Variable cycle engine control rule optimization method based on improved seat head whale migration algorithm

Abstract

The invention provides a variable cycle engine control rule optimization method based on an improved seat head whale migration algorithm, and belongs to the technical field of engine control, and the method comprises the steps: building a variable cycle engine model, and determining an optimization variable; according to the control mode of each variable cycle engine, constraint conditions and an objective function are determined, the control modes comprise a steady state control mode and a transition state control mode, and the steady state control mode comprises a minimum fuel consumption control mode, a maximum thrust control mode and a minimum turbine front temperature control mode; and based on the target function and the constraint condition, an improved whale migration algorithm is adopted to optimize each control mode to obtain an optimal control variable, and the improved whale migration algorithm comprises the steps of taking Tent mapping as initial migration whale group position mapping and fusing a multi-dimensional learning hunting strategy. According to the processing scheme, the convergence speed and the optimization effect of the engine control rule optimization method are improved, and the engine performance is improved.

Description

Technical Field

[0001] This application relates to the technical field of engine control, and particularly to an optimization method for the control law of a variable cycle engine based on an improved humpback whale migration algorithm. Background Technique

[0002] As a new generation of innovation direction for aviation power systems, variable cycle engines (VCEs) have demonstrated unique value in the fields of high-speed reconnaissance, airspace integration, and multi-mission platforms. Different from the fixed thermodynamic cycles of traditional turbofan / turbojet engines, VCEs achieve intelligent switching of thermodynamic cycle modes by dynamically reconstructing core parameters such as bypass ratio and inter-stage bleed of the compressor, enabling the aircraft to maintain optimal propulsion efficiency in differential tasks such as subsonic cruise, supersonic penetration, and super-maneuverability. When VCEs are in long-term service under extreme operating conditions, their performance degradation exhibits multi-dimensional coupling characteristics: the creep effect of high-temperature alloy blades leads to aerodynamic shape distortion, the spalling of thermal barrier coatings on silicon carbide-based ceramic matrix composites causes sudden changes in the roughness of the flow path, and even more, the fine particles generated by fuel coking can cause dynamic imbalance of the combustor swirler. These non-linear degradation mechanisms cause the engine characteristic map to drift, making the classical control law based on the nominal model prone to chain reactions such as insufficient surge margin or turbine overheating in the transient state.

[0003] In recent years, a large number of research results have been achieved in the optimization of aeroengine control laws. Technologies such as linear programming, reinforcement learning, and intelligent optimization algorithms have been used to optimize the control laws of turbofan, propfan, and turboshaft engines in the steady state and transient state. There have also been many studies on the optimization of the steady-state control law of VCEs, but so far, there is still a lack of relevant research on the design of the transient control law for this type of engine. Compared with turbofan and propfan engines, VCEs have stronger non-linear variable parameter characteristics and more adjustment variables, making it more difficult to design the transient multi-variable adjustment law of VCEs. In addition, in the design of the acceleration control law, these studies have not utilized the physical characteristics of the engine to solve the problem of engine state parameter jitter caused by the randomness of intelligent optimization algorithms.

[0004] A variety of solutions based on meta - heuristic optimization algorithms are proposed to address these issues. For example, a chaotic mapping strategy is embedded into the salp swarm algorithm to enhance the sensitivity to initial values, or the step - size adjustment mechanism of the krill herd algorithm is improved by drawing on the principles of bird - wing aerodynamics. In particular, the recently proposed peacock optimization algorithm, by simulating the multi - dimensional information interaction mechanism during peacock tail - spreading, exhibits better Pareto solution set distribution characteristics when solving the multi - variable strong - coupling optimization problem of VCE. However, when dealing with the sudden change of constraint conditions caused by engine degradation, these algorithms still suffer from the defect of insufficient inertia weight adaptability. Therefore, for the performance decline problem of variable - cycle engines, how to design an efficient, real - time optimization algorithm that can avoid local optimal solutions has become the key to promoting the application of variable - cycle engine control law optimization technology. Summary of the Invention

[0005] In view of this, an embodiment of the present application provides an optimization method for the control law of a variable - cycle engine based on an improved humpback whale migration algorithm, which at least partially solves the technical problems in the prior art that long - term service engines lack self - adaptive adjustment ability after component degradation and traditional optimization algorithms have poor accuracy.

[0006] An embodiment of the present application provides an optimization method for the control law of a variable - cycle engine based on an improved humpback whale migration algorithm, and the method includes: Establish a variable - cycle engine model, and determine optimization variables based on the variable - cycle engine model; For each control mode of the variable - cycle engine, determine the constraint conditions and the objective function based on the optimization variables. The control modes include a steady - state control mode and a transient control mode. The steady - state control mode includes a minimum fuel consumption control mode, a maximum thrust control mode, and a minimum turbine inlet temperature control mode; Based on the objective function and the constraint conditions, use the improved humpback whale migration algorithm to optimize the control law of each control mode to obtain the optimal control variables. The improved humpback whale migration algorithm includes using Tent mapping as the mapping of the initial migrating whale population positions and integrating a multi - dimensional learning hunting strategy.

[0007] According to a specific implementation manner of the embodiment of the present application, the optimization variables are: , The constraint conditions in the process of optimizing the control law of each control mode are described as: , where u is the optimization variable, W fb is the main combustion chamber fuel flow rate, A8 is the area of the tail - pipe throat, A9 is the afterburner fuel flow rate, A 38 is the area of the Flade bypass nozzle, α Fladeis the Flade vane angle, α fan is the fan vane angle, α CDFS is the CDFS vane angle, α HPC is the HPC vane angle, n f is the fan rotational speed, n c is the compressor rotational speed, SM f is the fan surge margin, SM cd is the CDFS surge margin, SM c is the compressor surge margin, P3 is the compressor outlet pressure, T 41 is the engine turbine inlet temperature, the subscript min represents the minimum value, and the subscript max represents the maximum value.

[0008] According to a specific implementation manner of the embodiment of the present application, the objective function and constraint conditions of the minimum fuel consumption control mode are expressed as: F1 = min sfc , wherein, F1 is the objective function of the minimum fuel consumption control mode, min sfc is the minimum value of the engine fuel consumption rate, s.t. is the constraint condition, I is the number of total inequality constraint conditions, F n is the engine thrust, const represents a constant; The objective function and constraint conditions of the maximum thrust control mode are expressed as: F2 = max F n , wherein, F2 is the objective function of the maximum thrust control mode, max F n is the maximum value of the engine thrust; The objective function and constraint conditions of the minimum turbine inlet temperature control mode are expressed as: F3 = min T 41 , wherein, F3 is the objective function of the minimum turbine inlet temperature control mode, min T 41 is the minimum value of the engine turbine inlet temperature.

[0009] According to a specific implementation manner of the embodiment of the present application, the objective function of the transient control mode adopts the adaptive variable weight coefficient method to transform the dual-objective function and multi-inequality constraint problem into an unconstrained optimization problem. The objective function expression of the transient control mode is: , wherein, minJ(k,σ) is the objective function of the transient control mode, ω1 and ω2 are the objective function weights, nc (k) is the compressor speed at the current k moment, T 41 (k) is the total temperature in front of the high-pressure turbine at the current k moment, n c,obj is the target value of the compressor speed, T 41,obj is the target value of the total temperature in front of the high-pressure turbine, σ is an infinitely large positive number, and g(x) is the cost function.

[0010] According to a specific implementation manner of an embodiment of the present application, the optimization of the control law for each control mode by using the improved humpback whale migration algorithm includes: Construct an initial population, the maximum number of iterations, variables, the spatial dimension of the optimization variables, and the boundaries of the search space, initialize the positions of the migrating whale group, and use the Tent mapping as the mapping of the initial positions of the migrating whale group; Sort the individuals in the migrating whale group in descending order according to the fitness value and / or position, take several individuals at the front of the sorting as leaders, calculate the average value of the positions of multiple leaders, and use the average value of the positions as the current position of the entire migrating whale group in the ocean; The individuals in the migrating whale group update their whale positions according to the migration rules under the action of the leaders; Update the whale positions based on the multi-dimensional learning hunting strategy to improve the quality of the search individuals and increase the search ability, and obtain the current best position and the current best fitness value; Use the greedy strategy to evaluate the fitness value of the individuals at the current best position, and retain the individuals valuable for the update of the population position to obtain the final global optimal position and the best fitness value.

[0011] According to a specific implementation manner of an embodiment of the present application, the calculation formula for the average value of the leader positions is: , where N L is the number of leaders, w y is the position of the y-th leader, W Mean is the average value of the leader positions.

[0012] According to a specific implementation manner of an embodiment of the present application, assume that the descending order of the migrating whale group is W1,..., W i-1 , W i , W i+1 ,..., W Npop , the whales with positions from W1 to W i-1 are leaders, the whales with positions from W i to W Npop are calves, W1 is set as the optimal individual W Best , W Npop is set as the worst individual; Individuals in the migrating whale group update the positions of the whales according to the migration rules under the leadership of the leader, including: Each young whale W i (i = N L +1,..., N pop ) moves towards its nearest previous whale W i-1 to perform the first position update; Each young whale moves along the direction given by the vector to perform the second position update, where rand(1, D) is a random number vector taken from the interval [0, 1] with the dimension of the optimization variable space D. The kinematic equation of the second position update is: , ; Each leader identifies and selects the best path towards the end point to perform the third position update. The kinematic equation of the third position update is: , where, is the new position, r1 and r2 are random number vectors with the dimension of the optimization variable space D generated from the interval [0, 1], L represents the starting point vector, U represents the end point vector, and U - L is the relative direction vector; When the new position satisfies , it replaces the current position, is the objective function corresponding to the new solution, is the objective function corresponding to the solution.

[0013] According to a specific implementation manner of the embodiment of the present application, updating the positions of the whales based on the multi-dimensional learning hunting strategy includes: Constructing a radius matrix based on the original positions and new positions of the whales; Constructing a neighborhood matrix based on the radius matrix and the Euclidean distance between the current individual and the alternative individuals; Generating new individuals by learning from multiple neighborhood matrices, where the d-th dimension of each new individual is updated based on the d-th dimension of a randomly selected individual. The new individuals are the positions of the whales updated based on the multi-dimensional learning hunting strategy.

[0014] According to a specific implementation manner of the embodiment of the present application, the expression of the radius matrix is: , The expression of the neighborhood matrix is: , The expression of the generated new individual is as follows: , where Radiusi(t) is the radius matrix, Neighbouri(t) is the neighborhood matrix, w i (t) is the current individual, w j (t) is the alternative individual, w new (t + 1) is the new position of individual i at the (t + 1)-th iteration, D is the dimension of the optimization variable space, N is the initial population, w i-DLH,j (t + 1) is the generated new individual, w i,d (t) is the updated position of individual i at the d-th dimension at the t-th iteration, w n,d (t) is the individual randomly selected by individual i at the d-th dimension at the t-th iteration, w r,d (t) is the reference position of individual i at the d-th dimension at the t-th iteration, and rand is a random function that generates a random number between 0 and 1.

[0015] According to a specific implementation manner of the embodiment of the present application, the expression of the greedy strategy is: , where w i (t + 1) is the position of individual i after the (t + 1)-th iteration, w i-new (t + 1) is the position of individual i that has not executed the multi-dimensional learning hunting strategy after the (t + 1)-th iteration, w i-DLH (t + 1) is the position of individual i after the (t + 1)-th iteration after the update of the multi-dimensional learning hunting strategy, f(w i-new ) is the objective function corresponding to w i-new , f(w i-DLH ) is the objective function corresponding to w i-DLH .

[0016] Beneficial effects: In the method for optimizing the control law of a variable cycle engine based on an improved humpback whale migration algorithm in the embodiment of the present application, by introducing Tent mapping and integrating the multi-dimensional learning hunting strategy, the global convergence performance of the algorithm is effectively enhanced. This solution aims to achieve multiple optimization goals: one is to reduce the fuel consumption rate and significantly improve the fuel utilization efficiency; the second is to output the maximum thrust at the peak of power demand to accurately meet the flight condition requirements; the third is to control the turbine inlet temperature to the lowest level to extend the service life of the turbine; the fourth is to strictly control the system parameters within the limit during the transient operation of the engine and at the same time achieve the shortest acceleration time. The specific beneficial effects are as follows: (1) The Tent mapping is adopted as the mapping of the initial migration position of the whale population to improve the optimization speed and solution accuracy of the algorithm; a multi-dimensional learning hunting strategy is introduced to improve the individual quality, enhance the search process and balance the exploration and exploitation stages. (2) The improved humpback whale migration algorithm is used to conduct numerical simulation verification on the intelligent optimization of the VCE control law to verify the feasibility of the proposed method. The engine performance optimization mode involved in the present invention includes the maximum thrust, the lowest fuel consumption, the lowest turbine inlet temperature under steady state, and the optimization of the acceleration performance under transient state. The optimization parameters are selected as the optimization variables. (3) The proposed improved optimization method is applied to the optimization of the engine control law, and simulation analysis is carried out and the simulation results are compared. This method has a fast convergence speed, good optimization effect, effectively reduces the fuel consumption rate and the lowest turbine inlet temperature of the variable cycle engine, improves the maximum thrust, shortens the acceleration time by 50%, and effectively improves the engine performance. Brief Description of the Drawings

[0017] In order to more clearly illustrate the technical solutions of the embodiments of the present application, the drawings required to be used in the embodiments will be briefly introduced below. Obviously, the drawings described below are only some embodiments of the present application. For those of ordinary skill in the art, other drawings can be obtained based on these drawings without creative efforts.

[0018] Figure 1 It is a flowchart of the variable cycle engine control law optimization method based on the improved humpback whale migration algorithm according to an embodiment of the present invention. Figure 2 It is a schematic diagram of multi-objective optimization according to an embodiment of the present invention. Figure 3 It is a schematic diagram of position update according to an embodiment of the present invention. Detailed Embodiments

[0019] The embodiments of the present application will be described in detail below with reference to the drawings.

[0020] The following describes the implementation manners of the present application through specific specific examples. Those skilled in the art can easily understand other advantages and effects of the present application from the content disclosed in this specification. Obviously, the described embodiments are only a part of the embodiments of the present application, rather than all the embodiments. The present application can also be implemented or applied through other different specific implementation manners. Various details in this specification can also be modified or changed based on different viewpoints and applications without departing from the spirit of the present application. It should be noted that, without conflict, the following embodiments and the features in the embodiments can be combined with each other. Based on the embodiments in the present application, all other embodiments obtained by those of ordinary skill in the art without making creative efforts belong to the scope of protection of the present application.

[0021] It should be noted that the following describes various aspects of the embodiments within the scope of the appended claims. It should be apparent that the aspects described herein can be embodied in a wide variety of forms, and any specific structure and / or function described herein is illustrative only. Based on the present application, those skilled in the art should understand that one aspect described herein can be implemented independently of any other aspect, and two or more of these aspects can be combined in various ways. For example, any number of the aspects described herein can be used to implement the device and / or practice the method. Additionally, this device and / or method can be implemented using other structures and / or functionality in addition to one or more of the aspects described herein.

[0022] It should also be noted that the diagrams provided in the following embodiments only illustrate the basic concept of the present application in a schematic manner. The diagrams only show the components related to the present application, rather than being drawn according to the number, shape, and size of the components in actual implementation. The types, quantities, and proportions of the components in its actual implementation can be arbitrarily changed, and the component layout type may also be more complex.

[0023] In addition, in the following description, specific details are provided to facilitate a thorough understanding of the examples. However, those skilled in the art will understand that the described aspects can be practiced without these specific details.

[0024] The applicant found in the research that in the meta - heuristic optimization algorithm, the Whale - migrating Algorithm (WMA) is an emerging bio - inspired optimization method based on the collaborative migration behavior of humpback whales. Compared with traditional methods, WMA combines the dynamics of leaders and followers with an adaptive migration strategy, effectively balancing the exploration and exploitation phases and improving its ability to avoid local optima and converge effectively.

[0025] Based on the above, an embodiment of the present application provides an optimization method for the control law of a variable cycle engine based on an improved humpback whale migration algorithm, which will be described in detail below with reference to Figures 1 to 3 as follows.

[0026] In one embodiment, with reference to Figure 1 , the optimization method for the control law of a variable cycle engine based on an improved humpback whale migration algorithm includes: Establish a variable cycle engine model, and determine optimization variables based on the variable cycle engine model; For each control mode of the variable cycle engine, determine the constraint conditions and the objective function based on the optimization variables. The control modes include a steady-state control mode and a transient control mode. The steady-state control mode includes a minimum fuel consumption control mode, a maximum thrust control mode, and a minimum turbine inlet temperature control mode; Based on the objective function and the constraint conditions, use the improved humpback whale migration algorithm to optimize the control law of each control mode to obtain the optimal control variables. The improved humpback whale migration algorithm includes using Tent mapping as the mapping of the initial migration whale population position and integrating a multi-dimensional learning hunting strategy.

[0027] In this embodiment, a new improved humpback whale migration algorithm is proposed. The proposed control law does not directly optimize the engine control parameters, but optimizes the controlled parameters (such as rotational speed, pressure ratio) and other adjustment parameters. Compared with directly optimizing the control parameters, adjusting the controlled parameters has the following advantages: First, since the engine is easily affected by external factors (such as flight altitude, gusts, etc.), if the control parameters are directly optimized, the control parameters need to be adjusted in real time according to the environment and flight state, and it is difficult for existing optimization algorithms to meet the requirements of both accuracy and real-time performance. Second, since the engine performance parameters cannot be directly measured, the usual control system cannot directly control the performance parameters. The method in this embodiment improves the humpback whale migration optimization algorithm and adopts a multi-dimensional learning hunting strategy for optimizing the steady-state and transient control laws of a variable cycle engine (VCE), improving the optimization effect of the control law and enhancing the performance of the engine.

[0028] In one embodiment, for the variable cycle engine model studied in this application, the optimization variables are: , (1) The constraint conditions in the process of optimizing the control law of each control mode are described as: , (2) where u is the optimization variable, W fb is the main combustion chamber fuel flow rate, A8 is the throat area of the tail nozzle, A9 is the afterburner fuel flow rate, A 38is the area of the Flade duct nozzle, α Flade is the angle of the Flade guide vane, α fan is the angle of the fan guide vane, α CDFS is the angle of the CDFS guide vane, α HPC is the angle of the HPC guide vane, n f is the fan speed, n c is the compressor speed, SM f is the fan surge margin, SM cd is the CDFS surge margin, SM c is the compressor surge margin, P3 is the compressor outlet pressure, T 41 is the engine turbine inlet temperature, the subscript min is the minimum value, and the subscript max is the maximum value.

[0029] The above formula can be expressed as: , (3) Among them, g(u) represents the inequality constraint condition, i represents the i-th inequality constraint condition, and I is the total number of inequality constraint conditions.

[0030] In one embodiment, the objective function and constraint conditions of the minimum fuel consumption control mode are expressed as: F1 = min sfc , (4) Among them, F1 is the objective function of the minimum fuel consumption control mode, min sfc is the minimum value of the engine fuel consumption rate, s.t. is the constraint condition, I is the total number of inequality constraint conditions, F n is the engine thrust, const represents a constant; The objective function and constraint conditions of the maximum thrust control mode are expressed as: F2 = max F n , (5) Among them, F2 is the objective function of the maximum thrust control mode, max F n is the maximum value of the engine thrust; The objective function and constraint conditions of the minimum turbine inlet temperature control mode are expressed as: F3 = min T 41 , (6) Among them, F3 is the objective function of the minimum turbine inlet temperature control mode, min T 41 is the minimum value of the engine turbine inlet temperature.

[0031] In specific implementation, both the optimization of the minimum fuel consumption control mode and the optimization of the minimum turbine inlet temperature mode are multi-objective optimizations. The objective of the optimization of the minimum fuel consumption control mode is to reach the expected thrust while minimizing the specific fuel consumption; the objective of the optimization of the minimum turbine inlet temperature mode is to reach the expected thrust while minimizing the turbine inlet temperature. The multi-objective optimization principle is as Figure 2 shown. By gradually iterative optimization, either objective 1 or objective 2 is made optimal. By selecting an appropriate weight W = [W1, W2], where W1 is the weight of objective 1 (minimum specific fuel consumption, minimum turbine inlet temperature) and W2 is the weight of objective 2 (constant thrust), the comprehensive performance of objective 1 and objective 2 is made optimal.

[0032] Combining formulas (4) to (6), the optimization of the engine control law can be expressed by the following non-linear programming problem: , (7) where h k (u) is the equality constraint condition, k represents the k-th equality constraint condition, and K is the total number of equality constraint conditions.

[0033] To solve the constrained optimization problem, a penalty function can be introduced, , (8) where F(u, σ) is the objective function with the penalty function introduced, and σ1 and σ2 are positive infinity numbers. In this way, the original constrained problem is transformed into an unconstrained problem. In the intelligent optimization process of the engine adaptive control law, an intelligent optimization algorithm is needed to find the best combination of optimization parameters to make the engine performance optimal.

[0034] In one embodiment, the objective function of the transient control mode adopts the adaptive variable weight coefficient method to transform the double-objective function and multi-inequality constraint problem into an unconstrained optimization problem. The expression of the objective function of the transient control mode is: , where minJ(k, σ) is the objective function of the transient control mode, ω1 and ω2 are the objective function weights respectively, n c (k) is the compressor speed at the current k-th moment, T 41 (k) is the total temperature at the inlet of the high-pressure turbine at the current k-th moment, n c,obj is the compressor speed target value, T 41,obj is the total temperature target value at the inlet of the high-pressure turbine, σ is a positive infinity number, and g(x) is the cost function.

[0035] In specific implementation, for the transient control mode, the key to the acceleration performance of the engine lies in achieving the shortest acceleration time, which can be expressed by the following expression: , (9) where t ac is the acceleration time, I’ is the rotor inertia, n is the rotor speed, n max is the speed at the maximum state, n idle is the speed at the idle state, and ΔH ax is the remaining power of the turbine during the acceleration process. To achieve the optimal acceleration control in each control cycle, the high-pressure rotor speed can be used as the objective function: , (10) where t’ is the integration time.

[0036] The total temperature T 41 in front of the high-pressure turbine can also effectively increase the turbine power. To comprehensively reflect the energy change of the engine operation, the total temperature T 41 in front of the high-pressure turbine and the high-pressure rotor speed are used as the optimization objectives at the same time. The discrete objective function is defined by the linear weighted method: , (11) where ω1 and ω2 are the weights of the objective functions respectively, n c (k) is the compressor speed at the current k-th moment, T 41 (k) is the total temperature in front of the high-pressure turbine at the current k-th moment, n c,obj is the target value of the compressor speed, and T 41,obj is the target value of the total temperature in front of the high-pressure turbine.

[0037] By adopting the adaptive variable weight coefficient method, the double-objective function and multi-inequality constraint problem are transformed into an unconstrained optimization problem: , (12) This method helps to achieve the maximum remaining power of the turbine, reduce the acceleration time, and ensure a high specific thrust.

[0038] In one embodiment, the improved humpback whale migration algorithm is used to optimize the control law of each control mode, including: Construct the initial population, the maximum number of iterations, variables, the spatial dimension of the optimization variables, and the boundaries of the search space, initialize the positions of the migrating whale population, and use the Tent mapping as the mapping of the initial positions of the migrating whale population; Sort the individuals in the migrating whale population in descending order according to the fitness value and / or position, take several individuals with the highest ranking as the leaders, calculate the average value of the positions of the multiple leaders, and use the average value of the positions as the current position of the entire migrating whale population in the ocean; The individuals in the migrating whale population update their positions according to the migration rules under the action of the leaders; Update the whale position based on the multi-dimensional learning hunting strategy to improve the quality of the search individuals and increase the search ability, and obtain the current best position and the current best fitness value; Adopt a greedy strategy to evaluate the fitness value of the individuals at the current best position, and retain the individuals valuable for the population position update to obtain the final global optimal position and the best fitness value.

[0039] In this embodiment, a design of an improved humpback whale migration algorithm (IWMA) is proposed. Through this method, IWMA overcomes the defects of the original WMA, further improves the optimization speed and solution accuracy, and provides an effective strategy for solving complex problems.

[0040] Furthermore, the calculation formula for the average value of the leader positions is: , where N L is the number of leaders, w y is the position of the y-th leader, and W Mean is the average value of the leader positions.

[0041] Furthermore, let the descending order of the migrating whale population be W1,...,W i-1 ,W i , W i+1 ,...,W Npop , the whales at positions from W1 to W i-1 are leaders, and the whales at positions from W i to W Npop are calves. W1 is set as the optimal individual W Best , and W Npop is set as the worst individual; The individuals in the migrating whale population update their whale positions according to the migration rules under the influence of the leaders, including: Each calf W i (i = N L +1,...,N pop ) moves towards the nearest previous whale W i-1 for the first position update; Each calf moves along the direction given by the vector for the second position update, where rand(1,D) is a random number vector taken from the interval [0,1] with the dimension of the optimization variable space D. The kinematic equation for the second position update is: , ; Each leader identifies and selects the best path towards the end point and performs a third position update. The kinematic equation for the third position update is as follows: , where is the new position, r1 and r2 are random number vectors of dimension D of the optimization variable space generated from the interval [0, 1] respectively, L represents the starting point vector, U represents the end point vector, and U - L is the relative direction vector; When the new position satisfies , replace the current position. is the value of the objective function corresponding to the new solution, is the value of the objective function corresponding to the solution.

[0042] Furthermore, updating the whale position based on the multi - dimensional learning hunting strategy includes: Constructing a radius matrix based on the original position and the new position of the whale; Constructing a neighborhood matrix based on the radius matrix and the Euclidean distance between the current individual and the alternative individual; Generating new individuals by learning from multiple neighborhood matrices, where the d - th dimension of each new individual is updated based on the d - th dimension of a randomly selected individual. The new individual is the whale position updated based on the multi - dimensional learning hunting strategy.

[0043] Furthermore, the expression of the radius matrix is: , The expression of the neighborhood matrix is: , The expression of the generated new individual is: , where Radiusi(t) is the radius matrix, Neighbouri(t) is the neighborhood matrix, w i (t) is the current individual, w j (t) is the alternative individual, w new (t + 1) is the new position of individual i at the (t + 1)-th iteration, D is the dimension of the optimization variable space, N is the initial population, w i-DLH,j (t + 1) is the generated new individual, w i,d (t) is the updated position of individual i at the d - th dimension at the t - th iteration, w n,d (t) is the individual selected randomly by individual i at the d - th dimension at the t - th iteration, w r,d(t) is the reference position of individual i in the d - dimension at the t - th iteration, and rand is a random function that generates a random number between 0 and 1.

[0044] Furthermore, the expression of the greedy strategy is: , where w i (t + 1) is the position of individual i after the (t + 1)-th iteration, w i-new (t + 1) is the position of individual i that has not executed the multi - dimensional learning hunting strategy after the (t + 1)-th iteration, w i-DLH (t + 1) is the position of individual i after the (t + 1)-th iteration after the multi - dimensional learning hunting strategy is updated, f(w i-new ) is the objective function corresponding to w i-new , and f(w i-DLH ) is the objective function corresponding to w i-DLH .

[0045] In one embodiment, the process of specifically optimizing the control law of each control mode by using the improved humpback whale migration algorithm includes the following steps: Step 1: Initialization Construct an initial population N, the maximum number of iterations t max , variables, the space dimension, and the upper and lower search range boundaries, and initialize the positions of the migrating whale population. To improve the speed and accuracy of the optimization algorithm, it is necessary to improve the uniformity of the initial population in the search space. In this embodiment, the Tent mapping is used as the mapping of the initial population position. Compared with the random generation method, the chaotic sequence has more excellent randomness, ergodicity, and regularity. The uniform distribution characteristic of the Tent mapping helps to improve the optimization speed and solution accuracy of the algorithm. The mathematical expression of the Tent mapping is shown as follows: , (13) where the chaotic parameter μ ∈ (0, 2] is proportional to the chaos property, i and j are the population number and the chaotic variable serial number respectively, is a chaotic sequence randomly generated between (0, 1).

[0046] Due to the high sensitivity of the Tent mapping to the selection of the initial value, this embodiment selects a variety of different initial values to generate the corresponding chaotic sequences and converts them into the search space of each individual. In the IWMA algorithm of this embodiment, the position of the i - th whale is expressed as: , (14) where lb and ub are the lower and upper limits of the search space respectively.

[0047] The position of the i-th migrating whale in the D-dimensional space is expressed as: , (15) where D is the spatial dimension of the optimization variable.

[0048] Step 2: Leader strategy In each migrating whale group, the individual with richer position knowledge and higher objective function value will guide and lead other members towards the destination. In the WMA algorithm, the parameter N L is introduced, which represents the number of whales with more experience (i.e., leaders). These leaders are individuals with better positions and higher objective function values.

[0049] , where N L is the number of leaders, w y is the position of the y-th leader, and W Mean is the average value of the leader positions.

[0050] Considering that it is desired to describe the actual position of the entire migrating whale group at any moment through a certain point on the ocean migration path, therefore, W Mean is defined as the average value of the current N L leader positions.

[0051] Step 3: Update position 3.1. Movement of the less experienced young whales towards their nearest neighbors Assume that all population members (whales) are sorted in descending order according to their fitness values and / or their positions: , where W1 is the best member (denoted as W Best ), and W Npop denotes the worst member. All young whales usually love to play, which leads each young whale to try to imitate the peer closest to its own age. Therefore, in this model, the movement of each less experienced member (young whale) is mainly affected by its nearest previous member W i-1 in the above sequence.

[0052] 3.2. Less experienced whales are guided by more experienced whales As mentioned above, the current position of the entire migrating whale group in the ocean is assumed to be the average value W Mean of the current positions of all the more experienced whales. If the distance between W Mean and W Best starts to shorten, it means that the entire group of more experienced whales is approaching W Best. In this case, the less experienced young whales must also start moving along the direction given by the vector , where rand(1,D) is a random number vector taken from the interval [0,1] with the dimension D of the optimization variable space. At this time, the kinematic equation for position update is: , (17) , (18) It should be noted that the new position will replace the current position W only when is satisfied. i .

[0053] 3.3. Discovery and search for new areas by experienced whales In a migrating whale group, experienced individuals (i.e., leaders) are responsible for identifying and selecting the best route to the destination. Research on tracking the migration trajectories of whales by satellite shows that two key factors affect the migration of humpback whales: First, it is the specific positions in the earth's gravitational field and magnetic field, which are represented by the vector in the model (such as the black dashed vector in Figure 3 ); Second, it is that whales can migrate along an approximate straight-line path between the starting point L and the ending point U during migration, and this phenomenon is modeled by the vector in the motion equation (see the blue dashed vector in Figure 3 ).

[0054] To simulate the random movement of whales around the main migration direction, two random parameter vectors r1 and r2 are used in this model. The purpose of setting these two parameters is to make the influence of the vectors in the motion equation always greater than the influence of the vectors throughout the migration period.

[0055] Finally, based on the following kinematic equation, the i-th leader whale searches for a suitable path towards the destination: , (19) where r1 and r2 are random number vectors generated from the interval [0,1] with the dimension D, L represents the position (i.e., the starting point) vector, and U - L is the relative direction vector. It should be noted that the new position will replace the current position W only when is satisfied. i . At the end of each WMA iteration, the migrating whale group will be sorted according to the quality of individuals, arranged from the best to the worst, and the top N L optimal members will be selected as the new leaders.

[0056] Step 4: Update the position by the DLH strategy Traditional WMA has low convergence and ultimately falls into the dilemma of local optimality. Therefore, DLH is introduced to improve the quality of search individuals and increase the search ability.

[0057] DLH generates the following alternative individuals: , (20) Among them, the radius matrix Radius is generated by subtracting the distance between the original and new positions, and the neighborhood matrix is constructed based on the Euclidean distance between the current individual w i (t) and the alternative individual w j (t).

[0058] , (21) By learning from many neighborhood matrices, DLH generates a new individual w i-DLH,j (t + 1), where the d-th dimension of each new individual is updated based on the d-th dimension of the randomly selected individual w n,d (t).

[0059] , (22) Recalculate the individual fitness value, and retain the current best position and the current best fitness value.

[0060] Finally, a greedy strategy is adopted to evaluate the fitness value of the current optimal individual, and the individuals that are more valuable for updating the population position are retained. The mathematical model is as follows: , (23) Among them, w i (t + 1) is the position of individual i after the (t + 1)-th iteration, w i-new (t + 1) is the position of individual i that has not executed the multi-dimensional learning hunting strategy after the (t + 1)-th iteration, and w i-DLH (t + 1) is the position of individual i after the update of the multi-dimensional learning hunting strategy at the (t + 1)-th iteration.

[0061] After the iteration ends, the best fitness value and the global optimal position are finally returned.

[0062] In view of the lack of adaptive adjustment ability of engines with long-term service after component degradation and the disadvantage of poor accuracy in traditional optimization algorithms, the embodiment of this application proposes an optimization scheme for the control law of variable cycle engines based on an improved humpback whale migration algorithm. By introducing Tent mapping and integrating a multi-dimensional learning hunting strategy, the global convergence performance of the algorithm is effectively enhanced. This scheme aims to achieve multiple optimization goals: First, reduce the fuel consumption rate and significantly improve the fuel utilization efficiency; Second, output the maximum thrust at the peak of power demand to accurately meet the flight condition requirements; Third, control the turbine inlet temperature to the minimum to extend the service life of the turbine; Fourth, during the transient operation of the engine, strictly control the system parameters from exceeding the limit and at the same time achieve the shortest acceleration time. The specific beneficial effects are as follows: (1) Propose an optimization method for the control law of variable cycle engines based on the improved humpback whale migration algorithm (IWMA). Use Tent mapping as the mapping of the initial migrating whale population position to improve the optimization speed and solution accuracy of the algorithm; introduce a multi-dimensional learning hunting strategy to improve the individual quality, enhance the search process, and balance the exploration and exploitation stages; (2) Use the improved humpback whale migration algorithm to conduct numerical simulation verification on the intelligent optimization of the VCE control law to confirm the feasibility of the proposed method. The engine performance optimization modes involved in the present invention include the optimization of the maximum thrust, the lowest fuel consumption, the lowest turbine inlet temperature under steady state, and the acceleration performance optimization under transient state. Select the optimization parameters as the optimization variables; (3) Apply the proposed improved algorithm to the optimization of the engine control law, conduct simulation analysis and compare the simulation results. The simulation results show that the IWMA has a faster convergence speed and better optimization effect than several classical intelligent optimization algorithms. It effectively reduces the fuel consumption rate and the lowest turbine inlet temperature of the VCE, increases the maximum thrust, and shortens the acceleration time by 50%.

[0063] The following describes the optimization method for the control law of variable cycle engines based on the improved humpback whale migration algorithm of this application with a specific embodiment.

[0064] (1) Minimum fuel consumption control mode At low Mach numbers, the fuel consumption rate of turbojet engines is higher than that of turbofan engines. However, due to the large bypass ratio, turbofan engines are not suitable for high Mach number flight conditions. Therefore, taking the subsonic cruise point (H = 5km, Ma = 0.8, H is the altitude, Ma is the Mach number) as an example, verify the minimum fuel consumption control method of the engine and use VCE for verification. The optimization objective function is set as , F r is the reference thrust. Compared with the reference point, the minimum fuel consumption rate is reduced by 5.35%.

[0065] (2) Maximum thrust control mode In this mode, taking the supersonic cruise point (H = 10 km, Ma = 1.5) as an example, the maximum thrust control method of VCE was simulated. The optimization objective function was set as fitness = 10000 / F n . Compared with the reference point, the maximum thrust increased by 27.59%.

[0066] (3) Minimum turbine inlet temperature control mode The minimum turbine inlet temperature control of VCE is usually applied to high-altitude and high-Mach flight. The goal of the minimum turbine inlet temperature control is to ensure that the gas flow temperature in front of the turbine does not exceed the maximum allowable temperature of the turbine material, thereby protecting the turbine. Taking the supersonic cruise point (H = 11 km, Ma = 1.4) as an example, the optimization method proposed in the present invention and various classical intelligent optimization algorithms were used to optimize the minimum turbine inlet temperature control mode. The optimization objective function was set as fitness = (F r - F n ) 2 + T 41 . Compared with the reference point, the minimum turbine inlet temperature decreased by 1.00%.

[0067] (4) Transient control mode The acceleration mode is a typical transient control mode. In this mode, under the working conditions of an altitude of 18 km and 0.8 Ma, the acceleration process of VCE was simulated and verified. The obtained acceleration time was 2.12 s, and the steady-state error of the fan percentage speed was the smallest, with an error value of 0.0009%.

[0068] In the embodiments provided by the present invention, the humpback whale migration optimization algorithm was improved based on the improved humpback whale migration algorithm variable cycle engine control law optimization method. A multi-dimensional learning hunting strategy was adopted for the optimization of the steady-state and transient control laws of VCE, aiming to improve the optimization effect of the control law and enhance the performance of the engine. The simulation results show that IWMA has a faster convergence speed and better optimization effect than several classical intelligent optimization algorithms. It effectively reduces the fuel consumption rate and the minimum turbine inlet temperature of VCE, increases the maximum thrust, and shortens the acceleration time by 50%.

[0069] The above is only the specific implementation manner of the present application, but the protection scope of the present application is not limited thereto. Any changes or substitutions that can be easily thought of by those skilled in the art within the technical scope disclosed in the present application should be covered within the protection scope of the present application. Therefore, the protection scope of the present application should be subject to the protection scope of the claims.

Claims

1. An optimization method for the control law of a variable cycle engine based on an improved humpback whale migration algorithm, characterized in that The method includes: Establishing a variable cycle engine model and determining optimization variables based on the variable cycle engine model; For each control mode of the variable cycle engine, determining constraint conditions and an objective function based on the optimization variables, where the control modes include a steady-state control mode and a transient control mode, and the steady-state control mode includes a minimum fuel consumption control mode, a maximum thrust control mode, and a minimum turbine inlet temperature control mode; Based on the objective function and the constraint conditions, using an improved humpback whale migration algorithm to optimize the control law of each control mode to obtain optimal control variables, where the improved humpback whale migration algorithm includes using Tent mapping as the mapping of the initial migrating whale population positions and integrating a multi-dimensional learning hunting strategy.

2. The optimization method for the control law of a variable cycle engine based on the improved humpback whale migration algorithm according to claim 1, wherein The optimization variables are: ， The constraint conditions in the process of optimizing the control law of each control mode are described as: ， Among them, u is the optimization variable, and W fb is the fuel flow rate of the main combustion chamber, A8 is the throat area of the nozzle, A9 is the afterburner fuel flow rate, and A 38 is the Flade bypass nozzle area, α Flade is the Flade guide vane angle, α fan is the fan guide vane angle, α CDFS is the CDFS guide vane angle, α HPC is the HPC guide vane angle, n f is the fan speed, n c is the compressor speed, SM f is the fan surge margin, SM cd is the CDFS surge margin, SM c is the compressor surge margin, P3 is the compressor outlet pressure, T 41 is the turbine inlet temperature of the engine. The subscript min represents the minimum value, and the subscript max represents the maximum value.

3. The optimization method for the control law of a variable cycle engine based on an improved humpback whale migration algorithm according to claim 2, wherein The objective function and constraint conditions of the minimum fuel consumption control mode are expressed as: F1 = min sfc ， Among them, F1 is the objective function of the minimum fuel consumption control mode, min sfc is the minimum value of the engine fuel consumption rate, s.t. is the constraint condition, I is the number of total inequality constraint conditions, F n is the engine thrust, and const represents a constant; The objective function and constraint conditions of the maximum thrust control mode are expressed as: F2 = maximum F n ， Among them, F2 is the objective function of the maximum thrust control mode, max F n is the maximum value of the engine thrust; The objective function and constraint conditions of the minimum turbine inlet temperature control mode are expressed as: F3 = minimum T 41 ， Among them, F3 is the objective function of the lowest turbine inlet temperature control mode, min T 41 is the minimum value of the engine turbine inlet temperature.

4. The method for optimizing the control law of a variable cycle engine based on an improved humpback whale migration algorithm according to claim 2, wherein For the transient control mode, the objective function uses an adaptive variable weight coefficient method to transform a double-objective function and a multi-inequality constraint problem into an unconstrained optimization problem, and the expression of the objective function of the transient control mode is: ， Among them, minJ(k,σ) is the objective function of the transition state control mode, ω1 and ω2 are the objective function weights respectively, and n c (k) is the compressor speed at the current k-th moment, T 41 (k) is the total temperature at the front of the high-pressure turbine at the current k-th moment, n c,obj is the target value of the compressor speed, T 41,obj is the target value of the total temperature at the front of the high-pressure turbine, σ is an infinitely large positive number, and g(x) is the cost function.

5. The optimization method for the control law of a variable cycle engine based on the improved humpback whale migration algorithm according to claim 1, wherein, Using the improved humpback whale migration algorithm to optimize the control law of each control mode includes: Constructing an initial population, a maximum number of iterations, variables, the spatial dimension of the optimization variables, and the boundaries of the search space, initializing the positions of the migrating whale population, and using Tent mapping as the mapping of the initial migrating whale population positions; Sorting the individuals in the migrating whale population in descending order according to the fitness value and / or position, taking several individuals at the front of the sorting as leaders, calculating the average value of the positions of the multiple leaders, and taking the average value of the positions as the current position of the entire migrating whale population in the ocean; The individuals in the migrating whale population update their whale positions according to the migration rules under the action of the leaders; Updating the whale positions based on the multi-dimensional learning hunting strategy to improve the quality of the search individuals and increase the search ability, obtaining the current best position and the current best fitness value; Using a greedy strategy to evaluate the fitness value of the individuals at the current best position and retaining the individuals valuable for the update of the population position to obtain the final global optimal position and the best fitness value.

6. The optimization method for the control law of a variable cycle engine based on an improved humpback whale migration algorithm according to claim 5, characterized in that, The calculation formula for the average value of the leader positions is: ， Among them, N L is the number of leaders, w y is the position of the y-th leader, W Mean is the average value of the leader positions.

7. The optimization method for the control law of a variable cycle engine based on the improved humpback whale migration algorithm according to claim 6, characterized in that, let The descending order of the migrating whale groups is W1,...,W i-1 ,W i , W i+1 ,...,W Npop , and the whales at positions from W1 to W i-1 are the leaders, and the whales at positions from W i to W Npop are the calves. W1 is set as the optimal individual W Best ,W Npop is set as the worst individual; The individuals in the migrating whale population update their whale positions according to the migration rules under the action of the leaders, including: Each young whale W i (i = N L + 1,..., N pop ) moves towards its nearest previous whale W i-1 for the first position update; Each young whale moves along the direction given by the vector to perform the second position update, where rand(1,D) is a random number vector taken from the interval [0,1] with the dimension of the optimization variable space being D, and the kinematic equation of the second position update is: ， ； Each leader identifies and selects the best path towards the end point for the third position update, and the kinematic equation for the third position update is: ， Among them, is the new position, r1 and r2 are respectively random number vectors with dimensions of the optimization variable space dimension D generated from the interval [0, 1], L represents the starting vector, U represents the ending vector, and U - L is the relative direction vector; When the new position satisfies , replace the current position with the value of the objective function corresponding to the new solution and the value of the objective function corresponding to the solution.

8. The optimized method for the control law of a variable cycle engine based on the improved humpback whale migration algorithm according to claim 7, wherein Updating the whale positions based on the multi-dimensional learning hunting strategy includes: Constructing a radius matrix based on the original position and the new position of the whale; Constructing a neighborhood matrix based on the radius matrix and the Euclidean distance between the current individual and the alternative individuals; Generate new individuals by learning from multiple neighborhood matrices, where the d-th dimension of each new individual is updated based on the d-th dimension of randomly selected individuals, and the new individuals are the whale positions updated based on the multi-dimensional learning hunting strategy.

9. The optimization method for the control law of a variable cycle engine based on an improved humpback whale migration algorithm according to claim 8, wherein The expression of the radius matrix is as follows: ， The expression of the neighborhood matrix is as follows: ， The expression of the generated new individuals is as follows: ， Among them, Radiusi(t) is the radius matrix, Neighbouri(t) is the neighborhood matrix, w i (t) is the current individual, w j (t) is the alternative individual, w new (t + 1) is the new position of individual i at the (t + 1)-th iteration, D is the dimension of the optimization variable space, N is the initial population, w i-DLH,j (t + 1) is the newly generated individual, w i,d (t) is the updated position of individual i at the t-th iteration in the d-th dimension, w n,d (t) is the individual randomly selected by individual i at the t-th iteration in the d-th dimension, w r,d (t) is the reference position of individual i at the t-th iteration in the d-th dimension, and rand is a random function that generates a random number between 0 and 1.

10. The optimization method for the control law of a variable cycle engine based on the improved humpback whale migration algorithm according to claim 9, wherein The expression of the greedy strategy is as follows: ， Among them, w i (t + 1) is the updated position of individual i at the (t + 1)-th iteration, w i-new (t + 1) is the position of individual i that has not executed the multi-dimensional learning hunting strategy after the (t + 1)-th iteration, w i-DLH (t + 1) is the position of individual i after the multi-dimensional learning hunting strategy is updated at the (t + 1)-th iteration, f(w i-new ) is the objective function corresponding to w i-new , f(w i-DLH ) is the objective function corresponding to w i-DLH .

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