Optimization method of variable cycle engine control law based on improved humpback whale migration algorithm

Abstract

The present application provides a method for optimizing the control laws of a variable-cycle engine based on an improved humpback whale migration algorithm, which belongs to the field of engine control technology. The method includes establishing a variable-cycle engine model and determining optimization variables; determining constraints and objective functions for each control mode of the variable-cycle engine, wherein the control modes include a steady-state control mode and a transitional control mode, wherein the steady-state control modes include a minimum fuel consumption control mode, a maximum thrust control mode, and a minimum turbine pre-temperature control mode; based on the objective function and constraints, each control mode is optimized using an improved humpback whale migration algorithm to obtain the optimal control variables. The improved humpback whale migration algorithm includes a tent map as the initial position map of the migrating whale group and a fusion multi-dimensional learning hunting strategy. The processing scheme of the present application improves the convergence speed and optimization effect of the engine control law optimization method, thereby enhancing engine performance.

Description

Technical Field

[0001] The present application relates to the field of engine control technology, and in particular to a method for optimizing variable cycle engine control laws based on an improved humpback whale migration algorithm. Background Art

[0002] Variable cycle engines (VCEs), a new generation of innovative aviation propulsion systems, demonstrate unique value in high-speed reconnaissance, integrated aerospace, and multi-mission platforms. Unlike the fixed thermodynamic cycles of conventional turbofan / turbojet engines, VCEs achieve intelligent switching of thermodynamic cycle modes by dynamically reconfiguring key parameters such as bypass ratio and compressor interstage bleed air. This allows the aircraft to maintain optimal propulsion efficiency across diverse missions, including subsonic cruise, supersonic penetration, and supermaneuverability. When subjected to long-term service under extreme operating conditions, VCE performance degradation exhibits multi-dimensional coupled characteristics: creep effects in high-temperature alloy blades lead to aerodynamic shape distortion, thermal barrier coatings on silicon carbide-based ceramic composites delamination cause sudden changes in flow path roughness, and, more seriously, microparticles generated by fuel coking can cause dynamic imbalance in the combustor swirler. These nonlinear degradation mechanisms cause drift in the engine's characteristic map, making it easy for classical control laws based on nominal models to trigger chain reactions such as insufficient surge margin or turbine overheating during transient states.

[0003] In recent years, a significant amount of research has been achieved in optimizing aeroengine control laws. Using techniques such as linear programming, reinforcement learning, and intelligent optimization algorithms, control law optimization has been achieved for turbofan, propfan, and turboshaft engines in both steady-state and transient states. While considerable research has been conducted on optimizing steady-state control laws for VCEs, research on the design of transient control laws for these aircraft remains lacking. Compared to turbofan and propfan engines, VCEs exhibit stronger nonlinear variable parameter characteristics and a greater number of control variables, making the design of transient multivariable control laws for VCEs more challenging. Furthermore, in designing acceleration control laws, these studies have not yet leveraged the physical characteristics of the engine to address the issue of engine state parameter jitter caused by the randomness of intelligent optimization algorithms.

[0004] To address these issues, various solutions based on metaheuristic optimization algorithms have been proposed, such as embedding a chaotic mapping strategy into the Salp Swarm algorithm to enhance initial value sensitivity, or improving the step-size adjustment mechanism of the Krill Swarm algorithm by drawing on the aerodynamic principles of bird wings. In particular, the recently proposed Peacock Optimization Algorithm, by simulating the multidimensional information interaction mechanism when a peacock spreads its feathers, exhibits superior Pareto solution set distribution characteristics when solving the VCE multivariable strongly coupled optimization problem. However, this type of algorithm still suffers from the drawback of insufficient inertia weight adaptation when dealing with sudden changes in constraints caused by engine degradation. Therefore, designing an efficient, real-time optimization algorithm that avoids local optimal solutions to address the performance degradation of variable cycle engines 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 a method for optimizing the control laws 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 engines in long-term service lack adaptive adjustment capabilities after component degradation, and that traditional optimization algorithms have poor accuracy.

[0006] The present application provides a method for optimizing control laws of a variable cycle engine based on an improved humpback whale migration algorithm, the method comprising:

[0007] establishing a variable cycle engine model, and determining optimization variables based on the variable cycle engine model;

[0008] Determining constraints and an objective function based on optimization variables for each variable cycle engine control mode, wherein the control mode includes a steady-state control mode and a transient control mode, wherein 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;

[0009] Based on the objective function and the constraints, an improved humpback whale migration algorithm is used to optimize the control law of each control mode to obtain the optimal control variables. The improved humpback whale migration algorithm includes tent mapping as the initial migrating whale group position mapping and a fusion multi-dimensional learning hunting strategy.

[0010] According to a specific implementation of the embodiment of the present application, the optimization variables are:

[0011] ,

[0012] The constraints in the process of optimizing the control law of each control mode are described as follows:

[0013] ,

[0014] Among them, u is the optimization variable, Wfb is the fuel flow rate of the main combustion chamber, A8 is the tail nozzle throat area, A9 is the afterburner fuel flow rate, A 38 is the Flade duct nozzle area, α Flade is the Flade guide vane angle, α fan is the fan guide blade 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 engine turbine front temperature, subscript min is the minimum value, subscript max is the maximum value.

[0015] According to a specific implementation of the embodiment of the present application, the objective function and constraint conditions of the minimum fuel consumption control mode are expressed as follows:

[0016] F1=min sfc

[0017] ,

[0018] 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, st is the constraint condition, I is the total number of inequality constraints, F n is the engine thrust, const represents a constant;

[0019] The objective function and constraints of the maximum thrust control mode are expressed as follows:

[0020] F2=max F n

[0021] ,

[0022] Among them, F2 is the objective function of the maximum thrust control mode, max F n is the maximum engine thrust;

[0023] The objective function and constraints of the minimum turbine pre-temperature control mode are expressed as follows:

[0024] F3=min T 41

[0025] ,

[0026] Among them, F3 is the objective function of the minimum turbine pre-temperature control mode, min T 41 It is the minimum temperature before the engine turbine.

[0027] According to a specific implementation of an embodiment of the present application, the objective function of the transition state control mode adopts an 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 transition state control mode is:

[0028] ,

[0029] Among them, minJ(k,σ) is the objective function of the transition state control mode, ω1 and ω2 are the weights of the objective function, n c (k) is the compressor speed at the current moment k, T 41 (k) is the total temperature before the high-pressure turbine at the current time k, n c,obj is the target value of compressor speed, T 41,obj is the target value of the total temperature before the high-pressure turbine, σ is an infinite positive number, and g(x) is the cost function.

[0030] According to a specific implementation of the embodiment of the present application, the improved humpback whale migration algorithm is used to optimize the control law of each control mode, including:

[0031] Construct the initial population, maximum number of iterations, variables, spatial dimension of optimization variables, and the boundary of the search space, initialize the position of the migrating whale group, and use the tent map as the initial migrating whale group position map;

[0032] Sort the individuals in the migrating whale group in descending order according to fitness value and / or position, select several individuals at the top of the ranking as leaders, calculate the average position of the multiple leaders, and use the average position as the current position of the entire migrating whale group in the ocean;

[0033] Individuals in a migrating whale group update their whale positions according to the migration rules under the guidance of the leader;

[0034] Based on the multi-dimensional learning hunting strategy, the whale position is updated to improve the quality of the search individuals and increase the search ability, and the current best position and the current best fitness value are obtained;

[0035] A greedy strategy is used to evaluate the fitness value of the individual in the current best position, and individuals that are valuable for updating the population position are retained to obtain the final global optimal position and best fitness value.

[0036] According to a specific implementation of the embodiment of the present application, the calculation formula of the average leader position is:

[0037] ,

[0038] Among them, N L is the number of leaders, w y is the position of the y-th leader, W Mean is the average leader position.

[0039] According to a specific implementation of the embodiment of the present application, the migrating whale groups are sorted in descending order as W1,...,W i-1 ,W i , W i+1 ,...,W Npop , positions are W1 to W i-1 The whale is the leader, and its position is W i To W Npop The whale is a juvenile whale, and W1 is set as the optimal individual W Best , W Npop Set as the worst individual;

[0040] Individuals in the migrating whale group, under the leadership of the leader, update their positions according to the migration rules, including:

[0041] Each whale calf W i (i=N L +1,...,N pop ) towards its nearest previous whale W i-1 Move and perform the first position update;

[0042] Each calf moves along the path defined by the vector Move in the given direction and perform the second position update, where rand(1,D) is a random number vector taken from the interval [0,1] and the dimension is the dimension D of the optimization variable space. The kinematic equation of the second position update is:

[0043] ,

[0044] ;

[0045] Each leader identifies and selects the best path toward the endpoint and performs a third position update, the kinematic equation of which is:

[0046] ,

[0047] in, is the new position, r1 and r2 are random number vectors generated from the interval [0,1] with the dimension D of the optimization variable space, L represents the starting vector, U represents the end vector, and UL is the relative direction vector;

[0048] When the new position meets When , replace the current position, for The objective function corresponding to the new solution is for Solve the corresponding objective function.

[0049] According to a specific implementation of an embodiment of the present application, updating the whale position based on a multi-dimensional learning hunting strategy includes:

[0050] Construct a radius matrix based on the whale's original position and the whale's new position;

[0051] Construct a neighborhood matrix based on the radius matrix and the Euclidean distance between the current individual and the candidate individuals;

[0052] New individuals are generated by learning from multiple neighborhood matrices, where the dth dimension of each new individual is updated based on the dth dimension of a randomly selected individual, and the new individual is the updated whale position based on the multidimensional learning hunting strategy.

[0053] According to a specific implementation of the embodiment of the present application, the radius matrix expression is:

[0054] ,

[0055] The neighborhood matrix expression is:

[0056] ,

[0057] The expression of the generated new individual is:

[0058] ,

[0059] Among them, Radiusi(t) is the radius matrix, Neighbouri(t) is the neighborhood matrix, and w i (t) is the current individual, w j (t) is the candidate individual, w new (t+1) is the new position of individual i at the t+1th iteration, D is the dimension of the optimization variable space, N is the initial population, w i-DLH,j (t+1) is the new individual generated, w i,d (t) is the updated position of individual i in the dth dimension at the tth iteration, w n,d (t) is the individual i in the tth iteration based on the randomly selected individual in the dth dimension, w r,d (t) is the reference position of individual i in the dth dimension at the tth iteration, and rand is a random function that generates a random number between 0 and 1.

[0060] According to a specific implementation of the embodiment of the present application, the expression of the greedy strategy is:

[0061] ,

[0062] Among them, w i (t+1) is the position of individual i after the t+1th iteration, w i-new (t+1) is the position of individual i after the t+1th iteration without executing the multi-dimensional learning hunting strategy, w i-DLH (t+1) is the position of individual i after the t+1th iteration after the multi-dimensional learning hunting strategy is updated, f(w i-new ) is w i-new The corresponding objective function, f(w i-DLH ) is w i-DLH The corresponding objective function.

[0063] Beneficial effects:

[0064] The variable cycle engine control law optimization method based on the improved humpback whale migration algorithm in the embodiment of this application effectively enhances the global convergence performance of the algorithm by introducing tent mapping and integrating multi-dimensional learning hunting strategies. This solution is committed to achieving multiple optimization goals: first, reducing fuel consumption rate and significantly improving fuel utilization efficiency; second, outputting maximum thrust at peak power demand, accurately matching flight operating conditions; third, controlling the turbine inlet temperature to a minimum to extend the turbine service life; fourth, during the transient operation of the engine, strictly controlling the system parameters from exceeding the limit while achieving the shortest acceleration time. The specific beneficial effects are as follows:

[0065] (1) Tent mapping is used as the initial location map of migrating whale groups to improve the optimization speed and solution accuracy of the algorithm; a multi-dimensional learning hunting strategy is introduced to improve individual quality, enhance the search process, and balance the exploration and exploitation stages;

[0066] (2) The improved humpback whale migration algorithm was used to conduct numerical simulation verification of the intelligent optimization of the VCE control law to confirm the feasibility of the proposed method. The engine performance optimization mode involved in the present invention includes the maximum thrust, minimum fuel consumption, minimum turbine inlet temperature in the steady state and the acceleration performance optimization in the transient state. The optimization parameters were selected as the optimization variables.

[0067] (3) The proposed improved optimization method was applied to the optimization of engine control laws, and simulation analysis was carried out and the simulation results were compared. The proposed method has a fast convergence speed and good optimization effect. It effectively reduces the fuel consumption rate and the minimum turbine inlet temperature of the variable cycle engine, increases the maximum thrust, shortens the acceleration time by 50%, and effectively improves the engine performance. BRIEF DESCRIPTION OF THE DRAWINGS

[0068] In order to more clearly illustrate the technical solutions of the embodiments of the present application, the following briefly introduces the drawings required for use in the embodiments. Obviously, the drawings described below are only some embodiments of the present application. For ordinary technicians in this field, other drawings can be obtained based on these drawings without any creative work.

[0069] Figure 1 Flowchart of a method for optimizing a variable cycle engine control law based on an improved humpback whale migration algorithm according to an embodiment of the present invention;

[0070] Figure 2 A schematic diagram of a multi-objective optimization principle according to an embodiment of the present invention;

[0071] Figure 3 FIG. 4 is a diagram showing a location update principle according to an embodiment of the present invention. DETAILED DESCRIPTION

[0072] The embodiments of the present application are described in detail below with reference to the accompanying drawings.

[0073] The following describes the embodiments of the present application through specific examples, and those skilled in the art can easily understand other advantages and effects of the present application from the contents 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 embodiments, and the details in this specification can also be modified or changed in various ways based on different viewpoints and applications without departing from the spirit of the present application. It should be noted that, in the absence of conflict, the features in the following embodiments and 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 work are within the scope of protection of this application.

[0074] It should be noted that various aspects of the embodiments within the scope of the appended claims are described below. 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 merely illustrative. Based on this application, it should be understood by those skilled in the art that an 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 aspects described herein can be used to implement an apparatus and / or practice a method. In addition, other structures and / or functionalities other than one or more of the aspects described herein can be used to implement this apparatus and / or practice this method.

[0075] It should also be noted that the illustrations provided in the following embodiments are only schematic illustrations of the basic concept of the present application. The illustrations only show components related to the present application and are not drawn according to the number, shape and size of components in actual implementation. In actual implementation, the type, quantity and proportion of each component can be changed at will, and the component layout type may also be more complicated.

[0076] Additionally, in the following description, specific details are provided to provide a thorough understanding of the examples. However, one skilled in the art will appreciate that the aspects described can be practiced without these specific details.

[0077] The applicant's research has identified the Humpback Whale Migrating Algorithm (WMA), a novel metaheuristic optimization method based on the collaborative migration behavior of humpback whales. Compared to traditional methods, the 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 achieve efficient convergence.

[0078] Based on the above content, the embodiment of the present application provides a variable cycle engine control law optimization method based on the improved humpback whale migration algorithm. Figures 1 to 3 Provide a detailed description.

[0079] In one embodiment, referring to Figure 1 , a variable cycle engine control law optimization method based on an improved humpback whale migration algorithm, the method comprising:

[0080] establishing a variable cycle engine model, and determining optimization variables based on the variable cycle engine model;

[0081] Determining constraints and an objective function based on optimization variables for each variable cycle engine control mode, wherein the control mode includes a steady-state control mode and a transient control mode, wherein 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;

[0082] Based on the objective function and the constraints, an improved humpback whale migration algorithm is used to optimize the control law of each control mode to obtain the optimal control variables. The improved humpback whale migration algorithm includes tent mapping as the initial migrating whale group position mapping and a fusion multi-dimensional learning hunting strategy.

[0083] This embodiment proposes a novel, improved humpback whale migration algorithm. The proposed control law does not directly optimize engine control parameters, but instead optimizes controlled parameters (such as speed and compression ratio) and other adjustable parameters. Adjusting controlled parameters offers the following advantages over directly optimizing control parameters. First, because engines are susceptible to external factors (such as flight altitude and wind gusts), direct optimization of control parameters requires real-time adjustment based on the environment and flight conditions. Existing optimization algorithms struggle to simultaneously meet both accuracy and real-time requirements. Second, because engine performance parameters cannot be directly measured, conventional control systems are unable to directly control them. The method in this embodiment improves the humpback whale migration optimization algorithm by employing a multidimensional learning-based hunting strategy for optimizing the steady-state and transient control laws of variable cycle engines (VCEs). This enhances the optimization of control laws and improves engine performance.

[0084] In one embodiment, for the variable cycle engine model studied in this application, the optimization variables are:

[0085] , (1)

[0086] The constraints in the process of optimizing the control law of each control mode are described as follows:

[0087] , (2)

[0088] Among them, u is the optimization variable, W fb is the fuel flow rate of the main combustion chamber, A8 is the tail nozzle throat area, A9 is the afterburner fuel flow rate, A 38 is the Flade duct nozzle area, α Flade is the Flade guide vane angle, α fan is the fan guide blade 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 engine turbine front temperature, subscript min is the minimum value, subscript max is the maximum value.

[0089] The above formula can be expressed as:

[0090] , (3)

[0091] Where g(u) represents the inequality constraint, i represents the i-th inequality constraint, and I is the total number of inequality constraints.

[0092] In one embodiment, the objective function and constraints of the minimum fuel consumption control mode are expressed as follows:

[0093] F1=min sfc

[0094] , (4)

[0095] 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, st is the constraint condition, I is the total number of inequality constraints, F n is the engine thrust, const represents a constant;

[0096] The objective function and constraints of the maximum thrust control mode are expressed as follows:

[0097] F2=max F n

[0098] , (5)

[0099] Among them, F2 is the objective function of the maximum thrust control mode, max F n is the maximum engine thrust;

[0100] The objective function and constraints of the minimum turbine pre-temperature control mode are expressed as follows:

[0101] F3=min T 41

[0102] , (6)

[0103] Among them, F3 is the objective function of the minimum turbine pre-temperature control mode, min T 41 It is the minimum temperature before the engine turbine.

[0104] In specific implementation, the optimization of the minimum fuel consumption control mode and the optimization of the minimum turbine inlet temperature mode are both multi-objective optimization. The goal of the minimum fuel consumption control mode optimization is to achieve the desired thrust value while minimizing the fuel consumption rate; the goal of the minimum turbine inlet temperature mode optimization is to achieve the desired thrust value while minimizing the turbine inlet temperature. The principle of multi-objective optimization is as follows Figure 2 As shown in the figure, through step-by-step iterative optimization, target 1 or target 2 is optimized. By selecting appropriate weights W=[W1,W2], where W1 is the weight of target 1 (lowest fuel consumption rate, lowest turbine inlet temperature), and W2 is the weight of target 2 (unchanged thrust), the comprehensive performance of target 1 and target 2 is optimized.

[0105] Combining formulas (4) to (6), the optimization of engine control law can be expressed as the following nonlinear programming problem:

[0106] , (7)

[0107] Among them, h k (u) is the equality constraint, k represents the kth equality constraint, and K is the total number of equality constraints.

[0108] In order to solve constrained optimization problems, a penalty function can be introduced.

[0109] , (8)

[0110] Here, F(u,σ) is the objective function that introduces a penalty function, and σ1 and σ2 are infinite positive numbers. This transforms the original constrained problem into an unconstrained one. During the intelligent optimization of engine adaptive control laws, an intelligent optimization algorithm is required to find the optimal combination of optimization parameters to achieve optimal engine performance.

[0111] In one embodiment, the objective function of the transition state control mode adopts an 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 transition state control mode is:

[0112] ,

[0113] Among them, minJ(k,σ) is the objective function of the transition state control mode, ω1 and ω2 are the weights of the objective function, n c (k) is the compressor speed at the current moment k, T 41 (k) is the total temperature before the high-pressure turbine at the current time k, n c,obj is the target value of compressor speed, T 41,obj is the target value of the total temperature before the high-pressure turbine, σ is an infinite positive number, and g(x) is the cost function.

[0114] In specific implementation, for the transient control mode, the key to the engine's acceleration performance is to achieve the shortest acceleration time, which can be expressed by the following expression:

[0115] , (9)

[0116] Among them, t ac is the acceleration time, I' is the rotor moment of inertia, n is the rotor speed, n max is the maximum speed, n idle is the speed at slow speed, ΔH axis the residual power of the turbine during the acceleration process. In order to achieve the best acceleration control in each control cycle, the high-pressure rotor speed can be used as the objective function:

[0117] , (10)

[0118] Where t' is the integration time.

[0119] Total temperature before high pressure turbine T 41 It can also effectively improve the turbine power. In order to fully reflect the energy changes of the engine, the total temperature before the high-pressure turbine T 41 The high-pressure rotor speed and the speed of the high-pressure rotor are simultaneously used as optimization targets. The discrete objective function is defined using the linear weighted method:

[0120] , (11)

[0121] Among them, ω1 and ω2 are the weights of the objective function, n c (k) is the compressor speed at the current moment k, T 41 (k) is the total temperature before the high-pressure turbine at the current time k, n c,obj is the target value of compressor speed, T 41,obj is the target value of the total temperature before the high-pressure turbine.

[0122] By adopting the adaptive variable weight coefficient method, the dual objective function and multi-inequality constraint problem is transformed into an unconstrained optimization problem:

[0123] , (12)

[0124] This approach helps achieve maximum turbine surplus power, reduces acceleration time, and ensures high specific thrust.

[0125] In one embodiment, the use of the improved humpback whale migration algorithm to optimize the control law of each control mode includes:

[0126] Construct the initial population, maximum number of iterations, variables, spatial dimension of optimization variables, and the boundary of the search space, initialize the position of the migrating whale group, and use the tent map as the initial migrating whale group position map;

[0127] Sort the individuals in the migrating whale group in descending order according to fitness value and / or position, select several individuals at the top of the ranking as leaders, calculate the average position of the multiple leaders, and use the average position as the current position of the entire migrating whale group in the ocean;

[0128] Individuals in a migrating whale group update their whale positions according to the migration rules under the guidance of the leader;

[0129] Based on the multi-dimensional learning hunting strategy, the whale position is updated to improve the quality of the search individuals and increase the search ability, and the current best position and the current best fitness value are obtained;

[0130] A greedy strategy is used to evaluate the fitness value of the individual in the current best position, and individuals that are valuable for updating the population position are retained to obtain the final global optimal position and best fitness value.

[0131] In this example, the design of an improved humpback whale migration algorithm (IWMA) is proposed. Through this approach, IWMA overcomes the shortcomings of the original WMA, further improves the optimization speed and solution accuracy, and provides an effective strategy for solving complex problems.

[0132] Furthermore, the calculation formula of the leader position average value is:

[0133] ,

[0134] Among them, N L is the number of leaders, w y is the position of the y-th leader, W Mean is the average leader position.

[0135] Furthermore, let the descending order of the migrating whale groups be W1,...,W i-1 ,W i , W i+1 ,...,W Npop , positions are W1 to W i-1 The whale is the leader, and its position is W i To W Npop The whale is a juvenile whale, and W1 is set as the optimal individual W Best , W Npop Set as the worst individual;

[0136] Individuals in the migrating whale group, under the leadership of the leader, update their positions according to the migration rules, including:

[0137] Each whale calf W i (i=N L +1,...,N pop ) towards its nearest previous whale W i-1 Move and perform the first position update;

[0138] Each calf moves along the path defined by the vector Move in the given direction and perform the second position update, where rand(1,D) is a random number vector taken from the interval [0,1] and the dimension is the dimension D of the optimization variable space. The kinematic equation of the second position update is:

[0139] ,

[0140] ;

[0141] Each leader identifies and selects the best path toward the endpoint and performs a third position update, the kinematic equation of which is:

[0142] ,

[0143] in, is the new position, r1 and r2 are random number vectors generated from the interval [0,1] with the dimension D of the optimization variable space, L represents the starting vector, U represents the end vector, and UL is the relative direction vector;

[0144] When the new position meets When , replace the current position, for The new solution corresponds to the value of the objective function, for The solution corresponds to the value of the objective function.

[0145] Furthermore, the updating of whale positions based on the multi-dimensional learning hunting strategy includes:

[0146] Construct a radius matrix based on the whale's original position and the whale's new position;

[0147] Construct a neighborhood matrix based on the radius matrix and the Euclidean distance between the current individual and the candidate individuals;

[0148] New individuals are generated by learning from multiple neighborhood matrices, where the dth dimension of each new individual is updated based on the dth dimension of a randomly selected individual, and the new individual is the updated whale position based on the multidimensional learning hunting strategy.

[0149] Furthermore, the radius matrix expression is:

[0150] ,

[0151] The neighborhood matrix expression is:

[0152] ,

[0153] The expression of the generated new individual is:

[0154] ,

[0155] Among them, Radiusi(t) is the radius matrix, Neighbouri(t) is the neighborhood matrix, and w i(t) is the current individual, w j (t) is the candidate individual, w new (t+1) is the new position of individual i at the t+1th iteration, D is the dimension of the optimization variable space, N is the initial population, w i-DLH,j (t+1) is the new individual generated, w i,d (t) is the updated position of individual i in the dth dimension at the tth iteration, w n,d (t) is the individual i in the tth iteration based on the randomly selected individual in the dth dimension, w r,d (t) is the reference position of individual i in the dth dimension at the tth iteration, and rand is a random function that generates a random number between 0 and 1.

[0156] Furthermore, the expression of the greedy strategy is:

[0157] ,

[0158] Among them, w i (t+1) is the position of individual i after the t+1th iteration, w i-new (t+1) is the position of individual i after the t+1th iteration without executing the multi-dimensional learning hunting strategy, w i-DLH (t+1) is the position of individual i after the t+1th iteration after the multi-dimensional learning hunting strategy is updated, f(w i-new ) is w i-new The corresponding objective function, f(w i-DLH ) is w i-DLH The corresponding objective function.

[0159] In one embodiment, the specific process of optimizing the control law of each control mode using the improved humpback whale migration algorithm includes the following steps:

[0160] Step 1: Initialization

[0161] Construct the initial population N and the maximum number of iterations t max , variables, spatial dimensions, and upper and lower search range boundaries, and initialize the position of the migrating whale group. In order 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. This embodiment uses Tent mapping as the initial population position mapping. Compared with the random generation method, the chaotic sequence has better randomness, ergodicity and regularity. The uniform distribution characteristics of Tent mapping help to improve the optimization speed and solution accuracy of the algorithm. The mathematical expression of Tent mapping is shown as follows:

[0162] , (13)

[0163] Among them, the chaos parameter μ∈(0,2] is proportional to the chaos, i and j are the population number and the chaotic variable number respectively. To randomly generate chaotic sequences between (0,1).

[0164] Since the Tent mapping is highly sensitive to the selection of initial values, this embodiment uses a variety of different initial values to generate 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:

[0165] , (14)

[0166] Among them, lb and ub are search spaces respectively. lower and upper limits.

[0167] The position of the i-th migrating whale in D-dimensional space Expressed as:

[0168] , (15)

[0169] Where D is the spatial dimension of the optimization variable.

[0170] Step 2: Leader Strategy

[0171] In each migrating whale group, individuals with richer location knowledge and higher objective function values will guide and lead other members towards their destination. In the WMA algorithm, the parameter N is introduced. L , represents the number of more experienced whales (i.e., leaders), which are individuals with better positions and higher objective function values.

[0172] ,

[0173] Among them, N L is the number of leaders, w y is the position of the y-th leader, W Mean is the average leader position.

[0174] Considering that we want to describe the actual position of the entire migrating whale group at any time by a certain point on the ocean migration path, we will use W Mean Defined as the current N L The average of the leader positions.

[0175] Step 3: Update Location

[0176] 3.1. Movement of less experienced juvenile whales toward their nearest neighbors

[0177] Assume that all population members (whales) are sorted in descending order by fitness value and / or their position: , where W1 is the best member (denoted as W Best ), W Npop As the worst member, all juveniles are usually playful, which leads each juvenile to try to imitate its closest-age companion. Therefore, in this model, each less experienced member (juvenile) The movement is mainly affected by the most recent member W in the above sequence. i-1 Influence.

[0178] 3.2. Less experienced whales are guided by more experienced whales

[0179] As mentioned before, the current position of the entire migrating whale group in the ocean is assumed to be the average of the current positions of all experienced whales, W Mean If W Mean With W Best The distance between them began to decrease, indicating that the entire experienced group of whales was approaching W Best In this case, the less experienced juvenile whale must also start to follow the vector Move in a given direction, where rand(1,D) is a random number vector taken from the interval [0,1] and the dimension is the dimension D of the optimization variable space. The kinematic equation for position update is:

[0180] , (17)

[0181] , (18)

[0182] It should be noted that the new location Only when satisfied When the current position W is replaced i .

[0183] 3.3. Discovering and searching new areas by experienced whales

[0184] In a migrating group of whales, experienced individuals (i.e., leaders) are responsible for identifying and choosing the best route to their destination. Studies tracking whale migration trajectories through satellites have shown that there are two key factors that influence humpback whale migration: first, the specific location in the Earth's gravitational and magnetic fields, represented in the model by the vector Indicates (such as Figure 3 Secondly, whales can migrate along an approximately straight line path between the starting point L and the end point U during migration. This phenomenon is represented in the motion equation by the vector Modeling (see Figure 3(blue dashed vector in ).

[0185] To simulate the random movements of whales around their main migration direction, two random parameter vectors, r1 and r2, are used in this model. These two parameters are set so that the influence of the vector in the motion equation is always greater than the influence of the vector throughout the migration.

[0186] Finally, the i-th leader whale finds a suitable path towards the destination based on the following kinematic equation:

[0187] , (19)

[0188] Among them, r1 and r2 are random number vectors with dimension D generated from the interval [0,1], L represents the position (i.e. starting point) vector, and UL is the relative direction vector. It should be noted that the new position Only when satisfied When the current position W is replaced i At the end of each WMA iteration, the migrating whale population is sorted according to the merits of the individuals, from best to worst, and the top N are selected. L The best member will be the new leader.

[0189] Step 4: DLH strategy update location

[0190] Traditional WMA has low convergence and eventually falls into the dilemma of local optimality. Therefore, DLH is introduced to improve the quality of search individuals and increase the search capability.

[0191] DLH generates the following replacement individuals:

[0192] , (20)

[0193] The radius matrix Radius is generated by subtracting the distance between the original and new positions, and the neighborhood matrix is based on the current individual w i (t) and alternative individuals w j (t) is constructed by the Euclidean distance between them.

[0194] ,(twenty one)

[0195] By learning from many neighborhood matrices, DLH generates new individuals w i-DLH,j (t+1), where the dth dimension of each new individual is based on a randomly selected individual w n,d (t) is updated in the dth dimension.

[0196] ,(twenty two)

[0197] Recalculate the individual fitness value and retain the current best position and the current best fitness value.

[0198] Finally, a greedy strategy is used to evaluate the fitness value of the current best individual and retain individuals that are more valuable for population position updates. Its mathematical model is as follows:

[0199] ,(twenty three)

[0200] Among them, w i (t+1) is the position of individual i after the t+1th iteration, w i-new (t+1) is the position of individual i after the t+1th iteration without executing the multi-dimensional learning hunting strategy, w i-DLH (t+1) is the position of individual i after the t+1th iteration after the multi-dimensional learning hunting strategy is updated.

[0201] After the iteration, the best fitness value and the global optimal position are finally returned.

[0202] The embodiment of the present application takes into account the lack of adaptive adjustment capabilities of long-term service engines after component degradation, and the disadvantage of poor accuracy of traditional optimization algorithms, and proposes a variable cycle engine control law optimization scheme based on the improved humpback whale migration algorithm. By introducing Tent mapping and integrating multi-dimensional learning hunting strategies, the global convergence performance of the algorithm is effectively enhanced. This scheme is committed to achieving multiple optimization goals: first, to reduce fuel consumption rate and significantly improve fuel utilization efficiency; second, to output maximum thrust at the peak power demand, accurately matching the flight operating conditions; third, to control the temperature before the turbine to a minimum and extend the service life of the turbine; fourth, during the transient operation of the engine, strictly control the system parameters not to exceed the limit, and at the same time achieve the shortest acceleration time. The specific beneficial effects are as follows:

[0203] (1) A variable cycle engine control law optimization method based on the improved humpback whale migration algorithm (IWMA) is proposed. The tent map is used as the initial position map of the migrating whale group 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 phases.

[0204] (2) The improved humpback whale migration algorithm was used to conduct numerical simulation verification of the intelligent optimization of 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, minimum fuel consumption, minimum turbine inlet temperature in steady state and acceleration performance optimization in transition state. As optimization variables;

[0205] (3) The proposed improved algorithm was applied to engine control law optimization, and simulation analysis and comparison of simulation results were performed. The simulation results show that IWMA converges faster and has better optimization effects than several classic intelligent optimization algorithms. It effectively reduces the VCE fuel consumption rate and minimum turbine inlet temperature, increases maximum thrust, and shortens the acceleration time by 50%.

[0206] The following describes the variable cycle engine control law optimization method based on the improved humpback whale migration algorithm of the present application with a specific embodiment.

[0207] (1) Minimum fuel consumption control mode

[0208] At low Mach numbers, turbojet engines have higher fuel consumption rates than turbofan engines. However, turbofan engines are not suitable for high Mach number flight conditions due to their large bypass ratio. Therefore, taking the subsonic cruise point (H=5km, Ma=0.8, H is the altitude, Ma is the Mach number) as an example, the minimum fuel consumption control method of the engine is verified using VCE verification. The optimization objective function is set as , F r The reference thrust is 1.35% lower than the baseline.

[0209] (2) Maximum thrust control mode

[0210] In this mode, taking the supersonic cruise point (H=10km,Ma=1.5) as an example, the maximum thrust control method of VCE is simulated. The optimization objective function is set to fitness=10000 / F n Compared to the benchmark, the maximum thrust increased by 27.59%.

[0211] (3) Minimum turbine pre-temperature control mode

[0212] VCE minimum turbine inlet temperature control is usually applied to high-altitude and high-Mach flight. The goal of minimum turbine inlet temperature control is to ensure that the airflow 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=11km, Ma=1.4) as an example, the optimization method proposed in this invention and various classic intelligent optimization algorithms are applied to optimize the minimum turbine inlet temperature control mode. The optimization objective function is set as fitness=(F r -F n ) 2 +T 41 Compared to the baseline, the minimum turbine inlet temperature decreased by 1.00%.

[0213] (4) Transition state control mode

[0214] The acceleration mode is a typical transient control mode. This mode was used to simulate the acceleration process of the VCE at an altitude of 18 km and an altitude of 0.8 Ma. The acceleration time was calculated to be 2.12 s, and the steady-state error of the fan percentage speed was minimized, with an error value of 0.0009%.

[0215] The embodiments provided by this invention improve the humpback whale migration optimization algorithm based on the modified humpback whale migration algorithm variable cycle engine control law optimization method. This algorithm employs a multidimensional learning hunting strategy for optimizing the steady-state and transient state control laws of the variable cycle engine (VCE). This aims to enhance the control law optimization effect and improve engine performance. Simulation results demonstrate that the IWMA converges faster and achieves better optimization results than several classic intelligent optimization algorithms. It effectively reduces the VCE's fuel consumption and minimum turbine inlet temperature, increases maximum thrust, and shortens acceleration time by 50%.

[0216] The above description is merely a specific embodiment of the present application, but the scope of protection of the present application is not limited thereto. Any changes or substitutions that can be easily conceived by a person skilled in the art within the technical scope disclosed in the present application should be included in the scope of protection of the present application. Therefore, the scope of protection of the present application should be based on the scope of protection of the claims.

Claims

1. A variable cycle engine control law optimization method based on an improved humpback whale migration algorithm, characterized in that: The method comprises: establishing a variable cycle engine model, and determining optimization variables based on the variable cycle engine model; Determining constraints and an objective function based on optimization variables for each variable cycle engine control mode, wherein the control mode includes a steady-state control mode and a transient control mode, wherein 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 constraints, an improved humpback whale migration algorithm is used to optimize the control law of each control mode to obtain the optimal control variable, wherein the improved humpback whale migration algorithm includes a tent map as an initial migrating whale group position map and a fusion multi-dimensional learning hunting strategy; The improved humpback whale migration algorithm is used to optimize the control law of each control mode, including: Construct the initial population, maximum number of iterations, variables, spatial dimension of optimization variables, and the boundary of the search space, initialize the position of the migrating whale group, and use the tent map as the initial migrating whale group position map; Sort the individuals in the migrating whale group in descending order according to fitness value and / or position, select several individuals at the top of the ranking as leaders, calculate the average position of the multiple leaders, and use the average position as the current position of the entire migrating whale group in the ocean; Individuals in a migrating whale group update their whale positions according to the migration rules under the guidance of the leader; Based on the multi-dimensional learning hunting strategy, the whale position is updated to improve the quality of the search individuals and increase the search ability, and the current best position and the current best fitness value are obtained; A greedy strategy is used to evaluate the fitness value of the individual in the current best position, and individuals that are valuable for updating the population position are retained to obtain the final global optimal position and the best fitness value; The method for updating the whale position based on the multidimensional learning hunting strategy includes: constructing a radius matrix based on the original position of the whale 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 candidate individuals; generating new individuals by learning from multiple neighborhood matrices, wherein the d-th dimension of each new individual is updated based on the d-th dimension of a randomly selected individual, and the new individuals are the updated whale positions based on the multidimensional learning hunting strategy.

2. The variable cycle engine control law optimization method based on the improved humpback whale migration algorithm according to claim 1 is characterized in that: The optimization variables are: ， The constraints in the process of optimizing the control law of each control mode are described as follows: ， Among them, u is the optimization variable, W fb is the fuel flow rate of the main combustion chamber, A8 is the tail nozzle throat area, A9 is the afterburner fuel flow rate, A 38 is the Flade duct nozzle area, α Flade is the Flade guide vane angle, α fan is the fan guide blade 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 engine turbine front temperature, subscript min is the minimum value, subscript max is the maximum value.

3. The variable cycle engine control law optimization method based on the improved humpback whale migration algorithm according to claim 2 is characterized in that: The objective function and constraints of the minimum fuel consumption control mode are expressed as follows: 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, st is the constraint condition, I is the total number of inequality constraints, F n is the engine thrust, const represents a constant; The objective function and constraints of the maximum thrust control mode are expressed as follows: F2=max F n ， Among them, F2 is the objective function of the maximum thrust control mode, max F n is the maximum engine thrust; The objective function and constraints of the minimum turbine pre-temperature control mode are expressed as follows: F3=min T 41 ， Among them, F3 is the objective function of the minimum turbine pre-temperature control mode, min T 41 It is the minimum temperature before the engine turbine.

4. The variable cycle engine control law optimization method based on the improved humpback whale migration algorithm according to claim 2 is characterized in that: The objective function of the transition state 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 transition state control mode is: ， Among them, minJ(k,σ) is the objective function of the transition state control mode, ω1 and ω2 are the weights of the objective function, n c (k) is the compressor speed at the current moment k, T 41 (k) is the total temperature before the high-pressure turbine at the current time k, n c,obj is the target value of compressor speed, T 41,obj is the target value of the total temperature before the high-pressure turbine, σ is an infinite positive number, and g(x) is the cost function.

5. The variable cycle engine control law optimization method based on the improved humpback whale migration algorithm according to claim 1 is characterized in that: The calculation formula for the leader position average 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 leader position.

6. The variable cycle engine control law optimization method based on the improved humpback whale migration algorithm according to claim 5 is characterized in that The descending order of the migrating whale groups is W1,...,W i-1 ,W i , W i+1 ,...,W Npop , positions are W1 to W i-1 The whale is the leader, and its position is W i To W Npop The whale is a juvenile whale, and W1 is set as the optimal individual W Best , W Npop Set as the worst individual; Individuals in the migrating whale group, under the leadership of the leader, update their positions according to the migration rules, including: Each whale calf W i (i=N L +1,...,N pop ) towards its nearest previous whale W i-1 Move and perform the first position update; Each calf moves along the path defined by the vector Move in the given direction and perform the second position update, where rand(1,D) is a random number vector taken from the interval [0,1] and the dimension is the dimension D of the optimization variable space. The kinematic equation of the second position update is: ， ； Each leader identifies and selects the best path toward the endpoint and performs a third position update, the kinematic equation of which is: ， in, is the new position, r1 and r2 are random number vectors generated from the interval [0,1] with the dimension D of the optimization variable space, L represents the starting vector, U represents the end vector, and UL is the relative direction vector; When the new position meets When , replace the current position, for The new solution corresponds to the value of the objective function, for The solution corresponds to the value of the objective function.

7. The variable cycle engine control law optimization method based on the improved humpback whale migration algorithm according to claim 6 is characterized in that: The radius matrix expression is: ， The neighborhood matrix expression is: ， The expression of the generated new individual is: ， Among them, Radiusi(t) is the radius matrix, Neighbouri(t) is the neighborhood matrix, and w i (t) is the current individual, w j (t) is the candidate individual, w new (t+1) is the new position of individual i at the t+1th iteration, D is the dimension of the optimization variable space, N is the initial population, w i-DLH,j (t+1) is the new individual generated, w i,d (t) is the updated position of individual i in the dth dimension at the tth iteration, w n,d (t) is the individual i in the tth iteration based on the randomly selected individual in the dth dimension, w r,d (t) is the reference position of individual i in the dth dimension at the tth iteration, and rand is a random function that generates a random number between 0 and 1.

8. The variable cycle engine control law optimization method based on the improved humpback whale migration algorithm according to claim 7 is characterized in that: The expression of the greedy strategy is: ， Among them, w i (t+1) is the updated position of individual i at the t+1th iteration, w i-new (t+1) is the position of individual i after the t+1th iteration without executing the multi-dimensional learning hunting strategy, w i-DLH (t+1) is the position of individual i after the t+1th iteration after the multi-dimensional learning hunting strategy is updated, f(w i-new ) is w i-new The corresponding objective function, f(w i-DLH ) is w i-DLH The corresponding objective function.

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