Engine model solving method adopting Newton-Raphson and feedforward neural network methods

Abstract

The invention belongs to the technical field of aero-engine modeling, and particularly relates to an engine model solving method adopting Newton-Raphson and feedforward neural network methods. According to the method, a mixed algorithm of a feed-forward neural network agent model and a Newton-Raphson method is combined, and a rough value of an iteration independent variable is directly predicted by adopting a feed-forward neural network, so that meaningless and local extremal regions on an iteration path can be avoided to a great extent, and high-quality iteration variables are quickly provided for the Newton-Raphson method; the convergence capability of the Newton method is greatly improved, the iteration step number is reduced, and the calculation speed of the Newton method is improved. And a normalized training set processing mode is adopted, so that the training set scale and the network scale are greatly reduced, the network estimation precision is improved, and the application complexity of the hybrid solving method is reduced. According to the hybrid solving method, the simulation solving convergence of the violent dynamic process of the dynamic real-time model of the engine is remarkably improved, and compared with a gradient method, the calculation speed is increased.

Description

Technical Field

[0001] This invention belongs to the field of aero-engine modeling technology, specifically relating to a method for solving engine models using Newton-Raphson and feedforward neural network methods. Background Technology

[0002] The hardware-in-the-loop simulation experiment of the engine system relies on a high-precision, high-speed engine dynamic real-time model. Compared with the nonlinear component-level model, the dynamic real-time model has several optimization items, such as simplifying thermodynamic functions and changing the forward difference of the dynamic process to backward difference. The real-time performance of the model is ensured by simplifying the nonlinear component-level model and using fast solution methods. Given the limited optimization space of the model, developing a dynamic real-time model solution method with high real-time performance and stability is of great significance for hardware-in-the-loop simulation experiments.

[0003] Currently, numerical solutions for the equilibrium equations of dynamic real-time models of aero-engines are similar to those for nonlinear component-level models, mainly falling into three categories. The first category is traditional gradient methods, including the Newton-Raphson algorithm, the Broyden quasi-Newton algorithm, and the N+1 point residual method. The second category is intelligent search methods, including genetic algorithms, differential evolution and its improved algorithms, and the tunicate swarm algorithm. The third category is hybrid algorithms, including the Newton-Raphson-particle swarm optimization hybrid algorithm, the Newton-Raphson-differential evolution hybrid algorithm, and the Broyden quasi-Newton-Levenberg-Marquardt hybrid algorithm. Each of these three types of algorithms has its own advantages and disadvantages when solving models. Traditional gradient methods have a relatively fast convergence speed, meeting the requirement of less than 10ms for single-step simulation in dynamic real-time hardware-in-the-loop modeling, and can provide accurate solutions. However, they lack global convergence capability and are prone to getting stuck in meaningless regions or local minima during iteration. Getting stuck in meaningless regions during dynamic calculations leads to divergence, making subsequent operating point calculations impossible. Intelligent search methods possess global convergence capabilities, but due to the large population size leading to excessive component adjustments, their computational efficiency and real-time performance are relatively low. Hybrid methods combine the high speed and accuracy of gradient descent with the global convergence of search algorithms, exhibiting better convergence in drastically dynamic processes and significantly improving computational efficiency compared to single search algorithms. However, existing hybrid algorithms still fail to meet the requirement of a single-step computation time within 10ms for dynamic real-time model simulation in computer simulation environments. The stability of single-step computation time is poor, with some operating points exceeding 10ms in computation time, and some hybrid algorithms are quite complex to apply.

[0004] Therefore, this invention provides a method for solving the mathematical model of an aero-engine using the Newton-Raphson method and the feedforward neural network method, which can meet the computational requirements of high precision, strong convergence, high speed and stable computation time in the dynamic real-time model simulation process of the engine. Summary of the Invention

[0005] The purpose of this invention is to overcome the shortcomings of existing technologies and provide a method for solving engine models using Newton-Raphson and feedforward neural network methods. This method combines a feedforward neural network surrogate model with a hybrid algorithm of Newton-Raphson method. The feedforward neural network surrogate model can locate the iterative independent variable to a small neighborhood of the convergent solution in one step, replacing the multi-step iterative steps in the early stage of Newton-Raphson method. This greatly avoids local extrema and meaningless regions, and provides good convergence conditions for the subsequent Newton-Raphson method, meeting the speed requirements of engine dynamic real-time model solvers.

[0006] To achieve the above objectives, the technical solution adopted by this invention is a method for solving engine models using Newton-Raphson and feedforward neural network methods, characterized by including: Step 1: Obtain the steady-state operating point and the dynamic operating point, and construct the steady-state training set and the dynamic training set; Using a dynamic real-time model of a variable cycle engine, and employing model solving methods such as adaptive differential evolution, which have good convergence but poor real-time performance, rules for selecting steady-state and dynamic operating points are established to obtain various performance parameters of the variable cycle engine at steady-state and dynamic operating points in batches. Rules for constructing steady-state and dynamic training sets are also established, with the relevant parameters of the obtained steady-state operating points forming the steady-state training set and the relevant parameters of the dynamic operating points forming the dynamic training set. Step 2: Design the steady-state operating point and dynamic operating point solutions for the feedforward neural network structure respectively; The networks required for calculating the steady-state operating point and dynamic operating point of the engine dynamic real-time model are designed separately, and the number of input layer parameters, the number of hidden layer nodes, the number of output layer parameters, and the node activation functions are set separately for the steady-state network and the dynamic network. Step 3: Establish a training method for the steady-state and dynamic operating point solving network. Train the steady-state and dynamic networks. After training, the program saves the complete steady-state and dynamic network parameters to a data file for subsequent use when solving the steady-state and dynamic operating points. The parameters include the node weights and biases of the hidden layer and the output layer. Step 4: Construct the steady-state operating point and dynamic operating point solution functions of the feedforward neural network for the dynamic real-time model of the variable cycle engine; Based on the feedforward neural network structure set in step two, a polynomial representing the iterative independent variable and the input speed and fuel supply is constructed, where the input speed and fuel supply are the function input variables and the iterative independent variable is the function output variable. The node weights and bias parameters stored in step three are added to the polynomial, and finally the steady-state operating point and dynamic operating point solution functions are obtained. Step 5: Establish a hybrid solver of Newton-Raphson-feedforward neural network; The hybrid solver comprises three stages. The first stage directly solves the problem using the Newton-Raphson method. If convergence is achieved, the subsequent two stages are skipped, the calculation ends, and convergence parameters are output. If convergence fails, the second stage proceeds to obtain the upper and lower bounds of the iterative independent variables. Based on the operating point input parameters, a feedforward neural network is used to estimate the iterative independent variables. The third stage uses the iterative independent variables estimated in the second stage as input to the Newton-Raphson method for recalculation. If convergence is achieved, the calculation outputs the result. If convergence fails, a coarse solution predicted by the feedforward neural network is output, along with a non-convergence warning message. Step 6: Establish the engine's steady-state operating point and dynamic operating point to solve the problem; A variable cycle engine is selected, and design point calculations are performed to obtain the parameters of each design point of the engine and the initial values ​​of the iterative independent variables. Based on the steady-state and dynamic operating point solutions, the input control parameters, the initial values ​​of the iterative independent variables, and the pressure, power, and flow balance between components, a corresponding common working equation set is established, and the residuals are calculated. The problem of solving the engine's steady-state and dynamic operating points is transformed into a problem of solving nonlinear equation sets. Step 7: Use the Newton-Raphson-feedforward neural network hybrid solver to solve for steady-state and dynamic operating points; first, execute the Newton-Raphson method to solve for the operating point, and determine whether the solution converges. If it converges, the calculation is completed and the calculation result is output. If it does not converge, proceed to the next step. Step 8: Initialize the upper and lower bounds of the iterative independent variables, determine whether it is a steady-state or dynamic operating point solution, select the corresponding feedforward neural network solution function, and estimate the iterative variables based on the engine input parameters; Step 9: The predicted iterative independent variables are used as inputs to the Newton-Raphson method, and the operating point calculation is completed again through iteration. If convergence is achieved, the convergence result is output. If convergence is not achieved, the iterative independent variables predicted by the feedforward neural network are substituted into the operating point solution process to calculate various performance parameters. The predicted solution of the feedforward neural network solution function is output. This solution has not been tested by residual iteration and is not an exact solution, but only an approximate coarse solution. A non-convergence prompt message is output. This completes the hybrid solution of the Newton-Raphson-feedforward neural network method for the engine model.

[0007] Furthermore, the steady-state operating point selection rule in step one is as follows: set a series of high-pressure shaft percentage physical speeds at an altitude of 0 km and a Mach number of 0, with a speed range of 75%~100% and a step size of 0.1%; the dynamic operating point selection rule in step one is as follows: at an altitude of 0 km and a Mach number of 0, discretize the three parameters of high-pressure shaft physical percentage speed, low-pressure shaft physical percentage speed, and oil supply, and set the ranges of 70%~100%, 30%~100%, and 0.2~2 kg / s respectively, with step sizes of 2%, 3%, and 0.2 kg / s respectively; The steady-state training set construction rule is as follows: each training sample in the steady-state training set contains the corresponding relative high-pressure shaft physical speed and iterative independent variables. The iterative independent variables include the ratio of the front fan pressure ratio, the ratio of the rear fan pressure ratio, the ratio of the compressor pressure ratio, the relative physical speed of the high pressure, the converted temperature at the combustion chamber outlet, the ratio of the high-pressure turbine pressure ratio, and the ratio of the low-pressure turbine pressure ratio. The dynamic training set construction rule is as follows: each training sample in the dynamic training set includes the corresponding relative high-pressure shaft physical speed, relative low-pressure physical speed, fuel supply, and iterative independent variables. The iterative independent variables include the ratio of the front fan pressure ratio, the ratio of the rear fan pressure ratio, the ratio of the compressor pressure ratio, the ratio of the high-pressure turbine pressure ratio, and the ratio of the low-pressure turbine pressure ratio.

[0008] Furthermore, the steady-state network in step two has a three-layer structure. The first input layer contains one input parameter: the engine low-pressure relative conversion speed. The second hidden layer has one layer with nine nodes. The third output layer contains seven output parameters: the front fan pressure ratio, the rear fan pressure ratio, the compressor pressure ratio, the high-pressure relative physical speed, the combustion chamber outlet conversion temperature, the high-pressure turbine pressure ratio, and the low-pressure turbine pressure ratio. The pressure ratio refers to the ratio of the operating point pressure ratio to the design point pressure ratio, which is in the range of [0,1]. The activation function of the hidden layer is selected as the hyperbolic tangent function. The dynamic network has a three-layer structure. The first input layer contains three input parameters: high-pressure relative converted speed, low-pressure relative physical speed, and converted fuel flow rate. The second hidden layer contains nine nodes. The third output layer contains five output parameters: front fan pressure ratio, rear fan pressure ratio, compressor pressure ratio, high-pressure turbine pressure ratio, and low-pressure turbine pressure ratio. The activation function for the hidden layer is also the hyperbolic tangent function.

[0009] Furthermore, the network training method for solving the steady-state operating point and dynamic operating point in step three is as follows: (1) Select the high and low pressure speed and oil supply for each input parameter of the steady-state and dynamic solution network, and the range of the iterative independent variable of the output parameter. Normalize each parameter using the maximum-minimum normalization method and save it for later use. (2) Based on the designed stable dynamic network structure and the stable dynamic training set, the stable dynamic network is trained respectively; The first step in training is to initialize the network by assigning a uniform random distribution to the weight matrix and bias vector in the interval [0,1]. Then, forward propagation is performed to calculate the predicted output under the current network parameters. The mean square error function is used to measure the error between the network output and the training samples. Then, backpropagation is performed to calculate the gradient of the weights and biases layer by layer, derive the partial derivatives of each parameter with respect to the output error, and then update the weights and biases. Backpropagation is performed using the chain rule. During the parameter update phase, the system employs a momentum term optimization strategy to alleviate the oscillation problem during training. (3) After the training of each output parameter subnetwork of the stable dynamic network is completed, the weight and bias values ​​of the network are saved for use by the solution function.

[0010] Furthermore, the common working equation set in step six refers to the physical constraints such as flow continuity, power balance, and pressure balance that the various sections and components of the engine satisfy at the steady-state operating point and the dynamic operating point. In science, it is represented as a combination of several equations, with the values ​​on both sides of each equation being equal. The problem described above is transformed into a nonlinear equation system problem by moving all the variables of the equation to one side of the equation, and the other side being the residual calculated by both sides. This transforms the linear equation system of iterative independent variable vector and physical quantity balance into a linear equation system of iterative independent variable vector and residual vector.

[0011] Furthermore, the Newton-Raphson iteration method in step seven specifically includes: (1) The difference operator replaces the differential operator to construct the Jacobian coefficient matrix; (2) The independent variable is the change of the iteration parameter, and the Gaussian elimination method is used to solve the linear equation system; (3) Obtain the change of the iteration variable, add it to the old iteration variable to update the iteration variable, evaluate the residual again, until the residual meets the convergence threshold or the calculation stops when the maximum number of steps is reached.

[0012] The beneficial effects of this invention are as follows: This invention provides a method for solving engine models using a Newton-Raphson and feedforward neural network approach. The feedforward neural network directly predicts the coarse values ​​of the iterative independent variables, which greatly avoids meaningless and local extrema regions on the iteration path, providing high-quality iterative variables for the Newton-Raphson method, significantly improving the convergence ability of the Newton method, and reducing the number of iterations, thus increasing the computational speed of the Newton method. The use of a normalized training set significantly reduces the size of the training set and the network, improving network estimation accuracy and reducing the application complexity of this hybrid solution method. During application, similarity conversion is used to handle the high-altitude operating point, improving the convergence ability of this hybrid solution method at the high-altitude operating point. This hybrid solution method significantly improves the convergence of the simulation of the engine's dynamic real-time model during intense dynamic processes and increases the computational speed compared to the gradient method. Simulations of the intense dynamic process of a variable-cycle engine during anti-surge and fuel-cutting verify the high convergence ability and fast solution capability of this hybrid method. Attached Figure Description

[0013] Figure 1 This is a flowchart of the present invention; Figure 2This is a steady-state network structure diagram of the time-varying cycle engine of the present invention; Figure 3 This is a dynamic network structure diagram of the time-varying cycle engine implemented in this invention; Figure 4 This defines the steady-state test area and selected operating point for implementation of the present invention. Figure 5 The results are simulations of the steady-state operating point using the Newton-Raphson method during the implementation of this invention. Figure 6 This refers to the fuel supply to the main combustion chamber during the dynamic anti-surge fuel cutting process in the implementation of this invention; Figure 7 The simulation results of the dynamic operating point of the Newton-Raphson method during the implementation of this invention; Figure 8 The simulation results of the steady-state operating point of the Newton-Raphson-differential evolution mixture method during the implementation of this invention; Figure 9 The simulation results of the dynamic operating point of the hybrid method of Newton-Raphson-differential evolution during the implementation of this invention; Figure 10 The simulation results of the steady-state operating point of the Newton-Raphson-feedforward neural network hybrid method during the implementation of this invention; Figure 11 The simulation results of the dynamic operating point of the Newton-Raphson-feedforward neural network hybrid method during the implementation of this invention are shown. Detailed Implementation

[0014] The principles and features of the present invention are described below with reference to the accompanying drawings. The examples given are only for explaining the present invention and are not intended to limit the scope of the present invention.

[0015] This invention provides a method such as Figure 1 The engine model solution method combining the Newton-Raphson-feedforward neural network method is shown, integrating the Newton-Raphson iteration method with a feedforward neural network. This invention utilizes the predictive power of the feedforward neural network to largely avoid meaningless and local extrema regions in the traditional Newton-Raphson iteration path, providing excellent initial values ​​for the Newton-Raphson method and significantly improving the convergence of the engine model's performance simulation during severe dynamic processes. To achieve the above objectives, this invention provides the following specific implementation method: An engine model solution method using the Newton-Raphson and feedforward neural network methods is shown, comprising the following steps: Step 1: Obtain the steady-state operating point and the dynamic operating point, and construct the steady-state training set and the dynamic training set; Using a dynamic real-time model of a variable cycle engine, and employing model solving methods such as adaptive differential evolution, which have good convergence but poor real-time performance, rules for selecting steady-state and dynamic operating points are established to obtain various performance parameters of the variable cycle engine at steady-state and dynamic operating points in batches. Rules for constructing steady-state and dynamic training sets are also established, with the relevant parameters of the obtained steady-state operating points forming the steady-state training set and the relevant parameters of the dynamic operating points forming the dynamic training set. Furthermore, the steady-state operating point selection rule in step one is as follows: set a series of high-pressure shaft percentage physical speeds at an altitude of 0 km and a Mach number of 0, with a speed range of 75%~100% and a step size of 0.1%; the dynamic operating point selection rule in step one is as follows: at an altitude of 0 km and a Mach number of 0, discretize the three parameters of high-pressure shaft physical percentage speed, low-pressure shaft physical percentage speed, and oil supply, and set the ranges of 70%~100%, 30%~100%, and 0.2~2 kg / s respectively, with step sizes of 2%, 3%, and 0.2 kg / s respectively; The steady-state training set construction rule is as follows: each training sample in the steady-state training set contains the corresponding relative high-pressure shaft physical speed and iterative independent variables. The iterative independent variables include the ratio of the front fan pressure ratio, the ratio of the rear fan pressure ratio, the ratio of the compressor pressure ratio, the relative physical speed of the high pressure, the converted temperature at the combustion chamber outlet, the ratio of the high-pressure turbine pressure ratio, and the ratio of the low-pressure turbine pressure ratio. The dynamic training set construction rule is as follows: each training sample in the dynamic training set includes the corresponding relative high-pressure shaft physical speed, relative low-pressure physical speed, fuel supply, and iterative independent variables. The iterative independent variables include the ratio of the front fan pressure ratio, the ratio of the rear fan pressure ratio, the ratio of the compressor pressure ratio, the ratio of the high-pressure turbine pressure ratio, and the ratio of the low-pressure turbine pressure ratio.

[0016] Step 2: Design the steady-state operating point and dynamic operating point solutions for the feedforward neural network structure respectively; The networks required for calculating the steady-state operating point and dynamic operating point of the engine dynamic real-time model are designed separately, and the number of input layer parameters, the number of hidden layer nodes, the number of output layer parameters, and the node activation functions are set separately for the steady-state network and the dynamic network. Furthermore, the steady-state network in step two has a three-layer structure, as shown in the figure below. Figure 2 One input parameter, low-pressure physical percentage speed (PCNF), is selected. The system includes one hidden layer with nine nodes. The output layer has seven iterative variables: front fan pressure ratio (ZFF), rear fan pressure ratio (ZRF), compressor pressure ratio (ZC), high-pressure relative physical speed (PCNC), combustion chamber outlet converted temperature (T4), high-pressure turbine pressure ratio (ZTH), and low-pressure turbine pressure ratio (ZTL). Each output parameter is output using a separate hidden layer with nine nodes, as shown below. Figure 1As shown in the dashed box, parameters after the first output parameter ZFF are omitted. The activation function used is the hyperbolic tangent sigmoid function as shown below; , The dynamic network described is a three-layer structure, as shown in the diagram. Figure 3 As shown, the input layer contains three parameters: engine state parameters High Pressure Percentage Physical Speed ​​(PCNC) and Low Pressure Percentage Physical Speed ​​(PCNF), and engine control parameters Fuel Flow Rate (…). m f The hidden layer also contains 9 nodes, and the output layer contains 5 parameters: the front fan pressure ratio (ZFF), the rear fan pressure ratio (ZRF), the compressor pressure ratio (ZC), the high-pressure turbine pressure ratio (ZTH), and the low-pressure turbine pressure ratio (ZTL). Each parameter is output using a hidden layer containing 9 nodes, as shown below. Figure 2 As shown in the dashed box, the parameters after the first output parameter ZFF are omitted. The activation function is also the Sigmoid function.

[0017] Step 3: Establish a training method for the steady-state and dynamic operating point solving network. Train the steady-state and dynamic networks. After training, the program saves the complete steady-state and dynamic network parameters to a data file for subsequent use when solving the steady-state and dynamic operating points. The parameters include the node weights and biases of the hidden layer and the output layer. Furthermore, the network training method for solving the steady-state operating point and dynamic operating point in step three is as follows: (1) Select the range of each input parameter (high and low pressure speed, oil supply) and output parameter (iteration independent variable) of the steady-state and dynamic solution network respectively, normalize each parameter by using the maximum-minimum normalization method, and save it for later use; The input and output parameters are converted to standard atmospheric conditions. The standard atmospheric conditions are as follows: , Assume the fan inlet temperature and pressure are as follows under the current flight conditions: , ,make: , The temperature similarity parameters are: , The similarity parameters for pressure are: , The similar parameters for rotational speed are: , The similar parameters for fuel supply are: , The similarity parameter for the pressure ratio is a constant 1.

[0018] After similarity processing, the ranges of each input parameter (high and low pressure relative conversion speed, conversion fuel supply) and output parameter (iterative independent variable) of the steady-state dynamic network are selected respectively. The parameters after similarity processing are normalized using the max-min normalization method and saved for later use. The normalization function is as follows: , (2) Based on the designed stable dynamic network structure and the stable dynamic training set, the stable dynamic network is trained respectively; The first step in training is to initialize the network by assigning a uniformly distributed random weight matrix and bias vector to the interval [0,1]. Then, forward propagation is performed to calculate the predicted output under the current network parameters. The calculation formulas for the hidden and output layers are shown below: , In the formula, For output of the hidden layer, For input, For input layer weights, For input layer bias, , In the formula, For the output layer results, For output layer weights, For output of the hidden layer, This is the bias for the hidden layer.

[0019] The training step limit is 1,000,000 steps, and the residual is set to 1e-7.

[0020] The mean squared error function shown below is used to measure the error between the network output and the training samples.

[0021] , Then, backpropagation is performed, calculating the gradients of the weights and biases layer by layer, deriving the partial derivatives of each parameter with respect to the output error, and then updating the weights and biases. A chain rule is used for backpropagation. During the parameter update phase, the system employs a momentum term optimization strategy to mitigate oscillations during training. Specifically, when the current error is below the threshold MThreshold, the update strategy incorporates the update direction from the previous round of parameters to enhance the network's inertia on the optimization path. The momentum term is expressed as follows: , in Let the learning rate be 1. Update the gradient for the parameters. =0.78 is the momentum factor. This is the weight increment from the previous round. The threshold for adding the momentum correction term is 1e-3.

[0022] (3) After the training of each output parameter subnetwork of the stable dynamic network is completed, the weight and bias values ​​of the network are saved for use by the solver.

[0023] Step 4: Construct the steady-state operating point and dynamic operating point solution functions of the feedforward neural network for the dynamic real-time model of the variable cycle engine; Based on the feedforward neural network structure set in step two, a polynomial representing the iterative independent variable and the input speed and fuel supply is constructed, where the input speed and fuel supply are the function input variables and the iterative independent variable is the function output variable. The node weights and bias parameters stored in step three are added to the polynomial, and finally the steady-state operating point and dynamic operating point solution functions are obtained. The steady-state solution function is as follows: Based on the set network structure, the relationship between the hidden layer and output in step three, and the stored network parameters, steady-state operating point and dynamic operating point performance prediction functions are constructed respectively. The steady-state operating point solution function is as follows: , The function for determining the dynamic operating point is as follows: ; Step 5: Establish a hybrid solver of Newton-Raphson-feedforward neural network; The hybrid solver comprises three stages. The first stage directly solves the problem using the Newton-Raphson method. If convergence is achieved, the subsequent two stages are skipped, the calculation ends, and the result is output. If convergence fails, the second stage proceeds to obtain the upper and lower bounds of the iterative independent variables. Based on the input parameters at the working point, a feedforward neural network is used to estimate the iterative independent variables. The third stage uses the iterative independent variables estimated in the second stage as input to the Newton-Raphson method. If convergence is achieved, the calculation result is output. If convergence fails, the iterative independent variables estimated by the feedforward neural network are input into the working point solution process, and the calculation result is output. This result does not meet the residual constraints but is relatively close to the converged result, representing a coarse solution. A non-convergence message is also output. Step 6: Establish the engine's steady-state operating point and dynamic operating point to solve the problem; A variable cycle engine is selected, and design point calculations are performed to obtain the parameters of each design point of the engine and the initial values ​​of the iterative independent variables. Based on the steady-state and dynamic operating point solutions, the input control parameters, the initial values ​​of the iterative independent variables, and the pressure, power, and flow balance between components, a corresponding common working equation set is established, and the residuals are calculated. The problem of solving the engine's steady-state and dynamic operating points is transformed into a problem of solving nonlinear equation sets. This invention patent employs a variable-cycle engine with first and second outer bypass ducts and a variable-area bypass duct ejector. During the solution process, after removing the control variables, there are 9 iterative independent variables. After subtracting the flow rates of the inner and outer bypass ducts to eliminate the ratios of the first outer bypass duct to the core engine bypass duct and the second outer bypass duct to the front fan inlet bypass duct, 7 iterative independent variables remain, corresponding to 7 residuals. These are the fan inner flow balance, high-pressure turbine flow balance, low-pressure turbine flow balance, hybrid static pressure balance, nozzle flow balance, low-pressure rotor power balance, and high-pressure rotor power balance.

[0024] Step 7: Use the Newton-Raphson-feedforward neural network hybrid solver to solve for steady-state and dynamic operating points; first, execute the Newton-Raphson method to solve for the operating point, and determine whether the solution converges. If it converges, the calculation is completed and the calculation result is output. If it does not converge, proceed to the next step. Furthermore, the Newton-Raphson iteration method in step seven specifically includes: (1) The difference operator replaces the differential operator to construct the Jacobian coefficient matrix; (2) The independent variable is the change of the iteration parameter, and the Gaussian elimination method is used to solve the linear equation system; (3) Obtain the change of the iteration variable, add it to the old iteration variable to update the iteration variable, evaluate the residual again, until the residual meets the convergence threshold or the calculation stops when the maximum number of steps is reached.

[0025] Step 8: Initialize the upper and lower limits of the iterative independent variables, determine whether it is a steady-state or dynamic operating point solution, convert the input parameters to a similar value of 0 km altitude, 0 Mach number, and standard temperature, then normalize according to the upper and lower limits, select the corresponding feedforward neural network solution function, and estimate the iterative variables based on the engine input parameters. Step 9: The predicted iterative independent variables are used as inputs to the Newton-Raphson method, and the operating point calculation is completed again through iteration. If convergence is achieved, the convergence result is output. If convergence is not achieved, the iterative independent variables predicted by the feedforward neural network are substituted into the operating point solution process to calculate various performance parameters. The predicted solution of the feedforward neural network solution function is output. This solution does not meet the residual constraint and is not an exact solution, but only an approximate solution. This completes the hybrid solution of the Newton-Raphson-feedforward neural network method for the engine model.

[0026] This invention provides the test results of engine model solving using the Newton-Raphson method and the feedforward neural network method, and compares them with the Newton-Raphson method and the Newton-Raphson-differential evolution method. The comparison results are as follows: 1. Steady-state dynamic calculation results using the Newton-Raphson method (1) Steady-state simulation The envelope shape is an irregular polygon. To cover as much of the envelope area as possible, 500 steady-state operating points were randomly selected within the envelope using Monte Carlo simulation. Within this region, 500 test operating points were discretized using a Gaussian distribution across three dimensions: height, Mach number, and low-pressure relative physical speed. The low-pressure relative physical speed ranged from 67% to 100%, covering most positive thrust conditions above idle. The random steady-state test points are shown below. Figure 4 The black discrete points in the central region are shown, and all subsequent steady-state test cases are constructed using this method.

[0027] Assuming no degradation in any engine health parameters, control parameters such as the front fan guide vanes, rear fan guide vanes, compressor guide vanes, low-pressure turbine guide vanes, rear bypass ejector, nozzle deflection vector angle, and nozzle deflection azimuth angle are set to a fixed variation of 0. Afterburner fuel flow, extraction power, and bleed air are also set to 0, and the pressure ratio regulator is set to a given nozzle throat area. Three solution methods are selected: the Newton-Raphson gradient method, the Newton-Raphson differential evolution hybrid method, and the Newton-Raphson feedforward neural network hybrid method.

[0028] Running the example yields the following results: Figure 5 The simulation results shown are the high-pressure relative physical speed NH, the low-pressure relative physical speed NL, the compressor outlet total pressure P3, the mixing chamber outlet total temperature T6, the convergence flag, and the operating point calculation time. Subgraph (e) shows that the gradient method has good convergence performance at the steady-state operating point. A 100% convergence rate was achieved for 500 Monte Carlo-randomly generated steady-state operating points within the full envelope. The average calculation time for the steady-state operating points marked in Figure (e) is 0.0022 s, which is consistent with the average level of the gradient method in terms of real-time performance.

[0029] (2) Dynamic simulation The real-time dynamic model solving process of the engine is the focus of this paper. To increase the testing pressure on the solving algorithm, this section sets up an anti-surge fuel cut-off process when the engine is operating at sea level. This extreme dynamic process is used to test the performance of the solving algorithm at a flight altitude of 0km and a flight Mach number of 0. It is assumed that there is no degradation of any engine health parameters. The control parameters of the front fan guide vane, rear fan guide vane, compressor guide vane, low-pressure turbine guide vane, rear bypass ejector, nozzle deflection vector angle, and nozzle deflection azimuth angle are all set to a fixed change of 0. The afterburner fuel flow, extraction power, and bleed air are also set to 0, and the pressure ratio regulator is set to a given tail nozzle throat area.

[0030] The dynamic process is as follows Figure 6As shown, the total duration is 12 seconds, with a time step of 0.025s and a total of 480 operating points. From 0 to 1 second, the fuel flow rate (mf) is consistently 0.77 kg / s. After 1 second, it increases by 0.02 kg / s every 0.025s to 2.44 kg / s, reaching 2.44 kg / s at 3.1s. The fuel supply remains at this value until 9s, at which point anti-surge fuel cut-off begins, instantly cutting off the fuel supply and reducing it to 0 kg / s for 0.125 seconds. Then, it is restored to 100% fuel supply, also for 0.125 seconds. One fuel cut-off-restoration cycle lasts 0.25 seconds, with four consecutive cycles lasting a total of 1 second. During the instantaneous cut-off and rapid restoration of fuel supply... Figure 9 The dynamic real-time model is characterized by a rapid decrease in engine speed. After four throttle jitter switches per second, surge can be effectively prevented. After 10 seconds, the fuel supply drops to 0.77 kg / s and lasts for 2 seconds. This 12-second period constitutes an anti-surge fuel cut-off simulation. This simulation includes a smooth acceleration process and an anti-surge fuel cut-off process, which puts significant pressure on the solution algorithm and allows for in-depth testing of the algorithm's capabilities. All subsequent dynamic simulations use this simulation.

[0031] Running the example yields the following results: Figure 7 The results shown also include NH, NL, P3, T6, convergence flags, and operating point time. Figure 7 As shown by the convergence criterion in (e), within the time frame of 0–9s, the acceleration process is relatively slow from 1–3.1s, and the fuel supply is constant from 3.1–9s, resulting in a mild change in engine state, allowing the gradient method to converge. In Figure (d), T6 increases significantly at 3.1s because the fuel quantity is increasing. Since the combustion delay is not considered in this model, the air-fuel ratio is high, and T6 continues to increase significantly at 3.1s. Therefore, the fuel supply... m f After stabilizing, it rose to a relatively high value before falling back. After 9 seconds... m f When the speed instantly drops to 0 kg / s, the gradient method diverges during the drastic change at point 345, making it impossible to calculate the engine state parameters and measured parameters at that point, as they are all abnormally large infinity. The iterative independent variable is also in an outlier state. The initial value of the next operating point in the dynamic process is the iterative independent variable corresponding to the convergence of the previous operating point, so it is impossible to continue calculating subsequent dynamic operating points. It can be seen that the gradient method has poor convergence in drastic dynamic processes. As shown in Figure (e), the average calculation time of the statistical gradient method for the convergence operating point is 0.00135s, which is significantly shorter than that for the steady-state operating point. This is because the time step of the dynamic process is only 0.025s. In such a short time, the engine state changes little, and fewer iterations are needed to calculate convergence.

[0032] The results show that the gradient method has a good convergence rate and fast convergence speed in steady-state processes, but it cannot converge in drastic dynamic changes such as anti-surge cutting, which leads to divergence in subsequent calculations. This indicates that the Newton-Raphson method has poor convergence in drastic dynamic processes, but a fast convergence speed.

[0033] 2. Steady-state dynamic calculation results of the Newton-Raphson-Differential Evolution method (1) Steady-state simulation First, a steady-state simulation was performed, selecting a steady-state operating point of 500 Ω using the same method. Figure 8 Figure (e) shows that the method has a 100% convergence rate. The average convergence time in Figure (f) is 0.00273s, which shows that the algorithm has sufficient convergence in steady state. The average convergence time is on the same order of magnitude as the gradient method, which greatly improves the real-time performance. However, in Figure (f), there are a few working points where the computation time is much longer than 0.00273s, which indicates that the method cannot meet the stability and real-time requirements of steady-state computation.

[0034] (2) Dynamic simulation Using the same dynamic process, obtain as Figure 9 The results of dynamic simulation are shown using the DE-GD hybrid algorithm. Figure 9 Figure (e) shows that the method has a 100% convergence rate. The average convergence time in Figure (f) is 0.00182s, which shows that the algorithm has sufficient convergence in dynamics. The average convergence time is on the same order of magnitude as the gradient method, which greatly improves the real-time performance. However, in Figure (f), there are a few working points where the calculation time is slightly longer than 0.00182s. Compared with the steady-state divergence, the 4ms calculation time still cannot stably meet the 10ms requirement of desktop real-time simulation. This shows that the method cannot meet the stable real-time requirements of dynamic calculation.

[0035] The Newton-Raphson-differential evolution method has an excellent convergence rate, achieving full convergence in both steady-state and dynamic states. While it has high convergence capability, its computation speed is also significantly improved compared to the Newton-Raphson method. However, its computation time stability is slightly poor, failing to meet the requirement of 10ms single working point for dynamic real-time simulation computation.

[0036] 3. Steady-state dynamic calculation results of the Newton-Raphson-feedforward neural network method (1) Steady-state results First, a steady-state simulation was performed, selecting a steady-state operating point of 500 Ω using the same method. Figure 10As shown in Figure (e), the method has a 100% convergence rate. The average convergence time in Figure (f) is 0.00232s, indicating sufficient convergence in steady state. Since this method terminates using the GD method, it can obtain an exact solution. While the average convergence time is on the same order of magnitude as the gradient method, significantly improving real-time performance, a small number of working points in Figure (f) have computation times much longer than 0.00232s. This reduction in time dispersion compared to the DE-GD hybrid method demonstrates that this method can meet the stable real-time requirements of steady-state computation.

[0037] (2) Dynamic results Using the same dynamic process, obtain as Figure 11 The FNN-GD hybrid algorithm shown is used to solve the dynamic simulation results. Figure 11 As shown in Figure (e), the method has a 100% convergence rate. The average convergence time in Figure (f) is 0.00122s, which is better than the 0.00135s of the Newton-Raphson method and the 0.00182s of the Newton-Raphson differential evolution hybrid method. It can be seen that the algorithm has sufficient convergence in dynamics, and the average convergence time is on the same order of magnitude as the gradient method, which greatly improves the real-time performance. However, in Figure (f), there are a few working points where the calculation time is slightly greater than 10ms. The time uncertainty is greatly reduced. This method can meet the stable real-time requirements of dynamic calculation.

[0038] The Newton-Raphson-feedforward neural network method combines the fast speed of feedforward neural networks with the exact solution capabilities of the Newton-Raphson method. It exhibits high convergence ability in both steady-state and dynamic processes while maintaining the ability to provide exact solutions. Furthermore, it boasts extremely high computational time stability, reaching the level of gradient method solutions, with computation times for most major operating points within 10ms. This significantly improves the computational time stability within a single simulation step, making it suitable as a high-speed, high-precision solver for dynamic real-time models of variable-cycle engines and other engine configurations. Comparison with the two other methods mentioned above highlights the superior convergence ability and real-time performance of this invention in drastic dynamic processes.

[0039] This invention provides a solution method combining Newton-Raphson and feedforward neural network methods. This method is a hybrid algorithm combining a feedforward neural network surrogate model and the Newton-Raphson method. The feedforward neural network surrogate model maps the input parameters and iterative independent variables of the aero-engine mathematical model. When solving for a single operating point of the dynamic real-time simulation model, the Newton-Raphson method is first run alone. If convergence is achieved, the operating point calculation is complete. If convergence fails, the hybrid Newton-Raphson-feedforward neural network solution process is entered. The input parameters are input to the feedforward neural network surrogate model, which predicts the iterative independent variables. A single prediction can locate the solution within the neighborhood of convergence. At this point, Newton-Raphson iteration is initiated until complete convergence is achieved, completing the operating point calculation. The feedforward neural network surrogate model used in this invention can locate the iterative independent variable to the vicinity of the convergent solution in one step, replacing the initial multi-step iteration of the Newton-Raphson method. This greatly avoids local extrema and meaningless regions, providing good convergence conditions for the subsequent Newton-Raphson method. The final convergence can be achieved by using the Newton-Raphson method with fewer iterations. This method has extremely strong convergence and faster computation speed than the Newton-Raphson method in drastic dynamic processes.

[0040] The above description is only a preferred embodiment of the present invention and is not intended to limit the present invention. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of the present invention should be included within the protection scope of the present invention.

Claims

1. A method for solving engine models using Newton-Raphson and feedforward neural network methods, characterized in that, Includes the following steps: Step 1: Obtain the steady-state operating point and the dynamic operating point, and construct the steady-state training set and the dynamic training set; Using a dynamic real-time model of a variable cycle engine, and employing model solving methods such as adaptive differential evolution, which have good convergence but poor real-time performance, rules for selecting steady-state and dynamic operating points are established to obtain various performance parameters of the variable cycle engine at steady-state and dynamic operating points in batches. Rules for constructing steady-state and dynamic training sets are also established, with the relevant parameters of the obtained steady-state operating points forming the steady-state training set and the relevant parameters of the dynamic operating points forming the dynamic training set. Step 2: Design the steady-state operating point and dynamic operating point solutions for the feedforward neural network structure respectively; The networks required for calculating the steady-state operating point and dynamic operating point of the engine dynamic real-time model are designed separately, and the number of input layer parameters, the number of hidden layer nodes, the number of output layer parameters, and the node activation functions are set separately for the steady-state network and the dynamic network. Step 3: Establish a training method for the steady-state and dynamic operating point solving network. Train the steady-state and dynamic networks. After training, the program saves the complete steady-state and dynamic network parameters to a data file for subsequent use when solving the steady-state and dynamic operating points. The parameters include the node weights and biases of the hidden layer and the output layer. Step 4: Construct the steady-state operating point and dynamic operating point solution functions of the feedforward neural network for the dynamic real-time model of the variable cycle engine; Based on the feedforward neural network structure set in step two, a polynomial representing the iterative independent variable and the input speed and fuel supply is constructed, where the input speed and fuel supply are the function input variables and the iterative independent variable is the function output variable. The node weights and bias parameters stored in step three are added to the polynomial, and finally the steady-state operating point and dynamic operating point solution functions are obtained. Step 5: Establish a hybrid solver of Newton-Raphson-feedforward neural network; The hybrid solver comprises three stages. The first stage directly solves the problem using the Newton-Raphson method. If convergence is achieved, the latter two stages are skipped, the calculation ends, and convergence parameters are output. If convergence fails, the second stage proceeds to obtain the upper and lower limits of the iterative independent variables. Based on the input parameters at the operating point, a feedforward neural network is used to estimate the iterative independent variables. The third stage uses the iterative independent variables estimated in the second stage as input to the Newton-Raphson method for recalculation. If convergence is achieved, the calculation outputs the result. If convergence fails, a coarse solution predicted by the feedforward neural network is output, along with a non-convergence message. Step 6: Establish the engine's steady-state operating point and dynamic operating point to solve the problem; A variable cycle engine is selected, and design point calculations are performed to obtain the parameters of each design point of the engine and the initial values ​​of the iterative independent variables. Based on the steady-state and dynamic operating point solutions, the input control parameters, the initial values ​​of the iterative independent variables, and the pressure, power, and flow balance between components, a corresponding common working equation set is established, and the residuals are calculated. The problem of solving the engine's steady-state and dynamic operating points is transformed into a problem of solving nonlinear equation sets. Step 7: Use the Newton-Raphson-feedforward neural network hybrid solver to solve for steady-state and dynamic operating points; first, execute the Newton-Raphson method to solve for the operating point, and determine whether the solution converges. If it converges, the calculation is completed and the calculation result is output. If it does not converge, proceed to the next step. Step 8: Initialize the upper and lower bounds of the iterative independent variables, determine whether it is a steady-state or dynamic operating point solution, select the corresponding feedforward neural network solution function, and estimate the iterative variables based on the engine input parameters; Step 9: The obtained iterative independent variables are used as inputs to the Newton-Raphson method, and the working point is calculated again through iteration. If convergence is achieved, the convergence result is output. If convergence is not achieved, the predicted solution of the feedforward neural network solution function is output. This solution has not been tested by residual iteration and is not an exact solution, but only an approximate coarse solution. The non-convergence prompt message is output. This completes the hybrid solution of the engine model using the Newton-Raphson-feedforward neural network method.

2. The engine model solution method using Newton-Raphson and feedforward neural network methods as described in claim 1, characterized in that: The steady-state operating point selection rule in step one is as follows: set a series of high-pressure shaft percentage physical speeds at an altitude of 0 km and a Mach number of 0, with a speed range of 75%~100% and a step size of 0.1%; the dynamic operating point selection rule in step one is as follows: at an altitude of 0 km and a Mach number of 0, discretize the three parameters of high-pressure shaft physical percentage speed, low-pressure shaft physical percentage speed, and oil supply, and set the ranges of 70%~100%, 30%~100%, and 0.2~2 kg / s respectively, with step sizes of 2%, 3%, and 0.2 kg / s respectively; The steady-state training set construction rule is as follows: each training sample in the steady-state training set contains the corresponding relative high-pressure shaft physical speed and iterative independent variables. The iterative independent variables include the ratio of the front fan pressure ratio, the ratio of the rear fan pressure ratio, the ratio of the compressor pressure ratio, the relative physical speed of the high pressure, the converted temperature at the combustion chamber outlet, the ratio of the high-pressure turbine pressure ratio, and the ratio of the low-pressure turbine pressure ratio. The dynamic training set construction rule is as follows: each training sample in the dynamic training set includes the corresponding relative high-pressure shaft physical speed, relative low-pressure physical speed, fuel supply, and iterative independent variables. The iterative independent variables include the ratio of the front fan pressure ratio, the ratio of the rear fan pressure ratio, the ratio of the compressor pressure ratio, the ratio of the high-pressure turbine pressure ratio, and the ratio of the low-pressure turbine pressure ratio.

3. The engine model solution method using Newton-Raphson and feedforward neural network methods as described in claim 1, characterized in that: The steady-state network in step two has a three-layer structure. The first input layer contains one input parameter: the engine low-pressure relative conversion speed. The second hidden layer has one layer with nine nodes. The third output layer contains seven output parameters: the front fan pressure ratio, the rear fan pressure ratio, the compressor pressure ratio, the high-pressure relative physical speed, the combustion chamber outlet conversion temperature, the high-pressure turbine pressure ratio, and the low-pressure turbine pressure ratio. The pressure ratio refers to the ratio of the operating point pressure ratio to the design point pressure ratio, which is in the range of [0,1]. The activation function of the hidden layer is selected as the hyperbolic tangent function. The dynamic network has a three-layer structure. The first input layer contains three input parameters: high-pressure relative converted speed, low-pressure relative physical speed, and converted fuel flow rate. The second hidden layer contains nine nodes. The third output layer contains five output parameters: front fan pressure ratio, rear fan pressure ratio, compressor pressure ratio, high-pressure turbine pressure ratio, and low-pressure turbine pressure ratio. The activation function for the hidden layer is also the hyperbolic tangent function.

4. The engine model solution method using Newton-Raphson and feedforward neural network methods as described in claim 1, characterized in that: The network training method for solving the steady-state operating point and dynamic operating point in step three is as follows: (1) Select the range of each input parameter (high and low pressure speed and oil supply) and output parameter (iteration independent variable) of the steady-state and dynamic solution network respectively, normalize each parameter using the maximum-minimum normalization method, and save it for later use; (2) Based on the designed stable dynamic network structure and the stable dynamic training set, the stable dynamic network is trained respectively; The first step in training is to initialize the network by assigning a uniform random distribution to the weight matrix and bias vector in the interval [0,1]. Then, forward propagation is performed to calculate the predicted output under the current network parameters. The mean square error function is used to measure the error between the network output and the training samples. Then, backpropagation is performed to calculate the gradient of the weights and biases layer by layer, derive the partial derivatives of each parameter with respect to the output error, and then update the weights and biases. Backpropagation is performed using the chain rule. During the parameter update phase, the system employs a momentum term optimization strategy to alleviate the oscillation problem during training. (3) After the training of each output parameter subnetwork of the stable dynamic network is completed, the weight and bias values ​​of the network are saved for use by the solution function.

5. The engine model solution method using Newton-Raphson and feedforward neural network methods as described in claim 1, characterized in that: The common working equation set in step six refers to the physical constraints such as flow continuity, power balance, and pressure balance that the various sections and components of the engine satisfy at the steady-state operating point and the dynamic operating point. It is represented in science as a combination of several equations, with the values ​​on both sides of each equation being equal. The problem described above is transformed into a nonlinear equation system problem by moving all the variables of the equation to one side of the equation, and the other side being the residual calculated by both sides. This transforms the linear equation system of iterative independent variable vector and physical quantity balance into a linear equation system of iterative independent variable vector and residual vector.

6. The engine model solution method using Newton-Raphson and feedforward neural network methods as described in any one of claims 1-5, characterized in that: The Newton-Raphson iteration method in step seven specifically includes: (1) The difference operator replaces the differential operator to construct the Jacobian coefficient matrix; (2) The independent variable is the change of the iteration parameter, and the Gaussian elimination method is used to solve the linear equation system; (3) Obtain the change of the iteration variable, add it to the old iteration variable to update the iteration variable, evaluate the residual again, until the residual meets the convergence threshold or the calculation stops when the maximum number of steps is reached.

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