Research on Integrated Optimization Design Method of High-Efficiency Motor Propeller System for UAVs With Multi-States

With the popularity of electric multi-rotor unmanned aerial vehicles (EMRUAV), the problem of low efficiency of the motor propeller system (MPS) becomes serious especially for EMRUAVs which have multiple working states. To solve this problem, an integrated optimization design method for high-efficiency MPS is proposed using an improved parallel particle swarm optimization and differential evolution (PSODE) hybrid algorithm. First, the brushless motor as well as the variable-speed and the adjustable-pitch propellers is modelled. Then considering the characteristics of the motor and the propeller sufficiently, an integrated optimization method for variable-speed and adjustable-pitch MPS is proposed by utilizing the improved PSODE. Specially, the self-organizing feature map theory is added to substitute the traditional “winner-take-all” method in the interactive study of the improved PSODE. Next, the optimization of a small electric-powered tilt quad rotor (TQR) which has four states: hovering, cruising, transition and maximum speed is carried out. At last, the wind-tunnel experiments are implemented to verify the feasibility and effectiveness of the proposed optimization method. The results indicate that the adjustable-pitch MPS is more suitable for EMRUAVs which have multiple working states, and that the improved PSODE has faster convergence speed and better global search ability than other optimization methods.


I. INTRODUCTION
The electric multi-rotor unmanned aerial vehicles (EMRUAV) have been used widely throughout the world [1]- [3]. However, such EMRUAVs behave badly in endurance and loading capacity which limits the expansion of their application fields [4]. One of the reasons is the low efficiency of their motor propeller systems (MPS) [5]- [7]. For small electric tilt-rotors and tailsitters, the problems become more serious because they have multiple working states where the MPS should always keep high efficiency. Thus an integrated optimization design method for MPS which can take the characteristics of the motor and propeller into consideration is necessary.
There are two main methods for motor modelling. One is the equivalent circuit model, and the other is the positive The associate editor coordinating the review of this manuscript and approving it for publication was Zhong Wu . polynomial loss model [5]. The former is simple and intuitive, but it does not consider motor losses. The latter can compute the actual motor efficiency relatively accurately [8], however, some of its parameters have to be obtained by experience or experimental tests, which will extend the design cycle. For propeller modelling, blade element method is the simplest, but it can not simulate the radial distribution of induced velocity. The computational fluid dynamic (CFD) method can simulate the working state of the propeller better, but the calculation period is too long. Vortex theory can also simulate the radial distribution of induced velocity, more importantly it has a faster calculation speed. So the vortex theory has been adopted in most of the existing studies [9]- [11].
Due to strong robustness, the genetic algorithm (GA) is often used in propeller optimization, but its convergence speed is slow [12]- [14]. The particle swarm optimization (PSO) has the advantages of simpler coding, less parameters, easier realization and faster convergence speed, but it is easy to fall into local optimal points [15]- [17]. The differential evolution (DE) is similar to the GA algorithm in terms of robustness and speed [18], [19]. Considering the characteristics of PSO and DE, some researchers proposed the PSODE hybrid algorithm to achieve both strong robustness and fast convergence speed. Besides, PSODE have several forms: serial, parallel and disordered, and among them the parallel PSODE has wider applications due to its good portability [20], [21]. Besides, the ''winner-take-all'' theory is generally adopted in interactive study of parallel PSODE, however, it is not in line with the competition law in real biological systems.
There are a lot of studies on the design method of the variable-speed MPS. Vu et al. [22] proposed a variable-speed MPS system sizing methodology for an agriculture multicopter. Dai et al. [23] proposed an analytical design-optimization method for electric propulsion systems of multicopter UAVs with desired hovering endurance. Du and Quan [24] optimized the propulsion system of the multicopter based on degree of controllability. But in the studies above, the whole optimization design problem was simplified and decoupled into several subproblems, which brought convenience to designers but the simplified method could not consider the characteristics of the motor or the propeller sufficiently. In [6], [8], [10], the propeller was optimized first, then the motor was selected according to the characteristics of the propeller, which couldn't achieve full potential of the motor and the propeller either. There were few studies which synthetically considered the characteristics of motor and propeller in design of MPS. Moreover, for EMRUAVs which have multiple working states, it is particularly difficult to give integrated design because of the need to keep high efficiency in all flight modes. Mahvelatishamsabadi and Emadi [25] investigated the effect of runway length on the electric propulsion system for an exceptionally short takeoff and landing electric air vehicles, and the results indicated that the required power for takeoff was incredibly higher than that in cruising mode.
In addition, EMRUAVs often employ variable-speed propellers (VSP) which have simple structures and operations as propulsion gears. However, the adjustable-pitch propellers (APP) are superior to the VSP with respect of the distribution rationality of the attack angle, force and power [26], [27]. Stevenson et al. [28] compared the energy consumption of VSP and APP for a small electric unmanned aerial vehicle, and the results indicated that the APP was proven to be more efficient than the VSP. Sheng and Sun [29], Gebauer et al. [30], and Henderson and Papanikolopoulos [31] carried out research on control and optimization of adjustable-pitch MPS for electric multicopters aimming at minimizing power consumption. The results showed that the adjustable-picth MPS could change the rotational speed and pitch at the same time, and there was an optimal combination of pitch and speed to get the minimum power. But in these studies, the motors served mainly to drive the propellers, and there was no integrated design of the system.
To solve the problem mentioned above, as shown in Figure 1, the brushless motor as well as the propeller is modelled first. Then the improved PSODE optimization method is proposed by adding the self-organizing feature map theory to the interactive study. On the basis, the integrated optimization design methods of variable-speed and adjustable-pitch MPS are obtained by considering the characteristics of the motor and the propeller sufficiently. Subsequently, taking a small electric-powered tilt quad rotor(TQR) for instance, the optimization and wind-tunnel experiments are carried out. The goals of this article are to: 1) Propose an integrated optimization design method of high-efficiency motor propeller system for UAVs with multi-states.  2) Compare the performance of the improved PSODE and other optimization algorithms. 3) Choose the more suitable one between the variable-speed and adjustable-pitch MPS for UAVs with multi-states. 4) Verify the effectiveness of the integrated optimization method by experiments.

A. BRUSHLESS MOTOR
Considering the advantages and disadvantages of the motor's equivalent circuit model and the positive polynomial loss model, the brushless motor is modelled by combining the two modeling methods mentioned above. The detailed modeling process can be found in our previous work [32]. Taking the XM3 motor as an example, its characteristic parameters which can be obtained from the manufacturer's data are shown in Table 1 where K v is the speed constant value, R is the internal resistance, and i 0 is the no-load current.
Then the XM3 motor is modelled as in [32]. The calculation results are shown in Figure 2. It can be seen that the motor has a larger efficiency at a certain speed and torque range. When this range is exceeded, the motor efficiency decreases rapidly.

B. PROPELLER
The propeller is modelled by the Goldstein vortex theory [11], [32]. The velocity and force acting on the blade element can be seen in Figure 3.
Taking the ClarkY airfoil as an example, it can be seen from Figures 4 and 5 that when the Reynolds number decreases, the drag coefficient increases but the lift coefficient decreases significantly. The selection of airfoil aerodynamic parameters under different Reynolds numbers will have a great influence on the accuracy of the calculation results. Thus the two-dimensional interpolation method is used to calculate the lift and drag coefficients with different Reynolds numbers.   Taking APC10 × 7 propeller as an example, it is calculated by the way mentioned above. Its airfoil distribution is S8037 at 0-0.5R, NACA4412 at 0.5-0.75R, ClarkY at 0.75R-R. Besides, the distributions of chord and twist angle are shown in Figure 6.
where, V (m/s) is the inflow velocity, n (r/s) is the rotational speed of the propeller, and D (m) is the diameter of the propeller.
The experimental values in Figures 7 and 8 are from [33]. We can see from Figure 7 that the force and power errors between the calculated and experimental value are less than   5% when the rotational speed is in the range of 3000 rpm to 7000 rpm. But when the rotational speed is in the range of 2000 rpm to 3000 rpm, the errors obtain a maximum value 15%. This is mainly because the force or the power in the range of 2000 rpm to 3000 rpm is very small, and a little bit of difference will cause a large error. In Figure 8, the force and power errors are less than 6%. So the calculation values of APC10 × 7 propeller are in good agreement with the experimental values no matter how large or small the inflow ratio is, and the Goldstein vortex theory can be used for the optimization design of MPS. Besides, in Figure 8, the x-axis represents the inflow ratio J which is defined in equation (1). In addition, it can be seen from Figures 7 and 8 that there is only a rotational speed which can get the target force at a certain forward speed or achieve the target speed under a certain force. So VSP can reduce the power only by optimizing its aerodynamic shape.
For APP, the twist angle is variable as shown in Figure 6. To facilitate analysis, the adjustable-pitch APC 10 × 7 propeller is obtained by adding an additional pitch angle to the APC 10 × 7 variable-speed propeller. Besides, the chord distribution is the same as that of the variable-speed propeller.
Two states for APP are calculated as shown in Figure 9. One is the state at which the propeller has a certain force of 3.5 N but different in flight speeds, the other is the state at which the propeller has a certain flight speed of 5m/s but different in forces. It can be seen that in both states we have an optimal pitch at which the propeller power has a minimum value. So the minimum power in APP can be achieved by optimizing not only the aerodynamic shape but also the pitch.
Besides, the propeller efficiency can be calculated as in equation (2). If the propeller is in static state, V in equation (1) should be replaced by the uniform induced velocity when calculating the inflow ratio J .
Then the characteristics of the motor and the propeller are analyzed as shown in Figure 10. The three thick solid lines represent the torque of the propeller with the change of the rotational speed under different working conditions. It can be seen that only when the torque has a suitable value, the MPS has a large efficiency. Besides, a reduction gear is usually used to keep both the motor and the propeller working in a good condition. But the addition of the reduction gear will increase the weight of the system. Moreover, for EMRUAVs which have multiple working states, the difficulty becomes greater than usual because these EMRUAVs need to achieve good motor propeller matches in multiple states.

III. IMPROVED PSODE HYBRID OPTIMIZATION ALGORITHM
An improved parallel PSODE hybrid optimization algorithm by adding the self-organizing feature map theory to interactive learning is proposed. VOLUME 8, 2020

A. PSO OPTIMIZATION ALGORITHM
The PSO algorithm assumes that there are M particles in a N-dimensional space, and any one of them has a certain flying speed. The steps of the algorithm are as follows: 1) Initialize each particle's basic parameters randomly, including its speed, position, historical optimal position and global optimal position. 2) Calculate the fitness value of each particle according to the fitness function. 3) For each particle, compare the current fitness value with the global optimal fitnes value. If the current one is better, it is choosed as the new global optimal value of the population. 4) Update each particle's velocity and position based on its original position, original velocity, historical optimal position and global optimal position, as shown in the following equations.
where, k is the iteration number, v i (k) is the velocity of the i th particle, x i (k) is the current position of the ith particle, gb i (k) is the global optimal position, c 1 and c 2 are the learing rates, r 1 and r 2 are random numbers independent of each other, and w is the weight coefficient. 5) If the optimization result is good enough or the number of iterations reaches the maximum value, end the iteration, otherwise it returns to step 2).

B. DE OPTIMIZATION ALGORITHM
In DE optimization, first the initial population is generated randomly, then the manipulations including mutation, crossover, and selection are carried out. Subsequently, according to each individual's fitness value, the good one is retained and the bad one is eliminated. At last, we start iterating until the convergence conditions are met. The mutation process is shown in equation (5) where x i1 , x i2 and x i3 are three different individuals after k iterations, and p F is the mutation factor.
The crossover process is shown in equation (6) where CR is the crossover factor, rand is a random number between 0 and 1, and randn(i) is a random positive integer between 0 and N .
The selection process is shown in equation (7) where f (·) is the fitness function. If the current fitness value is less than or equal to the historical one, the selection manipulation is carried out.

C. IMPROVED PARALLEL PSODE HYBRID OPTIMIZATION ALGORITHM
The improved parallel PSODE hybrid optimization algorithm is presented in Figure 11, which includes 6 steps: 1) Set basic parameters, including the population size M , learning factors c 1 and c 2 , weight coefficient w, mutation factor p F , and crossover factor CR 2) Divide the group into two populations, i.e., PSO and DE, and then initialize the populations randomly.  choose the best one of the individuals based on the fitness value. 5) Start interactive learning based on the theory of self-organizing feature map. 6) Determine whether the convergence condition is satisfied. If yes, end the optimization, otherwise return to step 3). In previous studies, the interactive learning is conducted by comparing the optimal values of PSO and DE directly and replacing the worse one by the better one. But considering that it is rare to see that the winner gains the whole awards in real biological system, the self-organizing feature map theory is introduced to the interactive study.
A simple self-organizing feature map shown in Figure 12 is taken for example to illustrate its principle. Assume that PSO and DE each has 25 individuals, and after a population update, the optimal individual is the one numbered 13 in PSO and 7 in DE. During information interacting, if the individual numbered 13 in PSO is better than the one numbered 7 in DE, then values of the individuals numbered 2, 6, 7, 8 and 12 in DE will be replaced by those of the individuals numbered 8, 12, 13, 14 and 18 in PSO.

IV. OPTIMIZATION DESIGN METHOD OF HIGH-EFFICIENCY MPS
The optimization design method of high-efficiency MPS mainly includes the following steps.
1) Determine the design variables, constraints and fitness functions according to the working states of EMRUAVs. 2) Obtain the results of the sensitivity analysis.
3) Compare the performance of the improved PSODE and other optimization algorithms. 4) Analyze the optimal configurations and get the most suitable one for the EMRUAVs with multi-states. Subsequently, taking a small electric TQR with variable-speed or adjustable-pitch MPS for instance, the integrated optimization of EMRUAVs which have multiple working states is carried out. The TQR has four states including hovering, cruising, maximum speed and transition, which can be seen in Table 2.
Besides, the MPS before optimization is as in Table 3. And it can be noticed that in hovering the power is low and  the motor efficiency is high, which meets the requirement. But in cruising the power is relatively higher. Therefore, the optimization design is necessary.

A. THE DESIGN VARIABLES, CONSTRAINTS AND FITNESS FUNCTION
During optimization, the motor XM3 is selected and the propeller diameter remains 20 inches. Considering that the thin airfoil has a high drag-rise Mach number as well as a small lift coefficient and that the thick airfoil has the opposite characteristics, the blade root adopts a thick airfoil, and the blade tip adopts a thin one. So the airfoil distribution is S8037 at 0-0.5R, NACA4412 at 0.5-0.75R, and ClarkY at 0.75R-R.
Choose pitch, chord, and taper ratio γ as design variables. Their ranges are as shown in equation (8). Besides, considering that the chord decreases linearly along the radial direction of the blade, chord at the location of 0.5 R is choosed as a reference for convenience. 1000 rpm ≤ n hover ≤ 8000 rpm 1000 rpm ≤ n cruise ≤ 8000 rpm (9) In addition, during the optimization of adjustable-pitch MPS, the rotational speeds in hovering and cruising are added as variables. The ranges of the rotational speeds are in equation (9).
The transition mode can be neglected due to its short duration. Then the optimization is constructed by introducing the requirements of the maximum speed state as constraints. o prevent stall, the attack angle at 0.7R of the propeller should be less than the stall angle. Besides, the power and current of MPS should be less than the motor's maximum sustainable power and current, and the propeller efficiency should VOLUME 8, 2020 be greater than 0.7. These constraints mentioned above are concluded as: where, α is the attack angle, α stall is the stall angle, P (·) is the power of the MPS, I (·) is the current of the MPS, and η (·) is the efficiency of the propeller. A typical mission profile of the small TQR in which the cruising time is 50 minutes and the hovering time is 10 minutes is analyzed. In order to get the minimum power consumption, the fitness function is determined as: min : En = 4( t hover P hover 60η hover + t cruise P cruise 60η cruise ) (11) where, En is the total power consumption, t hover is the hovering time, t cruise is the cruising time, P hover is the power of the propeller in hovering, P cruise is the power of the propeller in cruising, η hover is the motor efficiency in hovering and η cruise is the motor efficiency in cruising.

B. THE RESULTS OF THE SENSITIVITY ANALYSIS
In order to better analyze the influence of each variable on total power consumption, propeller power and motor efficiency, the sensitivity analysis is done first. And a simple way for sensitivity analysis is to get the main effect diagram of each variable. The main effect of a variable on a target value is the average target value in all trials when the variable is at a certain value. If the value of a variable is increased from a small one to a large one, the influences of this variable and the rest variables can be used to draw a main effect diagram. In Figures 13 to 16, low represents the minimum value of the variable, high represents the maximum value of the variable. Taking the variable pitch for instance, low is 8 inches, and high is 20 inches.

1) SENSITIVITY ANALYSIS OF THE VARIABLE-SPEED MPS
For the variable-speed MPS, the variable pitch has the most significant effects on the total power consumption and propeller power. Yet chord as well as γ has smaller effects. Besides, the variables pitch, chord, and γ have opposite effects on P hover and P cruise . The sensitivity of the total power consumption for the variable-speed MPS is shown in Figure 13. It can be seen from Figures 14 and 15 that chord is the main factor affecting the motor efficiency whether in cruising or hovering. This is mainly because chord has a large influence   on the torque of the propeller, and that the torque is directly related to the motor efficiency. In addition, it can be seen that the variables pitch, chord, and γ have opposite effects on η hover and η cruise too.

2) SENSITIVITY ANALYSIS OF THE ADJUSTABLE-PITCH MPS
For the adjustable-pitch MPS, the variables n hover , n cruise , pitch, chord and γ almost have equal effects on the total power consumption. n hover is the main factor affecting P hover , while n cruise is the main factor affecting P cruise . Besides, P hover (P cruise ) increases as n hover (n cruise ) increases. The sensitivity of the total power consumption for the adjustable-pitch MPS is shown in Figure 16.   In addition, n hover is the main factor affecting η hover , and n cruise is the main factor affecting η cruise . This is mainly because the motor efficiency is directly related to the rotational speed.

C. THE PERFORMANCE OF THE IMPROVED PSODE
As can be seen in Figures 17 and 18, the PSODE hybrid optimization algorithm has a faster convergence speed and stronger capacity to search globally compared with GA, PSO and DE.

D. THE OPTIMAL CONFIGURATIONS 1) THE OPTIMAL CONFIGURATION OF VARIABLE-SPEED MPS
The optimization results of the variable-speed MPS are shown in Table 4. The hovering power is increased, but the  cruising power is reduced. Considering the cruising time is 50 minutes which is much larger than the hovering time, the total power consumption is lower by 22.7% than that before optimization.
Taking the contour of chord and pitch for example, it can be seen from Figure 19 that the total power consumption is small in a large range near the point at which the optimization result is located. It indicates that the optimization result has a good safety margin and does not fall into the local optimum point.

2) THE OPTIMAL CONFIGURATION OF ADJUSTABLE-PITCH MPS
The optimization results of the adjustable-pitch MPS are shown in Table 5. The hovering power is increased, but the cruising power is significantly reduced. The motor efficiency is high whether in hovering or cruising. So the total power consumption is lower by 35.1% than that before optimization.
In addition, for variable-speed MPS the region where the optimum value is distributed is mostly in the range where pitch is between 8 inches and 16 inches, and the influences of the chord and γ are small. But for adjustable-pitch MPS the range of the optimal value distribution is wider. The variables pitch, γ as well as chord all have certain influences on the total power consumption. This is mainly due to the fact that the adjustable-pitch MPS can achieve the minimum power by optimizing not only the aerodynamic shape but also the pitch. VOLUME 8, 2020

3) COMPARATIVE ANALYSIS
Comparative analysis is carried out as follows. As can be seen from Figure 20, the chord of adjustable-pitch MPS is larger than that of the variable-speed MPS. There are many complicated reasons for this result. In hovering the required disk loading is larger, so in a certain range power decreases as chord grows. But the situation is opposite in cruising. Besides, for variable-speed MPS, as chord grows the motor efficiency increases in cruising but decreases in hovering. For adjustable-pitch MPS, the motor efficiency is mainly related to the rotational speed.
The twist angle distribution of variable-speed MPS is similar to that of adjustable-pitch MPS in hovering, but the twist angle of adjustable-pitch MPS in cruising increases significantly. This is because the inflow ratio is lager in cruising, which requires a large twist angle to get the optimal attack angle. Besides, It can be seen from Figure 21 that the lift drag ratio of the adjustable-pitch MPS is higher than that of the variable-speed MPS. This is due to the fact that the adjustable-pitch MPS can achieve the minimum power by changing not only the rotational speed but also the pitch.
min : En = 4(α 1 P hover η hover In addition, the equation 11 can be rewritten as equation 12 by taking α 1 as the scaling factor. As shown in Figure 22, as α 1 changes from 0 to 1, the total power consumption of the adjustable-pitch MPS is smaller than   that of the variable-speed MPS, which is consistent with the optimization results obtained before.
And taking the pareto front of the motor power as example, it can be seen from Figure 23 that the adjustable-pitch MPS is better than variable-speed MPS because it is easier for the adjustable-pitch MPS to balance the hovering with cruising working states for TQR.

V. EXPERIMENT VERIFICATION
In order to verify the rationality of the optimization method mentioned above, three propellers including VSP, APP in hovering and APP in cruising are machined based on the optimization results, which are shown in Figure 24. Then the  static experiment and the wind tunnel experiment at a wind speed of 25 m/s are carried out.
As shown in Figure 25, the experiments are implemented in a straight-through open low-speed wind tunnel. The size of the main open test section is 3.4 m (width) × 2.4 (height) m × 5 m (long). The axial turbulence of the airflow is 1.44% ∼ 2.31%, and the average angle is α = 0 • , β = 0.08 • . The test bench has a rotational speed sensor, a tension sensor, a torque sensor, a velocity sensor, a voltage and current sensor and so on. Besides, the accuracy of the speed sensor is ±0.05%, the accuracy of the velocity sensor is ±3% ∼ 8%, the accuracy of the voltage and current sensor is ±2%, and the comprehensive error of the tension and torque sensor is ±0.03%. A static test is carried out when the wind tunnel does not work. And the test points of the three propellers are shown in the optimization results above, which also can be seen in Table 6.
From Figures 26 to 29, it can be seen that the force and power calculation results are not much different from the    experiment results. In Figures 26 and 28, force errors between the calculated and experimental value are less than 8%. In Figures 27 and 29, the power errors reach 15% when the rotational speed is bigger than 2500 rpm, but we can accept it because they are in a small range. Therefore, the optimization results above are valid.    In addition, it can be seen from Figure 30 that the error between the value calculated by the combining model and experimental value is less than that by the equivalent circuit model when the current is greater than 3 A. The error is somewhat larger when the current is between 0-3 A, but this range is so small that we can ignore it.
And it can be seen from Table 7 that the motor's experimental efficiency is in good agreement with the motor's calculated efficiency.
Overall, whether the variable-speed MPS or the adjustable-pitch MPS, the test results are consistent with the calculated ones, which validates the rationality of the optimization method for EMRUAVs which have multiple working states.

1) An integrated optimization design method of
high-efficiency motor propeller system for UAVs with multi-states is proposed. 2) The improved parallel hybrid PSODE algorithm by introducing the self-organizing feature map theory to the interactive learning is more suitable for the design of high-efficiency MPS. Compared with GA, PSO, and DE, the algorithm has faster convergence speed and better global search ability. 3) For EMRUAVs which have multiple working states, the adjustable-pitch MPS is more suitable due to its ability to get the minimum power by optimizing not only the aerodynamic shape but also the picth. 4) The wind-tunnel experimental results are in good agreement with the calculated ones, which validates the rationality of the integrated optimization design method.

APPENDIX ABBREVIATIONS
The abbreviations mentioned above are listed in Table 8.