Optimization method for control parameters of aircraft anti-skid brake based on improved particle swarm algorithm

Abstract

The application belongs to the technical field of aircraft brake control, and discloses an aircraft anti-skid brake control parameter optimization method based on an improved particle swarm algorithm. The method comprises the following steps: establishing a mathematical model of an aircraft brake system and determining target parameters; obtaining model parameters of the mathematical model of the aircraft brake system; initializing parameters of the improved particle swarm algorithm; adjusting inertia weight and acceleration coefficient of the particle swarm algorithm by adopting a second-order oscillation link; updating and iterating particles; performing boundary crossing processing and anti-skid processing on the particles after updating and iteration; comparing the fitness value of each particle after updating with a current optimal fitness value, and updating the optimal value; performing a differential mutation operation on the particles, and updating the optimal value; and stopping until the maximum iteration number is reached. The method solves the problem that in the field of aircraft brakes, optimal brake control law parameters are difficult to select in order to achieve short-distance and high-efficiency braking.

Description

TECHNICAL FIELD

[0001] The application belongs to the technical field of aircraft brake control, and particularly relates to an aircraft anti-skid brake control parameter optimization method based on an improved particle swarm algorithm. BACKGROUND

[0002] With the continuous development of the military and civil aviation fields in China, more and more aircrafts with large tonnage and high speed appear, and the importance of the aircraft anti-skid brake system is increasingly highlighted. Data shows that the incidence of accidents in the landing brake stage reaches 49.1% in various aircraft safety accidents, and the reasonable selection of the anti-skid brake control parameters is very crucial for the aircraft anti-skid brake controller as the core component of the aircraft brake system.

[0003] If the anti-skid brake control parameters are too small, the anti-skid brake system will not be sensitive, which will lead to tire lock and even tire burst. If the anti-skid brake control parameters are too large, the anti-skid brake system will frequently act, which will lead to a long brake distance. The existing aircraft brake control algorithm parameters are mostly selected by the manual parameter adjustment method, which is more dependent on the debugging experience of engineers, and it is difficult to select the optimal parameters of the anti-skid brake control algorithm to achieve short-distance and high-efficiency braking. SUMMARY

[0004] The purpose of the application is to provide an aircraft anti-skid brake control parameter optimization method based on an improved particle swarm algorithm, which solves the problem of difficulty in selecting optimal brake control law parameters in the field of aircraft braking to achieve short-distance and high-efficiency braking.

[0005] The technical scheme of the application is:

[0006] An aircraft anti-skid brake control parameter optimization method based on an improved particle swarm algorithm, the method comprising:

[0007] S1, establishing a mathematical model of the aircraft brake system and determining target parameters;

[0008] S2, obtaining model parameters of the mathematical model of the aircraft brake system;

[0009] S3, initializing parameters of the improved particle swarm algorithm;

[0010] S4, adjusting the inertia weight and acceleration coefficient of the particle swarm algorithm by using a second-order oscillation link;

[0011] S5, updating and iterating the particles;

[0012] S6, performing boundary handling and anti-skid handling on the updated and iterated particles;

[0013] S7, compare the updated fitness value of each particle with the current optimal fitness value, and update the optimal value;

[0014] S8, perform differential mutation operation on the particles, and update the optimal value by using S6 and S7;

[0015] S9, increase the iteration number by 1, and return to S4 until the maximum iteration number is reached.

[0016] The characteristics and further improvements of the technical scheme of the present application are:

[0017] In S1, the mathematical model of the aircraft brake system includes: an aircraft dynamics model, a brake servo valve model, a tire and runway model, an anti-skid control model, a front wheel dynamics model and a main wheel dynamics model; the target parameter is the brake distance output from the aircraft dynamics model.

[0018] In S2, the model parameters of the mathematical model of the aircraft brake system are specifically: the brake distance Distance output from the aircraft dynamics model, the aircraft speed P_Speed, the wheel speed W_Speed output from the main wheel dynamics model, and the proportional link coefficient Kp, the differential link coefficient Kd and the aircraft reference speed deceleration rate Dg in the anti-skid control model.

[0019] In S2, the brake distance Distance output from the aircraft dynamics model is taken as the target parameter, the aircraft speed P_Speed output from the aircraft dynamics model and the wheel speed W_Speed output from the main wheel dynamics model are taken as the algorithm restriction conditions, and the proportional link coefficient, the differential link coefficient and the aircraft reference speed deceleration rate in the anti-skid control model are taken as the algorithm input variables.

[0020] In S3, the parameters of the improved particle swarm algorithm are initialized, specifically including: the size N of the population, N being an integer; the maximum iteration number Max_iter, Max_iter being an integer; the dimension d, d being an integer; the iteration number iter, the initial value iter=1;

[0021] N groups of optimization parameters are determined to be initialized, and a set X is obtained: X=[X1,X2...X i ...X N ], wherein x i =[X Kp , X Kd , X Dg ], and the N groups of optimization parameters are initialized in a set range, wherein X Kp , X Kd , X Dg are respectively the proportional link coefficient, the differential link coefficient and the aircraft reference speed deceleration rate in the anti-skid control model;

[0022] The target fitness value is initialized as the brake distance Distance output by the aircraft dynamics model.

[0023] S4 specifically is:

[0024] 1) The velocity update formula after introducing the second-order oscillation link is shown as formula (7), and the update formula of the gth generation particle i is as follows:

[0025] v i (g+1) = ωv i (g) + c1r1(pbest i (g) - (1 + ξ1)x i (g) + ξ1x i (g-1)) + c2r2(gbest i (g) - (1 + ξ2)x i (g) + ξ2x i (g-1)) (7)

[0026] In the formula, ω is the inertia weight value of the particle; c1 and c2 are acceleration constants; r1 and r2 are random numbers between 0 and 1; pbest is the local optimum, which is the best position of itself after iteration; gbest is the global optimum, which is the best position of the global, that is, the best position experienced by the entire group; ξ1 and ξ2 are random numbers, which are taken as:

[0027] after the preset number of iterations:

[0028] 2) The inertia weight ω

[0029]

[0030] In the formula, ω max and ω min are the initial and final inertia weights of iteration, respectively;

[0031] 3) The two acceleration coefficients in the algorithm are updated as follows:

[0032]

[0033] In the formula, c 1，ini and c 1,fin represent the initial value and the final value of c1, respectively; c 2,ini and c 2，fin represent the initial value and the final value of c2, respectively, and c 2,ini = 0.5 and c 2,fin = 2.5.

[0034] S6 specifically is:

[0035] The speed and position of the new individual after iterative updating are subjected to range constraint and border crossing processing:

[0036]

[0037] In the formula, P_Speed is the aircraft speed, W_Speed is the wheel speed, when the slip ratio is greater than 0.8, it is considered that the deep skid situation exists, and the corresponding fitness value is set to infinity Inf.

[0038] In S8, the differential mutation operation is performed on the particle, and specifically:

[0039] The particle is subjected to the differential mutation operation, the individual after mutation is substituted into the mathematical model of the aircraft brake system to obtain the fitness value, compared with the optimal self before mutation, a new optimal fitness value is selected, and is recorded as Pbest.

[0040] The differential mutation operation is shown in formula (12), y id is a new individual, x id is the current individual, x ad and x bd are two individuals randomly selected from the current generation, L d and H d are the upper and lower bounds of the original population, P r is a selection probability.

[0041]

[0042] In the above formula, when the randomly generated number between 0 and 1 is less than P r , the new individual is generated according to the original rule, and if the randomly generated number is greater than P r , the new individual is generated according to the differential mutation operation.

[0043] The improved particle swarm optimization algorithm proposed in the application can optimize the key parameters of the anti-skid brake control algorithm with better optimization effect. By introducing a second-order oscillation link to directly increase the population diversity, and using an adaptive adjustment strategy for the inertia weight coefficient and the acceleration coefficient to improve the global and local search ability of the particles. In addition, the proposed algorithm combines the differential mutation algorithm to increase the diversity of particles in the late iteration in a probabilistic manner. The application can interactively transmit multiple parameters of the aircraft brake system Simulink model, thereby automatically optimizing multiple key parameters of the anti-skid brake control. Compared with the results of manual experience parameter adjustment, the brake distance is shorter and the brake efficiency is higher. The improved particle swarm optimization algorithm proposed in the application not only can converge more quickly compared with the traditional particle swarm optimization algorithm, but also can jump out of the local optimum to find the anti-skid brake control parameters with shorter brake distance. BRIEF DESCRIPTION OF DRAWINGS

[0044] Figure 1 Simulink model of aircraft brake system

[0045] Figure 2 Model parameter interaction block diagram

[0046] Figure 3 Flow chart of improved PSO algorithm for parameter optimization of aircraft anti-skid brake control algorithm DETAILED DESCRIPTION

[0047] The specific embodiments of the present application are further described below in conjunction with the accompanying drawings.

[0048] The technical solution proposed by the present application is to use the improved particle swarm optimization method of fusing second-order oscillation link and differential mutation strategy to optimize the key parameters of aircraft anti-skid brake control algorithm, and the specific process is as follows:

[0049] Step one: establish a mathematical model of the aircraft brake system and determine the objective function

[0050] The Simulink model of the aircraft brake system is established, which specifically includes an aircraft dynamics model, a brake servo valve model, a tire and runway model, an anti-skid control model, a front wheel dynamics model, and a main wheel dynamics model, and the cross-linking relationship is as shown in Figure 1 The present application encapsulates different functional models in different modules to facilitate the establishment of a clear model profile. The optimization goal of the present application is the brake distance Distance output from the aircraft dynamics module.

[0051] Step two: obtain model parameters and set parameters of the optimization algorithm

[0052] The Simulink model of the aircraft brake system provides all the parameters required by the optimization algorithm. The present application outputs the brake distance Distance, aircraft speed P_Speed, and wheel speed W_Speed in the model to the Workspace of Matlab as inputs of the optimization algorithm, and sets the three key parameters to be optimized, i.e., the proportional link coefficient Kp, the differential link coefficient Kd, and the aircraft reference speed deceleration rate Dg in the anti-skid control model, as global variables.

[0053] The basic parameters of the improved particle swarm algorithm proposed by the present application include: the size of the population N, N is an integer; the maximum number of iterations Max_iter, Max_iter is an integer; the dimension of the particle d, d is an integer; the number of iterations is iter, the initial value iter=1.

[0054] Step three: initialize the population speed and position

[0055] Determine N groups of parameters to be optimized for initialization, and obtain a set X: X=[X1, X2... X i ...X N ], wherein X i One or more combinations of parameters can be selected according to engineering actual requirements.

[0056] Step four: initialize target fitness value

[0057] Input each group of parameters into the Simulink model of the aircraft brake system, and the model output corresponds to the fitness value, which is used as the evaluation system of the individual optimal and global optimal brake parameter set.

[0058] Step five: introduce a second-order oscillation link to update the parameter set

[0059] The present application introduces a second-order oscillation link to directly increase population diversity on the basis of the standard particle swarm algorithm, and adopts an adaptive adjustment strategy for the inertia weight coefficient and the acceleration coefficient to strengthen the global search ability and the local search ability of the particles.

[0060] Step six: particle boundary crossing processing and wheel slip processing

[0061] The speed and position of the new individual after iteration update are subjected to range constraint and processing. The value of the new individual is substituted into the Simulink model for calculation, the P_Speed aircraft speed and W_Speed wheel speed collected in step two are used to determine the wheel slip condition, and the particles crossing the boundary are further excluded.

[0062] Step seven: fitness value comparison

[0063] The updated fitness value of each particle is compared with the current optimal fitness value, and if it is better, it is taken as the current best position Pbest.

[0064] Step eight: fusion differential mutation operation

[0065] The differential mutation operation is performed on the particles, the mutated individual is substituted into the Simulink model to obtain the fitness value, which is compared with the optimal value before mutation, a new optimal fitness value is selected, and is recorded as Pbest. The purpose is to increase the diversity of particles in the later iteration period in a probabilistic manner.

[0066] Step nine: the individual after differential mutation is subjected to boundary crossing processing and wheel locking processing according to step six.

[0067] Step ten: compare all Pbest and Gbest, and update Gbest.

[0068] Step eleven: the iteration number iter is added by 1, and it is checked whether the stop condition is met, if yes, the search is ended, otherwise, return to step five.

[0069] The application is a method for optimizing parameters of an airplane anti-skid brake control algorithm by using an improved particle swarm optimization method with a fusion second-order oscillation link and a differential variation strategy, and a specific flow is as shown in Figure 3 The method is implemented according to the following steps.

[0070] Step one: a mathematical model of an airplane brake system is established, and a target function is determined

[0071] The model of the airplane brake system is composed of an airplane dynamics model, a brake servo valve model, a tire and runway model, an anti-skid control model, a front wheel dynamics model and a main wheel dynamics model. The mathematical models of the above parts are dynamically connected, and the mathematical model of the airplane brake system can be built, as shown in Figure 1 .

[0072] 1) Airplane dynamics model

[0073] The airplane is disturbed by many external factors during the landing and taxiing process, which complicates the force condition of the wheels and has a great impact on the brake process. The dynamics and motion model of the airplane is composed of the front and main wheel dynamics model and the airplane dynamics model, as shown in formula (1)

[0074]

[0075] In the formula, T is the engine thrust; F x is the aerodynamic drag; F x1 and F x2 are the friction forces of the main and front wheels with the ground; F s is the aerodynamic drag of the drag chute; M is the mass; g is the gravitational acceleration; F y is the lift; N1 and N2 are the main and front wheel loads; H is the height of the center of gravity; h t and h s are the distances between the thrust and drag lines and the horizontal line of the center of gravity; a and b are the distances between the center of gravity and the center lines of the main and front wheels; and I is the moment of inertia.

[0076] 2) Brake servo valve model

[0077] The brake servo valve model determines the dynamic characteristics of the hydraulic system. In this paper, it is simplified as a second-order system, and its transfer function is shown in formula (2):

[0078]

[0079] 3) Tire and runway model

[0080] The variation of the engagement coefficient can effectively describe the characteristics between the tire and the track. The engagement coefficient between the wheel and the ground is a multivariable control parameter. This paper only considers the influence of the slip ratio. In a braking process, this paper sets up only one type of track, and there is only one fixed engagement coefficient corresponding to each slip ratio.

[0081] 4) Anti-slip control model

[0082] Anti-skid control is the core model of the entire braking system. It collects the speed signals of the wheels and generates corresponding anti-skid control electrical signals based on these signals. These signals then control the servo valve to adjust the braking pressure. Specifically, when the wheel speed decreases too quickly, slippage is detected, and a large current is output to the servo valve to release the braking pressure. This model mainly consists of anti-skid braking control laws, and the selection of the parameters of these laws directly affects the aircraft's braking distance and braking efficiency.

[0083] 5) Main wheel dynamics model

[0084] The main wheel dynamics model includes the braking system model, the wheel model, and the landing gear model.

[0085] The braking device model refers to the calculation model of the braking torque. The functional relationship between the braking torque and the pressure is shown in formula (3):

[0086]

[0087] In the formula, μ mc n is the coefficient of friction; mc R is the number of friction surfaces; R is the outer friction radius of the brake disc; r is the inner friction radius of the brake disc; P b P0 is the braking pressure; P1 is the minimum braking pressure.

[0088] The wheel model controls the wheel speed by the torque difference between the braking torque and the engagement torque. The wheel speed can be derived according to the law of rotational inertia, as shown in formula (4):

[0089]

[0090] In the formula, M b V is the braking torque; J is the moment of inertia of a single wheel; V ω The linear velocity of the main wheel axle; M is the angular acceleration of the main engine wheel; j This refers to the combined torque.

[0091] The landing gear model can be simplified to a damping-spring system because the buffers on the landing gear have a significant impact on the performance of the wheel braking system. The thermodynamic compression of the oil and gas in the oil-gas buffer system during the aircraft's takeoff can be ignored, as shown in formula (5).

[0092]

[0093] N1 and N2 are the forces of the main and front bumpers acting on the body; and are the compression and rate of change of the main and front bumpers; and are the stiffness and damping coefficients of the main and front bumpers.

[0094] 6) Front wheel dynamics model

[0095] The front wheel dynamics model includes a wheel model and a landing gear model, the wheel model is shown in formula (4), and the landing gear model is shown in formula (5).

[0096] The target function to be optimized by the present application is Figure 1 The brake distance output by the aircraft dynamics model in the formula (6) is the entire sliding distance of the aircraft from landing to stopping.

[0097]

[0098] Distance is the brake distance calculated by the aircraft brake system Simulink simulation model; V(t) is the brake wheel speed in the aircraft brake system Simulink simulation model.

[0099] Step two: obtain model parameters and set the parameters of the algorithm optimization strategy

[0100] The aircraft brake system Simulink model provides all the parameters required by the optimization algorithm, and the present application mainly collects the brake distance Distance, the aircraft speed P_Speed and the wheel speed W_Speed in the aircraft brake system model.

[0101] Step three: initialize the population speed and position

[0102] The intelligent optimization algorithm given by the present application is an improved second-order oscillation particle swarm algorithm combined with a differential mutation strategy, and the basic parameters include: the size of the population N, N is an integer; the maximum number of iterations Max_iter, Max_iter is an integer; the dimension d, d is an integer; the number of iterations is iter, the initial value iter=1.

[0103] Determine N groups of optimization parameters for initialization to obtain the set X: X=[X1,X2...X i ...X N ], wherein X i The parameter combination can be selected according to the actual engineering requirements, and the X i of the present application is [X Kp, X Kd ,X Dg ], the N groups of parameters are initialized in a set range, wherein X Kp , X Kd , X Dg are proportional, differential and deceleration rate coefficients of the brake control model respectively.

[0104] Step four: initialize target fitness value

[0105] Input each group of parameters into the Simulink model of the aircraft brake system, and the model output corresponds to the fitness value (i.e. brake distance Distance), which is used as the evaluation system of the individual optimal and global optimal brake parameter set.

[0106] Step five: introduce a second-order oscillation link to update the parameter set

[0107] The second-order oscillation link and the differential mutation link are introduced in the standard particle swarm algorithm to increase the population diversity, and the inertia weight coefficient and the acceleration coefficient are adaptively adjusted to strengthen the global search ability and the local search ability of the particles.

[0108] 1) In the standard particle swarm algorithm iteration update formula, the velocity update formula after introducing the second-order oscillation link is shown as formula (7), and the update formula of the gth generation particle i is as follows:

[0109] v i (g+1)=ωv i (g)+c1r1(pbest i (g)-(1+ξ1)x i (g)+ξ1x i (g-1))+c2r2(gbest i (g)-(1+ξ2)x i (g)+ξ2x i (g-1)) (7)

[0110] In the formula, ω is the inertia weight value of the particle, c1 and c2 are acceleration constants, or learning factors, r1 and r2 are random numbers between 0 and 1, pbest is the local optimum, i.e. the best position of itself after iteration, and gbest is the global optimum, i.e. the best position of the global optimum, which is the best position experienced by the whole group.

[0111] ξ1 and ξ2 are random numbers, which are taken as:

[0112] in the early stage of algorithm iteration, and taken as:

[0113] At the early stage of algorithm iteration, ξ1, ξ2 is large, according to the improved velocity update formula, the algorithm has strong global search ability. At the later stage of iteration, ξ1, ξ2 is small, which can enhance the local search ability of the algorithm, and it is easy to find the optimal solution. After introducing the second-order oscillation, the flight speed of the particle is related to the current position and the change of the current position, which can make the particle move in a better direction.

[0114] 2) In the standard particle swarm optimization algorithm, the inertia weight ω is an important parameter to balance the global search ability and the local search ability of the algorithm. If ω is decreased with the increase of the iteration number, such as formula (8), it can make the algorithm have a larger ω in the early stage, enhance the global search ability of the algorithm, and have a smaller ω in the later stage of the algorithm, enhance the local search ability of the algorithm.

[0115]

[0116] In the formula, ω max and ω min are the initial and final inertia weights, respectively, ω max = 0.9, ω min = 0.4.

[0117] 3) The two acceleration coefficients in the algorithm are updated as follows:

[0118]

[0119] In the formula, c 1,ini and c 1,fin represent the initial value and the final value of c1, respectively, c 1，ini = 2.5, c 1,fin = 0.5; c 2,ini and c 2,fin represent the initial value and the final value of c2, respectively, c 2,ini = 0.5, c 2,fin = 2.5. As can be seen from the improved update formula, with the increase of the iteration number, c1 decreases and c2 increases, so that the algorithm has strong global search ability in the early stage of iteration, and the algorithm also has local search ability in the later stage of iteration.

[0120] Step six: particle boundary processing and wheel slip processing

[0121] The range constraint and boundary processing are performed on the speed and position of the new individual after iteration update. In the simulation process, there are some wheel slipping and locking conditions, which lead to the sharp decrease of wheel speed or even zero. Although the locking of the wheel may show a shorter brake distance in the optimization result, this situation is very dangerous in the process of airplane braking, which can easily cause airplane side slip and other dangerous accidents, so it needs to be removed from the result set.

[0122]

[0123] In the formula, P_Speed is the aircraft speed, W_Speed is the wheel speed, when the slip ratio is greater than 0.8, it is considered that there is deep skid, and the corresponding fitness value is set to infinity Inf.

[0124] Step seven: fitness value comparison

[0125] The updated fitness value of each particle is compared with the current optimal fitness value, if better, it is taken as the current best position Pbest.

[0126] Step eight: fusion differential mutation operation

[0127] The differential mutation operation is performed on the particle, the mutated individual is substituted into the Simulink model to calculate the fitness value, which is compared with the optimal value before mutation, the new optimal fitness value is selected and recorded as Pbest. The differential mutation operation is shown in formula (12), y id is the new individual generated, x id is the current individual, x ad and x bd are two individuals randomly selected from the current generation, L d and H d are the upper and lower bounds of the original population, P r is a selection probability, usually set to 0.005.

[0128]

[0129] In the above formula, when the randomly generated number between 0 and 1 is less than P r , the new individual is generated according to the original rule, if the randomly generated number is greater than P r , the new individual is generated according to the differential mutation operation. It can be analyzed that in the early stage of the whole population iteration, x ad -x bd is large, the difference of the generated new individual is greater, and the diversity is stronger. In the later stage of the whole population iteration, the population diversity will decrease, x ad -x bd will also be small, the difference of the generated new individual is small, which can approach the global optimum, so with the iteration process, the differential mutation operation makes the algorithm better in balancing the global optimum and the local optimum.

[0130] Step nine: the individual after differential mutation is processed according to step six.

[0131] Step ten: compare all Pbest and Gbest, update Gbest.

[0132] Step eleven: the iteration number iter is added by 1, and it is checked whether the stop condition is met, if yes, the search is ended, otherwise, return to step five.

[0133] The simulation analysis is respectively carried out by using the standard PSO algorithm and the improved PSO algorithm. The PSO finds the optimal value earlier, but from the optimization process, it can be seen that the convergence speed is slow in the early stage, and the final optimization enters the local optimum. The improved PSO algorithm has fast convergence speed in the early stage, and the brake distance is shorter in the final optimization. In summary, the improved PSO algorithm can not only converge more quickly, but also jump out of the local optimum to find the antiskid brake control parameter with shorter brake distance compared with the traditional particle swarm optimization algorithm.

[0134] The improved particle swarm optimization algorithm can optimize the key parameters of the antiskid brake control algorithm with better optimization effect. The second-order oscillation link is introduced to directly increase the population diversity, and the adaptive adjustment strategy is used for the inertia weight coefficient and the acceleration coefficient to improve the global and local search ability of the particles. In addition, the algorithm combines the differential mutation algorithm to increase the diversity of the particles in the later iteration period in a probabilistic manner. Figure 2 As shown in the figure, the improved particle swarm optimization algorithm can automatically optimize the key parameters of the antiskid brake control by scripting programming to interactively transmit the parameters of the aircraft brake system Simulink model, so that the antiskid brake control parameters with shorter brake distance and higher brake efficiency can be found compared with the results based on artificial experience. The improved particle swarm optimization algorithm can not only converge more quickly, but also jump out of the local optimum to find the antiskid brake control parameter with shorter brake distance compared with the traditional particle swarm optimization algorithm.

Claims

1. A method for optimizing aircraft anti-skid braking control parameters based on an improved particle swarm optimization algorithm, characterized in that, The method includes: S1, Establish a mathematical model of the aircraft braking system and determine the target parameters; In S1, the mathematical model of the aircraft braking system includes: an aircraft dynamics model, a brake servo valve model, a tire and runway model, an anti-skid control model, a front wheel dynamics model, and a main wheel dynamics model; The target parameter is the braking distance output from the aircraft dynamics model; S2, obtain the model parameters of the mathematical model of the aircraft braking system; In S2, the specific model parameters for obtaining the mathematical model of the aircraft braking system are: braking distance Distance and aircraft speed P_Speed ​​output by the aircraft dynamics model, wheel speed W_Speed ​​output by the main wheel dynamics model, and proportional element coefficient Kp, differential element coefficient Kd and aircraft reference speed deceleration rate Dg in the anti-skid control model. In S2, the braking distance Distance output by the aircraft dynamics model is used as the target parameter, the aircraft speed P_Speed ​​output by the aircraft dynamics model and the wheel speed W_Speed ​​output by the main wheel dynamics model are used as algorithm constraints, and the proportional element coefficient, differential element coefficient and aircraft reference speed deceleration rate in the anti-skid control model are used as algorithm input variables. S3, Initialize the parameters of the improved particle swarm algorithm; In S3, the parameters for initializing the improved particle swarm optimization algorithm specifically include: population size N, where N is an integer; maximum number of iterations Max_iter, where Max_iter is an integer; dimension d, where d is an integer; and the number of iterations lter, with an initial value of lter = 1. N sets of optimization parameters are determined and initialized to obtain a set X: X = [X1, X2, ..., X...]. i ...X N ], where X i =[X Kp X Kd ,X Dg ], initialize N sets of optimization parameters within a set range, where X Kp X Kd X Dg These are the proportional element coefficient, the differential element coefficient, and the aircraft reference speed deceleration rate in the anti-skid control model, respectively. The initial target fitness value is the braking distance Distance output by the aircraft dynamics model; S4 employs a second-order oscillatory element to adjust the inertial weights and acceleration coefficients of the particle swarm algorithm; S5, updates and iterates the particles; S6, which handles out-of-bounds issues and anti-slip measures for the updated particles; S7, compare the updated fitness value of each particle with the current best fitness value, and update the best value; S8 performs a differential mutation operation on the particles and updates the optimal value using the values ​​from S6 and S7. S9, increment the iteration count by 1, return to S4, until the maximum number of iterations is reached.

2. The method for optimizing aircraft anti-skid braking control parameters based on an improved particle swarm optimization algorithm according to claim 1, characterized in that, S4 specifically refers to: 1) The velocity update formula after introducing the second-order oscillation element is shown in formula (7), and the update formula for particle i in the g-th generation is as follows: v i (g+1)=ωv i (g)+c1r1(pbest i (g)-(1+ξ1)x i (g)+ξ1x i (g-1))+c2r2(gbest i (g)-(1+ξ2)x i (g)+ξ2x i (g-1)) (7) In the formula, ω is the inertial weight of the particle; c1 and c2 are acceleration constants; r1 and r2 are random numbers between 0 and 1; pbest is the local optimum, which is the best position of the particle itself after iteration; gbest is the global optimum, which is the best position experienced by the entire group. ξ1 and ξ2 are random numbers, selected before the preset number of iterations: Take the result after a preset number of iterations: 2) Inertia weight ω in the standard particle swarm optimization algorithm In the formula, ω max and ω min These are the initial and final inertia weights for the iteration, respectively. 3) The two acceleration coefficients in the algorithm are updated in the following way: In the above formula, c 1,ini and c 1,fin These represent the initial and final values ​​of c1, respectively; c 2,ini and c 2,fin Let c represent the initial and final values ​​of c2, respectively. 2,ini =0.5, c 2,fin =2.

5.

3. The method for optimizing aircraft anti-skid braking control parameters based on an improved particle swarm optimization algorithm according to claim 1, characterized in that, S6 specifically refers to: Range constraints and out-of-bounds handling are applied to the velocity and position of the new individual after iterative updates: In the formula, P_Speed ​​is the aircraft speed and W_Speed ​​is the wheel speed. When the slip ratio is greater than 0.8, it is considered that there is a deep slip situation, and the corresponding fitness value is set to infinity Inf.

4. The method for optimizing aircraft anti-skid braking control parameters based on an improved particle swarm optimization algorithm according to claim 1, characterized in that, In S8, the particle differential mutation operation is performed as follows: Perform differential mutation on the particles, substitute the mutated individuals into the mathematical model of the aircraft braking system to obtain the fitness value, compare it with the original best fitness value, select the new better fitness value, and record it as Pbest. The difference mutation operation is shown in equation (12), y id It is a newly generated individual, x id It is the current individual, x ad and x bd Two individuals, L, are randomly selected from the current generation. d and H d It is the upper and lower bounds of the original group, P r It is a choice probability; In the above formula, when the number randomly generated between 0 and 1 is less than P... r Then, new individuals are generated according to the original rules. If the number of randomly generated individuals is greater than P... r Then, a new individual is generated according to the differential mutation operation.

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