Adaptive control method for accelerating process of aero-engine based on bayesian optimization
By combining Bayesian optimization methods with the GPR model and EI learning function, the problems of large computational load and local optima in the dynamic law optimization of adaptive cyclic engines are solved, achieving efficient performance optimization under multi-dimensional control variables and ensuring the engine's optimal performance in the global scope.
Patent Information
- Authority / Receiving Office
- CN · China
- Patent Type
- Patents(China)
- Current Assignee / Owner
- NORTHWESTERN POLYTECHNICAL UNIV
- Filing Date
- 2023-12-28
- Publication Date
- 2026-06-12
Smart Images
Figure CN117742157B_ABST
Abstract
Description
Technical Field
[0001] This invention relates to the field of aero-engine control technology, and in particular to an adaptive cyclic engine acceleration process control method based on Bayesian optimization. Background Technology
[0002] An adaptive cycle engine is a wide-range, multi-peak, and multi-equilibrium-point engine system that utilizes the heat energy generated by the combustion of intake gases and fuel to increase the engine's potential and kinetic energy, thereby increasing its overall energy. During aircraft operation, the engine is required to meet the maximum thrust demand during high Mach number cruise while ensuring that it does not overheat, surge, or experience other issues throughout its flight envelope, thus maximizing safe flight.
[0003] Figure 1 The diagram shows the structure of an adaptive cycle engine. As can be seen from the diagram, the adaptive cycle engine is a complex mechanical system consisting of an intake, fan, mode selection valve, front bypass ejector, core engine-driven fan stage, compressor, combustion chamber, high and low pressure turbines, rear bypass ejector, mixing chamber, and tail nozzle. For an adaptive cycle engine, the engine fan guide vane angle, high-pressure compressor inlet guide vane angle, CDFS guide vane angle, mode selection valve area, front adjustable area bypass ejector opening, rear adjustable area bypass ejector opening, and tail nozzle throat area can all be adjusted.
[0004] Compared to traditional turbofan engines, adaptive cycle turbofan engines have a large number of optimizable parameters and constraints. Optimal performance in the dynamic process requires the combined adjustment of numerous adjustable geometric parameters. Furthermore, the engine's transient process is a nonlinear time-varying system, and the constraints are also mostly nonlinear. Therefore, for adaptive cycle engines, the acceleration law optimization problem can be summarized as a dynamic optimization problem with nonlinear constraints, aiming to maximize thrust. With multi-mission flight placing increasingly stringent stability and reliability requirements on aero-engines, more precise adjustment of optimal control variables is needed to meet the maximum operating envelope range under specific operational requirements.
[0005] Traditional methods typically employ algorithms such as SQP, genetic algorithms, and particle swarm optimization to solve engine dynamics optimization problems. These methods are all built under a defined mathematical model and cannot accurately seek the optimal performance point under uncertain conditions. Furthermore, these methods are only applicable to sample sets with a small number of control variables. When faced with multidimensional control variables, the computational load is large, the memory consumption is high, and it is impossible to accurately find the optimal performance or make approximate estimates. They also suffer from problems such as getting trapped in local optima.
[0006] Traditional methods typically employ the Sequential Quadrature Calculation (SQP) algorithm to solve engine dynamics performance optimization problems. However, SQP requires a defined function as the descent process check, making it unsuitable for black-box functions with unknown input-output relationships. Furthermore, because SQP uses gradient descent to find the optimal value, it cannot guarantee that the solution at the end of each iteration will satisfy the constraints; it can only guarantee that the optimal design point meets the constraints. In addition, when dealing with multiple control variables, SQP is computationally intensive, consumes a lot of memory, and is prone to getting trapped in local optima, resulting in inaccurate performance estimations. Summary of the Invention
[0007] To overcome the above technical problems, the present invention aims to provide an adaptive cyclic engine acceleration performance control method based on Bayesian optimization. For an adaptive cyclic engine, the input and output parameters have extremely complex functional relationships. By using a Bayesian algorithm to construct a surrogate model, the relationship between the input and output parameters is treated as a black-box function to construct the adaptive engine model, greatly simplifying the computational workload in the solution process. By establishing a learning function and utilizing its ability to seek the optimal point globally based on probability, the global optimum is iteratively solved, thereby obtaining the optimal performance point of the adaptive cyclic engine.
[0008] To achieve the above objectives, the technical solution adopted by the present invention is as follows:
[0009] The adaptive cycle engine acceleration process control method based on Bayesian optimization includes the following steps;
[0010] Step 1: Establish a mathematical model of the dynamic process of the adaptive cycle engine and build a GPR model based on this model;
[0011] Step 2: Solve for the optimal point in the current iteration using the particle swarm optimization algorithm;
[0012] Step 3: Establish the EI learning function to find the optimal prediction point at the next time step based on the current reference point;
[0013] Step 4: Based on the global function optimum obtained in Step 3, substitute it into the adaptive cyclic engine dynamic process mathematical model established in Step 1, solve for the parameters of each section during engine operation, and analyze them.
[0014] Step one specifically involves:
[0015] By selecting a specific operating point at a certain height, Mach number, and low-pressure rotor speed, and substituting it into the mathematical model of the engine dynamic process, the input and output parameters at the current operating point can be obtained.
[0016] The mathematical model of the engine dynamic process is expressed as follows:
[0017]
[0018]
[0019]
[0020]
[0021] in, For low-pressure rotor acceleration, n is the acceleration of the high-voltage rotor. L For the low-pressure rotor speed, n H N is the high-voltage rotor speed. LT For low-pressure rotor shaft work, N HT For high-pressure rotor shaft work, N F To do work for the fan, N CDFS To drive the fan stage of the core machine, η ML For low pressure shaft efficiency, η MH For high-pressure shaft efficiency, J L J is the moment of inertia of the low-voltage rotor. H W is the moment of inertia of the high-voltage rotor. in W is the inlet gas flow rate of the volumetric cavity control unit. out H is the outlet gas flow rate of the volumetric cavity control volume. in H is the total enthalpy of the imported gas. out T is the total enthalpy of the outlet gas. in T represents the total temperature of the imported gas. out P represents the total temperature of the outlet gas. in P is the total pressure of the inlet gas. out V represents the total pressure of the outlet gas and V represents the volume of the control volume.
[0022] The closed-loop control parameters are selected as independent variables. Latin hypercube sampling is used near the operating point parameters calculated in step one. The sampled control parameters are substituted into the adaptive cycle engine dynamic process mathematical model established in step one to obtain the corresponding target data. A Gaussian process-compliant GPR model is established based on the sampled input and output parameters.
[0023]
[0024] Where m(x) represents the prior distribution, and k(x, x′) represents the prior covariance function at different points x and x′.
[0025] Step two specifically involves:
[0026] Each iteration of the GPR model adds new input parameters, and the optimal point of the GPR model is continuously updated as the number of iterations increases. The particle swarm optimization algorithm is used to quickly solve for local optima, which greatly reduces the time required for optimization.
[0027]
[0028] The third step is specifically: based on the GPR model obtained in the second step, solve for the posterior mean and posterior variance of the model, as shown in equation (15).
[0029]
[0030] in, Indicates that the i-th element is κ(x) (i) The N-dimensional column vector of x is given by the squared exponential function chosen as the covariance function.
[0031] The EI learning function, constructed based on the posterior mean and posterior variance, estimates the probability that each point is an extreme point of the function. The EI learning function reflects the degree of search value for each point, and the extreme point of the function is also the next search point. The global search is performed using the EI function. When the EI function converges to a small value, the optimization process terminates, and the optimal point of the global function is obtained.
[0032] Assuming the current observation point The next most likely observation point is x + The corresponding observed value is f(x), if The improvement amount at the optimal observation point is like The improvement is then 0. To maximize the improvement, the expected improvement is defined as:
[0033]
[0034] Where μ(x) is the mean at the current iteration point, and σ(x) is the variance at the current iteration point. Let be the distribution function of the current iteration point. Let be the probability density function of the current iteration point.
[0035] By employing the particle swarm optimization algorithm, the maximum value of the aforementioned EI function can be obtained, thus revealing the current observation point.
[0036] When the value of the EI function is less than a small tolerance Δ EI The calculation of the EI function is stopped at this point, as shown in equation (17):
[0037] EI(x + )<Δ EI(17)
[0038] at this time,
[0039] The beneficial effects of the present invention.
[0040] (1) The GPR model constructed in this invention predicts the true value of the validation sample with a low error level, which is consistent with the parameter changes in the actual operation of the engine and can effectively simplify the complexity of the optimization algorithm.
[0041] (2) The expected increment at the best guess point is quantified based on the EI learning function. By using the EI function to train and update the GPR model, it can maximize the understanding of the global maximum point and obtain more accurate demand satisfaction points under different engine operating conditions. Attached image description:
[0042] Figure 1 This is a schematic diagram of an adaptive cycle engine.
[0043] Figure 2 The flowchart shows the Bayesian performance optimization algorithm. Detailed Implementation
[0044] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.
[0045] Aero-engine performance optimization control is a control method that uses a mathematical model of the airborne propulsion system to optimize the performance of the propulsion system online.
[0046] The basic principle is to find the optimal match of engine control variables while ensuring safe engine operation, and to maximize the performance potential of the engine in a certain aspect, thereby achieving the optimal performance of one or more performance indicators. Existing research on engine control law optimization is a deterministic study conducted under defined mathematical models and boundary conditions. However, in engine design, to ensure safe operation of the engine throughout the entire flight envelope, a large stability margin is usually reserved. Therefore, existing research methods under deterministic boundaries do not quantify the impact of the uncertainty of control parameters and boundary conditions on the control law. To address this, this invention proposes a Bayesian optimization-based method for optimizing engine acceleration process control laws.
[0047] The control law of engine acceleration process can be described as a dynamic optimization problem with nonlinear constraints, with the goal of maximizing thrust.
[0048] For an adaptive cycle engine, the control variables that can be selected are:
[0049] u = [W fb W fa A8, α fan α com α cdfs A msv A fvabi A rvabi ] T (18)
[0050] Among them, W fb Main combustion chamber fuel flow rate, W fa A is the fuel flow rate in the afterburner, A8 is the area of the exhaust nozzle throat, and α is the fuel flow rate in the afterburner. fan For the fan guide vane angle, α com For the compressor guide vane angle, α cdfs For CDFS guide vane angle, A msv Select the valve area for the mode, A fvabi For the opening of the adjustable area duct ejector, A rvabi The opening of the adjustable area duct ejector is then determined.
[0051] In the process of designing control laws and optimizing control systems, the above nine adjustable variables are used as optimization variables. The optimal adjustment scheme is found within the adjustable range of control variables shown in Equation (2), thereby maximizing the real-time performance of the engine.
[0052]
[0053] Where min represents the lower limit of the corresponding parameter and max represents the upper limit of the corresponding parameter.
[0054] In addition to the above nine control variable constraints, many constraints on the stable and safe operation of the engine must also be considered, such as ensuring that the high-pressure turbine inlet temperature does not exceed the limit, the high-pressure rotor does not exceed the limit, and the compressor operating curve is far from the surge boundary, in order to ensure the normal and stable operation of the engine. Therefore, the constraints should also include engine safety constraints as shown in equation (3):
[0055]
[0056] Where, n l For the low-pressure rotor speed, n h T is the high-voltage rotor speed. 41 SM represents the high-pressure turbine inlet temperature. fan For fan surge margin, SM com For compressor surge margin, SM cdfsThis provides surge margin for the core machine drive fan stage.
[0057] If the aircraft needs to optimize for maximum thrust during acceleration, then the mathematical expression for the maximum thrust control mode can be represented by equation (4):
[0058]
[0059] Where F is the engine thrust, g i (u) represents the constraints expressed by equations (12) and (13).
[0060] Using the nine control variables mentioned above as optimization inputs and maximum thrust as optimization output, the input variable x follows a Gaussian distribution, and its randomness is determined by the joint probability density function (PDF) φ. n (x) is used to represent this.
[0061] Assume that the input variable x and the objective function g(x) follow independent standard Gaussian distributions:
[0062]
[0063] Where m(x) represents the prior distribution, and κ(x, x′) represents the prior covariance function at different points x and x′.
[0064] Given a set of training data Given an N×n dimensional sample matrix, Let y be an N-dimensional column vector. (i) =g(x (i) ). Following a Gaussian distribution, therefore the vector Follows an N-dimensional Gaussian distribution, vector The mean is covariance matrix The (i, j)th element is represented as κ(x) (i) x (j) The likelihood function can be expressed as the joint probability density function of the Gaussian vector.
[0065] The GPR model is constructed using the training data as follows:
[0066]
[0067] Where, μ g (x) represents the prior mean of the GPR model, c g (x, x′) represents the prior variance of the GPR model.
[0068] The posterior mean and posterior variance are calculated as shown in equation (7):
[0069]
[0070] in, Indicates that the i-th element is κ(x) (i) The N-dimensional column vector of x is given by the squared exponential function chosen as the covariance function.
[0071] This Gaussian distribution can be based on μ g (x) and To estimate the unknown output value at any point.
[0072] The Expected Improvement (EI) learning function is used to find the maximum a posteriori estimate in the probabilistic model, thereby obtaining the iterative value with the maximum expectation. The point with the largest observed value in the previous evaluation is selected first, assuming the current observation point... The next most likely observation point is x + The corresponding observed value is f(x), if The improvement amount at the optimal observation point is like The improvement is then 0. To maximize the improvement, the expected improvement is defined as:
[0073]
[0074] Where μ(x) is the mean at the current iteration point, and σ(x) is the variance at the current iteration point. Let be the distribution function of the current iteration point. Let be the probability density function of the current iteration point.
[0075] By employing the particle swarm optimization algorithm, the maximum value of the aforementioned EI function can be obtained, thus revealing the current observation point.
[0076] The EI function quantifies f(x) at point x relative to the current best guess point x. * The expected increment at a given point is obtained by using the EI function to train and update the GPR model, thereby maximizing its ability to recognize global maxima.
[0077] When the value of the EI function is less than a small tolerance Δ EI The calculation of the EI function stops when the time is right, as shown in equation (9):
[0078] EI(x + )<Δ EI (26)
[0079] at this time,
[0080] The specific steps are shown in Table 1.
[0081] Table 1. Pseudocode of Bayesian Optimization Algorithm
[0082]
[0083]
[0084] To achieve the above objectives, the present invention provides the following technical solution:
[0085] like Figure 2 As shown, the method provided by this invention consists of four steps, and considers the engine as a whole as a model example to quantify the uncertainty of each parameter, as detailed below:
[0086] Step 1: Establish a mathematical model of the adaptive cycle engine dynamic process and build a GPR model based on this model. Select operating points at specific altitudes, Mach numbers, and low-pressure rotor speeds, substitute them into the engine dynamic process mathematical model, and solve for the input and output parameters at the current operating point. Select closed-loop control parameters as independent variables, perform Latin hypercube sampling near the operating point parameters calculated in Step 1, and substitute the sampled control parameters as inputs into the adaptive cycle engine dynamic process mathematical model established in Step 1 to obtain the corresponding target data.
[0087] Using H=0, Ma=0, CNF=95 as the operating point, twenty sets of data were extracted near the operating point using the Latin hypercube group sampling method. Table 2 shows five of these sampling data sets.
[0088] Table 2 Sampling data for Latin hypercube groups
[0089]
[0090]
[0091] For adaptive cycle engines, the acceleration law optimization problem can be summarized as a dynamic optimization problem with nonlinear constraints, aiming to maximize thrust. As multi-mission flight places increasingly stringent stability and reliability requirements on aero engines, it is necessary to more precisely adjust the optimal control variables to meet the maximum operating envelope range under specific operational needs.
[0092] The performance optimization process of an adaptive cycle engine acceleration is essentially a performance optimization process with maximum thrust as the optimization objective under the condition of ensuring engine safety. The objective function is shown in equation (10). To ensure the realization of mission segments requiring high thrust, such as takeoff and acceleration climb, the constraints of parameters such as fuel consumption rate on this process can be sacrificed. At this time, the control condition is only the fuel flow rate W. fb The area of the tail nozzle throat is A8, and the area of the rear duct ejector is A. rvabiThe constraints are shown in equation (11). A GPR model is constructed using the sampling results.
[0093] maxf(u)=F (27)
[0094]
[0095] Step 2: Solve for the optimal point in the current iteration using the particle swarm optimization algorithm. Each iteration of the GPR model introduces new input parameters, therefore the optimal point of the GPR model needs to be continuously updated with the number of iterations. The particle swarm optimization algorithm can be used to solve for local optima.
[0096] Step 3: Establish the EI learning function to find the optimal prediction point for the next time step based on the current reference point. When the EI function converges to a small value, the optimization process terminates, and the global function's optimal point is obtained.
[0097] Step 4: Based on the global function optimum obtained in Step 3, substitute it into the adaptive cyclic engine dynamic process mathematical model established in Step 1, solve for the parameters of each section during engine operation, as shown in Table 3, and analyze them.
[0098] Table 3 Optimization Results
[0099] FN SMF SMC DFS SMC CNF CNC DFS CNC WFB A8 95710.85 0.4262 0.1477 0.2255 0.9733 0.9994 0.9997 0.2345 0.1278
[0100] Table 3 presents the verification of adaptive cyclic engine performance optimization based on Bayesian optimization algorithm at operating points H=0, Ma=0, CNF=95, with closed-loop control parameters u=[W fb A8, A rvabi As a control variable, the maximum thrust is optimized. As shown in Table 3, the low-pressure rotor speed n... l High-voltage rotor speed n h Fan surge margin SM fan Compressor surge margin SM com Core machine drive fan stage surge margin SM cdfs The algorithm satisfies the safety constraints shown in equation (3) and ensures that the thrust value is maximized in the global range, which proves the effectiveness of the algorithm.
Claims
1. An adaptive cyclic engine acceleration process control method based on Bayesian optimization, characterized in that, Includes the following steps; Step 1: Establish a mathematical model of the dynamic process of the adaptive cycle engine and build a GPR model based on this model; Step 2: Solve for the optimal point in the current iteration using the particle swarm optimization algorithm; Step 3: Establish the EI learning function to find the optimal prediction point at the next time step based on the current reference point; Step 4: Based on the global function optimum obtained in Step 3, substitute it into the adaptive cyclic engine dynamic process mathematical model established in Step 1, solve for the parameters of each section during engine operation, and analyze them. Step two specifically involves: Each iteration of the GPR model adds new input parameters, and the optimal point of the GPR model is continuously updated as the number of iterations increases. The particle swarm optimization algorithm is used to quickly solve for local optima. （6） Assuming the current observation point The next most likely observation point is The corresponding observed value is ,like The improvement amount at the optimal observation point is ,like If the improvement is zero, then the expected improvement is defined as: （8） in, This is the mean at the current iteration point. The variance at the current iteration point. Let be the distribution function of the current iteration point. Let be the probability density function of the current iteration point; The particle swarm optimization algorithm is used to find the maximum value of the EI function mentioned above, and the current observation point is obtained. ; When the value of the EI function is less than a small tolerance The calculation of the EI function is stopped at this point, as shown in equation (9): （9） at this time, .
2. The adaptive cyclic engine acceleration process control method based on Bayesian optimization according to claim 1, characterized in that, Step one specifically involves: By selecting a specific operating point at a certain altitude, Mach number, and low-pressure rotor speed, and substituting it into the mathematical model of the engine dynamic process, the input and output parameters at the current operating point are obtained. The mathematical model of the engine dynamic process is expressed as follows: （1） （2） （3） （4） in, For low-pressure rotor acceleration, For high-pressure rotor acceleration, For low-pressure rotor speed, This refers to the high-voltage rotor speed. For low-pressure rotor shaft power, For high-pressure rotor shaft power, To do work for the fan, To drive the fan stage of the core machine, For low pressure shaft efficiency, For high-pressure shaft efficiency, For the rotational inertia of the low-pressure rotor, The moment of inertia of the high-voltage rotor. The inlet gas flow rate of the volumetric cavity control unit. The outlet gas flow rate of the volumetric cavity control unit. This is the total enthalpy of the imported gas. The total enthalpy of the exported gas. The total temperature of the imported gas. The total temperature of the outlet gas. This refers to the total pressure of the imported gas. The total pressure of the outlet gas. To control the volume; The closed-loop control parameters are selected as independent variables. Latin hypercube sampling is used near the operating point parameters calculated in step one. The sampled control parameters are then substituted into the adaptive cycle engine dynamic process mathematical model established in step one to obtain the corresponding target data. Based on the sampled input and output parameters, a Gaussian process-compliant GPR model is established. （5） in, Describe the prior distribution, Indicates different points and The prior covariance function.
3. The adaptive cyclic engine acceleration process control method based on Bayesian optimization according to claim 1, characterized in that, The third step specifically involves: calculating the posterior mean and posterior variance of the model based on the GPR model obtained in the second step, as shown in equation (7): （7） in, Indicates the first The elements are of For a column vector, the squared exponential function is chosen as the covariance function. ; The EI learning function, constructed based on the posterior mean and posterior variance, estimates the probability that each point is an extreme point of the function. The EI function is used for global search. When the EI function converges to a small value, the optimization process terminates, and the optimal point of the global function is obtained.