Aero-engine steady-state performance optimization method and system, storage medium and electronic device

Abstract

The application provides an aero-engine steady-state performance optimization method and system, a storage medium and an electronic device, and relates to the technical field of aero-engine control and performance optimization. The method comprises the following steps: obtaining steady-state working condition input and selecting an optimization mode, determining a control variable vector and its physical boundary, constructing a main objective function and a constraint condition, constructing a comprehensive evaluation function comprising an objective term and a penalty function term, performing iterative optimization by using an improved whale optimization algorithm, and outputting optimal control variables and performance indexes. The application improves the robustness and engineering realizability of the optimization process by rewriting the thrust constant type equality constraint into an error threshold form; the penalty function mechanism is used to uniformly process multiple types of constraints, which facilitates the solution by swarm intelligence algorithms; the improved whale optimization algorithm is used to enhance the global search capability and avoid falling into local optimization, so as to realize optimal control of the steady-state performance of the aero-engine under the premise of meeting safety constraints.

Description

Technical Field

[0001] This application relates to the field of aero-engine control and performance optimization technology, and more specifically, to an aero-engine steady-state performance optimization method and system, storage medium and electronic equipment. Background Technology

[0002] As the core power plant of aircraft, the performance optimization of aero-engines plays a decisive role in flight safety, economy, and environmental impact. At different flight phases and operating points, aero-engines need to meet diverse performance objectives, including but not limited to fuel economy during cruise, thrust response during acceleration, and protection of hot-end components under high thermal load conditions. Modern aero-engines are typically equipped with multiple adjustable components and control variables, and these variables have complex nonlinear relationships with engine performance indicators, making steady-state performance optimization a challenging engineering task.

[0003] Existing methods may be sensitive to initial values ​​and prone to getting trapped in local optima if traditional analytical optimization or local search methods are used; if strict equality constraints (such as constant thrust) are directly applied, the feasibility and robustness may also be limited under model error and numerical discretization conditions.

[0004] Therefore, a technical solution is needed that can optimize steady-state performance combinations under constraints and express engineering constraints such as constant thrust in a more feasible way to improve the usability of the method in engineering models. Summary of the Invention

[0005] This application provides a method and system for optimizing the steady-state performance of an aero-engine, a storage medium, and electronic equipment, thereby providing a method for optimizing the steady-state performance of an aero-engine to achieve global optimal engine performance while ensuring operational safety.

[0006] According to a first aspect of this application, a method for optimizing the steady-state performance of an aero-engine is provided, comprising the following steps: obtaining the steady-state operating condition input of the aero-engine, and selecting a steady-state optimization mode according to engineering objectives, wherein the steady-state optimization mode includes at least one of a minimum fuel consumption mode, a maximum thrust mode, and a minimum turbine inlet temperature mode; determining the control variable vector and its physical boundary, and calling a steady-state performance calculation model; the steady-state performance calculation model outputting steady-state performance indicators and safety boundary parameters according to the control variable vector and the steady-state operating condition input; constructing a main objective function and constructing constraints according to the steady-state optimization mode; the constraints include at least thrust error threshold constraints and safety inequality constraints; constructing a comprehensive evaluation function containing an objective term and a penalty function term, wherein the objective term is determined based on the main objective function, and the penalty function term is used to penalize candidate solutions that violate constraints; using an improved whale optimization algorithm, iteratively optimizing the comprehensive evaluation function within the physical boundary to obtain the optimal control variable; and outputting the optimal control variable and its corresponding steady-state performance indicator.

[0007] In one embodiment of this application, the thrust error threshold constraint is in the form of an absolute error. or relative error form ;in, The thrust calculated for the model, Given the target thrust under a given working condition, and This is a preset threshold.

[0008] In one embodiment of this application, the improved whale optimization algorithm includes at least one of the following improvement strategies: updating the convergence factor of the algorithm using a nonlinear strategy; introducing an adaptive weight coefficient that varies with the number of iterations during the position update process; performing random difference mutation on individuals in the population and using a greedy selection to retain better individuals; and using a quasi-backward learning strategy to generate the initial population.

[0009] In one embodiment of this application, during the iterative process of the improved whale algorithm, when the updated individual exceeds the boundary... At that time, boundary repair processing is performed to truncate or map the outbound components back to the boundary range. This is the lower bound of the control variable vector. This is the upper limit of the control variable vector.

[0010] In one embodiment of this application, the method further includes a model uncertainty processing step: quantifying the uncertainty of the steady-state performance calculation model in predicting safety boundary parameters to obtain an uncertainty value corresponding to the current operating condition; dynamically tightening the boundary of the safety inequality constraint based on the uncertainty value to generate an adaptive safety constraint boundary; wherein, when constructing the comprehensive evaluation function, the penalty function term is constructed based on the thrust error threshold constraint and the adaptive safety constraint boundary.

[0011] In one embodiment of this application, the dynamic tightening of the boundary of the safety inequality constraint is specifically implemented as follows: for lower limit constraints, the original lower limit value is increased by an offset that is positively correlated with the uncertainty value; for upper limit constraints, the original upper limit value is decreased by an offset that is positively correlated with the uncertainty value.

[0012] In one embodiment of this application, quantifying the uncertainty of the steady-state performance calculation model in predicting safety boundary parameters includes: establishing a statistical relationship of model prediction errors based on historical data; and querying or calculating the prediction uncertainty value corresponding to the safety boundary parameters based on real-time operating condition input.

[0013] According to a second aspect of this application, a steady-state performance optimization system for an aero-engine is provided, comprising: a condition and mode selection module, used to acquire the steady-state condition input of the aero-engine and select a steady-state optimization mode according to engineering objectives, wherein the steady-state optimization mode includes at least one of a minimum fuel consumption mode, a maximum thrust mode, and a minimum turbine inlet temperature mode; a steady-state performance calculation module, used to determine the control variable vector and its physical boundaries, and call a steady-state performance calculation model; wherein the steady-state performance calculation model outputs steady-state performance indicators and safety boundary parameters according to the control variable vector and the steady-state condition input; and an objective and constraint construction module, used for... A primary objective function is constructed based on the steady-state optimization mode, and constraints are established. These constraints include at least thrust error threshold constraints and safety inequality constraints. A comprehensive evaluation function construction module is used to construct a comprehensive evaluation function containing an objective term and a penalty function term, wherein the objective term is determined based on the primary objective function, and the penalty function term is used to penalize candidate solutions that violate the constraints. An optimization solution module is used to iteratively optimize the comprehensive evaluation function within the physical boundary using an improved whale optimization algorithm to obtain the optimal control variable. An output module is used to output the optimal control variable and its corresponding steady-state performance index.

[0014] According to a third aspect of this application, an electronic device is provided, comprising: a processor; and a memory for storing one or more programs that, when executed by the processor, cause the processor to perform the method described above.

[0015] According to a fourth aspect of this application, a computer-readable storage medium is provided having a computer program stored thereon, which, when executed by a processor, implements the method described above.

[0016] The exemplary embodiments of this application provide a method for optimizing the steady-state performance of aero-engines. By acquiring the steady-state operating condition input of the aero-engine and selecting a steady-state optimization mode based on engineering objectives, the method achieves performance optimization requirements for different flight phases and operating points. The steady-state optimization mode includes at least one of the following: minimum fuel consumption mode, maximum thrust mode, and minimum turbine inlet temperature mode. By determining the control variable vector and its physical boundaries and invoking the steady-state performance calculation model, the model outputs steady-state performance indicators and safety boundary parameters based on the control variable vector and steady-state operating condition input, establishing a mapping relationship between engine performance and control variables. A main objective function is constructed based on the steady-state optimization mode, and constraints are established. These constraints include at least thrust error threshold constraints and safety inequality constraints, transforming traditional strict equality constraints into a more engineering-practical error threshold form, thus improving the robustness of the optimization process.

[0017] By constructing a comprehensive evaluation function comprising an objective term and a penalty function term, where the objective term is determined based on the main objective function and the penalty function term is used to penalize candidate solutions that violate constraints, unified processing of multiple constraints is achieved. An improved whale optimization algorithm is employed to iteratively optimize the comprehensive evaluation function within the physical boundary to obtain the optimal control variables. Algorithm improvements enhance both global search capability and local exploitation capability, avoiding getting trapped in local optima. The optimal control variables and their corresponding steady-state performance indices are output, providing accurate optimization results for engine control.

[0018] This application addresses the instability and convergence issues in the optimization process caused by strict equality constraints in existing technologies. By introducing thrust error threshold constraints, the optimization remains feasible and robust even with model errors and numerical approximations. By incorporating multiple types of constraints into the comprehensive objective function through a penalty function, it facilitates the use of swarm intelligence methods for solving the problem. Furthermore, by improving the whale optimization algorithm, it performs combined optimization of steady-state control variables under variable boundary and safety constraints, thereby obtaining the optimal set of control variables that satisfies the objectives of different control modes. This significantly enhances the engineering practicality and reliability of steady-state performance optimization for aero-engines.

[0019] It should be understood that the above general description and the following detailed description are exemplary and explanatory only, and do not limit this application. Attached Figure Description

[0020] The accompanying drawings, which are incorporated in and form part of this specification, illustrate embodiments consistent with this application and, together with the description, serve to explain the principles of this application. It is obvious that the drawings described below are merely some embodiments of this application, and those skilled in the art can obtain other drawings based on these drawings without any inventive effort. In the drawings:

[0021] Figure 1 A flowchart illustrating an air-engine steady-state performance optimization method according to an exemplary embodiment of this application is shown schematically. Figure 2 The illustration schematically depicts a steady-state optimization principle for the minimum fuel consumption mode according to an exemplary embodiment of this application. Figure 3 The illustration schematically shows a maximum thrust mode steady-state optimization principle according to an exemplary embodiment of this application; Figure 4 The illustration schematically depicts a steady-state optimization principle for the lowest turbine inlet temperature mode according to an exemplary embodiment of this application. Figure 5 An optimized simulation verification diagram of the lowest fuel consumption mode under cruising conditions according to an exemplary embodiment of this application is illustrated. Figure 6 An optimized simulation verification diagram of the maximum thrust mode in an intermediate state according to an exemplary embodiment of this application is illustrated schematically. Figure 7 An optimized simulation verification diagram of the lowest turbine inlet temperature mode under rated conditions according to an exemplary embodiment of this application is illustrated schematically. Figure 8 A flowchart illustrating the model uncertainty handling steps of an exemplary embodiment of this application is shown schematically. Figure 9 A block diagram of an aircraft engine steady-state performance optimization system according to an exemplary embodiment of this application is illustrated schematically. Figure 10 The schematic diagram illustrates a module diagram of an electronic device according to an exemplary embodiment of this application. Detailed Implementation

[0022] Exemplary embodiments will now be described more fully with reference to the accompanying drawings. However, these exemplary embodiments can be implemented in many forms and should not be construed as limited to the examples set forth herein; rather, these embodiments are provided to make this application more comprehensive and complete, and to fully convey the concept of the exemplary embodiments to those skilled in the art. The described features, structures, or characteristics can be combined in any suitable manner in one or more embodiments. In the following description, numerous specific details are provided to give a full understanding of the embodiments of this application. However, those skilled in the art will recognize that the technical solutions of this application can be practiced with one or more of the specific details omitted, or other methods, components, apparatus, steps, etc., can be employed. In other instances, well-known technical solutions are not shown or described in detail to avoid obscuring various aspects of this application.

[0023] Furthermore, the accompanying drawings are merely illustrative of this application and are not necessarily drawn to scale. The same reference numerals in the drawings denote the same or similar parts, and therefore repeated descriptions of them will be omitted. Some block diagrams shown in the drawings are functional entities and do not necessarily correspond to physically or logically independent entities. These functional entities can be implemented in software, in one or more hardware modules or integrated circuits, or in different network and / or processor devices and / or microcontroller devices.

[0024] The flowcharts shown in the accompanying drawings are merely illustrative and do not necessarily include all steps. For example, some steps may be broken down, while others may be combined or partially combined; therefore, the actual execution order may change depending on the specific circumstances. Furthermore, all the terms "first" and "second" used below are for distinction purposes only and should not be construed as limiting the scope of this application.

[0025] In the steady-state performance optimization of aero-engines, the presence of multiple adjustable components and coupled variables leads to a significant nonlinear relationship between steady-state performance indicators and control variables. Furthermore, system operation is strictly limited by safety constraints such as surge margin and temperature upper limits. Traditional analytical optimization methods or local search methods are sensitive to initial values ​​and prone to getting trapped in local optima when dealing with such problems, failing to guarantee global optimality. Moreover, the common engineering requirement of constant thrust, if expressed as a strict equality constraint, suffers significant limitations in feasibility and robustness under model errors and numerical discretization conditions.

[0026] If the above problems are not resolved, optimizing the steady-state performance of aero-engines at different flight phases will face serious challenges. During cruise, failure to effectively reduce fuel consumption will impact flight economy; during acceleration or maneuvering, failure to reach maximum thrust will limit flight performance; and under high thermal load conditions, improper turbine inlet temperature control will jeopardize engine safety. Therefore, the unreliability of optimization results may lead to frequent triggering of safety protection mechanisms in the control system, reducing flight stability, thereby affecting the full utilization of engine performance and increasing maintenance costs and safety risks.

[0027] Based on the above problems, the exemplary embodiments of this application provide a method and system for optimizing the steady-state performance of an aero-engine, aiming to achieve the global optimization of engine performance while ensuring the safe operation of the aero-engine.

[0028] Figure 1 A flowchart illustrating an exemplary embodiment of the steady-state performance optimization method for an aero-engine is shown below. (Reference) Figure 1 The method for optimizing the steady-state performance of an aero-engine may include the following steps: Step S110: Obtain the steady-state operating condition input of the aero-engine and select the steady-state optimization mode according to the engineering objectives. The steady-state optimization mode includes at least one of the minimum fuel consumption mode, maximum thrust mode and minimum turbine inlet temperature mode.

[0029] In practical applications, the steady-state performance optimization method for aero-engines aims to adjust the control variables of the aero-engine to achieve specific performance targets under stable operating conditions, such as minimum fuel consumption, maximum thrust output, or minimum turbine inlet temperature, while meeting various safety operating limits.

[0030] Steady-state operating condition inputs refer to the set of environmental and operational parameters of an aero-engine under a certain stable operating state, such as at least one of flight altitude, Mach number, atmospheric temperature, atmospheric pressure, engine speed command, total intake pressure, and total intake temperature. These input parameters define the engine's current operating environment and target state. Engineering objectives refer to the performance optimization directions set according to actual mission requirements or design requirements during aero-engine operation. Common engineering objectives include pursuing fuel efficiency, maximizing power output, or extending component life.

[0031] In an exemplary embodiment of this application, the steady-state optimization mode can be a variety of preset optimization modes provided according to different engineering objectives. These modes guide the optimization process, focusing it on specific performance indicators.

[0032] For example, modes include: Minimum fuel consumption mode, which is an optimization-oriented mode aimed at minimizing fuel consumption per unit of thrust, focusing on reducing fuel consumption; Maximum thrust mode, which is an optimization-oriented mode aimed at maximizing engine output thrust, focusing on increasing thrust output; and Minimum turbine inlet temperature mode, which is an optimization-oriented mode aimed at minimizing the gas temperature at the turbine's first-stage guide vane inlet, focusing on reducing thermal load to protect hot-end engine components.

[0033] In practical applications, various methods can be used to acquire the steady-state operating condition input of an aero-engine and select the steady-state optimization mode. For example, the steady-state operating condition input can be obtained by the operator manually inputting parameters such as the current flight altitude, Mach number, and ambient temperature; or, it can be obtained by collecting real-time operating data such as engine speed, pressure, and temperature through a sensor network connected to the engine control system. Regarding the selection of the steady-state optimization mode, the operator can directly select "minimum fuel consumption mode," "maximum thrust mode," or "lowest turbine inlet temperature mode" on the control interface according to the current mission requirements; or, the system can automatically select "minimum fuel consumption mode" during the cruise phase and "maximum thrust mode" during the takeoff phase based on preset flight phase logic.

[0034] Step S120: Determine the control variable vector and its physical boundary, and call the steady-state performance calculation model; the steady-state performance calculation model outputs steady-state performance indicators and safety boundary parameters based on the control variable vector and steady-state operating condition input.

[0035] In an exemplary embodiment of this application, the control variable vector can refer to a set of adjustable parameters that can be actively adjusted by the engine control system and directly affect steady-state performance. It may include a set of adjustable components or control quantities, such as nozzle throat area, mode selection valve area, ejector area, guide vane angles at each stage, fan / compressor speed, etc.; this vector is denoted as... Its dimensions It is determined by both the engine type and the degrees of freedom of control.

[0036] Physical boundaries refer to the allowed range of values ​​for each control variable in the control variable vector. These boundaries are typically determined by engine design limitations, mechanical strength, or safe operating requirements, ensuring that the control variables vary within a reasonable and safe range. The boundary constraints satisfied by each control variable are: ,in, This is the lower bound of the control variable vector. This is the upper limit of the control variable vector.

[0037] In practical applications, steady-state performance calculation models can be constructed based on component-level modeling, lookup table interpolation, surrogate models, or data-driven methods. In this application, the steady-state performance calculation model is primarily a nonlinear mathematical model based on the component method. This model decomposes the aero-engine into physical components (such as the inlet, fan, compressor, combustion chamber, turbine, nozzle, etc.), and each component is described using a set of nonlinear equations (such as mass conservation, energy conservation, momentum conservation, and flow and efficiency parameters based on component characteristic diagrams) according to its aerodynamic and thermodynamic characteristics. The component models are coupled and iteratively solved under common operating conditions (continuous flow, pressure balance, power balance, etc.), ultimately forming a high-fidelity nonlinear system capable of simulating the engine's steady-state performance within its full envelope. This model is an industry-standard tool for engine design, analysis, and control; its inputs are control variables u and operating condition w, and its outputs are thrust Fn, fuel consumption rate sfc, and turbine inlet temperature T. 41 Key physical quantities such as surge margins (SM) at various levels are included. The optimization method in this application is based on such an engineering model with clear physical meaning, ensuring the interpretability and engineering feasibility of the optimization results.

[0038] Steady-state performance indicators refer to the key performance parameters exhibited by an aero-engine under steady-state operation, such as engine thrust, fuel consumption rate per unit time, and turbine inlet temperature. These indicators directly reflect the engine's operating efficiency and capability. Safety boundary parameters refer to the various safety limits that an aero-engine must adhere to during operation to prevent engine damage or dangerous situations. Common safety boundary parameters include surge margin (to prevent compressor instability), upper limit of combustion chamber outlet temperature, and upper limit of rotor speed.

[0039] In this embodiment, the steady-state performance calculation model is encapsulated as a black-box calculation interface. After receiving the control variable vector u and the steady-state operating condition input, it synchronously outputs the above-mentioned performance indicators and safety boundary parameters, providing a data foundation for subsequent target construction and constraint verification. This model can be deployed in ground support systems, engine health management units, or full-authority digital electronic controllers.

[0040] Step S130: Construct the main objective function based on the steady-state optimization mode, and construct the constraints; the constraints shall include at least the thrust error threshold constraint and the safety inequality constraint.

[0041] In practical applications, the main objective function can be a scalar function to be minimized or maximized based on the selected steady-state optimization mode. During the optimization process, according to the selected steady-state optimization mode, this function quantifies the performance index that needs to be optimized (minimized or maximized).

[0042] Under the minimum fuel consumption mode, the corresponding main objective function can be expressed as follows: .

[0043] In maximum thrust mode, the corresponding primary objective function can be expressed as follows: Or equivalently represented as .

[0044] Under the lowest turbine inlet temperature mode, the corresponding main objective function can be expressed as: .

[0045] Here, constraints can refer to a series of restrictions that the control variable vector must satisfy during the optimization process. These constraints include thrust error threshold constraints (ensuring that the thrust is near the target value) and safety inequality constraints (ensuring that the engine operates within a safe range).

[0046] In practical applications, thrust error threshold constraints can refer to the constraints on the thrust calculated by the model. With target thrust The allowable range of deviation between them is set; this constraint adopts both absolute error and relative error forms, which are used to ensure the consistency of accuracy under low thrust conditions and high thrust conditions respectively.

[0047] Specifically, its absolute error can be expressed as follows: Its relative error can be expressed as follows: ,in, and This is a preset threshold.

[0048] In an exemplary embodiment of this application, the thrust error threshold constraint is constructed as a constraint condition that allows the thrust to fluctuate within a preset error range, replacing the strict thrust equality constraint. This allows for small errors within an acceptable range, improving the feasibility of the constraint. This represents a key reasoning leap from theoretical algorithms to engineering applications. Its fundamental value lies in acknowledging and properly handling the unavoidable model errors and numerical uncertainties in engineering optimization. This transformation first ensures the solvability of the optimization problem, opening a feasible search path for the algorithm in a biased model space, avoiding solution failures caused by demanding absolute precision. Furthermore, it transforms constraint violations into guideable gradient information, enabling the penalty function to smoothly pull the search back to the feasible region, significantly improving the algorithm's convergence efficiency. More importantly, the preset error threshold provides a design margin for model uncertainty, making the optimization results inherently robust; simultaneously, this limited fluctuation space allows the algorithm to intelligently balance performance and constraints, thereby discovering engineering optimal solutions that are more economical than rigidly satisfying the equality. Therefore, this design is not only a mathematical relaxation, but also a core mechanism that guides the entire optimization process to operate reliably, efficiently, and intelligently in a real engineering environment.

[0049] Specifically, the absolute error form is suitable for scenarios with fixed-order thrust deviation requirements, such as maintaining a consistent tolerance for the absolute value of thrust deviation under low or high thrust conditions. Another approach is to set a fixed thrust deviation range to ensure that the optimized thrust output always falls within this range. The relative error form is more suitable for scenarios with percentage thrust deviation requirements, such as allowing a larger allowable thrust deviation at different thrust levels, thus maintaining the relative accuracy of the optimization results over a wide range of operating conditions. For example, a maximum allowable percentage thrust deviation can be set, or an error band proportional to the target thrust can be defined.

[0050] Safety inequality constraints can refer to one-sided allowable ranges set for various safety boundary parameters, including at least surge margin constraints and / or upper temperature limits, such as SM(u)≥SM min This indicates that the surge margin is not lower than the minimum permissible value, T 41 (u)≤T 41,max This indicates that the turbine inlet temperature does not exceed the material's tolerance limit.

[0051] In this application, the constraints do not introduce additional decision variables and are all expressed in the form of explicit or implicit functions of the control variable u; the thrust error threshold constraint replaces the traditional equality constraint, giving the algorithm the ability to obtain feasible solutions even when model prediction bias exists; and the safety inequality constraint ensures that all candidate solutions are within the engine's physical safety envelope.

[0052] Step S140: Construct a comprehensive evaluation function that includes an objective term and a penalty function term, wherein the objective term is determined based on the main objective function, and the penalty function term is used to penalize candidate solutions that violate constraints.

[0053] In an exemplary embodiment of this application, the objective term is the part of the comprehensive evaluation function directly related to the main objective function, reflecting the core performance indicators that the optimization algorithm needs to minimize or maximize. The penalty function term is the part of the comprehensive evaluation function used to penalize candidate solutions that violate constraints. When a candidate solution does not meet the preset constraints, the penalty function term will generate a large positive value, thereby reducing the fitness of the candidate solution and guiding the optimization algorithm to avoid infeasible regions.

[0054] Therefore, when constructing a comprehensive evaluation function that includes an objective term and a penalty function term, it can be implemented as follows: the objective term can directly adopt the main objective function constructed above. The penalty function term can be designed such that when any constraint condition is violated, such as when the thrust error exceeds a threshold or the surge margin falls below the safety lower limit, the penalty function term will immediately generate a large fixed penalty value and add it to the objective term, thereby significantly increasing the comprehensive evaluation function value of the candidate solution that violates the constraint.

[0055] In practical applications, the comprehensive evaluation function can be expressed as: (1) in, The first term is the objective term, and the sum of the last two terms is the penalty function term. For sufficiently large positive numbers, It can be used to express safety boundaries such as surge margin, upper temperature limit, and upper pressure limit; when expressed using "thrust error threshold", it can be... Selected as and order correspond or .

[0056] For dual-objective scenarios involving "target + thrust error," the objective term can be constructed using either variable weighting or fixed weighting methods. (2) in, and As a weight, in the lowest fuel consumption mode In the lowest turbo inlet temperature mode The thrust deviation term can be defined as: (3) Alternatively, it can be defined as: (4) The comprehensive evaluation function constructed above ensures that the penalty term is 0 when the constraint meets the threshold requirement; when the constraint exceeds the threshold, the penalty term increases with the degree of exceeding the limit, thereby guiding the optimization process back to the vicinity of the feasible region.

[0057] Step S150: Using the improved whale optimization algorithm, the comprehensive evaluation function is iteratively optimized within the physical boundary to obtain the optimal control variable.

[0058] In practical applications, the improved whale optimization algorithm is a swarm intelligence-based optimization algorithm that simulates the predatory behavior of whales to perform a global search. By introducing specific improvement strategies, this algorithm aims to be an adaptive and enhanced metaheuristic search method based on the standard whale optimization algorithm and tailored to the characteristics of the steady-state optimization problem of aero-engines. This aims to improve optimization efficiency, convergence speed, and reduce the risk of getting trapped in local optima.

[0059] In this application, the improved whale optimization algorithm includes at least one of the following improvement strategies: updating the convergence factor of the algorithm using a nonlinear strategy; introducing an adaptive weight coefficient that changes with the number of iterations during the position update process; performing random difference mutation operation on individuals in the population and using a greedy selection to retain better individuals; and using a quasi-backward learning strategy to generate the initial population.

[0060] The nonlinear strategy employed to update the convergence factor aims to dynamically adjust the algorithm's global search (exploration) and local search (exploitation) capabilities. Traditional linearly decreasing convergence factors may not adequately adapt to the needs of different optimization stages. Nonlinear strategies, such as exponential decay or sigmoid decay, allow the convergence factor to change slowly in the early stages of optimization to enhance global exploration capabilities and prevent premature convergence; while in the later stages, the change accelerates to enhance local exploitation capabilities and improve convergence accuracy. For example, the convergence factor can be calculated using an exponential or logarithmic function based on the ratio of the current iteration count to the maximum iteration count, thus achieving nonlinear variation.

[0061] Introducing an adaptive weight coefficient that varies with the number of iterations during the position update process aims to further refine the balance between exploration and development in the algorithm. This weight coefficient influences whether an individual updates its position more based on its current position or the position of the current best individual. For example, in the early stages of optimization, a larger weight coefficient can be assigned to encourage the individual to explore a wider range; while in the later stages of optimization, the weight coefficient can be gradually decreased, making the individual more inclined to perform a finer search near the current best solution. This adaptive weight coefficient can be designed to decrease linearly with the number of iterations, or it can be adjusted using a nonlinear function (such as a concave or convex function).

[0062] Performing random difference mutation on individuals in the population and employing a greedy selection strategy to retain better individuals enhances the algorithm's ability to escape local optima and maintains population diversity. Random difference mutation generates new candidate solutions by utilizing the differences between individuals in the population, thus introducing new search directions and preventing the algorithm from getting trapped in local optima. For example, three different individuals can be randomly selected from the current population, and mutated individuals can be generated through a weighted combination of difference vectors. Subsequently, a greedy selection strategy is adopted, meaning that only individuals with better fitness values ​​than the original individuals are retained in the next generation of the population, thereby ensuring the continuous improvement of the overall quality of the population.

[0063] A quasi-backward learning strategy is employed to generate the initial population, aiming to improve its quality and diversity and provide a better starting point for subsequent optimization processes. Traditional random initialization methods may result in uneven distribution or low quality of the initial population, affecting the algorithm's convergence speed and final optimization accuracy. The quasi-backward learning strategy considers the "backward" or "quasi-backward" position corresponding to each randomly generated individual and selects the better individuals to construct the initial population, thus making the initial population more widely distributed in the search space and closer to the global optimum. For example, for each randomly generated individual, its quasi-backward solution can be calculated based on its position in the search space, and then the two can be compared to select the individual with the better fitness value to join the initial population.

[0064] This application's scheme organically integrates nonlinear strategy-based convergence factor updates, adaptive weight coefficients, random difference mutation operations with greedy selection, and a quasi-backward learning strategy into the whale optimization algorithm. This allows the algorithm to better balance global exploration and local exploitation during the optimization process. The nonlinear convergence factor and adaptive weight coefficients work synergistically to dynamically adjust the algorithm's search range and accuracy, ensuring efficient search capabilities at different optimization stages. The random difference mutation operation and greedy selection mechanism effectively increase population diversity, helping the algorithm escape local optima and avoid premature convergence. The quasi-backward learning strategy lays a high-quality initial foundation for the entire optimization process, giving the algorithm stronger optimization potential from the outset. These improved strategies work together to enhance the robustness and optimization efficiency of the whale optimization algorithm, enabling it to find the optimal control variables for the steady-state performance of aero-engines more accurately and quickly.

[0065] In one exemplary embodiment of this application, taking the improved whale optimization algorithm to minimize F(u) as an example, in the initialization phase, the population size N and the maximum number of iterations are first set. And randomly generate an initial solution set within the boundary. ,in, It corresponds to the control variable vector u.

[0066] Next, fitness assessment is performed, and the F(u) value corresponding to each individual is calculated as fitness.

[0067] Finally, an iterative update is performed. The standard whale-optimized encirclement and search update can be described as follows: (5) in, This represents the current iteration number. , Indicates the best location for searching proxies. Represents a position vector. b yes Random numbers in the data, These are random coefficients that control the spiral motion, and their values ​​range from [ 1,1].

[0068] In addition, the whale optimization algorithm also applies a random search agent to perform a global search to explore the optimal position, so as to avoid getting trapped in local optima, as shown in the following equation: (6) in, For random search locations; In other words, a It is the convergence factor. aDuring the update process, the value will decrease from 2 to 0, where r is a random number in the interval [0,1], and t... max This represents the maximum iteration time.

[0069] In the shrinking encirclement model, the algorithm gradually attempts to update the prey position towards the globally optimal position: (7) The population mechanism of the algorithm and the population update mechanism can be summarized as follows: (8) Where p is a random probability factor, representing the probability value of determining the update policy, and .

[0070] The basic whale optimization algorithm still suffers from drawbacks such as low solution accuracy, slow convergence speed, and susceptibility to local optima. Therefore, this application improves the whale optimization algorithm from three aspects: population initialization, position update strategy, and prevention of local optima.

[0071] Improved nonlinear convergence factor: Due to the convergence factor a Linear changes are insufficient for effectively adjusting global search and local exploitation capabilities. Therefore, the linear decay function will be replaced with a non-linear function to regulate the early-stage global search and later-stage local exploitation capabilities. One of the following forms can be adopted: (9) in, The parameter is related to the expression, where t is the current iteration number. It is the maximum convergence factor.

[0072] Next, an adaptive weighting strategy is introduced: when an individual engages in encirclement predation or spiral updates, a weighting coefficient is introduced. Adjust the update step size: (10) in, Representing the Individual whales, For the first The original position vector of each individual in generation t. Let be the globally optimal position vector of the t-th generation population. For the first The new position vector of each individual after the update in generation t. It can adapt to changes during iteration to maintain population diversity or enhance convergence.

[0073] Introducing a random difference mutation strategy: To reduce the probability of getting trapped in local optima, difference mutation is performed on individuals. (11) in, These are randomly selected and distinct indices from the population. Let be the position vectors of three randomly selected, distinct individuals from the population. For the first The variation vector generated by differential mutation of each individual Let be the variable factor. (12) This aims to achieve the selection of the "better option before and after mutation." Among these, For the first The final position vector of each individual in the (t+1)th generation, where Z is a placeholder for the candidate solution set. The objective function is denoted as .

[0074] In this embodiment of the application, during the iterative process of the improved whale algorithm, when the updated individual exceeds the boundary... At this time, boundary repair processing is performed to truncate or map the out-of-bounds components back to the boundary range. Specifically, the following formula is used: (13) in, Representing the One decision variable, Representing the Individual, the first The position value of each dimension in the (t+1)th generation. Representing the The lower bound (minimum value) of each decision variable. Representing the The upper bound (maximum value) of each decision variable.

[0075] Specifically, boundary repair processing can refer to the technical operation of correcting the legitimacy of candidate solutions that go beyond the preset physical feasible domain during the optimization process; this operation can be a local constraint satisfaction mechanism that is executed independently for a single component and does not depend on the state of other dimensions.

[0076] In this embodiment of the application, the operation is used to ensure that all candidate control variables are always within the actual adjustable engineering physical range of the aero-engine, so as to avoid failure of steady-state performance calculation model call, abnormal output or generation of unrealizable control commands due to numerical out-of-bounds errors.

[0077] For any dimension If the first Individual, the first Position values ​​in each dimension Then set the component as the lower bound value. ;like Then set the component as the upper bound value. The physical boundary can refer to the set of control variable value ranges determined by the structural characteristics of the aero-engine, actuator stroke limits, sensor ranges, and safe operation specifications, such as the adjustable range of compressor guide vane angle, the mechanical limit of fuel metering valve opening, and the rated upper and lower limits of fan speed. The physical boundary can be a static range that is pre-calibrated and stored in the system configuration parameters, or it can be a real-time boundary that changes dynamically with the operating conditions.

[0078] Finally, the outbound components are truncated or mapped back to the boundary range.

[0079] This application, for example, can obtain the legal control variable components using a truncation method: directly replacing out-of-bounds values ​​with the corresponding boundary extreme values, i.e. This application can also obtain legal control variable components using methods such as mirror mapping: when season ;when season Furthermore, this application can also use random resampling to obtain valid control variable components: within the interval A new random number is generated within the component using a uniform distribution as the new value for that component.

[0080] This application obtains candidate solutions that conform to the physical boundaries based on any of the above methods, thereby maintaining all individuals in the population within a legal input space that can be effectively analyzed and responded to by the steady-state performance calculation model.

[0081] This application ensures that all candidate control variables are strictly within the preset physical boundaries by performing boundary repair processing immediately after each position update, combined with any feasible method such as truncation, mirror mapping, or random resampling. On this basis, the iterative optimization of the comprehensive evaluation function within the physical boundaries as defined in this application is substantially realized. This avoids problems such as abnormal model calculations, misjudgment of safety boundaries, or infeasibility of optimal solutions caused by out-of-bounds inputs, and significantly improves the robustness and engineering usability of the optimization process.

[0082] Step S160: Output the optimal control variables and their corresponding steady-state performance indices.

[0083] The optimal control variable can be the vector of control variables obtained through the above iterations that makes the comprehensive evaluation function achieve its optimal value. This vector can be directly sent to the engine actuators to drive the engine into a new steady-state operating point. Specifically, it can satisfy... When using the fitness convergence criterion, the optimal control variables and their corresponding steady-state performance indices are obtained.

[0084] The corresponding steady-state performance index can refer to the following: Thrust obtained after inputting the steady-state performance calculation model Fuel consumption rate Turbine inlet temperature The output results, etc., constitute a verifiable basis for the optimization effect.

[0085] This application maps engineering objectives to switchable steady-state optimization modes, relaxes rigid thrust equality constraints into error threshold constraints, transforms multiple safety boundaries into quantifiable inequality constraints, and models them as a single-objective optimization problem using a penalty function mechanism. Based on this, an improved whale optimization algorithm with boundary adaptability and convergence enhancement characteristics is employed to achieve efficient global optimization within the physical boundaries of the control variables. The final optimal control variables not only satisfy performance optimization but also maintain strong robustness and engineering feasibility under model uncertainty and system disturbances, effectively solving the optimization failure problem caused by model mismatch, strong nonlinearity, and multiple safety coupling in existing technologies.

[0086] The following example will provide a more detailed explanation of the above technical solution: Suppose an aero-engine, during cruise operations, needs to achieve minimum fuel consumption while maintaining thrust near a target value to sustain flight speed. At different flight phases and operating points, the aero-engine needs to meet different performance objectives. For example, it needs to pursue minimum fuel consumption during cruise, maximum thrust during acceleration or maneuvering, and minimum turbine inlet temperature under rated or high thermal load conditions to meet hot-end margin requirements. However, existing technologies face the following challenges in solving these problems: nonlinear and multi-constraint coupling issues, limitations of traditional optimization methods, and difficulties in engineering implementation of strict equality constraints become apparent. There are complex nonlinear relationships between engine fuel consumption and multiple performance indicators such as thrust, turbine inlet temperature, surge margin, and control variables such as nozzle throat area and guide vane angle. Traditional optimization methods struggle to find the control combination that minimizes fuel consumption while ensuring constant thrust.

[0087] The method in this application embodiment will solve this problem according to the following process: First, the system acquires the steady-state operating conditions of the aircraft engine, such as the current flight altitude of 10,000 meters, Mach number of 0.8, and ambient temperature of -50 degrees Celsius. Based on the engineering objectives of the cruise mission, the system selects the minimum fuel consumption mode as the steady-state optimization mode.

[0088] Next, the system determines the control variable vector, including parameters such as the nozzle throat area, fan guide vane angle, and compressor guide vane angle. The physical boundaries of these control variables are set; for example, the nozzle throat area is between 0.5 square meters and 1.0 square meters, and the guide vane angles are between 0 degrees and 30 degrees. Subsequently, the system invokes the aero-engine steady-state performance calculation model. This model receives the current operating condition input and the control variable vector, calculates and outputs steady-state performance indicators and safety boundary parameters such as engine thrust, fuel consumption rate, turbine inlet temperature, and surge margin.

[0089] Then, based on the minimum fuel consumption model, the main objective function is constructed to minimize the engine's fuel consumption rate. Simultaneously, constraints are established. For thrust requirements, a thrust error threshold constraint is set, requiring that the absolute error between the actual thrust and the target thrust (e.g., 50 kN) does not exceed ±2 kN. Furthermore, safety inequality constraints are set, such as requiring a surge margin greater than 15% and a turbine inlet temperature below 1800 Kelvin.

[0090] Based on this, a comprehensive evaluation function is constructed. The objective term of this function is the aforementioned fuel consumption rate. Simultaneously, penalty function terms are constructed to address thrust error threshold constraints, surge margin constraints, and turbine inlet temperature constraints. When any constraint is violated—for example, if the error between the actual thrust and the target thrust exceeds 2 kN, or the surge margin is less than 15%—the penalty function term will generate a large penalty value, which is added to the fuel consumption rate, thus significantly increasing the comprehensive evaluation function value of the combination of control variables that violate the constraints.

[0091] Subsequently, an improved whale optimization algorithm is employed to iteratively optimize the comprehensive evaluation function within the physical boundaries of the control variables. The algorithm initializes a population containing multiple candidate control variable combinations. In each iteration, the algorithm simulates whale predation behavior, updating the position of each candidate solution in the population through mechanisms such as encirclement predation, spiral updates, and random search. For example, if a candidate solution results in a low surge margin after the update, its comprehensive evaluation function value will increase due to the penalty function term, thus leading to its elimination or relocation from that region in subsequent iterations. Through continuous iteration, the algorithm gradually guides the population to the region that satisfies all constraints and has the lowest fuel consumption rate.

[0092] Finally, when the algorithm converges or reaches the maximum number of iterations, it outputs the optimal combination of control variables (such as a specific nozzle throat area, fan guide vane angle, and compressor guide vane angle) and its corresponding steady-state performance indicators (such as minimum fuel consumption rate, thrust that meets the thrust error threshold, and turbine inlet temperature and surge margin that meet safety requirements).

[0093] Through the above process, this method transforms a complex nonlinear multi-constraint optimization problem into an easily solvable unconstrained optimization problem, and effectively avoids the limitation of traditional methods being prone to getting trapped in local optima through the improved whale optimization algorithm. Simultaneously, by transforming the strict thrust equality constraint into an error threshold constraint, the feasibility and robustness of the optimization results in practical engineering are significantly improved. This addresses the need for aero-engines to meet different performance objectives at different flight phases and operating points, such as pursuing minimum fuel consumption during cruise, maximum thrust during acceleration or maneuvering, and minimum turbine inlet temperature to meet hot-end margin requirements under rated or high thermal load conditions.

[0094] In practical applications, refer to Figure 2 This paper presents a schematic diagram of the steady-state optimization principle for the minimum fuel consumption mode. Figure 2 In the diagram, the horizontal axis represents the converted flow rate, the vertical axis represents the pressure ratio, the isoefficiency lines are circular, and the dashed lines represent the isothrust lines. Current operating point. This is the operating point before optimization; the optimal operating point b is the operating point corresponding to the minimum fuel consumption mode. The purpose of the constant thrust line is to optimize the fuel consumption rate while ensuring that the thrust change is less than a certain ε. From the current operating point... The process of reaching the optimal operating point b is the optimization process involved in this application. Specifically, in this mode, the optimization objective is to minimize the fuel consumption rate, and threshold constraints are set according to the thrust deviation, while inequality constraints (such as the lower limit of surge margin, the upper limit of temperature, etc.) are superimposed. During the iteration process, the thrust error threshold and safety constraints are introduced into the penalty function term through the comprehensive evaluation function, so that the penalty term is zero or small when the constraint is satisfied, and increases when the constraint is exceeded, thereby guiding the population to converge to the feasible region.

[0095] Reference Figure 3 This paper presents a schematic diagram of the steady-state optimization principle for the maximum thrust mode. Figure 3 In the diagram, the horizontal axis represents the converted flow rate, and the vertical axis represents the pressure ratio. This is the operating point before optimization; the optimal operating point is the operating point corresponding to the maximum thrust mode. The boundary lines are limits for engine margin, speed, temperature, etc. From the current operating point... The process of reaching the optimal operating point b is the optimization process involved in this application. Specifically, in this mode, the optimization objective is to maximize thrust, and it is subject to safety inequality constraints (such as the lower limit constraint of surge margin and the upper limit constraint of temperature). During the iteration process, if a candidate solution causes the safety constraints to exceed the limits, its penalty function term increases, which degrades its fitness and is suppressed in the population update, thereby causing the optimal solution to tend to the feasible region near the safety boundary.

[0096] Reference Figure 4 This paper presents a schematic diagram of the steady-state optimization principle for the lowest turbine inlet temperature mode. Figure 4In the diagram, the horizontal axis represents the converted flow rate, the vertical axis represents the pressure ratio, and the curve represents the standard operating line. Standard operating point. This is the operating point before optimization; the optimal operating point b is the operating point corresponding to the minimum turbine inlet temperature mode. The dashed line represents the constant turbine inlet temperature line. The dashed line from point b to point b is the constant thrust line. The purpose of the constant thrust line is to optimize the turbine inlet temperature while ensuring that the thrust change is less than a certain ε. The boundary line is the engine margin limit line. From the operating point... The process of reaching operating point b is the optimization method involved in this application. Specifically, in this mode, the optimization objective is to minimize the turbine inlet temperature, while setting a threshold constraint on the thrust error to ensure that the thrust meets the target requirements. Inequality safety constraints are also superimposed, and through a penalty function, the optimization process reduces... At the same time, it is constrained within the thrust error and safety boundary threshold.

[0097] Furthermore, embodiments of this application also provide optimized simulation verification diagrams under different states, wherein, Figure 5 The simulation verification diagram shows the optimized fuel consumption mode under cruising conditions. Figure 5 In (a), the horizontal axis represents the number of iterations for optimization, and the vertical axis represents the fuel consumption rate (i.e., the optimization target, finding the minimum value). The fact that its value no longer changes with the number of iterations indicates that the iterative process is convergent. Figure 5 In (b), the horizontal axis represents the number of optimization iterations, and the vertical axis represents the thrust (i.e., optimization constraint). If the thrust change is less than the threshold, it means that the thrust change is within the constraint.

[0098] Figure 6 This is an optimized simulation verification diagram of the maximum thrust mode under intermediate conditions, where the intermediate state refers to the maximum state without afterburner. Figure 6 In (a), the horizontal axis represents the number of iterations for optimization, and the vertical axis represents the driving force (i.e., the optimization target, finding the maximum value). The fact that its value no longer changes with the number of iterations indicates that the iterative process is convergent. Figure 6 In (b), the horizontal axis represents the number of optimization iterations, and the vertical axis represents the compression component margin (i.e., optimization constraint). If the margin is less than the threshold, it means that the margin is within the constraint.

[0099] Figure 7 This is an optimized simulation verification diagram for the lowest turbine inlet temperature mode under rated conditions. The rated conditions refer to a state before optimization. Figure 7 In (a), the horizontal axis represents the number of iterations for optimization, and the vertical axis represents the turbine inlet temperature (i.e., the optimization target, the minimum value). The fact that its value no longer changes with the number of iterations indicates that the iterative process is convergent. Figure 7 In (b), the horizontal axis represents the number of optimization iterations, and the vertical axis represents the thrust (i.e., optimization constraint). If the thrust change is less than the threshold, it means that the thrust change is within the constraint.

[0100] In some embodiments described above in this application, the steady-state performance optimization method for aero-engines outputs steady-state performance indicators and safety boundary parameters through a steady-state performance calculation model, and constructs a comprehensive evaluation function based on these for optimization. However, in practical applications, the prediction of safety boundary parameters by the steady-state performance calculation model often involves certain uncertainties. These uncertainties may stem from factors such as model simplification, parameter errors, or environmental disturbances, leading to deviations between model predictions and actual engine behavior. If these factors are not considered, the optimization result may theoretically satisfy the constraints, but in actual operation, it may pose risks such as violating the true safety boundary, suboptimal performance, or decreased robustness, thereby affecting the reliability and safety of aero-engine operation.

[0101] Therefore, in the scenario of real-time adaptive optimization across the entire flight envelope, how to enable the optimization algorithm to generate a control strategy with high robustness and safety for the real engine even when there are uncertainties in the model is a key problem that this application needs to further solve.

[0102] Figure 8 A flowchart illustrating the model uncertainty handling steps of an exemplary embodiment of this application is shown schematically. (Reference) Figure 8 The uncertainty handling steps for this model may include the following: Step S810: Quantify the uncertainty of the steady-state performance calculation model in predicting the safety boundary parameters, and obtain the uncertainty value corresponding to the current working condition.

[0103] The model uncertainty handling step aims to improve the robustness and safety of the optimization results, ensuring that the obtained optimal control variables can still enable the safe and stable operation of the aero-engine even when there are biases in the model predictions.

[0104] Safety boundary parameters can refer to key physical quantities used to determine the safe operating status of an engine, such as surge margin, turbine inlet temperature, compressor outlet pressure, and combustion chamber outlet temperature. Prediction uncertainty can be a quantitative indicator characterizing the reliability of the model's prediction results for a certain safety boundary parameter. For example, it can be the standard deviation of the predicted value of the parameter, the half-width of the 95% confidence interval, the root mean square error of the prediction residual, or the variance term based on the output of Gaussian process regression. Prediction uncertainty reflects the fluctuation range or confidence level of the steady-state performance calculation model's output of the safety boundary parameter under the current steady-state operating condition input. It serves as the basis for subsequent dynamic tightening of the constraint boundary and directly participates in the construction of the penalty function term in the comprehensive evaluation function.

[0105] In practical applications, quantifying the uncertainty of the steady-state performance calculation model's prediction of safety boundary parameters to obtain the uncertainty value corresponding to the current operating condition refers to evaluating the potential deviation range between the model's predicted value and the actual value through some method. This can be achieved in various ways. For example, a statistical relationship of model prediction error can be established based on historical data; or the prediction uncertainty value corresponding to the safety boundary parameters can be queried or calculated based on real-time operating condition input.

[0106] Establishing a statistical relationship for model prediction errors based on historical data refers to analyzing the deviations or errors generated by the steady-state performance calculation model when predicting safety boundary parameters using accumulated aero-engine operating data, test data, or simulation data. This statistical relationship can be established in various ways. For example, regression analysis methods, such as linear regression, multinomial regression, or nonlinear regression, can be used to fit the relationship between the model prediction error and the actual value. Machine learning methods, such as support vector machines, neural networks, or Gaussian process regression, can be used to learn from a large amount of historical data and build a prediction model for the error. Alternatively, the historical error data can be fitted with a statistical distribution, for example, assuming that the error follows a normal distribution, t-distribution, or other suitable probability distribution, and estimating its mean and variance. The purpose of establishing this statistical relationship is to provide a quantitative basis and reference for subsequently evaluating the uncertainty of model predictions under real-time operating conditions.

[0107] Based on real-time operating condition input, querying or calculating the predicted uncertainty value corresponding to the safety boundary parameter can refer to determining the possible error range or degree of uncertainty of the predicted safety boundary parameter under the current operating condition when the current real-time operating condition input (e.g., flight altitude, Mach number, ambient temperature, throttle position, etc.) is obtained during the actual operation of the aero-engine. This is done using the statistical relationship of the previously established model prediction error. Specific implementation methods may include: if the statistical relationship is established in the form of a lookup table, the corresponding uncertainty value can be obtained directly by querying the table based on the real-time operating condition input; if the statistical relationship is established in the form of a mathematical model or machine learning model, the real-time operating condition input is used as the model input, and the mean, variance, standard deviation, or confidence interval of the predicted safety boundary parameter under the current operating condition is obtained through calculation or inference. These statistics can then be used as the predicted uncertainty value. The purpose of this step is to apply general statistical relationships to specific real-time scenarios, thereby obtaining an accurate uncertainty assessment for the current operating condition.

[0108] This exemplary implementation first utilizes a large amount of historical data to systematically analyze and establish the error statistics of the steady-state performance calculation model when predicting safety boundary parameters. This provides a solid foundation for understanding and quantifying the model's uncertainty. Subsequently, during the actual operation of the aero-engine, when real-time operating condition input is received, the method can accurately query or calculate the predicted uncertainty value corresponding to the safety boundary parameter under the current operating condition based on the established statistical relationships. This two-stage processing method ensures the accuracy and real-time nature of uncertainty quantification. The predicted uncertainty value obtained in this way can provide a reliable basis for the subsequent dynamic tightening of the safety inequality constraints, allowing the safety margin to be adjusted according to the actual uncertainty of the model prediction, rather than using a fixed conservative value. This not only improves the safety of the optimization process and avoids safety risks caused by model prediction deviations, but also avoids performance losses caused by excessive conservatism, thereby maximizing the performance potential of the aero-engine while ensuring safety.

[0109] The uncertainty of the steady-state performance calculation model in predicting the safety boundary parameters can be obtained by using machine learning methods, such as Gaussian process regression or neural networks, to learn the relationship between the model prediction error and the operating parameters, and then predict the uncertainty value under the current operating conditions.

[0110] Step S830: Based on the uncertainty value, dynamically tighten the boundary of the safety inequality constraint to generate an adaptive safety constraint boundary. In the process of constructing the comprehensive evaluation function, the penalty function term is constructed based on the thrust error threshold constraint and the adaptive safety constraint boundary.

[0111] In the exemplary embodiments of this application, the original safety constraints can be adjusted based on the quantified degree of uncertainty to reserve a certain safety margin. This tightening is "dynamic," meaning that the degree of tightening varies according to the magnitude of the uncertainty under the current operating conditions, rather than remaining fixed. For example, for lower limit constraints, the original lower limit value is increased by an offset positively correlated with the uncertainty value; while for upper limit constraints, the original upper limit value is decreased by an offset positively correlated with the uncertainty value. In this way, even if the model prediction has some error, the actual operating parameters can fall within the tightened safety boundary with a high probability, thereby avoiding reaching the true physical limits.

[0112] It should be noted that lower bound constraints can refer to minimum allowable value restrictions imposed on safety boundary parameters, such as surge margin. Calculate the rotational speed The original lower boundary limit can be the theoretical minimum threshold of the safety parameters output by the steady-state performance calculation model under calibration conditions, and its value is determined by engine design specifications or airworthiness certification requirements. Uncertainty values ​​can refer to the predicted deviation range of the safety boundary parameters under the current operating conditions, estimated based on the statistical distribution of historical prediction errors, such as standard deviation, confidence interval half-width, or quantile deviation. Positive correlation offsets can be correction quantities obtained by mapping the uncertainty values ​​through a monotonically increasing function, such as a linear proportional term. Or segmented threshold term max ,in , , Preset non-negative coefficients; The role of this offset in this application is to adjust the original lower limit upward, making the constraint conditions more stringent, so that when there is uncertainty in the model prediction, the actual surge margin can still be guaranteed to be no lower than the lower limit after conservative reinforcement, and avoid insufficient safety margin due to optimistic prediction.

[0113] Similarly, upper bound constraints can refer to the maximum allowable value limit imposed on safety boundary parameters, such as turbine inlet temperature. Exhaust temperature The original boundary upper limit value can be the design limit value determined by the allowable temperature of the engine hot-end component material, or the operating upper limit specified in the airworthiness clause; the positive correlation offset is defined in the aforementioned lower limit constraint, that is, its value increases monotonically with the increase of the uncertainty value, and does not introduce sign reversal.

[0114] The purpose of this offset in this application is to adjust the original upper limit downward, making the constraints more stringent, thereby triggering the temperature limit protection in advance when there is a risk of positive deviation in the model's prediction of high-temperature parameters, and preventing the actual temperature from exceeding the physical safety boundary.

[0115] When constructing the comprehensive evaluation function, the penalty function term is built based on the thrust error threshold constraint and the adaptive safety constraint boundary. This means that during the optimization process, any candidate solution that violates these constraints will be penalized. The role of the penalty function term is to transform the constraints into part of the objective function, ensuring that the optimization algorithm, when searching for the optimal solution, not only minimizes the main objective function but also avoids or minimizes violations of the constraints. By incorporating the adaptive safety constraint boundary into the construction of the penalty function term, it ensures that the optimization algorithm, during iterative optimization, prioritizes finding solutions that meet stricter safety requirements, thereby improving the reliability of the optimization results.

[0116] In practical applications, the specific process of handling model uncertainties can be achieved through the following technical means: Model Uncertainty Quantification and Real-Time Evaluation Module: Based on the existing engine steady-state performance calculation model, a model uncertainty quantification and real-time evaluation module is added. This module does not change the core performance calculation logic, but focuses on evaluating the potential deviations between the model prediction results (especially key safety constraints such as surge margin and turbine inlet temperature) and the actual engine state.

[0117] The process can be as follows: In the offline phase, statistical analysis is performed on the prediction errors of the engine model under different operating conditions using a large amount of historical flight data, bench test data, and Monte Carlo simulation methods to establish the probability distribution or uncertainty interval of the model error (e.g., by calculating the root mean square error, standard deviation, or maximum deviation between the predicted and actual values). This uncertainty data can be stored as a lookup table or queried in real time using a simple regression model.

[0118] During the online phase, in the real-time adaptive optimization process, this module queries or calculates the model prediction uncertainties of key safety constraints under the current engine operating conditions (such as altitude, Mach number, and thrust requirements) in real time. For example, it can obtain an estimated error standard deviation σ_SM(u) and σ_T. 41 (u).

[0119] Next, an adaptive safety margin adjustment mechanism is introduced: before constructing the comprehensive evaluation function, an adaptive safety margin adjuster is introduced.

[0120] Its working process can be that the traditional safety constraint is a fixed value, such as SM(u)≥SM. min and T 41 (u)≤T 41,max To address model uncertainty, the adaptive safety margin adjuster dynamically adjusts the effective boundaries of these safety constraints based on the real-time uncertainty values ​​provided by the model uncertainty quantification and real-time evaluation module.

[0121] For "greater than or equal to" type constraints (such as surge margin): the new effective constraint becomes SM(u)≥SM min +kSM σ_SM(u). Here, kSM is a preset safety factor (e.g., 2 or 3, corresponding to a 2-sigma or 3-sigma confidence level), and σ_SM(u) is the standard deviation of the uncertainty in the model's predicted surge margin. This means that the greater the uncertainty in the model's prediction of the surge margin, the higher the lower limit of the surge margin that the optimization algorithm needs to satisfy, thus reserving a larger safety margin for the real engine.

[0122] For "less than or equal to" type constraints (such as turbine inlet temperature): the new effective constraint becomes T. 41 (u) ≤T41,max -k_T 41 σ_T 41 (u). Wherein, k_T 41 It is the safety factor, σ_T 41 (u) is the standard deviation of the uncertainty in the model's prediction of the turbine inlet temperature. The greater the uncertainty in the model's prediction of the turbine inlet temperature, the lower the upper limit of the turbine inlet temperature that the optimization algorithm needs to meet, in order to prevent the actual temperature from exceeding the limit.

[0123] Finally, the enhanced comprehensive evaluation function and the improved whale algorithm optimization are determined: the basis for constructing the comprehensive evaluation function containing penalty function terms and using the improved whale algorithm for iterative optimization is to dynamically adjust its input parameters (constraint boundaries).

[0124] Specifically, the improved whale algorithm will use these adaptively adjusted safety constraint boundaries to calculate the penalty function term during iterative optimization. For example, the comprehensive evaluation function will become:

[0125] in, Represents the original objective function. , Represents the penalty factor. This represents the surge margin corresponding to the current solution u. The lower limit of the design margin represents the surge margin. An adaptive safety margin representing surge margin. The safety factor represents the surge margin. This represents the turbine inlet temperature corresponding to the current solution u. This represents the design upper limit of the turbine inlet temperature. An adaptive safety margin representing the turbine inlet temperature. The safety factor represents the turbine inlet temperature.

[0126] The improved whale algorithm will continue its iterative process, searching for the control variable u that minimizes this enhanced F(u). .

[0127] The exemplary embodiments of this application provide a method for optimizing the steady-state performance of aero-engines. During the optimization process, the primary objective function and the thrust deviation term are weighted and fused to form a comprehensive objective function. This allows the optimization process to simultaneously consider both the core performance optimization of the engine and the accuracy of thrust output. This solves the problem of insufficient thrust accuracy that may occur when optimizing with only a single primary objective function. In the optimization process, the algorithm no longer passively satisfies thrust constraints but actively considers thrust accuracy as part of the optimization objective, thereby achieving a better balance between core performance and thrust accuracy. The resulting control variables not only enable the engine to achieve excellent core performance indicators under specific operating conditions but also ensure that the thrust output is very close to the target value, significantly improving the practicality and reliability of the optimization results. This allows the engine to respond to commands more accurately during mission execution, improving the adaptability and safety of flight missions.

[0128] It should be noted that although the steps of the method in this application are described in a specific order in the accompanying drawings, this does not require or imply that the steps must be performed in that specific order, or that all the steps shown must be performed to achieve the desired result. Additional or alternative steps may be omitted, multiple steps may be combined into one step, and / or one step may be broken down into multiple steps.

[0129] Furthermore, this example embodiment also provides a system for optimizing the steady-state performance of an aero-engine.

[0130] Figure 9 A block diagram illustrating an exemplary embodiment of an aero-engine steady-state performance optimization system of this application is shown. (Reference) Figure 9 The aero-engine steady-state performance optimization system 900 according to an exemplary embodiment of this application may include: a working condition and mode selection module 910, a steady-state performance calculation module 920, an objective and constraint construction module 930, a comprehensive evaluation function construction module 940, an optimization solution module 950, and an output module 960.

[0131] Specifically, the operating condition and mode selection module 910 can be used to acquire the steady-state operating condition input of the aero-engine and select a steady-state optimization mode according to the engineering objectives. The steady-state optimization mode includes at least one of the minimum fuel consumption mode, maximum thrust mode, and minimum turbine inlet temperature mode. The steady-state performance calculation module 920 can be used to determine the control variable vector and its physical boundaries, and call the steady-state performance calculation model. The steady-state performance calculation model outputs steady-state performance indicators and safety boundary parameters based on the control variable vector and the steady-state operating condition input. The objective and constraint construction module 930 can be used to construct the main objective and constraint based on the steady-state optimization mode. The objective function is determined, and constraints are constructed. The constraints include at least thrust error threshold constraints and safety inequality constraints. The comprehensive evaluation function construction module 940 can be used to construct a comprehensive evaluation function containing an objective term and a penalty function term. The objective term is determined based on the main objective function, and the penalty function term is used to penalize candidate solutions that violate the constraints. The optimization solution module 950 can be used to iteratively optimize the comprehensive evaluation function within the physical boundary using an improved whale optimization algorithm to obtain the optimal control variable. The output module 960 can be used to output the optimal control variable and its corresponding steady-state performance index.

[0132] Since the functional modules of the aero-engine steady-state performance optimization system in this application are the same as those in the above-described method implementation, they will not be repeated here.

[0133] From the above description of the embodiments, those skilled in the art will readily understand that the exemplary embodiments described herein can be implemented by software or by combining software with necessary hardware. Therefore, the technical solutions according to the embodiments of this application can be embodied in the form of a software product, which can be stored in a non-volatile storage medium (such as a CD-ROM, USB flash drive, external hard drive, etc.) or on a network, including several instructions to cause a computing device (such as a personal computer, server, terminal device, or network device, etc.) to execute the methods according to the embodiments of this application.

[0134] Furthermore, the above figures are merely illustrative of the processes included in the method according to exemplary embodiments of this application, and are not intended to be limiting. It is readily understood that the processes shown in the above figures do not indicate or limit the temporal order of these processes. Additionally, it is readily understood that these processes may be executed synchronously or asynchronously, for example, in multiple modules.

[0135] It should be noted that although several modules or units for the device used to perform actions have been mentioned in the detailed description above, this division is not mandatory. In fact, according to the embodiments of this application, the features and functions of two or more modules or units described above can be embodied in one module or unit. Conversely, the features and functions of one module or unit described above can be further divided and embodied by multiple modules or units.

[0136] In an exemplary embodiment of this application, an electronic device capable of implementing the above-described method is also provided.

[0137] Those skilled in the art will understand that various aspects of the present invention can be implemented as systems, methods, or program products. Therefore, various aspects of the present invention can be specifically implemented in the following forms: entirely in hardware, entirely in software (including firmware, microcode, etc.), or in a combination of hardware and software, collectively referred to herein as “circuit,” “module,” or “system.”

[0138] The following reference Figure 10 To describe an electronic device 1000 according to this embodiment of the present invention. Figure 10 The electronic device 1000 shown is merely an example and should not impose any limitations on the functionality and scope of use of the embodiments of the present invention.

[0139] like Figure 10 As shown, the electronic device 1000 is manifested in the form of a general-purpose computing device. The components of the electronic device 1000 may include, but are not limited to: at least one processing unit 1010, at least one storage unit 1020, a bus 1030 connecting different system components (including storage unit 1020 and processing unit 1010), and a display unit 1040.

[0140] The storage unit 1020 stores program code that can be executed by the processing unit 1010, causing the processing unit 1010 to perform the steps described in the "Exemplary Methods" section of this specification according to various exemplary embodiments of the present invention. For example, the processing unit 1010 can perform the method steps shown in the figure.

[0141] Storage unit 1020 may include readable media in the form of volatile storage units, such as random access memory (RAM) 10201 and / or cache memory 10202, and may further include read-only memory (ROM) 10203.

[0142] Storage unit 1020 may also include a program / utility 10204 having a set (at least one) program module 10205, such program module 10205 including but not limited to: operating system, one or more application programs, other program modules and program data, each or some combination of these examples may include an implementation of a network environment.

[0143] Bus 1030 can represent one or more of several types of bus structures, including a memory cell bus or memory cell controller, a peripheral bus, a graphics acceleration port, a processing unit, or a local bus using any of the multiple bus structures.

[0144] Electronic device 1000 can also communicate with one or more external devices 1070 (e.g., keyboard, pointing device, Bluetooth device, etc.), one or more devices that enable a user to interact with electronic device 1000, and / or any device that enables electronic device 1000 to communicate with one or more other computing devices (e.g., router, modem, etc.). This communication can be performed via input / output (I / O) interface 1050. Furthermore, electronic device 1000 can also communicate with one or more networks (e.g., local area network (LAN), wide area network (WAN), and / or public networks, such as the Internet) via network adapter 1060. As shown, network adapter 1060 communicates with other modules of electronic device 1000 via bus 1030. It should be understood that, although not shown in the figures, other hardware and / or software modules can be used in conjunction with electronic device 1000, including but not limited to: microcode, device drivers, redundant processing units, external disk drive arrays, RAID systems, tape drives, and data backup storage systems.

[0145] Through the above description of the embodiments, those skilled in the art will readily understand that the exemplary embodiments described herein can be implemented by software or by combining software with necessary hardware. Therefore, the technical solutions according to the embodiments of this application can be embodied in the form of a software product, which can be stored in a non-volatile storage medium (such as a CD-ROM, USB flash drive, external hard drive, etc.) or on a network, including several instructions to cause a computing device (such as a personal computer, server, terminal device, or network device, etc.) to execute the methods according to the embodiments of this application.

[0146] In exemplary embodiments of this application, a computer-readable storage medium is also provided, on which a program product capable of implementing the methods described above is stored. In some possible embodiments, various aspects of the present invention can also be implemented as a program product comprising program code that, when the program product is run on a terminal device, causes the terminal device to perform the steps of the various exemplary embodiments of the present invention described in the "Exemplary Methods" section above.

[0147] The program product for implementing the above-described method according to embodiments of the present invention can employ a portable compact disc read-only memory (CD-ROM) and include program code, and can run on a terminal device, such as a personal computer. However, the program product of the present invention is not limited thereto. In this document, the readable storage medium can be any tangible medium containing or storing a program that can be used by or in conjunction with an instruction execution system, apparatus, or device.

[0148] The program product may employ any combination of one or more readable media. A readable medium may be a readable signal medium or a readable storage medium. A readable storage medium may be, for example, but not limited to, an electrical, magnetic, optical, electromagnetic, infrared, or semiconductor system, apparatus, or device, or any combination thereof. More specific examples of readable storage media (a non-exhaustive list) include: an electrical connection having one or more wires, a portable disk, a hard disk, random access memory (RAM), read-only memory (ROM), erasable programmable read-only memory (EPROM or flash memory), optical fiber, portable compact disk read-only memory (CD-ROM), optical storage devices, magnetic storage devices, or any suitable combination thereof.

[0149] Computer-readable signal media may include data signals propagated in baseband or as part of a carrier wave, carrying readable program code. Such propagated data signals may take various forms, including but not limited to electromagnetic signals, optical signals, or any suitable combination thereof. A readable signal medium may also be any readable medium other than a readable storage medium, capable of sending, propagating, or transmitting programs for use by or in conjunction with an instruction execution system, apparatus, or device.

[0150] The program code contained on the readable medium may be transmitted using any suitable medium, including but not limited to wireless, wired, optical fiber, RF, etc., or any suitable combination thereof.

[0151] Program code for performing the operations of this invention can be written in any combination of one or more programming languages, including object-oriented programming languages ​​such as Java and C++, and conventional procedural programming languages ​​such as C or similar languages. The program code can execute entirely on the user's computing device, partially on the user's device, as a standalone software package, partially on the user's computing device and partially on a remote computing device, or entirely on a remote computing device or server. In cases involving remote computing devices, the remote computing device can be connected to the user's computing device via any type of network, including a local area network (LAN) or a wide area network (WAN), or it can be connected to an external computing device (e.g., via the Internet using an Internet service provider).

[0152] Furthermore, the above figures are merely illustrative of the processes included in the method according to exemplary embodiments of the present invention, and are not intended to be limiting. It is readily understood that the processes shown in the above figures do not indicate or limit the temporal order of these processes. Additionally, it is readily understood that these processes may be executed synchronously or asynchronously, for example, in multiple modules.

[0153] Other embodiments of this application will readily conceive of by those skilled in the art upon consideration of the specification and practice of the disclosure herein. This application is intended to cover any variations, uses, or adaptations of this application that follow the general principles of this application and include common knowledge or customary techniques in the art not disclosed herein. The specification and embodiments are to be considered exemplary only, and the true scope and spirit of this application are indicated by the claims.

[0154] It should be understood that this application is not limited to the precise structure described above and shown in the accompanying drawings, and various modifications and changes can be made without departing from its scope. The scope of this application is limited only by the appended claims.

Claims

1. A method for optimizing the steady-state performance of an aero-engine, characterized in that, Includes the following steps: The steady-state operating condition input of the aero-engine is obtained, and a steady-state optimization mode is selected according to the engineering objectives. The steady-state optimization mode includes at least one of the following: minimum fuel consumption mode, maximum thrust mode, and minimum turbine inlet temperature mode. The control variable vector and its physical boundaries are determined, and the steady-state performance calculation model is invoked; the steady-state performance calculation model outputs steady-state performance indicators and safety boundary parameters based on the control variable vector and the steady-state operating condition input. The main objective function is constructed based on the steady-state optimization mode, and constraints are constructed; the constraints include at least thrust error threshold constraints and safety inequality constraints. Construct a comprehensive evaluation function that includes an objective term and a penalty function term, wherein the objective term is determined based on the main objective function, and the penalty function term is used to impose penalties on candidate solutions that violate constraints; An improved whale optimization algorithm is used to iteratively optimize the comprehensive evaluation function within the physical boundary to obtain the optimal control variables; Output the optimal control variable and its corresponding steady-state performance index.

2. The method according to claim 1, characterized in that, The thrust error threshold constraint is in absolute error form. or relative error form ;in, The thrust calculated for the model, Given the target thrust under a given working condition, and This is a preset threshold.

3. The method according to claim 1 or 2, characterized in that, The improved whale optimization algorithm includes at least one of the following improvement strategies: The convergence factor of the algorithm is updated using a nonlinear strategy; An adaptive weight coefficient that varies with the number of iterations is introduced during the position update process; Perform random difference mutation on the individuals in the population, and use a greedy selection to retain the better individuals; A quasi-reverse learning strategy is used to generate the initial population.

4. The method according to claim 1, characterized in that, During the iterative improvement of the whale algorithm, when the updated individual exceeds the boundary... At that time, boundary repair processing is performed to truncate or map the outbound components back to the boundary range. This is the lower bound of the control variable vector. This is the upper limit of the control variable vector.

5. The method according to claim 1, characterized in that, The method also includes a model uncertainty handling step: The uncertainty of the steady-state performance calculation model in predicting the safety boundary parameters is quantified to obtain the uncertainty value corresponding to the current operating condition; Based on the aforementioned uncertainty value, the boundary of the safety inequality constraint is dynamically tightened to generate an adaptive safety constraint boundary. Specifically, when constructing the comprehensive evaluation function, the penalty function term is constructed based on the thrust error threshold constraint and the adaptive safety constraint boundary.

6. The method according to claim 5, characterized in that, The specific implementation of dynamically tightening the boundary of the safety inequality constraint is as follows: For lower bound constraints, the original boundary lower bound value is increased by an offset that is positively correlated with the uncertainty value; For upper limit constraints, the original boundary upper limit value is reduced by an offset that is positively correlated with the uncertainty value.

7. The method according to claim 5, characterized in that, The quantification of the uncertainty in the prediction of the safety boundary parameters by the steady-state performance calculation model includes: Establish statistical relationships between model prediction errors based on historical data; Based on the real-time operating conditions input, the predicted uncertainty value corresponding to the safety boundary parameter can be queried or calculated.

8. A steady-state performance optimization system for an aero-engine, characterized in that, include: The operating condition and mode selection module is used to acquire the steady-state operating condition input of the aero-engine and select the steady-state optimization mode according to the engineering objectives. The steady-state optimization mode includes at least one of the minimum fuel consumption mode, maximum thrust mode and minimum turbine inlet temperature mode. The steady-state performance calculation module is used to determine the control variable vector and its physical boundary, and to call the steady-state performance calculation model; the steady-state performance calculation model outputs steady-state performance indicators and safety boundary parameters based on the control variable vector and the steady-state operating condition input. The objective and constraint construction module is used to construct the main objective function based on the steady-state optimization mode and to construct the constraint conditions; the constraint conditions include at least the thrust error threshold constraint and the safety inequality constraint. The comprehensive evaluation function construction module is used to construct a comprehensive evaluation function that includes an objective term and a penalty function term, wherein the objective term is determined based on the main objective function, and the penalty function term is used to impose penalties on candidate solutions that violate constraints; The optimization module is used to iteratively optimize the comprehensive evaluation function within the physical boundary using an improved whale optimization algorithm to obtain the optimal control variables. The output module is used to output the optimal control variable and its corresponding steady-state performance index.

9. An electronic device, characterized in that, include: processor; A memory for storing one or more programs, which, when executed by the processor, cause the processor to implement the method as described in any one of claims 1 to 7.

10. A computer-readable storage medium having a computer program stored thereon, characterized in that, When the computer program is executed by a processor, it implements the method as described in any one of claims 1 to 7.

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