An airport refueling vehicle low-carbon scheduling method based on an enhanced BP neural network
By optimizing the route scheduling of airport refueling trucks using an enhanced BP neural network, the problems of flight delays and increased carbon emissions in large-scale scheduling were solved, achieving high-precision and stable scheduling results.
Patent Information
- Authority / Receiving Office
- CN · China
- Patent Type
- Patents(China)
- Current Assignee / Owner
- SOUTHEAST UNIV
- Filing Date
- 2023-11-09
- Publication Date
- 2026-06-19
Smart Images
Figure CN117592695B_ABST
Abstract
Description
Technical Field
[0001] This invention relates to the field of vehicle routing and scheduling, specifically to a low-carbon scheduling method for airport refueling trucks based on an enhanced BP neural network. Background Technology
[0002] As airports expand in scale and volume, problems such as high flight delay rates and insufficient ground equipment allocation are becoming increasingly prominent. One significant reason for airport flight delays is the delay in ground operations. Ground operations have strict procedures; for example, the next ground service can only proceed after a refueling truck has completed its refueling service. Therefore, ensuring the rational scheduling of refueling trucks is crucial for subsequent ground operations. Currently, most airports rely on manual scheduling for refueling trucks, which is prone to inappropriate route planning, exacerbating flight delays and increasing carbon emissions. Current research on vehicle carbon emissions primarily focuses on measuring emissions, with limited research on the carbon emissions from vehicle scheduling. Airport refueling trucks, as large vehicles, generate higher carbon emissions than smaller cars. A key measure for achieving energy conservation and emission reduction is to start with vehicle scheduling, planning rational routes, and reducing operating costs.
[0003] Refueling truck scheduling falls under the Vehicle Routing Problem (VRP), which involves rationally organizing vehicle routes, times, and numbers under certain constraints to sequentially fulfill service demands within a given area. This is an NP-hard problem. The challenge lies in optimizing the various mutually influencing and constraining objectives.
[0004] Currently, solutions to the VRP problem are mainly divided into the following three categories: (1) Exact algorithms. These are algorithms that can find the optimal solution within a small range, mainly including branch and bound, dynamic programming, and exhaustive search. (2) Intelligent biomimetic algorithms. These algorithms seek the optimal vehicle scheduling strategy by simulating the intelligent behavior of biological groups through multiple iterations. They have characteristics such as adaptability and randomness, such as genetic algorithms and ant colony algorithms. (3) Machine learning algorithms. Their core lies in the interactive learning between the scheduling strategy and the external environment. Through training with effective scheduling strategy data, they infinitely approach the optimal scheduling strategy. Commonly used algorithms include artificial neural networks and reinforcement learning.
[0005] The disadvantages of existing technologies are: (1) In the exact algorithm, it is limited to solving small-scale scheduling problems. However, airport refueling truck scheduling has many factors to consider and is a large-scale problem, which is not suitable for this type of algorithm. (2) In the intelligent bionic algorithm, the algorithm has strong environmental adaptability, but it is easy to get trapped in local optima. The optimization time is significantly affected by the individual distribution. (3) In the machine learning algorithm, parameter learning often adopts the traditional gradient descent optimization algorithm, which uses a fixed learning rate for all parameters. The convergence speed is slow and it is easy to get trapped in local optima. Summary of the Invention
[0006] The purpose of this invention is to provide a low-carbon scheduling method for airport refueling trucks based on an enhanced BP neural network, which can rationally organize the routes, times, and quantities of refueling trucks under the constraints of specific application scenarios to sequentially fulfill the service needs of each flight at the target airport.
[0007] To achieve the above functions, this invention designs a low-carbon scheduling method for airport refueling trucks based on an enhanced BP neural network, executing the following steps S1-S4 to complete the scheduling of refueling trucks:
[0008] Step S1: Collect network topology information of the target airport, operating status data of refueling trucks, and operating status data of flights. Calculate the carbon emissions of each refueling truck, construct a low-carbon optimization scheduling model for refueling trucks consisting of multivariate parameters, with the goal of minimizing the total carbon emissions of refueling trucks, and establish corresponding constraints.
[0009] Step S2: Based on the enhanced BP neural network, the multivariate parameter optimization problem in the low-carbon optimization scheduling model of refueling trucks is transformed into three single-variable sub-optimization problems, namely the gradient vector square sum optimization problem, the actual learning rate optimization problem, and the weight vector optimization problem. The gradient vector square sum v0, the actual learning rate α0, and the weight vector ω1 are initialized, and v0, α0, and ω1 are updated sequentially to obtain the updated gradient vector square sum v1, the actual learning rate α1, and the weight vector ω2.
[0010] Step S3: Using the sum of squared gradient vectors v1, the actual learning rate α1, and the weight vector ω2 as inputs to the enhanced BP neural network, iteratively optimize the enhanced BP neural network until the preset convergence condition is met, thus obtaining the weight vector ω of the enhanced BP neural network. T ;
[0011] Step S4: Verify the stability and convergence of the enhanced BP neural network based on Lyapunov stability theory.
[0012] Beneficial effects:
[0013] This invention designs a low-carbon scheduling method for airport refueling trucks based on an enhanced BP neural network, achieving the following technical effects:
[0014] 1. An airport refueling truck route scheduling model based on an enhanced BP neural network is proposed. A lower bound function of the learning rate is introduced into the neural network to avoid premature convergence of the adaptive gradient descent algorithm and improve the prediction accuracy of route scheduling.
[0015] 2. To prove the convergence and stability of the enhanced BP neural network algorithm, Lyapunov stability theory and mathematical derivation were combined to ensure the stability and reliability of the results of the airport refueling truck scheduling model.
[0016] 3. Various airport refueling truck route scheduling scenarios were designed, and the applicability and accuracy of the proposed method were verified by comparison with other models.
[0017] Compared with the prior art, the advantages of the present invention include:
[0018] 1. An airport refueling truck route scheduling model based on an enhanced BP neural network avoids premature convergence of the adaptive gradient descent algorithm and improves the prediction accuracy of route scheduling.
[0019] 2. By combining Lyapunov stability theory with mathematical derivation, the stability and reliability of the airport refueling truck scheduling model results are guaranteed. Attached Figure Description
[0020] Figure 1 This is a flowchart of a low-carbon dispatching method for airport refueling trucks based on an enhanced BP neural network, according to an embodiment of the present invention.
[0021] Figure 2 This is a comparison chart of carbon emissions per unit time under different flight sizes according to embodiments of the present invention;
[0022] Figure 3 This is a comparison chart of the ratio of refueling trucks to aircraft under different flight scales according to embodiments of the present invention;
[0023] Figure 4 This is a comparison chart of the loss values of the neural network algorithm under different flight scales provided in the embodiments of the present invention;
[0024] Figure 5 This is a comparison chart of the operational time complexity under different flight sizes according to embodiments of the present invention. Detailed Implementation
[0025] The present invention will be further described below with reference to the accompanying drawings. The following embodiments are only used to more clearly illustrate the technical solution of the present invention, and should not be used to limit the scope of protection of the present invention.
[0026] This invention relates to the Vehicle Routing Problem (VRP), which involves rationally organizing vehicle routes, times, and quantities under certain constraints to sequentially fulfill service demands within a given area.
[0027] The method designed in this invention is based on an enhanced BP neural network: a lower bound function for the learning rate is introduced into the neural network to avoid premature convergence of the adaptive gradient descent algorithm and improve the prediction accuracy of path scheduling.
[0028] Reference Figure 1 The present invention provides a low-carbon scheduling method for airport refueling trucks based on an enhanced BP neural network, which executes the following steps S1-S4 to complete the scheduling of refueling trucks:
[0029] Step S1: Collect network topology information of the target airport, operating status data of refueling trucks, and operating status data of flights. Calculate the carbon emissions of each refueling truck, construct a low-carbon optimization scheduling model for refueling trucks consisting of multivariate parameters, with the goal of minimizing the total carbon emissions of refueling trucks, and establish corresponding constraints.
[0030] The specific steps of step S1 are as follows:
[0031] Step S1.1: Obtain target airport network topology information, refueling truck operation status data, and flight operation status data, including the number of flights, parking position location, number of parking positions, number of refueling trucks, flight schedule, and fuel refueling service time.
[0032] The target airport has a total of n flights within a unit flight operation plan period, and the flight set is as follows: There are a total of m refueling trucks, forming a refueling truck set. Assume that the public assembly point for refueling trucks and the parking positions corresponding to each flight remain fixed, and define... A public outpost for refueling trucks, a set of fixed nodes. ,in Define the aircraft parking stand node; The edge set between the public refueling station and the flight parking position nodes is represented by an undirected graph. Describe the network topology relationship between the point set L and the edge set E, that is, the network topology relationship between the common settlement of the refueling truck set and the parking positions of each flight, and define variables. For nodes and Path distance between For refueling trucks from the node arrive The passage time, For refueling trucks Arrival Flight At that moment, For refueling trucks to fly Fuel refueling service hours For refueling trucks Arrival Flight From the parking position to the flight Waiting time for arrival; if This indicates that the refueling truck arrived at the flight first. Stop position; conversely This indicates the flight Arrive at the parking position before the refueling truck; Boolean variable For refueling trucks The path identifier is used to identify the refueling truck. From node After departure, is it necessary to go to the node? Driving, if you need to go to the node If driving in that location, ,otherwise ;
[0033] Step S1.2: Construct the total carbon emission model for refueling vehicles as follows:
[0034] ;
[0035] Where C represents the total carbon emissions generated by all refueling trucks providing fuel refueling services to various flights within the unit's planned period. The carbon emissions per kilowatt of power produced by a fuel truck engine, measured in kg / kW. For refueling trucks The weight, in kg. For a given path The characteristic constant coefficients on, Where 'a' is the acceleration of the refueling truck, in m / s². 2 , The rolling resistance coefficient, For a given vehicle model, the characteristic constant coefficients are... A represents the projected area of the refueling truck, in meters. 2 , Air density, unit: kg / m³ 3 , Where u is the traction coefficient and u is the speed of the refueling truck, in km / h.
[0036] Step S1.3: Based on the total carbon emission model of refueling trucks, and with the goal of minimizing the total carbon emissions of refueling trucks, establish a low-carbon optimization scheduling model for refueling trucks as follows:
[0037] ;
[0038] The constraints of the low-carbon optimization scheduling model for refueling trucks are as follows:
[0039] ;
[0040] ;
[0041] ;
[0042] ;
[0043] ;
[0044] ;
[0045] ;
[0046] In the low-carbon optimization scheduling model for refueling trucks, Let be the carbon emission function with respect to path R, representing the minimum total carbon emissions, V represent the set of refueling trucks, k represents the kth refueling truck, and E is the edge set between the common station of the refueling truck set and the flight parking stand node.
[0047] The corresponding constraints of the low-carbon optimization scheduling model for refueling trucks are Equations (1)-(7), where: Equation (1) constrains that only one refueling truck provides fuel refueling service for a flight; Equations (2)-(4) ensure that a refueling truck departs from the depot, provides fuel refueling service for the flight, and then returns to the depot to wait for the next task; constraint Equation (5) represents the refueling truck Complete the previous flight After refueling, then prepare for the next flight. The refueling process needs to meet time constraints; Equation (6) defines R as the set of paths to the solution to the problem, which is a vector composed of nodes. Represents the path scheme assigned to the k-th vehicle; constraint (7) represents Path and and Relationship;
[0048] Step S2: Based on the enhanced BP neural network, the multivariate parameter optimization problem in the low-carbon optimization scheduling model of refueling trucks is transformed into three single-variable sub-optimization problems, namely the gradient vector square sum optimization problem, the actual learning rate optimization problem, and the weight vector optimization problem. The gradient vector square sum v0, the actual learning rate α0, and the weight vector ω1 are initialized, and v0, α0, and ω1 are updated sequentially to obtain the updated gradient vector square sum v1, the actual learning rate α1, and the weight vector ω2.
[0049] The specific steps of step S2 are as follows:
[0050] Step S2.1: Using a genetic algorithm, with airport network topology information and refueling truck operation status data as input and corresponding refueling truck scheduling strategies as output, the input scenario is changed multiple times to obtain multiple refueling truck scheduling strategies as training data for the neural network.
[0051] Step S2.2: Considering the premature convergence problem during the optimization process of the genetic algorithm, an improved BP neural network is used to train the genetic algorithm to learn the optimal scheduling scheme data. Adaptive Gradient Descent (AdaGrad) is used to correct the parameters, and a lower bound function for the learning rate is set based on AdaGrad to complete the mapping from the input to the output of the BP neural network.
[0052] Initialize the gradient vector sum of squares v0=0 for the enhanced BP neural network, the actual learning rate α0=0.1, and the weight vector ω1=0.1;
[0053] Step S2.3: Update v0 to obtain v1 as follows:
[0054] ;
[0055] In the formula, g0 is the initialized gradient vector;
[0056] Update α0 to obtain α1 as follows:
[0057] ;
[0058] ;
[0059] in, , This is a diagonal matrix with values of 0.1 at the diagonal positions. It is a monotonically increasing function with a range of . As the number of iterations t increases, the learning rate tends to... This is to prevent the actual learning rate from approaching 0. , For a fixed learning rate, This represents the actual learning rate. It is a diagonal matrix, where each diagonal position represents the sum of squared gradients of the corresponding weights after t iterations. It is a smoothing term to avoid the denominator being 0, and its value is generally taken as 0. ;
[0060] Update ω1 to obtain ω2 as follows:
[0061] ;
[0062] In the formula, g1 is the gradient vector after one iteration. Indicates projection transformation, Given the original data point set and M(y) as the projection transformation matrix, the following relationship exists:
[0063] ;
[0064] in, , , It is a symmetric matrix with positive definite properties. ;
[0065] Project update weights that are not in the domain to the domain. Expanding this, we get the following formula:
[0066] ;
[0067] Obtain the updated sum of squared gradient vectors v1, the actual learning rate α1, and the weight vector ω2.
[0068] Step S3: Using the sum of squared gradient vectors v1, the actual learning rate α1, and the weight vector ω2 as inputs to the enhanced BP neural network, iteratively optimize the enhanced BP neural network until the preset convergence condition is met, thus obtaining the weight vector ω of the enhanced BP neural network. T ;
[0069] The specific method for step S3 is as follows:
[0070] Using the sum of squared gradient vectors v1, the actual learning rate α1, and the weight vector ω2 as inputs to the enhanced BP neural network, the enhanced BP neural network is iteratively optimized as follows:
[0071] ;
[0072] ;
[0073] ;
[0074] In the formula, g t Let t be the gradient vector after t iterations; ;
[0075] The enhanced backpropagation neural network is optimized T times until the preset convergence condition is met, thus obtaining the updated weight vector ω of the enhanced backpropagation neural network. T .
[0076] Step S4: Verify the stability and convergence of the enhanced BP neural network based on Lyapunov stability theory.
[0077] In step S4, the objective function for constructing the enhanced BP neural network is:
[0078] definition This represents the actual output of the p-th neuron in the t-th iteration of the enhanced BP neural network. This represents the ideal output of the p-th neuron in the t-th iteration. For loss function, , This is the loss value. The regret value after T iterations, which is the difference between the loss of the online learning algorithm and the loss of the offline learning algorithm, is used as a performance evaluation metric for the online learning algorithm. With the goal of minimizing, the objective function for constructing the enhanced BP neural network is as follows:
[0079] ;
[0080] in, .
[0081] According to Lyapunov's stability theory, the method to verify the stability of an enhanced backpropagation (BP) neural network is as follows: if the learning rate... Then the enhanced BP neural network is stable in the Lyapunov sense.
[0082] The proof is as follows:
[0083] Constructing Lyapunov functions ;
[0084] ;
[0085] Among them, positive real numbers , satisfy If the learning rate ,but ; Known , Then the enhanced BP neural network is stable.
[0086] According to Lyapunov stability theory, the convergence condition of an enhanced BP neural network is as follows:
[0087] make ,exist , If the following relationship is satisfied , ,but:
[0088] ;
[0089] Then the enhanced BP neural network converges.
[0090] The proof is as follows:
[0091] assumed , satisfy , , where any convex feasible set Then we have:
[0092] ;
[0093] make , We can obtain:
[0094] ;
[0095] Performing an identity transformation on the above equation, we obtain:
[0096] ;
[0097] ;
[0098] in:
[0099] ;
[0100] The first inequality in the above equation is derived from the following formula:
[0101] ;
[0102] The second inequality is derived from Jensen's inequality, the third from Cauchy's inequality, and the fourth from the following equation:
[0103] ;
[0104] in addition,
[0105] ;
[0106] ;
[0107] In summary, we can conclude that:
[0108] ;
[0109] The following is an example of a low-carbon dispatching method for airport refueling trucks based on an enhanced BP neural network designed using this invention:
[0110] The dataset in this example is derived from a portion of the data recorded at Nanjing Lukou Airport on June 25, 2022.
[0111] Using a two-hour cycle, the number of flights awaiting refueling in different time periods can be categorized into five types: 10, 20, 30, 40, and 50. The system model's parameter settings are as follows: Cd =0.4, A=3m 2 τ = 2.11 kg / kW. Since vehicle delays cause greater losses than waiting, a waiting cost coefficient is set. The delay cost coefficient is 10. The dataset is set to 40, with the refueling truck's speed at 20 km / h and its mass at 16000 kg, traveling uniformly on designated airport roads. The dataset is shown in Table 1 below.
[0112] Table 1 Partial Experimental Data
[0113]
[0114] Simulation experiments compare evaluation metrics under four different models:
[0115] The algorithm proposed in this invention is compared with the branch and bound method, genetic algorithm, and BP neural network algorithm in terms of four indicators: carbon emissions, the ratio of refueling trucks to flights, neural network loss value, and algorithm running time. A comparison chart of carbon emissions per unit time under different flight scales is provided below. Figure 2 A comparison chart of the ratio of refueling trucks to aircraft for different flight sizes is provided. Figure 3 A comparison chart of loss values for neural network algorithms under different flight scales is provided. Figure 4 A comparison chart of the operational time complexity under different flight sizes is provided. Figure 5 .
[0116] The embodiments of the present invention have been described in detail above with reference to the accompanying drawings. However, the present invention is not limited to the above embodiments. Within the scope of knowledge possessed by those skilled in the art, various changes can be made without departing from the spirit of the present invention.
Claims
1. A low-carbon scheduling method for airport refueling trucks based on an enhanced BP neural network, characterized in that, Perform the following steps S1-S4 to complete the dispatching of the refueling truck: Step S1: Collect network topology information of the target airport, operating status data of refueling trucks, and operating status data of flights. Calculate the carbon emissions of each refueling truck, construct a low-carbon optimization scheduling model for refueling trucks consisting of multivariate parameters, with the goal of minimizing the total carbon emissions of refueling trucks, and establish corresponding constraints. Step S2: Based on the enhanced BP neural network, the multivariate parameter optimization problem in the low-carbon optimization scheduling model of refueling trucks is transformed into three single-variable sub-optimization problems, namely the gradient vector square sum optimization problem, the actual learning rate optimization problem, and the weight vector optimization problem. The gradient vector square sum v0, the actual learning rate α0, and the weight vector ω1 are initialized, and v0, α0, and ω1 are updated sequentially to obtain the updated gradient vector square sum v1, the actual learning rate α1, and the weight vector ω2. The specific steps of step S2 are as follows: Step S2.1: Using a genetic algorithm, with airport network topology information and refueling truck operation status data as input and corresponding refueling truck scheduling strategies as output, the input scenario is changed multiple times to obtain multiple refueling truck scheduling strategies as training data for the neural network. Step S2.2: Initialize the gradient vector sum of squares v0=0, the actual learning rate α0=0.1, and the weight vector ω1=0.1 for the enhanced BP neural network; Step S2.3: Update v0 to obtain v1 as follows: ； In the formula, g0 is the initialized gradient vector; Update α0 to obtain α1 as follows: ； ； in, , This is a diagonal matrix with values of 0.1 at the diagonal positions. It is a monotonically increasing function with a range of . , , For a fixed learning rate, This represents the actual learning rate. It is a diagonal matrix, where each diagonal position represents the sum of squared gradients of the corresponding weights after t iterations. It is a smoothing term to avoid the denominator being 0; Update ω1 to obtain ω2 as follows: ； In the formula, g1 is the gradient vector after one iteration. Indicates projection transformation, Given the original data point set and M(y) as the projection transformation matrix, the following relationship exists: ； in, , , It is a symmetric matrix with positive definite properties. ; Project update weights that are not in the domain to the domain. Expanding this, we get the following formula: ； Obtain the updated sum of squared gradient vectors v1, the actual learning rate α1, and the weight vector ω2; Step S3: Using the sum of squared gradient vectors v1, the actual learning rate α1, and the weight vector ω2 as inputs to the enhanced BP neural network, iteratively optimize the enhanced BP neural network until the preset convergence condition is met, thus obtaining the weight vector ω of the enhanced BP neural network. T ; The specific method for step S3 is as follows: Using the sum of squared gradient vectors v1, the actual learning rate α1, and the weight vector ω2 as inputs to the enhanced BP neural network, the enhanced BP neural network is iteratively optimized as follows: ； ； ； In the formula, g t Let t be the gradient vector after t iterations; ; It is a monotonically increasing function; The enhanced backpropagation neural network is optimized T times until the preset convergence condition is met, thus obtaining the updated weight vector ω of the enhanced backpropagation neural network. T ; Step S4: Verify the stability and convergence of the enhanced BP neural network based on Lyapunov stability theory.
2. The low-carbon scheduling method for airport refueling trucks based on an enhanced BP neural network according to claim 1, characterized in that, The specific steps of step S1 are as follows: Step S1.1: Obtain target airport network topology information, refueling truck operation status data, and flight operation status data, including the number of flights, parking position location, number of parking positions, number of refueling trucks, flight schedule, and fuel refueling service time. The target airport has a total of n flights within a unit flight operation plan period, and the flight set is as follows: There are a total of m refueling trucks, forming a refueling truck set. Assume that the public assembly point for refueling trucks and the parking positions corresponding to each flight remain fixed, and define... A public outpost for refueling trucks, a set of fixed nodes. ,in Define the aircraft parking stand node; The edge set between the public refueling station and the flight parking position nodes is represented by an undirected graph. Describe the network topology relationship between the point set L and the edge set E, that is, the network topology relationship between the common settlement of the refueling truck set and the parking positions of each flight, and define variables. For nodes and Path distance between For refueling trucks from the node arrive The passage time, For refueling trucks Arrival Flight At that moment, For refueling trucks to fly Fuel refueling service hours For refueling trucks Arrival Flight From the parking position to the flight Waiting time for arrival; if This indicates that the refueling truck arrived at the flight first. Stop position; conversely This indicates the flight It arrived at the parking position before the refueling truck; Boolean variables For refueling trucks The path identifier is used to identify the refueling truck. From node After departure, is it necessary to go to the node? Driving, if you need to go to the node If driving in that location, ,otherwise ; Step S1.2: Construct the total carbon emission model for refueling vehicles as follows: ； Where C represents the total carbon emissions generated by all refueling trucks providing fuel refueling services to various flights within the unit planning period. The carbon emissions for every kilowatt of power produced by a refueling truck engine. For refueling trucks The weight, For a given path The characteristic constant coefficients on, Where 'a' is the acceleration of the refueling truck. The rolling resistance coefficient, For a given vehicle model, the characteristic constant coefficients are... A is the projected area of the refueling truck. air density, Where u is the traction coefficient and u is the speed of the refueling truck. Step S1.3: Based on the total carbon emission model of refueling trucks, and with the goal of minimizing the total carbon emissions of refueling trucks, establish a low-carbon optimization scheduling model for refueling trucks as follows: ； The constraints of the low-carbon optimization scheduling model for refueling trucks are as follows: ； ； ； ； ； ； ； In the low-carbon optimization scheduling model for refueling trucks, Let V be the carbon emission function with respect to path R, V represent the set of refueling trucks, k represent the kth refueling truck, and E be the edge set between the common station of the refueling truck set and the flight parking stand node.
3. The low-carbon scheduling method for airport refueling trucks based on an enhanced BP neural network according to claim 1, characterized in that, In step S4, the objective function for constructing the enhanced BP neural network is: definition This represents the actual output of the p-th neuron in the t-th iteration of the enhanced BP neural network. This represents the ideal output of the p-th neuron in the t-th iteration. For loss function, , The loss value. Let the regret value be the value after T iterations. With the goal of minimizing, the objective function for constructing the enhanced BP neural network is as follows: ； in, .
4. The low-carbon scheduling method for airport refueling trucks based on an enhanced BP neural network according to claim 3, characterized in that, In step S4, based on Lyapunov stability theory, the method to verify the stability of the augmented BP neural network is as follows: if the learning rate... Then the enhanced BP neural network is stable in the Lyapunov sense.
5. A low-carbon scheduling method for airport refueling trucks based on an enhanced BP neural network according to claim 4, characterized in that, In step S4, according to Lyapunov stability theory, the convergence condition of the enhanced BP neural network is as follows: make ,exist , If the following relationship is satisfied , ,but: ； Then the enhanced BP neural network converges.