CN115935769A - Airplane anti-skid brake control parameter optimization method based on improved particle swarm optimization - Google Patents
Airplane anti-skid brake control parameter optimization method based on improved particle swarm optimization Download PDFInfo
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Abstract
The invention belongs to the technical field of airplane brake control, and discloses an airplane antiskid 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 braking system, and determining target parameters; obtaining model parameters of a mathematical model of an aircraft braking system; initializing parameters of the improved particle swarm algorithm; adjusting the inertia weight and the acceleration coefficient of the particle swarm algorithm by adopting a second-order oscillation link; updating and iterating the particles; performing border crossing processing and anti-slip processing on the updated and iterated particles; comparing the updated fitness value of each particle with the current optimal fitness value, and updating the optimal value; carrying out differential variation operation on the particles and updating an optimal value; until a maximum number of iterations is reached. The problem that in the field of airplane braking, in order to realize short-distance and high-efficiency braking, the optimal braking control law parameters are difficult to select is solved.
Description
Technical Field
The invention belongs to the technical field of airplane brake control, and particularly relates to an airplane antiskid brake control parameter optimizing method based on an improved particle swarm algorithm.
Background
With the continuous development of military and civil aviation fields in China, the number of large-tonnage and high-speed airplanes is increased, and the importance of an airplane anti-skid braking system is more and more prominent. The data show that in various airplane safety accidents, the accident rate in the landing and braking stage reaches 49.1%, and the reasonable selection of the antiskid brake control parameters is very critical when the airplane antiskid brake controller is used as a core component of an airplane brake system.
If the antiskid brake control parameter is selected to be too small, the antiskid of the brake system is insensitive, and the tire is locked or even blown out. If the antiskid brake control parameter is selected too large, the antiskid brake system can be frequently actuated in an antiskid mode, and the braking distance is too long. The parameter selection of the existing airplane brake control algorithm is mostly carried out by a manual parameter adjusting method, and the parameter selection is relatively dependent on self debugging experience of engineers, so that the optimal parameter of the antiskid brake control algorithm is difficult to select to realize short-distance and high-efficiency braking.
Disclosure of Invention
The purpose of the invention is: the method is used for solving the problem that optimal brake control law parameters are difficult to select in the field of airplane braking in order to realize short-distance and high-efficiency braking.
The technical scheme of the invention is as follows:
an aircraft antiskid brake control parameter optimizing method based on an improved particle swarm algorithm, the method comprising the following steps:
s1, establishing a mathematical model of an aircraft brake system, and determining target parameters;
s2, obtaining model parameters of a mathematical model of the aircraft brake system;
s3, initializing parameters of the improved particle swarm algorithm;
s4, adjusting the inertia weight and the acceleration coefficient of the particle swarm algorithm by adopting a second-order oscillation link;
s5, updating and iterating the particles;
s6, performing border crossing processing and anti-slip processing on the updated and iterated particles;
s7, comparing the updated fitness value of each particle with the current optimal fitness value, and updating the optimal value;
s8, carrying out differential variation operation on the particles, and adopting updated optimal values of S6 and S7;
and S9, adding 1 to the iteration times, and returning to S4 until the maximum iteration times is reached.
The technical scheme of the invention has the characteristics and further improvements that:
in S1, the mathematical model of the aircraft braking system comprises: the system comprises 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 target parameter is a braking distance output from an aircraft dynamics model.
In S2, the model parameters of the mathematical model of the aircraft brake system are obtained specifically as follows: the braking Distance output by the aircraft dynamics model, the aircraft Speed P _ Speed, the aircraft wheel Speed W _ Speed output by the main wheel dynamics model, and a proportional link coefficient Kp, a differential link coefficient Kd and an aircraft reference Speed deceleration rate Dg in the anti-skid control model.
In S2, the braking Distance output by the aircraft dynamics model is used as a target parameter, the aircraft Speed P _ Speed output by the aircraft dynamics model, the aircraft wheel Speed W _ Speed output by the main wheel dynamics model are used as algorithm limiting conditions, and the proportional link coefficient, the differential link coefficient and the aircraft reference Speed deceleration rate in the antiskid control model are used as algorithm input variables.
In S3, initializing parameters of the improved particle swarm algorithm specifically includes: the size N of the population is an integer; the maximum iteration times Max _ iter are integers; dimension d, d being an integer; the iteration number is iter, and the initial value iter =1;
determining N groups of optimizing parameters for initialization to obtain a set X: x = [ X = 1 ，X 2 ...X i ...X N ]Wherein X is i ＝[X Kp ，X Kd ，X Dg ]Initializing N sets of optimization parameters within a set range, wherein X Kp 、x Kd 、X Dg Proportional link coefficients, differential link coefficients and airplane reference speed deceleration rate in the anti-skid control model are respectively;
and initializing a target fitness value as a braking Distance output by the aircraft dynamics model.
S4 specifically comprises the following steps:
1) The velocity updating formula after the second-order oscillation link is introduced is shown as a formula (7), and the updating formula of the g-th generation particle i is shown as follows:
v t (g+1)＝ωv i (g)+c 1 r 1 (pbest i (g)-(1+ξ 1 )x i (g)+ξ 1 x i (g-1))+c 2 r 2 (gbest i (g)-(1+ξ 2 )x i (g)+ξ 2 x i (g-1)) (7)
where ω is the inertial weight value of the particle; c1, c 2 Is an acceleration constant; r1, r2 are random numbers between 0 and 1; pbest is locally optimal and is used as the best position of the self after iteration; the gbest is the global optimum, and is the best position experienced by the whole group as the global best position;
ξ 1 ，ξ 2 taking the following as random numbers before presetting iteration times:
taking after the preset iteration times:
2) Inertia weight omega in standard particle swarm algorithm
In the formula, ω max And ω min Iterative initial and final inertial weights, respectively;
3) The following updating method is adopted for the two acceleration coefficients in the algorithm:
in the above formula, c 1，ini And c 1，fin Each represents c 1 Initial and final values of (a); c. C 2，ini And c 2，fin Each represents c 2 Taking the initial value and the final value of (c) 2，ini ＝0.5，c 2，fin ＝2.5。
S6 specifically comprises the following steps:
and (3) carrying out range constraint and border crossing processing on the speed and the position of the new individual after iterative update:
in the formula, P _ Speed is the airplane Speed, W _ Speed is the airplane wheel Speed, when the slip ratio is greater than 0.8, it is considered that the deep slip condition exists, and the corresponding fitness value is set as infinity Inf.
In S8, performing differential mutation on the particles, specifically:
carrying out differential variation operation on the particles, substituting the varied individuals into a mathematical model of an airplane brake system to obtain a fitness value, comparing the fitness value with the self-optimal value before variation, selecting a new optimal fitness value, and recording the new optimal fitness value as Pbest;
the differential mutation operation is shown in equation (12), y id Is a 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 Is the upper and lower bound of the original population, P r Is a selection probability;
in the above formula, when the randomly generated number between 0 and 1 is less than P r Then according to the original methodGenerating a new entity if the randomly generated number is greater than P r Then a new individual is generated according to the differential mutation operation.
The beneficial effects of the invention are: the improved particle swarm optimization algorithm provided by the invention can optimize the key parameters of the antiskid brake control algorithm with a better optimization effect. The population diversity is directly increased by introducing a second-order oscillation link, and meanwhile, an adaptive adjustment strategy is adopted for an inertia weight coefficient and an acceleration coefficient to improve the global and local searching capability of the particles. Furthermore, the proposed algorithm incorporates a differential mutation algorithm to increase the diversity of the particles in a probabilistic manner late in the iteration. The method can interactively transmit a plurality of parameters of the Simulink model of the aircraft brake system, so that a plurality of key parameters of anti-skid brake control are automatically optimized. Compared with the result of adjusting parameters based on manual experience, the braking distance is shorter, and the braking efficiency is higher. Compared with the traditional particle swarm optimization algorithm, the improved particle swarm optimization algorithm provided by the invention not only can be used for converging more quickly, but also can jump out the local optimal method for finding the anti-skid brake control parameter with a shorter brake distance.
Drawings
FIG. 1 is a Simulink model of an aircraft braking system;
FIG. 2 is a model parameter interaction block diagram;
FIG. 3 is a flow chart of an improved PSO algorithm for aircraft antiskid brake control algorithm parameter optimization.
Detailed Description
The following further describes embodiments of the present invention with reference to the drawings.
The technical scheme provided by the invention is that an improved particle swarm optimization method integrating a second-order oscillation link and a differential variation strategy is utilized to optimize key parameters of an airplane antiskid brake control algorithm, and the specific process is as follows:
the method comprises the following steps: establishing a mathematical model of an aircraft braking system and determining an objective function
The method comprises the steps of establishing a Simulink model of an aircraft brake system, wherein the Simulink model specifically comprises an aircraft dynamic model, a brake servo valve model, a tire and runway model, an anti-skid control model, a front wheel dynamic model and a main wheel dynamic model, and the cross-linking relation is shown in figure 1. The invention encapsulates different functional models in different modules to facilitate the creation of a clean model profile. The optimization objective of the present invention is the braking Distance output from the aircraft dynamics module.
Step two: obtaining model parameters and setting parameters of optimization algorithm
The Simulink model of the aircraft braking system provides all the parameters required for the optimization algorithm. According to the method, the braking Distance, the airplane Speed P _ Speed and the airplane wheel Speed W _ Speed in the model are output to WorkSpace of Matlab as the input of an optimization algorithm, and three key parameters to be optimized, namely a proportional link coefficient Kp, a differential link coefficient Kd and an airplane reference Speed deceleration rate Dg, in the antiskid control model are set as global variables.
The basic parameters of the improved particle swarm optimization algorithm provided by the invention comprise: the size N of the population is an integer; the maximum iteration times Max _ iter is an integer; the particle dimensions d, d are integers; the number of iterations is iter Initial value of iter ＝1
Step three: initializing population velocity and location
Determining N groups of parameters to be optimized for initialization to obtain a set X: x = [ X = 1 ，X 2 …X i …X N ]Wherein X is i The combination of one or more parameters may be selected according to the actual requirements of the project.
Step four: initializing a target fitness value
And inputting each group of parameters to a Simulink model of the aircraft brake system, and outputting corresponding fitness values by the model to serve as an evaluation system of the individual optimal and global optimal brake parameter sets.
Step five: introducing a second-order oscillation link to update the parameter set
On the basis of a standard particle swarm algorithm, on one hand, a second-order oscillation link is introduced to directly increase the population diversity, and on the other hand, an adaptive adjustment strategy is adopted for an inertia weight coefficient and an acceleration coefficient, so that the global search capability and the local search capability of particles are enhanced.
Step six: particle boundary crossing handling and wheel skid handling
And (5) carrying out range constraint and processing on the speed and the position of the new individual after iterative update. And substituting the value of the new individual into a Simulink model for calculation, judging the wheel skidding condition by using the P _ Speed airplane Speed and the W _ Speed airplane Speed collected in the step two, and further removing out-of-range particles.
Step seven: fitness value comparison
And comparing the updated fitness value of each particle with the current optimal fitness value, and if the updated fitness value of each particle is better, taking the updated fitness value as the current best position Pbest.
Step eight: fused differential mutation operations
And carrying out differential variation operation on the particles, substituting the varied individuals into a Simulink model to obtain a fitness value, optimally comparing the fitness value with the self value before variation, selecting a new better fitness value, and recording the new better fitness value as Pbest. The aim is to increase the diversity of the particles in a probabilistic manner late in the iteration.
Step nine: and (5) carrying out border crossing treatment and airplane wheel locking treatment on the individuals after the differential mutation according to the sixth step.
Step ten: and comparing all Pbest with Gbest and updating Gbest.
Step eleven: and adding 1 to the iteration number iter, checking whether a stop condition is met, if the stop condition is met, ending the search, and otherwise, returning to the fifth step.
The invention discloses a method for optimizing parameters of an airplane antiskid brake control algorithm by using an improved particle swarm optimization method integrating a second-order oscillation link and a differential variation strategy, which is specifically implemented according to the following steps as shown in a flow chart 3:
the method comprises the following steps: establishing a mathematical model of an aircraft braking system and determining an objective function
The model of the airplane brake system comprises an airplane dynamics model, a brake servo valve model, a tire and runway model, an anti-skid control model, a front wheel dynamics model, a main wheel dynamics model and the like. And (3) dynamically connecting the mathematical models of the parts to build a mathematical model of the airplane brake system, as shown in figure 1.
1) Aircraft dynamics model
The airplane is interfered by a plurality of external factors in the landing and running process, so that the stress condition of the airplane wheel is complicated, and the braking process is greatly influenced. The power and motion model of the airplane consists of a front wheel dynamic model, a main wheel dynamic model and an airplane dynamic model, and is shown in a formula (1)
In the formula, T is engine thrust; f x Is the aerodynamic resistance; f x1 And F x2 The friction force between the main wheel and the front wheel and the ground is adopted; f s Is the pneumatic resistance of the drag parachute; m is mass; g is gravity acceleration; f y Is a lifting force; n is a radical of 1 And N 2 The load of the main wheel and the front wheel is taken; h is the height of the center of gravity of the airplane; h is t And h s The distance between the thrust line and the resistance line 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 wheel and the front wheel; and I is the moment of inertia.
2) Brake servo valve model
The brake servo valve model determines the hydraulic system dynamics. This is simplified to a second order system, the transfer function of which is shown in equation (2):
3) Tire and runway model
The characteristic between the tires/runways can be effectively described by combining the change rule of the coefficients. The combination coefficient of the wheel and the ground is a multivariable control parameter, only the influence of the slip rate is considered, only one runway is arranged in the braking process, and only one fixed combination coefficient is corresponding to each slip rate.
4) Anti-skid control model
The antiskid control is a core model of the whole brake system, collects speed signals of the wheels, generates corresponding antiskid control electric signals according to the speed signals, further controls the servo valve to adjust the brake pressure, namely judges that skidding occurs when the speed of the wheels is reduced too fast, outputs a large current to the servo valve, and relieves the brake pressure. The model mainly comprises an antiskid brake control law, and the selection of parameters of the antiskid brake control law can directly influence the braking distance and the braking efficiency of the airplane.
5) Main wheel dynamics model
The main wheel dynamics model includes a brake device model, a wheel model, and a landing gear model.
The brake device model is a calculation model of the brake torque, and the functional relationship between the brake torque and the pressure is shown in formula (3):
in the formula, mu mc Is the coefficient of friction; n is a radical of an alkyl radical mc The number of the friction surfaces; r is the friction outer radius of the brake disc; r is the friction inner radius of the brake disc; p b The braking pressure is used; p 0 Is the minimum brake pressure.
The wheel model controls the wheel speed by the moment difference of the braking moment and the combining moment. The wheel speed can be obtained according to the law of rotational inertia, and is specifically shown in formula (4):
in the formula, M b The braking moment is used; j is the moment of inertia of a single wheel; v ω The linear velocity of the wheel axle of the main wheel;
is the angular acceleration of the main engine wheel; m j To couple the moments.
The landing gear model can be simplified into a damping-spring system, because the buffer on the landing gear has a large influence on the performance of the wheel braking system, and the thermodynamic compression condition of oil and gas of the oil and gas buffer system in the airplane sliding process can be ignored, as shown in formula (5):
in the formula, N 1 And N 2 The force acting on the machine body by the main buffer and the front buffer; y is 1 、Y 1 And Y 2 、Y 2 The compression amount and the change rate of the main buffer and the front buffer are used; kappa N1 、c 1 And kappa N2 、c 2 The rigidity coefficient and the damping coefficient on the main buffer and the front buffer.
6) Front wheel dynamics model
The front wheel dynamics model comprises a wheel model and an undercarriage model, wherein the wheel model is shown in a formula (4), and the undercarriage model is shown in a formula (5).
The objective function to be optimized in the invention is the braking distance output by the aircraft dynamics model in fig. 1, the braking distance refers to the whole sliding distance from landing to stopping of the aircraft, and the mathematical formula of the braking distance is shown in formula (6).
In the formula, distance is a braking Distance calculated by a Simulink simulation model of an aircraft braking system; v (t) is the speed of a brake wheel in a Simulink simulation model of the aircraft brake system.
Step two: obtaining model parameters and setting parameters of algorithm optimization strategy
The method mainly collects the braking Distance, the airplane Speed P _ Speed and the airplane wheel Speed W _ Speed in the airplane braking system model.
Step three: initializing population velocity and location
The intelligent optimization algorithm provided by the invention is an improved second-order oscillation particle swarm algorithm fused with a differential variation strategy, and the basic parameters comprise: the size N of the population is an integer; the maximum iteration times Max _ iter is an integer; dimension d, d being an integer; the iteration number is iter, and the initial value iter =1.
Determining N groups of optimizing parameters for initialization to obtain a set X: x = [ X ] 1 ，X 2 ...X i ...x N ]Wherein X is i The parameter combination can be selected according to the actual requirements of the project, and the invention X i ＝[X Kp ，X Kd ，X Dg ]Initializing N sets of parameters within a set range, wherein x Kp 、X Kd 、x Dg The proportional coefficient, the differential coefficient and the deceleration rate coefficient of the brake control model are respectively.
Step four: initializing a target fitness value
And inputting each group of parameters to a Simulink model of the aircraft braking system, and outputting a corresponding fitness value (namely braking Distance) by the model to serve as an evaluation system of the individual optimal and global optimal braking parameter set.
Step five: introducing a second-order oscillation link to update the parameter set
According to the invention, a second-order oscillation link and a differential variation link are introduced on the basis of a standard particle swarm algorithm to increase the population diversity, and an adaptive adjustment strategy is adopted for an inertia weight coefficient and an acceleration coefficient to enhance the global search capability and the local search capability of particles.
1) In the standard particle swarm optimization iterative updating formula, the velocity updating formula after the second-order oscillation link is introduced is shown as a formula (7), and the updating formula of the g-th generation particle i is shown as follows:
v i (g+1)＝ωv i (g)+c 1 r 1 (pbest t (g)-(1+ξ 1 )x i (g)+ξ 1 x i (g-1))+c 2 r 2 (gbest i (g)-(1+ξ 2 )x i (g)+ξ 2 x i (g-1)) (7)
where ω is the inertial weight value of the particle; c. C 1 、c 2 Is an acceleration constant, otherwise known as a learning factor; r is a radical of hydrogen 1 、r 2 Is a random number between 0 and 1; pbest is local optimum, namely the best position of the self after iteration; the gbest is global optimum, i.e. the best position of the global, is the best bit experienced by the whole populationAnd (4) placing.
ξ 1 ，ξ 2 Taking the following numbers at the earlier stage of algorithm iteration as random numbers:
taking at the later stage of algorithm iteration:
ζ early in algorithm iteration 1 ζ 2 And the algorithm has stronger global search capability according to the improved speed updating formula. In the later stage xi of iteration 1 ，ξ 2 The method is small, can enhance the local search capability of the algorithm, and is easy to find the optimal solution. After the second-order oscillation is introduced, the flight speed of the particles is related to the current position and the change of the current position, so that the particles can move to a better direction.
2) The inertial weight omega in the standard particle swarm algorithm is an important parameter for balancing the global search capability and the local search capability of the algorithm. If a method that the omega is decreased along with the increase of the iteration times is adopted, as shown in a formula (8), the algorithm can have larger omega in the initial stage, the global search capability of the algorithm is enhanced, and the omega is smaller in the later stage of the algorithm, and the local search capability of the algorithm is enhanced.
In the formula, omega max And ω min Respectively, iteration initial and final inertia weights, and taking omega max ＝0.9，ω min ＝0.4。
3) The invention adopts the following updating mode for two acceleration coefficients in the algorithm:
in the above formula, c 1，ini And c 1，fin Each represents c 1 Taking the initial value and the final value of (c) 1，ini ＝2.5，c 1，fin ＝0.5；c 2，ini And c 2，fin Each represents c 2 Taking the initial value and the final value of c 2，ini ＝0.5，c 2，fin =2.5. The improved updating formula shows that as the iteration number increases, c 1 Is lowered to c 2 And the global searching capability of the particles in the initial iteration stage of the algorithm is very strong, and the local searching capability is also realized in the later iteration stage of the algorithm.
Step six: particle boundary crossing processing and wheel skid processing
And performing range constraint and border crossing processing on the speed and the position of the new individual after iterative update. In the simulation process, there are some situations where the wheels skid and lock, resulting in a sharp decrease in wheel speed or even zero. Although the optimal result of the locking of the airplane wheel may show that the braking distance is short, the situation is very dangerous in the braking process of the airplane, and dangerous accidents such as sideslip of the airplane and the like are easily caused, so that the situation needs to be removed from the result in a centralized way.
In the formula, P _ Speed is the airplane Speed, W _ Speed is the airplane wheel Speed, when the slip ratio is greater than 0.8, it is considered that the deep slip condition exists, and the corresponding fitness value is set as infinity Inf.
Step seven: fitness value comparison
And comparing the updated fitness value of each particle with the current optimal fitness value, and if the updated fitness value is better, taking the updated fitness value as the current best position Pbest.
Step eight: fused differential mutation operations
And carrying out differential variation operation on the particles, substituting the varied individuals into a Simulink model to obtain a fitness value, comparing the fitness value with the self-optimal value before variation, selecting a new optimal fitness value, and recording the new optimal fitness value as Pbest. The differential mutation operation is shown in equation (12), y id Is generated byNew 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 Is the upper and lower bound of the original population, P r Is a selection probability, which is typically set to 0.005.
In the above formula, when the randomly generated number between 0 and 1 is less than P r Generating new individuals according to the original rule, if the random generated number is larger than P r Then a new individual is generated according to the differential mutation operation. Through analysis, x is obtained at the initial stage of the whole population iteration ad -x bd Larger, the larger the difference of the generated new individuals is, the stronger the diversity is, at the later stage of the whole population iteration, the population diversity can be reduced, x ad -x bd The difference of the generated new individuals is small, and the difference can approach to the global optimum, so that the algorithm is better in the aspect of balancing the global optimum and the local optimum by the differential variation operation along with the progress of the iterative process.
Step nine: and (5) carrying out boundary crossing processing and wheel skidding processing on the individuals after the difference variation according to the sixth step.
Step ten: and comparing all Pbest and Gtest, and updating Gtest.
Step eleven: and adding 1 to the iteration number iter, checking whether a stop condition is met, if so, finishing the search, and otherwise, returning to the step five.
Simulation analysis was performed using the standard PSO algorithm and the improved PSO algorithm, respectively. Although the optimal value is found earlier by PSO, the early convergence speed is low as seen from the optimization process, and finally the optimization enters local optimization. And the improved PSO algorithm has high early convergence speed, and the final optimized braking distance is shorter. In conclusion, compared with the traditional particle swarm optimization algorithm, the improved PSO algorithm provided by the invention not only can be more rapidly converged, but also can jump out the local optimal search for the anti-skid brake control parameter with a shorter brake distance.
The improved particle swarm optimization algorithm provided by the invention can optimize the key parameters of the antiskid brake control algorithm with a better optimization effect. The population diversity is directly increased by introducing a second-order oscillation link, and meanwhile, an adaptive adjustment strategy is adopted for an inertia weight coefficient and an acceleration coefficient to improve the global and local searching capability of the particles. Furthermore, the proposed algorithm incorporates a differential mutation algorithm to increase the diversity of the particles in a probabilistic manner late in the iteration. As shown in fig. 2, the invention can interactively transmit a plurality of parameters of the Simulink model of the aircraft brake system through script programming, thereby automatically optimizing a plurality of key parameters of the anti-skid brake control. Compared with the result of adjusting parameters based on manual experience, the braking distance is shorter, and the braking efficiency is higher. Compared with the traditional particle swarm optimization algorithm, the improved particle swarm optimization algorithm provided by the invention not only can be used for converging more quickly, but also can jump out the local optimal method for finding the anti-skid brake control parameter with a shorter brake distance.
Claims (8)
1. An aircraft anti-skid brake control parameter optimizing method based on an improved particle swarm algorithm is characterized by comprising the following steps:
s1, establishing a mathematical model of an aircraft brake system, and determining target parameters;
s2, obtaining model parameters of a mathematical model of the aircraft brake system;
s3, initializing parameters of the improved particle swarm algorithm;
s4, adjusting the inertia weight and the acceleration coefficient of the particle swarm algorithm by adopting a second-order oscillation link;
s5, updating and iterating the particles;
s6, performing border crossing processing and anti-slip processing on the updated and iterated particles;
s7, comparing the updated fitness value of each particle with the current optimal fitness value, and updating the optimal value;
s8, carrying out differential variation operation on the particles, and adopting updated optimal values of S6 and S7;
and S9, adding 1 to the iteration times, and returning to S4 until the maximum iteration times is reached.
2. The method for optimizing the parameters of the antiskid brake control of an aircraft based on the improved particle swarm optimization algorithm according to claim 1,
in S1, the mathematical model of the aircraft braking system comprises: the system comprises 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 target parameter is a braking distance output from an aircraft dynamics model.
3. The method for optimizing the parameters of the antiskid brake control of an aircraft based on the improved particle swarm optimization algorithm according to claim 2,
in S2, the model parameters of the mathematical model of the aircraft braking system are obtained specifically as follows: the braking Distance output by the aircraft dynamics model, the aircraft Speed P _ Speed, the aircraft wheel Speed W _ Speed output by the main wheel dynamics model, and a proportional link coefficient Kp, a differential link coefficient Kd and an aircraft reference Speed deceleration rate Dg in the anti-skid control model.
4. The method for optimizing the parameters of the antiskid brake control of an aircraft based on the improved particle swarm optimization algorithm according to claim 3,
in S2, the braking Distance output by the aircraft dynamics model is used as a target parameter, the aircraft Speed P _ Speed output by the aircraft dynamics model, the aircraft wheel Speed W _ Speed output by the main wheel dynamics model are used as algorithm limiting conditions, and the proportional link coefficient, the differential link coefficient and the aircraft reference Speed deceleration rate in the antiskid control model are used as algorithm input variables.
5. The method for optimizing the parameters of the aircraft antiskid brake control based on the improved particle swarm optimization algorithm according to claim 1,
in S3, initializing parameters of the improved particle swarm algorithm specifically includes: the size N of the population is an integer; the maximum iteration times Max _ iter is an integer; dimension d, d being an integer; the iteration number is iter, and the initial value iter =1;
determining N groups of optimizing parameters for initialization to obtain a set X: x = [ X = 1 ，X 2 ...X i ...X N ]Wherein X is i ＝[X Kp ，X Kd ，X Dg ]Initializing N sets of optimization parameters within a set range, wherein X Kp 、X Kd 、X Dg Proportional link coefficients, differential link coefficients and airplane reference speed deceleration rate in the anti-skid control model are respectively;
and initializing a target fitness value as a braking Distance output by the aircraft dynamics model.
6. The method for optimizing the parameters of the antiskid brake control of an aircraft based on the improved particle swarm optimization algorithm according to claim 5,
s4 specifically comprises the following steps:
1) The velocity updating formula after the second-order oscillation link is introduced is shown as a formula (7), and the updating formula of the g-th generation particle i is shown as follows:
v i (g+1)＝ωv i (g)+c 1 r 1 (pbest t (g)-(1+ξ 1 )x i (g)+ξ 1 x i (g-1))+c 2 r 2 (gbest i (g)-(1+ξ 2 )x i (g)+ξ 2 x i (g-1)) (7)
where ω is the inertial weight value of the particle; c. C 1 、c 2 Is an acceleration constant; r is 1 、r 2 Is a random number between 0 and 1; pbest is locally optimal and is used as the best position of the self after iteration; the gbest is the global optimum, and is the best position experienced by the whole group as the global best position;
ξ 1 ，ξ 2 taking the following as random numbers before presetting iteration times:
taking after the preset iteration times:
2) Inertia weight omega in standard particle swarm algorithm
In the formula, ω max And omega min Iterative initial and final inertial weights, respectively;
3) The following updating method is adopted for the two acceleration coefficients in the algorithm:
in the above formula, c 1，ini And c 1，fin Each represents c 1 Initial and final values of (a); c. C 2，ini And c 2，fin Each represents c 2 Taking the initial value and the final value of c 2，ini ＝0.5，c 2，fin ＝2.5。
7. The method for optimizing the parameters of the antiskid brake control of an aircraft based on the improved particle swarm optimization algorithm according to claim 1,
s6 specifically comprises the following steps:
and (3) carrying out range constraint and border crossing processing on the speed and the position of the new individual after iterative update:
in the formula, P _ Speed is the airplane Speed, W _ Speed is the airplane wheel Speed, when the slip ratio is greater than 0.8, it is considered that the deep slip condition exists, and the corresponding fitness value is set as infinity Inf.
8. The method for optimizing the antiskid brake control parameter of the aircraft based on the improved particle swarm optimization algorithm according to claim 1, wherein in S8, the differential variation operation is performed on the particles, specifically:
carrying out differential variation operation on the particles, substituting the varied individuals into a mathematical model of an airplane brake system to obtain a fitness value, comparing the fitness value with the self-optimization value before variation, selecting a new better fitness value, and recording the new better fitness value as Pbest;
the differential mutation operation is shown in equation (12), y id Is a 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 Is the upper and lower bound of the original population, P r Is a selection probability;
in the above formula, when the randomly generated number between 0 and 1 is less than P r Generating new individuals according to the original rule, if the randomly generated number is larger than P r Then a new individual is generated according to the differential mutation operation.
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| CN117950311A (en) * | 2024-03-27 | 2024-04-30 | 济南大学 | Self-adaptive aircraft brake cooling fan PID control method |
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| CN117092905B (en) * | 2023-10-19 | 2024-02-02 | 济南大学 | Optimal robust control method based on improved aircraft brake cooling fan |
| CN117950311A (en) * | 2024-03-27 | 2024-04-30 | 济南大学 | Self-adaptive aircraft brake cooling fan PID control method |
| CN117950311B (en) * | 2024-03-27 | 2024-06-11 | 济南大学 | Self-adaptive aircraft brake cooling fan PID control method |
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