Gradient-enhanced response surface model based method for calculating interior ballistic performance

Abstract

The application provides a gradient-enhanced response surface model-based internal ballistic performance calculation method, which comprises the following steps: determining the end time of the ascending section according to an experimental curve, and then calculating the pressure-time curve of the engine by using a zero-dimensional internal ballistic calculation model; and obtaining a second curve of the standard stable section and the descending section according to the end time of the ascending section. By selecting key time nodes in the ascending section, a second-order polynomial response surface model is constructed with the measured parameters as the input and the gradient information as the constraint, so that the pressure curve of the ascending section is quickly and accurately predicted. Finally, the ascending section curve and the second curve are combined to form the internal ballistic performance curve of the solid engine. The application can improve the accuracy of the ascending section prediction under the condition of small samples and the consistency of the physical trend while maintaining the calculation efficiency, and provides effective support for the reliable evaluation and safe design of the internal ballistic performance of the solid engine.

Description

Technical Field

[0001] This invention generally relates to the field of solid rocket motor technology, and specifically to a method for calculating internal ballistic performance based on a gradient-enhanced response surface model. Background Technology

[0002] Accurate prediction of the ballistic performance of solid rocket motors is crucial for ensuring their structural safety and reliable operation. During the ignition ascent phase, transient effects such as propellant erosion and uneven flame propagation cause the combustion chamber pressure to rise rapidly and fluctuate dramatically, making accurate prediction difficult. Significant prediction errors can lead to critical structures like the engine casing being subjected to loads exceeding design limits, impacting system safety. Furthermore, uncertainties such as propellant variations and ambient temperature further complicate prediction.

[0003] Currently, the following methods are mainly used in engineering to predict the performance of the rising segment: The Kriging model-based approach treats pressure changes as a Gaussian stochastic process and makes predictions by establishing a statistical mapping relationship between the data set and the pressure response. The steps include: discretizing the experimental pressure curve into segments, establishing Kriging models at each time point and optimizing hyperparameters, and finally combining them to form a time-series surrogate model.

[0004] The method based on the classical polynomial response surface model uses an explicit polynomial to describe the mapping relationship between variables and pressure. Specifically, the rising segment is extracted and discretized into several time nodes. A second-order polynomial model is constructed at each node, and the coefficients are fitted using the least squares method. Finally, the predicted values ​​at each node are connected to form a complete curve.

[0005] However, existing technologies have significant drawbacks: the Kriging method requires kernel function selection, hyperparameter optimization, and dense matrix operations during training, which is computationally complex and time-consuming, making it difficult to meet the requirements of efficient design. Although the polynomial response surface methodology is computationally simple, its coefficient solution relies solely on fitting discrete pressure values, without introducing gradient information reflecting the physical change trend as a constraint. This leads to the predicted curve easily deviating from the actual process under small sample sizes, making it difficult to capture the rapid changes in the rising phase, and resulting in insufficient consistency between prediction accuracy and trend.

[0006] Therefore, there is an urgent need for a method to predict the performance of the internal ballistic ascent phase that can maintain efficient computation and utilize gradient information to improve accuracy and trend consistency. Summary of the Invention

[0007] In view of the above-mentioned defects or deficiencies in the existing technology, it is desirable to provide a method for calculating internal ballistic performance based on the gradient-enhanced response surface model.

[0008] This invention provides a method for calculating internal ballistic performance based on a gradient-enhanced response surface model; the pressure variation curve of the solid rocket motor combustion chamber over time starts from the initial moment and includes an ascending segment, a steady segment, and a descending segment; The methods include: S1: Obtain the end time of the normalized rising segment; S2: Acquire the data set of the solid rocket motor; the data set includes: propellant density, combustion area, burning rate coefficient, gas pressure index, nozzle throat cross-sectional area, characteristic velocity, and combustion chamber free volume; S3: Input the data set into the zero-dimensional internal ballistic calculation model, and calculate the second curve representing the stable segment and descent segment of the solid rocket motor's internal ballistic trajectory based on the end time of the ascent segment; the zero-dimensional internal ballistic calculation model is used to calculate the pressure change curve of the solid rocket motor's combustion chamber over time based on the data set; S4: Select N time nodes from the initial time to the end time of the rising segment; the time nodes include the initial time and the end time of the rising segment; S5: Based on the data set, a second-order polynomial response surface model and gradient constraints are used to optimize the polynomial coefficients. Then, based on the second curve, the rising segment curves of the solid rocket motor combustion chamber pressure at N time nodes are calculated. S6: Plot the rising segment curve and the second curve in the same coordinate system to obtain the internal ballistic performance curve of the solid rocket motor.

[0009] According to the technical solution provided by the present invention, obtaining the end time of the normalized rising segment includes: S1-1: Obtain the first curve obtained from the experiment and normalized to represent the change of pressure in the combustion chamber of the solid rocket motor over time; the horizontal axis of the first curve represents time, and the vertical axis represents pressure. S1-2: Extract the end time of the pressure rise segment in the solid rocket motor combustion chamber based on the first curve.

[0010] According to the technical solution provided by the present invention, extracting the end time of the pressure rise segment in the combustion chamber of a solid rocket motor based on the first curve includes: S1-2-1: Obtain the maximum pressure value in the first curve; S1-2-2: Extract multiple horizontal axis coordinates from the first curve corresponding to the points where the pressure is equal to the maximum pressure value by a set multiple; S1-2-3: Take the smallest horizontal axis coordinate among multiple horizontal axis coordinates as the end time of the rising segment.

[0011] According to the technical solution provided by the present invention, the data set is input into a zero-dimensional internal ballistic calculation model, and a second curve characterizing the stable segment and descent segment of the solid rocket motor's internal ballistic trajectory is calculated based on the end time of the ascent segment, including: The dataset is input into a zero-dimensional internal ballistic calculation model to calculate a third curve that characterizes the pressure in the combustion chamber of a solid rocket motor when the gas flow velocity in the combustion chamber is below the velocity threshold. Discard the portion of the third curve between the initial time and the end time of the rising segment, and use the remaining portion as the second curve.

[0012] According to the technical solution provided by the present invention, the method for selecting N time nodes in the time period between the initial time and the end time of the rising segment includes: The initial time is taken as the first time node, and the end time of the rising segment is taken as the Nth time node; The second to the (N-1)th time nodes are selected at equal intervals; or, multiple extreme points of the rising segment in the first curve are sequentially used as the second to the (N-1)th time nodes.

[0013] According to the technical solution provided by the present invention, based on the data set, a second-order polynomial response surface model and gradient constraints are used to optimize the polynomial coefficients. Then, based on the second curve, the rising segment curves of the solid rocket motor combustion chamber pressure corresponding to N time nodes are calculated, including: S5-1: Construct a second-order polynomial response surface model; the input of the second-order polynomial response surface model is the dataset and simulation data, and the output is the pressure value at each time point; S5-2: Input the data set into the second-order polynomial response surface model to calculate the pressure values ​​corresponding to the first N-1 time nodes, and obtain the pressure values ​​of the first N-1 rising segments; S5-3: Take the pressure value at the end of the rising segment of the second curve as the pressure value corresponding to the Nth time node to obtain the pressure value at the end of the rising segment. S5-4: Based on the pressure values ​​of the first N-1 rising segments and the pressure value at the end of the rising segment, the rising segment curve of the solid rocket motor combustion chamber pressure change with time is obtained.

[0014] According to the technical solution provided by the present invention, the process of constructing a second-order polynomial response surface model includes: S5-1-1: Construct an initial response surface model; the input of the initial response surface model is a dataset and simulation data, and the output is the pressure values ​​at multiple time points, and includes multiple unknown polynomial coefficients; S5-1-2: Construct the objective optimization function based on the initial response surface model; S5-1-3: Based on the objective optimization function, an optimization algorithm is used to optimize the coefficients of multiple polynomials to obtain the optimal polynomial coefficients; S5-1-4: Substitute the optimal polynomial coefficients into the initial response surface model to obtain a second-order polynomial response surface model.

[0015] According to the technical solution provided by the present invention, in the process of optimizing multiple polynomial coefficients using an optimization algorithm, the gradient information of the first curve is used as a constraint condition to solve the polynomial coefficients in the iterative process, thereby accelerating the convergence of the optimization algorithm.

[0016] The beneficial effects of this invention are as follows: To address the problems of computational complexity and insufficient accuracy and trend consistency in existing solid rocket motor internal ballistic prediction methods, this invention proposes a hybrid prediction method integrating experimental data and a physical model. This method first determines the end time of the ascent phase based on experimental curves, then calculates the stationary and descent phase curves using a zero-dimensional internal ballistic model. Based on this, by selecting key time nodes within the ascent phase, a second-order polynomial response surface model is constructed, using measured parameters as input and gradient information as constraints, thereby achieving rapid and high-precision prediction of the ascent phase pressure curve. Finally, the ascent phase curve and the second curve are combined to form the solid rocket motor internal ballistic performance curve. This invention significantly improves the accuracy and physical trend consistency of ascent phase prediction under small sample conditions while maintaining computational efficiency, providing effective support for the reliable evaluation and safe design of solid rocket motor internal ballistic performance. Attached Figure Description

[0017] Other features, objects, and advantages of the invention will become more apparent from the following detailed description of non-limiting embodiments with reference to the accompanying drawings: Figure 1 This is a flowchart illustrating the internal ballistic performance calculation method based on the gradient-enhanced response surface model. Detailed Implementation

[0018] The present invention will now be described in further detail with reference to the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are merely illustrative of the invention and not intended to limit it. Furthermore, it should be noted that, for ease of description, only the parts relevant to the invention are shown in the accompanying drawings.

[0019] It should be noted that, unless otherwise specified, the embodiments and features described in the present invention can be combined with each other. The present invention will now be described in detail with reference to the accompanying drawings and embodiments.

[0020] refer to Figure 1This invention provides a method for calculating internal ballistic performance based on a gradient-enhanced response surface model. The pressure variation curve of the solid rocket motor combustion chamber over time starts from the initial moment and includes an upward segment, a steady segment, and a downward segment.

[0021] To address the aforementioned technical problems beyond just data-level solutions, this embodiment incorporates the following steps into a computer system, utilizing the computer system to complete these steps and thus resolve issues arising under real-world conditions. Therefore, all steps of the method in this embodiment are executed by the computer system, including: S1: Obtain the end time of the normalized rising segment, including: S1-1: Obtain the first curve obtained from the experiment and normalized to represent the change of pressure in the combustion chamber of the solid rocket motor over time; the horizontal axis of the first curve represents time, and the vertical axis represents pressure. The specific experimental procedure is as follows: The solid rocket motor is installed in a fixed device on the ground, and the propellant inside the motor is ignited to generate thrust. The pressure change between the fixed device and the solid rocket motor over time is then measured and normalized to obtain the first curve.

[0022] It should be noted that the pressure change curve measured under experimental conditions will not be exactly the same as the pressure change curve of a solid rocket motor under actual flight conditions, but the pressure change trend is the same. Therefore, this embodiment considers first determining the end time of the ascent phase based on experimental data, then calculating the ascent phase curve, as well as the curves of the steady phase and descent phase, using two different methods respectively, and finally stitching the curves together to form the internal ballistic performance curve of the solid rocket motor.

[0023] Based on the above approach, while maintaining computational efficiency, the accuracy and consistency of the ascent phase prediction under small sample conditions are improved, providing effective support for the reliable evaluation and safe design of the internal ballistic performance of solid rocket motors.

[0024] S1-2: Extract the end time of the pressure rise segment in the solid rocket motor combustion chamber based on the first curve, including: S1-2-1: Obtain the maximum pressure value in the first curve; S1-2-2: Extract multiple horizontal axis coordinates from the first curve corresponding to the points where the pressure is equal to the maximum pressure value by a set multiple; S1-2-3: Take the smallest horizontal axis coordinate among multiple horizontal axis coordinates as the end time of the rising segment.

[0025] Specifically, the multiplier is set at 0.9.

[0026] Because existing prediction methods have large errors in predicting the pressure during the ascent phase, while the errors in predicting the pressure during the steady and descent phases are smaller, this embodiment adopts a unique segmented prediction method. Different methods are used to predict the pressure during the ascent phase, as well as the steady and descent phases, and then the results are finally spliced ​​together to form the internal ballistic performance curve of the solid rocket motor.

[0027] Studies have shown that from the initial moment, the pressure initially increases rapidly, reaches its first peak, and then decreases significantly with fluctuations. The pressure then stabilizes at around 80% of the initial peak pressure for a period of time, followed by a slight increase before rapidly decreasing to zero. The entire process can be roughly divided into an upward phase, a stable phase, and a downward phase.

[0028] However, existing technologies do not predict the pressure curves of each segment separately, thus lacking a unified method for accurately dividing the rising, stable, and falling segments for segmented prediction. In this embodiment, the first curve obtained from the experiment is used as a reference to extract the end time of the rising segment, so as to accurately segment the segments and predict the pressure change curve of each segment over time.

[0029] S2: Acquire a set of data during the flight or test of the solid rocket motor; the set of data includes: propellant density, combustion area, burning rate coefficient, gas pressure index, nozzle throat cross-sectional area, characteristic velocity, and combustion chamber free volume; In this embodiment, the methods for collecting each parameter in the dataset include: Propellant density: Usually provided by the propellant manufacturer or obtained through standard physical measurement methods such as hydrostatic weighing, it is an inherent physical property parameter of the propellant.

[0030] Combustion area: Based on the geometric configuration (such as star-shaped, tubular, etc.) of the solid propellant grain design drawings, it is obtained by calculating the instantaneous or average area of ​​the combustion surface of the propellant grain and is a structural design parameter of the engine.

[0031] Burning rate coefficient and gas pressure index: These are obtained through propellant burning rate measurement experiments. Typically, in a standard experimental engine (such as a target line engine), the linear burning rate of the propellant is measured under different operating pressures, and then fitted according to the burning rate law to obtain the burning rate coefficient and pressure index of the propellant formulation.

[0032] The cross-sectional area of ​​the nozzle throat is determined directly based on the design dimensions of the engine nozzle throat. For nozzles with a fixed throat diameter, this value is a constant; for nozzles with ablation-prone throat liners or adjustable nozzles with nozzle needles, the instantaneous or equivalent throat area under design conditions can be used.

[0033] Characteristic velocity: This is a comprehensive reflection of the propellant's energy characteristics, usually obtained through thermodynamic calculations of the propellant or through data from ground experiments (measuring the average pressure during steady-state operation). throat area and mass flow rate Using the formula The result is obtained by reverse engineering and used as a known input parameter.

[0034] Combustion chamber free volume: refers to the initial gas phase space volume within the combustion chamber not occupied by the propellant grain. It can be calculated based on the difference between the internal geometric dimensions of the engine combustion chamber and the initial volume of the propellant grain, and serves as a structural design parameter for the engine.

[0035] S3: Input the data set into the zero-dimensional internal ballistic calculation model, and calculate the second curve representing the stable segment and descent segment of the solid rocket motor's internal trajectory based on the end time of the ascent segment, including: The dataset is input into a zero-dimensional internal ballistic calculation model to calculate a third curve that characterizes the pressure in the combustion chamber of a solid rocket motor when the gas flow velocity in the combustion chamber is below the velocity threshold. Discard the portion of the third curve between the initial time and the end time of the rising segment, and use the remaining portion as the second curve.

[0036] Specifically, the flow velocity threshold is 15 m / s. The zero-dimensional internal ballistic calculation model is used to calculate the pressure variation curve of the solid rocket motor combustion chamber over time based on the dataset.

[0037] For engines where the combustion gas flow velocity within the combustion chamber is below a velocity threshold, a zero-dimensional internal ballistic calculation model can be used to solve for the combustion chamber pressure. The fundamental differential equation for calculating the combustion chamber pressure over time using the zero-dimensional internal ballistic calculation model is:

[0038] in, t For time, The combustion chamber pressure, For propellant density, For the burning area, This is the combustion rate coefficient. This refers to the gas pressure index. This refers to the cross-sectional area of ​​the nozzle throat. Characteristic velocity, This refers to the free volume of the combustion chamber. For specific heat ratio The function is calculated using the following formula:

[0039] By inputting the collected data set into the zero-dimensional internal ballistic calculation model and discarding the curve before the end of the ascent phase, a second curve representing the stable and descent phases of the solid rocket motor's internal ballistic trajectory can be obtained.

[0040] This embodiment fully leverages the advantages of the zero-dimensional model in terms of high prediction accuracy and fast computational efficiency during the stable combustion phase, providing a reliable and physically meaningful benchmark for the latter half of the entire ballistic curve. Simultaneously, by discarding the model's calculation results in the ascent phase (which typically suffers from significant deviations due to transient effects) and combining them with subsequent dedicated prediction methods for the ascent phase, a hybrid prediction strategy of "segmented processing and complementary advantages" is achieved.

[0041] S4: Select N time nodes from the initial time to the end time of the rising segment; the time nodes include the initial time and the end time of the rising segment; The specific methods of step S4 include: The initial time is taken as the first time node, and the end time of the rising segment is taken as the Nth time node; The second to the (N-1)th time nodes are selected at equal intervals; or, multiple extreme points of the rising segment in the first curve are sequentially used as the second to the (N-1)th time nodes.

[0042] In the first implementation, the method of selecting the 2nd to N-1th time nodes at equal intervals is suitable for cases where there are few extreme values ​​in the rising segment of the first curve; that is, the ratio of the number of extreme values ​​to the duration of the rising segment is less than or equal to 1 (unit: 1 / millisecond).

[0043] For example, if the duration of the rising segment is 30 milliseconds and the number of extreme values ​​in the rising segment of the first curve is less than 30, then an equal-interval selection method is used.

[0044] In this case, the number of selected time points is greater than or equal to the value when the rise segment duration is in milliseconds, and less than or equal to twice the value when the rise segment duration is in milliseconds. Following the example above, at least 30 and at most 60 time points should be selected.

[0045] In the second embodiment, the method of taking multiple extreme points of the rising segment in the first curve as the 2nd to N-1th time nodes in sequence is applicable to the case where there are many extreme points in the first curve; that is, the ratio of the number of extreme points to the value of the rising segment duration in milliseconds is greater than 1 (unit: 1 / millisecond).

[0046] When there are many extreme values ​​in the rising segment of the first curve, simply selecting values ​​at equal intervals is insufficient to accurately reflect the fluctuation state of multiple extreme values; conversely, shortening the selection interval to increase the number of selections also makes it difficult to guarantee that each time point is exactly at an extreme point. Therefore, selecting time points based on the number of extreme points in the rising segment of the first curve can more accurately reflect the fluctuation state of multiple extreme values. Based on this approach, the fluctuation state of the pressure value in the rising segment is first determined, and then combined with subsequent optimization of the pressure value, so that the final rising segment curve is closer to the rising segment curve in actual flight.

[0047] S5: Based on the aforementioned dataset, a second-order polynomial response surface model and the gradient constraints of the first curve are used to optimize the polynomial coefficients. Then, based on the second curve, the rising segment curves of the solid rocket motor combustion chamber pressure corresponding to N time nodes are calculated, including: S5-1: Construct a second-order polynomial response surface model; the input of the second-order polynomial response surface model is a data set, and the output is the pressure value at each time node; Step S5-1 includes: S5-1-1: Construct an initial response surface model; the input of the initial response surface model is a dataset, and the output is the pressure values ​​at multiple time points, and it contains multiple unknown polynomial coefficients; The mathematical form of the initial response surface model is as follows:

[0048] in, Indicates time node Predicted pressure values; The vector representation of the polynomial coefficients, b j = x= This indicates the main factors affecting solid rocket motors. This indicates the number of parameters contained in the data set.

[0049] S5-1-2: Construct the objective optimization function based on the initial response surface model; S5-1-3: Based on the objective optimization function, an optimization algorithm is used to optimize the coefficients of multiple polynomials to obtain the optimal polynomial coefficients; Furthermore, during the optimization process of finding the multiple polynomial coefficients using the optimization algorithm, the gradient information of the first curve is used as a constraint condition to solve the polynomial coefficients in the iterative process, thereby accelerating the convergence of the optimization algorithm.

[0050] Specifically, the polynomial coefficients of traditional response surface models are usually solved using the least squares method. The least squares method only focuses on the fitting accuracy for a single data point and does not consider the gradient constraint information between data points. Therefore, it is difficult to guarantee the consistency between the predicted curve and the actual ignition process in the case of small samples.

[0051] To ensure that the predicted rising curve better reflects the actual ignition process, this invention proposes a coefficient solution method with gradient constraints. This method uses the gradient information from experimental data as a constraint to solve for the polynomial coefficients. This coefficient solution optimization method can be expressed as:

[0052] in, Vector representation of a polynomial; For the rising segment Each time point A vector composed of measured pressure values; and These represent the first and second ascending segments, respectively. Measured and predicted pressure values ​​at each time point, and the measured pressure value at the initial time corresponding to the time point. and predicted pressure value All are 0; and They represent the first The time span between each time point and the first and last time points.

[0053] Measured pressure value at the last time point and predicted pressure value Take the first pressure value of the steady segment and the pressure value at the end of the ascending segment calculated in the zero-dimensional internal trajectory.

[0054] The optimization algorithm described above, which optimizes the polynomial coefficients, is subject to constraints, all of which are strong. These constraints may cause the optimization algorithm to fail to converge during the solution process. To facilitate numerical computation, this embodiment uses a weighted method to transform it into an unconstrained optimization problem.

[0055] The search range is set with the lower limit set to 0 and the upper limit set to 1.1 times the maximum pressure value in the first curve.

[0056] Based on the above methods, the objective optimization function Represented as:

[0057] about Differentiation yields the derivative function:

[0058] in, Optimize the function for the objective. It is a polynomial vector.

[0059] Setting the above expression to 0, we get Numerical solution:

[0060] By substituting the data from the pressure-time curve obtained in the experiment and the data from the zero-dimensional internal ballistic simulation into the above formula, the polynomial coefficients can be obtained to complete the construction of the surrogate model.

[0061] Where C1 and C2 are the coefficients in the derivative function, and are represented by the following formulas:

[0062]

[0063] Based on the above method, the polynomial coefficients that satisfy the objective optimization function being equal to 0 are the optimal solution. Substituting them into the initial response surface model yields a second-order polynomial response surface model suitable for pressure prediction of the current model of solid rocket motor.

[0064] S5-1-4: Substitute the optimal polynomial coefficients into the initial response surface model to obtain a second-order polynomial response surface model.

[0065] By introducing gradient information from experimental curves as strong constraints, the traditional least squares method effectively overcomes the shortcomings of only fitting discrete points and ignoring physical change trends, and significantly improves the consistency between the predicted curve and the actual ignition process under small sample conditions.

[0066] A weighted approach is used to transform a strongly constrained optimization problem into an easily solvable unconstrained form. While strictly maintaining the gradient guidance direction, this avoids convergence difficulties and numerical instability issues during the optimization process. Mathematically, this modeling and solution strategy ensures that the model possesses both the efficiency of polynomial computation and incorporates the gradient constraints of physical laws, thereby achieving simultaneous and accurate capture of the "form and potential" of pressure changes during the ascending phase.

[0067] S5-2: Input the data set into the second-order polynomial response surface model to calculate the pressure values ​​corresponding to the first N-1 time nodes, and obtain the pressure values ​​of the first N-1 rising segments; S5-3: Take the pressure value at the end of the rising segment of the second curve as the pressure value corresponding to the Nth time node to obtain the pressure value at the end of the rising segment. S5-4: Based on the pressure values ​​of the first N-1 rising segments and the pressure value at the end of the rising segment, the rising segment curve of the solid rocket motor combustion chamber pressure change with time is obtained.

[0068] In this embodiment, the multiple time points are arranged in chronological order.

[0069] Since the obtained rising and steady segments need to be connected with the falling segment, in order to ensure the continuity of the entire curve after the connection, it is necessary to ensure that the pressure at the end of the rising segment is equal to the pressure at the beginning of the steady segment.

[0070] To meet the above conditions, this embodiment only predicts the pressure values ​​of the first N-1 rising segments, while making the pressure value of the Nth rising segment directly equal to the pressure at the beginning of the steady segment, so as to ensure the continuity of the curve.

[0071] Specifically, the pressure values ​​of the first N-1 rising segments and the pressure value at the end of the rising segment are connected sequentially by straight lines according to the time sequence to form the rising segment curve.

[0072] In this embodiment, since the duration of the rising segment is short, about 30 milliseconds, and according to the setting method of the time nodes mentioned above, there will be no peak and valley values ​​between two adjacent points. At this time, the error between connecting two adjacent points with a straight line and the actual rising segment curve is small and can be ignored.

[0073] In other implementations, the pressure value of the Nth rising segment may not be directly equal to the pressure at the beginning of the steady segment; instead, when drawing the complete curve in S6, the two points may be connected by a straight line.

[0074] S6: Plot the rising segment curve and the second curve in the same coordinate system to obtain the internal ballistic performance curve of the solid rocket motor.

[0075] By employing piecewise assignment and linear interpolation, a complete upward pressure prediction curve is generated efficiently and reliably. First, a pre-constructed second-order polynomial response surface model is used to rapidly calculate the pressure sequence for the first N-1 time points, obtaining a pressure sequence reflecting the influence of input parameters. The pressure value at the Nth node (the end of the upward segment) is directly assigned as the starting pressure of the stationary segment (taken from the second curve). This operation ensures the strict equality of pressure values ​​at the junction of the upward and stationary segments, physically guaranteeing the continuity of the entire ballistic curve. Finally, by linearly connecting these discrete points, a smooth and continuous upward segment prediction curve is formed with extremely low computational cost. This method inherits the computational efficiency of the response surface model and introduces physical consistency constraints from the zero-dimensional model through boundary assignment, thus achieving fast, stable, and naturally connected upward segment prediction under small sample conditions.

[0076] Finally, the ascending segment curve and the second curve can be plotted on the same coordinate system to obtain the internal ballistic performance curve of the solid rocket motor; thus completing the prediction of the internal ballistic performance of the solid rocket motor.

[0077] The above description is merely a preferred embodiment of the present invention and an explanation of the technical principles employed. Those skilled in the art should understand that the scope of the invention is not limited to the specific combination of the above-described technical features, but also includes other technical solutions formed by arbitrary combinations of the above-described technical features or their equivalents without departing from the inventive concept. For example, technical solutions formed by substituting the above-described features with (but not limited to) technical features with similar functions disclosed in this invention.

Claims

1. A method for calculating interior ballistic performance based on a gradient-enhanced response surface model, characterized in that, The pressure change curve of the solid rocket motor combustion chamber over time starts from the initial moment and includes the rising segment, the steady segment, and the falling segment; The methods include: S1: Obtain the end time of the normalized rising segment; S2: Acquire the data set of the solid rocket motor; the data set includes: propellant density, combustion area, burning rate coefficient, gas pressure index, nozzle throat cross-sectional area, characteristic velocity, and combustion chamber free volume; S3: Input the data set into the zero-dimensional internal ballistic calculation model, and calculate the second curve representing the stable segment and descent segment of the solid rocket motor's internal ballistic trajectory based on the end time of the ascent segment; the zero-dimensional internal ballistic calculation model is used to calculate the pressure change curve of the solid rocket motor's combustion chamber over time based on the data set; S4: Select N time nodes from the initial time to the end time of the rising segment; the time nodes include the initial time and the end time of the rising segment; S5: Based on the data set, a second-order polynomial response surface model and gradient constraints are used to optimize the polynomial coefficients. Then, based on the second curve, the rising segment curves of the solid rocket motor combustion chamber pressure at N time nodes are calculated. S6: Plot the rising segment curve and the second curve in the same coordinate system to obtain the internal ballistic performance curve of the solid rocket motor.

2. The method for calculating internal ballistic performance based on a gradient-enhanced response surface model according to claim 1, characterized in that, Obtain the end time of the normalized rising segment, including: S1-1: Obtain the first curve obtained from the experiment and normalized to represent the change of pressure in the combustion chamber of the solid rocket motor over time; the horizontal axis of the first curve represents time, and the vertical axis represents pressure. S1-2: Extract the end time of the pressure rise segment in the solid rocket motor combustion chamber based on the first curve.

3. The method for calculating internal ballistic performance based on a gradient-enhanced response surface model according to claim 2, characterized in that, The end time of the pressure rise phase in the solid rocket motor combustion chamber is extracted based on the first curve, including: S1-2-1: Obtain the maximum pressure value in the first curve; S1-2-2: Extract multiple horizontal axis coordinates from the first curve corresponding to the points where the pressure is equal to the maximum pressure value by a set multiple; S1-2-3: Take the smallest horizontal axis coordinate among multiple horizontal axis coordinates as the end time of the rising segment.

4. The method for calculating internal ballistic performance based on a gradient-enhanced response surface model according to claim 1, characterized in that, The dataset is input into a zero-dimensional internal ballistic calculation model, and a second curve characterizing the stable and descent phases of the solid rocket motor's internal trajectory is calculated based on the end time of the ascent phase, including: The dataset is input into a zero-dimensional internal ballistic calculation model to calculate a third curve that characterizes the pressure in the combustion chamber of a solid rocket motor when the gas flow velocity in the combustion chamber is below the velocity threshold. Discard the portion of the third curve between the initial time and the end time of the rising segment, and use the remaining portion as the second curve.

5. The method for calculating internal ballistic performance based on a gradient-enhanced response surface model according to claim 2, characterized in that, The method for selecting N time points in the time interval between the initial time and the end time of the rising phase is as follows: The initial time is taken as the first time node, and the end time of the rising segment is taken as the Nth time node; The second to the (N-1)th time nodes are selected at equal intervals; or, multiple extreme points of the rising segment in the first curve are sequentially used as the second to the (N-1)th time nodes.

6. The method for calculating internal ballistic performance based on a gradient-enhanced response surface model according to claim 2, characterized in that, Based on the aforementioned dataset, a second-order polynomial response surface model and gradient constraints are used to optimize the polynomial coefficients. Then, based on the second curve, the rising segment curves of the solid rocket motor combustion chamber pressure at N time nodes are calculated, including: S5-1: Construct a second-order polynomial response surface model; the input of the second-order polynomial response surface model is a data set, and the output is the pressure value at each time node; S5-2: Input the data set into the second-order polynomial response surface model to calculate the pressure values ​​corresponding to the first N-1 time nodes, and obtain the pressure values ​​of the first N-1 rising segments; S5-3: Take the pressure value at the end of the rising segment of the second curve as the pressure value corresponding to the Nth time node to obtain the pressure value at the end of the rising segment. S5-4: Based on the pressure values ​​of the first N-1 rising segments and the pressure value at the end of the rising segment, the rising segment curve of the solid rocket motor combustion chamber pressure change with time is obtained.

7. The method for calculating internal ballistic performance based on a gradient-enhanced response surface model according to claim 6, characterized in that, The process of constructing a second-order polynomial response surface model includes: S5-1-1: Construct an initial response surface model; the input of the initial response surface model is a dataset, and the output is the pressure values ​​at multiple time points, and it contains multiple unknown polynomial coefficients; S5-1-2: Construct the objective optimization function based on the initial response surface model; S5-1-3: Based on the objective optimization function, an optimization algorithm is used to optimize the coefficients of multiple polynomials to obtain the optimal polynomial coefficients; S5-1-4: Substitute the optimal polynomial coefficients into the initial response surface model to obtain a second-order polynomial response surface model.

8. The method for calculating internal ballistic performance based on a gradient-enhanced response surface model according to claim 7, characterized in that, In the process of using the optimization algorithm to find the optimal polynomial coefficients, the gradient information of the first curve is used as a constraint to solve the polynomial coefficients in the iterative process, which is used to accelerate the convergence of the optimization algorithm.

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