An engine parameter sensitivity analysis method and related device

Abstract

The application discloses an engine parameter sensitivity analysis method and related equipment, and relates to the field of rocket engines. By combining qualitative and quantitative analysis, the design parameters that significantly affect the performance deviation of the engine are identified, and a corresponding deviation propagation model is established. First, a performance calculation model based on the interior ballistic equation is constructed, a set of design parameters is determined, and a parameter sample space is generated through statistical distribution. A qualitative global sensitivity analysis method is used for preliminary screening to screen out a set of sensitive parameters that affect the performance index. Then, a quantitative global sensitivity analysis method based on variance decomposition is used to calculate the sensitivity index of each parameter. Finally, the propagation relationship between the parameter deviation and the performance deviation is accurately described through sorting and establishing a deviation model. The application effectively improves the comprehensiveness and accuracy of the sensitivity analysis, and can provide scientific guidance for engine design optimization, performance prediction and deviation management.

Description

Technical Field

[0001] This specification relates to the field of rocket engines, and more specifically, this application relates to a method and related equipment for sensitivity analysis of engine parameters. Background Technology

[0002] Traditional engine performance evaluation methods typically focus on the optimization analysis of a single or a few design parameters, neglecting the complex interactions that may exist between these parameters. As engine design becomes increasingly complex, single-parameter optimization is no longer sufficient to meet the demands of modern design. Therefore, how to systematically evaluate and analyze the interrelationships of multiple design parameters and their impact on engine performance has become a crucial problem that urgently needs to be solved.

[0003] To address this challenge, researchers have proposed a parameter sensitivity analysis method. This method quantifies the impact of various design parameters on engine performance, thus providing a more precise optimization direction for engine design. Sensitivity analysis not only reveals the independent contribution of each design parameter to performance but also identifies the interactions between parameters and their uncertain impact on performance. Through sensitivity analysis, designers can more effectively identify key parameters during the design phase, thereby prioritizing these key factors in engineering practice to achieve the goals of optimized design and improved performance.

[0004] However, existing sensitivity analysis methods often have limitations, especially when dealing with high-dimensional, multi-parameter systems, where the analysis process is complex and computationally intensive. Traditional local sensitivity analysis methods, such as the local derivative method based on single parameter changes, cannot comprehensively reflect the interactions between parameters; while global sensitivity analysis methods, such as the Sobol method, can more comprehensively assess the influence of parameters, their computational complexity is high and they require a large amount of simulation data. To address this issue, this invention proposes a comprehensive sensitivity analysis method combining qualitative and quantitative analysis. By first performing qualitative screening and then using global sensitivity analysis based on variance decomposition, both analytical efficiency and accuracy of results are improved.

[0005] Furthermore, engine performance deviations are not only dependent on a single parameter, but are also affected by fluctuations in multiple design parameters. Therefore, how to establish a model that can effectively describe the propagation relationship of these deviations has become a key issue in the design optimization process. Summary of the Invention

[0006] The summary section introduces a series of simplified concepts, which will be further explained in detail in the detailed description section. This summary section is not intended to limit the key and essential technical features of the claimed technical solution, nor is it intended to determine the scope of protection of the claimed technical solution.

[0007] Firstly, this application proposes a method for sensitivity analysis of engine parameters, including: An engine performance calculation model is constructed, wherein the engine performance calculation model is based on the internal ballistic equation to characterize the mapping relationship between engine design parameters and performance indicators, wherein the performance indicators include one or more of combustion chamber pressure, thrust, total impulse, specific impulse and operating time; Determine the set of design parameters that affect engine performance indicators, and set the statistical distribution type and value range for each design parameter to generate a parameter sample space; Based on the above parameter sample space, a qualitative global sensitivity analysis method is used to preliminarily screen the above design parameters and obtain a set of candidate sensitive parameters that have a significant impact on the above performance indicators. Under the premise of fixing the non-sensitive parameters that have little impact on the above performance indicators, a quantitative global sensitivity analysis method based on variance decomposition is used to calculate the sensitivity index of each candidate sensitive parameter to the above performance indicators for the above candidate sensitive parameter set. Based on the above sensitivity indicators, the degree of influence of engine design parameters on performance deviation is ranked to determine the main parameters affecting engine performance deviation. Based on the aforementioned key influencing parameters, an engine performance deviation model is established to characterize the propagation relationship between the deviations of these key influencing parameters and engine performance deviations.

[0008] In one feasible implementation, the above-mentioned construction of the engine performance calculation model includes: An internal ballistic calculation model is established based on the engine combustion process. The aforementioned internal ballistic calculation model includes at least the mass conservation equation, the gas state equation, and the nozzle flow relationship. Under the premise of the preset basic assumptions, the differential equation of the combustion chamber pressure changing with time is solved numerically to obtain the engine combustion chamber pressure curve; Based on the combustion chamber pressure curve mentioned above, the engine thrust curve is further calculated, and the total impulse, specific impulse, and operating time are calculated from the thrust curve.

[0009] In one feasible implementation, the above-mentioned determination of the set of design parameters affecting engine performance indicators, and the setting of statistical distribution type and value range for each design parameter, generating a parameter sample space, includes: The engine structural parameters, propellant burning rate parameters, nozzle geometric parameters, nozzle ablation parameters, and working environment parameters are classified and organized to form an initial design parameter set. Set corresponding statistical distribution models for each design parameter, and determine the parameter value range based on the preset coefficient of variation or statistical confidence interval; Based on the above statistical distribution model, random sampling is performed on each design parameter to generate a parameter sample space for sensitivity analysis.

[0010] In one feasible implementation, based on the aforementioned parameter sample space, a qualitative global sensitivity analysis method is used to initially screen the aforementioned design parameters to obtain a set of candidate sensitive parameters that significantly affect the aforementioned performance indicators, including: The Morris screening method is used to sample the above parameter sample space to design a design so that only one design parameter changes in adjacent samples. Based on the engine performance calculation model, the corresponding performance index output is calculated under the disturbance conditions of each parameter. Calculate the mean and standard deviation of the base effects for each design parameter, and qualitatively evaluate the sensitivity of the design parameters based on the mean and standard deviation of the base effects, thereby selecting a set of candidate sensitive parameters.

[0011] In one feasible implementation, under the premise of fixing the non-sensitive parameters that have little impact on the performance indicators, a quantitative global sensitivity analysis method based on variance decomposition is used to calculate the sensitivity index of each candidate sensitive parameter to the performance indicators for the set of candidate sensitive parameters, including: Fix the above-mentioned insensitive parameters to their statistical mean or nominal value; A parameter sampling matrix is ​​constructed based on candidate sensitive parameters, and analysis samples are generated using pseudo-random or quasi-random sampling methods. Based on the engine performance calculation model, the performance index output results corresponding to the sample are calculated. By decomposing the variance of the performance index output, the first-order sensitivity index and the total effect sensitivity index of each candidate sensitivity parameter are calculated.

[0012] In one feasible implementation, based on the aforementioned sensitivity index, the influence of engine design parameters on performance deviations is ranked to determine the main influencing parameters of engine performance deviations, including: Based on the first-order sensitivity index corresponding to each candidate sensitive parameter, the degree of independent influence of the design parameters is ranked. Based on the overall effect sensitivity index corresponding to each candidate sensitive parameter, the comprehensive influence of the design parameters is ranked. Based on the preset sensitivity threshold or the ranking results, design parameters that contribute more to engine performance deviation than the threshold are identified as the main influencing parameters.

[0013] In one feasible implementation, the engine performance deviation model is established based on the aforementioned key influencing parameters to characterize the propagation relationship of deviations in the key influencing parameters on engine performance deviations, including: The relative deviations of the aforementioned main influencing parameters are used as model input variables, and the relative deviations of engine performance indicators are used as model output variables. Based on multivariate Taylor expansion or polynomial approximation methods, a functional relationship model between engine performance deviation and deviation of major influencing parameters is constructed. The above performance deviation model is fitted and validated using numerical simulation samples or historical test data to obtain an engine performance deviation model that can be used for performance deviation prediction.

[0014] Secondly, the present invention also proposes an engine parameter sensitivity analysis system, comprising: A construction unit is used to construct an engine performance calculation model, wherein the engine performance calculation model is based on the internal ballistic equation to characterize the mapping relationship between engine design parameters and performance indicators, and the performance indicators include one or more of combustion chamber pressure, thrust, total impulse, specific impulse and operating time; The generation unit is used to determine the set of design parameters that affect engine performance indicators, and to set the statistical distribution type and value range for each design parameter, thereby generating a parameter sample space. The preliminary screening unit is used to perform preliminary screening of the above design parameters based on the above parameter sample space using a qualitative global sensitivity analysis method, and to obtain a set of candidate sensitive parameters that have a significant impact on the above performance indicators. The calculation unit is used to calculate the sensitivity index of each candidate sensitive parameter to the above performance index by adopting a quantitative global sensitivity analysis method based on variance decomposition for the above candidate sensitive parameter set, under the premise of fixing non-sensitive parameters that have little impact on the above performance index. The sorting unit is used to sort the influence of engine design parameters on performance deviations according to the above sensitivity indicators, and to determine the main influencing parameters of engine performance deviations. A unit is established to build an engine performance deviation model based on the aforementioned main influencing parameters, so as to characterize the propagation relationship of the deviation of the aforementioned main influencing parameters on the engine performance deviation.

[0015] Thirdly, the present invention also proposes an electronic device comprising: a memory and a processor, characterized in that the processor is used to execute a computer program stored in the memory to implement the steps of the engine parameter sensitivity analysis method as described in any of the first aspects.

[0016] Fourthly, the present invention also proposes a computer-readable storage medium having a computer program stored thereon, characterized in that, when the computer program is executed by a processor, it implements the steps of the engine parameter sensitivity analysis method as described in any one of the first aspects.

[0017] In summary, this invention provides a parameter sensitivity analysis method combining qualitative and quantitative analysis. By accurately identifying design parameters that significantly impact engine performance deviations, it offers more scientific guidance for engine design optimization. Traditional methods often focus on local sensitivity analysis, failing to comprehensively assess the impact of multi-parameter interactions on performance. This invention combines the advantages of the Morris and Sobol methods, enabling not only preliminary screening of the influence of individual parameters but also precise quantification of the sensitivity of each parameter and the combined impact of their interactions on performance through variance decomposition. This innovative analytical framework significantly improves the comprehensiveness and accuracy of sensitivity analysis. Secondly, this invention establishes an engine performance deviation model using methods such as multivariate Taylor expansion, accurately describing how deviations in multiple design parameters propagate and affect the overall engine performance. This performance deviation model effectively predicts changes in engine performance and provides a theoretical basis for deviation management and tolerance allocation, thereby ensuring high reliability and consistency of the engine during manufacturing and use. Furthermore, this invention solves the computational complexity problem of traditional sensitivity analysis methods when dealing with high-dimensional, multi-parameter systems. By combining qualitative screening and quantitative sensitivity analysis, this invention not only improves computational efficiency but also significantly reduces computational costs while maintaining accuracy. In summary, this invention has significant technical advantages in engine design optimization, performance prediction, and deviation control. Its methodology has high engineering application value and can effectively improve the scientificity and accuracy of engine design.

[0018] Other advantages, objectives and features of this application will be apparent in part from the description which follows, and in part from what those skilled in the art will understand through study and practice of this application. Attached Figure Description

[0019] Various other advantages and benefits will become apparent to those skilled in the art upon reading the following detailed description of preferred embodiments. The accompanying drawings are for illustrative purposes only and are not intended to limit this specification. Furthermore, the same reference numerals denote the same parts throughout the drawings. In the drawings: Figure 1 This is a schematic flowchart of an engine parameter sensitivity analysis method provided in an embodiment of this application; Figure 2 A schematic flowchart of a Morris method provided in this application embodiment; Figure 3 A schematic flowchart of a Sobol method provided in an embodiment of this application; Figure 4 This is a schematic diagram of a maximum pressure deviation model provided in an embodiment of this application; Figure 5A schematic diagram of an average pressure deviation model provided in an embodiment of this application; Figure 6 A schematic diagram of a maximum thrust deviation model provided in an embodiment of this application; Figure 7 A schematic diagram of an average thrust deviation model provided in an embodiment of this application; Figure 8 A schematic diagram of a total impulse deviation model provided in an embodiment of this application; Figure 9 A schematic diagram of a specific impulse deviation model provided in an embodiment of this application; Figure 10 A schematic diagram of a working time deviation model provided in an embodiment of this application; Figure 11 A structural schematic diagram of an engine parameter sensitivity analysis system provided in this application embodiment; Figure 12 This is a schematic diagram of an electronic device structure provided in an embodiment of this application. Detailed Implementation

[0020] The terms "first," "second," "third," "fourth," etc. (if present) in the specification, claims, and accompanying drawings of this application are used to distinguish similar objects and are not necessarily used to describe a specific order or sequence. It should be understood that such data can be interchanged where appropriate so that the embodiments described herein can be implemented in a sequence other than that illustrated or described herein. Furthermore, the terms "comprising" and "having," and any variations thereof, are intended to cover non-exclusive inclusion; for example, a process, method, system, product, or apparatus that comprises a series of steps or units is not necessarily limited to those steps or units explicitly listed, but may include other steps or units not explicitly listed or inherent to such processes, methods, products, or apparatus. The technical solutions of the embodiments of this application will now be clearly and completely described in conjunction with the accompanying drawings. Obviously, the described embodiments are only a part of the embodiments of this application, and not all of them.

[0021] Please see Figure 1 This is a flowchart illustrating an engine parameter sensitivity analysis method provided in an embodiment of this application, which may specifically include: S110. Construct an engine performance calculation model, wherein the engine performance calculation model is based on the internal ballistic equation to characterize the mapping relationship between engine design parameters and performance indicators, and the above performance indicators include one or more of combustion chamber pressure, thrust, total impulse, specific impulse and operating time. S120. Determine the set of design parameters that affect engine performance indicators, and set the statistical distribution type and value range for each design parameter to generate a parameter sample space. S130. Based on the above parameter sample space, a qualitative global sensitivity analysis method is used to preliminarily screen the above design parameters to obtain a set of candidate sensitive parameters that have a significant impact on the above performance indicators. S140. Under the premise of fixing the non-sensitive parameters that have little impact on the above performance indicators, for the above set of candidate sensitive parameters, a quantitative global sensitivity analysis method based on variance decomposition is used to calculate the sensitivity index of each candidate sensitive parameter to the above performance indicators. S150. Based on the above sensitivity indicators, rank the degree of influence of engine design parameters on performance deviation, and determine the main influencing parameters of engine performance deviation. S160. Based on the above main influencing parameters, establish an engine performance deviation model to characterize the propagation relationship between the deviation of the above main influencing parameters and the engine performance deviation.

[0022] For example, this embodiment provides a parameter sensitivity analysis method based on an engine performance calculation model. By analyzing the sensitivity of each design parameter, the main factors affecting engine performance deviation are identified, and a corresponding deviation propagation model is established.

[0023] First, an engine performance calculation model based on internal ballistic equations was constructed. This model describes the relationship between engine design parameters and performance indicators, including combustion chamber pressure, thrust, total impulse, specific impulse, and operating time, using internal ballistic equations. These performance indicators are closely related to changes in design parameters; therefore, an accurate performance calculation model is the foundation for sensitivity analysis.

[0024] For each performance indicator of the engine, a set of relevant design parameters was determined, and a suitable statistical distribution type and value range were assigned to each parameter. For example, design parameters might include propellant density, nozzle throat diameter, and combustion chamber pressure; the value ranges for these parameters were obtained from literature or historical data. By randomly sampling these parameters, a parameter sample space can be generated, providing data support for subsequent sensitivity analysis.

[0025] Qualitative global sensitivity analysis methods (such as the Morris method) are used for initial screening of design parameters. In this step, we generate a sample of parameters and calculate the base effect (degree of influence) of different design parameters on performance indicators by calculating the performance output of each sample. By calculating the mean and standard deviation of the base effect, we can screen out a set of candidate sensitive parameters that have a significant impact on performance indicators. This screening process helps us identify key influencing factors among numerous design parameters.

[0026] After identifying the candidate sensitive parameters, we fix the less sensitive parameters and further employ a quantitative global sensitivity analysis method based on variance decomposition (such as the Sobol method) to calculate the sensitivity index of each candidate sensitive parameter to the performance index. This method allows us to quantify the sensitivity of each parameter, i.e., the degree of influence of individually changing a design parameter on engine performance, as well as the impact of the interaction of multiple parameters on performance.

[0027] Based on the calculated sensitivity indices, we ranked all design parameters to determine the degree of influence of each parameter on performance deviation. After ranking, we can identify the design parameters with the greatest impact on performance deviation, thus determining the main influencing parameters of engine performance deviation. These parameters are key factors in design optimization and performance prediction.

[0028] Based on the identified key influencing parameters, we further established an engine performance deviation model to characterize the propagation relationship between the deviations of these key influencing parameters and engine performance deviations. This model quantifies the impact of fluctuations in the deviation source parameters on performance deviations through multivariate Taylor expansion or other approximation methods, thus providing a basis for subsequent deviation analysis and optimization design.

[0029] In summary, this invention provides a parameter sensitivity analysis method combining qualitative and quantitative analysis. By accurately identifying design parameters that significantly impact engine performance deviations, it offers more scientific guidance for engine design optimization. Traditional methods often focus on local sensitivity analysis, failing to comprehensively assess the impact of multi-parameter interactions on performance. This invention combines the advantages of the Morris and Sobol methods, enabling not only preliminary screening of the influence of individual parameters but also precise quantification of the sensitivity of each parameter and the combined impact of their interactions on performance through variance decomposition. This innovative analytical framework significantly improves the comprehensiveness and accuracy of sensitivity analysis. Secondly, this invention establishes an engine performance deviation model using methods such as multivariate Taylor expansion, accurately describing how deviations in multiple design parameters propagate and affect the overall engine performance. This performance deviation model effectively predicts changes in engine performance and provides a theoretical basis for deviation management and tolerance allocation, thereby ensuring high reliability and consistency of the engine during manufacturing and use. Furthermore, this invention solves the computational complexity problem of traditional sensitivity analysis methods when dealing with high-dimensional, multi-parameter systems. By combining qualitative screening and quantitative sensitivity analysis, this invention not only improves computational efficiency but also significantly reduces computational costs while maintaining accuracy. In summary, this invention has significant technical advantages in engine design optimization, performance prediction, and deviation control. Its methodology has high engineering application value and can effectively improve the scientificity and accuracy of engine design.

[0030] In one feasible implementation, the above-mentioned construction of the engine performance calculation model includes: An internal ballistic calculation model is established based on the engine combustion process. The aforementioned internal ballistic calculation model includes at least the mass conservation equation, the gas state equation, and the nozzle flow relationship. Under the premise of the preset basic assumptions, the differential equation of the combustion chamber pressure changing with time is solved numerically to obtain the engine combustion chamber pressure curve; Based on the combustion chamber pressure curve mentioned above, the engine thrust curve is further calculated, and the total impulse, specific impulse, and operating time are calculated from the thrust curve.

[0031] For example, in this embodiment, an internal ballistic calculation model based on the engine combustion process is constructed. This model characterizes the relationship between engine design parameters and performance indicators through the mass conservation equation, the gas state equation, and the nozzle flow relationship.

[0032] First, a zero-dimensional internal ballistic calculation model was established based on the engine's combustion process. This model is based on the principles of mass and energy conservation of the gases within the combustion chamber, describing the engine's combustion process through mass conservation equations and gas state equations. Specifically, the mass conservation equations consider the mass change of the propellant and the mass accumulation of the gas flow within the combustion chamber, while the gas state equations relate the thermodynamic state of the gas to physical quantities such as temperature and pressure within the combustion chamber. Furthermore, the nozzle flow relations are used to describe the behavior of the gas flow within the nozzle, and the flow velocity at the nozzle exit and the state of the nozzle throat are further derived.

[0033] In internal ballistic calculation models, the pressure change in the combustion chamber over time is a core component. Based on the aforementioned mass conservation and gas law, a differential equation describing the pressure change in the combustion chamber over time was established. By presupposing basic assumptions (such as uniform pressure within the combustion chamber and no significant pressure drop caused by gas flow), this differential equation was numerically solved to obtain the pressure change curve of the combustion chamber over time during engine combustion. This pressure curve reflects the changes in key parameters during combustion and is an important foundation for deriving engine performance.

[0034] Based on the combustion chamber pressure curve, the engine's thrust curve was further calculated. Thrust calculation primarily relies on the nozzle flow characteristics and combustion chamber pressure; an appropriate nozzle thrust calculation formula is used to derive the thrust-time curve. The thrust curve provides the engine's actual thrust output at different time points, allowing for the calculation of performance indicators such as total impulse (i.e., the cumulative thrust during engine operation) and specific impulse (fuel consumption efficiency per unit thrust). Operating time is calculated by evaluating the thrust curve against a standard operating time definition to determine the engine's actual operating time under specified conditions.

[0035] Specifically, the zero-dimensional internal ballistic calculation equation does not consider the influence of combustion chamber gas flow on propellant combustion; this represents the most fundamental case for engines. The following basic assumptions are made: 1. The pressure inside the combustion chamber is uniform, and the pressure drop caused by the flow of combustion gas is negligible. That is, the gas velocity in the combustion chamber is very small, and the pressure distribution can be regarded as uniform. The pressure at all points in the combustion chamber is equal. This is the "zero-dimensional" pressure calculation.

[0036] 2. The burning rate is uniform at all points on the burning surface of the charge, and the influence of erosion combustion is ignored.

[0037] 3. Combustion products are single-component gases with average properties, obeying the perfect gas law.

[0038] 4. The flow in the nozzle is quasi-steady, and the nozzle flow rate can be used. express.

[0039] 5. There is no heat loss in the combustion chamber.

[0040] The fundamental relationships underlying "zero-dimensional" internal ballistic calculations are the conservation of mass and the equation of state for gases.

[0041] Taking the free volume of the entire combustion chamber as the control volume, and following the principle of mass conservation, the mass generation rate of the combustion gas within the combustion chamber is... It is divided into two parts: one part is discharged through the nozzle, which is the mass flow rate of the nozzle. The other part is used to increase the amount of fuel gas stored in the free volume of the combustion chamber, with a growth rate of [missing information]. .

[0042] Then we have the mass equation: (1) in: Gas density; : Free volume of combustion chamber; :time; Propellant density; : Burning surface area Burning rate; Flow rate coefficient; : Cross-sectional area of ​​the nozzle throat; : A function of specific heat ratio k; The gas constant of the fuel gas; : Combustion chamber gas temperature; Propellant characteristic velocity The growth rate of the free combustion gas storage in the combustion chamber can be expressed as: (2) Therefore, the mass increase rate of the combustion chamber fuel gas consists of two parts: first, the increase in fuel gas density, and second, the increase in the free volume of the combustion chamber. The increase in the free volume of the combustion chamber should equal the volume vacated due to the reduction in propellant charge volume caused by propellant combustion, that is: (3) From equations (1) to (3), we get (4) The equation of state of the gas Taking the derivative with respect to time, and considering the temperature and composition of the gas as constants, and assuming no heat loss in the combustion chamber, the gas temperature can be... Take the adiabatic combustion temperature of the propellant ,have to (5) Introducing the combustion rate relationship: (6) Then equation (4) becomes (7) In equation (7) The magnitude is approximately 0.01, which is negligible compared to 1.

[0043] Introducing Relational Expressions .

[0044] Finally, we can obtain (8) Equation (8) is the basic differential equation for calculating the change of combustion chamber pressure with time in "zero-dimensional" internal ballistics.

[0045] Once the combustion chamber pressure has been established and the operating phase begins, the pressure rises to its maximum value and then stabilizes relatively. This can be considered... Then, the equilibrium pressure formula can be obtained from equation (8).

[0046] (9) The pressure curve can be obtained from the zero-dimensional internal ballistic equations, and further, the thrust curve can be obtained, as shown in the formula: (10) (10) (11) in, Specific heat ratio; Pressure at the nozzle exit section; For ambient pressure, it can be calculated using the formula for standard atmospheric pressure. The calculation shows that, among which At sea level, atmospheric pressure is the standard pressure. For temperature lapse rate, The standard temperature at sea level To measure height, The molar mass of air; The nozzle exit area, , The nozzle exit diameter; The nozzle exit area, , This refers to the diameter of the nozzle throat.

[0047] The pressure at the nozzle exit section in the formula It can be determined by the expansion ratio ε and the pressure in the combustion chamber. To determine this, assuming no shock waves or flow separation occur within the nozzle, the relationship is as follows: (12) Given the expansion ratio, it can be calculated numerically. The value of is then calculated. .

[0048] The total stroke calculation formula is: (13) in, For the length of the charge, For the charge end area, This refers to the charge density.

[0049] When the Ft curve is known, we have (14) The total value can be obtained by integration.

[0050] The formula for calculating specific impulse is: (15) (16) again (17) Having already obtained the total impulse, the specific impulse formula is easily derived: (18) The operating time of a solid rocket motor includes the total time it takes to generate thrust, i.e., the sum of the ascent time, the operating time, and the descent time, calculated as follows: Ascending phase: (19)

[0051] Working section: (20) (twenty one) (twenty two) (twenty three) (twenty four) Descent phase: (25) To ensure a consistent standard for determination, the following conventional method is typically used: the starting point is when the engine pressure continuously rises to 0.3 MPa or the thrust rises to 10% of the maximum thrust after engine ignition, and the ending point is when the engine pressure continuously drops to 0.3 MPa or the thrust drops to 10% of the maximum thrust after engine shutdown. The time interval between these two points is taken as the working time.

[0052] Through the above steps, a complete engine performance calculation model was successfully constructed. This model can not only calculate core parameters such as combustion chamber pressure and thrust, but also derive key performance indicators such as total impulse, specific impulse, and operating time. This calculation model forms the basis for engine design optimization and performance evaluation, providing strong support for subsequent sensitivity analysis and performance deviation modeling.

[0053] In one feasible implementation, the above-mentioned determination of the set of design parameters affecting engine performance indicators, and the setting of statistical distribution type and value range for each design parameter, generating a parameter sample space, includes: The engine structural parameters, propellant burning rate parameters, nozzle geometric parameters, nozzle ablation parameters, and working environment parameters are classified and organized to form an initial design parameter set. Set corresponding statistical distribution models for each design parameter, and determine the parameter value range based on the preset coefficient of variation or statistical confidence interval; Based on the above statistical distribution model, random sampling is performed on each design parameter to generate a parameter sample space for sensitivity analysis.

[0054] For example, a series of design parameters can be extracted based on the calculation formulas of performance parameters such as thrust, total impulse, and specific impulse. It should be noted that some parameters affect each other, and it is necessary to consider whether there is any duplication or omission.

[0055] Calculating thrust requires determining the thrust coefficient. The thrust coefficient calculation formula shows that external pressure must be considered during the calculation process. As the rocket engine's flight altitude changes, the external pressure also changes. According to the standard atmospheric pressure formula, the ambient pressure can be calculated from the engine's operating altitude.

[0056] Burning rate calculation formula ,in , The temperature sensitivity coefficient of the combustion rate. For ambient temperature, This is a reference temperature (usually 20℃).

[0057] The nozzle throat diameter needs to take into account the ablation of the throat liner material. In this paper, a carbon / carbon composite material is used for the throat liner. According to the literature, its thermal ablation rate is: .

[0058] The structural coefficient of the throat liner material depends on the processing structure of the carbon / carbon composite material and the number of particles contained in the combustion gas. This represents the density of the carbon / carbon composite material.

[0059] Nozzle flow loss coefficient , For the calculated diameter of the deflector plate, This is the nozzle convergence angle.

[0060] airflow expansion loss coefficient , This is the nozzle expansion angle.

[0061] Considering factors affecting internal ballistic calculations within the engine, and taking into account factors such as the operating environment and manufacturing processes, the following 19 parameters were selected for sensitivity analysis. These parameters all follow a normal distribution with the measured values ​​as the mean. Based on the "3σ" principle of normal distribution, that is, the data are distributed within the interval (u... The probability in (3σ, u+3σ) is 0.99, and this interval is used as the range of parameter values. Since the objective function of the Morris and Sobol methods is a scalar, it cannot handle the pressure-time curve of the internal ballistic calculation. Therefore, the engine performance indicators pressure, thrust, total impulse, specific impulse, and operating time are used as the output results of the internal ballistic calculation, and parameter sensitivity analysis is performed on each of them.

[0062] According to the research method of the present invention, the sample space of parameters for sensitivity analysis is shown in Table 1.

[0063] Table 1. Parameter Classification, Values, and Distribution

[0064] In one feasible implementation, based on the aforementioned parameter sample space, a qualitative global sensitivity analysis method is used to initially screen the aforementioned design parameters to obtain a set of candidate sensitive parameters that significantly affect the aforementioned performance indicators, including: The Morris screening method is used to sample the above parameter sample space to design a design so that only one design parameter changes in adjacent samples. Based on the engine performance calculation model, the corresponding performance index output is calculated under the disturbance conditions of each parameter. Calculate the mean and standard deviation of the base effects for each design parameter, and qualitatively evaluate the sensitivity of the design parameters based on the mean and standard deviation of the base effects, thereby selecting a set of candidate sensitive parameters.

[0065] For example, the sampling design is first performed using the Morris screening method based on the generated parameter sample space. In the Morris screening method, it is ensured that only one design parameter changes between adjacent samples. This means that during sensitivity analysis, only one parameter's value is perturbed, while the values ​​of other parameters remain unchanged. The advantage of this method is that it can quickly identify which design parameters have the greatest impact on performance indicators and avoid the complex interaction effects caused by simultaneous changes in multiple parameters.

[0066] Based on the constructed engine performance calculation model, the performance index output under each parameter perturbation condition was calculated. Specifically, the design parameters corresponding to each sample point in the parameter sample space were input into the performance calculation model to obtain the perturbed performance output results. These output results correspond to how engine performance indicators (such as combustion chamber pressure, thrust, total stroke, etc.) change under different design parameter perturbations.

[0067] After obtaining the performance index outputs under all disturbance conditions, the elementary effect (EE) of each design parameter was calculated. The elementary effect is an important indicator for measuring the impact of a parameter on performance indicators. Its calculation involves multiple sampling calculations for the disturbances of each design parameter to determine the degree of influence of that parameter on performance changes. Specifically, the mean of the elementary effect reflects the average impact of the parameter on the performance indicators, while the standard deviation reflects whether the change in the parameter has significant uncertainty.

[0068] Based on the calculated mean and standard deviation of the base effects, a qualitative assessment of the sensitivity of each design parameter is performed. Generally, a larger mean base effect indicates a more significant impact of the parameter on performance. A larger standard deviation of the base effects indicates greater uncertainty in the parameter's impact. This qualitative assessment method allows for the initial screening of the set of design parameters that significantly affect engine performance, i.e., the candidate set of sensitive parameters.

[0069] Specifically, such as Figure 2 As shown, Figure 2 This application provides a schematic flowchart of a Morris method according to an embodiment. When generating Morris samples, B... J1 is a (m+1)×m parameter sample matrix, where each row represents a parameter sample, and m is the number of model parameters; J1 is a (m+1)×1 matrix, and Jm is a (m+1)×m matrix, with all elements being 1; B is a matrix (bij)(m+1)×m, where bij=1 when j≤i, i=1, 2, …, m, and 0 otherwise; D For an m×m diagonal matrix, each diagonal element has an equal probability of being ±1; P Let B be an m×m random confusion matrix. The generated parameter sample matrix is ​​B. It has the following characteristics: the model parameter samples in two adjacent rows have exactly one different parameter value, while the remaining m-1 model parameters have exactly the same value.

[0070] The Morris method qualitatively measures the sensitivity of a parameter by calculating the mean and variance of the base effects of the model parameters. The sensitivity of a parameter is positively correlated with the mean of the base effects, and the interaction between the parameter and other parameters is positively correlated with the standard deviation of the base effects.

[0071] The formula for calculating the basic effect (EE) of the model parameters is as follows: (26) In the formula: x1, x2, ..., x3 are the base effect values ​​of the i-th model parameter; x1, x2, ..., x3 are the values ​​of the model parameters. The objective function is denoted as .

[0072] To avoid When the value is less than 0, the positive and negative values ​​cancel each other out, and the adjusted mean is used. Replace the mean u: (27) In the formula: The base effect value is calculated for the j-th sample of the i-th model parameter; n is the number of model parameter samples.

[0073] The larger the mean of the base effects of a model parameter, the higher its sensitivity; the larger the standard deviation of the base effects, the greater the interaction between that parameter and other model parameters. In general, the larger the mean and variance of the base effects of a model parameter, the greater its sensitivity.

[0074] The perturbation factor is calculated based on the number of levels. To ensure the stability of the results, a large Morris sample (greater than 4000) should be generated. The mean of the base effect of each parameter under different objective functions is calculated using the base effect calculation formula of the model parameters. The parameters are sorted from largest to smallest. The parameters that are earlier in the list are more sensitive and have a greater impact on engine performance. A certain number of parameters are selected from the beginning to the end, and these parameters are considered to be the main factors affecting the deviation of engine performance.

[0075] The sensitivity of combustion chamber pressure, average thrust, total impulse, specific impulse, and operating time to each parameter was calculated using the Morris method. Different deviation sources showed different sensitivities to the same objective function, and different objective functions showed different sensitivities to the same deviation source. The parameters were sorted according to their EE values, as shown in Table 2.

[0076] Table 2 Parameter Sensitivity Order Table

[0077] Parameters with higher EE values ​​are more sensitive and rank higher in the order. The results in the table show that dt, n, L, c Parameters such as a, D0, and T0 are ranked relatively high and have high sensitivity, while α, C, h, ... , These parameters all appear in the later positions and have low sensitivity. To further and more accurately analyze parameter sensitivity, we fix the parameters with lower sensitivity, α, C, and h. , Sobol analysis will be conducted subsequently.

[0078] In one feasible implementation, under the premise of fixing the non-sensitive parameters that have little impact on the performance indicators, a quantitative global sensitivity analysis method based on variance decomposition is used to calculate the sensitivity index of each candidate sensitive parameter to the performance indicators for the set of candidate sensitive parameters, including: Fix the above-mentioned insensitive parameters to their statistical mean or nominal value; A parameter sampling matrix is ​​constructed based on candidate sensitive parameters, and analysis samples are generated using pseudo-random or quasi-random sampling methods. Based on the engine performance calculation model, the performance index output results corresponding to the sample are calculated. By decomposing the variance of the performance index output, the first-order sensitivity index and the total effect sensitivity index of each candidate sensitivity parameter are calculated.

[0079] For example, in performing quantitative sensitivity analysis, non-sensitive parameters with minimal impact on performance metrics are first fixed. These non-sensitive parameters are typically identified in the previous screening step using the Morris method and have small base effects and low sensitivity. Therefore, to simplify subsequent calculations and improve analytical efficiency, the values ​​of these non-sensitive parameters are set to their statistical mean or nominal value, keeping them constant throughout the analysis.

[0080] After fixing the non-sensitive parameters, the next step is to construct a parameter sampling matrix based on the set of candidate sensitive parameters. This matrix contains all possible combinations of values ​​for the candidate sensitive parameters. To ensure the comprehensiveness and representativeness of the sample space, pseudo-random or quasi-random sampling methods are used to generate the analysis samples. For example, the Latin hypercube sampling (LHS) method can be used to uniformly distribute the sample points, ensuring that all possible values ​​of each parameter are effectively covered. This sampling method generates a large number of sample points, which will be used for subsequent performance calculations and sensitivity analysis.

[0081] After generating parameter samples, these samples are input into the previously established engine performance calculation model. The model calculates the engine's performance output based on the design parameters corresponding to each sample point, such as combustion chamber pressure, thrust, total impulse, and specific impulse. This method yields the performance output results corresponding to each parameter combination, providing necessary calculation data for subsequent sensitivity analysis.

[0082] After obtaining the performance output results corresponding to the samples, variance decomposition is performed on the output variance of the performance index. Variance decomposition can decompose the total output variance into the parts caused by each design parameter and its interaction effects. Specifically, the contribution of each candidate sensitive parameter to the performance index is calculated, and the sensitivity of each design parameter is quantified by calculating its first-order sensitivity index (i.e., the influence of a single parameter on the performance output variance) and the total effect sensitivity index (i.e., the contribution of the interaction between the parameter and other parameters to the output variance).

[0083] In one feasible implementation, based on the aforementioned sensitivity index, the influence of engine design parameters on performance deviations is ranked to determine the main influencing parameters of engine performance deviations, including: Based on the first-order sensitivity index corresponding to each candidate sensitive parameter, the degree of independent influence of the design parameters is ranked. Based on the overall effect sensitivity index corresponding to each candidate sensitive parameter, the comprehensive influence of the design parameters is ranked. Based on the preset sensitivity threshold or the ranking results, design parameters that contribute more to engine performance deviation than the threshold are identified as the main influencing parameters.

[0084] For example, by ranking the sensitivity of design parameters, the parameters with the greatest impact on engine performance deviation are identified. Specifically, based on the first-order sensitivity index and the total effect sensitivity index of each candidate sensitive parameter, the main parameters affecting engine performance deviation are determined. The specific implementation steps are as follows: First, the design parameters are ranked according to their independent influence based on the first-order sensitivity index (also known as the "main effect") corresponding to each candidate sensitive parameter. The first-order sensitivity index reflects the degree of influence of each design parameter on the performance output variance when it changes individually. Specifically, the contribution of each design parameter to the performance index under different disturbance conditions is calculated, and all design parameters are ranked according to the magnitude of their contributions. The ranked results indicate which design parameters have a significant impact on performance changes without considering the influence of other parameters.

[0085] Next, the overall influence of the design parameters is ranked based on the total effect sensitivity index corresponding to each candidate sensitive parameter. The total effect sensitivity index considers not only the independent influence of each design parameter on the performance index, but also the interaction between parameters. Therefore, this index can more comprehensively reflect the overall influence of each design parameter in the entire system. By calculating the interaction between the parameter and other parameters and its contribution to the variance of the performance output, all design parameters are ranked a second time to obtain a ranking of overall influence.

[0086] After ranking the first-order sensitivity indices and the overall effect sensitivity indices, the main influencing parameters are selected by setting sensitivity thresholds or based on the ranking results. Sensitivity thresholds can be set based on engineering experience, typically selecting parameters that contribute significantly to performance deviations as the main influencing parameters. If the sensitivity values ​​of these main influencing parameters are higher than the preset thresholds, it indicates that they have a significant impact on engine performance deviations. Therefore, these parameters are used as key design parameters for further optimization or tolerance allocation.

[0087] Specifically, assuming , Let N be two independent N×k dimensional sampling matrices, where N is the number of samplings, i=1,2,…,k; j=1,2,…,N, and let N be the sampling number. ( Let represent a matrix whose i-th column comes from B(A) and the remaining columns come from A(B). The existing formulas for calculating the statistics for each order of sensitivity are as follows. The choice of different statistics affects the convergence speed of the algorithm. Studies have found that the estimates of (c)(f)(j) perform well.

[0088] Calculate first order hour The estimated value is: (a) (b) (c) ; Calculate the total order hour The estimated value is: (d) (e) ;(f)

[0089] Calculate the general order hour The estimated value is: (g) ;Note: ;(h) ;Note: ;(i) (j) .

[0090] This invention selects the Sobol sampling method. Figure 3 This is a flowchart illustrating a Sobol method provided in an embodiment of this application. The algorithm is as follows: A 2k-dimensional sequence of length N is generated using Sobol pseudo-random numbers; the first k columns are denoted as A, and the last k columns as B; calculation... ;calculate .

[0091] The method described in this embodiment ranks the design parameters based on first-order sensitivity and total effect sensitivity indices, and identifies the main influencing parameters that have the greatest impact on engine performance deviations. These main influencing parameters are key bases for further engine performance optimization, design adjustments, and tolerance analysis, helping to improve the engine's design accuracy and performance stability.

[0092] In one feasible implementation, the engine performance deviation model is established based on the aforementioned key influencing parameters to characterize the propagation relationship of deviations in the key influencing parameters on engine performance deviations, including: The relative deviations of the aforementioned main influencing parameters are used as model input variables, and the relative deviations of engine performance indicators are used as model output variables. Based on multivariate Taylor expansion or polynomial approximation methods, a functional relationship model between engine performance deviation and deviation of major influencing parameters is constructed. The above performance deviation model is fitted and validated using numerical simulation samples or historical test data to obtain an engine performance deviation model that can be used for performance deviation prediction.

[0093] For example, the relative deviations of key influencing parameters are used as input variables. These deviations are those selected from the aforementioned sensitivity analysis of key influencing parameters. The relative deviation of each design parameter represents the range of fluctuation or uncertainty of that parameter. For instance, if there is a certain difference between the actual value and the theoretical design value of a design parameter, and this difference will occur during actual production or use, then the relative deviation of this difference can be used as model input. Using these relative deviations, the model can predict the impact of these parameter changes on engine performance.

[0094] After determining the model inputs, a functional relationship model between engine performance deviations and deviations of key influencing parameters is constructed using multivariate Taylor expansion or polynomial approximation methods. Multivariate Taylor expansion simplifies model calculations and provides accurate approximate results when considering relatively small parameter deviations. This method allows the relationship between deviations in engine performance indicators (such as thrust, specific impulse, and total impulse) and deviations of key design parameters to be modeled as a function, accurately describing how these deviations propagate through design parameters and affect the final engine performance.

[0095] After establishing the performance deviation model, the model was fitted and validated using numerical simulation samples or historical experimental data. Specifically, known simulation samples or experimental data were used to adjust the parameters in the model to ensure that the model accurately reflects the actual situation. Through multiple validations and fittings, a validated performance deviation model was obtained. This model can accurately predict the impact of different design parameter deviations on engine performance deviations, further supporting engine design optimization and uncertainty analysis.

[0096] Specifically, based on the engine combustion chamber pressure:

[0097] Due to factors such as the usage environment and manufacturing process, it is believed that Ab, At, Tf, a, n and All of these parameters have a certain degree of deviation, and their mean and variance are known. By importing the mean of these parameters into the pressure expression, the mean pressure can be obtained.

[0098] A mathematical model for theoretical prediction of engine performance is established, and the relationship between parameter deviation and performance deviation is analyzed. Assuming that a certain performance parameter Qj is determined by n deviation source parameters x1-xn, the theoretical relationship between the performance parameter and the deviation sources is:

[0099] If we use mi (i=1,2,…,n) to represent the target value of parameter xi, (representing its corresponding performance target value), then we have The deviation between the source parameter xi and its target value mi, denoted as Δxi, can be expressed as Δxi = xi - mi; the performance parameter Qj and the performance target value... The deviation between them, ΔQj, can be expressed as: Therefore, the expression for the performance deviation ΔQj can be obtained as follows: (28) Expanding the above equation using the multivariate Taylor formula, considering that the key deviation source parameters and performance fluctuate around their target values, and the design parameters deviate very little from their target values, the engine performance parameters can be expanded in the second order at the target values ​​of the deviation source parameters. Without considering the remainder terms of the second order or higher in the Taylor expansion, the Taylor expansion of the engine performance Qj and the expression for the performance deviation ΔQj are shown in the following two equations.

[0100] +…+ (29) (30) Knowing the main sources of performance deviation, we model the deviation based on theoretical relationships, with the independent variable being the relative error of the deviation source, defined as follows: Where: μ is the mean, Let be the value of the sampling point, and be the performance deviation, characterized by a percentage fluctuation. Then the performance deviation model can be written as: (31) in, The coefficients are undetermined polynomials. A performance deviation model is used for fitting and parameter identification.

[0101] Deviation modeling is performed based on the sensitive parameters obtained from performance deviation tracing. All sensitive parameters for each performance parameter are arranged in order as a group, with a coefficient of variation of 2%. Each sensitive parameter is randomly selected within a given range, and 20,000 sample points are randomly selected. The lsqcurvefit function is used for nonlinear fitting.

[0102] like Figure 4 As shown, Figure 4 A schematic diagram of a maximum pressure deviation model provided in this application embodiment. Parameter identification results are shown in Table 3: Table 3. Identification results of maximum pressure parameters

[0103] Deviation formula: Error rmse=0.0030 in, Corresponding sequentially to the length L of the propellant column, and the charge density Characteristic velocity c , outer diameter of charge D0, pressure index n, nozzle throat diameter dt, burning rate coefficient a.

[0104] like Figure 5 As shown, Figure 5 A schematic diagram of an average pressure deviation model provided in this application embodiment. Parameter identification results are shown in Table 4: Table 4. Results of Average Pressure Parameter Identification

[0105] Deviation formula: The error rmse = 0.0071 in, Corresponding sequentially to the length L of the propellant column, and the charge density Characteristic velocity c , outer diameter of propellant D0, pressure index n, nozzle throat diameter dt, initial propellant temperature Ta, and burning rate coefficient a.

[0106] like Figure 6As shown, Figure 6 A schematic diagram of a maximum thrust deviation model provided for an embodiment of this application. Parameter identification results are shown in Table 5: Table 5. Identification results of maximum thrust parameters

[0107] Deviation formula: The error rmse = 0.0032 in, Corresponding sequentially to the length L of the propellant column, and the charge density Characteristic velocity c , outer diameter of propellant D0, pressure index n, nozzle throat diameter dt, initial propellant temperature Ta, and burning rate coefficient a.

[0108] like Figure 7 As shown, Figure 7 A schematic diagram of an average thrust deviation model provided for an embodiment of this application. Parameter identification results are shown in Table 6: Table 6. Identification Results of Average Thrust Parameters

[0109] Deviation formula: The error rmse = 0.0084 in, Corresponding sequentially to the length L of the propellant column, and the charge density Characteristic velocity c The outer diameter of the propellant charge is D0, the pressure index is n, the combustion temperature is Tf, the initial propellant temperature is Ta, and the burning rate coefficient is a.

[0110] like Figure 8 As shown, Figure 8 A schematic diagram of a total impulse deviation model provided for an embodiment of this application. Parameter identification results are shown in Table 7: Table 7. Results of Total Impact Parameter Identification

[0111] Deviation formula: The error rmse = 0.0097 in, Corresponding sequentially to the length L of the propellant column, and the charge density Characteristic velocity c Specific heat ratio k, thickness E, outer diameter of charge D0.

[0112] like Figure 9 As shown, Figure 9 A schematic diagram of a specific impulse deviation model provided in an embodiment of this application. Parameter identification results are shown in Table 8: Table 8. Identification results of specific impulse parameters

[0113] Deviation formula: Error rmse=0.0027 in, Corresponding to characteristic velocities c , specific heat ratio k, nozzle throat diameter dt.

[0114] like Figure 10 As shown, Figure 10 A schematic diagram of a working time deviation model provided in an embodiment of this application. Parameter identification results are shown in Table 9: Table 9. Identification Results of Working Time Parameters

[0115] Deviation formula: The error rmse = 0.0114 in, Corresponding to the charge density , thickness E, outer diameter of propellant D0, pressure index n, combustion temperature Tf, nozzle throat diameter dt, initial propellant temperature Ta, burning rate coefficient a.

[0116] Secondly, this invention also proposes an engine parameter sensitivity analysis system, such as... Figure 11 As shown, it includes: Construction unit 21 is used to construct an engine performance calculation model, wherein the engine performance calculation model is based on the internal ballistic equation to characterize the mapping relationship between engine design parameters and performance indicators, and the performance indicators include one or more of combustion chamber pressure, thrust, total impulse, specific impulse and operating time; The generation unit 22 is used to determine the set of design parameters that affect engine performance indicators, and to set the statistical distribution type and value range for each design parameter, thereby generating a parameter sample space. The preliminary screening unit 23 is used to perform preliminary screening of the above design parameters based on the above parameter sample space using a qualitative global sensitivity analysis method, and to obtain a set of candidate sensitive parameters that have a significant impact on the above performance indicators. The calculation unit 24 is used to calculate the sensitivity index of each candidate sensitive parameter to the above performance index by adopting a quantitative global sensitivity analysis method based on variance decomposition for the above candidate sensitive parameter set, under the premise of fixing non-sensitive parameters that have little impact on the above performance index. The sorting unit 25 is used to sort the influence of engine design parameters on performance deviation according to the above sensitivity index, and to determine the main influencing parameters of engine performance deviation. Establishment unit 26 is used to establish an engine performance deviation model based on the above-mentioned main influencing parameters, so as to characterize the propagation relationship of the deviation of the above-mentioned main influencing parameters on the engine performance deviation.

[0117] In one feasible implementation, an engine parameter sensitivity analysis system may also perform any step of the method proposed in the first aspect.

[0118] Thirdly, the present invention also proposes an electronic device 300, such as... Figure 12 As shown, it includes a memory 310, a processor 320, and a computer program 311 stored in the memory 310 and executable on the processor. When the processor 320 executes the computer program 311, it implements the steps of the engine parameter sensitivity analysis method as described in any of the first aspects.

[0119] Fourthly, the present invention also proposes a computer-readable storage medium having a computer program stored thereon, characterized in that, when the computer program is executed by a processor, it implements the steps of the engine parameter sensitivity analysis method as described in any one of the first aspects.

[0120] The above embodiments are only used to illustrate the technical solutions of this application, and are not intended to limit them. Although this application has been described in detail with reference to the foregoing embodiments, those skilled in the art should understand that modifications can still be made to the technical solutions described in the foregoing embodiments, or equivalent substitutions can be made to some of the technical features. Such modifications or substitutions do not cause the essence of the corresponding technical solutions to deviate from the spirit and scope of the technical solutions of the embodiments of this application.

Claims

1. A method of engine parameter sensitivity analysis, characterized by, include: An engine performance calculation model is constructed, wherein the engine performance calculation model is based on the internal ballistic equation to characterize the mapping relationship between engine design parameters and performance indicators, wherein the performance indicators include one or more of combustion chamber pressure, thrust, total impulse, specific impulse and operating time; Determine the set of design parameters that affect engine performance indicators, and set the statistical distribution type and value range for each design parameter to generate a parameter sample space; Based on the parameter sample space, a qualitative global sensitivity analysis method is used to preliminarily screen the design parameters to obtain a set of candidate sensitive parameters that have a significant impact on the performance index. Under the premise of fixing the non-sensitive parameters that have little impact on the performance index, a quantitative global sensitivity analysis method based on variance decomposition is used to calculate the sensitivity index of each candidate sensitive parameter to the performance index for the candidate sensitive parameter set. Based on the aforementioned sensitivity index, the degree of influence of engine design parameters on performance deviation is ranked to determine the main influencing parameters of engine performance deviation; Based on the aforementioned key influencing parameters, an engine performance deviation model is established to characterize the propagation relationship between the deviation of the key influencing parameters and the engine performance deviation.

2. The engine parameter sensitivity analysis method according to claim 1, characterized in that, The construction of the engine performance calculation model includes: An internal ballistic calculation model is established based on the engine combustion process. The internal ballistic calculation model includes at least the mass conservation equation, the gas state equation, and the nozzle flow relationship. Under the premise of the preset basic assumptions, the differential equation of the combustion chamber pressure changing with time is solved numerically to obtain the engine combustion chamber pressure curve; Based on the combustion chamber pressure curve, the engine thrust curve is further calculated, and the total impulse, specific impulse, and operating time are calculated from the thrust curve.

3. The engine parameter sensitivity analysis method according to claim 1, characterized in that, The process of determining the set of design parameters affecting engine performance indicators, setting the statistical distribution type and value range for each design parameter, and generating a parameter sample space includes: The engine structural parameters, propellant burning rate parameters, nozzle geometric parameters, nozzle ablation parameters, and working environment parameters are classified and organized to form an initial design parameter set. Set corresponding statistical distribution models for each design parameter, and determine the parameter value range based on the preset coefficient of variation or statistical confidence interval; Based on the statistical distribution model, random sampling is performed on each design parameter to generate a parameter sample space for sensitivity analysis.

4. The engine parameter sensitivity analysis method according to claim 1, characterized in that, Based on the parameter sample space, a qualitative global sensitivity analysis method is used to initially screen the design parameters, obtaining a set of candidate sensitive parameters that significantly affect the performance indicators, including: The Morris screening method is used to sample the parameter sample space to design a design so that only one design parameter changes in adjacent samples. Based on the engine performance calculation model, the corresponding performance index output is calculated under the disturbance conditions of each parameter. The mean and standard deviation of the base effects of each design parameter are calculated, and the sensitivity of the design parameters is qualitatively evaluated based on the mean and standard deviation of the base effects, thereby selecting a set of candidate sensitive parameters.

5. The engine parameter sensitivity analysis method according to claim 1, characterized in that, Under the premise of fixing non-sensitive parameters that have little impact on the performance index, a quantitative global sensitivity analysis method based on variance decomposition is used for the candidate sensitive parameter set to calculate the sensitivity index of each candidate sensitive parameter to the performance index, including: The insensitive parameter is fixed to its statistical mean or nominal value; A parameter sampling matrix is ​​constructed based on candidate sensitive parameters, and analysis samples are generated using pseudo-random or quasi-random sampling methods. Based on the engine performance calculation model, the performance index output results corresponding to the sample are calculated. By decomposing the variance of the performance index output, the first-order sensitivity index and the total effect sensitivity index of each candidate sensitivity parameter are calculated.

6. The engine parameter sensitivity analysis method according to claim 1, characterized in that, Based on the sensitivity index, the influence of engine design parameters on performance deviations is ranked to determine the main parameters affecting engine performance deviations, including: Based on the first-order sensitivity index corresponding to each candidate sensitive parameter, the degree of independent influence of the design parameters is ranked. Based on the overall effect sensitivity index corresponding to each candidate sensitive parameter, the comprehensive influence of the design parameters is ranked. Based on the preset sensitivity threshold or the ranking results, design parameters that contribute more to engine performance deviation than the threshold are identified as the main influencing parameters.

7. The engine parameter sensitivity analysis method according to claim 1, characterized in that, The establishment of an engine performance deviation model based on the main influencing parameters to characterize the propagation relationship of deviations in the main influencing parameters on engine performance deviations includes: The relative deviation of the main influencing parameters is used as the model input variable, and the relative deviation of the engine performance index is used as the model output variable. Based on multivariate Taylor expansion or polynomial approximation methods, a functional relationship model between engine performance deviation and deviation of major influencing parameters is constructed. The performance deviation model is fitted and validated using numerical simulation samples or historical test data to obtain an engine performance deviation model that can be used for performance deviation prediction.

8. An engine parameter sensitivity analysis system, characterized in that, include: A construction unit is used to construct an engine performance calculation model, wherein the engine performance calculation model is based on the internal ballistic equation to characterize the mapping relationship between engine design parameters and performance indicators, and the performance indicators include one or more of combustion chamber pressure, thrust, total impulse, specific impulse and operating time; The generation unit is used to determine the set of design parameters that affect engine performance indicators, and to set the statistical distribution type and value range for each design parameter, thereby generating a parameter sample space. The preliminary screening unit is used to perform preliminary screening of the design parameters based on the parameter sample space using a qualitative global sensitivity analysis method, to obtain a set of candidate sensitive parameters that have a significant impact on the performance index. The calculation unit is used to calculate the sensitivity index of each candidate sensitive parameter to the performance index by adopting a quantitative global sensitivity analysis method based on variance decomposition for the candidate sensitive parameter set, under the premise of fixing non-sensitive parameters that have little impact on the performance index. The sorting unit is used to sort the influence of engine design parameters on performance deviation according to the sensitivity index, and to determine the main influencing parameters of engine performance deviation. A modeling unit is established based on the main influencing parameters to build an engine performance deviation model, thereby characterizing the propagation relationship between the deviation of the main influencing parameters and the engine performance deviation.

9. An electronic device, comprising: The memory and processor are characterized in that the processor is used to execute a computer program stored in the memory to implement the steps of the engine parameter sensitivity analysis method as described in any one of claims 1-7.

10. A computer-readable storage medium having a computer program stored thereon, characterized in that, When the computer program is executed by the processor, it implements the steps of the engine parameter sensitivity analysis method as described in any one of claims 1-7.

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