Energy consumption optimization method for average consistency data aggregation in random networks

Abstract

This invention discloses a method for optimizing the average consistency data aggregation energy consumption of a consistent random network, comprising the following steps: Step 1, establishing the communication connection relationship between a pre-arranged ideal network and a random network; Step 2, performing perceptual aggregation based on the average consistency theory and the communication connection relationship to obtain the consistency aggregation algorithm equation for the random network; Step 3, establishing the consistency aggregation algorithm equation to realize the consistency aggregation energy consumption, consistency aggregation gain, and convergence rate at convergence; Step 4, solving for the minimum consistency aggregation energy consumption to obtain the optimal solution for the communication link connection probability of the random network; Step 5, adjusting all communication link probabilities in the random network to the optimal solution for the communication link connection probability.

Description

Technical Field

[0001] This invention relates to the field of wireless network control methods, specifically a method for optimizing energy consumption through average consistency data aggregation in random networks. Background Technology

[0002] Data aggregation technology reduces the amount of data forwarding in vehicular wireless networks by decreasing the forwarding of redundant data, thus extending the network's lifespan. Mobility in vehicular wireless networks, interference in wireless sensor networks and ad hoc networks, and wireless channel fading all cause topology (connectivity) to change over time. Dynamic network topology, limited computing power, and limited energy supply all pose challenges to accurate data aggregation. Consistent synchronization algorithms, which utilize the exchange of local state information between network nodes, achieve convergence of states among all nodes. Because they do not require global network information or maintenance of network topology, they are now widely used in data aggregation.

[0003] The paper [Li S, Oikonomou G, Tryfonas T, et al. A distributed consensus algorithm for decision making in service-oriented internet of things[J].IEEE Transactions on Industrial Informatics, 2014, 10(2): 1461-1468.] proposes a cluster-based distributed algorithm. This algorithm first calculates local consensus, and then iteratively combines the local clusters to achieve global consensus, thereby improving the robustness and reliability of the decision-making process.

[0004] To address the challenges of data volume, communication latency, and information security in IoT networks, the literature [Yu H, Chen H, Zhao S, et al. Distributed soft clustering algorithm for IoT based on finite time average consensus[J]. IEEE Internet of Things Journal, 2020, 8(21): 16096-16107.] proposes a distributed soft clustering algorithm for IoT. Each IoT node may have data from multiple clusters. Considering that the main task of soft clustering is to calculate each cluster center in a weighted average manner, a finite time average consensus algorithm is used to implement distributed clustering.

[0005] Regarding the consistency problem in random networks, Hatano Y et al. studied the consistency problem in random information networks in the literature [Hatano Y, Mesbahi M. Agreement over random networks[J].IEEE Transactions on Automatic Control,2005,50(11):1867-1872.]. The information channels between communication entities are probabilistically connected, and the network topology changes over time. The concept of stochastic stability is used to discuss the asymptotic consistency problem of the network.

[0006] In the paper [Boyd S, Ghosh A, Prabhakar B, et al. Randomized gossipalgorithms[J].IEEE transactions on information theory,2006,52(6):2508-2530.], Boyd S et al. studied the consensus computation problem under arbitrary network topology based on the randomized Gossip algorithm. The network topology changes continuously with the addition of new nodes and the departure of old nodes, and the average consensus time depends on the second largest eigenvalue of the double random matrix.

[0007] The paper [Qin J, Wang J, Shi L, et al. Randomized consensus-based distributed Kalman filtering over wireless sensor networks[J].IEEE Transactions on Automatic Control, 2020, 66(8):3794-3801.] proposes a distributed Kalman filtering algorithm based on random Gossip, and provides a mean square convergence analysis of the algorithm. Under the condition of sufficient convergence, it is proved that the proposed algorithm theoretically achieves better mean square error performance than the non-cooperative distributed Kalman filtering algorithm.

[0008] In summary, existing methods for consistent data aggregation in random networks have provided the design of aggregation algorithms, convergence, and convergence time analysis, but have not yet studied how to improve the energy efficiency of data aggregation methods from the perspective of node power control. Summary of the Invention

[0009] This invention provides an energy consumption optimization method for average consistency data aggregation in random networks, in order to solve the problem of poor energy efficiency in existing random network data aggregation methods.

[0010] To achieve the above objectives, the technical solution adopted by the present invention is as follows:

[0011] A method for optimizing the energy consumption of average consistency data aggregation in random networks includes the following steps:

[0012] Step 1: Assume the pre-arranged ideal network is a connected undirected network, and all communication links in the random network have the same probability. Based on algebraic topological graph theory, establish the topological graph of the random network. Based on the topological graph and considering the fading channel, establish the communication connection relationship between the pre-arranged ideal network and the random network.

[0013] Step 2: Based on the average consistency theory and combined with the communication connection relationship established in Step 1, perform perceptual aggregation on the random network to obtain the consistency aggregation algorithm equation of the random network.

[0014] Step 3: Establish the energy consumption of consistent aggregation when the consistent aggregation algorithm equation achieves convergence of (α,γ), as well as the consistent aggregation gain and convergence rate;

[0015] Step 4: Solve the problem with the goal of minimizing the energy consumption of consistent aggregation. The consistent aggregation gain with the minimum convergence rate is obtained as the optimal solution for consistent aggregation gain. Then, based on the optimal solution for consistent aggregation gain, the optimal solution for the communication link connection probability of the random network is obtained.

[0016] Step 5: Adjust the probabilities of all communication links in the random network to the optimized solution of communication link connection probabilities obtained in Step 4.

[0017] In the further step 4, a distributed iterative method is used to solve the problem and obtain the optimal solution for the communication link probability of the random network.

[0018] In the further step 4, the goal is to minimize the energy consumption of consistent aggregation, and a data retransmission mechanism is added to the consistent aggregation energy consumption to solve the problem, so as to obtain the relationship between the communication link connection probability and the number of data retransmissions in the random network.

[0019] In step 5, the probabilities of all communication links and the number of retransmissions in the random network are adjusted to conform to the aforementioned relationship.

[0020] This invention studies data aggregation in wireless networks under fading channels from the perspective of stochastic consistency theory. It optimizes aggregation energy consumption by controlling node transmit power and data packet retransmission. It provides a distributed method for determining the optimal transmit power and the number of data retransmissions, which enables wireless networks to have lower communication energy consumption for data transmission in confined spaces and improves the lifespan of wireless networks. Attached Figure Description

[0021] Figure 1 This is a pseudocode diagram for solving optimization problem P1 in Embodiment 1 of the present invention.

[0022] Figure 2 This is a schematic diagram of multiple retransmissions in the aggregation state in Embodiment 1 of the present invention. Wherein (a) is the link probability of multiple retransmissions; (b) is the broadcast time of multiple retransmissions.

[0023] Figure 3 This is a network topology with N=63 nodes in Embodiment 2 of the present invention. Wherein (a) is an ideal network G; and (b) is a random network G(k).

[0024] Figure 4 This refers to node state x in Embodiment 2 of the present invention. i (k) Iteration curve.

[0025] Figure 5 Iteration error in Embodiment 2 of the present invention Iteration curve.

[0026] Figure 6 In Embodiment 2 of the present invention, the gain μ is set to 1 / d. max and μ * The p(k) iteration curve at time.

[0027] Figure 7 In Embodiment 2 of the present invention, the gain μ is set to 1 / d. max and μ * The relationship curve between f(p) and p.

[0028] Figure 8 In Embodiment 2 of the present invention, when the probability p takes different values, f e The curve showing the relationship between (p,K) and K. Detailed Implementation

[0029] To enable those skilled in the art to better understand the present invention, the embodiments will be described in detail below with reference to the accompanying drawings and examples. This will allow for a full understanding of how the present invention uses technical means to solve technical problems and achieve corresponding technical effects, and to facilitate its implementation. The embodiments of the present invention and the various features within them can be combined with each other without conflict, and all resulting technical solutions are within the protection scope of the present invention.

[0030] Obviously, the described embodiments are only some, not all, of the embodiments of the present invention. All other embodiments obtained by those skilled in the art based on the embodiments of the present invention without inventive effort should fall within the scope of protection of the present invention.

[0031] It should be noted that the terms "comprising" and "having" and any variations thereof in the specification, claims and accompanying drawings of this invention are intended to cover non-exclusive inclusion. For example, a process, method, system, product or device that includes a series of steps or units is not necessarily limited to those steps or units that are explicitly listed, but may include other steps or units that are not explicitly listed or that are inherent to such processes, methods, products or devices.

[0032] Example 1

[0033] like Figure 1 As shown in the figure, this embodiment discloses a method for optimizing the energy consumption of average consensus data aggregation in random networks, including the following steps:

[0034] Step 1: Assume the pre-arranged ideal network is a connected undirected network, and all communication links in the random network have the same probability. Based on algebraic topological graph theory, establish the topology graph of the random network. Based on the topology graph and considering the fading channel, establish the communication connection relationship between the pre-arranged ideal network and the random network.

[0035] Specifically, let the communication relationships between the pre-arranged ideal network nodes be G = (V, E, A), where V = {1, ..., N} is the set of nodes in network G, and N represents the number of nodes in the ideal network; edge set Let E represent the communication relationship between N nodes. If node j can receive information from node i, then {i,j}∈E; otherwise, ... And it is assumed that there are no self-connections in the network, i.e. Let A be the adjacency matrix of network G. If {i,j}∈E, then A ij =1, otherwise A ij =0. Graph G is an undirected connected graph, that is... {i,j}∈E means {j,i}∈E, and if there is a communication between any two nodes in network G. In network G, define N i ={j|(j,i)∈E,i≠j} represents the set of input neighbor nodes of node i, d i =|N i | represents the in-degree of node i. The in-degree matrix of network G is D = diag{d i The Laplace matrix is ​​defined as L = DA, and satisfies L T =L,L1 N =0 N .

[0036] In this embodiment, we first consider an ideal network G consisting of N nodes arranged in a pre-configured manner. In this case, there is no channel fading in signal transmission between nodes. Communication between nodes uses half-duplex mode, meaning that information cannot be received and sent simultaneously. In the ideal network G, the transmission power of node i is denoted as P.i When node i is P i Transmitted signal x i At that time, the signal x received at node j ji for:

[0037] x ji =x i +v ji ,

[0038] Where v ji With a mean of 0 and a variance of Additive noise. Signal x ji The signal-to-noise ratio can be expressed as SNR = G ij P i The gain coefficient d ij α is the Euclidean distance between nodes i and j; α is the path loss coefficient.

[0039] Suppose when x ji When the signal-to-noise ratio is greater than a certain threshold, signal x i Only then can it be successfully received. In an ideal network G, let P be... i0 The power when a communication link exists between nodes i and j, i.e., when the signal-to-noise ratio is greater than the threshold SNR. T =G ij P i0 At that time, node j can receive information from node i. At communication power P i0 The pre-arranged ideal network consisting of N nodes is denoted as G = (V, E, A).

[0040] Regarding the communication topology G of the ideal network, this embodiment makes the following assumptions.

[0041] Assumption: All nodes have power P i When broadcasting information, the ideal network G under an ideal channel is a connected network, and the coefficient K between all neighboring nodes is... ij They are the same and are a known value.

[0042] It should be noted that restricted communication environments such as subways and tunnels can cause signal attenuation in wireless signal transmission, reducing transmission power P. i The communication link between nodes i and j is a probabilistically connected case, and its value is related to the channel fading model. When information transmission passes through a fading channel, the information received by node j from i can be represented as:

[0043] x ji =r ji x i +v ji

[0044] Where r jiThis is the channel fading coefficient from node i to j. Thus, signal x... ji The signal-to-noise ratio can be expressed as SNR = r ji G ij P i The probability that a communication link exists between node i and node j is:

[0045] p ij =Pr{SNR≥SNR T}

[0046] As can be seen from the literature [Hasna MO, Alouini M S. End-to-end performance of transmission systems with relays over Rayleigh-fading channels[J]. IEEE transactions on Wireless Communications, 2003, 2(6): 1126-1131.], Rayleigh fading can well describe the multipath fading characteristics under constrained communication environments. The fading coefficient r under Rayleigh fading... ji If it follows an exponential distribution with variance of 1, then the link probability p ij It can be represented as In a fading channel, the probability of node j successfully receiving information from i is greatly reduced. When node i uses power P 0i When sending information, the communication link probability p ij It is only 0.3679.

[0047] The uncertainty of transmission links between nodes leads to a dynamic change in network topology. Let G(k) be a random network under fading channels, and let E(k) and A(k) be the corresponding edge set and adjacency matrix, respectively. If (i, j) ∈ E(k), then A... ij (k) = 1; otherwise A ij (k) = 0. Using δ ij (k) indicates whether the communication link between nodes i and j exists at time k, δ ij (k) = 1 indicates the existence of a communication link; conversely, it indicates the absence of a communication link. Thus:

[0048]

[0049] Due to the channel fading coefficient r ji The randomness of the link from node i to j in a random network G(k) is such that the link has a probability p. ij Connectivity. The communication connection between the ideal network and the random network is shown in formula (1):

[0050] A ij (k)=Aij δ ij (k) (1),

[0051] Let D(k) be the degree matrix of the random network G(k), where D(k) is a diagonal matrix with diagonal elements as follows:

[0052]

[0053] Then the Laplace matrix of the random network G(k) is L(k) = D(k) - A(k).

[0054] Step 2: Based on the average consistency theory and combined with the communication connection relationship established in Step 1, perform perceptual aggregation on the random network to obtain the consistency aggregation algorithm equation of the random network.

[0055] On a random network G(k) considering fading channels, perceptual aggregation based on average consistency theory yields the equation shown in formula (2):

[0056]

[0057] Where μ is the aggregate gain to be designed. The state of the random network G(k) is denoted as x(k) = [x1(k), ..., x2(k)]. N (k)] T The matrix form of formula (2), i.e., the consistency aggregation algorithm equation, is shown in formula (3):

[0058]

[0059] Where W(k) = I N -μL(k).

[0060] The equation for the consistent aggregation algorithm has the following definition.

[0061] Definition 1: Convergence. For a random sequence {x(k) (k = 0, 1, ...)}, if...

[0062]

[0063] The sequence is said to converge to the random number x by mean square. ave .

[0064] Definition 2: Convergence Time. A random sequence {x(k) (k = 0, 1, ...)} converges to a random number x in a mean square. ave Define its (α, γ)-convergence time T k for:

[0065]

[0066] Formula (4) is used to express that x(k) tends towards x with error α and probability γ. ave The minimum time is independent of the initial value x(0), where ||v|| represents the l2 norm of vector v.

[0067] Step 3: Establish the energy consumption of consistent aggregation when the consistent aggregation algorithm equation achieves convergence of (α, γ), as well as the consistent aggregation gain and convergence rate.

[0068] In this embodiment, let the ideal channel SNR of node i be... T The transmit power is P 0i In the case of Rayleigh fading, the communication link is p ij The transmit power of probabilistically connected signals is then... For a random network G(k) with N nodes, assume that the probability of all communication links is p ij Let p be the number of nodes with the same state information and τ be the number of nodes broadcasting their state information at a time. Then, the energy consumption E of the consistent aggregation algorithm when (α,γ) converges is... N for:

[0069]

[0070] In formula (5), (α,γ) represents the convergence time T. k The link link probability p is influenced by the random network topology, specifically the ideal network G and the link probability p under fading channels. Assuming a fixed arrangement of the ideal network G, the link link probability p can be controlled by adjusting the node transmit power, thereby controlling the consistent aggregation energy consumption E. N Adjustments.

[0071] For a random network G(k) caused by fading channels, this embodiment studies how to minimize the energy consumption of consistent aggregation under (α,γ) convergence by controlling the link probability p, that is, to realize the energy consumption optimization problem as shown in Equation (6):

[0072]

[0073] Based on low-power wireless communication mode, this embodiment studies the energy consumption optimization problem of nodes performing consistent data aggregation in the wake-up state by controlling the link probability p: During the wake-up period, the node broadcasts the aggregation state according to the link probability p, receives the aggregation state of neighboring nodes, and performs a data aggregation based on the random consistency theory; after completing a data aggregation task, the node enters a sleep state until the next wake-up time.

[0074] This embodiment provides the following lemma:

[0075] For a random network G(k), with adjacency coefficient Aij (k) When designing according to formula (1), if the convergence rate ρ(C) of the consensus aggregation algorithm equation is... W If α < 1, then the consistency aggregation algorithm equation (3) can achieve mean square consistent convergence, and its (α,γ)-convergence time T k It has the following form:

[0076]

[0077] in

[0078] The following is a distributed design of the consistent aggregation gain μ, as shown in Theorem 1.

[0079] Theorem 1, for equation (3) of the consensus aggregation algorithm, states that when the random network G(k) has the same link probability p and the ideal network G is a connected network, we have:

[0080] 1) If the uniformity gain μ satisfies the following formula (8):

[0081]

[0082] Then ρ(C) W If ) < 1 holds, the mean square convergence of the consistency aggregation algorithm equation (3) is achieved;

[0083] 2) Furthermore, if the aggregation gain μ satisfies:

[0084]

[0085] The convergence rate ρ(C) of equation (3) of the consensus aggregation algorithm is... W It has the form of formula (9):

[0086]

[0087] in λ and λ2(L) are the maximum degree and algebraic connectivity of the ideal network G, respectively, and λ N (L) represents the largest eigenvalue of the Laplace matrix L of the ideal network G.

[0088] The proof of Theorem 1 is as follows:

[0089] First, prove that when μ satisfies formula (8), ρ(C W The condition ) < 1 holds true. For a random network G(k) with the same link probability p, assume that there are no self-loops in network G, and that there is a communication link between any nodes i and l that satisfies Because of C W =E[(W T (l)-Π N )(W(l)-ΠN After simplification, we can obtain formula (10):

[0090]

[0091] in

[0092] In equation (10), let e be... ij =E[L T (l)L(l)] ij Considering L(k) = D(k) - A(k) and A ij (k)=A ij δ ij (k), then e ij It can be written in the following form:

[0093]

[0094] Where d i ,d j and d ij These are the degrees of nodes i and j, and the number of their common neighbors, respectively. Since G(k) has the same link probability p, then... Such a matrix The (i,j)th element is:

[0095]

[0096] For a random network G(k) with the same link probability p, the matrix E[L] can be used to... T [(k)L(k)] is written as p 2 L 2 +2p(1-p)L, matrix Therefore, matrix C W It can be represented as C W =I N -Π N -(2μp-2μ 2 p(1-p))L+μ 2 p 2 L 2 .

[0097] For a connected ideal network G, 0 is a single real root of matrix L, and its eigenvector is 1. N Meanwhile, matrix Π N It has an eigenvector of 1 N The matrix C has an eigenvalue of 0, and all other N-1 eigenvalues ​​are 0. Therefore, matrix C... W N-1 non-zero eigenvalues ​​λ i (C W It can be written as shown in formula (11):

[0098]

[0099] Through derivation, it can be obtained that when formula (8) is satisfied, ρ(C) W ) < 1.

[0100] Next, we prove ρ(C) W Distributed computing.

[0101] In equation (11), let: We can obtain:

[0102] λ i (C W )=1-μpΓ(λ i (L)).

[0103] Due to μλ i (L)>0, and when equation (8) is satisfied, ρ(C) W If ) < 1, then Γ(λ) holds. i (L))>0. Regarding λ i (L) for Γ(λ) i (L)) Taking the first derivative, we get:

[0104]

[0105] Thus Γ(λ) i (L)) Maximum value occurs Place.

[0106] because Then [λ2(L),λ N Within the range of (L)], Γ(λ) i (L)) has a maximum value. Therefore, the data aggregation rate is ρ(C) W )=max[1-μpΓ(λ2(L)),1-μpΓ(λ N (L))]. Let ΔΓ=Γ(λ) N (L))-Γ(λ2(L)), which can be calculated to obtain:

[0107] ΔΓ=[2-2μ(1-p)-μp(λ2(L)+λ N (L))](λ N (L)-λ2(L)),

[0108] That is, when When ΔΓ≥0 holds, ρ(C W The event occurs at λ2(L) and can be expressed as shown in equation (9).

[0109] Combining equations (7) and (9), it can be seen that when the aggregation accuracy requirements α and γ are known, the (α,γ)-convergence time T k With convergence rate ρ(C) W The value of ρ(C) is directly proportional to the value of C. W The smaller the value of T, the better. k The smaller the value, the fewer iterations are needed for the aggregation algorithm to achieve the required accuracy of α and γ; increasing the p value and / or λ²(L) can reduce ρ(C). W This reduces the (α,γ)-convergence time T. k .

[0110] As can be seen from the reference [Bullo F. Lectures on network systems[M]. Santa Barbara, CA: KindleDirect Publishing, 2019.], for a connected undirected graph, we have d max ≤λ N (L)≤2d max This holds true, therefore regarding the aggregation gain μ The conditional formula (8) can be transformed into formula (12):

[0111]

[0112] At this point, the value of the aggregation gain μ depends only on the link probability p and the maximum in-degree d of the ideal network G. max .

[0113] Step 4: Solve the problem with the goal of minimizing the energy consumption of consistent aggregation. The consistent aggregation gain with the minimum convergence rate is obtained as the optimal solution for consistent aggregation gain. Then, based on the optimal solution for consistent aggregation gain, the optimal solution for the communication link connection probability of the random network is obtained.

[0114] In this embodiment, when optimizing energy consumption by controlling the transmit power of the control node, two cases can be considered: one is that the uniform aggregation gain μ is a fixed value, and the other is that the uniform aggregation gain μ is a value to be optimized.

[0115] (1) The uniform aggregation gain μ is a fixed value.

[0116] Assuming the ideal network G is known and μ is a fixed value, μ can be chosen as 1 / d according to formula (8). max Then we have:

[0117]

[0118] Among them, a0=2μ(μ-1)λ2(L), All values ​​are known. Consistent polymerization energy consumption E N It can be represented as:

[0119]

[0120] When τ, α, γ are known, E N The minimization problem formula (6) is transformed into P1 as shown in formula (13):

[0121]

[0122] The iterative solution of formula (13) can be expressed as formula (14):

[0123]

[0124] Where Δ is the iteration step size. When iterating according to formula (14), a threshold ε is set; when the difference between two iteration values ​​is |p... k+1 -p k The iteration process ends when |≤ε. The solution process for optimization problem P1 is as follows: Figure 1 The pseudocode for solving this problem is shown in Algorithm 1.

[0125] (2) The aggregate gain μ is the value to be optimized.

[0126] For the optimization problem formula (6), when μ is the value to be optimized, the optimization problem can be solved by the distributed iteration method: when the link probability p and λ2(L) are known, design the value of μ such that ρ(C W To minimize μ, we obtain the optimal solution μ. * Based on the optimized solution μ * Design the p value so that ρ(C) W To minimize the probability of communication link optimization, we obtain the solution p. * ; after repeating this process multiple times, the optimization ends when the deviation between two adjacent iterations is sufficiently small, yielding the optimal solution μ. * and p * Specifically:

[0127] Step 1: In equation (9), when p and λ2(L) are known values, we can obtain the result that makes ρ(C W The minimum value of μ is specifically represented as:

[0128]

[0129] Step 2: Transfer μ * Substituting into equation (9), we can obtain ρ(C) W Organized into:

[0130]

[0131] Thus, f(p) in optimization problem P1 can be transformed into:

[0132]

[0133] Its iterative solution can be expressed as:

[0134]

[0135] Applying Algorithm 1 can find the value when |p k+1 -p k The optimal solution p when |≤ε * .

[0136] This embodiment also considers energy consumption optimization for multiple data retransmissions. By studying the multiple data retransmission mechanism, the probability of successful data transmission reception is increased, thereby reducing the energy consumption of consistent data aggregation.

[0137] Specifically, for probabilistic data transmission between sensing nodes i and j, if the transmission power of node i is P i =-P 0i In LNP, the probability that node j successfully receives data from node i is p. If, during the k-th data aggregation, node i receives data with a probability of P... i Send x i (k) After K iterations of state i, the probability that node j successfully receives information i is shown in formula (15):

[0138] p(K) = 1 - (1 - p) K (15),

[0139] Thus, the link connection probability p(K) between i and j can be adjusted by designing the number of retransmissions K, thereby regulating the energy consumption of consistent data aggregation.

[0140] Assume that the probability of successful single data reception p and the number of data retransmissions K are the same for all nodes in the network, and that a node enters a sleep state after retransmitting state data once, only waking up when the next state data retransmission occurs or when information from a neighboring node is received. Multiple retransmissions of aggregated state data are as follows: Figure 2 As shown, the duration of a single state broadcast by a node is τ, and the total duration of K state broadcasts is Kτ.

[0141] At (α,γ)-convergence time T k For a perception layer network with N nodes, the energy consumption for consensus aggregation is as follows:

[0142]

[0143] Substituting the p(K) expression shown in equation (15) into equation (9), we obtain the convergence rate as shown in equation (16):

[0144]

[0145] Simplifying equation (16), we obtain equation (17):

[0146]

[0147] in:

[0148]

[0149] At this point, the energy consumption E for uniform aggregation N It can be written as:

[0150]

[0151] Therefore, the aggregation energy consumption optimization problem, with the number of transmissions K and the link probability p as adjustment parameters, can be expressed as:

[0152]

[0153] st0<p<1, K≥1.

[0154] In this embodiment, compared with the aggregation energy consumption optimization problem formula (13) under power control, the data retransmission method can obtain a higher link probability by increasing the number of data transmissions at a lower probability p, as shown in formula (15).

[0155] As can be seen from equation (17), by increasing the number of signal transmissions K, ρ(C) can be increased. W If the value of α,γ is taken, then the (α,γ)-convergence time T of the consistent aggregation is... k Reducing the number of retransmissions K will also increase the energy consumption of state transmission per iteration. The increase.

[0156] The following analysis is a method for determining the number of retransmissions K to achieve lower energy consumption in the data retransmission method, i.e., when f(p,K)≥f2(p,K).

[0157] Assume both methods have the same (α,γ)-convergence time T. k That is, without considering the transmit power during data retransmission, the probability is p(K) = 1 - (1 - p) K The transmit power in data retransmission mode is set according to p. Thus, the power loss function in formula (13) can be rearranged as:

[0158]

[0159] Due to ρ(C) W Since f2(p,K) < 1, to make f2(p,K) ≥ f(p,K), we need to:

[0160] log[1-(1-p) K ]≥logp / K. (19)

[0161] From equation (19), we can obtain At this time, data retransmission consumes less energy. The range of p values ​​for different K values ​​can be calculated:

[0162] When K = 1, if 0 < p < 1, then f(p,1) = f2(p,1);

[0163] When K = 2, if 0.3820 ≤ p < 1, then f2(p,2) ≥ f(p,2);

[0164] When K = 3, if 0.3177 ≤ p < 1, then f2(p,3) ≥ f(p,3);

[0165] When K = 4, if 0.2755 ≤ p < 1, then f2(p,4) ≥ f(p,4);

[0166] When K = 5, if 0.2452 ≤ p < 1, then f2(p,5) ≥ f(p,5).

[0167] The above analysis shows that to achieve higher aggregation energy efficiency, the number of data transmissions K is inversely proportional to the single-link probability p; the smaller the value of p, the larger the required value of K. When the single-link probability 0.3820 ≤ p < 1, the data retransmission mode has an energy consumption advantage, that is... For all cases, f2(p,K)≥f(p,K) holds true. When the single-link probability is 0<p<0.3820, energy efficiency can be improved by increasing the number of data retransmissions K. For example, when 0.3177≤p<0.3820, lower aggregate energy consumption can be obtained by transmitting data 3 times.

[0168] Step 5: Adjust the probabilities of all communication links in the random network to the optimized solution of the communication link connection probabilities obtained in Step 4, or adjust the probabilities of all communication links and the number of retransmissions in the random network to conform to the relationship when implementing the data retransmission mechanism.

[0169] Example 2

[0170] This embodiment discloses a simulation experiment of the optimization method of Embodiment 1.

[0171] This embodiment will verify the effectiveness of the method proposed in this paper on the MATLAB simulation platform.

[0172] (1) Communication topology and parameter settings.

[0173] Network communication topology such as Figure 3 As shown, where Figure 3 (a) is an ideal topology. Figure 3 (b) represents a random topology under one scenario. Based on the characteristics of communication environments in confined spaces such as tunnels, N = 63 sensing nodes are evenly distributed across a 6*6*1000m area. 3 Within a narrow space, sensing nodes are positioned at the top center and 3 meters high on both sides, with the gateway node positioned at the top center of the entrance. The communication radius of each node in the pre-arranged ideal network is 50 meters. The network topology of the ideal communication network (a) can be calculated as λ²(L) = 0.0223, and the maximum in-degree of the network is d. max =4.

[0174] Curves and tables were plotted based on the average results of 1000 algorithm runs. In each run, the initial state of the node was randomly selected between [0, 10]. The time for a single state transmission by the node (including signal transmission and state switching) was τ = 100 μs, and the probability aggregation error was α = 10. -3 γ = 90%, the algorithm iterates 200 times.

[0175] (2) Convergence analysis.

[0176] First, a convergence analysis of the consistent data aggregation algorithm proposed in Example 1 under a random network topology is given. In this example, the link probability is set to p = 0.5, and according to... Choose μ = 0.38. Define the data aggregation state error as... in This represents the aggregate mean of the node states. The state x of a subset of nodes is represented during a single run of the algorithm. i (k), and the state error of some nodes after 1000 runs. The mean iteration curve is shown below. Figure 4 and Figure 5 As shown.

[0177] from Figure 4 and Figure 5 It can be seen that in a random network, as the number of iterations increases, the node state x... i (k) can tend to a certain fixed value, and the average uniform aggregation method proposed in Example 1 is convergent; aggregation deviation It exhibits a monotonically decreasing trend. When p = 0.5, after 110 iterations, All values ​​are less than 0.01, indicating that the consistent aggregation method has a certain degree of accuracy.

[0178] (3) Power control effectiveness analysis.

[0179] exist Figure 3 On the ideal network shown in (a), the effectiveness of the optimization method proposed in Example 1 is analyzed through simulation. The aggregate gain is calculated according to μ = 1 / d.max Take a fixed value of 0.25 and an optimized value. At that time, the iterative curve of the link probability p(k) is as follows: Figure 6 (Iteration step size Δ = 10) -5 The relationship curve between the objective function f(p) and the link probability p is shown below. Figure 7 As shown.

[0180] from Figure 6 and Figure 7 It can be seen that when μ takes a fixed value of 0.25 and an optimized value of μ, respectively... * At that time, the proposed optimization algorithm Algorithm 1 for p(k) all converged, and the obtained optimized value p * The values ​​are 0.4103 and 0.4624 respectively; the optimized value p obtained in the range of p∈(0,1) is... * Both are globally minimum, meaning the random network G(k) can find the link probability with the minimum aggregation energy consumption; relatively speaking, by optimizing the aggregation gain μ, a lower aggregation energy consumption f(p) can be obtained. * ).

[0181] (4) Data retransmission validity analysis.

[0182] To verify the effectiveness of the proposed data retransmission method, this embodiment compares the energy consumption during K data retransmissions with the energy consumption under power control. It is assumed that both methods have the same (α,γ)-convergence time T. k Without considering data retransmission, the transmission power is calculated as p(K) = 1 - (1 - p). K The settings are as follows: where p is the link probability under data retransmission, and the aggregation gain under both methods is set according to... Settings. Define f with p and K as parameters. e (p,K)=log[1-(1-p) K ]-logp / K, used to represent the energy consumption saved by the data retransmission method, if f e (p,K)>0 indicates that the data retransmission method has lower energy consumption. Figure 8 The expression f is given when p takes values ​​in the interval [0.05, 0.6]. e The relationship curve between (p,K) and K.

[0183] from Figure 8 As can be seen, when the single transmission probability p is sufficiently large, for example, p greater than 0.4, the data retransmission method has an absolute advantage in reducing the energy consumption of data aggregation; while when the single transmission probability is less than or equal to 0.15, increasing the single transmission power p is more effective in reducing the energy consumption of data aggregation. Therefore, to improve the energy efficiency of the data aggregation method, the node power P can be increased. i =-P0i LNP control ensures that the link probability p during a single transmission is greater than 0.4, and the final link probability between nodes is further increased through a data retransmission mechanism.

[0184] The preferred embodiments of the present invention have been described in detail above with reference to the accompanying drawings. These embodiments are merely descriptions of preferred embodiments and are not intended to limit the scope or concept of the invention. The specific technical features described in the above embodiments can be combined in any suitable manner without contradiction. Such combinations, as long as they do not violate the spirit of the present invention, should also be considered as part of this disclosure. To avoid unnecessary repetition, the present invention will not further describe the various possible combinations.

[0185] This invention is not limited to the specific details of the above embodiments. Within the scope of the technical concept of this invention and without departing from the design idea of ​​this invention, all modifications and improvements made by those skilled in the art to the technical solutions of this invention should fall within the protection scope of this invention. The technical content for which protection is sought in this invention has been fully described in the claims.

Claims

1. A method for optimizing energy consumption in random network average consistency data aggregation, characterized in that, Includes the following steps: Step 1: Assume the pre-arranged ideal network is a connected undirected network, and all communication links in the random network have the same probability. Based on algebraic topological graph theory, establish the topological graph of the random network. Based on the topological graph and considering the fading channel, establish the communication connection relationship between the pre-arranged ideal network and the random network. Step 2: Based on the average consistency theory and combined with the communication connection relationship established in Step 1, perform perceptual aggregation on the random network to obtain the consistency aggregation algorithm equation of the random network. On a random network G(k) considering fading channels, perceptual aggregation based on average consistency theory yields the equation shown in formula (1): Where μ is the aggregation gain, k is the number of iterations, and x i (k), x j (k) represent the states of nodes i and j during the k-th iteration, respectively, x i (k+1) represents the state of node i in the (k+1)th iteration, A ij (k) represents the communication connection status between node i and node j, and its value is 1 or 0; Step 3: Establish the energy consumption of consistent aggregation when (α,γ) converges, as well as the consistent aggregation gain and convergence rate; in (α,γ), α represents the error and γ represents the probability. Let the ideal channel SNR of node i be... T The transmit power is P 0i In the case of Rayleigh fading, the communication link is p ij The transmit power of probabilistically connected signals is then... For a random network G(k) with N nodes, assume that the probability of all communication links is p ij Let p be the same as the node's single state information broadcast time length and τ be the same as the node's single broadcast time length; then the energy consumption E of the consensus aggregation algorithm when (α,γ) converges is... N for: Where T k Let E be the convergence time of a random network that converges with error α and probability γ. ti Let i be the energy consumption during a single iteration of node i; In formula (2), the convergence time T k The link probability p is influenced by the random network topology, i.e., it depends on the ideal network G and the link probability p under fading channels. Assuming the ideal network G is fixedly arranged, the link probability p can be controlled by adjusting the node transmit power, thereby achieving control over the consistent aggregation energy consumption E. N Adjustments; Step 4: Solve for the goal of minimizing the energy consumption of consistent aggregation. The consistent aggregation gain with the minimum convergence rate is obtained as the optimal solution for consistent aggregation gain. Then, based on the optimal solution for consistent aggregation gain, the optimal solution for the communication link connection probability of the random network is obtained. In Step 4, a distributed iterative method is used to solve for the optimal solution for the communication link probability of the random network. In Step 4, the goal is to minimize the energy consumption of consistent aggregation. A data retransmission mechanism is added to the consistent aggregation energy consumption to solve for the relationship between the communication link connection probability and the number of data retransmissions of the random network. Step 5: Adjust the probabilities of all communication links in the random network to the optimized solution of communication link connection probabilities obtained in Step 4; In step 5, the probabilities of all communication links and the number of retransmissions in the random network are adjusted to conform to the aforementioned relationship.

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