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Article

Integrated Low Electromagnetic Interference Design Method for Small, Fixed-Wing UAVs for Magnetic Anomaly Detection

by
Jiahao Ge
*,
Jinwu Xiang
and
Daochun Li
School of Aeronautic Science and Engineering, Beihang University, No.37 XueYuan Road, Haidian District, Beijing 100191, China
*
Author to whom correspondence should be addressed.
Drones 2024, 8(8), 347; https://doi.org/10.3390/drones8080347
Submission received: 15 May 2024 / Revised: 22 June 2024 / Accepted: 24 June 2024 / Published: 25 July 2024
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Abstract

:
Unmanned aerial vehicles (UAVs) equipped with magnetic airborne detectors (MADs) represent a new combination for underground or undersea magnetic anomaly detection. The electromagnetic interference (EMI) generated by a UAV platform affects the acquisition of weak magnetic signals by the MADs, which brings unique conceptual design difficulties. This paper proposes a systematic and integrated low-EMI design method for small, fixed-wing UAVs. First, the EMI at the MAD is analyzed. Second, sensor layout optimization for a single UAV is carried out, and the criteria for the sensor layout are given. To enhance UAV stability and resist atmospheric disturbances at sea, the configuration is optimized using an improved genetic algorithm. Then, three typical multi-UAV formations are analyzed. Finally, the trajectory is designed based on an analysis of its influence on EMI at the MAD. The simulation results show that the low-EMI design can keep MADs away from the EMI sources of UAVs and maintain flight stability. The thread-like formation is the best choice in terms of mutual interference and search width. The results also reveal the close relationship between the low-EMI design and flight trajectory. This research can provide a reference for the conceptual design and trajectory optimization of small, fixed-wing UAVs for magnetic anomaly detection.

1. Introduction

The use of UAVs carrying sensors is an efficient way to perceive environments in a wide range of situations [1]. In recent years, magnetic anomaly searching using UAVs has become an emerging and efficient search method. It can be applied in multiple fields, for example, underground magnetic mineral resource exploration; undersea aircraft wreckage searching, such as for MH370 [2]; and anti-submarine warfare. The characteristics of these scenes are vast mission areas and scattered and concealed targets with magnetic signals, which precisely form the purpose of combining the advantages of UAVs, such as long endurance and flexible maneuverability. As an effective cross-media magnetic anomaly detection tool [3], an MAD is not affected by the medium or any hydrological characteristics, and it has the advantages of continuous search, rapid response, and high positioning accuracy [4,5]. Among the existing search platforms, such as rotorcrafts and ships, airborne search is a more efficient, fast, and flexible method. An MAD detects the magnetic anomalies of a geomagnetic field to determine the potential locations of targets.
Small, fixed-wing UAVs have unique advantages in terms of endurance and maneuverability. With the evolution of sensor miniaturization, the application of small, fixed-wing magnetic anomaly detection UAVs is becoming possible. The usage of small UAVs carrying MADs to replace or assist traditional detection methods can liberate the latter and improve the efficiency-to-cost ratio of a search mission. In addition, the common task modes of UAVs, including single-aircraft search [6] and co-operative search via multi-UAV formations [7,8,9], can greatly enhance search abilities.
MADs measure the anomalies in a geomagnetic field to detect suspicious magnetic targets, the signal of which is usually at the nT level because of the composite materials used and small debris, whereas that of a geomagnetic field is roughly tens of μ T . Any form of interference may reduce the target’s acquisition possibility [10,11], including the largest interference source: the UAV itself. The high-frequency EMI generated by electrical equipment can be eliminated using filtering, and thus, the main EMI at the MAD comes from the airframe of a UAV with a low-frequency attribute. The EMI projection on the geomagnetic line is the actual interference at the MAD.
Over the past few decades, outstanding contributions have been made to magnetic compensation based on the Tolles–Lawson (T-L) equation [12,13] or modified T-L equation [14], and the design of a UAV can weaken the influence of the low-frequency EMI at the source, which is rarely considered. In addition, the function of magnetic compensation is limited [15] because its parameters are highly correlated, which is also called multicollinearity [16,17], making it difficult to realize unbiased estimation [18].
Considering the fact that EMI changes with the relationship between position and distance between the MAD and the UAV [19], UAV design can, therefore, be beneficial for weakening this influence. An improper sensor layout will submerge the target signal into the noise, which makes any detection invalid. In order to avoid EMI from the airframe and other electrical equipment, the MAD should be placed at a weak EMI position on the airframe, such as the tail or outer part of the wing [20,21]. The sensor layout includes not only the layout of the MAD on a single UAV but also the layout of MADs in a multi-UAV formation, where UAVs interfere with MADs. Although a multi-UAV formation with certain search strategies improves the ability of multiple MADs, an improper formation design may lead to ability reduction. In conclusion, the layout design of MADs should be seriously considered. At the same time, EMI is highly coupled with the trajectory of a UAV [19,22,23]. According to the azimuth relationship between the body-fixed frame, ∑ b , and the geomagnetic line, the EMI of the airframe at the MAD is related to the flight heading and Euler angles of the UAV [23]. Therefore, the trajectory of a UAV affects the actual EMI at the MAD.
In addition to the airframe EMI itself, the flight trajectory of the magnetic anomaly detector also needs to avoid environmental EMI as much as possible. For example, in marine magnetic anomaly detection scenarios, the complex EMI generated by ocean currents and swells [24,25] affects the planned flight altitude. Aside from that, the attitude angle oscillation caused by the complex ocean wind field will lead to dramatic changes in EMI. Consequently, flight stability is also closely related to the effectiveness of the MAD [22].
This paper focuses on reducing EMI at the MAD when searching with a magnetic anomaly signal using UAVs, and the contributions are reflected in three aspects:
(1) A UAV configuration suitable for carrying an MAD is proposed. Sensor layout and stability optimization are carried out, and the sensor layout criteria are given.
(2) For a co-operative search using multiple UAVs, the benefits of three typical formations are analyzed in terms of minimum mutual EMI and maximum detection width.
(3) The influence of the search trajectory on an MAD is analyzed, and the flight altitude, heading, and attitude are established.
The illustration of a low-EMI design method is organized as follows: In Section 2, the coupling relationship of EMI at the MAD and a UAV is modeled, and then a typical search mission profile is given. In Section 3, the detailed solution framework is proposed, including mass estimation, sensor layout design, formation analysis, and low-EMI trajectory design. In Section 4, the effects of reducing the EMI at the MAD and improving the search efficiency of MADs are verified through numerical simulation. Future developments and some experimental results are discussed in Section 5. Finally, conclusions are drawn in Section 6.

2. Modeling and Typical Profile

2.1. EMI Modeling of a UAV

In accordance with the generation mechanism of EMI, Leliak [23] divided the EMI of aircraft at the MAD into interference-related and interference-unrelated maneuvers. The EMI unrelated to maneuvers mainly comes from the low-frequency or DC EMI generated by electrified wire and the high-frequency EMI produced by airborne electrical equipment (such as switch circuits, etc.). The mutual EMI cancellation of the former can be realized using parallel or twisted wires [26], whereas the latter can be eliminated using low-pass filtering or shielding with high-permeability materials. The EMI related to maneuvers shows low-frequency characteristics, which are mainly caused by the movement of a UAV airframe in the geomagnetic field, which is difficult to eliminate using a shielding device.
In the 1950s, the T-L equation divided the airframe EMI into a permanent magnetic field B P , induced magnetic field B I , and an eddy current magnetic field. As UAVs widely use non-ferromagnetic composite materials, wing skin does not produce a closed eddy current when cutting geomagnetic lines; hence, the eddy current field can be ignored [22].
The T-L equation can be used to describe the EMI of a UAV airframe as the vector sum of the permanent magnetic field and the induced magnetic field, which can be expressed as
B = B P + B I B P = P 1 i + P 2 j + P 3 k B I = A 3 × 3 B be
where P i i = 1 , 2 , 3 are components of B P along the axes of ∑ b . B be are components of geomagnetic field B e in ∑ b . A 3 × 3 ∈ R   3 × 3 is the coefficient matrix, and its elements A i , j represent the influence of the i-axis component of the geomagnetic field on the j-axis of ∑ b .
The essence of P is the three-axis components of a UAV permanent magnetic field at the MAD, and the essence of A is the influence of the UAV ferromagnetic elements cutting geomagnetic lines during flight among the axes of ∑ b . Both of these are affected by metal parts, such as the engine, landing gear, steering gear, steel bearing, etc., and the magnetic components magnetized by a geomagnetic field. Therefore, the usage of ferromagnetic material should be reduced to weaken EMI intensity.
Due to multicollinearity, the EMI of a UAV at the MAD cannot be fully compensated, and the EMI of a UAV body will still interfere with the MAD after compensation [27]. Thus, B can be decomposed into the constant interference distributed along the three axes of ∑ b . Therefore, its projection, denoted as B M , on the geomagnetic line changes with UAV maneuvers.

2.2. UAV Motion Model

To describe the coupling relationship between EMI and a UAV, it is necessary to establish a more detailed six degrees of freedom (DoF) UAV kinematic and dynamic model. The kinematic model of a UAV can be provided using
x ˙ = V cos γ cos θ y ˙ = V cos γ sin θ h ˙ = V sin γ λ ˙ = ω y cos ψ − ω z sin ψ / cos Ω Ω ˙ = ω y sin ψ + ω z cos ψ ψ ˙ = ω x − ω y cos ψ + ω z sin ψ tan Ω
where x , y , h is the UAV position co-ordinates, V is the velocity, γ is the flight path angle, θ is the flight heading angle, ω x , ω y , ω z is the angular velocity of rotation around the airframe axis, m is the mass of UAV, and λ , Ω , ψ is the Euler angles of the UAV, which are the pitch angle, yaw angle, and roll angle, respectively.
The dynamic model of UAV can be given by [22]
m V ˙ = P cos α cos β − F D − m g sin γ m V γ ˙ = P sin α cos γ c + cos α sin β sin γ c − F W sin γ c + F L cos γ c − m g cos γ − m V cos γ θ ˙ = P sin α sin γ c − cos α sin β cos γ c + F W cos γ c + F L sin γ c ω ˙ x = M x − J z − J y ω y ω z + J y z ω z 2 − ω y 2 / J x ω ˙ y = J z M y − J y z M z + 1 + J y − J x J y z ω x ω y + J z − J x J z ω x ω z + J y z 2 ω y ω z / J y J z − J y z 2 ω ˙ z = J y M z − J y z M y + J x J y + J y 2 − J y z 2 ω x ω y + J x − J z J y z ω x ω z − J y J y z ω x ω z / J y J z − J y z 2
where γ c is the velocity tilt angle, M x , M y , M z is the moment around the airframe axis, g is gravity acceleration, P is thrust, and J is the moment of the inertia matrix of the UAV. F w , F D , F L is the aerodynamic lateral, drag, and lift forces, respectively.

2.3. Coupling Modeling of EMI and a UAV

For the convenience of quantitative analysis, the UAV EMI along the axes of ∑ b is denoted as B x , B y , and B z , which are produced by equivalent current elements ( I x d l x , I y d l y , and I z d l z ) via the Biot–Savart law. Then, the EMI acting at the MAD B M can be expressed as
B M = cos X cos Y cos Z B
where X, Y, and Z are the azimuth angles of B e in ∑ b , for which the cosine values can be expressed as
c X = c ψ c Ω − s λ s ψ s Ω c I s θ ˜ − c λ s ψ s I − c ψ s Ω + s λ s ψ c Ω c I c θ ˜ c Y = − c λ s Ω c I s θ ˜ + s λ s I + c λ c Ω c I c θ ˜ c Z = s ψ c Ω + s λ c ψ s Ω c I s θ ˜ + c λ c ψ s I + s ψ s Ω − s λ c ψ c Ω c I c θ ˜
where s and c are short for sin ( · ) and cos ( · ) . λ , ψ , and Ω are the pitch, roll, and yaw angles, respectively. I and D are the geomagnetic inclination and declination. θ is the flight heading, and θ ˜ = θ − D is the magnetic heading.
The corresponding geometry relationship is shown in Figure 1.

2.4. Typical Mission Profile

The typical flight profile of fixed-wing magnetic anomaly detection in UAVs is related to the performance characteristics of the MAD, which is roughly divided into five parts, as shown in Figure 2.
(1) MADs are deployed and are calibrated after the UAV takes off;
(2) UAVs climb to the required altitude to form formations and then cruise;
(3) The UAVs arrive at the key area where the target is suspected to exist;
(4) The altitude is lowered to expand the search range undersea, and the formation speed is slowed down;
(5) The target region is detected in “lawnmower” mode until all the suspected target locations in the area are determined.
After the task is over, the UAVs are recovered. The implementation of stages (2)~(4) is determined by the trajectory, including altitude, flight heading, and attitude, which are in accordance with Equation (5).

3. Solution Framework for Low-EMI Design

By taking marine magnetic anomaly detection as a typical scenario case, an integrated design framework is proposed, which includes four main modules, as shown in Figure 3.
The integrated design steps can be summarized into five steps:
First, based on the mission requirements, the payload mass is determined, and a reasonable cruising speed is selected to ensure the correct flight ground speed for the search.
Second, by combining the flight time requirements and the designed payload mass, the UAV gross mass iteration is carried out to obtain a converged estimated value.
Third, a MAD deployment method for magnetic anomaly sensors is proposed. The UAV layout at the cost of flight stability is optimized. Then, the UAV detailed design is carried out, including airfoil selection, wing design, etc., to match the aerodynamic design results, with the lift-to-drag ratio calculated iteratively.
Fourth, for multi-UAV collaborative searches, the EMI mutual interference, search width, and missed detections of three typical formations are analyzed.
Finally, based on the background EMI generated by the ocean, an optimal flight altitude is selected. Then, the heading and attitude of the search trajectory are optimized based on the coupling relationship between UAV EMI and the trajectory.

3.1. Mass Estimation of Gross Mass

The gross mass of the UAV, m TO , includes the empty weight m E , fuel mass m F , and payload mass m PL of the UAV, among which the empty weight includes the structural mass m S , avionics mass m EQ , and engine mass m EN of the UAV, which can be expressed as
m TO = m E + m F + m PL
It can be transferred into
m TO = m PL 1 − m E / m TO − m F / m TO
where m E / m TO is the mass coefficient of the empty UAV, and m F / m TO is the fuel mass coefficient.
(1) The estimation of the mass coefficient of the empty UAV,
m E / m TO , can be calculated based on the following empirical equation:
m E m TO = K c A m TO C K vs
where K c = 0.96 , A = 2.05 , C = − 0.18 , and K vs = 1 . 0 , which are empirical estimation coefficients [28].
(2) Estimation of the fuel mass coefficient:
The entire mission can be divided into five sections:
(i) The engine is started, preheated, and warmed up;
The starting mass is m TO , the ending mass is m 1 , and the fuel factor is m 1 / m TO .
(ii) Take off and climb to cruising altitude;
The starting mass is m 1 , the ending mass is m 2 , and the fuel factor is m 2 / m 1 .
(iii) Cruise flight;
The corresponding starting mass is m 2 , the ending mass is m 3 , and the fuel coefficient for this section can be calculated using the Breguet range equation [29]:
T cr = L / D C cr ln m 3 m 2
where T cr is the cruising flight time, and C cr is the fuel consumption rate.
Take a cruising flight duration of 13 h. When considering harsh flight conditions, the lift-to-drag ratio during cruise flight is 90% of the design lift-to-drag ratio. The fuel coefficient for the third stage is m 3 / m 2 .
(iv) Spiral and standby; The corresponding starting mass is m 3 , the ending mass is m 4 , the hovering time is 0.5 h, the lift-to-drag ratio is the design lift-to-drag ratio, and the other conditions are the same as Equation (9). The fuel coefficient for the fourth stage is m 5 / m 4 .
(v) Descend height, recover, and engine stop.
The corresponding starting mass is m 4 , the ending mass is m 5 , and the fuel factor for this section is m 5 / m 4 .
Assuming that residual fuel reserves and unusable fuel account for 6% of the total fuel mass, the fuel mass coefficient can be calculated using the following equation:
m F / m TO = 1 − ( m 1 / m TO ) ∏ i = 1 4 m i + 1 / m i / 0.94
(3) Engine mass:
The relationship between the rated power and the mass of the piston engine used in UAVs can be obtained using statistics and data fitting. Assuming that the cruising flight power is 80% of the engine’s rated power, the engine mass can be approximately estimated from the cruising flight power.
(4) Gross mass iteration:
The fuel consumption rate is calculated from the cruise flight power:
C cr = P cr η P η EN Q = m TO g V L / D η P η EN Q
where η P is the propeller efficiency, η EN is the engine efficiency, V is the cruise velocity, and Q is the fuel calorific value ( MJ / kg ).
Then, iteratively solve Equation (7) using an initial value of m TO , which is combined with the selection of the engine, and finally, the estimated mass of the entire aircraft and its mass distribution results can be obtained.

3.2. Sensor Layout Design

When considering EMI and stability, the MAD should be deployed in a position where flight stability is guaranteed and EMI is weak. Most of the existing UAVs locate sensors in their nose or belly, which will lead the sensor to suffer strong EMI and vibration. In addition, placing the MAD on the wing tip or tail will bring challenges to trim and stability. If it is always hanging down, it is not conducive to launching or landing, and it will also bring difficulties to the structural design.
When taken together, this paper proposes an ingenious MAD layout in which the MAD is connected to the fuselage through a rotatable probe rod. The MAD is stored at the rear to facilitate UAV storage and launch. After the UAV takes off, its rod unfolds and hangs down. The layout not only keeps the MAD away from the EMI sources but also locates the center of gravity (CG) of the UAV further down, which is beneficial to flight stability. In addition, when the aerodynamic angles are disturbed, an additional damping moment is generated by the sensor mass, which promotes the rapid decay of the oscillation.
In this layout, the position of the MAD can be described by the length of the probe rod and its connection position on the fuselage. It is necessary to optimize the parameters to minimize the change in the inertia moment during deployment while ensuring stability and improving safety.
When ignoring the rod’s mass, the mass of a UAV without an MAD is denoted as M, and the MAD mass is denoted as m. As shown in Figure 4, the mass distribution is simplified into two mass points.
A UAV rotates freely around its CG. At the beginning of a deployment, the CG is located at MAC w / 4 , and we set it to ( 0 , 0 ) ; MAC w is the length of the wing’s average aerodynamic chord. The co-ordinate of M is ( − x 1 , 0 ) , whereas that of m is ( x 2 + l , 0 ) . They satisfy the following conditions:
M x 1 + m x 2 + l = 0 I y ϑ = 0 = M x 1 2 + m x 2 + l 2
where I y is the longitudinal moment of inertia of the UAV, and ϑ is the azimuth of the probe rod.
When the MAD deflects the ϑ angle downward slowly and uniformly, the CG meets the following:
M x 1 + m x 2 + l cos ϑ = M + m x CG ϑ M x 1 + m − l cos ϑ = M + m y CG ϑ
Then, the longitudinal moment of inertia around the CG can be written as
I y ϑ = M r M 2 ϑ + m r m 2 ϑ r M ϑ = x 1 − x CG ϑ 2 + y CG 2 r m ϑ = x 2 + l cos ϑ − x CG ϑ 2 + l sin ϑ + y CG ϑ 2
When taking flight safety into account, x f , the available position of the CG ranges from − MAC w / 8 to 0. Therefore, when MAD deployment is completed, the CG should meet x f ≤ x CG π / 2 ≤ 0 . When the MAD is not equipped, a UAV should still fly with x f < x 1 < 0 . In order to minimize the EMI at the MAD, l should be optimized to reach the maximum value ( f 1 ), and the minimum average change rate of I ϑ should be ensured ( f 2 ), which can be expressed as
f 1 = max l f 2 = min 0 ≤ ϑ ≤ π 2 ∂ I y ϑ / ∂ ϑ
During deployment, lateral stability is enhanced due to the decrease in y CG .

3.3. Flight Stability Design of a UAV

The low-level ocean wind field changes rapidly, and its continuous wind and wind shear lead to sudden changes in airspeed and aerodynamic angles [30], which brings great challenges to the longitudinal stability of a UAV. For the UAV to avoid stalling and spinning due to a bad wind field, it is essential to further ensure UAV longitudinal stability.
Ignore the aerodynamic drag of the MAD. The wing area, S w , the position of the CG x cg , the tail arm length l ht , and the horizontal tail installation angle, I ht , are selected as the design variables. The static stability of the UAV in steady flight is taken as the optimization cost function, which is expressed as
min J = κ 1 J sm + κ 2 J pm
where κ 1 , 2 are weight coefficients, and J sm and J pm are the static stability margin and pitching moment, respectively.
The static stability margin, J sm , can be expressed as [31]
J sm = x cg MA C w − C L α X ¯ acw − η ht C L ht α S ht S w X ¯ acht C L α + η ht C L ht α S ht S w
where C L α is a derivative of the lift coefficient to the angle of attack (AoA). X ¯ acw and X ¯ acht are the normalized positions of the wing and horizontal tail aerodynamic center, respectively. η ht is the ratio of the dynamic pressure of the tail to the free flow pressure, which characterizes the airflow characteristics of the tail, and its typical value is 0.9 for optimization [28]. C L ht α is the derivative of the tail lift coefficient with respect to the AoA. S ht and S w are the wetted areas of the horizontal tail and wing.
The pitching moment, J pm , can be expressed as [31]
J pm = η ht q S ht 1 − ∂ ε / ∂ α C L ht α α ht S ht l ht S w MA C w + q S w C mw + m g l sin α
where q is the dynamic pressure. C mw is the pitching moment coefficient, which can be estimated from the pitching moment coefficient of the two-dimensional airfoil C m 0 _ airfoil , the aspect ratio A R , and the sweep angle Λ [28]. ∂ ε / ∂ α = 1.62 C L α / π A R is the derivative of the downwash angle to the AoA. α ht = I ht is the AoA of the horizontal tail in steady flight.
The optimization constraints include (1) the upper and lower bounds of the design variables and (2) the lift of the whole aircraft, which should be greater than its gravity. The lift margin can be expressed as
Δ L = q S w C L w + η ht q S ht C L ht α α ht − M + m g
where C L w is the lift coefficient of the wing.
To cope with the above-mentioned problem, a genetic algorithm based on a disaster mechanism (DM-GA) was designed. We have discussed this method in our recent work [31], which demonstrates superior optimization performance. An intuitive explanatory diagram of DM-GA is shown in Figure 5.
In UAV configuration optimization, the variables are wing area S w , CG position x cg , length of tail arm l ht , and the installation angle of horizontal tail I ht . Their coding type for chromosomes is real coding, and the problem is carried out in the solution space of the real number field.
For each generation, after selecting the elitists as the parents, the two-point crossover method is adopted to generate new individuals. Then, probability-based mutation measures are used to increase gene diversity.
When a densely distributed group of individuals appears in a certain generation, disaster occurs; (1) some individuals in the group are eliminated to reduce the proportion of the gene in the entire population. (2) A population-wide mutation operation with a high probability of mutation is performed simultaneously. This criterion can be written as
J a v g ≥ Ξ J max
where J a v g and J max are the average and maximum fitness of a certain generation, respectively. 0.5 < Ξ < 1 is a density factor that characterizes individual concentration.
In the actual optimization process, among those individuals with fitness exceeding Ξ J max , the top a % are considered to have survived the disaster, while the rest are eliminated. The missing individuals are supplemented by individuals with fitness not exceeding Ξ J max , with a high probability of mutation. In the new round of the genetic search process, for the old population of individuals who survived the disaster due to their good or suboptimal fitness, they will provide guidance on convergence trends for the search for a new population of individuals.
To sum up, the DM-GA can avoid becoming stuck in local optima using the disaster mechanism, and this prevents the process from becoming a simple or completely random search.

3.4. Formation Design of Multi-UAVs

The formation affects the layout and performance of multiple sensors [32], including mutual EMI and maximum detection width. In this section, three typical formations in Figure 6 are analyzed.
Formations (a) and (c) are isosceles triangles in the horizontal and vertical planes, respectively, whereas formation (b) is thread-like in the airspace. φ is the formation angle.
B j i denotes the EMI at the MAD, j, in formation (i), which can be expressed as
B j a = cos X cos Y cos Z B j
We assume that the target can be enveloped by a sphere of radius r. The influence of formation on the maximum detection width is shown in Figure 7.
For formation (a) in the horizontal plane, the maximum detection width, d a , should ensure that the target is not missed, which can be expressed as
l I a = 4 R r / cos φ d a = 8 R r
where l I a is the distance between UAV 1 (or 3) and 2, and R is the effective MAD detection range.
Similarly, the shape of formation (c) in the vertical plane satisfies
l I c = 2 r sin φ + 2 R r cos φ − R sin φ d c = 2 l I c cos φ φ ∈ 0 , arctan r / R r
When φ = 0 , formations (a) and (c) degenerate into formation (b).

3.5. Design of Flight Trajectory with Low EMI

3.5.1. Flight Altitude Design with Minimum Ocean Magnetic Field

Ocean swells and currents can be regarded as macroscopic motions of abundant charged particles. For the size of a UAV, the current can be considered to be a moving electrified body with finite thickness and infinite length [24], and its electromagnetic field is
B oc = − 1 2 σ μ 0 V oc B e z d oc
where σ is the seawater conductivity, μ 0 is the vacuum permeability, V oc is the velocity of the current, B e z is the vertical component of geomagnetism, and d oc is the current thickness.
The background magnetic field that is excited by swells in the atmosphere can be expressed as
B x = 1 4 i A β 2 k h − 1 exp − k h B z = 1 4 A β 2 k h + 1 exp − k h h < 0 , i n t h e a t m o s p h e r e
where i = − 1 , A = a k B e sin I + i cos I cos θ oc , a is the swell height, β = μ 0 σ g 2 / ω 3 , k = ω 2 / g is the angular wave number, ω is the swells’ dominant frequency, and g is the acceleration of gravity.
It is assumed that swells represent the superposition of numerous random waves on the current surface, the spectral function of which is unimodal [25]. Therefore, the swells can be equivalent to a simple harmonic, with the frequency of the spectral peak as its angular frequency.
However, the detection range of an MAD is limited. Increasing UAV height means shortening the detection range of the underwater part and the attenuation of the target’s weak magnetic signal. On the contrary, reducing flight height means the enhancement of the target’s signal, but it also makes the MAD suffer enhanced ocean EMI. This creates a contradiction in the altitude design of the trajectory.

3.5.2. Heading and Attitude Design of a UAV

In accordance with Equation (5), the EMI generated by a UAV at the MAD is not only related to the magnetic parameters of the T-L equation itself but is also closely related to the geomagnetic coefficients and trajectory parameters, including heading and attitude.
When UAVs search the area stably, Equation (5) is approximated using a small angle assumption:
c X c Y c Z = A I , θ ˜ λ Ω ψ + B I , θ ˜ A I , θ ˜ = 0 c I c θ ˜ − s I s I − c I s θ ˜ 0 − c I c θ ˜ 0 c I s θ ˜ B I , θ ˜ = c I s θ ˜ c I c θ ˜ s I T
The influence of heading and attitude on cos ( X , Y , Z ) is expressed more intuitively by Equation (26). For the same target region, θ will affect θ ˜ . Moreover, when a UAV descends its altitude for close reconnaissance, an inappropriate pitch angle may lead to different EMI amplitudes, resulting in the loss of the target signal. Consequently, it is crucial to arrange a suitable pitch angle range when descending according to the characteristics of the MAD.

4. Design Example and Results

The mission requires a total flight time of 14 h, with an effective cruise of no less than 13 h. The payloads include the MAD (2 kg) and other devices, totaling 10 kg. The power system uses aviation kerosene and dual-cylinder two-stroke piston engines. The minimum ground speed for search is 100 km/h (27.7 m/s), and the maximum climbing speed is 5 m/s. Moreover, it should be able to withstand a level 5 sea state, where the swell height is about 4 m and the wind force is level 6. The values of the other design parameters are shown in Table 1.
Considering the fact that the wingspan is larger than its length, this paper assumes that I x d l x = 30 I y d l y = 30 I z d l z = 30 I U d l U , where I U d l U is the equivalent current element.
The geomagnetic declination angle is D = π / 36 , and the inclination is I = π / 3 in the mission area. It is assumed that the target radius is r = 10 m and the effective detection range is R = 500 m.
A note of caution is due here. Considering the harsh flight environment, the design value of the lift-to-drag ratio is conservatively selected as 10. To ensure a certain effective search ground speed under level 5 sea conditions, a cruising flight speed of V = 40 m/s is selected when there is no wind.

4.1. Overall Scheme and Parameters of a UAV

4.1.1. Configuration and Layout

As shown in Figure 8, for the sake of long endurance flights with lower drag, the configuration adopts a bi-tail-boom and gull-wing layout; the stiffness of this structure is better than that of a conventional layout under the same amount of materials.
The gull-wing layout not only maintains the internal connectivity of the fuselage but also lowers the CG and, thus, enhances flight stability. The dihedral angle of the inner wing will reduce the static derivative and increase lateral static stability. For the sake of avoiding the Dutch roll caused by excessive lateral stability and improving flight performance, the outboard wing is designed to have an inverted dihedral [33].

4.1.2. Mass Estimation and Aerodynamic Parameters

When combined with Figure 2 and the corresponding velocity requirements of profile [34,35], the wing load is designed to be 25 kg / m 2 . The fuel coefficient method [28] is used to iteratively estimate the gross mass of the aircraft.
The fitting results between the rated power and piston engine mass are shown in Figure 9.
During the iteration process, we have m 1 / m TO = 0.98 , m 2 / m 1 = 0.96 , m 3 / m 2 = 0.7847 , m 5 / m 4 = 0.9916 , and m 5 / m 4 = 0.985 . Then, it can be obtained that m F / m TO = 0.2966 . The mass distribution is obtained accordingly, as shown in Table 2.
In the conceptual design stage, Clark Y was selected as the wing airfoil, and the symmetrical airfoil NACA 0009 was selected as the tail airfoil. It is assumed that the 1/4 of the chord length of the wing root is the aerodynamic focus. In addition, thrust passes through the mass center of the whole aircraft. Other constant parameters are shown in Table 3.
The relationship between the relevant parameters of the UAV is shown in Figure 10, Figure 11 and Figure 12.
As shown in Figure 10, the gross mass increases with the cruising duration and payload mass. However, the cruising time has a greater impact on the gross mass than the payload mass.
When the payload is 17 kg and cruises for 13 h (the same as RQ-21 UAV [36]), the estimated gross mass is 57.2 kg, which is close to the mass of RQ-21 (61 kg), indicating the rationality of the design process.
As shown in Figure 11, the proportion of fuel mass increases with cruising duration and is not closely related to the payload mass.
As shown in Figure 12, the proportion of UAV structural mass first increases rapidly with the increase in cruising duration and payload mass; then, it tends to flatten, and the ratio of the total aircraft mass tends to be a constant value of 33%.
So far, the relationship between UAV mass, the proportion of fuel-to-structural mass, cruising duration, and payload mass has been obtained, which can provide a reference basis for the design of small, fixed-wing magnetic anomaly detection UAVs.

4.2. Low-EMI Design Results for a UAV

4.2.1. Results of the Sensor Layout Design

After optimization, I y is a constant independent of ϑ , which is expressed as
I y = M m l 2 M + m
Now, l max = [ ( M + m ) / ( 8 m ) ] MAC w and x 1 = x 2 = − MAC w / 8 . This indicates that the reasonably designed MAD layout can realize that the (1) MAD is farthest from the fuselage, (2) I y does not vary with the CG, and (3) longitudinal flight stability is maintained during MAD deployment.
The design results also give the intuitive placement criteria of the probe rod, i.e., the rotation axis of the rod should be placed under the CG of the UAV when the MAD is not equipped.

4.2.2. Results of Flight Stability Design

In UAV configuration optimization, the variables and their domains are as follows: the wing area is S w ∈ [ 1.5 , 2.0 ]   m 2 , the CG position is x cg ∈ [ − 0.3 , 0.3 ]   m , the length of the tail arm is l ht ∈ [ 0.8 , 1.5 ]   m , and the installation angle of the horizontal tail is I ht ∈ [ − 3.0 ° , − 1.0 ° ] .
The proposed DM-GA was used to optimize the configuration, and a classical GA was used as a comparison. For both algorithms, the maximum number of generations was 400, the population was 50, and the weight coefficient was κ = [ 0.6 , 0.4 ] T . As for the disaster mechanism, the survival proportion was set to a % = 20 % .
After optimization, S w = 1.59   m 2 , X cg = 0.142   m , l ht = 0.985   m , and I ht = − 2.96 ° . Through optimization, the longitudinal static stability was enhanced while meeting the lift demand of the UAV. The optimization process converges gradually, as shown in Figure 13.
By comparing DM-GA to a classical GA, it can be found that DM-GA is superior to the classical GA.
(1) In terms of fitness, under the same population size, DM-GA and the classical GA can achieve almost the same static stability margin. However, DM-GA can achieve better pitch moment results, therefore achieving better longitudinal stability.
Although the disaster mechanism causes more fluctuations in individual fitness during the optimization process, it precisely reflects the advantage of avoiding local optima.
(2) As for convergence efficiency, DM-GA requires fewer generations than the classical GA. This is because genetic algorithms have high optimization efficiency in the initial stage and can generate good individuals. Those who survive the disaster play a guiding role in the convergence of the entire population, which improves the overall efficiency of the algorithm.
Once the layout optimization is completed, the moment of inertia of the UAV without an MAD can be roughly estimated through the empirical distribution of the mass in the airframe, which is J x , J y , J z , J y z = 2.691 , 1.392 , 2.769 , 1.303   kg · m 2 .
In Equation (3), the relationship between the AoA and C L , C D , and the pitch moment coefficient, C m , as well as the lift-to-drag ratio, C L / C D , and efficiency, C L 3 / 2 / C D , is shown in Figure 14a,b. The relationship between the sideslip angle, β , and the lateral force coefficient, C W , roll moment coefficient, C n , and yaw moment coefficient, C l , is shown in Figure 14c.
In the range of available AoAs, the lift coefficient is linearly related to the AoA and meets the lift demand. The pitching moment coefficient is linearly related to the AoA, with C m 0 = − 0.1246 and C m α = − 0.0339 . It shows that the UAV has strong stability when the AoA changes suddenly due to gusts, which meets the design requirements in the conceptual design stage.

4.3. Results of the Formation Design

Figure 15 shows the formation analysis in stable flight.
The range of φ of formations (a) and (b) is much larger than that of formation (c). Within the range of the available φ of formation (c), the mutual interference between formation (a) and (c) is similar, whereas that of formation (b) is the least. The reason is that the UAVs in formation (b) are collinear along the wingspan, and the EMI generated by I x d l x is 0.
The maximum detection width of formations (a) and (b) is equal, which is 1565.7 m. In order to keep the formation in the vertical plane compact, the distance between UAV1 and UAV3 decreases with the increase in UAV2 height, which reduces the search width. Therefore, the maximum detection width of formation (c) decreases with the increase in φ .
In conclusion, with regard to EMI and the detection width among UAVs, the thread-like formation (b) is the best for multi-UAV searches.

4.4. Trajectory Design

4.4.1. Selection of Flight Height

The EMI generated by the ocean was analyzed, as shown in Figure 16. It is assumed that the current thickness is 100 m and the velocity is 2 m/s.
When the main peak heights of the swell spectrum are 3 m, 4 m, and 5 m, respectively, the peak frequencies are all π / 5 . The EMI generated by the current is 9.39 nT. The EMI produced by the swells will still be around 0.2 nT at 100 m, and the higher the swell is, the stronger the EMI intensity will be.
When the main wave peak is 4 m, and the peak frequencies are π / 2 , π / 5 , and π / 10 , respectively, the more intense the swell fluctuation is, the stronger the EMI will be. Moreover, the EMI is equivalent to the target’s magnetic signal at the height of 100 m.
This indicates that the better the sea condition is, the lower the flight altitude for close reconnaissance is. When considering Table 1, the flight altitude should not be less than 100 m.

4.4.2. Heading and Attitude

The compensated T-L equation parameters in Zhang and Lin [37] were selected for simulation.
P = 7.56 , 1.74 , 0.25 T A = − 1.50 − 4.90 − 0.82 − 0.28 2.14 − 1.53 − 0.30 − 1.78 − 0.29
When the UAV flies steadily (Euler angles are all 0) and θ ∈ [ − π , π ] , the B M of the single UAV is as shown in Figure 17a, which is similar to the sine curve. There are two heading angles ( θ 1 * = − 2.98   rad and θ 2 * = − 0.22   rad ), which can make B M = 0 . When the UAV flies back and forth at heading angles of θ 1 * and θ 2 * , it searches the target area in the “lawnmower” mode. When combing the UAV motion models (Equations (2) and (3)), B M will theoretically be zero all the time, as shown in Figure 17b.
In stage (4) of the profile, λ descending will affect the EMI at the MAD. The influence of pitch angle when λ ∈ [ − π / 12 , π / 12 12 ] is simulated, and the result is shown in Figure 18.
When θ = θ 2 * , the average EMI is lower, which also confirms the discussion of the heading in Figure 17a. On the other hand, the pitch angle of the UAV is approximately proportional to B. Therefore, the UAV should choose a pitch angle that is as small as possible to descend smoothly to avoid contact interruption between the MAD and the target.

5. Discussion

It should be noted and emphasized that the design of magnetic anomaly detection UAVs, indeed, requires complex and comprehensive system engineering.
Although this paper takes marine magnetic anomaly detection as a typical scenario case, in fact, all aviation magnetic anomaly detections have similar general requirements, such as longitudinal stability and flight trajectory, rather than being limited to the specific case in this paper. This is because aviation detection needs to maintain flight stability, i.e., the stability requirement for the measurement line. Moreover, aviation magnetic anomaly detection requires the additional avoidance of aircraft EMI and background EMI.
According to the incomplete measurements and experiments at the current stage, the main source of airframe EMI is the magnetization of the metal airframe components from the geomagnetic field and their movement when cutting geomagnetic lines. These metal components mainly include the piston engine, landing gear, metal connectors, fasteners, etc. In addition, commonly used alloys containing 8% to 14% nickel, such as can be found in certain screws and nuts, can amplify magnetic disturbance. Therefore, the application of advanced, nonmetallic materials in the future may reduce airframe EMI intensity. Meanwhile, a matching EMI model also needs to be developed.
The purpose of aviation magnetic anomaly detection trajectory planning, whether flying over the ocean or on land, is to minimize the magnetic disturbance of the environment and airframe on the MAD while completing the mission area search. Usually, the higher the flight altitude, the smaller the background EMI. However, at the same time, the weaker the magnetic anomaly signal of the target, the smaller the detection range underwater or underground. Sometimes, the frequencies of the two are even similar. The notion of this paper is to consider background EMI to select a proper flight altitude and then design the search trajectory. In fact, it is a method of compromise in terms of reducing or decoupling a three-dimensional (3D) trajectory into a 2D plane trajectory and a 1D altitude, taking into account the fact that 3D trajectory comprehensively requires prior information on background EMI in mission areas.

6. Conclusions

Small UAVs carrying MADs for magnetic anomaly signal search tasks are effective, but the EMI produced by UAVs and the environment affect the efficiency of the MAD. This paper focuses on the low-EMI technology of small, fixed-wing magnetic anomaly search UAVs, including sensor layout design, stability optimization, multi-UAV formation selection, and flight trajectory design. In this paper, a deployable sensor layout based on a gull-wing configuration is proposed, and its stability is optimized, which can not only reduce EMI at the MAD but can also enhance the flight stability of the UAV. Multi-UAV co-operation can improve search efficiency, and the thread-like formation can effectively avoid the EMI among aircraft and ensure maximum detection width. In addition, the trajectory has a great influence on the efficiency of the MAD. Flight altitude should be selected according to sea conditions to avoid marine EMI. Reasonable flight heading selection can greatly reduce the EMI of the UAV platform at the MAD. When UAVs descend to detect an area closely, flight altitude should be emphasized, and the pitch angle should be small and change slowly.
In the future, optimum layout and trajectory designs can be further improved and made more reliable by refining the EMI model. The design of small-volume storage and fast delivery/retrieval will also contribute to the rapid application of such UAVs to civilian and even military domains.

Author Contributions

Conceptualization, J.G. and J.X.; methodology, J.G.; software, J.G.; validation, J.G., J.X. and D.L.; formal analysis, D.L.; investigation, J.G.; resources, J.G.; data curation, J.G.; writing—original draft preparation, J.G.; writing—review and editing, D.L.; visualization, D.L.; supervision, J.X.; project administration, J.X.; funding acquisition, J.G. and J.X. All authors have read and agreed to the published version of the manuscript.

Funding

This research is supported by the Postdoctoral Fellowship Program of CPSF under Grant Number GZC20233371.

Data Availability Statement

The data presented in this study are available upon request from the corresponding author due to legal reasons.

Conflicts of Interest

The authors declare no conflicts of interest.

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Figure 1. Basic geometry of EMI and a UAV. (a) Geometry of the azimuth angles. (b) Geometric coupling relationship.
Figure 1. Basic geometry of EMI and a UAV. (a) Geometry of the azimuth angles. (b) Geometric coupling relationship.
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Figure 2. Flight profile of a small, fixed-wing magnetic anomaly detection UAV.
Figure 2. Flight profile of a small, fixed-wing magnetic anomaly detection UAV.
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Figure 3. Design framework of a small, fixed-wing magnetic anomaly detection UAV.
Figure 3. Design framework of a small, fixed-wing magnetic anomaly detection UAV.
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Figure 4. The process of MAD deployment.
Figure 4. The process of MAD deployment.
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Figure 5. Diagram of DM-GA.
Figure 5. Diagram of DM-GA.
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Figure 6. Classic multi-UAV formations.
Figure 6. Classic multi-UAV formations.
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Figure 7. Geometry of the formations.
Figure 7. Geometry of the formations.
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Figure 8. Configuration of a small, fixed-wing magnetic anomaly detection UAV.
Figure 8. Configuration of a small, fixed-wing magnetic anomaly detection UAV.
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Figure 9. Fitting curve of engine mass.
Figure 9. Fitting curve of engine mass.
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Figure 10. Relationship between UAV mass estimation, cruise duration, and payload mass.
Figure 10. Relationship between UAV mass estimation, cruise duration, and payload mass.
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Figure 11. Relationship between UAV fuel mass ratio, cruise duration, and payload mass.
Figure 11. Relationship between UAV fuel mass ratio, cruise duration, and payload mass.
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Figure 12. Relationship between UAV structural mass ratio, cruise duration, and payload mass.
Figure 12. Relationship between UAV structural mass ratio, cruise duration, and payload mass.
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Figure 13. Optimization process and results.
Figure 13. Optimization process and results.
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Figure 14. Main aerodynamic parameters. (a) AoA-related parameters. (b) Lift-to-drag ratio and efficiency. (c) Sideslip angle-related parameters.
Figure 14. Main aerodynamic parameters. (a) AoA-related parameters. (b) Lift-to-drag ratio and efficiency. (c) Sideslip angle-related parameters.
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Figure 15. Mutual interference analysis of MAD formation.
Figure 15. Mutual interference analysis of MAD formation.
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Figure 16. Distribution of ocean magnetic field with height.
Figure 16. Distribution of ocean magnetic field with height.
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Figure 17. Low EMI search trajectory design. (a) Effect of heading on EMI. (b) Search trajectory in “lawnmower” mode.
Figure 17. Low EMI search trajectory design. (a) Effect of heading on EMI. (b) Search trajectory in “lawnmower” mode.
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Figure 18. Effect of pitch angle on EMI.
Figure 18. Effect of pitch angle on EMI.
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Table 1. UAV design parameters.
Table 1. UAV design parameters.
ParameterValue
UAV parametersPropeller efficiency0.8
Engine efficiency0.3
Fuel calorific/(MJ/kg)42.9
Sensor detection width/m1000
Payload mass/kg10
MAD/kg2
AerodynamicsLift–drag ratio10
Wing load/( kg / m 2 )25
Sea condition (level 5)Wind speed/(m/s)10.8~13.8
Table 2. Iteration results of UAV mass.
Table 2. Iteration results of UAV mass.
Mass CompositionMass/kgRatio-to-Gross Mass/%
fuel mass11.2129.66
empty weightstructure12.5833.28
piston engine25.3
onboard equipment25.3
subtotal16.5843.88
mass of pay loads1026.46
gross mass37.79100
Table 3. Designparameters.
Table 3. Designparameters.
ParameterValueParameterValue
aspect ratio (AR)16 η ht 0.9
taper ratio (TR)0.8 C L w α 0.096
AR of horizontal tail7 C m 0 _ airfoil − 0.1
TR of horizontal tail1volume of horizontal tail0.5
∂ ε / ∂ α 0.033volume of vertical tail0.1
C L ht α 0.075air viscosity 1.789 × 10 − 5
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Ge, J.; Xiang, J.; Li, D. Integrated Low Electromagnetic Interference Design Method for Small, Fixed-Wing UAVs for Magnetic Anomaly Detection. Drones 2024, 8, 347. https://doi.org/10.3390/drones8080347

AMA Style

Ge J, Xiang J, Li D. Integrated Low Electromagnetic Interference Design Method for Small, Fixed-Wing UAVs for Magnetic Anomaly Detection. Drones. 2024; 8(8):347. https://doi.org/10.3390/drones8080347

Chicago/Turabian Style

Ge, Jiahao, Jinwu Xiang, and Daochun Li. 2024. "Integrated Low Electromagnetic Interference Design Method for Small, Fixed-Wing UAVs for Magnetic Anomaly Detection" Drones 8, no. 8: 347. https://doi.org/10.3390/drones8080347

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