Liquid rocket engine linearization mathematical modeling method, system, medium, and apparatus

Abstract

A liquid rocket engine linearization mathematical modeling method, system, medium and equipment, in the method, based on the simulation of the nonlinear mathematical model of the liquid rocket engine, the linearization parameters are obtained, which are flattened into one-dimensional data, a Transformer time series prediction model combining self-attention mechanism is constructed, a loss function is constructed by using matrix form, nonlinear system data and single-step prediction linearization model, a Transformer time series prediction model is built combined with the loss function, and the model is trained, and the linearization model predicted by the final model after the model converges.

Description

Technical Field

[0001] This invention relates to the field of liquid rocket engine technology, and in particular to a linearized mathematical modeling method, system, medium, and equipment for liquid rocket engines. Background Technology

[0002] Liquid rocket engines, as the core of launch vehicle propulsion, are typical complex thermohydrodynamic systems—comprising multiple independent dynamic components with close inter-coupling relationships, and requiring continuous operation under extremely harsh conditions. In this context, even minor operational anomalies can rapidly escalate into destructive failures, resulting in significant economic losses. Therefore, conducting research on the health management of liquid rocket engines is of paramount practical importance for ensuring the safety of space missions.

[0003] Modeling is a fundamental prerequisite for health monitoring of liquid rocket engines. By constructing accurate physical and data-driven models, the engine's operating status can be assessed in real time, anomalies can be detected promptly, and failures can be prevented in advance, ultimately improving the engine's reliability and safety. However, taking the Space Shuttle main engine as an example, its mathematical mechanism model belongs to a multivariable nonlinear complex fluid dynamics model: not only is the solution process of nonlinear differential equations extremely difficult, but research on the performance of the control system also faces many complex challenges. Therefore, for practical engineering control personnel, linearizing the engine's nonlinear dynamic characteristics first, and then using mature linear system design methods to complete the analysis and synthesis of the control system, has become a more feasible technical approach.

[0004] The most commonly used linearization method in the current engineering field is to derive a linearized model using the first-order Taylor expansion of a nonlinear model. From an engineering practice perspective, linearized models of complex systems are mainly obtained through analytical methods or system identification methods (small deviation methods). Analytical linearization requires a complete mathematical model as its foundation, involving a rigorous Taylor expansion of each equation. However, for large and complex systems, this method is not only time-consuming and laborious but also extremely computationally complex. In contrast, system identification methods determine the input-output relationship through experiments, thereby capturing the linear dynamic characteristics of the system. However, both methods have significant limitations in model accuracy, making it difficult to quickly obtain high-precision linearized models of liquid rocket engines, and thus failing to fully meet the application requirements of health management.

[0005] The information disclosed in the background section is only for enhancing the understanding of the background of this invention, and therefore may contain information that does not constitute prior art known to those skilled in the art. Summary of the Invention

[0006] To address the problem that existing methods cannot quickly obtain high-precision linearized models, this invention provides a linearized mathematical modeling method, system, medium, and device for liquid rocket engines. Based on the self-attention mechanism of physical information neural networks and Transformer time series models, it achieves rapid solution of high-precision linearized models while preserving their physical properties.

[0007] A linearized mathematical modeling method for liquid rocket engines includes:

[0008] Step A: Simulation is performed based on the nonlinear mathematical model of the liquid rocket engine, and perturbations are injected according to the small deviation method. The linearization parameters are obtained by combining the discrete linearization calculation formula. Finally, it is flattened into one-dimensional data. To perform time series forecasting;

[0009] Step B: Construct a Transformer time series prediction model incorporating a self-attention mechanism, inputting one-dimensional data. Linearized parameter sequence for predicting future times And reconstruct it into matrix form. The Transformer time series prediction model includes a relative position encoding layer, two attention layers, and a prediction layer with two hidden layers. It uses the ReLU function for non-linear activation, and the calculation formula for the attention layer is as follows:

[0010] ,

[0011] Step C: Under a single operating condition, the change in control quantity is zero. The linearized model expression for single-step prediction after discretization is as follows:

[0012]

[0013] in, , , These are single-step predictions, and the goal is to fit the target value. , ;

[0014] Step D: Then use matrix form Nonlinear system data The loss function is constructed by combining the single-step prediction linearization model as follows:

[0015]

[0016] in, The weights assigned to different loss terms, , Used to describe the data loss of the Transformer time series forecasting model.

[0017] Step E: Build a Transformer time series prediction model using the loss function, train the model, and after convergence, obtain the final linearized model prediction. .

[0018] In the linearized mathematical modeling method for liquid rocket engines described above, step A includes:

[0019] Step A1: Simulate the liquid rocket engine under 100% operating conditions using a nonlinear mathematical model of the liquid oxygen / liquid hydrogen rocket engine. The model is expressed as follows:

[0020] Let x be the state variable, u be the input variable, y be the observation variable, f be the nonlinear state equation, and h be the nonlinear observation equation.

[0021] In the initial input Under the influence of this action, the model converges to the operating point 0. Add a small perturbation to the input of the original nonlinear system The model reconverged to the operating point 1. The state variables, input variables, and observation variables collected at different operating points are used as the training dataset for the entire algorithm.

[0022] Step A2: Construct a linearized model using the small deviation method, as shown in the following equation:

[0023]

[0024] in, , m represents the number of sensors selected from the model, and n represents the number of state variables selected from the model.

[0025] Step A3: Replace the continuous derivative with the discrete partial derivative to obtain the following equation:

[0026]

[0027] Therefore, the linearized model parameter matrix at different time points under operating point 0 can be obtained. t represents different points in time.

[0028] Step A4: Linearize the model Expand the data row by row and then concatenate them to obtain one-dimensional data. .

[0029] In the linearized mathematical modeling method for liquid rocket engines, the small perturbation is a set of random small-amplitude input perturbations around 100% rated operating conditions, used to generate a training dataset covering different local operating points.

[0030] In the linearized mathematical modeling method for liquid rocket engines, the Adams optimization algorithm is used to update the trainable parameters of the model, and the learning rate of 0.05 can be dynamically adjusted.

[0031] In the linearized mathematical modeling method for liquid rocket engines described above, the nonlinear mathematical model is a multivariable nonlinear dynamic model of the liquid oxygen / liquid hydrogen liquid rocket engine of the Space Shuttle main engine.

[0032] A system for performing the method includes:

[0033] The simulation module performs simulations based on a nonlinear mathematical model of a liquid rocket engine, injects disturbances using a small-deviation method, and obtains linearization parameters by combining the discrete linearization calculation formula. Finally, it is flattened into one-dimensional data. To perform time series forecasting;

[0034] The building block constructs a Transformer time series prediction model that incorporates a self-attention mechanism, taking one-dimensional data as input. Linearized parameter sequence for predicting future times And reconstruct it into matrix form. The Transformer time series prediction model includes a relative position encoding layer, two attention layers, and a prediction layer with two hidden layers. It uses the ReLU function for non-linear activation. The formula for calculating the attention layer between the k-th sequence and other sequences is as follows:

[0035] ,

[0036] The linearized model expression for the discrete module and its single-step prediction is as follows:

[0037]

[0038] in, , , These are single-step predictions, and the goal is to fit the target value. , ;

[0039] The loss module is then used in matrix form. Nonlinear system data The loss function is constructed by combining the single-step prediction linearization model as follows:

[0040]

[0041] in, The weights assigned to different loss terms, Used to describe the data loss of the Transformer time series forecasting model.

[0042] The training module uses a loss function to build a Transformer time series prediction model, trains the model, and after convergence, the final linearized model prediction is obtained. .

[0043] A computer storage medium including computer instructions that, when run on a computer, cause the computer to perform the method.

[0044] An electronic device, the electronic device comprising:

[0045] Memory, processor, and computer programs stored in memory and executable on the processor, wherein,

[0046] The processor implements the method when executing the program.

[0047] Compared with existing technologies, the present invention has the following advantages: Compared with traditional small-deviation linearization, the present invention utilizes physical information neural networks and Transformer time series models to optimize the small-deviation linearization model, which can improve the accuracy of the linearization model while maintaining physical characteristics; at the same time, it solves the problem of high computational complexity of existing high-precision linearization methods such as Carleman linearization, effectively reducing algorithm complexity and improving time efficiency and engineering application capabilities. Attached Figure Description

[0048] Various other advantages and benefits of the present invention will become apparent to those skilled in the art upon reading the detailed description of the preferred embodiments below. The accompanying drawings are for illustrative purposes only and are not intended to limit the invention. It is obvious that the drawings described below are merely some embodiments of the invention, and those skilled in the art can obtain other drawings based on these drawings without any inventive effort. Furthermore, the same reference numerals denote the same parts throughout the drawings.

[0049] In the attached diagram:

[0050] Figure 1 This is an overall flowchart of the high-precision linearization method for nonlinear models of liquid rocket engines described in this invention;

[0051] Figure 2Schematic diagram of the mathematical model of the SSME liquid oxygen-liquid hydrogen rocket engine;

[0052] Figure 3 Diagram of the Transformer time series forecasting model architecture;

[0053] Figure 4 The training flowchart for a high-precision linearized solution model built on a physical information neural network and a Transformer model.

[0054] The present invention will be further explained below with reference to the accompanying drawings and embodiments. Detailed Implementation

[0055] Specific embodiments of the invention will now be described in more detail with reference to the accompanying drawings. While specific embodiments of the invention are shown in the drawings, it should be understood that the invention may be implemented in various forms and should not be limited to the embodiments set forth herein. Rather, these embodiments are provided so that this invention will be thorough and complete, and will fully convey the scope of the invention to those skilled in the art.

[0056] It should be noted that certain terms are used in the specification and claims to refer to specific components. Those skilled in the art will understand that different terms may be used to refer to the same component. This specification and claims do not distinguish components based on differences in terminology, but rather on differences in function. The terms "comprising" or "including" used throughout the specification and claims are open-ended and should be interpreted as "comprising but not limited to." The following descriptions are preferred embodiments for carrying out the invention; however, these descriptions are for the purpose of understanding the general principles of the specification and are not intended to limit the scope of the invention. The scope of protection of this invention is determined by the appended claims.

[0057] To facilitate understanding of the embodiments of the present invention, further explanations and descriptions will be provided below with reference to the accompanying drawings and specific embodiments. The accompanying drawings do not constitute a limitation on the embodiments of the present invention.

[0058] like Figures 1 to 4 As shown, the linearization mathematical modeling method for liquid rocket engines includes the following steps:

[0059] Step A: Based on the nonlinear mathematical model of the liquid rocket engine, such as... Figure 2 As shown, the mathematical model of a liquid rocket engine is expressed as the formula: Simulations were performed, and disturbances (within 5%) were injected using the small-deviation method. Combined with the discrete linearization calculation formula, the linearization parameters, i.e., the discrete state matrix, were obtained. and observation matrix : Finally, the steady-state operating data were taken and flattened into one-dimensional data. For time series forecasting, `batch` refers to the number of steady-state operating segments under different operating conditions. Here, only one steady-state operating condition is considered, so `batch=1`. `length` represents the number of samples taken within a specific steady-state operating segment. The matrix represents the state matrix. Control matrix Observation matrix Feedforward matrix The shapes are state matrices. , , , A dimensional matrix. u represents the control variable. m, n, r represent the number, or dimension, of the observation y, state variable x, and control variable u, respectively.

[0060] Small Deviation Method: First, for linearization of nonlinear systems, the small deviation method is mostly used in engineering. Its essence is to expand the nonlinear function around the equilibrium point into a Taylor series while retaining its first-order linear terms. Assume the mathematical description of the nonlinear system is as shown in equation (1).

[0061]

[0062] x - state variable, u - input variable, y - observation variable, f - nonlinear state equation, h - nonlinear observation equation;

[0063] Using the small deviation method, a certain steady-state operating point of the system is selected. As the equilibrium point, a first-order Taylor expansion of the original nonlinear system yields the following equation (2).

[0064]

[0065] The SSME model is modeled modularly using the Simulink software in Matlab, and the Jacobian method cannot be directly used to differentiate the nonlinear model expression to obtain the parameter matrices of the linearized model. Therefore, the parameters of its linearized model should be solved according to equation (3). First, assume the state matrix... Control Matrix Observation matrix Feedforward matrix The shapes are state matrices. , , , 3D matrix.

[0066]

[0067] in,

[0068] 1) , , , .

[0069] 2) It can be seen as At steady-state operating point about The incremental form of the partial derivative.

[0070] The above calculation method can be seen as replacing the original partial derivative formula of the nonlinear system with the incremental form of the partial derivative. Therefore, this paper can give the physical meaning of the small deviation linearization method, that is, by adding a small deviation, also known as a small perturbation, to a certain state variable of the nonlinear system. ,and and This is due to the changes in other variables caused by the disturbance, whose ratios are described by different parameter matrices, thus establishing a linear relationship between them.

[0071] Variables in substitution , , The simplified model is shown in equation (4).

[0072]

[0073] In engineering practice, the selection of observation vectors is isolated from input variables. Therefore, observation vectors often do not have a direct linear relationship with input variables. .

[0074] Discretization formula:

[0075] Due to the high-order term loss of the small deviation method and the numerical fluctuations and interference factors in the simulation process of the nonlinear model, the accuracy of the obtained linearized model is low

[12]

[13] . In practical applications, the linearized model used is the discretized model. Here, we use the Euler method to discretize the above matrix to obtain the discretized model in equation (5).

[0076]

[0077] in, It is a discretized system matrix. , is the discretized input matrix. For discrete sampling time, It is an identity matrix.

[0078] It is not difficult to see that when the sampling time When it approaches 0, Approaching the unit array, Approximating a zero matrix, the state equation becomes a follow-up equation to the state of the previous time step. The accuracy of this linearized model is simultaneously affected by the sampling time and the accuracy of the small-bias method. The observation matrix... Discretization is unaffected by sampling time and depends only on linearization accuracy. Therefore, the linearization accuracy for small deviations depends only on the accuracy of the observation matrix.

[0079]

[0080] Step B: Construct a Transformer time series prediction model incorporating a self-attention mechanism, inputting one-dimensional data. Linearized parameter sequence for predicting future times And reconstruct it into the form of state matrix and observation matrix. This paper introduces the Transformer time series model and utilizes its self-attention mechanism to model the flattened linearized parameter sequence. This effectively captures the long-range dependencies and nonlinear dynamic characteristics of parameter changes between different time steps, thereby achieving high-precision prediction. The Transformer time series prediction model includes a relative position encoding layer, two attention layers, and a prediction layer with two hidden layers to achieve output dimensionality reduction. ReLU function is used for nonlinear activation. The calculation formula for the attention layer is as follows:

[0081] ,

[0082] Step C: Under a single operating condition, the change in the control variable. The linearized model expression for single-step prediction after discretization is zero is as follows:

[0083]

[0084] in, , , These are single-step predictions, and the goal is to fit the state variable data and the observed variable data. , . , To correspond to the steady-state values ​​of the engine operating conditions, so as to ensure that the engine's physical constraints are met;

[0085] Step D: Then use the matrix form obtained from the model prediction. Nonlinear system simulation data The loss function is constructed by combining the single-step prediction linearization model as follows:

[0086]

[0087] in, The weights assigned to different loss terms, Used to describe the data loss of the Transformer time series forecasting model.

[0088] Step E: Build a Transformer time series prediction model by combining the loss function, such as... Figure 3 As shown. The overall training model is as follows. Figure 1 See the table below for details.

[0089] The model training settings are as follows: The Transformer model uses two attention layers and a standard neural network with two hidden layers. The activation function is ReLU, a custom multivariate loss function is used, the Adams optimizer is employed, and the learning rate is 0.005. The runtime environment is as follows: CPU: Core i5-10400F @ 2.90GHz; RAM: 16GB; GPU: GTX1660; Programming language: Python 3.6; TensorFlow 2.0. After model convergence, the final linearized model prediction is obtained. .

[0090] Overall parameters of the model

[0091]

[0092] In a preferred embodiment of the linearized mathematical modeling method for liquid rocket engines, step A includes:

[0093] Step A1: Simulate the liquid rocket engine under 100% operating conditions using a nonlinear mathematical model of the liquid oxygen / liquid hydrogen rocket engine. The model is expressed as follows:

[0094]

[0095] In the input Under the influence of this action, the model converges to the operating point 0. Add a small perturbation to the input of the original nonlinear system The model reconverged to the operating point 1. The state variables, input variables, and observation variables collected at different operating points are used as the training dataset for the entire algorithm.

[0096] Step A2: Construct a linearized model using the small deviation method, as shown in the following equation:

[0097]

[0098] in, , m represents the number of sensors selected from the model, and n represents the number of state variables selected from the model.

[0099] Step A3: Replace the continuous derivative with the discrete partial derivative to obtain the following equation:

[0100]

[0101] This allows us to obtain the linearized model parameter matrix at different time points under operating point 0. t represents different points in time.

[0102] Step A4: Linearize the model Expand by row and concatenate to obtain one-dimensional data. .

[0103] In a preferred embodiment of the linearized mathematical modeling method for liquid rocket engines, the small perturbation is a set of random small-amplitude input perturbations around 100% rated operating conditions, used to generate a training dataset covering different local operating points.

[0104] In a preferred embodiment of the linearized mathematical modeling method for liquid rocket engines, the Adams optimization algorithm is used to update the trainable parameters of the model, and the learning rate of 0.05 can be dynamically adjusted.

[0105] In a preferred embodiment of the linearized mathematical modeling method for liquid rocket engines, the nonlinear mathematical model is a multivariable nonlinear dynamic model of the liquid oxygen / liquid hydrogen liquid rocket engine of the Space Shuttle main engine.

[0106] A system for performing the method includes:

[0107] The simulation module performs simulations based on a nonlinear mathematical model of a liquid rocket engine, injects disturbances using a small-deviation method, and obtains linearization parameters by combining the discrete linearization calculation formula. Finally, it is flattened into one-dimensional data. To perform time series forecasting;

[0108] The building block constructs a Transformer time series prediction model that incorporates a self-attention mechanism, taking one-dimensional data as input. Linearized parameter sequence for predicting future times And reconstruct it into matrix form. The Transformer time series prediction model includes a relative position encoding layer, two attention layers, and a prediction layer with two hidden layers. It uses the ReLU function for non-linear activation, and the calculation formula for the attention layer is as follows:

[0109] ,

[0110] The linearized model expression for the discrete module and its single-step prediction is as follows:

[0111]

[0112] in, , , These are single-step predictions, and the goal is to fit the target value. , ;

[0113] The loss module is then used in matrix form. Nonlinear system data The loss function is constructed by combining the single-step prediction linearization model as follows:

[0114]

[0115] in, The weights assigned to different loss terms, Used to describe the data loss of the Transformer time series forecasting model.

[0116] The training module uses a loss function to build a Transformer time series prediction model, trains the model, and after convergence, the final linearized model prediction is obtained. .

[0117] A computer storage medium including computer instructions that, when run on a computer, cause the computer to perform the method.

[0118] An electronic device, the electronic device comprising:

[0119] Memory, processor, and computer programs stored in memory and executable on the processor, wherein,

[0120] The processor implements the method when executing the program.

[0121] In one embodiment, such as Figure 1 The diagram shows the overall process of a high-precision linearization method for a nonlinear model of a liquid rocket engine, proposed in this invention, which integrates a physical information neural network with a self-attention mechanism. The following is an example of the linearization of the nonlinear mathematical model of the SSME liquid oxygen-liquid hydrogen rocket engine, and the specific implementation includes the following steps:

[0122] Step A: First, simulation is performed based on the existing mathematical model of the liquid rocket engine. Perturbations are injected using the small deviation method, and the linearization parameters are obtained by combining the discrete linearization calculation formula. Finally, it is flattened into one-dimensional data. To perform time series forecasting.

[0123] The specific steps of step A are as follows:

[0124] Step A1: Simulate the liquid rocket engine under 100% operating conditions using the existing SSME liquid oxygen / liquid hydrogen rocket engine mathematical model. Figure 2 . Figure 2 The following is an explanation in Table 1. The diagram on the right shows three types of connecting pipes and one rigid connection. Taking HPOT and HPOP as examples, the high-pressure oxygen turbine and high-pressure oxygen pump are rigidly connected. The rest are connected by pipes, including oxygen feed lines, fuel lines, and fuel gas lines.

[0125] Table 1

[0126]

[0127] The model can be expressed as follows:

[0128]

[0129] First, for the SSME nonlinear system, at the input Under this effect, the model will converge to the operating point 0. To obtain the changes in both the state and observed variables and improve the generalization performance of the model, a small perturbation is added to the input of the original nonlinear system. At this point, the model will reconverge to operating point 1. Meanwhile, this paper will collect state variables, input variables, and observed variables from different operating points, namely... , This serves as the training dataset for the entire algorithm.

[0130] Step A2: Construct a linearized model using the small deviation method, as shown in the following equation:

[0131]

[0132] in, , m is the number of sensors selected from the model, and n is the number of state variables selected from the model.

[0133] Step A3: By replacing the continuous derivative with the discrete partial derivative, we can obtain the following equation:

[0134]

[0135] This allows us to obtain the linearized model parameter matrix at different time points under operating point 0. t represents different points in time.

[0136] Step A4: Linearize the model Expand by row and concatenate to obtain one-dimensional data. .

[0137] Step B: Process the obtained parameter matrix The Transformer time series model is applied for prediction to obtain... And reconstruct it into matrix form. The Transformer time series model architecture used is as follows: Figure 3 As shown, it includes a relative position encoding layer, two attention layer layers, and a prediction layer with two hidden layers, using the ReLU function to achieve non-linear activation. The calculation formula for the attention layer is:

[0138]

[0139] Step C: Under a single operating condition, the change in the control quantity is zero. Therefore, the optimized linearized model expression for the discrete single-step prediction can be derived as follows:

[0140]

[0141] in, , , These are single-step predictions, and the goal is to fit the target value. , .

[0142] Step D: Then, use the linearized model predicted by the time series model. Nonlinear system data The loss function is constructed by combining the single-step prediction linearization model as follows:

[0143]

[0144] in, The weights assigned to different loss terms, This describes the data loss of the Transformer time series forecasting model.

[0145] Step E: As Figure 4 As shown, this invention combines the loss function of step D to build the network model in step B, trains the model, and after the model converges, the final linearized model predicted by the model is obtained. This is the final high-precision linearized model of the algorithm. The Adams optimization algorithm is used to update the trainable parameters of the model, with a learning rate of 0.05 that can be dynamically adjusted. The operating environment is as follows: CPU: Core i5-10400F @ 2.90GHz; RAM: 16GB; GPU: GTX1660; Programming language: Python 3.9; TensorFlow 2.0.

[0146] Furthermore, this invention utilizes small-deviation linearization and discrete partial derivative calculation to provide an initial parameter sequence for a locally linear approximation of complex nonlinear systems. However, its accuracy is limited by the linear assumption of the operating point neighborhood, and it is difficult to capture the nonlinear evolution of parameters during the system's dynamic process. Therefore, this invention introduces the Transformer time series model, using its self-attention mechanism to model the flattened linearized parameter sequence. This effectively captures the long-range dependencies and nonlinear dynamic characteristics of parameter changes between different time steps, thereby achieving high-precision prediction and interpolation.

[0147] More importantly, purely data-driven predictions may violate the fundamental dynamic constraints of physical systems. Therefore, this invention innovatively embeds physical information constraints: the loss term forces the neural network to strictly follow the inherent physical evolution laws of the system while learning data patterns, ensuring that the obtained linearized model not only has high fitting accuracy but also good physical interpretability and extrapolation stability.

[0148] In summary, this technical approach overcomes the shortcomings of traditional Taylor expansion methods, such as computational complexity, weak generalization ability, and lack of physical consistency, by deeply integrating a triple mechanism of "data-driven modeling + physical law constraints + temporal dynamic perception". While significantly reducing the complexity of engineering implementation, it realizes the construction of a high-fidelity, real-time linearized mathematical model of the nonlinear system of liquid rocket engines over a wide range of operating conditions, laying a reliable model foundation for subsequent tasks such as health monitoring, robust control, and fault diagnosis.

[0149] Although embodiments of the present invention have been described above in conjunction with the accompanying drawings, the present invention is not limited to the specific embodiments and application fields described above. The specific embodiments described above are merely illustrative and instructive, and not restrictive. Those skilled in the art can make many other forms based on the guidance of this specification and without departing from the scope of protection of the claims of the present invention, and all of these are within the scope of protection of the present invention.

Claims

1. A linearized mathematical modeling method for liquid rocket engines, characterized in that, Includes the following steps: Step A: Simulation is performed based on the nonlinear mathematical model of the liquid rocket engine, and perturbations are injected according to the small deviation method. The linearization parameters are obtained by combining the discrete linearization calculation formula. Finally, it is flattened into one-dimensional data. To perform time series forecasting; Step B: Construct a Transformer time series prediction model incorporating a self-attention mechanism, inputting one-dimensional data. Linearized parameter sequence for predicting future times And reconstruct it into matrix form. The Transformer time series prediction model includes a relative position encoding layer, two attention layers, and a prediction layer with two hidden layers. It uses the ReLU function for non-linear activation. The formula for calculating the attention layer between the sequence at time step k and other sequences is as follows: ； Step C: Under a single operating condition, the change in control quantity is zero. The linearized model expression for single-step prediction after discretization is as follows: ； in, , , These are single-step predictions, and the goal is to fit the target value. , ; Step D: Then use matrix form Nonlinear system data The loss function is constructed by combining the single-step prediction linearization model as follows: ； in, The weights assigned to different loss terms, , Used to describe the data loss of the Transformer time series forecasting model. Step E: Build a Transformer time series prediction model using the loss function, train the model, and after convergence, obtain the final linearized model prediction. .

2. The linearized mathematical modeling method for liquid rocket engines according to claim 1, characterized in that, Preferably, step A includes: Step A1: Simulate the liquid rocket engine under 100% operating conditions using a nonlinear mathematical model of the liquid oxygen / liquid hydrogen rocket engine. The model is expressed as follows: x is the state variable, u is the input variable, y is the observation variable, f is the nonlinear state equation, and h is the nonlinear observation equation. ； In the initial input Under the influence of this action, the model converges to the operating point 0. Add a small perturbation to the input of the original nonlinear system The model reconverged to the operating point 1. The state variables, input variables, and observation variables collected at different operating points are used as the training dataset for the entire algorithm. Step A2: Construct a linearized model using the small deviation method, as shown in the following equation: ； in, , m represents the number of sensors selected from the model, and n represents the number of state variables selected from the model. Step A3: Replace the continuous derivative with the discrete partial derivative to obtain the following equation: ； Therefore, the linearized model parameter matrix at different time points under operating point 0 can be obtained. t represents different points in time. Step A4: Linearize the model Expand the data row by row and then concatenate them to obtain one-dimensional data. .

3. The linearized mathematical modeling method for liquid rocket engines according to claim 2, characterized in that, The small perturbation consists of multiple sets of random small-amplitude input perturbations around 100% rated operating conditions, used to generate a training dataset covering different local operating points.

4. The linearized mathematical modeling method for liquid rocket engines according to claim 1, characterized in that, The Adams optimization algorithm is used to update the model's trainable parameters, with a learning rate of 0.05 that can be dynamically adjusted.

5. The linearized mathematical modeling method for liquid rocket engines according to claim 1, characterized in that, The nonlinear mathematical model is a multivariable nonlinear dynamic model of the liquid oxygen / liquid hydrogen liquid rocket engine of the Space Shuttle main engine.

6. A system for performing the method as described in any one of claims 1-5, characterized in that, It includes: The simulation module performs simulations based on a nonlinear mathematical model of a liquid rocket engine, injects disturbances using a small-deviation method, and obtains linearization parameters by combining the discrete linearization calculation formula. Finally, it is flattened into one-dimensional data. To perform time series forecasting; The building block constructs a Transformer time series prediction model that incorporates a self-attention mechanism, taking one-dimensional data as input. Linearized parameter sequence for predicting future times And reconstruct it into matrix form. The Transformer time series prediction model includes a relative position encoding layer, two attention layers, and a prediction layer with two hidden layers. It uses the ReLU function for non-linear activation, and the calculation formula for the attention layer is as follows: ； The linearized model expression for the discrete module and its single-step prediction is as follows: ； in, , , These are single-step predictions, and the goal is to fit the target value. , ; The loss module is then used in matrix form. Nonlinear system data The loss function is constructed by combining the single-step prediction linearization model as follows: ； in, The weights assigned to different loss terms, Used to describe the data loss of the Transformer time series forecasting model. ; The training module uses a loss function to build a Transformer time series prediction model, trains the model, and after convergence, the final linearized model prediction is obtained. .

7. A computer storage medium, characterized in that, The storage medium includes computer instructions that, when executed on a computer, cause the computer to perform the method as described in any one of claims 1-5.

8. An electronic device, characterized in that, The electronic device includes: Memory, processor, and computer programs stored in memory and executable on the processor, wherein, When the processor executes the program, it implements the method as described in any one of claims 1-5.

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