A gas turbine modeling method and system based on a physically embedded multi-fidelity neural network

Abstract

The application discloses a gas turbine modeling method and system based on a physical embedded multi-fidelity neural network, and relates to the technical field of gas turbine performance simulation and intelligent modeling. The method comprises the following steps: a low-fidelity physical module containing a forward differentiable component interpolation submodule and a combustor mapping submodule with trainable parameters is constructed; an operating condition is received, and a common operating line is solved by using a forward differentiable iterative algorithm to output a low-fidelity prediction result and reserve a calculation graph; a multi-fidelity fusion neural network is constructed, and after the low-fidelity prediction result and input are spliced in features, a high-fidelity prediction result is mapped and output; based on the error of the prediction result and experimental data, an automatic differentiation mechanism is used to make the back propagation gradient penetrate the calculation graph, and end-to-end joint optimization is realized. The application can improve the accuracy of overall performance prediction of the system while reserving the constraints of the thermodynamic mechanism of the equipment.

Description

Technical Field

[0001] This invention relates to the field of gas turbine performance simulation and intelligent modeling technology, and in particular to a gas turbine modeling method and system based on physically embedded multifidelity neural networks. Background Technology

[0002] As complex thermodynamic equipment, gas turbines have fundamental application requirements in the dynamic performance evaluation and condition monitoring of turbine power generation systems. Establishing a model that conforms to its actual dynamic characteristics is a prerequisite for achieving reliable equipment control and health management. Current gas turbine modeling methods mainly include physical mechanism modeling based on internal flow field characteristics and one-dimensional thermodynamic cycles, as well as data-driven modeling based on operating parameters.

[0003] Physical mechanism models typically employ a thermodynamic cycle calculation framework, reflecting the physical conservation laws within the equipment and the aerodynamic and thermodynamic characteristics of its components. However, due to simplified assumptions regarding complex flow and combustion processes, these models may exhibit performance predictions under varying operating conditions or long-term degradation that deviate from actual equipment operating conditions. Pure data-driven modeling methods often utilize neural network algorithms to handle multi-dimensional state variable mapping relationships, and with the support of extensive experimental data, they can closely match the specific operating characteristics of the equipment. Conventional data-driven models are black-box structures, lacking internal thermodynamic mechanism constraints. When deviating from the training sample distribution or facing insufficiently covered operating conditions, the output results may deviate from the actual physical boundary laws.

[0004] Hybrid modeling schemes integrating physical mechanisms and data-driven networks are gradually becoming a research direction in this field. Existing physics-data integration schemes tend to combine mechanistic models and data networks in a hierarchical manner, with network structure training and parameter updates of the mechanistic modules typically being independent processes. Because traditional numerical analysis solutions are difficult to directly integrate with the automatic differentiation mechanisms in current deep learning frameworks, gradients during backpropagation are prone to computational graph truncation when crossing thermodynamic calculation modules, making it difficult for hybrid models to achieve deep joint iterative updates of physical-level parameters and network-level weights. Summary of the Invention

[0005] In view of the above-mentioned situation of the prior art, the present invention provides a gas turbine modeling method and system based on physical embedded multi-fidelity neural network, so as to realize end-to-end joint optimization of physical mechanism module parameters and data fusion network weights, thereby improving the parameter prediction accuracy of gas turbine model under dynamic and variable operating conditions.

[0006] In a first aspect, the present invention provides a gas turbine modeling method based on physically embedded multi-fidelity neural networks, comprising: A low-fidelity physical module is constructed, which internally includes a forward-differentiable component interpolation submodule and a combustion chamber mapping submodule with trainable parameters. The system receives the operating condition input of the gas turbine, processes it through the low-fidelity physics module, uses a forward differentiable iterative algorithm to solve the common operating line of the gas turbine to output a low-fidelity prediction result, and retains the computational graph of the forward differentiable iterative algorithm during the solution process. A multi-fidelity fusion neural network is constructed. The low-fidelity prediction result and the operating condition input are concatenated and then input into the multi-fidelity fusion neural network to map and output a high-fidelity prediction result. Based on the calculation error between the high-fidelity prediction results and the actual experimental data, an automatic differentiation mechanism is used to make the backpropagation gradient generated by the error penetrate the computation graph and be fed back to the low-fidelity physics module, so as to achieve end-to-end joint optimization of the weights of the multi-fidelity fusion neural network and the parameters inside the low-fidelity physics module.

[0007] Optionally, before receiving the operating condition input from the gas turbine, a data acquisition and preprocessing step is also included: The dynamic acceleration process data of the gas turbine is acquired, and the dynamic signal containing speed and temperature is averaged using a sliding window to extract candidate points. An evaluation window is set with the candidate point as the center. When the speed difference and temperature difference within the evaluation window both meet the preset stability conditions, the corresponding candidate point is determined as a quasi-steady-state operating point and used as the dataset for network training.

[0008] Optionally, the component interpolation submodule includes a compressor interpolation subnetwork and a turbine interpolation subnetwork; The low-fidelity physical module converts the pre-acquired component characteristic map data into tensors and registers them as buffer parameters. When given the speed and flow rate input, it locates the adjacent speed line intervals through tensor operators, and sequentially performs linear interpolation of the corresponding data points within a single speed line and weighted interpolation between adjacent speed lines to output the characteristic parameters of the corresponding component in a differentiable form.

[0009] Optionally, the combustion chamber mapping submodule is a multilayer perceptron network; The multilayer perceptron network receives normalized rotational speed, fuel flow rate, compressor outlet temperature, compressor outlet pressure, and air-fuel ratio as input layer features, and outputs scalar variables within a preset range through hidden layer mapping. The low-fidelity physics module maps the scalar variables into combustion efficiency and total pressure loss coefficient of the combustion chamber, which are constrained by physical boundaries, through a physical scaling formula.

[0010] Optionally, the step of using a forward-differentiable iterative algorithm to solve for the common operating line of the gas turbine includes: The difference between the actual converted flow rate of the gas turbine and the converted flow rate predicted based on the component interpolation submodule is defined as the residual function; The airflow is updated using the gradient descent method with a preset step size. In each iteration, the component interpolation submodule and the combustion chamber mapping submodule are called sequentially to update the internal thermodynamic parameters, and the residual function is recalculated until the convergence tolerance requirement is met.

[0011] Optionally, the output low-fidelity prediction result includes: After the iterative algorithm converges, the compressor outlet temperature, turbine inlet temperature, turbine exhaust temperature and electrical power are calculated using the final converged air flow rate, the corresponding combustion efficiency and the total pressure loss coefficient of the combustion chamber, combined with thermodynamic formulas. The above calculation results are then combined into a vector form as the low-fidelity prediction result.

[0012] Optionally, the multi-fidelity fusion neural network internally includes a linear correction network and a nonlinear correction network configured in parallel; The linear correction network is a fully connected layer without an activation function, used to extract systematic linear bias; the nonlinear correction network is a multi-layer fully connected network with an activation function, used to fit the nonlinear residuals that are difficult to capture by the low-fidelity prediction results.

[0013] Optionally, the multi-fidelity fusion neural network further includes an adaptive fusion mechanism; The adaptive fusion mechanism configures independent learnable fusion weights for each output variable and limits the learnable fusion weights to a preset range. The output of the linear correction network is multiplied element-wise with the learnable fusion weights, and the output of the nonlinear correction network is multiplied element-wise with the complementary weights. The results of the two operations are added together to obtain the final high-fidelity prediction result.

[0014] Optionally, the end-to-end joint optimization process uses mean squared error as the loss function and combines it with an early stopping strategy. When the validation set loss does not decrease within a preset number of consecutive rounds, the training is stopped and the model parameters with the lowest validation set loss are restored.

[0015] Secondly, the present invention provides a gas turbine modeling system based on physically embedded multi-fidelity neural networks, comprising: Memory, used to store computer programs; A processor for executing a computer program stored in the memory, which, when executed by the processor, implements the steps of the gas turbine modeling method based on physically embedded multifidelity neural networks as described in any one of the first aspects.

[0016] The present invention has achieved the following beneficial effects: This invention constructs a low-fidelity physics module containing a forward-differentiable component interpolation submodule and a combustion chamber mapping submodule. During the solution of the common operating line of the gas turbine, a tensor operator is used to preserve the computational graph structure, allowing the backpropagation gradient of errors generated during network training to penetrate the thermodynamic mechanism calculation module and be propagated back to the underlying physical parameters. This network structure connects the automatic differentiation paths between the mechanism equation nodes and the data-driven framework nodes, achieving end-to-end joint optimization of the physics module and the multi-fidelity fusion neural network. Combined with a multilayer perceptron network and a parallel linear and nonlinear dual-channel correction structure, the final high-fidelity prediction results not only learn and absorb the dynamic characteristics of real bench test data but also satisfy the objective thermodynamic constraints and boundary conditions within the gas turbine.

[0017] Other features and advantages of the invention will be set forth in the following description, and will be apparent in part from the description, or may be learned by practicing the invention. The objects and other advantages of the invention may be realized and obtained by means of the structures particularly pointed out in the written description and the accompanying drawings.

[0018] The technical solution of the present invention will be further described in detail below with reference to the accompanying drawings and embodiments. Attached Figure Description

[0019] The accompanying drawings are provided to further illustrate the invention and form part of the specification. They are used in conjunction with embodiments of the invention to explain the invention and do not constitute a limitation thereof. In the drawings: Figure 1 This is a flowchart illustrating the overall process of a gas turbine modeling method based on a physically embedded multi-fidelity neural network in an embodiment of the present invention. Figure 2 This is a block diagram illustrating the internal structure of the low-fidelity physical module in an embodiment of the present invention. Figure 3 This is a flowchart of the quasi-steady-state operating point screening and data preprocessing in an embodiment of the present invention; Figure 4 This is a flowchart illustrating the solution of the common working line using a forward differentiable iterative algorithm in an embodiment of the present invention. Figure 5 This is an architecture diagram of the multi-fidelity fusion neural network and adaptive fusion mechanism in an embodiment of the present invention; Figure 6This is a structural block diagram of a gas turbine modeling system based on a physically embedded multi-fidelity neural network in an embodiment of the present invention. Detailed Implementation

[0020] The technical solutions of the embodiments of this application 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. All other embodiments obtained by those skilled in the art based on the embodiments of the present invention without creative effort are within the scope of protection of the present invention.

[0021] Gas turbine modeling technology has application value in the dynamic performance evaluation and condition monitoring of turbine power generation systems. When establishing a gas turbine model, computational fluid dynamics simulation methods provide flow field characteristic data, while one-dimensional thermodynamic cycle models provide a steady-state calculation framework. This application provides a gas turbine modeling method based on a physically embedded multi-fidelity neural network. This method reconstructs the thermodynamic solution process through tensor operators, establishing a computational graph containing forward differentiable paths to achieve parameter updates for the physical mechanism module and the data-driven network.

[0022] like Figure 1 As shown, this invention discloses a gas turbine modeling method based on a physical embedded multi-fidelity neural network, including the step of constructing a low-fidelity physical module, such as... Figure 2 As shown, the low-fidelity physics module internally includes a forward-differentiable component interpolation submodule and a combustion chamber mapping submodule with trainable parameters. Specifically, the component interpolation submodule is used to perform tensor quantization reading of characteristic map data and numerical interpolation operations in continuous space, and the combustion chamber mapping submodule is used to output combustion efficiency and total pressure loss coefficient constrained by physical range based on operating condition parameters.

[0023] The system receives the operating condition input from the gas turbine, processes it through the low-fidelity physics module, and uses a forward-differentiable iterative algorithm to solve for the common operating line of the gas turbine, outputting a low-fidelity prediction result. The computational graph of the forward-differentiable iterative algorithm is retained during the solution process. It can be understood that the common operating line solution process is a numerical root-finding process based on the law of mass conservation to find the flow matching point between the compressor and turbine. By calling tensor operators supporting an automatic differentiation framework in the forward computation, the system can record the dependencies of variables in each iteration and generate a directed acyclic computational graph structure.

[0024] A multi-fidelity fusion neural network is constructed. The low-fidelity prediction result and the operating condition input are concatenated and then input into the multi-fidelity fusion neural network, which then maps and outputs a high-fidelity prediction result. Specifically, the low-fidelity prediction result serves as a reference physical state quantity, which, together with the operating condition input, constitutes the input feature layer of the fusion network. The multi-fidelity fusion neural network outputs corrected performance parameter prediction values ​​through internal matrix multiplication and activation function operations.

[0025] Based on the calculation error between the high-fidelity prediction results and the actual experimental data, an automatic differentiation mechanism is used to allow the backpropagation gradient generated by the error to penetrate the computational graph and be propagated back to the low-fidelity physics module. This enables end-to-end joint optimization of the weights of the multi-fidelity fusion neural network and the parameters within the low-fidelity physics module. Specifically, during the backpropagation phase, the error gradient is not only used to update the connection weight matrix of the multi-fidelity fusion neural network, but also, based on the previously preserved computational graph node paths, propagated back to the perceptron parameter matrix of the combustion chamber mapping submodule and the buffer tensor of the component interpolation submodule.

[0026] Before implementing the gas turbine modeling method based on physically embedded multi-fidelity neural networks, data acquisition and preprocessing steps are performed. Specifically, dynamic acceleration process data of the gas turbine is acquired, and a sliding window is used to average the dynamic signals containing speed and temperature to extract candidate points. The raw data in this embodiment comes from a ground test bench of a certain type of single-shaft micro gas turbine. The test bench is equipped with physical measuring instruments such as optical speed sensors, K-type thermocouples, and fuel flow meters. K-type thermocouples are installed at the compressor outlet, turbine inlet, and turbine outlet sections, respectively. The generator output power is calculated from the product of the measured constant voltage and current. The sampling frequency of the data acquisition system is set to 100Hz, the single continuous recording duration is 200 seconds, and the working range covers the range from 50% to 100% of the rated speed. The total amount of raw sample data is 20,000.

[0027] For the acquired raw time series sampling data, such as Figure 3 As shown, a steady-state point selection procedure is executed. The sliding window duration is set to 0.1 seconds, corresponding to 10 consecutive sampling points. Arithmetic averages are performed on the speed, fuel flow, temperature, and electrical power signals within this sliding window. The resulting arithmetic average is used as a candidate data point at a given time node. This sliding average operation reduces random measurement noise during sensor acquisition and compresses the data dimensionality.

[0028] An evaluation window is set centered on the candidate point. When both the speed difference and temperature difference within the evaluation window meet the preset stability conditions, the corresponding candidate point is determined as a quasi-steady-state operating point and used as the dataset for network training. Specifically, a stability evaluation window with a total length of 1 second is formed by taking a time span of 0.5 seconds forward and backward from the timestamp corresponding to the candidate point as the center point. Within this evaluation window, the maximum and minimum values ​​of the speed signal are extracted, and their absolute difference is calculated. If the speed difference is less than or equal to 200 rpm, the speed stability condition is met. Simultaneously, within this evaluation window, the maximum and minimum values ​​of the turbine inlet temperature signal are extracted, and their absolute difference is calculated. If the temperature difference is less than or equal to 10K, the temperature stability condition is met. A candidate point is designated as a quasi-steady-state operating point if and only if it simultaneously meets the above speed stability and temperature stability conditions. By traversing all candidate points extracted by the sliding window, a high-fidelity experimental data feature set is constructed for subsequent neural network training.

[0029] When constructing the low-fidelity physics module, component characteristic diagrams of the compressor and turbine are acquired. These characteristic diagrams can be obtained through pre-constructed 3D computational fluid dynamics simulations. The simulation conditions cover 50% to 100% of the rated speed range, and six equally spaced speed characteristic curves are set. For each speed curve, 8 to 12 steady-state operating points are calculated by adjusting the outlet boundary conditions (i.e., setting the outlet static pressure to vary equally within the range of 100 kPa to 300 kPa), and the corresponding relationships between the air mass flow rate, pressure ratio, and isentropic efficiency are recorded.

[0030] The component interpolation submodule includes a compressor interpolation subnetwork and a turbine interpolation subnetwork. The low-fidelity physics module converts pre-acquired component characteristic map data into tensors and registers them as buffer parameters. Given a speed and flow rate input, it uses tensor operators to locate adjacent speed ranges, sequentially performing linear interpolation of corresponding data points within a single speed range and weighted interpolation between adjacent speed ranges, outputting the characteristic parameters of the corresponding component in a differentiable form. For the compressor interpolation subnetwork, the characteristic map is set to include speed ranges, and the corresponding discrete speed value set is a known sequence. A specific speed range contains multiple data points, recording the flow rate, pressure ratio, and efficiency at that speed. After receiving the input speed and air flow rate, the search and sorting operator in the deep learning framework is invoked to determine the indices of adjacent speed ranges that meet the conditions. If the input speed exceeds the closed interval range, its index is located to the nearest boundary speed range for extrapolation.

[0031] After determining the speed range, flow rate interpolation is performed on the corresponding speed line. The tensor comparison operator is invoked to find two flow rate reference points adjacent to the current airflow value. Then, the interpolated pressure ratio along that speed line is calculated using the following formula: ; In the formula, the parameters are specifically defined as follows: This represents the interpolated pressure ratio calculated and output under the currently located specific speed line; This represents the intrinsic pressure ratio data corresponding to the left reference point adjacent to the input flow rate, extracted from the tensor data; This represents the intrinsic pressure ratio data corresponding to the right reference point adjacent to the input flow rate, extracted from the tensor data; This represents the intrinsic airflow data extracted from the tensor data corresponding to the right reference point adjacent to the input flow rate; This represents the intrinsic airflow data extracted from the tensor data corresponding to the left reference point adjacent to the input flow rate; This represents the instantaneous value of the input airflow received by the low-fidelity physics module in the current calculation cycle. If the input airflow exceeds the flow range of this speed line, the value of the nearest endpoint is used for linear extrapolation. The isentropic efficiency value under this speed line is calculated using the same operational logic.

[0032] Repeat the flow interpolation process described above on adjacent speed lines to calculate the corresponding pressure ratio and isentropic efficiency on the higher boundary line. After completing the single-line interpolation, calculate the linear weighting between speeds. Based on the relative position of the input speed within the positioning interval, the weighting formula is as follows: ; In the formula, the parameters are specifically defined as follows: This represents the linearly weighted value of the relative position calculated within the interval between two adjacent speed lines for the current input speed. This represents the instantaneous input rotational speed value received by the low-fidelity physics module during the current forward simulation phase; This represents the intrinsic rotational constant value corresponding to the lower boundary rotational speed line located by the tensor search operator; This represents the intrinsic rotational constant value corresponding to the higher boundary rotational speed line located by the tensor search operator.

[0033] Based on the calculated relative position weights, the final compressor pressure ratio and compressor isentropic efficiency are calculated through linear combination tensor operations. ; In the formula, the parameters are specifically defined as follows: This represents the final compressor pressure ratio value after continuous rotational speed space two-dimensional interpolation calculation; This represents the linear weighted weight of the relative positions within the rotational speed range obtained from the above calculation steps; This represents the pressure ratio calculation result obtained by performing one-dimensional interpolation based on the flow input at a lower boundary speed line; This represents the pressure ratio calculation result obtained by performing one-dimensional interpolation based on the flow input at a higher boundary speed line.

[0034] ; In the formula, the parameters are specifically defined as follows: This represents the final output value of the compressor's isentropic efficiency after two-dimensional interpolation calculation in the continuous rotational speed space. This represents the linear weighted average of relative positions within the speed range; This represents the isentropic efficiency calculation result obtained by performing one-dimensional interpolation based on the flow input at a lower boundary speed line; This represents the isentropic efficiency calculation result obtained by performing one-dimensional interpolation based on the flow input at a higher boundary speed line.

[0035] Specifically, the tensor search operator is used to locate adjacent characteristic intervals by inputting the expansion ratio. Then, one-dimensional linear interpolation is performed to calculate the converted flow rate and isentropic efficiency. Finally, a weighted output is calculated by combining the speed weights. After receiving the input speed and expansion ratio, the turbine outputs the turbine converted flow rate and turbine isentropic efficiency. The speed positioning, one-dimensional linear interpolation, and weighted calculation across speed lines in the calculation process all utilize tensor operators based on a deep learning framework, ensuring that the overall computational path maintains complete continuous differentiability.

[0036] Furthermore, the combustion chamber mapping submodule is a multilayer perceptron network; the multilayer perceptron network receives normalized speed, fuel flow rate, compressor outlet temperature, compressor outlet pressure, and fuel-air ratio as input layer features, and outputs scalar variables within a preset range through hidden layer mapping; the low-fidelity physics module maps the scalar variables into combustion efficiency and total pressure loss coefficient of the combustion chamber, which are constrained by physical boundaries, through a physical scaling formula.

[0037] Specifically, the input layer of the multilayer perceptron network contains 5 neuron sensing nodes. The input feature sequence includes: normalized rotational speed, normalized fuel flow rate, normalized compressor outlet temperature, normalized compressor outlet pressure, and normalized system air-fuel ratio. The normalization data processing operation adopts the minimum-maximum normalization algorithm to strictly map the physical state quantities of each dimension to a closed interval. The specific closed interval value is set to [-1, 1]. The hidden layer of the multilayer perceptron network contains 1 layer with 64 neuron connection nodes. The activation function of the hidden layer is configured as the hyperbolic tangent function parameter. The output layer of the multilayer perceptron network contains 2 neuron computing nodes, and the activation function of the output layer is configured as the Sigmoid function. After truncation processing by this function, the output layer generates two dimensionless scalar variables located in the open interval (0, 1). In order to convert the dimensionless scalar variables into actual thermodynamic state parameters, the low-fidelity physics module performs a one-dimensional linear transformation according to the following scaling formula: ; In the formula, the parameters are specifically defined as follows: This represents the calculated value of the actual combustion efficiency of the combustion chamber, mapped by this one-dimensional linear transformation. This represents the baseline constant for combustion efficiency, which is pre-set based on the lower limit of combustion physics. It represents the combustion efficiency fluctuation margin constant set in advance based on the combustion limit state; This represents the first dimensionless scalar variable generated after the output layer of the multilayer perceptron network is processed by the Sigmoid function. In the specific parameter configuration criteria of this embodiment, constants... Set to 0.8, a constant. Set to 0.2.

[0038] ; In the formula, the parameters are specifically defined as follows: This represents the calculated value of the true total pressure loss coefficient of the combustion chamber, output through a one-dimensional linear transformation mapping. This represents the pre-defined physical lower limit basis constant for the total pressure loss coefficient; This represents the pre-defined total pressure loss coefficient fluctuation margin constant; This represents the second dimensionless scalar variable generated after the output layer of the multilayer perceptron network is processed by the Sigmoid function. In the specific parameter configuration criteria of this embodiment, constants... Set to 0.9, a constant. Set to 0.1.

[0039] The common operating line of the gas turbine is solved using a forward differentiable iterative algorithm, such as... Figure 4 As shown, the process includes: defining the difference between the actual converted flow rate of the gas turbine and the converted flow rate predicted based on the component interpolation submodule as the residual function; updating the air flow rate based on the gradient descent method with a preset step size; in each iteration, sequentially calling the component interpolation submodule and the combustion chamber mapping submodule to update the internal thermodynamic parameters, and recalculating the residual function until the convergence tolerance requirement is met.

[0040] Specifically, the mathematical definition of the common working line residual function is as follows: ; In the formula, the parameters are specifically defined as follows: This represents the numerical value of the forward iteration residual function with air mass flow rate as the calculation variable. This represents the actual turbine inlet flow rate calculated based on the aerodynamic parameters under the current cycle conditions. This represents the turbine predicted flow rate value output after querying the characteristic tensor by inputting parameters into the turbine interpolation subnetwork; This represents the detected value of the compressor inlet air mass flow rate, an independent variable, in the current execution step.

[0041] The actual conversion flow rate calculation process is derived based on the following gas state conversion formula: ; In the formula, the parameters are specifically defined as follows: This represents the calculated equivalent flow rate at the turbine inlet. This represents the compressor inlet air mass flow rate value in the current iteration step; This represents the measured fuel flow rate value input from the sensor's operating conditions. This represents the pre-defined standard atmospheric reference pressure constant at sea level; This represents the characteristic value of the absolute pressure at the combustion chamber outlet, i.e., the turbine inlet pressure, calculated according to the total pressure loss reduction formula. This represents the characteristic value of the total temperature at the combustion chamber outlet, i.e., the turbine inlet temperature, calculated based on the combustion energy conservation equation. This represents the pre-set standard atmospheric reference temperature constant at sea level. In this embodiment, The value is set to 367400 Pa. The value is set to 1100K.

[0042] For the iterative solution process, the forward differentiable iterative algorithm uses a gradient descent update operation structure with a fixed step size to continuously correct the airflow detection variable based on the residual: ; In the formula, the parameters are specifically defined as follows: Indicates the first The compressor inlet air mass flow rate value generated in the next iteration step; Indicates the first The compressor inlet air mass flow rate value, which is used as the independent variable input in the next iteration step; This represents the pre-configured control step size constant for iterative solution; Indicates the first The residual function value is calculated after inputting the flow rate independent variable in the next iteration step. In this embodiment, the iteration control step size is... The initial air mass flow rate is set to 0.1. The algorithm's initial air mass flow rate benchmark is set as the product of the input fuel flow rate and the engine speed ratio, with a preset coefficient set to 50. The rated engine speed is used for dimensionless processing. The maximum allowed number of iterations is limited to 100, and the convergence tolerance threshold for the algorithm's exit condition is set to a residual absolute value that is strictly less than 0.001.

[0043] In the data stream of a single iterative loop, the system sequentially executes function calls: extracts the current airflow and speed variables and inputs them into the compressor interpolation submodule; tensor operations generate pressure ratio and efficiency results; combining the intake environment pressure and temperature constant, algebraic operations are performed to obtain the compressor outlet section pressure and temperature status; the obtained pressure and temperature status, along with the operating speed and the converted air-fuel ratio characteristics, are sent to the multilayer perceptron network; the network forward propagates and outputs the dynamic combustion efficiency and loss coefficient under the current state; the energy conservation equation is executed to obtain the combustion chamber outlet turbine inlet temperature and pressure status; the turbine expansion ratio is generated, its value being equal to the quotient of the combustion chamber outlet pressure and the fixed turbine exhaust boundary pressure (104365 Pa); the expansion ratio and speed are input into the turbine interpolation subnetwork to extract the graph-converted flow rate; the actual converted flow rate and the graph-converted flow rate are summarized and subtracted to obtain the residual value; the airflow input value for the next round is calculated using the step size parameter. The tensor addition, multiplication, and table lookup / replacement operations within the above loop are all synchronously recorded in the computation graph of the automatic differential object.

[0044] The output low-fidelity prediction result includes: after the iterative algorithm converges, using the final converged air flow rate and the corresponding combustion efficiency and the total pressure loss coefficient of the combustion chamber, combined with thermodynamic formulas to calculate the compressor outlet temperature, turbine inlet temperature, turbine exhaust temperature and electrical power, and combining the above calculation results into a vector form as the low-fidelity prediction result.

[0045] The calculation and reconstruction process of the compressor outlet temperature adopts the following isentropic compression relationship: ; In the formula, the parameters are specifically defined as follows: This represents the predicted compressor outlet airflow temperature output by thermodynamic conversion calculations. This represents the set ambient intake reference temperature constant. This represents the final pressure ratio calculation result output by the compressor interpolation submodule when the iteration convergence is determined; This represents the isobaric and isovolumetric specific heat constant of the compressed air inside the compressor components; This represents the final isentropic efficiency calculation result output by the compressor interpolation submodule when the iterative convergence determination is completed. In the specific physical settings of this embodiment, The value is 288.15K, and the specific heat ratio is... The value is 1.4 under compressor conditions.

[0046] The calculation and reconstruction process of the turbine inlet temperature adopts the following combustion chamber heat balance relationship: ; In the formula, the parameters are specifically defined as follows: This represents the predicted value of the highest gas temperature before the turbine, output from the thermal balance calculation. This represents the compressor outlet gas temperature obtained from the isentropic compression formula described in the preceding steps. This indicates the current fuel flow rate input value received by the system. This represents the physical lower heating value constant of the fuel used in the system pre-calibration; This represents the dynamic combustion efficiency evaluation value output by the combustion chamber mapping submodule based on the operating conditions when the iteration converges. This represents the final compressor inlet air mass flow rate matching value determined by the convergence of the iterative root-finding algorithm; This represents the isobaric specific heat capacity constant of the high-temperature combustion gas within the turbine inlet temperature range. In the specific physical settings of this embodiment, the specific heat capacity constant... The value is 1005 J / (kg·K). In this embodiment, conventional aviation kerosene is used as the fuel, and the LHV constant is specifically set to 43100 kJ / kg.

[0047] The calculation and reconstruction process of turbine exhaust temperature adopts the following polytropic expansion relationship: ; In the formula, the parameters are specifically defined as follows: This represents the predicted turbine exhaust temperature output from the expansion calculation process. This represents the maximum gas temperature input value before the turbine, derived from the aforementioned heat balance formula. This represents the isentropic efficiency output value calculated by the turbine interpolation submodule based on the expansion ratio when the iteration converges. This represents the turbine expansion ratio assessment value determined when the iteration converges, based on the pressures at the front and rear sections of the turbine. This represents the isobaric and isovolumetric specific heat constant of the expanding gas inside the turbine component.

[0048] The calculation and reconstruction process of the gas turbine output electrical power adopts the following energy subtraction relationship: ; In the formula, the parameters are specifically defined as follows: This represents the estimated value of the effective shaft-end electrical power output of the entire mechanical power generation system. This represents the confirmed value of the compressor inlet air mass flow rate extracted by the algorithm upon convergence. This indicates the system's input fuel flow control value; This represents the isobaric specific heat capacity constant of the working fluid; This represents the predicted turbine inlet gas temperature generated by the calculation. This represents the predicted turbine exhaust temperature value generated by the calculation. This represents the predicted compressor outlet temperature value generated by the calculation. Indicates the ambient intake reference temperature constant; This represents the overall physical efficiency constant of the mechanical transmission components as defined by the system. This represents the physical efficiency constant of the magnetoelectric conversion of the generator assembly, as set by the system. In the specific physical settings of this embodiment, the transmission efficiency... The value is 0.99, representing the power generation efficiency. The value is set to 0.99. The calculated power value is converted to kW using a unit conversion command. After completing the above state calculations, the system concatenates these four state indicators in the tensor dimension to form a sequence vector of low-fidelity prediction results.

[0049] Furthermore, such as Figure 5 As shown, the multi-fidelity fusion neural network internally includes parallel linear correction networks and nonlinear correction networks. The linear correction network is a fully connected layer without activation functions, used to extract systematic linear deviations. The nonlinear correction network is a multi-layer fully connected network with activation functions, used to fit the nonlinear residuals that are difficult to capture by the low-fidelity prediction results. An axis-wise concatenation operation is performed between the working condition feature input and the low-fidelity prediction result vector to obtain a composite six-dimensional feature combination input vector.

[0050] For a linear correction network channel, its data stream undergoes an affine space transformation through a single fully connected matrix operation, with the mapping algebra formula as follows: ; In the formula, the parameters are specifically defined as follows: This represents the linear prediction bias correction vector that is finally output by the linear correction network branch through matrix multiplication and addition. This represents the set of system weight matrix parameters instantiated and configured in the linear correction network layer; This represents a six-dimensional feature combination input vector formed by sequentially concatenating the original set of operating condition inputs and the set of low-fidelity prediction results; This represents the set of system bias term vector parameters instantiated and configured in the linear correction network layer. This processing branch prohibits the deployment of any non-linear activation function operations.

[0051] For a nonlinear correction network channel, its network topology consists of cascaded, multi-layered fully connected computational layers. The total number of hidden layers is set to two, with each hidden layer uniformly configured with 512 perceptual neurons. The activation function mechanism for the network layers uniformly calls the LeakyReLU function with a negative slope parameter set to 0.01, and Dropout regularization nodes are injected into this channel during the training phase. The forward propagation calculation formula for any hidden layer at any network depth is defined as follows: ; In the formula, the parameters are specifically defined as follows: Indicates the current depth index is The hidden layer generates the output feature tensor matrix data after performing regularization truncation and nonlinear activation function operations; This represents a regularization function operator that randomly replaces some neuron values ​​within the feature matrix with zeros according to a preset ratio (set to 0.1). This indicates the invocation of the modified linear unit activation function operator with a small negative slope to avoid neuron deactivation; Indicates the current depth index is The learnable weight parameter matrix that is bound to the hidden layer and can participate in the reverse update; Indicates indexing from the previous depth The preceding feature tensor matrix data passed in after the hidden layer operation is completed; Indicates the current depth index is The hidden layers are bound to learnable bias term parameter vectors that can participate in reverse updates. The input feature tensor matrix received by the first layer of the network is equivalent to the aforementioned combined input vector. The final output layer structure is simplified to a single fully connected layer that abandons the activation function, which converges to generate a four-dimensional nonlinear prediction bias correction vector.

[0052] The multi-fidelity fusion neural network further includes an adaptive fusion mechanism; the adaptive fusion mechanism configures independent learnable fusion weights for each output variable and limits the learnable fusion weights to a preset range; the output of the linear correction network is multiplied element-wise with the learnable fusion weights, and the output of the nonlinear correction network is multiplied element-wise with the complementary weights, and the results of the two operations are added together as the final high-fidelity prediction result.

[0053] The channel combination weighted calculation formula for the high-fidelity prediction result vector is as follows: ; In the formula, the parameters are specifically defined as follows: This represents the overall value of the high-fidelity prediction result vector output after being superimposed and integrated through a dual-channel weighting mechanism. This means that after the Sigmoid function is called to truncate the data, its value is strictly limited to the learnable fusion weight allocation vector inside the (0,1) interval boundary. This represents the numerical value of the linear prediction bias correction vector transmitted after the aforementioned linear correction network channel calculation; This represents the Hadamard product operator, which dispatches computer instructions to perform element-wise multiplication on tensors of the same dimension. This represents the complementary weight allocation vector share retained for nonlinear branches, obtained by subtracting the learnable weights from the constant matrix. This represents the numerical value of the nonlinear prediction bias correction vector transmitted after the aforementioned nonlinear correction network channel calculation. During the initial loading phase of the network structure, the initial values ​​of each element in the fusion weight vector are uniformly set to 0.5.

[0054] Furthermore, the end-to-end joint optimization process uses mean squared error as the loss function and combines it with an early stopping strategy. When the validation set loss does not decrease within a preset number of consecutive rounds, the training is stopped and the model parameters with the lowest validation set loss are restored.

[0055] The overall mean squared error loss function is used as the error metric during model training and optimization, and its calculation formula is defined as follows: ; In the formula, the parameters are specifically defined as follows: This represents the scalar value of the global average mean squared error loss function calculated by summing all data within the current batch of operations. This represents the upper limit of the total number of sample data entries contained in a single batch fed into the tensor buffer during the currently executing network training or offline verification process. The index parameter represents the traversal iteration index of a single data sample point that is currently being extracted from the buffer for individual error norm calculation. Indicates the forward reception of the fusion network model. A high-fidelity prediction result vector is generated by calculation and inference after inputting the features of each sample; This indicates that the extracted data is matched with the first [unclear] from the bench test dataset after steady-state screening preprocessing. Each sample corresponds to a true measurement label baseline vector.

[0056] During the reverse training phase of the model network weights, the Adam adaptive optimization algorithm controller is invoked to perform gradient descent updates of the network parameters. The initial learning rate parameter inside the controller is set to 0.001. To limit the norm growth of the tensor parameter matrix, an L2 regularization term with a weight decay coefficient of 0.0001 is configured for the controller. Based on the loss values ​​obtained in the current batch, the deep learning framework automatically extracts the node partial derivatives of all registered parameters to generate the parameter gradient matrix.

[0057] In the core action of this optimization, the error backpropagation gradient sequence generated by the loss function at the top layer sequentially penetrates the pre-constructed forward differentiable iterative computation graph structure path within the low-fidelity physics module. This path connects the residual operation node, the thermal parameter algebra node, and the data interpolation node. The gradient is continuously backpropagated along this node path, directly reaching the perceptron weight matrix data bits in the bottom hidden layer of the combustion chamber mapping submodule, as well as the one-dimensional interpolation buffer tensor scaling parameter bits configured in the component interpolation submodule. Through continuous gradient penetration updates, the end-to-end joint parameter optimization operation is completed. The system synchronously executes validation process control including early stopping judgment. When the validation set loss status flag shows a non-decreasing trend over 100 consecutive training generations, the controller blocks the current gradient update action and calls the memory copy instruction to roll back and overwrite the network topology parameters and operation parameters to the parameter configuration file in the historical record pool where the validation set loss reaches the minimum value.

[0058] In addition, such as Figure 6 As shown, this embodiment of the invention also provides a gas turbine modeling system based on a physically embedded multi-fidelity neural network, comprising a memory and a processor. The memory is used to load a program operation sequence, which includes reading speed and pressure data from a sensor interface layer, calculating the arithmetic mean based on a sliding window of a predetermined length, performing difference comparison to determine steady-state characteristics, loading interpolation characteristic data into tensor memory, initiating the aforementioned differentiable iterative residual solution step and allocating space to save the computational graph information of the gradient flow path during the solution process, calling a linear and nonlinear dual-channel neural network structure to perform multi-matrix multiplication and fusion operator actions, and after obtaining the loss parameters, calling a chain-reverse operation controller to update the interpolation data matrix and neuron connection weights within the memory. The processor executes this computational flow and outputs key physical quantity characteristic values ​​for each state section of the gas turbine, which are used as the benchmark for equipment condition diagnosis.

[0059] The various embodiments in this specification are described in a progressive manner, and the same or similar parts between the various embodiments can be referred to mutually. For the apparatus or system disclosed in the embodiments, the description is relatively simple, and the relevant technical implementation details can be found in the method section.

[0060] Those skilled in the art will further recognize that the units and algorithm steps of the various examples described in conjunction with the embodiments disclosed herein can be implemented in electronic hardware, computer software, or a combination of both. Whether these functions are implemented in hardware or software depends on the specific application and design constraints of the technical solution. The steps of the methods or algorithms described in conjunction with the embodiments disclosed herein can be implemented directly in hardware, software modules executed by a processor, or a combination of both. The software modules can be located in random access memory, memory, read-only memory, electrically programmable read-only memory, electrically erasable programmable read-only memory, registers, hard disks, removable disks, compact optical disc read-only memory, or any other form of storage medium known in the art. The solutions provided by the present invention have been described in detail above. Specific examples have been used to illustrate the principles and implementation methods of the present invention. The description of the above embodiments is only for the purpose of helping to understand the methods and logical structure of the present invention. At the same time, for those skilled in the art, based on the ideas of the present invention, there will be corresponding changes in the specific implementation methods and application scope. Therefore, the content of this specification should not be construed as a limitation of the present invention.

Claims

1. A gas turbine modeling method based on physically embedded multi-fidelity neural networks, characterized in that, include: A low-fidelity physical module is constructed, which internally includes a forward-differentiable component interpolation submodule and a combustion chamber mapping submodule with trainable parameters. The system receives the operating condition input of the gas turbine, processes it through the low-fidelity physics module, uses a forward differentiable iterative algorithm to solve the common operating line of the gas turbine to output a low-fidelity prediction result, and retains the computational graph of the forward differentiable iterative algorithm during the solution process. A multi-fidelity fusion neural network is constructed. The low-fidelity prediction result and the operating condition input are concatenated and then input into the multi-fidelity fusion neural network to map and output a high-fidelity prediction result. Based on the calculation error between the high-fidelity prediction results and the actual experimental data, an automatic differentiation mechanism is used to make the backpropagation gradient generated by the error penetrate the computation graph and be fed back to the low-fidelity physics module, so as to achieve end-to-end joint optimization of the weights of the multi-fidelity fusion neural network and the parameters inside the low-fidelity physics module.

2. The gas turbine modeling method based on physically embedded multi-fidelity neural networks according to claim 1, characterized in that, Before receiving the operating condition input from the gas turbine, the process also includes data acquisition and preprocessing steps: The dynamic acceleration process data of the gas turbine is acquired, and the dynamic signal containing speed and temperature is averaged using a sliding window to extract candidate points. An evaluation window is set with the candidate point as the center. When the speed difference and temperature difference within the evaluation window both meet the preset stability conditions, the corresponding candidate point is determined as a quasi-steady-state operating point and used as the dataset for network training.

3. The gas turbine modeling method based on physically embedded multi-fidelity neural networks according to claim 1, characterized in that, The component interpolation submodule includes a compressor interpolation subnetwork and a turbine interpolation subnetwork; The low-fidelity physical module converts the pre-acquired component characteristic map data into tensors and registers them as buffer parameters. When given the speed and flow rate input, it locates the adjacent speed line intervals through tensor operators, and sequentially performs linear interpolation of the corresponding data points within a single speed line and weighted interpolation between adjacent speed lines to output the characteristic parameters of the corresponding component in a differentiable form.

4. The gas turbine modeling method based on physically embedded multi-fidelity neural networks according to claim 1, characterized in that, The combustion chamber mapping submodule is a multilayer sensor network; The multilayer perceptron network receives normalized rotational speed, fuel flow rate, compressor outlet temperature, compressor outlet pressure, and air-fuel ratio as input layer features, and outputs scalar variables within a preset range through hidden layer mapping. The low-fidelity physics module maps the scalar variables into combustion efficiency and total pressure loss coefficient of the combustion chamber, which are constrained by physical boundaries, through a physical scaling formula.

5. The gas turbine modeling method based on physically embedded multi-fidelity neural networks according to claim 4, characterized in that, The step of using a forward differentiable iterative algorithm to solve for the common operating line of the gas turbine includes: The difference between the actual converted flow rate of the gas turbine and the converted flow rate predicted based on the component interpolation submodule is defined as the residual function; The airflow is updated using the gradient descent method with a preset step size. In each iteration, the component interpolation submodule and the combustion chamber mapping submodule are called sequentially to update the internal thermodynamic parameters, and the residual function is recalculated until the convergence tolerance requirement is met.

6. The gas turbine modeling method based on physically embedded multi-fidelity neural networks according to claim 5, characterized in that, The output low-fidelity prediction results include: After the iterative algorithm converges, the compressor outlet temperature, turbine inlet temperature, turbine exhaust temperature and electrical power are calculated using the final converged air flow rate, the corresponding combustion efficiency and the total pressure loss coefficient of the combustion chamber, combined with thermodynamic formulas. The above calculation results are then combined into a vector form as the low-fidelity prediction result.

7. The gas turbine modeling method based on physically embedded multi-fidelity neural networks according to claim 1, characterized in that, The multi-fidelity fusion neural network contains parallel linear correction networks and nonlinear correction networks. The linear correction network is a fully connected layer without an activation function, used to extract systematic linear bias; the nonlinear correction network is a multi-layer fully connected network with an activation function, used to fit the nonlinear residuals that are difficult to capture by the low-fidelity prediction results.

8. The gas turbine modeling method based on physically embedded multi-fidelity neural networks according to claim 7, characterized in that, The multi-fidelity fusion neural network also includes an adaptive fusion mechanism; The adaptive fusion mechanism configures independent learnable fusion weights for each output variable and limits the learnable fusion weights to a preset range. The output of the linear correction network is multiplied element-wise with the learnable fusion weights, and the output of the nonlinear correction network is multiplied element-wise with the complementary weights. The results of the two operations are added together to obtain the final high-fidelity prediction result.

9. The gas turbine modeling method based on physically embedded multi-fidelity neural networks according to claim 1, characterized in that, The end-to-end joint optimization process uses mean squared error as the loss function and combines it with an early stopping strategy. When the validation set loss does not decrease within a preset number of consecutive rounds, training is stopped and the model parameters with the lowest validation set loss are restored.

10. A gas turbine modeling system based on physically embedded multi-fidelity neural networks, characterized in that, include: Memory, used to store computer programs; A processor is configured to execute a computer program stored in the memory, which, when executed by the processor, implements the steps of the gas turbine modeling method based on a physically embedded multifidelity neural network as described in any one of claims 1 to 9.

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