Road adhesion coefficient prediction method based on enhanced northern eagle-Elman neural network

Abstract

A road adhesion coefficient prediction method based on an enhanced northern eagle-Elman neural network comprises the following steps: firstly, loading a data set, dividing the data set into training data and test data, carrying out normalization processing, determining the number of neurons in a hidden layer, and determining the number of neurons in the hidden layer; then, an enhanced northern eagle algorithm ENGO is utilized to optimize an initial weight set in the Elman neural network, the absolute error sum of training data is used as a fitness function to calculate a fitness value, the enhanced northern eagle algorithm ENGO continuously performs prey detection and pursuit escape in a solution space, and an optimal solution is gradually approached; and after the optimal weight of the neural network is updated, carrying out optimal neural network training, and carrying out data reverse normalization to obtain the output of the road adhesion coefficient. According to the method, the Elman neural network is optimized through the enhanced northern eagle algorithm ENGO, the defect that the improved PSO-Elman neural network is prone to falling into a local extremum is overcome, and then the precision of road adhesion coefficient prediction is improved.

Description

Technical Field

[0001] The invention belongs to the technical field of road adhesion coefficient prediction, and in particular relates to a road adhesion coefficient prediction method based on an enhanced northern goshawk-Elman neural network. Background Art

[0002] In recent years, with the continuous upgrading of automobile intelligence and networking and the rapid development of vehicle active safety technology and related control strategies, how to ensure the safe driving of vehicles in emergency braking situations is particularly important. In this process, the state of the vehicle is one of the most important factors, among which the road adhesion coefficient is a key factor affecting vehicle performance and safety.

[0003] Existing road adhesion coefficient estimation methods can be divided into two types: cause-based and effect-based. The cause-based road adhesion coefficient estimation method analyzes various physical factors related to the road adhesion coefficient to establish a mathematical model that reflects the relationship between each factor and the road adhesion coefficient, but its complexity will increase the labor cost; the effect-based identification method estimates the road adhesion coefficient by analyzing the vehicle dynamic response caused by road surface changes. At present, there are many control algorithms used to predict the road adhesion coefficient, such as Kalman filter estimator, sliding mode observer, neural network, etc. Among them, patent application No. 202410229732.1 proposes a road adhesion coefficient estimation method based on the WOA-BP model, establishes a three-degree-of-freedom vehicle dynamics model, obtains the nonlinear fitting relationship between the road adhesion coefficient and the vehicle state quantity, and establishes a WOA-BP neural network model to estimate the actual road adhesion coefficient, but only establishing the three degrees of freedom of the vehicle may limit the accuracy and reliability of its vehicle operation process. Patent application number 202211212250.2 proposes a road adhesion coefficient prediction method based on an improved PSO-Elman neural network, which improves the accuracy of road adhesion coefficient prediction. However, the improved particle swarm optimization (PSO) algorithm is prone to fall into the defect of local extreme values ​​for functions with multiple local extreme points, and may not be able to obtain the correct result in the shortest time. Summary of the invention

[0004] In view of the problem that the improved PSO algorithm is prone to fall into local extreme values ​​for a function with multiple local extreme value points and may not be able to obtain the correct result in the shortest time, the present invention provides a road adhesion coefficient prediction method based on an enhanced northern goshawk-Elman neural network. The method optimizes the Elman neural network through the enhanced northern goshawk algorithm ENGO, overcomes the defect that the improved PSO-Elman neural network is prone to fall into local extreme values, and thus improves the accuracy of road adhesion coefficient prediction.

[0005] The technical solution adopted by the present invention to solve its technical problem is:

[0006] A method for predicting road adhesion coefficient based on an enhanced northern goshawk-Elman neural network comprises the following steps:

[0007] Using a vehicle sensor to obtain initial vehicle data of the target vehicle; determining the longitudinal acceleration a of the target vehicle in a braking state based on the initial vehicle data x , lateral acceleration a y , wheel steering angle δ i 、Wheel angular velocity w i and yaw angular velocity γ; according to the longitudinal acceleration a x , lateral acceleration a y , wheel steering angle δ i 、Wheel angular velocity w i And the yaw rate γ, calculate the estimated longitudinal speed v of the car x , lateral vehicle speed estimate v y , wheel slip angle estimation value α i , longitudinal slip rate estimate λ i ;

[0008] The longitudinal acceleration a collected by the car when driving on roads with different adhesion coefficients x , lateral acceleration a y , wheel steering angle δ i 、Wheel angular velocity w i and the yaw rate γ, and the estimated longitudinal speed v of the vehicle x , lateral vehicle speed estimate v y , wheel slip angle estimation value α i , longitudinal slip rate estimate λ i Composition vector group [a x a y δ i w i γv x v y α i λ i] is used as the input of the corresponding ENGO-Elman neural network unit, and the estimated value of the road adhesion coefficient μ is used as the output.

[0009] The processing steps of the ENGO-Elman neural network unit are as follows: first, load the data set, divide the data set into training data and test data, and perform normalization processing to determine the number of hidden layer neurons. Then, use the enhanced northern goshawk algorithm ENGO to optimize the initial weights set in the Elman neural network, and use the absolute error of the training data as the fitness function to calculate the fitness value. The enhanced northern goshawk algorithm ENGO continuously detects prey and pursues escape in the solution space, gradually approaching the optimal solution. After completing the update of the optimal weights of the neural network, the optimal neural network training is performed, and the output of the road adhesion coefficient is obtained after the data is denormalized.

[0010] The Elman neural network is used to predict the road adhesion coefficient, and its error function is:

[0011] E(μ)=[μ a -μ(n)] 2 / twenty one)

[0012] Where: E(μ) is the error function, μ a is the actual road adhesion coefficient, and μ(n) is the nth predicted value of the road adhesion coefficient.

[0013] The enhanced northern goshawk algorithm ENGO is used to optimize the weights of the Elman neural network. The error function value of the neural network is used as the fitness function of the enhanced northern goshawk algorithm ENGO, where the fitness function is a measure of the pros and cons of the spatial positions of the northern goshawk and its prey. The smaller the fitness function, the better the weight training of the neural network. The fitness function is used to optimize the weights of the Elman neural network through the enhanced northern goshawk algorithm ENGO to find the optimal weights.

[0014] Furthermore, the prediction method further comprises the following steps:

[0015] In the enhanced northern goshawk algorithm ENGO, the hunting strategy of the northern goshawk algorithm NGO can be divided into two steps: prey detection and pursuit escape. Inspired by these different hunting steps, the mathematical model developed by the NGO algorithm is detailed as follows:

[0016] Step 1: Prey Detection Step

[0017] In the initial stage of the northern goshawk's hunting process, it randomly selects its prey and attacks it quickly. The mathematical representation of the northern goshawk's behavior in this step is as follows:

[0018] P i =X k,i=1,2,…,N;k=1,2,…,i-1,…,N (2)

[0019] Where: P i is the prey location selected by the i-th northern goshawk, X k is the position of the kth goshawk in the population, k is a random integer in the range of [1, N].

[0020] The goshawk first randomly selects prey. The position of the selected prey is used to evaluate the fitness of the current prey to decide whether the goshawk will attack. After the goshawk selects the prey, it calculates the fitness value of this selection and updates its position:

[0021]

[0022] Where: F Pi represents the fitness value of the prey position corresponding to the i-th northern goshawk, F i represents the fitness value of the i-th northern goshawk position, is the new position of the i-th northern goshawk in the j-th dimension, x i,j is the original position of the i-th northern goshawk in the j-th dimension, p i,j represents the position of the corresponding prey of the i-th northern goshawk in the j-th dimension, r is a random number generated in [0,1], and I is a random integer with a value of 1 or 2.

[0023] After all dimensions are updated, the new position and new fitness value of the i-th northern goshawk are generated:

[0024]

[0025] Where: F i new,p1 is the updated fitness value of the i-th northern goshawk, is the new position of the i-th northern goshawk, X i The position of the i-th northern goshawk after choosing between the old position and the new position.

[0026] Step 2: Chase and escape steps

[0027] After being attacked by a northern goshawk, the prey will try to escape. During the pursuit, the northern goshawk is very fast and can catch the prey in various situations. Assuming that the hunting occurs within the range of the attack radius R, the mathematical representation of the northern goshawk's behavior in this step is as follows:

[0028]

[0029] Where: t represents the current iteration count, and T represents the maximum iteration limit. represents the new position of the i-th northern goshawk in the second step, represents the new position of the i-th northern goshawk in the j-th dimension in the second step, F i new,p2 Corresponding to the updated fitness value of the i-th northern goshawk after this step.

[0030] During the iterative optimization process, the NGO algorithm may encounter challenges such as suboptimal convergence accuracy and sensitivity to local optimality. The method of NGO initializing the initial population depends on random initialization. Although this strategy is simple in nature, it may harm the diversity of the group's solutions, thereby limiting the scope of exploration. In addition, as inferred from Equation (4), NGO adopts a greedy selection strategy to update the position of the population during the prey detection phase, which increases the risk of the algorithm falling into a local optimal state as the iteration proceeds. In order to overcome these limitations, the reverse learning strategy formulated by the initial population is combined with the Cauchy-Gauss mutation strategy, and finally an enhanced northern goshawk algorithm optimization is formed.

[0031] Furthermore, the optimization method also includes the following specific implementation steps:

[0032] Step 1: Reverse learning strategy

[0033] The reverse learning strategy is a heuristic strategy that aims to improve population initialization, enhance diversity, and improve exploration capabilities. This strategy expands the coverage of the search field by leveraging existing solutions to generate their "reverse" counterparts. In recent years, many researchers have adopted this strategy in various research fields and achieved better performance and faster convergence.

[0034] Let the solution of the i-th northern goshawk be x i =(x i,1 ,x i,2 ,…,x i,D ), where i = 1, 2, ..., N; D is the search dimension; the position reverse solution is defined as follows:

[0035] x′ i,j =δ·(lb j +ub j )-x i,j (8)

[0036] Where: δ is a random variable uniformly distributed between 0 and 1, x i,j is the solution of the ith individual in the jth dimension, x′ i,j is the value corresponding to x i,j The reverse solution of j is in the range of 1 to D, which indicates the dimension of the solution space. The lower and upper bounds of the j-th dimension are lb j andub jRepresentation; the overall initialization process based on reverse learning is as follows:

[0037] (1) Generate an initial population of northern goshawks by random initialization, which contains N individuals;

[0038] (2) Apply reverse learning to create reverse solutions for each initial population member to form a reverse population;

[0039] (3) Combine the initial population and the reverse population to form a new population of 2N.

[0040] Step 2: Cauchy-Gaussian mutation strategy

[0041] In the population position update step of the prey detection step, the Cauchy-Gauss mutation strategy is introduced. This strategy mutates each current individual and compares its position before and after the mutation, thereby selecting a more superior position for the next iteration. This strategy enhances the algorithm's ability to escape local optimality. Individuals with the highest fitness level are selected. To perform mutation, the formula is as follows:

[0042]

[0043] Where: where σ represents the position of the best individual after mutation, 2 is the standard deviation of the mutation, Cauchy(0,σ 2 ) and Gauss(0,σ 2 ) are different random variables, where Cauchy(0,σ 2 ) conforms to the Cauchy distribution law, Gauss(0,σ 2 ) conforms to the Gaussian distribution law, and both are dynamic parameters that are adaptively adjusted with iterations; 1 and λ 2 The value range is 0 to 1. During the entire optimization process, 1 Gradually decrease, λ 2 Gradually grow so that the algorithm can break out of its current stagnant state.

[0044] Furthermore, the enhanced northern goshawk algorithm ENGO continuously detects and chases prey in the solution space, gradually approaches the optimal solution and outputs the optimal weights of the neural network. The ENGO-Elman neural network is used to predict the road adhesion coefficient, and finally outputs the estimated road adhesion coefficient μ:

[0045]

[0046] Where: is the road adhesion coefficient prediction function.

[0047] In order to more fully compare the recognition performance of EGNO-Elman neural network and improved PSO-Elman neural network, the root mean square error E rmse To evaluate the recognition accuracy of the road adhesion coefficient, the expression is as follows:

[0048]

[0049] Where: N is the number of data simulated in the test set, μ a is the actual road adhesion coefficient, and μ(n) is the nth predicted value of the road adhesion coefficient.

[0050] The beneficial effects of the present invention are mainly manifested in:

[0051] The enhanced northern goshawk algorithm ENGO is combined with the Elman neural network structure to establish the ENGO-Elman neural network prediction model. The actual values ​​​​are compared with the predicted values ​​​​obtained by the algorithm. The prediction model optimized by the enhanced northern goshawk is better and the predicted data is more accurate. BRIEF DESCRIPTION OF THE DRAWINGS

[0052] Figure 1 It is a principle block diagram of the present invention.

[0053] Figure 2 It is the work flow chart of the present invention.

[0054] Figure 3 This is the topological structure diagram of the Elman neural network.

[0055] Figure 4 It is a comparison curve chart of the actual value of the road adhesion coefficient under various road conditions, the predicted value of the improved PSO-Elman neural network and the predicted value of the ENGO-Elman neural network. DETAILED DESCRIPTION

[0056] The present invention will be further described below in conjunction with the accompanying drawings.

[0057] like Figure 1 As shown, a road adhesion coefficient prediction method based on an enhanced northern goshawk-Elman neural network includes the following steps: using a vehicle sensor to obtain initial vehicle data of a target vehicle; determining the longitudinal acceleration a of the target vehicle in a braking state according to the initial vehicle data; x , lateral acceleration a y , wheel steering angle δ i 、Wheel angular velocity w i and yaw angular velocity γ; according to the longitudinal acceleration a x , lateral acceleration a y , wheel steering angle δ i、Wheel angular velocity w i And the yaw rate γ, calculate the estimated longitudinal speed v of the car x , lateral vehicle speed estimate v y , wheel slip angle estimation value α i , longitudinal slip rate estimate λ i ;

[0058] The longitudinal acceleration a collected by the car when driving on roads with different adhesion coefficients x , lateral acceleration a y , wheel steering angle δ i 、Wheel angular velocity w i and the yaw rate γ, and the estimated longitudinal speed v of the vehicle x , lateral vehicle speed estimate v y , wheel slip angle estimation value α i , longitudinal slip rate estimate λ i Composition vector group [a x a y δ i w i γv x v y α i λ i ] is used as the input of the corresponding ENGO-Elman neural network unit, and the estimated value of the road adhesion coefficient μ is used as the output.

[0059] like Figure 2 As shown, the ENGO-Elman neural network unit includes the following processing steps:

[0060] Firstly, the data set is loaded and divided into training data and test data, which are normalized and the number of neurons in the hidden layer is determined. Then, the enhanced northern goshawk algorithm ENGO is used to optimize the initial weights set in the Elman neural network. The fitness value is calculated with the absolute error of the training data as the fitness function. The enhanced northern goshawk algorithm ENGO continuously detects prey and pursues and escapes in the solution space, gradually approaching the optimal solution. After completing the update of the optimal weights of the neural network, the optimal neural network training is performed, and the output of the road adhesion coefficient is obtained after the data is denormalized.

[0061] The Elman neural network is used to predict the road adhesion coefficient, and its error function is:

[0062] E(μ)=[μ a -μ(n)] 2 / twenty one)

[0063] Where: E(μ) is the error function, μ ais the actual road adhesion coefficient, and μ(n) is the nth predicted value of the road adhesion coefficient.

[0064] The enhanced northern goshawk algorithm ENGO is used to optimize the weights of the Elman neural network. The error function value of the neural network is used as the fitness function of the enhanced northern goshawk algorithm ENGO, where the fitness function is a measure of the pros and cons of the spatial positions of the northern goshawk and its prey. The smaller the fitness function, the better the weight training of the neural network. The fitness function is used to optimize the weights of the Elman neural network through the enhanced northern goshawk algorithm ENGO to find the optimal weights.

[0065] In the enhanced northern goshawk algorithm ENGO, the hunting strategy of the northern goshawk algorithm NGO can be divided into two steps: prey detection and pursuit escape. Inspired by these different hunting steps, the mathematical model developed by the NGO algorithm is detailed as follows:

[0066] Step 1: Prey Detection Step

[0067] In the initial stage of the northern goshawk's hunting process, it randomly selects its prey and quickly attacks it. The mathematical expression of the northern goshawk's behavior in this step is as follows:

[0068] P i =X k ,i=1,2,…,N;k=1,2,…,i-1,…,N (2)

[0069] Where: P i is the prey location selected by the i-th northern goshawk, X k is the position of the kth goshawk in the population, k is a random integer in the range of [1, N].

[0070] The goshawk first randomly selects prey. The position of the selected prey is used to evaluate the fitness of the current prey to decide whether the goshawk will attack. After the goshawk selects the prey, it calculates the fitness value of this selection and updates its position:

[0071]

[0072] Where: F Pi represents the fitness value of the prey position corresponding to the i-th northern goshawk, F i represents the fitness value of the i-th northern goshawk position, is the new position of the i-th northern goshawk in the j-th dimension, x i,j is the original position of the i-th northern goshawk in the j-th dimension, p i,j represents the position of the corresponding prey of the i-th northern goshawk in the j-th dimension, r is a random number generated in [0,1], and I is a random integer with a value of 1 or 2.

[0073] After all dimensions are updated, the new position and new fitness value of the i-th northern goshawk are generated:

[0074]

[0075] Where: F i new,p1 is the updated fitness value of the i-th northern goshawk, is the new position of the i-th northern goshawk, X i The position of the i-th northern goshawk after choosing between the old position and the new position.

[0076] Step 2: Chase and escape steps

[0077] After being attacked by a northern goshawk, the prey will try to escape. During the pursuit, the northern goshawk is very fast and can catch the prey in various situations. Assuming that the hunting occurs within the range of the attack radius R, the mathematical expression of the northern goshawk's behavior in this step is as follows:

[0078]

[0079] Where: t represents the current iteration count, and T represents the maximum iteration limit. represents the new position of the i-th northern goshawk in the second step, represents the new position of the i-th northern goshawk in the j-th dimension in the second step, F i new,p2 Corresponding to the updated fitness value of the i-th northern goshawk after this step.

[0080] During the iterative optimization process, the NGO algorithm may encounter challenges such as suboptimal convergence accuracy and sensitivity to local optimality. The method used by the NGO algorithm to initialize the initial population depends on random initialization. Although this strategy is simple in nature, it may harm the diversity of the population's solutions, thereby limiting the scope of exploration. In addition, as can be inferred from Equation (4), the NGO algorithm adopts a greedy selection strategy to update the position of the population during the prey detection phase, which increases the risk of the algorithm falling into a local optimal state as the iteration proceeds. In order to overcome these limitations, the reverse learning strategy formulated by the initial population is combined with the Cauchy-Gauss mutation strategy, ultimately forming an enhanced northern goshawk algorithm optimization.

[0081] Furthermore, the optimization method also includes the following specific implementation steps:

[0082] Step 1: Reverse learning strategy

[0083] The reverse learning strategy is a heuristic strategy that aims to improve population initialization, enhance diversity, and improve exploration capabilities. This strategy expands the coverage of the search field by leveraging existing solutions to generate their "reverse" counterparts. In recent years, many researchers have adopted this strategy in various research fields and achieved better performance and faster convergence.

[0084] Let the solution of the i-th northern goshawk be x i =(x i,1 ,x i,2 ,…,x i,D ), where i = 1, 2..., N; D is the search dimension. The position reverse solution is defined as follows:

[0085] x′ i,j =δ·(lb j +ub j )-x i,j (8)

[0086] Where: δ is a random variable uniformly distributed between 0 and 1, x i,j is the solution of the ith individual in the jth dimension, x′ i,j is the value corresponding to x i,j The reverse solution of j is in the range of 1 to D, which indicates the dimension of the solution space. The lower and upper bounds of the j-th dimension are lb j andub j Representation; the overall initialization process based on reverse learning is as follows:

[0087] (1) Generate an initial population of northern goshawks by random initialization, which contains N individuals;

[0088] (2) Apply reverse learning to create reverse solutions for each initial population member to form a reverse population;

[0089] (3) Combine the initial population and the reverse population to form a new population of 2N.

[0090] Step 2: Cauchy-Gaussian mutation strategy

[0091] In the population position update step of the prey detection step, the Cauchy-Gauss mutation strategy is introduced. This strategy mutates each current individual and compares its position before and after the mutation, thereby selecting a more superior position for the next iteration. This strategy enhances the algorithm's ability to escape local optimality. Individuals with the highest fitness level are selected. To perform mutation, the formula is as follows:

[0092]

[0093] Where: where σ represents the position of the best individual after mutation, 2 is the standard deviation of the mutation, Cauchy(0,σ 2 ) and Gauss(0,σ 2 ) are different random variables, where Cauchy(0,σ 2 ) conforms to the Cauchy distribution law, Gauss(0,σ 2 ) conforms to the Gaussian distribution law, and both are dynamic parameters that are adaptively adjusted with iterations; 1 and λ 2 The value range is 0 to 1. During the entire optimization process, 1 Gradually decrease, λ 2 Gradually grow so that the algorithm can break out of its current stagnant state.

[0094] Furthermore, the enhanced northern goshawk algorithm ENGO continuously detects and chases prey in the solution space, gradually approaches the optimal solution and outputs the optimal weights of the neural network. The ENGO-Elman neural network is used to predict the road adhesion coefficient, and finally outputs the estimated road adhesion coefficient μ:

[0095]

[0096] Where: is the road adhesion coefficient prediction function.

[0097] In order to more fully compare the recognition performance of EGNO-Elman neural network and improved PSO-Elman neural network, the root mean square error E rmse To evaluate the recognition accuracy of the road adhesion coefficient, the expression is as follows:

[0098]

[0099] Where: N is the number of data simulated in the test set, μ a is the actual road adhesion coefficient, and μ(n) is the nth predicted value of the road adhesion coefficient.

[0100] like Figure 3 As shown in the figure, the Elman neural network structure is mainly composed of an input layer, a hidden layer, a receiving layer, and an output layer. It has the characteristics of recursive connections and can capture the temporal dependencies between data. Therefore, it shows good performance in many sequence modeling tasks.

[0101] like Figure 4As shown in the figure, the predicted change curves of the road adhesion coefficient of vehicles using the EGNO-Elman neural network road adhesion coefficient prediction method and the improved PSO-Elman neural network road adhesion coefficient prediction method on various road surfaces. In the figure, "actual value", "improved PSO-Elman" and "ENGO-Elman" respectively represent the actual value of the road adhesion coefficient, the improved PSO-Elman neural network predicted value and the ENGO-Elman neural network predicted value.

[0102] As can be seen from the figure, the prediction of the road adhesion coefficient by the ENGO-Elman neural network is better than that by the improved PSO-Elman neural network. The root mean square error of the ENGO-Elman neural network is 0.0313, and the root mean square error of the improved PSO-Elman neural network is 0.0426. The root mean square error of the ENGO-Elman neural network is 26.52% lower than that of the improved PSO-Elman neural network. This shows that the ENGO-Elman neural network has a higher prediction accuracy.

[0103] As a heuristic search algorithm, the enhanced northern goshawk algorithm ENGO has excellent global search capabilities and efficient local optimization characteristics. Therefore, the present invention uses the enhanced northern goshawk algorithm to optimize the Elman neural network, which can greatly improve the dynamic characteristics of the neural network and effectively avoid the influence of local extreme values ​​on the prediction. The enhanced northern goshawk algorithm enhances the population diversity and fitness value by simulating the hunting behavior of the northern goshawk, and further improves the convergence speed and prediction accuracy of the algorithm. Therefore, the Elman neural network optimized based on the enhanced northern goshawk has higher accuracy and stability in the prediction of the road adhesion coefficient.

Claims

1. A method for predicting road adhesion coefficient based on an enhanced northern goshawk-Elman neural network, characterized in that: The prediction method comprises the following steps: Using a vehicle sensor to obtain initial vehicle data of the target vehicle; determining the longitudinal acceleration a of the target vehicle in a braking state based on the initial vehicle data x , lateral acceleration a y , wheel steering angle δ i 、Wheel angular velocity w i and yaw angular velocity γ; according to the longitudinal acceleration a x , lateral acceleration a y , wheel steering angle δ i 、Wheel angular velocity w i And the yaw rate γ, calculate the estimated longitudinal speed v of the car x , lateral vehicle speed estimate v y , wheel slip angle estimation value α i , longitudinal slip rate estimate λ i ; The longitudinal acceleration a collected by the car when driving on roads with different adhesion coefficients x , lateral acceleration a y , wheel steering angle δ i 、Wheel angular velocity w i and the yaw rate γ, and the estimated longitudinal speed v of the vehicle x , lateral vehicle speed estimate v y , wheel slip angle estimation value α i , longitudinal slip rate estimate λ i Composition vector group [a x a y δ i w i γ v x v y α i λ i ] is used as the input of the corresponding ENGO-Elman neural network unit, and the estimated value of the road adhesion coefficient μ is used as the output; The processing steps of the ENGO-Elman neural network unit are as follows: first, load the data set, divide the data set into training data and test data, and perform normalization processing to determine the number of hidden layer neurons. Then, use the enhanced northern goshawk algorithm ENGO to optimize the initial weights set in the Elman neural network, and use the absolute error of the training data as the fitness function to calculate the fitness value. The enhanced northern goshawk algorithm ENGO continuously detects prey and pursues escape in the solution space, gradually approaching the optimal solution. After completing the update of the optimal weights of the neural network, the optimal neural network training is performed, and the output of the road adhesion coefficient is obtained after the data is denormalized.

2. The method for predicting road adhesion coefficient based on enhanced Northern Goshawk-Elman neural network as claimed in claim 1, characterized in that: The prediction method further comprises the following steps: The Elman neural network is used to predict the road adhesion coefficient, and its error function is: E(μ)=[μ a -μ(n)] 2 / 2 (1) Where: E(μ) is the error function, μ a is the actual road adhesion coefficient, μ(n) is the nth predicted value of the road adhesion coefficient; The enhanced northern goshawk algorithm ENGO is used to optimize the weights of the Elman neural network, and the neural network error function value is used as the fitness function of the enhanced northern goshawk algorithm ENGO. The fitness function is a measure of the pros and cons of the spatial positions of the northern goshawk and its prey. The smaller the fitness function, the better the weight training of the neural network. The fitness function is used to optimize the weights of the Elman neural network through the enhanced northern goshawk algorithm ENGO to find the optimal weights.

3. The method for predicting road adhesion coefficient based on enhanced Northern Goshawk-Elman neural network as claimed in claim 2, characterized in that: The prediction method further comprises the following steps: In the enhanced northern goshawk algorithm ENGO, the hunting strategy of the northern goshawk algorithm NGO can be divided into two steps: prey detection and pursuit escape: Step 1: Prey Detection Step In the initial stage of the northern goshawk's hunting process, it randomly selects prey and quickly attacks; in this step, the mathematical expression of the northern goshawk's behavior is as follows: P i =X k ,i=1,2,…,N;k=1,2,…,i-1,…,N (2) Where: P i is the prey location selected by the i-th northern goshawk, X k is the position of the kth goshawk in the population, k is a random integer in the range [1, N]; The goshawk first randomly selects prey. The position of the selected prey is used to evaluate the fitness of the current prey to decide whether the goshawk attacks. After the goshawk selects the prey, it calculates the fitness value of this selection and updates its position: Where: F Pi represents the fitness value of the prey position corresponding to the i-th northern goshawk, F i represents the fitness value of the i-th northern goshawk position, is the new position of the i-th northern goshawk in the j-th dimension, x i,j is the original position of the i-th northern goshawk in the j-th dimension, p i,j represents the position of the corresponding prey of the i-th northern goshawk in the j-th dimension, r is a random number generated in [0,1], and I is a random integer with a value of 1 or 2; After all dimensions are updated, the new position and new fitness value of the i-th northern goshawk are generated: Where: is the updated fitness value of the i-th northern goshawk, is the new position of the i-th northern goshawk, X i is the position of the i-th northern goshawk after choosing between the old position and the new position; Step 2: Chase and escape steps After being attacked by a northern goshawk, the prey will try to escape; assuming that the hunt occurs within the attack radius R, the mathematical expression of the northern goshawk's behavior in this step is as follows: Where: t represents the current iteration count, T represents the maximum iteration limit; represents the new position of the i-th northern goshawk in the second step, represents the new position of the i-th northern goshawk in the j-th dimension in the second step, Corresponding to the updated fitness value of the i-th northern goshawk after this step; The Northern Goshawk algorithm NGO combines the reverse learning strategy formulated by the initial population with the Cauchy-Gaussian mutation strategy, and finally forms an enhanced Northern Goshawk algorithm optimization.

4. The method for predicting road adhesion coefficient based on enhanced Northern Goshawk-Elman neural network as claimed in claim 3, characterized in that: The prediction method further comprises the following steps: Step 1: Reverse learning strategy Let the solution of the i-th northern goshawk be x i =(x i,1 ,x i,2 ,…,x i,D ), where i = 1, 2, ..., N; D is the search dimension; the position reverse solution is defined as follows: x’ i,j =δ·(lb j +ub j )-x i,j (8) Where: δ is a random variable uniformly distributed between 0 and 1, x i,j is the solution of the ith individual in the jth dimension, x' i,j is the value corresponding to x i,j The reverse solution of j is in the range of 1 to D, which indicates the dimension of the solution space. The lower and upper bounds of the j-th dimension are lb j andub j Representation; the overall initialization process based on reverse learning is as follows: (1) Generate an initial population of northern goshawks by random initialization, which contains N individuals; (2) Apply reverse learning to create reverse solutions for each initial population member to form a reverse population; (3) Combine the initial population and the reverse population to form a new population of 2N; Step 2: Cauchy-Gaussian mutation strategy In the population position update step of the prey detection step, the Cauchy-Gauss mutation strategy is introduced; this strategy selects the individual with the highest fitness level by mutating each current individual and comparing its position before and after mutation. To perform mutation, the formula is as follows: Where: where σ represents the position of the best individual after mutation, 2 is the standard deviation of the mutation, Cauchy(0,σ 2 ) and Gauss(0,σ 2 ) are different random variables, where Cauchy(0,σ 2 ) conforms to the Cauchy distribution law, Gauss(0,σ 2 ) conforms to the Gaussian distribution law, and both are dynamic parameters that are adaptively adjusted with iterations; the value range of λ1 and λ2 is 0 to 1. During the entire optimization process, λ1 gradually decreases and λ2 gradually increases, allowing the algorithm to get rid of the current stagnant state.

5. The method for predicting road adhesion coefficient based on enhanced Northern Goshawk-Elman neural network according to claim 3 or 4, characterized in that: The prediction method further comprises the following steps: The enhanced northern goshawk algorithm ENGO continuously detects prey and pursues escape in the solution space, gradually approaches the optimal solution and outputs the optimal weights of the neural network; the ENGO-Elman neural network is used to predict the road adhesion coefficient, and finally outputs the estimated value of the road adhesion coefficient μ: Where: is the road adhesion coefficient prediction function.

6. The method for predicting road adhesion coefficient based on enhanced Northern Goshawk-Elman neural network as claimed in claim 5, characterized in that: The prediction method further comprises the following steps: using the root mean square error E rmse To evaluate the recognition accuracy of the road adhesion coefficient, the expression is as follows: Where: N is the number of data simulated in the test set, μ a is the actual road adhesion coefficient, and μ(n) is the nth predicted value of the road adhesion coefficient.

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