CN113973281B

CN113973281B - Unmanned aerial vehicle Internet of things system and method for balancing energy consumption and service life of sensor

Info

Publication number: CN113973281B
Application number: CN202111251127.7A
Authority: CN
Inventors: 林晓辉; 毕宿志; 承楠; 代明军; 王晖; 郭重涛; 苏恭超
Original assignee: Shenzhen University
Current assignee: Shenzhen University
Priority date: 2021-10-26
Filing date: 2021-10-26
Publication date: 2022-09-27
Anticipated expiration: 2041-10-26
Also published as: CN113973281A

Abstract

The invention relates to a method for balancing energy consumption and service life of sensors in an Internet of things system of an unmanned aerial vehicle, wherein the Internet of things system of the unmanned aerial vehicle comprises a plurality of sensors and at least one unmanned aerial vehicle which is respectively communicated with the sensors, and the method comprises the following steps: s1, calculating the minimum system node transmission energy consumption based on the data load of each sensor; s2, calculating the service life of the sensor based on the residual node energy and the transmission energy consumption of each sensor: s3, describing energy fairness among the sensors based on fairness indexes; s4, adjusting the bandwidth of the sensor and/or the hovering position of the unmanned aerial vehicle based on the maximum fairness index, the minimum system node transmission energy consumption, the data load and the remaining node energy to balance system energy consumption and sensor life.

Description

Unmanned aerial vehicle Internet of things system and method for balancing energy consumption and service life of sensor

Technical Field

The invention relates to the field of unmanned aerial vehicles and Internet of things, in particular to a method for balancing energy consumption and service life of sensors in an unmanned aerial vehicle Internet of things system and the unmanned aerial vehicle Internet of things system.

Background

The rise of internet of things (IoT) systems enables us to access real-time information of the surrounding environment. However, collecting internet of things data in hostile and inaccessible areas without infrastructure support is a challenging problem due to the inherent physical limitations associated with miniature sensors. One possible solution to this problem is to use a flexible and controllable Unmanned Aerial Vehicle (UAV) to collect ground data and forward it to a remote cloud for further processing. Under the scene of the internet of things of the unmanned aerial vehicle, a limited battery power supply carried by the miniature sensor must be effectively utilized, so that the service life of the internet of things system is prolonged.

In order to prolong the service life of the internet of things system, the currently adopted method mostly minimizes the total energy consumption of the sensor. However, in a scheme where total energy consumption is minimized, non-uniformities between sensors are effectively ignored, which can lead to an imbalance in energy consumption, which in turn leads to premature depletion of the "weak" sensor power supply leading to node failure. Therefore, minimizing the total energy consumption is not effective in extending system life due to the energy consumption imbalance between sensors, and may actually cause some overloaded nodes to prematurely drain their battery energy.

Disclosure of Invention

The technical problem to be solved by the present invention is to provide a method and a system for balancing energy consumption of sensors in a controllable unmanned aerial vehicle internet of things system, which can properly solve the problem of energy balance among the sensors, thereby prolonging the system life as much as possible.

The technical scheme adopted by the invention for solving the technical problems is as follows: a method for balancing energy consumption and service life of sensors in an Internet of things system of unmanned aerial vehicles is constructed, the Internet of things system of unmanned aerial vehicles comprises a plurality of sensors and at least one unmanned aerial vehicle which is respectively communicated with the sensors, and the method comprises the following steps:

s1, calculating the transmission energy consumption of the minimum system node based on the data load of each sensor;

s2, calculating the service life of the sensor based on the residual node energy and the energy consumption of each sensor:

s3, describing energy fairness among the sensors based on fairness indexes;

s4, adjusting the bandwidth of the sensor and/or the hovering position of the unmanned aerial vehicle based on the maximum fairness index, the minimum system node transmission energy consumption, the data load and the remaining node energy to balance system energy consumption and sensor life.

The invention adopts another technical scheme for solving the technical problem that an unmanned aerial vehicle internet of things system is constructed, and the unmanned aerial vehicle internet of things system comprises a plurality of sensors and at least one unmanned aerial vehicle which is respectively communicated with the sensors, a processor and a computer program stored on the processor, wherein when the computer program is executed by the processor, the method for balancing the energy consumption and the service life of the sensors in the unmanned aerial vehicle internet of things system is realized.

By implementing the method for balancing the energy consumption and the service life of the sensor in the unmanned aerial vehicle internet of things system and the unmanned aerial vehicle internet of things system, the balance of the energy consumption and the service life of the sensor is realized by discussing the influence of the data load of the sensor and the energy of the residual nodes on the minimum energy consumption and the service life of the sensor and adjusting the bandwidth of the sensor and/or the hovering position of the unmanned aerial vehicle.

Drawings

The invention will be further described with reference to the accompanying drawings and examples, in which:

fig. 1 is a flow chart of a method of balancing energy consumption and lifetime of sensors in an internet of things system for unmanned aerial vehicles of the present invention;

FIG. 2 illustrates the meaning of symbols employed in the method illustrated in FIG. 1;

FIG. 3 shows a data acquisition system including two sensors;

4A-4C illustrate unmanned aerial vehicle hover positions for sensors at maximum fairness indices at different data loads, remaining node energies;

5A-5C illustrate sensor bandwidth at maximum fairness index for different data loads, remaining node energy;

6A-6C illustrate the effect of utility function on sensor bandwidth, transmit power, and lifetime;

FIG. 7 illustrates a graph of energy efficiency versus fairness index;

fig. 8 shows the corresponding search algorithm for the optimal flight trajectory of the drone;

FIG. 9 illustrates a search algorithm for jointly optimizing bandwidth, power level, and flight specification using a block coordinate descent method;

figure 10 shows the flight trajectory of a drone at different levels of fairness;

FIG. 11 shows sensor lifetime as a function of fairness level;

FIG. 12 illustrates energy efficiency and fairness balancing;

figure 13 shows a drone optimized flight trajectory of another preferred embodiment of the invention;

FIG. 14 shows a schematic diagram of optimized sensor lifetime versus α change.

Detailed Description

In order to make the objects, technical solutions and advantages of the present invention more apparent, the present invention is described in further detail below with reference to the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are merely illustrative of the invention and are not intended to limit the invention.

In the present invention, we assume that M sensors are scattered over the ground, and the coordinates of sensor i are represented by (x) _i ，y _i ) Wherein 1. ltoreq. i.ltoreq.M. To collect ground information, an Unmanned Aerial Vehicle (UAV) is sent to collect data from a plurality of sensors. According to safety regulations, we assume that the drone flies at a constant height H. The coordinates of the drone projection on the ground are denoted (Ux, Uy). Therefore, the distance between the drone and the sensor i is:

since the drone is high in height, for ease of explanation we assume that the channel between the drone and the ground sensors conforms to the line-of-sight transmission model. Furthermore, it is assumed that the doppler effect caused by the flight of the drone is perfectly compensated. Thus, the channel power gain between the UAV and sensor i can be characterized by the following free-space path loss model:

wherein beta is ₀ Is a reference distance d ₀ Channel power at 1 m. N is a radical of ₀ Representing the power density of white noise, P _i Represents the transmission power of sensor i, B _i Representing the bandwidth of sensor i, the ATG channel capacity can be written as:

for the sensor of the internet of things, the energy efficiency seriously affects the service life of the system. Thus, given the amount of node data, conventional solutions aim to minimize the total transmission energy consumption of the system nodes, thereby maximizing the system energy efficiency. However, as previously mentioned, minimization of total energy consumption may result in an imbalance of energy consumption between sensors. Therefore, the method of the invention aims to discuss how to balance the energy consumption and the service life of the sensors in the unmanned aerial vehicle internet of things system.

Fig. 1 is a flow chart of a method of balancing energy consumption and lifetime of sensors in an internet of things system for unmanned aerial vehicles according to the present invention. As shown in fig. 1, in step S1, the minimum system node transmission energy consumption is first calculated based on the data load of each sensor.

In order to distribute energy consumption fairly in the system, the data load and the remaining node energy of each sensor should be considered. Specifically, the minimization of the total energy consumption can be expressed as:

0≤P _i ≤P _max (5)

wherein A is _i Representing the data load of sensor i, B _i Indicates the bandwidth, g, of sensor i _i Indicating the channel gain, N, of sensor i ₀ Representing the white noise power density, P _i Denotes the transmission power of the sensor i, B denotes the system bandwidth, M denotes the number of sensors, T denotes the data transmission timing, P denotes the data transmission timing _max The maximum sending power of the sensor is represented, i is more than or equal to 1 and less than or equal to M, and both i and M are positive integers; constraint (4) represents an orthogonal bandwidth allocation of the system bandwidth among M sensors, so there is no transmission interference internally. The constraint (5) requires that the transmission power of each sensor should not exceed the maximum value P _max . Constraint (6) is a performance requirement, which means that each sensor should upload its sensor data within the data transfer time period T.

In the optimization problem (P1), the transmission power P _i And bandwidth B of sensor i _i Are two independent variables and can be separately processed. We can demonstrate that the bandwidth B of a given sensor i _i The objective function (P1) is relative to P _i However, low transmit power also means low throughput and longer transmission delay, we still need to satisfy the constraint (6) and therefore the optimum P of (P1) _i At the boundary of the constraint (6), we have

It can be written as:

substituting (7) into (P1), the original question only has one variable B left _i I.e. can be simplified and converted into:

note that the objective function of (P2) is relative to B _i Is convex (see appendix B) and constraint (4) is affine, and thus (P2) is convex and can be easily solved using some convenient optimization tool (e.g., CVX).

In step S2, sensor life is calculated based on the remaining node energy and energy consumption of each sensor.

Let us assume that in each data collection round, the data load to be uploaded by each sensor is A _i With corresponding energy consumption of

The remaining node energy of sensor i is E _i . Thus, for each round, sensor i will have its battery powered

Part for data transmission and the sensor (wheel) has a lifetime of

Bringing in

Namely to obtain

To distribute energy consumption fairly throughout the network, we want no significant difference in sensor lifetime, and e _i And E _i In a suitable ratio. Therefore, in step S3, we describe energy fairness among the sensors using a fairness index, which is defined as follows:

by this definition, we can see that J ranges from

In particular to

Is the minimum fairness index and corresponds to the minimum fairness where only one sensor performs data transmission for each round. And J ≠ 1 is the maximum fairness index and corresponds to the maximum fairness, i.e., the fairest energy consumption, where for each round all users consume the same proportion of the remaining node energy, i.e., for any i ≠ J,

in this case, all sensors have equal lifetimes (perfect fairness).

In step S4, the bandwidth of the sensor and/or the hover position of the drone is adjusted based on a maximum fairness index, the minimum system node transmission energy consumption, the data load, and the remaining node energy to balance system energy consumption and sensor lifetime.

Data payload for given system A _i The objective function of minimizing (P2) is equivalent to maximizing the system energy efficiency. It can be observed in (P2) that the energy consumption of the sensor is highly dependent on the bandwidth, data load and channel gain in each round of data collection. On the other hand, in addition to the above factors, the energy fairness in (8) is also related to the remaining node energy { E ] of each sensor _i Are closely related. However, neglecting this factor in (P2) may lead to unfairness in power consumption and premature exhaustion of some sensors. Thus, two distinct performance metrics, energy efficiency and energy fairness, cannot be optimized simultaneously.

To illustrate this phenomenon, FIG. 3 shows a circuit including twoA data acquisition system of each sensor. As shown in fig. 3, set the interval between two sensors as D, select the drone directly over the straight line connecting the two sensors, fix the hovering height of the drone as H, and change its horizontal position X from the first sensor along the straight line. For each fixed location, solve (P2) to obtain the optimal bandwidth { B } _i } _opt And allocating the optimal bandwidth { B } _i } _opt Carry into the constraint (7) to calculate the optimum transmit power { P } _i } _opt . Based on the optimal bandwidth { B _i } _opt And the optimal transmission power { P } _i } _opt The energy fairness is calculated according to constraint (8). Adjusting a bandwidth of the sensor and/or a hover position of the drone based on J-1, the data load, and the remaining node energy to balance system energy consumption and sensor lifetime. In the invention, when the data loads of the two sensors are equal to the energy of the residual nodes, the hovering position of the unmanned aerial vehicle is the middle point of a straight line, and the two sensors averagely share the system bandwidth; when the data load of the first sensor is less than the data load of the second sensor, the hover position of the drone is near the second sensor or more bandwidth is allocated to the second sensor; when the remaining node energy of the first sensor is less than the remaining node energy of the second sensor, the hover position of the drone is close to the first sensor or more bandwidth is allocated to the first sensor.

When setting the relevant parameter to

1MHz for B, 300 m for D, 50 m for H, 10 s for T, P _max 1W. The results are shown in FIGS. 4A to 4C.

Fig. 4A shows the hover position of the drone when the two sensor data loads and the remaining node energy are equal and the energy fairness is J-1. At this point, the optimal hover position for energy fairness is exactly the midpoint of the straight line. This is readily understood. The midpoint indicates that the two sensors have symmetric channel gains. Thus, for equal data loads, at this point they consume equal energy in data transmission, thus achieving maximum energy fairness (J ═ 1). Furthermore, at the intermediate point, the system bandwidth is shared equally by both sensors, thereby minimizing the total energy consumption.

However, in FIG. 4B, when the data loads of the two sensors are different, such as A ₁ ＜A ₂ The sensor 2 needs to take on more data load. Therefore, to minimize the objective function of (P2), we need to reduce its weight by bringing the drone close to the sensor

Thereby increasing its channel gain g ₂ . Also, to obtain J-1, the drone must also hover closer to the sensor 2 to reduce its energy consumption.

In FIG. 4C, when the remaining node energies of the two sensors are different, e.g., E ₁ ＜E ₂ . In this case, in order to compensate for this energy imbalance, it is achieved

The drone needs to be closer to the sensor 1 to reduce the energy consumption in its data transmission. However, the remaining node energies are not considered in (P2), so the optimal location for total energy consumption remains at the midpoint shown in the figure.

4A-4C, we have demonstrated that the hover position of a drone can impact overall energy consumption and energy fairness. In addition to the hover position of the drone, bandwidth allocation also affects both metrics. To gain insight into this, we also performed a number of calculations using equations (7) and (8). The results are shown in FIG. 5. In this case, we let the drone be fixed at an intermediate point. The other parameters are the same as in fig. 4A-4C. The bandwidth allocated to the sensor can significantly affect its power consumption. The more bandwidth allocated, the more energy is saved.

Also, we observe a similar phenomenon in fig. 5A. When the data loads of the two sensors are equal to the residual node energy, if the total bandwidths of the two sensors are equal, the energy efficiency and the energy fairness are optimal. However, when the data load or remaining node energy is unbalanced, more bandwidth is allocated to the "weaker" node (S2 in fig. 5B and S1 in fig. 4C), so that the two sensors consume exactly the same proportion of their remaining node energy (J ═ 1). To minimize the total energy consumption, more bandwidth sharing is always allocated to the sensors with heavier data load (S2 in fig. 5B).

From the energy fairness index given in (8), we can see that J-1 corresponds to the fairest energy consumption, where all sensors consume the same proportion of energy residual energy on data transmission. However, as we discussed earlier, maximum energy fairness (J ═ 1) is only applicable to those applications that obey the "least law", where the lifetime of the system depends on the "weakest" sensor (e.g., intrusion detection) whose lifetime is the shortest. To extend the lifetime of this "weakest" sensor, more bandwidth must be allocated to it, which inevitably reduces the energy efficiency of the other sensors. Thus, depending on the particular application, we can achieve a suitable level of fairness, thereby extending the life cycle of the system.

For each round, sensor i consumes its remaining node energy in uploading data, so its lifetime can be expressed as

Therefore, in a further preferred embodiment of the invention, an α -fairness is proposed to balance the energy consumption. For any x ≧ 0, set U _α (x) A utility function representing the fairness α is given by:

we assume x _i ＝L _i The problem of energy consumption equalization based on alpha-fairness becomes the problem of maximizing the alpha-utility function, which is B _i Is given by:

discussion 1: when α is 0, the objective function can be written as

Thus, (P3) becomes a given energy budget E _i The throughput maximization problem of (2); when alpha is 1, U ₁ (B _i ) Neither convex nor concave, and therefore, (P3) is a non-convex optimization problem; when alpha is more than or equal to 2, U _α (B _i ) Relative to B _i Is concave (see appendix C) and thus (P3) is a convex problem. Hereafter, we only discuss the balance of energy consumption in the range of α ≧ 2. Specifically, when α is 2, the original problem degenerates to

In this case, E is equal if the remaining node energies of all sensors are equal, i.e., for any i ≠ j _i ＝E _j Then (P3) would be equivalent to (P2). Thus, when α is 2 and E _i ＝E _j Incidentally, (P2) is a special case of (P3).

Discussion 2: the setting of α reflects the fairness of the scheme. The larger alpha, the smaller the energy consumption difference between the sensors. Specifically, when α → ∞, (P3) will become a max-min optimization problem, where its solution causes all sensors to have equal lifetimes.

To evaluate the constraint relationship between energy efficiency and energy consumption fairness, we again use the same scenario in fig. 3 to demonstrate how α affects bandwidth allocation, energy efficiency, fairness, and sensor lifetime. Specifically, we change α in (P3), and then the influence of α on the above variables under the conditions of different data loads, remaining node energy, unmanned aerial vehicle hover position. Unless otherwise specified in the figure, the system parameters are equivalent to those shown in FIG. 3, described above. The calculation results are shown in fig. 6A to 6C.

In FIGS. 6A-6C, we consider three cases: (1) equal data payload and equal remaining node energy, but unequal channel gain; (2) equal residual node energy and equal channel gain, but unequal data loading; and (3) equal data payload and equal channel gain, but unequal remaining node energy. A shorter distance from the drone means a higher channel gain, which is advantageous for data transmission. For these two sensors, we call the sensor with longer distance, heavier data load, or less remaining node energy budget the "weak" sensor because it has a shorter lifetime than the other sensor.

In scenario (1), the drone is fixed between two sensors, closer to sensor S1, x _u Sensor S2 is therefore a "weak" sensor, meaning that it consumes more energy per unit data transmission. As shown in fig. 6A-6C, as we increase α, the bandwidth allocated to sensor S2 also increases, thereby compensating for its higher path loss. Accordingly, the bandwidth share of S1 decreases as α increases. Further, for a given data load and a specified upload time, the sensor S2 may reduce its transmit power to transmit data when more bandwidth is allocated. Conversely, in the case of less allocated bandwidth, the sensor S1 must increase its transmit power in order to complete the data load within the time limit.

In scenario (2), when the data loads of the two sensors are not equal, namely A ₁ ＜A ₂ When, sensor S2 is a "weak" sensor. Similarly, as shown in FIGS. 6A-6C, an increase in α will result in more bandwidth allocation and lower transmit power for sensor S2. In contrast, the sensor S1 must increase its transmit power because less bandwidth is allocated to it.

In scenario (3), when the remaining node energies of the two sensors are not equal, i.e. E ₁ ＜E ₂ When, sensor S1 is a "weak" sensor. An increase in α can balance the energy consumption between the two sensors, since the two sensors will consume closer proportions of energy in each round. Thus, as shown in FIGS. 6A-6C, we can observe that the bandwidth allocation of sensor S1 increases and the transmit power decreases, while the trend for sensor S2 is reversed. Furthermore, as α increases, we can see in fig. 6C that the difference in lifetime of the two sensors decreases, which means that the two sensors transmitThe energy consumption of the sensor becomes more balanced.

For the three cases, we also plot the energy efficiency against the fairness index, as shown in fig. 7, where α varies from 2 to 26. Energy efficiency is defined as the ratio of the total data transmitted to the total energy consumption of the two sensors. The fairness index is defined in constraint (8). In the figure we can clearly see the restrictive relation between efficiency and fairness. An increase in α may reduce the difference in energy consumption of the two nodes. This is accomplished by allocating more bandwidth for a "weak" sensor while letting another sensor consume more energy. Unfortunately, the energy saved for a "weak" sensor cannot compensate for the extra energy consumed in other sensors, thereby reducing overall energy efficiency.

In the foregoing embodiments, with the drone hover position fixed, we observe that the lifetime of each internet of things sensor is affected by many factors — the location of the drone, the allocated bandwidth, the data load, and the remaining node energy. Therefore, these factors should be considered in the energy balance of the entire network. In a further preferred embodiment of the present invention, it is considered that during the flight of the drone, the drone starts from the starting point and flies to the destination. During the flight towards the destination, the bandwidth allocated to each sensor, the associated transmission power and the trajectory of the drone should be jointly optimized so as to properly control the energy consumption of each sensor. As the drone moves, the upstream channel gain of each sensor is also a time-varying function. Therefore, the allocated bandwidth and transmit power of the sensor should also be dynamically adjusted to accomplish the data upload task. Therefore, the optimization in a mobile scenario becomes more complex than in a fixed scenario.

In a further preferred embodiment of the present invention, there is provided a method for balancing energy consumption and lifetime of sensors in an unmanned aerial vehicle internet of things system based on α -fairness, including S1, calculating sensor lifetime based on remaining node energy and transmission energy consumption of each sensor: s2, establishing an alpha-utility function based on alpha-fairness based on the service life of the sensor, and solving the alpha-utility function to obtain the optimal flight track of the unmanned aerial vehicle; and S3, controlling the flight of the unmanned aerial vehicle based on the optimal flight trajectory.

In the preferred embodiment, we assume that the drone is used to collect delay tolerant periodic sensory data from ground sensors. The symbols used in this section are the same as those of the previous embodiment. The data load needing to be uploaded to the unmanned aerial vehicle by the sensor i in each data transmission time limit T is A _i . The remaining node energy of sensor i is E _i . Without loss of generality, the flight trajectory of the unmanned aerial vehicle on the horizontal plane is q (t) ═ U _x (t)，U _y (t)]Wherein T is more than or equal to 0 and less than or equal to T, U _x (t) and U _y (t) is the coordinates of the drone on the aircraft at time t. The height of the unmanned aerial vehicle is H, and the maximum flying speed is v _max . The bandwidth allocated to the sensor is B _i (t) the transmission power of the sensor is P _i (t) of (d). Our goal in this section is joint optimization { B _i (t)，P _i (t), q (t), to maximize the α -utility function in (P3).

To simplify the mathematical analysis and calculation, we discretize the time range T into N equidistant time slots, each time slot having a duration δ, and T ═ N δ. Thus, the flight trajectory of the drone is q (t) can be fitted with N straight-line sequences q

Representing the instantaneous horizontal position of the drone at the nth slot, where q ₀ And q is _N Respectively, the starting point and the end point of the unmanned aerial vehicle. Accordingly, the bandwidth allocated to sensor i in the nth time slot may be approximately B _i (n) and the associated transmit power and channel gain are each P _i (n) and g _i (n) of (a). Thus, the energy consumption of sensor i can be written as:

therefore, sensor lifetime

We can rewrite the system utility function to:

which is a function of bandwidth, transmit power, and drone trajectory.

When alpha is more than or equal to 2, the maximum value of the utility function

Is equivalent to

Thus, the optimization problem can be expressed as:

C3：0≤P _i (n)≤P _max ，1≤i≤M，1≤n≤N

C4：||q _n -q _n-1 ||≤v _max δ，1≤n≤N

C5：q ₀ ＝q0，q _N ＝qF

in the optimization problem (P4), the objective function is the sum of the alpha powers of all the sensor power consumption components. Constraint C1 is a QoS requirement, which means that each sensor i needs to upload a certain amount of data to the UAV within time limit T. Constraint C2 represents the total system bandwidth shared between all sensors. The constraint C3 is the maximum transmit power. ConstrainingThe formula C4 requires that the instantaneous speed of the drone cannot exceed a maximum value. Constraint C5 is the starting and ending constraints for the drone. In (P4), we have three optimization variables

We can observe that as alpha ≧ 2, the objective function is relative to

Is convex. C1 relative to

And

is convex (see appendix D). C3 and C5 are obviously convex. The left side (LHS) of C4 is convex with respect to the coordinates of the drone, so C4 is also convex. However, C1 needs to handle the channel gain g in a logarithmic function _i (n) which is highly correlated with the instantaneous trajectory q (n) of the drone. Thus, C1 is relative to

Is not convex and thus (P4) is not convex.

To solve (P4), we decompose it into two sub-problems (P4a) and (P4b) and iteratively solve. Specifically, in (P4a), we first determine the trajectory of the drone, then jointly optimize the bandwidth allocation and the power policy of the sensors

Then, we use the output of (P4a) as the input of (P4b) and optimize the flight trajectory of the drone

To minimize the distance of the ground sensor from the track. Furthermore, if the sensor is weaker, it should be closer to the track. In solving (P4b), we transform the non-convex problem into a convex form and provide a processable computational method. The output of (P4b) is used as (P4a)The input is in the next iteration. This process will continue until the algorithm converges. Considering the trajectory of the drone, the subproblem (P4a) can be written as:

s.t.C1，C2，C3

as described above, in (P4a), the objective function and all constraints are convex, and thus (P4a) is a convex problem that can be easily solved using CVX.

In the objective function, α reflects the level of fairness in energy consumption between sensors. The larger the value, the fairer the energy consumption. Especially when α ∞ is + ∞, the balancing scheme becomes "completely fair" because all sensors consume their respective same proportion of energy when uploading data. And (P4a) can be rewritten as:

s.t.C1，C2，C3

from the output of (P4a), we need to optimize the flight trajectory of the drone

Our goal is to minimize the sum of the squares of the distance of each sensor to the flight trajectory, thereby minimizing the energy consumption of data upload. Furthermore, in trajectory design, if we let drones fly closer to those "weak" sensors, we can better balance network node energy consumption. In (P4b), after discretizing, the trajectory of the drone

Is approximated by n connected straight lines and respectively corresponds to the track segments in n time slots. For a segment (1. ltoreq. N. ltoreq.N), we can use the midpoint q of the corresponding line _n ＝(q _x (n)，q _y (n)) to represent the instantaneous position of the drone at time instant n. For each sensor i, in the N-segment trajectory, we select the K (1 ≦ K ≦ N) (K closest segments) segment nearest to sensor i for optimization. The corresponding set of trajectory segments may be denoted ω _i ＝{ω _i，1 ，ω _i，2 ，…，ω _i，K }，

K is more than or equal to 1 and less than or equal to K. Note that for any two sensors i and j (1 ≦ i ≠ j ≦ M), there may be overlap of ω i and ω j. For any sensor i and segment n, we further define Δ (i, n) ═ 1 if q is _n ∈ω _i Otherwise, Δ (i, n) is 0. The coordinate of the sensor i on the ground is S _i ＝(x _i ，y _i ). Thus, the sub-problem (P4b) can be expressed as:

s.t.C1，C2，C3，C4，C5

the minimization objective function (P4b) is to optimize the flight trajectory of the drone with the goal of minimizing the square and distance of the drone. By introducing weighting coefficients in the function

We make the trajectory closer to those "weak" sensors. Specifically, the large A of the weak sensor _i Or small E _i Resulting in an increase in the value of the objective function. Therefore, minimizing the objective function may force the drone closer to this "weak" sensor, thereby reducing its energy consumption and balancing it appropriately.

In addition, the fair coefficient alpha (alpha is more than or equal to 2) in the objective function can strengthen the trend, and the large alpha can obviously increase the weighting coefficient, so that the unmanned aerial vehicle can approach the weak sensor more, and the value of the objective function is reduced. In (P4b), the cube root of α -2 can guarantee a moderate increase in the weighting coefficient.

The objective function of (P4b) is a convex quadratic equation. As described above, the constraint C1 in (P4b) is relative to

Is non-convex. To solve, we use the SCA method to convert C1 into a convex processable form, resulting in a sub-optimal solution. We rewrite this constraint to be:

note that the left side in constraint (12) is relative to | | | q _n -S _i || ² Is convex. In the SCA method, we can iteratively optimize the trajectory increment until the objective function converges. In particular, in the (l +1) th iteration,

where (u) _l ，v _l ) Is the track increment. Let

We obtained qnl +1-Si2+ H2 ═ qnl-Si2+ H2+ σ. For simplification, let

and in (l +1) iterations, the first order taylor approximation to the left of constraint (12) can be written as:

in the (l +1) th iteration, the current

We adopt the lower bound

Approximate constraint (12) left

To obtain

Because of the fact that

Is that

If constraint C7 is satisfied, then constraint C1 is automatically satisfied. It can be easily observed that C7 is quadratic in constraint and, more importantly, it is relative (u) _l ，v _l ) Is convex. Thus, in each iteration l, we optimize the trajectory increment (u) in turn (P4c) _l ，v _l ) Then we can get a sub-optimal approximate solution of (P4 b). The corresponding search algorithm for the optimal flight trajectory is shown in fig. 8.

s.t.C2，C3，C4，C5，C7

We solve the non-convex problem (P4) using a block coordinate descent method, the algorithm is shown in fig. 9. Specifically, in algorithm 2, we can get a sub-optimal solution to the original problem by iteratively optimizing bandwidth allocation, power level (P4a) and drone trajectory (P4 c). Furthermore, as with each iteration of algorithm 1, the generated drone trajectory is closer and closer to the sensor set, and under this updated trajectory, the generated optimal target value (P4a) does not increase during the iteration, which ensures convergence of algorithm 2.

In a preferred embodiment, to evaluate the effect of the energy balancing scheme, we designed two scenarios in whichOne drone was assigned to a 100m x 100m square area to collect ground data. The flying height of the unmanned aerial vehicle is 5m, and the maximum speed v _max 5 m/s. Other parameter settings were as follows: b2 MHz, T100 s, P _max 1W. In both cases, sensors with different data loads and remaining node energies are scattered in the area. In scenario A, we have two sensors S1 and S2 with a data payload of

Residual node energy

In order to eliminate unfairness caused by sensor placement, two sensors are symmetrically placed on two sides of an initial track respectively, and coordinates are S respectively ₁ (30, 70) m and S ₂ (70, 30) m. The starting and final positions of the drone are q0 ═ 0, 0) m and qF ═ 100, 100) m. The initial trajectory of the drone is a straight line connecting q0 and qF. In this scenario, we set K to 20. Further, when α → ∞, we set α to a sufficiently large value of 1500 for the convenience of calculation of (P4 c). For function

At t, x > 0, we derive f (x) to obtain

For any v > 0, v-1. gtoreq. lnv. Thus, it is possible to provide

Therefore f' (x) ≧ 0, and f (x) is a non-decreasing function, which means that the objective function of (P1) is relative to the transmit power P _i Is non-decrementing.

For function

At x > 0, obtainTo obtain

And

thus f (x) is relatively x-convex.

For α ≧ 2, x > 0, consider utility function U _α (x)＝x ^1-α V. (1-. alpha.) let

And utility function and B _i Correlated to become U _α (B _i )＝f ^α-1 (B _i ) V. (1-a), here,

relative to B _i Is convex (see previous formula), so we obtain f (B) _i )＞0，f″(B _i ) Is greater than 0 to U _α (B _i ) Solution B to _i Derivative of (D) to obtain U _α (B _i )＝-f ^α-2 (B _i )f′(B _i ) And U ″) _α (B _i )＝-[(α-2fα-3Bif′2Bi+fα-2Bif″(Bi)]Since alpha is not less than 2 and f 'Bi > 0, U alpha' Bi is not more than 0 and thus U _α (B _i ) is concave.

For the

It can be observed that it is an increasing function of P and

thus, its relative P is concave. Thus, when B is considered, its second derivative is

Thus, f is concave with respect to B. Thus, it is possible to provide

Is concave.

Fig. 10 is the flight trajectory of the drone under different degrees of fairness. The two sensors are placed symmetrically beside the initial trajectory. S1 is a "weak" sensor in this case, taking into account the data load and energy budget of the two sensors. We can observe that as the fairness α increases, we can design a mechanism to adjust the flight trajectory closer to the sensor 1, thereby reducing its energy consumption in data upload.

Fig. 11 is sensor lifetime as a function. The results show that as α increases, the life span of the two sensors will tend to converge. In particular, if α ∞ is + ∞, both sensors will deplete their energy at the same time, which also means "perfect fairness". However, it also shows that the magnitude of the lifetime reduction of S2 is much greater than the magnitude of the lifetime increase of S1. This is because, as α increases, the additional power consumption in S2 may be several times the power saving of S1, resulting in a decrease in the overall energy efficiency of the system.

The energy efficiency of the two sensors is compared to α as shown in fig. 12. As α increases, energy efficiency of S1 increases, while energy efficiency of S2 decreases. This is because a higher fairness α allows S1 to transmit its buffered data using more allocated bandwidth and lower transmit power. In addition, the track adjustment also shortens the transmission distance, and further reduces the energy consumption of S1. In contrast, for S2, the less the bandwidth allocation after the track adjustment, the higher the path loss, resulting in deterioration of energy efficiency.

The tradeoff between energy efficiency and fairness is shown in fig. 12. We can clearly see that these two metrics conflict with each other. As more resources are allocated to the weaker sensor, the additional energy consumed by the other sensor greatly exceeds the energy saved by the weaker sensor, resulting in a reduction in energy efficiency of the overall system. This is at the expense of pursuing energy fairness.

In scenario B, to evaluate the scalability of the solution, the number of sensors is increased to seven, with the coordinates of each sensor: s ₁ ＝(5，50)m，S ₂ ＝(20，25)m，S ₃ ＝(30，70)m，S ₄ ＝(40，35)m，S ₅ ＝(85，65)m，S ₆ ＝(70，30)m，S ₇ (60, 80) m. As shown in fig. 12. Data load and remaining node energy settings for the sensor

And

in scenario B, we set K10. The starting point and the end point of the drone are q0 ═ 0, 0) m and qF ═ 100, 0) m, respectively. The initial flight path is a semicircle connecting q0 and qF. S1, S3, S5, and S7 are "weak" sensors in view of data load and energy budget. To enhance the power life of weak sensors, the designed trajectories should be closer to them, thereby improving channel quality and reducing power consumption in data transmission. The optimized trajectory is shown in fig. 13. In the figure we can see that this mechanism based on a-fairness and energy balance can achieve this function, since a larger a can force the drone closer to the upper sensors, compensating for its faster energy dissipation. The relationship between the sensor lifetime and the change in α is shown in fig. 14. As a increases, the lifetime of the weak sensor may increase significantly as more bandwidth is allocated and channel quality improves. Also, it was observed that when α becomes large enough, the lifetimes of all sensors tend to converge, indicating "perfect energy fairness".

The setting of the fairness α depends on the specific application scenario. Of the seven sensors, if only one sensor is sufficient to accomplish the task (e.g., air humidity monitoring in a vineyard), we can set α to 2, thereby saving the energy of the strongest sensor. If all seven nodes are critical sensors and a failure of any one node could lead to a system crash (e.g., intrusion alarms), then we can set α ∞, thereby increasing the lifetime of the "weakest" sensor and allowing all sensors to have the same lifetime. If we have specific requirements on the lifetime of some key sensors, for example, S4, S5, and S5 are lifetime requirements (L4 ≧ 950, L5 ≧ 850, L6 ≧ 1000), we need α ≦ 8, α ≦ 3, and α ≦ 6, respectively, by examining the numbers in FIG. 14. Therefore, in this particular application scenario, we can set α to 6 to meet the requirement.

The invention discusses the energy balance problem of a ground sensor in an unmanned aerial vehicle Internet of things system. The influence of bandwidth allocation and unmanned aerial vehicle position on energy efficiency and energy fairness is analyzed firstly. A trade-off relationship between the two conflict metrics is also disclosed. To extend the system lifetime, we propose an alpha-fairness based approach to balance the energy consumption between sensors. Specifically, we have designed an alpha utility function by considering the data load, energy budget and geographical location of all sensors. To maximize this function, we decompose it into two sub-problems, and then iteratively optimize bandwidth allocation, sensor power levels, and drone trajectories using BCD methods. And the influence of the fairness alpha on the service life of the sensor, the energy efficiency and the flight track of the unmanned aerial vehicle is analyzed by combining the numerical value result. In addition, we find that, according to a specific application scenario, we can use the coefficient α as a "control knob" to adaptively adjust the energy consumption of the sensor, thereby maximizing the effort of prolonging the system life. This finding is useful because it can provide some insight to network practitioners in algorithm design and product implementation.

Accordingly, the present invention can be realized in hardware, software, or a combination of hardware and software. The present invention can be realized in a centralized fashion in at least one computer system, or in a distributed fashion where different elements are spread across several interconnected computer systems. Any kind of computer system or other apparatus adapted for carrying out the methods of the present invention is suited. A typical combination of hardware and software could be a general purpose computer system with a computer program that, when being loaded and executed, controls the computer system such that it carries out the methods described herein.

The present invention may also be implemented by a computer program product, comprising all the features enabling the implementation of the methods of the invention, when loaded in a computer system. The computer program in this document refers to: any expression, in any programming language, code or notation, of a set of instructions intended to cause a system having an information processing capability to perform a particular function either directly or after either or both of the following: a) conversion to other languages, codes or symbols; b) reproduced in a different format.

While the invention has been described with reference to specific embodiments, it will be understood by those skilled in the art that various changes may be made and equivalents may be substituted without departing from the scope of the invention. In addition, many modifications may be made to adapt a particular situation or material to the teachings of the invention without departing from its scope. Therefore, it is intended that the invention not be limited to the particular embodiment disclosed, but that the invention will include all embodiments falling within the scope of the appended claims.

The above description is only for the purpose of illustrating the preferred embodiments of the present invention and is not to be construed as limiting the invention, and any modifications, equivalents and improvements made within the spirit and principle of the present invention are intended to be included within the scope of the present invention.

Claims

1. A method of balancing energy consumption and lifetime of sensors in an internet of things system of unmanned aerial vehicles, the internet of things system of unmanned aerial vehicles comprising a plurality of sensors and at least one unmanned aerial vehicle in communication with the plurality of sensors, respectively, the method comprising the steps of:

s2, calculating the service life of the sensor based on the residual node energy and the transmission energy consumption of each sensor:

s3, describing energy fairness among the sensors based on fairness indexes;

s4, adjusting the bandwidth of the sensor and/or the hovering position of the unmanned aerial vehicle based on a maximum fairness index, the minimum system node transmission energy consumption, the data load and the remaining node energy to balance system energy consumption and sensor life;

the step S1 further includes the steps of:

s11, calculating the minimum system node transmission energy consumption based on the data load of each sensor according to the following formula:

0≤P _i ≤P _max (5)

wherein A is _i Representing the data load of sensor i, B _i Indicates the bandwidth, g, of sensor i _i Indicating the channel gain, N, of sensor i ₀ Representing the power density of white noise, P _i Denotes transmission power of sensor i, B denotes system bandwidth, M denotes number of sensors, T denotes data transmission timing, P denotes data transmission timing _max The maximum transmission power of the sensor is represented, i is more than or equal to 1 and less than or equal to M, and both i and M are positive integers;

s12 based on

Calculating the transmission power P of each sensor i _i ：

S13, transmitting power P _i Brought into (P1) toCalculating the minimum system node transmission energy consumption:

the step S2 further includes the steps of:

s21, calculating the energy consumption of each sensor for each data transmission based on the data load of each sensor:

s22, calculating the service life of the sensor based on the residual node energy and the energy consumption of each sensor:

wherein E _i Representing the remaining node energy of sensor i;

the step S3 further includes the steps of:

s31, describing energy fairness among the plurality of sensors based on the fairness index:

wherein J is in the range

The J ═ 1 is the maximum fairness index and corresponds to the maximum fairness.

2. The method for balancing energy consumption and life span of sensors in internet of things system of unmanned aerial vehicle according to claim 1, wherein the step S4 further comprises the steps of:

s41, setting the interval between the two sensors to be D, selecting the unmanned aerial vehicle right above a straight line connecting the two sensors, fixing the hovering height of the unmanned aerial vehicle to be H, and changing the horizontal position x of the unmanned aerial vehicle, which is far away from the first sensor, along the straight line;

s42, for each fixed location, solving (P2) to obtain the optimal bandwidth { B } _i } _opt And allocating the optimal bandwidth { B } _i } _opt Carry into the constraint (7) to calculate the optimum transmit power { P } _i }opt；

S43, based on the optimal bandwidth { B _i } _opt And the optimal transmit power { P } _i Opt, calculating the energy fairness according to constraint (8);

s44, adjusting the bandwidth of the sensor and/or the hovering position of the drone based on J-1, the data load and the remaining node energy to balance system energy consumption and sensor lifetime.

3. The method for balancing energy consumption and life span of sensors in the unmanned aerial vehicle internet of things system according to claim 2, wherein in the step S44:

when the data loads of the two sensors are equal to the energy of the residual nodes, the hovering position of the unmanned aerial vehicle is a straight middle point, and the two sensors share the system bandwidth on average;

when the data load of the first sensor is less than the data load of the second sensor, the hover position of the drone is near the second sensor or more bandwidth is allocated to the second sensor;

when the remaining node energy of the first sensor is less than the remaining node energy of the second sensor, the hover position of the drone is near the first sensor or more bandwidth is allocated to the first sensor.

4. A drone internet of things system comprising a plurality of sensors and at least one drone communicating with each of the plurality of sensors, characterized by further comprising a processor and a computer program stored on the processor, the computer program when executed by the processor implementing the method of balancing energy consumption and lifetime of sensors in the drone internet of things system according to any one of claims 1-3.