[n\_1hL\_m+1{{s}_{j}}=MEAN\left( n\_1h{{L}_{j,f}} \right)+STD\left( n\_1h{{L}_{j,f}} \right);\] 8 n_1hC_m+1sj=∑j=Jj(n_1hL_m+1sj); \[n\_1hC\_m+1{{s}_{j}}=\sum\nolimits_{j=J}^{j}{\left( n\_1hL\_m+1{{s}_{j}} \right)};\]

Note: To create such the LSs, an assumption was made that if the series of n_1hL_j,f values for the chosen index j contains only single non-zero data, then the sum of the mean value plus 1, 2, or 3 standard deviation will be equal to the value of the non-zero data.

The aforementioned approach assumes that each flight, regardless of its duration, has the same impact on the LS representative for the whole flight session.

In the next approach, the authors decided to check the case when the impact of each flight will depend on the time share in the entire flight session. The time-shares of all flights were summed for each ΔLL and used as the “weight coefficients” to generate the weighted load spectra representing mean plus 1, 2, or 3 standard deviations or representing an LS-weighted envelope.

The “weight coefficient” is applied to each ΔLL step and is defined by the following formula (9):

For ΔLL=j, 9 wj=∑f=1Fsgn(n_1hLj,f)∗tf/tT. \[{{w}_{j}}=\sum\nolimits_{f=1}^{F}{\sgn \left( n\_1h{{L}_{j,f}} \right)}*{{t}_{f}}\text{/}{{t}_{T}}.\]

The sgn function takes the value 0 or 1 depending on whether at least one load cycle occurred for a given ΔLL = j in flight f.

In the case of the LS-weighted envelope, the formulas (5) and (6) are modified.

Example: for ΔLL = j, 5a n_1hL_wenvj=MAXf=1F(n_1hLj,f)∗wj; \[n\_1hL\_wen{{v}_{j}}=MAX_{f=1}^{F}\left( n\_1h{{L}_{j,f}} \right)*{{w}_{j}};\] 6a n_1hC_wenvj=∑j=Jj(n_1hL_wenvj); \[n\_1hC\_wen{{v}_{j}}=\sum\nolimits_{j=J}^{j}{\left( n\_1hL\_wen{{v}_{j}} \right)};\]

where, j is an index related to ΔLL value and f is an index of the flight.

In the same manner, the formulas for the load spectra representing the weighted values of mean value plus 1, 2, or 3 standard deviations were also modified.

The results of both approaches are presented in Fig. 8.

Figure 8.

As one can see, the difference between the direct and weighted n_1hC values depends on the ΔLL and exceeds one order for higher ΔLL values. According to the P-M hypothesis, it may significantly influence the calculated value of fatigue life. The graph also shows that the LS envelope gives the results located between the lines corresponding to m+1s and m+3s – both for ILSs based on the direct and weighted values of n_1hL_j,f. This shows that instead of using the MEAN and STD functions, it is better to use the LS envelope procedure as it produces similar results, and there is no need for an exception for the case where there is only a single indication in the dataset for a given ΔLL.

The LS-weighted envelope lies in the entire range of ΔLL above aggregated LS, but for large values of n_1hC (above 200 load cycles/h corresponding to ΔLL<5), it coincides with LS envelope, while for small values of n_1hC (below 3 load cycles/h corresponding to ΔLL>10), it is very close to the aggregated LS.

Such a position of the curves means that the probability that n_1hC will exceed the value represented by LS envelope is small^* in the range of coincidences with the LS-weighted envelope, and large^* in the range where the LS-weighted envelope is close to the aggregated LS. This conclusion can be proved by the chart presented in the next section (Fig. 9) showing the development of both LS envelopes when the number of flights increases.

Figure 9.

Considering the LS representative for the flight session, and knowing that the LS envelope represents the conservative LS, while the aggregated LS represents the nonconservative LS, we can conclude that the LS-weighted envelope represents the semi-conservative LS.

Before proceeding to a full comparative analysis of the load spectra of both UAVs, preliminary analyses of the PW-ZOOM’s load spectra were performed. Because the X-8 was operated in conditions of moderate turbulence, 10 PW-ZOOM flights performed under similar conditions were selected. During those analyses, it was fully confirmed that all calculation methods used for the X-8 produced similar dependencies in the case of PW-ZOOM as well. The main difference that was found is only the range of variability for ΔLL and n_1hL values. In comparison with the X-8, the maximum ΔLL value for PW-ZOOM is about 50% lower. Also, the number of load cycles for higher ΔLL values is much lower. Generally, this means that PW-ZOOM’s flights in similar flight conditions are much calmer than those in the case of X-8 (fewer oscillations of n_z value). For this reason, for further comparative analysis, it was decided to take all PW-ZOOM flights into account – regardless of weather conditions, because the PW-ZOOM’s load range will be more similar to that of the X-8. The effect of this decision is presented in Fig. 9 in the form of the LS envelopes: normal and weighted. One can see that both the range of load variation and the number of load cycles for higher ΔLL values increased significantly for the flight session covering all the 26 flights.

Comparison of the X-8 and PW-ZOOM load spectra in photogrammetric flights was processed for two cases: entire flights (i.e., a manual take-off and landing plus an autonomic flight along the programmed photogrammetry path) and selected photogrammetry-only parts (i.e., flight controlled automatically by the autopilot). 10 X-8 flight logs and 23 PW-ZOOM flight logs were used for the analysis.

Figure 10 presents the charts representing LS envelopes and LS-weighted envelopes of entire flights of both X-8 and PW-ZOOM planes. As one can see, the range of load variations is nearly the same, but the differences of the numbers of load cycles per 1 h for the same case of curve exceed one order of magnitude. This means that the X-8 LS may produce higher fatigue wear (see next section). Figure 11 presents the same charts for the photogrammetric part of the flights only. In this case, there is a big difference in the range of load variation (i.e., the PW-ZOOM flies in a calmer way in terms of load oscillation range and number of load cycles).

Figure 10.

Figure 11.

Fragments of the load spectra in which the number of load cycles per hour is in the range of 10³ to 10⁴ coincide with the range of small oscillations of acceleration resulting from the natural dynamic characteristics of the aircraft autopilot system. This means that in addition to the traditional sources like gusts or maneuver, these characteristics affect the load factor variation.

An important dynamic feature of an aircraft designed for photogrammetric tasks is dynamic response to gust. The flight must be stable, and all oscillations caused by gusts should be effectively dumped.

In the case of “sharp edged” gusts (Leishman, 2022), the increase in the load factor can be described by the following formula: 10 Δnz=ρ2⋅SQ⋅dCldα⋅η⋅w⋅V, \[\Delta {{n}_{z}}=\frac{\rho }{2}\cdot \frac{S}{Q}\cdot \frac{d{{C}_{l}}}{d\alpha }\cdot \eta \cdot w\cdot V,\]

where ρ is air density, S is wings area, Q is aircraft mass, c_l is the lift force coefficient, is the angle of attack, w is the value of the vertical gust, V is current airspeed, and η is the gust mitigation factor.

The most important factors related to the plane are the wing loading and the dC_l/dα characteristic. To investigate the impact of the gust on both aircraft, calculations were carried out for gusts in the range 5 m/s to +5 m/s occurring at the cruising speeds of each aircraft (i.e., 70 km/h for X-8 and 100 km/h for PW-ZOOM). Due to the fact that the gust mitigation factor for the same gust value w may be different for both aircraft, the calculations were carried out for the whole range of variability of this parameter starting from 0.1 up to 1. The values of Δn_z were recalculated to the values of ΔLL.

Figure 12 shows that the influence of the gust is almost half of the PW-ZOOM case. This fact explains why the PW-ZOOM’s LS is much milder than that in the X-8.

Figure 12.

The aim of this part of the work was to check whether the differences in the dynamic behavior of both planes resulting in different load spectra translate into differences in the quality of the material obtained during photogrammetric missions. The distribution of photo-points on the Earth’s surface was adopted as a qualitative criterion because it is important for the orthophotomap production process. The term photo-point refers to the trace of intersection of the optical axis of the camera with the plane located at the height of 0-AGL (i.e., the take-off level). One PW-ZOOM flight and one X-8 flight were selected for the analysis. Both selected flights were performed in light wind to eliminate the possible influence of turbulence resulting from the flow around uneven terrain. The analysis procedure is explained for the X-8 flight (log20150630_121339). The flight altitude was 300 m. During flight, the optical axis of the camera was oscillating, as shown in Fig. 13.

Figure 13.

Photos were taken every 2 s during the flight, but only photos from the zone marked with a dashed line were selected for analysis (i.e., when X-8 flew straight along the programmed photogrammetric grid –see Fig. 14a and 14b). A two-step analysis process was applied: first, the distances between each two consecutive photo-points were calculated (Fig. 14c), and then the mean value and the standard deviation were determined for this set of distances. The standard deviation of distances between two consecutive photo-points was adopted as a measure of the photo-points dispersion. In the case of a very regular scattering of photo-points, the expected result would be close to zero. For the considered flight of X-8, the result is equal to 10.44 m. The same process applied for the PW-ZOOM flight gave the result 7.05 m. This means that the prediction that there is a relationship between the LS and the quality of the photogrammetric material has been confirmed, although this relationship is not as strong as one might expect looking at the ILS differences in Figs. 10 and 11.

Figure 14.

The purpose of this section is to compare the fatigue effect of X-8 and PW-ZOOM load spectra applied to the same structural element. In these considerations, it does not matter what element it is and how it is loaded. Only its fatigue properties are important, i.e., the number of cycles to failure at a given amplitude of the load factor variation. The considerations are based on the Palmgren–Miner hypothesis, which is applied in the classic way (see Report AFS-120-73-2 issued by EMD 1973): 11 D=∑i=1lniNi=1, \[D=\sum\nolimits_{i=1}^{l}{\frac{{{n}_{i}}}{{{N}_{i}}}=1,}\]

where i is an index of constant amplitude load block; n is a number of cycles in the load block (defined here as a load cycles having the same ΔLL value), and N is the number of cycles to failure.

The following simplifying assumptions have been made:

The number of load cycles to failure depends only on the value of the load increment ΔLL. It means that the number of load cycles to failure is the same in the cells of the HC array that lie along the selected line parallel to the zero diagonal (see gray cells in the array presented in Fig. 3). In fact, the number of cycles to failure depends not only on the amplitude of the load cycle but also on the mean value of the load cycle. However, for some structural materials, the isolines of the constant number of cycles to failure in the operating load range are near-parallel to this diagonal, which justifies the previous assumption.

The evaluation of fatigue life was performed for two cases: the LS for entire flights and the LS for the photogrammetry part only. In each case, two approaches were adopted: conservative (using the LS envelope) and semi-conservative (using the weighted LS envelope). The synthetic results of the calculations are presented in the graph in Fig. 15.

Figure 15.

As one can see, the fatigue characteristics of the material adopted for the calculations gave quite realistic results of fatigue life estimation.

The milder LS of the PW-ZOOM leads to a much greater calculated fatigue life than that of the X-8 LS for all the considered fatigue characteristics. This concerns the results of both the analysis of the entire flights and the analysis of only photogrammetric parts.