A turbofan engine performance optimization control method based on a multi-strategy improved artificial vole algorithm

Abstract

This invention discloses a performance optimization control method for turbofan engines based on a multi-strategy improved artificial lemming algorithm, belonging to the field of optimization control. Firstly, by integrating nonlinear slow decay time parameters, dimensional cross-multiplication strategies, and an adaptive t-distribution perturbation mechanism, a multi-strategy improved artificial lemming algorithm is provided. This invention achieves superior convergence compared to other algorithms by reconstructing the position update mechanism, especially in optimizing the maximum thrust performance of turbofan engines under different operating conditions, providing reliable technical support for realizing the thrust potential exploitation and comprehensive performance improvement of aero-engines.

Description

Technical Field

[0001] This invention discloses a turbofan engine performance optimization control method based on a multi-strategy improved artificial lemming algorithm, belonging to the field of optimization control. Background Technology

[0002] As the heart of an aircraft, the performance requirements for engines are constantly increasing. They not only need higher thrust and better fuel efficiency, but also excellent reliability and environmental friendliness. How to optimize the overall performance of an engine while meeting multiple performance targets has become an important research topic, which will have a profound impact on the future development of the aviation industry and aircraft technology.

[0003] The aviation industries of various countries have been committed to improving the performance of turbofan engines. Performance Seeking Control (PSC) optimizes the engine by integrating information from both the aircraft and the engine, seeking the optimal control variables and control laws to bring several performance indicators of the engine to their best values, thereby fully realizing the engine's performance potential. Turbofan engine performance seeking control mainly includes maximum thrust mode, minimum fuel consumption mode, and minimum turbine temperature mode.

[0004] Currently, existing research on the PSC problem mainly employs model-based optimization algorithms such as linear programming and sequential quadratic programming. These methods typically offer high computational efficiency, can meet real-time control requirements to some extent, and have achieved certain performance improvements in constant thrust minimum fuel consumption and maximum thrust control modes. However, these methods often rely on local approximations or piecewise modeling of the engine's nonlinear characteristics. When the optimization process involves multiple control parameters and their strong coupling relationships, the problem search space expands significantly, the applicability of the model is limited, and the optimization results become highly sensitive to initial conditions and operating points, thus reducing the ability to obtain the global optimum.

[0005] As the complexity of aero-engine systems continues to increase, their Power Stability and Control (PSC) problems are increasingly characterized by high dimensionality, strong nonlinearity, and multi-condition coupling. To address these issues, some research has introduced heuristic optimization algorithms, simulating natural population behavior or employing heuristic search mechanisms to solve complex optimization problems. These methods do not rely on precise gradient information, thus overcoming, to some extent, the dependence of traditional optimization methods on model accuracy. They exhibit strong global search capabilities when handling non-convex, multimodal optimization problems and have been applied to performance control modes such as maximum thrust and minimum fuel consumption of engines, achieving corresponding performance improvements.

[0006] Nevertheless, existing PSC methods still face several key technical bottlenecks in engineering applications: on the one hand, traditional optimization algorithms are prone to getting trapped in local optima under complex nonlinear conditions, making it difficult to guarantee the stability and robustness of the optimization results; on the other hand, existing heuristic optimization algorithms still have shortcomings in terms of search efficiency, parameter adaptation capability, and computational overhead. When they are directly applied to the performance optimization control of aero-engines, it is difficult to achieve an effective balance between global search capability and real-time requirements, thus limiting their engineering application value in actual flight control systems.

[0007] In summary, under current technological conditions, there is a lack of a performance optimization control method that can adapt to the strong coupling of multiple parameters and the changing characteristics of multiple operating conditions in aero-engines, while simultaneously taking into account global optimization capabilities and computational efficiency. This has become a technical problem that urgently needs to be solved in the field of aero-engine PSC (Power Strain Control). Summary of the Invention

[0008] The purpose of this invention is to overcome the shortcomings of the prior art and provide a turbofan engine performance optimization control method based on the Multi-strategy Improved Artificial Lemming Algorithm (MSI-ALA). This method can effectively solve the problem of thrust extremum capture under multivariable strong coupling environment in the maximum thrust control mode. This invention is reconstructed based on the Artificial Lemming Algorithm (ALA). It retains the inherent advantages of the algorithm, such as global exploration using Brownian motion and strong robustness to nonlinear space search. It also solves the problems of premature convergence and local deadlock in handling high-dimensional control parameters of turbofan engines through the following improvements: (1) Using a nonlinear slow decay convergence factor based on the square cosine curve, the decay path of the time parameter is reconstructed so that the convergence factor always maintains a high exploration intensity in the early and middle stages of the optimization cycle, which effectively prolongs the global search time and ensures a wider initial coverage in the complex full envelope of the engine; (2) Introducing cross-sectional and cross-sectional methods. The strategy is to perform longitudinal reconstruction and information exchange of random dimensions on the individuals in each iteration, and generate new solutions by using cross-combination between dimensions, thereby eliminating the global convergence stagnation caused by local dimension traps in the multidimensional solution space; (3) Add an adaptive t-distribution perturbation mutation mechanism, apply dynamic scale perturbation based on the current iteration number to the global optimal individuals, and utilize the adaptive evolution characteristics of the t-distribution from "long-tail jump" to "local fine-tuning" as the iteration number increases, and force the algorithm to get rid of the pseudo-extreme point by a high-precision oscillation mechanism at the end of the optimization, which significantly improves the maximum thrust capture accuracy and optimization efficiency of the engine in the steady-state operation stage.

[0009] The technical solution of the present invention: A performance optimization control method for turbofan engines based on a multi-strategy improved artificial lemming algorithm, comprising the following steps: Step A: Problem construction of maximum thrust control mode; Step B: Improve the original artificial lemming algorithm optimization scheme; Step C-1, Nonlinear slow decay time parameters; Time parameters Instead, use a slow decay time parameter based on the squared cosine curve: (17) Improved The decline is more gradual in the early and middle stages of the iteration, allowing the lemming population to maintain a high level of active energy for a longer period of time; Step C-2, Dimensional Cross-Style Strategy; In each iteration, a dimensional crossover strategy is introduced; this strategy generates more competitive offspring by rearranging the dimensions of individuals in the population and exchanging information; the formula for updating the vertical crossover position is as follows: (18) in, and Two different individuals randomly selected from the population in the 1st... The components of the dimension, for Random weighting factors between dimensions; through cross-reconstruction on specific dimensions, the algorithm can break the mutual constraints between dimensions, allowing individuals trapped in local optima to have the opportunity to escape in the dimensional space; Step C-3: Adaptive t-distribution perturbation variation; Introducing an adaptive approach based on the number of iterations Distributed perturbation mechanism; The distribution combines the characteristics of the Gaussian and Cauchy distributions; its probability density function varies with the degrees of freedom. Evolving with changes; causing For the current global optimal position Implement the following perturbation to generate new candidate solutions : (19) in, Describing the degrees of freedom as of Distribute random numbers; in the early stages of iteration, The distribution exhibits a "long-tail" characteristic similar to the Cauchy distribution, giving the optimal individual a large random jump step size, enhancing its ability to escape traps; with the number of iterations... The increase, The distribution gradually approaches a Gaussian distribution, and the perturbation range shrinks accordingly, thus providing high-precision local oscillation search in the later stages of optimization. Step C: Use the improved artificial lemming algorithm for turbofan engine performance optimization control.

[0010] Furthermore, step A specifically includes: maximum thrust of turbofan engine The constrained optimization problem of the control mode is as follows: (1) Among control variables , Represents control variables A single component in This represents the feasible region of each variable. and Let be the lower and upper bounds of a single variable, respectively. The range of values ​​for can be expressed as: (2) The control variable is: main fuel flow rate. Tail nozzle area The constraint is: total temperature at the combustion chamber outlet. Low-pressure turbine outlet total temperature Low-pressure rotor speed High-voltage rotor speed Fan surge margin Compressor surge margin Air-fuel ratio in the main combustion chamber ; This indicates the maximum total temperature at the combustion chamber outlet. This indicates the maximum low-pressure turbine outlet total temperature. Indicates the maximum low-pressure rotor speed. Indicates the maximum high-voltage rotor speed. This indicates the critical value for fan surge margin. This represents the critical value for compressor surge margin. Indicates the maximum air-fuel ratio in the main combustion chamber. This indicates the minimum air-fuel ratio in the main combustion chamber.

[0011] Furthermore, the optimization scheme of the original artificial lemming algorithm in step B is specifically as follows: Step 2.1: Use ALA as a tool to solve the performance optimization control PSC problem; ALA, as a population-based intelligent optimization algorithm, requires randomly generating an initial lemming population in the solution space; let the population size be... The dimensions of the optimization problem are , No. Only lemmings in the first Initial position of dimensional variable Randomly generate between given upper and lower bounds using the following formula: (3) in, and Representing the first Upper and lower bounds for dimensional variables. for Random numbers within a range that follow a uniform distribution. , The generated initial population matrix Include There are several candidate solutions; after initialization and during each iteration, the algorithm calculates the fitness value of each individual and marks the individual with the best current fitness as the global optimum, denoted as . ; Step 2.2: Introduce time-varying dynamic parameters into ALA to control the switching of the algorithm between different behavior modes; First, define a non-linearly decreasing time parameter. It simulates the effects of environmental stress on lemming behavior over time: (4) in This represents the current iteration number. This represents the maximum number of iterations. Then, based on The algorithm further constructs the energy factor This is used to characterize the current active energy level of lemmings. (5) when At that time, the population was in the exploratory stage; when At this time, the lemmings' energy decreases, and the population enters the development phase; Introducing direction markers into the algorithm : (6) By introducing a time parameter that varies with time Energy factors Directional signs This controls the algorithm to switch between the following modes: Mode 1: When the corresponding algorithm is in a high-energy state And random probability Lemmings instinctively initiate long-distance migrations; these migrations are not directional movements but rather population dispersal behaviors influenced by environmental randomness. To simulate this process, the algorithm introduces Brownian motion; Brownian motion provides a random and ergodic step size, helping the algorithm quickly jump out of the current area and cover the unknown search space; its position update formula is as follows: (7) in, It is a random vector that follows a standard normal distribution, simulating the random step size affected by the environment during migration; This represents a lemming individual randomly selected from the current population, representing social interaction behavior within the migrating group; yes A random vector between these values ​​is used to adjust the weights of individuals moving closer to the optimal solution or closer to random individuals. It is the first i Only lemmings in the first t The position after the next iteration; Mode 2: When energy factors And random probability The algorithm simulates digging behavior, using a sine function to simulate the fluctuations in digging action, aiming to perform a broad oscillating search in the vicinity of the current area; its mathematical model is as follows: (8) Among them, the mining coefficient Dynamically changes with the number of iterations: (9) In this strategy, the sine term A nonlinear fluctuation factor is introduced to simulate changes in excavation depth; Mode 3: When the lemmings find a suitable habitat, the corresponding algorithm enters a low-energy state. And random probability At this time, the ALA algorithm employs a spiral search strategy; this movement allows the lemming to hover outwards or inwards from the current optimal solution, thereby performing a high-precision search of the local area; its mathematical expression is: (10) Among them, the spiral term The calculation depends on the distance between the individual and the food source. : (11) (12) here, yes Random numbers between; Pattern 4: When And random probability The algorithm simulates the behavior of evading predators. To reflect the suddenness, unpredictability, and alternating long and short step lengths of the escape action, ALA integrates the Levy flight mechanism. Levy flight is a random walk that follows a heavy-tailed distribution, and its mathematical model is as follows: (13) in, It is an adaptive escape coefficient that decreases linearly with the iteration process, reflecting the decline in lemming physical strength as the escape time increases: (14) The step size vector representing Levy's flight is generated by the Mantegna algorithm: (15) in and All follow a normal distribution. ; After each generation of the population completes the position update, it is essential to ensure that all individuals remain within the feasible region of the problem; therefore, the algorithm will update the newly generated positions. Perform boundary checks: If the value of a certain dimension exceeds the set boundary... If so, it will be forcibly corrected to the corresponding boundary value; Step 2.3: To ensure the population evolves in a better direction, ALA employs a greedy selection strategy to decide whether to retain a new position; only if the new position... The fitness value is better than that of the original position. Only then is the individual's status updated: (16).

[0012] The beneficial effects of this invention are as follows: Through the above-mentioned strategy improvement, an improved algorithm with higher optimization efficiency and convergence accuracy compared to the original algorithm is provided. Furthermore, it can optimize engine performance indicators under the maximum thrust control mode under the harsh conditions of strong coupling of turbofan engine control variables and complex and variable operating environment. This effectively solves the problems of premature convergence and local deadlock in the optimization process, providing reliable technical support for realizing thrust potential exploitation, comprehensive performance improvement, and adaptive optimization control within the entire thrust envelope of aero-engines. Attached Figure Description

[0013] Figure 1 This is a block diagram of the algorithm structure of the present invention.

[0014] Figure 2 This is a comparison chart of the convergence of different optimization algorithms for a single-peaked test function.

[0015] Figure 3 This is a comparison chart of the convergence of different optimization algorithms for the multi-peak test function.

[0016] Figure 4 This is a comparison chart of the convergence of different optimization algorithms for the mixed test function.

[0017] Figure 5 This is a comparison chart of the convergence of different optimization algorithms for the composite test function.

[0018] Figure 6 It is the system response result obtained by introducing the control solution provided by the optimization controller as input at the 10th second during the dynamic operation of the engine nonlinear model. Detailed Implementation

[0019] To make the technical solution of the present invention and the technical problem it solves clearer, the technical solution of the present invention will be specifically described below in conjunction with the above-mentioned invention content and accompanying drawings.

[0020] A performance optimization control method for turbofan engines based on a multi-strategy improved artificial lemming algorithm, comprising the following steps: Step A: Problem construction of maximum thrust control mode.

[0021] Maximum thrust control mode is a control mode that optimizes engine thrust to the maximum. It requires that when the aircraft climbs and accelerates, the engine should generate the maximum possible thrust while ensuring safe operation.

[0022] For an engine operating in maximum thrust mode, the fan guide vane angle and the angle of the compressor guide vanes It has already reached its maximum value. To further increase thrust, the fuel quantity needs to be adjusted. and tail nozzle area To achieve this. Add , reduce While it can increase the engine's net thrust, it leads to a decrease in the surge margin of the fan and compressor, an increase in the high / low pressure shaft rotor speed, and an increase in the total outlet temperature of the combustion chamber and low-pressure turbine, thereby increasing the risk of engine overheating, overspeeding, unstable combustion, and surge. Therefore, by treating these physical limitations as constraints, a constrained optimization problem for the maximum thrust control mode is formed as follows: (1) Among control variables Its value range is: (2) The control variable is: main fuel flow rate. Tail nozzle area The constraint is: total temperature at the combustion chamber outlet. Low-pressure turbine outlet total temperature Low-pressure rotor speed High-voltage rotor speed Fan surge margin Compressor surge margin Air-fuel ratio in the main combustion chamber . superscript Subscript They represent The maximum and minimum values.

[0023] Step B: Basic principles of the artificial lemming algorithm.

[0024] This invention utilizes ALA as a tool for solving the PSC problem. The ALA algorithm abstracts these four biological behaviors into mathematical models, each corresponding to a different search strategy within the algorithm. Specifically, long-distance migration and burrowing constitute the exploration phase of the algorithm, aiming to broadly search the solution space; while foraging and predator avoidance constitute the development phase, dedicated to discovering the optimal solution in a local area through fine-grained searching. Furthermore, ALA employs an energy decay mechanism to dynamically adjust the balance between exploration and development, thereby enhancing its ability to escape local optima and robustly converge to the global optimum.

[0025] As a population-based intelligent optimization algorithm, ALA first needs to randomly generate an initial lemming population within the solution space. Assume the population size is... The dimensions of the optimization problem are , No. Only lemmings in the first Initial position of dimension Randomly generate between given upper and lower bounds using the following formula: (3) in, and Representing the first Upper and lower bounds for dimensional variables. for Random numbers within a range that follow a uniform distribution. , The generated initial population matrix Includes There are several candidate solutions. After initialization and during each iteration, the algorithm calculates the fitness value of each individual and marks the individual with the best current fitness as the global optimum, denoted as . .

[0026] To simulate the changing behavioral patterns of lemmings in nature in response to environmental stress, ALA introduces a dynamic parameter that varies over time to control the switching of the algorithm between different behavioral patterns.

[0027] First, define a non-linearly decreasing time parameter. It simulates the effects of environmental stress on lemming behavior over time: (4) in This represents the current iteration number. This represents the maximum number of iterations. Based on... The algorithm further constructs the energy factor. This is used to characterize the current active energy level of lemmings. (5) Energy Factor It is a core indicator for balancing exploration and development. When When this occurs, it indicates that the lemmings are energetic and the population is in the exploratory phase (long-distance migration or burrowing); when At this time, lemmings have reduced energy and tend to stay in specific areas, and the population enters a development phase (foraging or avoiding predators).

[0028] In addition, to increase the randomness and diversity of search directions, directional markers were introduced. : (6) By introducing a time parameter that varies with time Energy factors Directional signs This controls the algorithm to switch between the following modes: When excessive population density leads to food shortage, corresponding to the high-energy state of the algorithm... At this time, lemmings will instinctively initiate long-distance migrations. In the ALA algorithm, if the random probability... If so, the strategy will be activated to perform a global exploration.

[0029] Long-distance migration is not a directional movement, but rather a population dispersal behavior influenced by environmental randomness. To simulate this process, the algorithm introduces Brownian motion. Brownian motion provides a random and ergodic step size, helping the algorithm quickly jump out of the current region and cover the unknown search space. Its position update formula is as follows: (7) in, It is a random vector that follows a standard normal distribution, simulating the random step size affected by the environment during migration; This represents a lemming individual randomly selected from the current population, representing social interaction behavior within the migrating group; yes A random vector between these values ​​is used to adjust the weights of individuals moving closer to the optimal solution or closer to random individuals. It is the first i Only lemmings in the first t The position after the next iteration. Through this mechanism, the algorithm can maintain a high population diversity in the early stages, effectively avoiding getting trapped in local optima.

[0030] Lemmings, as adept diggers, rely heavily on burrowing for survival and reproduction. In algorithms, this corresponds to another pattern in the exploration phase. That is, when the energy factor... And random probability At that time, the algorithm simulates mining behavior.

[0031] Unlike disordered migration, digging behavior exhibits a certain periodicity and rhythm. The algorithm uses a sine function to simulate the fluctuations in digging action, aiming to perform a broad oscillating search in the vicinity of the current area. Its mathematical model is as follows: (8) Among them, the mining coefficient Dynamically changes with the number of iterations: (9) In this strategy, the sine term A nonlinear fluctuation factor was introduced to simulate changes in mining depth. This sinusoidal fluctuation-based search strategy effectively complements long-distance migration and further enhances the algorithm's global exploration capabilities.

[0032] Once the lemmings find a suitable habitat, the algorithm enters a low-energy state. They establish relatively fixed foraging areas, using their keen sense of smell to search for food around the burrow. At this stage, the algorithm focuses on local exploitation.

[0033] When random probability The ALA algorithm simulates a spiral foraging process. To model the efficient food-searching path of lemmings within a limited area, the algorithm employs a spiral search strategy. This movement allows the lemming to spiral outwards or inwards from the current optimal solution, thus enabling a high-precision search of the local area. Its mathematical expression is: (10) Among them, the spiral term The calculation depends on the distance between the individual and the food source. : (11) (12) here, yes The formula uses a periodic combination of trigonometric functions to simulate the meandering path of lemmings during foraging, greatly improving the algorithm's convergence accuracy near the optimal solution.

[0034] When faced with danger, lemmings exhibit highly explosive escape behaviors, including running quickly or making deceptive movements to confuse predators. And random probability The algorithm simulates this behavior of evading predators. To reflect the suddenness, unpredictability, and alternating long and short step lengths of the escape action, ALA integrates the Levy flight mechanism. Levy flight is a random walk that follows a heavy-tailed distribution, and its mathematical model is as follows: (13) in, It is an adaptive escape coefficient that decreases linearly with the iteration process, reflecting the decline in lemming physical strength as the escape time increases: (14) The step size vector representing Levy's flight is generated by the Mantegna algorithm: (15) in and All follow a normal distribution. Introducing the Levy flight strategy allows the algorithm to occasionally produce long-distance abrupt jumps even during the development phase. This greatly enhances the algorithm's ability to escape local extremum traps and avoids premature convergence.

[0035] After each generation of the population completes its position update, it must be ensured that all individuals remain within the feasible region of the problem. Therefore, the algorithm will update the newly generated positions. Perform boundary checks: If the value of a certain dimension exceeds the set boundary... If so, it will be forcibly corrected to the corresponding boundary value.

[0036] Finally, to ensure the population evolves in a better direction, ALA employs a greedy selection strategy to decide whether to retain a new position. Only if the new position... The fitness value is better than that of the original position. Only then is the individual's status updated: (16) This mechanism ensures the convergence of the algorithm, enabling the population quality to steadily improve during the iteration process.

[0037] Step C: Improve the strategy of the original artificial lemming algorithm.

[0038] To address the shortcomings in convergence accuracy and premature convergence that the standard ALA algorithm often suffers when dealing with complex high-dimensional optimization problems, this patent improves the algorithm's ability to escape local optima and handle strong coupling of control variables by improving the energy decay mechanism, introducing a cross-sectional strategy, and an adaptive perturbation mechanism.

[0039] Step C-1, Nonlinear slow decay time parameter In standard ALA, the time parameter use The function decreases non-linearly. Analysis reveals that the function decreases rapidly in the middle of the iteration, leading to an increase in the energy factor. Prematurely reducing the time to below the development threshold limits the algorithm's exploration time in the global space. To extend the exploration phase and enhance the thoroughness of the global search, this patent introduces a slow decay time parameter based on a squared cosine curve: (17) Improved The lemming population experiences a more gradual decline in the early and middle stages of iteration, allowing it to maintain a high level of activity for a longer period. This enables more thorough path searching within the complex full envelope, effectively improving the algorithm's global optimization robustness in the multi-modal solution space.

[0040] Step C-2, Dimensional Cross-Style Strategy To address the strong coupling between control parameters of turbofan engines and prevent the algorithm from becoming stuck in local optima in certain dimensions, leading to overall convergence stagnation, this patent introduces a cross-sectional strategy in each iteration. This strategy rearranges the dimensions of the population and exchanges information to generate more competitive offspring. The formula for updating the vertical cross-sectional position is as follows: (18) in, and Two different individuals randomly selected from the population in the 1st... The components of the dimension, for Random weighting factors are used between dimensions. By cross-reconstructing on specific dimensions, the algorithm can break the mutual constraints between dimensions, allowing individuals trapped in local optima to have the opportunity to escape in the dimensional space. This significantly enhances the algorithm's ability to handle multivariate strongly coupled problems and effectively solves the premature convergence problem.

[0041] Step C-3, Adaptive t-distribution perturbation variation To further improve the convergence accuracy of the algorithm in the late optimization stage and prevent the global optimum from being found. Stagnation, this patent introduces an adaptive approach based on the number of iterations. Distribution perturbation mechanism. The distribution combines the characteristics of the Gaussian and Cauchy distributions, and its probability density function varies with the degrees of freedom. It evolves with changes. This patent order For the current global optimal position Implement the following perturbation to generate new candidate solutions : (19) in, Describing the degrees of freedom as of Distribute random numbers. In the early stages of the iteration, The distribution exhibits a "long-tail" characteristic similar to the Cauchy distribution, giving the optimal individual a larger random jump step size, enhancing its ability to escape traps; with the number of iterations... The increase, As the distribution gradually approaches a Gaussian distribution, the perturbation range shrinks, thus providing high-precision local oscillation search in the later stages of optimization. This adaptive evolution mechanism ensures that the algorithm maintains good dynamic performance at different search stages.

[0042] The structural block diagram of the present invention is as follows: Figure 1 As shown. To evaluate the effectiveness and accuracy of this invention, this study used the CEC2017 standard test set for experimental testing, comparing it with the basic ALA algorithm, and also selected three representative algorithms from recent years for comparative analysis. The algorithms tested included the Whale Optimization Algorithm (WOA), the Coati Optimization Algorithm (COA), and the Ivy algorithm (LVYA). To ensure the fairness of the comparison, all algorithms were run in a unified hardware and software environment and used the same common parameter settings (population size N=30, maximum number of iterations Max_iter=5000).

[0043] The CEC2017 test set includes 30 test functions. F1-F3 are unimodal test functions used to verify the convergence accuracy of the algorithm; F4-F10 are multimodal test functions, mainly used to test the algorithm's ability to escape local optima; F11-F20 and F21-F30 are mixed and composite functions, respectively. These two types of functions have complex compositions and contain additional biases and weights, further increasing the difficulty of algorithm optimization. To more intuitively compare the convergence process of each algorithm, this patent presents a comparison chart of the convergence curves of all test functions in a 30-dimensional case. Figure 2 , Figure 3 , Figure 4 , Figure 5 The average fitness convergence curves of the single-peak test function, multi-peak test function, mixed function, and composite function are shown after running 10 times independently. As can be seen from the figure, the MSI-ALA algorithm has a significant advantage over other comparative algorithms in terms of convergence speed and accuracy, with faster solution efficiency and less tendency to get trapped in local optima.

[0044] Subsequently, MSI-ALA was applied to the performance optimization problem of solving the maximum thrust control mode of a turbofan engine. All programs in this invention were tested using an Intel i7-13650 processor with a clock speed of 2.6GHz, and the high-precision timing API function QueryPerformanceCounter() was used to obtain the runtime of the code segments. Based on this, a high-precision timing API function was selected. ,Mach number , , as well as , The tests were conducted at these three operating points.

[0045] In the maximum thrust optimization experiment, the limiting parameters set during the optimization process are: 0.26 m 2 , 0.47m 2 , 1650 K, 1020 K, 14200 rpm 8500 rpm 0.1, 0.1, 0.0285, 0.008. The population size of the heuristic optimization algorithm is set to 1024, and the number of iterations is 50.

[0046] Table 1 shows the comparison results before and after optimization under this control mode. It can be seen that through optimized control of maximum thrust, thrust increases of 13.52%, 21.42%, and 15.72% were achieved under the three operating conditions, respectively. The optimized engine control parameters significantly improved thrust and effectively enhanced overall performance. Meanwhile, key engine parameters are as follows: , , , None of them exceeded the limit. , as well as All of these are within the prescribed range and meet the expected requirements for safe and stable operation.

[0047] Table 1. Optimization Results for Maximum Thrust

[0048] Figure 6 This test examines the maximum thrust optimization results. The engine's nonlinear model operates in dynamic mode, and the optimization control input is applied at 10 seconds. The graphs show that under given operating conditions, the engine responds rapidly and eventually stabilizes at the optimized thrust result, verifying the effectiveness of the maximum thrust optimization control. Under different operating conditions, changes in the control input result in varying degrees of abrupt response changes.

[0049] In summary, addressing the challenge of balancing global optimization accuracy and the ability to escape local optima in the high-dimensional nonlinear search space of turbofan engine control variables with strong coupling, this invention proposes a multi-strategy improved artificial lemming algorithm. Experimental results demonstrate that this method achieves superior convergence compared to other algorithms by reconstructing the position update mechanism, and incorporates three key improvement techniques: a nonlinear slow decay time parameter, a dimensional cross-multiplication strategy, and an adaptive t-distribution perturbation mechanism. These improvements effectively balance the algorithm's global exploration and local exploitation capabilities, enabling optimal control of the engine's maximum thrust even under complex envelope conditions.

[0050] Those skilled in the art should understand that the embodiments described in this invention are merely illustrative and not restrictive. Technical features in different embodiments can be freely combined according to actual needs to achieve better technical effects. Based on the technical guidance provided by this invention, relevant researchers can reasonably deduce and implement other feasible technical variations. It should be particularly noted that modifications to the technical solutions of the embodiments, or the use of equivalent alternatives to replace some technical features, should be considered within the scope of protection of this application, as long as they do not depart from the core concept of this technical solution.

Claims

1. A performance optimization control method for turbofan engines based on a multi-strategy improved artificial lemming algorithm, characterized in that, The steps are as follows: Step A: Problem construction of maximum thrust control mode; Step B: Improve the original artificial lemming algorithm optimization scheme; Step C-1, Nonlinear slow decay time parameters; Time parameters Instead, use a slow decay time parameter based on the squared cosine curve: （17） Improved The decline is more gradual in the early and middle stages of the iteration, allowing the lemming population to maintain a high level of active energy for a longer period of time; Step C-2, Dimensional Cross-Style Strategy; In each iteration, a dimensional crossover strategy is introduced; this strategy generates more competitive offspring by rearranging the dimensions of individuals in the population and exchanging information; the formula for updating the vertical crossover position is as follows: （18） in, and Two different individuals randomly selected from the population in the 1st... The components of the dimension, for Random weighting factors between dimensions; through cross-reconstruction on specific dimensions, the algorithm can break the mutual constraints between dimensions, allowing individuals trapped in local optima to have the opportunity to escape in the dimensional space; Step C-3: Adaptive t-distribution perturbation variation; Introducing an adaptive approach based on the number of iterations Distributed perturbation mechanism; The distribution combines the characteristics of the Gaussian and Cauchy distributions; its probability density function varies with the degrees of freedom. Evolving with changes; causing For the current global optimal position Implement the following perturbation to generate new candidate solutions : （19） in, Describing the degrees of freedom as of Distribute random numbers; in the early stages of iteration, The distribution exhibits a "long-tail" characteristic similar to the Cauchy distribution, giving the optimal individual a large random jump step size, enhancing its ability to escape traps; with the number of iterations... The increase, The distribution gradually approaches a Gaussian distribution, and the perturbation range shrinks accordingly, thus providing high-precision local oscillation search in the later stages of optimization. Step C: Use the improved artificial lemming algorithm for turbofan engine performance optimization control.

2. The turbofan engine performance optimization control method based on a multi-strategy improved artificial lemming algorithm according to claim 1, characterized in that, Step A specifically involves: maximum thrust of turbofan engine The constrained optimization problem of the control mode is as follows: （1） Among control variables , Represents control variables A single component in This represents the feasible region of each variable. and Let be the lower and upper bounds of a single variable, respectively. The range of values ​​for can be expressed as: （2） The control variable is: main fuel flow rate. Tail nozzle area The constraint is: total temperature at the combustion chamber outlet. Low-pressure turbine outlet total temperature Low-pressure rotor speed High-voltage rotor speed Fan surge margin Compressor surge margin Air-fuel ratio in the main combustion chamber ; This indicates the maximum total temperature at the combustion chamber outlet. This indicates the maximum low-pressure turbine outlet total temperature. Indicates the maximum low-pressure rotor speed. Indicates the maximum high-voltage rotor speed. This indicates the critical value for fan surge margin. This represents the critical value for compressor surge margin. Indicates the maximum air-fuel ratio in the main combustion chamber. This indicates the minimum air-fuel ratio in the main combustion chamber.

3. The turbofan engine performance optimization control method based on a multi-strategy improved artificial lemming algorithm according to claim 2, characterized in that, The optimization scheme of the original artificial lemming algorithm in step B is as follows: Step 2.1: Use ALA as a tool to solve the performance optimization control PSC problem; ALA, as a population-based intelligent optimization algorithm, requires randomly generating an initial lemming population in the solution space; let the population size be... The dimensions of the optimization problem are , No. Only lemmings in the first Initial position of dimensional variable Randomly generate between given upper and lower bounds using the following formula: （3） in, and Representing the first Upper and lower bounds for dimensional variables. for Random numbers within a range that follow a uniform distribution. , The generated initial population matrix Include There are several candidate solutions; after initialization and during each iteration, the algorithm calculates the fitness value of each individual and marks the individual with the best current fitness as the global optimum, denoted as . ; Step 2.2: Introduce time-varying dynamic parameters into ALA to control the switching of the algorithm between different behavior modes; First, define a non-linearly decreasing time parameter. It simulates the effects of environmental stress on lemming behavior over time: （4） in This represents the current iteration number. This represents the maximum number of iterations. Then, based on The algorithm further constructs the energy factor This is used to characterize the current active energy level of lemmings. （5） when At that time, the population was in the exploratory stage; when At this time, the lemmings' energy decreases, and the population enters the development phase; Introducing direction markers into the algorithm : （6） By introducing a time parameter that varies with time Energy factors Directional signs This controls the algorithm to switch between the following modes: Mode 1: When the corresponding algorithm is in a high-energy state And random probability Lemmings instinctively initiate long-distance migrations; these migrations are not directional movements but rather population dispersal behaviors influenced by environmental randomness. To simulate this process, the algorithm introduces Brownian motion; Brownian motion provides a random and ergodic step size, helping the algorithm quickly jump out of the current area and cover the unknown search space; its position update formula is as follows: （7） in, It is a random vector that follows a standard normal distribution, simulating the random step size affected by the environment during migration; This represents a lemming individual randomly selected from the current population, representing social interaction behavior within the migrating group; yes A random vector between these values ​​is used to adjust the weights of individuals moving closer to the optimal solution or closer to random individuals. It is the first i Only lemmings in the first t The position after the next iteration; Mode 2: When energy factors And random probability The algorithm simulates digging behavior, using a sine function to simulate the fluctuations in digging action, aiming to perform a broad oscillating search in the vicinity of the current area; its mathematical model is as follows: （8） Among them, the mining coefficient Dynamically changes with the number of iterations: （9） In this strategy, the sine term A nonlinear fluctuation factor is introduced to simulate changes in excavation depth; Mode 3: When the lemmings find a suitable habitat, the corresponding algorithm enters a low-energy state. And random probability At this time, the ALA algorithm employs a spiral search strategy; this movement allows the lemming to hover outwards or inwards from the current optimal solution, thereby performing a high-precision search of the local area; its mathematical expression is: （10） Among them, the spiral term The calculation depends on the distance between the individual and the food source. : （11） （12） here, yes Random numbers between; Pattern 4: When And random probability The algorithm simulates the behavior of evading predators. To reflect the suddenness, unpredictability, and alternating long and short step lengths of the escape action, ALA integrates the Levy flight mechanism. Levy flight is a random walk that follows a heavy-tailed distribution, and its mathematical model is as follows: （13） in, It is an adaptive escape coefficient that decreases linearly with the iteration process, reflecting the decline in lemming physical strength as the escape time increases: （14） The step size vector representing Levy's flight is generated by the Mantegna algorithm: （15） in and All follow a normal distribution. ; After each generation of the population completes the position update, it is essential to ensure that all individuals remain within the feasible region of the problem; therefore, the algorithm will update the newly generated positions. Perform boundary checks: If the value of a certain dimension exceeds the set boundary... If so, it will be forcibly corrected to the corresponding boundary value; Step 2.3: To ensure the population evolves in a better direction, ALA employs a greedy selection strategy to decide whether to retain a new position; only if the new position... The fitness value is better than that of the original position. Only then is the individual's status updated: （16）。

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