Solid rocket engine grain parameter global sensitivity analysis method

Abstract

The invention provides a solid rocket engine grain parameter global sensitivity analysis method. The method comprises the following steps: constructing an initial Kriging model and a learning function of a solid rocket engine grain; screening sample points by using a learning function, adding the screened sample points into a sample point set, and updating the reference Kriging model to obtain an iterative Kriging model; according to the current iteration Kriging model and the reference Kriging model, whether the current iteration Kriging model meets the precision requirement is judged; if the current iteration Kriging model does not meet the precision requirement, continuing to update the Kriging model; and if the iterative Kriging model meets the precision requirement, calculating to obtain a first-order sensitivity index and a total effect index by using the constructed Kriging model. And the whole calculation process does not need to call the finite element again for calculation, so that the large-scale calculation amount required by the finite element simulation process is saved, and the calculation efficiency is remarkably improved.

Description

Technical Field

[0001] This invention generally relates to the field of solid rocket motor design technology, and specifically to a method for global sensitivity analysis of propellant parameters in solid rocket motors. Background Technology

[0002] As the energy carrier and load-bearing component of an engine, the structural integrity and reliability of composite solid propellant grains directly affect the engine's performance and lifespan. Propellant materials exhibit significant viscoelasticity and temperature sensitivity. Furthermore, the process parameters of the propellant grains fluctuate during casting, curing, and other manufacturing stages, resulting in significant random uncertainties in the performance of the propellant charge structure.

[0003] Throughout its lifespan, a propellant charge is subjected to a combination of complex loads, including temperature loads, gravity loads, and ignition decompression loads. In engineering practice, the maximum strain in the region most likely to fail within the propellant structure is typically a key concern, as this directly impacts the structural integrity of the charge. However, there is a highly nonlinear relationship between the extreme strain value and the input parameters, and numerous factors influence this relationship (including propellant elastic modulus, Poisson's ratio, coefficient of thermal expansion, load conditions, and geometric parameters).

[0004] In existing technologies, constructing a global high-precision proxy model requires a large amount of finite element simulation calculations, and a large amount of computing resources are consumed in areas with very low information content, resulting in low computing efficiency. Summary of the Invention

[0005] In view of the above-mentioned defects or deficiencies in the prior art, it is desirable to provide a global sensitivity analysis method for solid rocket motor propellant grain parameters.

[0006] This invention provides a method for global sensitivity analysis of propellant grain parameters in solid rocket motors, comprising: S1: Construct the initial Kriging model of the solid rocket motor propellant grain; the input of the Kriging model is the sample points randomly selected from the total sample data set to form the sample point set, and the maximum strain corresponding to the sample points in the sample point set obtained by finite element simulation; the output is the maximum strain response value and standard deviation corresponding to the sample point; the sample point corresponds to a combination of multiple propellant grain parameter values. The parameters of the propellant grain include: linear expansion coefficient, Poisson's ratio at cooling, equilibrium modulus, zero stress temperature, Poisson's ratio at ignition, peak pressure, axial acceleration, as well as the time required to reach peak pressure, wing length, wing width, wing depth, arc radius, corner radius, and wing tilt angle of the propellant grain of the solid rocket motor. S2: Construct a learning function; the learning function is used to filter the remaining sample points in the total data set that do not belong to the sample point set according to the calculated learning function value, and add the remaining sample point corresponding to the smallest learning function value to the sample point set to update the Kriging model; S3: Use the learning function to filter the remaining sample points corresponding to the smallest learning function value, and add the remaining sample points corresponding to the smallest learning function value to the sample point set. Update the reference kriging model using the updated sample point set to obtain the iterative kriging model. The initial reference kriging model is the initial kriging model, and the subsequent models are the previous iterative kriging model. S4: Based on the current iterative kriging model and the reference kriging model, determine whether the current iterative kriging model meets the accuracy requirements; If the accuracy requirement is not met in this iteration of the Kriging model, then repeat steps S2-S4. If the kriging model obtained in this iteration meets the accuracy requirements, then the kriging model obtained in this iteration will be used as the optimized kriging model, and step S5 will be performed. S5: Based on the optimized Kriging model, the first-order sensitivity index and the total effect index of the propellant parameters are calculated; the first-order sensitivity index and the total effect index are used to reflect the degree of influence of each propellant parameter on the maximum strain.

[0007] According to the technical solution provided by the present invention, the initial kriging model for constructing a solid rocket motor propellant grain includes: S1-1: Construct a sample data set; the sample data set contains multiple sample points, and each sample point corresponds to a combination of multiple drug column parameter values; S1-2: Randomly select a portion of sample points from the total sample data set to form a sample point set; S1-3: Calculate the maximum strain corresponding to all sample points in the sample point set to obtain multiple first maximum strains; S1-4: Based on the sample point set and multiple first maximum strains, an initial Kriging model is constructed.

[0008] According to the technical solution provided by the present invention, the construction of the learning function includes: S2-1: Obtain the initial learning function; the initial function is used to update the Kriging model of the solid rocket motor propellant grain according to the number of iterations; S2-2: Input the remaining sample points in the total sample data set that have not been added to the sample point set into the initial Kriging model, and calculate the maximum strain response value and the corresponding standard deviation for each remaining sample point; S2-3: Based on the maximum strain response value and the corresponding standard deviation of each remaining sample point, the learning function of the Kriging model is constructed.

[0009] According to the technical solution provided by the present invention, the initial learning function has a distance adjustment factor to avoid excessive clustering of sample points; The process of obtaining the initial learning function includes: Construct an active learning function; Update the distance adjustment factor based on the current iteration count; An initial learning function is constructed based on the distance adjustment factor and the active learning function.

[0010] According to the technical solution provided by the present invention, the remaining sample points corresponding to the smallest learning function value are selected using the learning function, and the remaining sample points corresponding to the smallest learning function value are added to the sample point set. The updated sample point set is then used to update the reference kriging model to obtain an iterative kriging model, comprising: Update the sample point set according to the learning function; Calculate the maximum strain corresponding to all sample points in the sample point set to obtain multiple second maximum strains; Based on the sample point set and multiple second maximum strains, an iterative kriging model is constructed.

[0011] According to the technical solution provided by the present invention, updating the sample point set according to the learning function includes: The maximum strain response value and the corresponding standard deviation of each remaining sample point are input into the learning function to obtain multiple learning function values; The remaining sample points corresponding to the smallest learning function value are added to the sample point set.

[0012] According to the technical solution provided by the present invention, determining whether the current iterative kriging model meets the accuracy requirements includes: Input the remaining sample points corresponding to the minimum learning function value into the current iteration of the Kriging model and calculate the first iteration standard deviation; Input the remaining sample points corresponding to the minimum learning function value into the reference Kriging model and calculate the standard deviation of the second iteration. If the absolute value of the difference between the first iteration standard deviation and the second iteration standard deviation is less than or equal to the set threshold, it is determined that the accuracy requirement is met; otherwise, it is determined that the accuracy requirement is not met.

[0013] According to the technical solution provided by the present invention, based on the optimized Kriging model, the first-order sensitivity index and total effect index of the drug column parameters are calculated, including: S5-1: Generate the first and second sample points according to the distribution of sample points in the total sample data set; S5-2: Replace the column in the matrix corresponding to the first sample point that has not been replaced with a column in the matrix corresponding to the second sample point to obtain the third sample point; one column of the third sample point is the same as one column of the second sample point, and the remaining columns are the same as the remaining columns of the first sample point. S5-3: Repeat step S5-2 to obtain multiple third sample points; S5-4: Input the first sample point, the second sample point, and multiple third sample points into the optimized Kriging model, and calculate the maximum strain response value of the first sample point, the maximum strain response value of the second sample point, the multiple maximum strain response values ​​of the multiple third sample points, as well as the standard deviation of the first sample point, the standard deviation of the second sample point, and the multiple standard deviations of the multiple third sample points. S5-5: The first-order sensitivity index and the total effect index are calculated based on the maximum strain response value of the first sample point, the maximum strain response value of the second sample point, the multiple maximum strain response values ​​of multiple third sample points, and the standard deviations of the first sample point, the second sample point, and the multiple standard deviations of multiple third sample points.

[0014] The beneficial effects of this invention are as follows: Given that propellant grains are subjected to a combination of complex operating conditions such as temperature loads, gravity loads, and ignition decompression loads throughout their entire lifecycle, this invention provides a global sensitivity analysis method for solid rocket motor propellant grain parameters. This method involves constructing an initial Kriging model and a learning function for the solid rocket motor propellant grain; using the learning function to select the remaining sample points corresponding to the minimum learning function value, and adding these remaining sample points to a sample point set; updating the reference Kriging model using the updated sample point set to obtain an iterative Kriging model; determining whether the current iterative Kriging model meets the accuracy requirements based on the current iterative Kriging model and the reference Kriging model; if the current iterative Kriging model does not meet the accuracy requirements, continuing to update the Kriging model; if the current iterative Kriging model meets the accuracy requirements, then using the constructed Kriging model to calculate the first-order sensitivity index and the total effect index. The entire calculation process using the Kriging model does not require re-calling finite element simulation, saving the large-scale computational load required for finite element simulation, thus significantly improving computational efficiency. Then, the influence of each propellant column parameter on the maximum strain can be analyzed, so as to optimize the design of each parameter of the propellant column that has a greater impact on the maximum strain. Attached Figure Description

[0015] 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 a global sensitivity analysis method for solid rocket motor propellant grain parameters. Figure 2 The graph shows the analysis results of the first-order sensitivity index calculated according to the method of this invention. Figure 3 The maximum strain when a single parameter changes; Figure 4 This is a schematic diagram of the signal connection relationships of electronic devices.

[0016] Among them, 500 is electronic equipment; 501 is CPU; 502 is ROM; 503 is RAM; 504 is bus; 505 is I / O interface; 506 is input section; 507 is output section; 508 is storage section; 509 is communication section; 510 is driver; and 511 is removable medium. Detailed Implementation

[0017] 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.

[0018] 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.

[0019] Example 1 refer to Figure 1 This invention provides a method for global sensitivity analysis of propellant grain parameters in solid rocket motors, comprising: S1: Construct the initial Kriging model of the solid rocket motor propellant grain; the input of the Kriging model is the sample points randomly selected from the total sample data set to form the sample point set, and the maximum strain corresponding to the sample points in the sample point set obtained by finite element simulation; the output is the maximum strain response value and standard deviation corresponding to the sample point; the sample point corresponds to a combination of multiple propellant grain parameter values. Step S1 specifically includes: S1-1: Construct a sample data set; the sample data set contains multiple sample points, and each sample point corresponds to a combination of multiple drug column parameter values; Specifically, the parameters of the propellant grain include the linear expansion coefficient, Poisson's ratio at cooling, equilibrium modulus, zero-stress temperature, Poisson's ratio at ignition, peak pressure, axial acceleration, as well as the time required to reach peak pressure, wing length, wing width, wing depth, arc radius, corner radius, and wing tilt angle.

[0020] The parameters of the aforementioned drug column all satisfy a normal distribution with different means and standard deviations; therefore, in this embodiment, multiple specific values ​​for each parameter are randomly selected according to their respective distribution patterns. Then, the multiple specific values ​​of various parameters are combined to obtain multiple sample points; and finally, a sample data set is constructed.

[0021] S1-2: Randomly select a portion of sample points from the total sample data set to form a sample point set; For example, if the total sample data set contains 100 sample points, 20 of them are randomly selected to form a sample point set. As the Kriging model is subsequently optimized and updated, the number of sample points in the sample point set will continuously increase.

[0022] The learning function values ​​corresponding to the added sample points are all relatively small. As the number of iterations increases, the learning function values ​​corresponding to the sample points used to update the Kriging model will generally be smaller, thus allowing the Kriging model to be gradually optimized.

[0023] S1-3: Calculate the maximum strain corresponding to all sample points in the sample point set to obtain multiple first maximum strains; In this embodiment, finite element simulation is performed using Abaqus software to calculate the strain corresponding to the sample points.

[0024] The specific process is as follows: In the Abaqus software, a scenario identical to that in this embodiment is created, and the parameters of the drug column corresponding to the sample point are input into it to complete the simulation and obtain the maximum strain corresponding to the sample point.

[0025] S1-4: Based on the sample point set and multiple first maximum strains, an initial Kriging model is constructed.

[0026] Specifically, the core process of building a Kriging model can be divided into the following 7 steps: I. Data Preparation and Quality Inspection: Collect the coordinates and attribute values ​​(corresponding to the first maximum strain) of all sample points in the sample point set, check for outliers, anisotropy, and duplicate points, and perform coordinate transformation or data stratification if necessary.

[0027] II. Exploratory Spatial Data Analysis (ESDA): Plotting spatial distribution maps, histograms, and normal distribution maps; determining whether the data follows a normal / log-normal distribution; identifying trend terms (drift); and deciding which kriging form to use.

[0028] III. Calculation of Experimental Variogram: The semivariogram is calculated by grouping by distance and direction. Angle tolerance and distance tolerance can be set for irregular sampling.

[0029] IV. Fitting the theoretical variogram model: Based on the experimental variogram, select a spherical, exponential, or Gaussian model, and determine the anisotropy parameters through weighted least squares, maximum likelihood, or cross-validation.

[0030] V. Kriging Model Establishment and Weight Calculation: For any position to be estimated, s0, a system of linear equations is constructed based on the principles of unbiasedness and minimizing the estimation variance. For generalized Kriging, a drift constraint matrix needs to be added.

[0031] VI. Interpolation Prediction and Variance Output: After obtaining the weights, predict all unknown points within the study area and output the prediction accuracy, i.e., the Kriging variance.

[0032] VII. Model Validation and Verification: Cross-validation (leave-one-out or k-fold) is used to calculate indicators such as prediction error, root mean square error (RMSE), and average standard error (ASE). If the accuracy does not meet the requirements, the variogram is refitted or the trend order and neighborhood strategy are adjusted until the accuracy requirements are met.

[0033] In this embodiment, after obtaining the Kriging model, it is necessary to set the parameters required for constructing the Kriging model, namely the correlation scale parameter, the lower bound of the parameter, and the upper bound of the parameter; thereby constructing the initial Kriging model.

[0034] Specifically, the correlation scale parameter is set to 0.1, and the lower bound of the parameter is set to 10. -5 The upper limit of the parameter is set to 20.

[0035] S2: Construct a learning function; the learning function is used to filter the remaining sample points in the total data set that do not belong to the sample point set according to the calculated learning function value, and add the remaining sample point corresponding to the smallest learning function value to the sample point set to update the Kriging model; Step S2 specifically includes: S2-1: Obtain the initial learning function; the initial function is used to update the Kriging model of the solid rocket motor propellant grain according to the number of iterations; the initial learning function has a distance adjustment factor to avoid excessive clustering of sample points, including: An active learning function is constructed based on the folded normal distribution. :

[0036] in, This represents the mean. Indicates standard deviation, Represents the cumulative distribution function. π represents the mathematical constant pi, and exp(·) represents the natural exponential function.

[0037] To enhance the priority of remaining sample points that are far from existing sample points in the sample point set, an exponential distance adjustment factor is introduced to give higher weight to the remaining sample points that are far from existing sample points in the sample point set, thereby avoiding excessive concentration of sample points.

[0038] The specific formula for adjusting the exponential distance is as follows:

[0039] in, The distance evaluation function represents the remaining sample points. γ Indicates the distance adjustment factor. This represents the minimum distance from a sample point to an existing sample point in the sample point set. This represents the minimum distance between any two remaining sample points and any existing sample points. X represents the maximum distance between two existing sample points, and X represents the remaining sample points. i and X j Let i and j represent the i-th and j-th remaining sample points, respectively, that is, any two remaining sample points.

[0040] γ A smaller value indicates a lower preference for remaining sample points that are far from existing sample points; in the later iterations of the Kriging model construction process, γ A larger value means that sampling gradually concentrates in areas farther away from the sample point set, thereby improving the sampling efficiency of unexplored areas.

[0041] The distance adjustment factor is updated based on the current iteration count, specifically including:

[0042] in, As the initial adjustment factor, The maximum adjustment factor, i Indicates the current iteration number. This indicates the maximum number of iterations.

[0043] During each iteration, the distance adjustment factor is calculated based on the current iteration number. γ The specific value of the distance adjustment factor and the active learning function are used to construct the initial learning function.

[0044] Specifically, the initial learning function FNWS' for:

[0045] in, This represents the active learning function that is substituted into the absolute value of the prediction function of the Kriging model.

[0046] Specifically, considering the need for a small standard deviation in the Kriging model prediction, and to avoid excessive concentration of sample points in local areas, this embodiment proposes an active learning function and introduces a distance adjustment factor into it. This assigns higher weights to the remaining sample points that are far from the concentrated sample points, thereby preventing excessive concentration of sample points.

[0047] S2-2: Input the remaining sample points in the total sample data set that have not been added to the sample point set into the initial Kriging model, and calculate the maximum strain response value and the corresponding standard deviation for each remaining sample point; In step S2-2, the entire calculation process does not require calling the finite element simulation again, thus achieving a significant improvement in calculation efficiency.

[0048] S2-3: Based on the maximum strain response value and the corresponding standard deviation of each remaining sample point, the learning function of the Kriging model is constructed.

[0049] The Kriging model's prediction function follows a normal distribution, and its absolute value follows a folded normal distribution. If the maximum strain response predicted by the Kriging model is... The standard deviation is Substituting into the active learning function, we get:

[0050] in, This represents the active learning function that is substituted into the absolute value of the prediction function of the Kriging model.

[0051] Substituting the maximum strain response value and corresponding standard deviation of the remaining sample points into the initial learning function yields the learning function. FNWS Represented as:

[0052] S3: Update the reference kriging model using the learning function to obtain the iterative kriging model; Step S3 specifically involves: using the learning function to filter the remaining sample points corresponding to the smallest learning function value, adding the remaining sample points corresponding to the smallest learning function value to the sample point set, and using the updated sample point set to update the reference kriging model to obtain the iterative kriging model. Wherein, the initial reference kriging model is the initial kriging model, and the subsequent reference kriging models are the previous iterations; Specifically, it includes: S3-1: Update the sample point set according to the learning function, including: S3-1-1: Input the maximum strain response value and the corresponding standard deviation of each remaining sample point into the learning function to obtain multiple learning function values; The maximum strain response value and the corresponding standard deviation of each remaining sample point are calculated by step S2-2. Therefore, the maximum strain response value is taken as Standard deviation as Substitute the values ​​into the learning function to calculate the learning function value.

[0053] S3-1-2: Add the remaining sample points corresponding to the smallest learning function value to the sample point set.

[0054] After each update, the number of sample points in the sample point set will increase by one. Following the example above, initially 20 sample points are randomly selected to form the sample point set; after one update, the sample point set will have one more sample point, becoming 21 sample points.

[0055] Since the learning function values ​​corresponding to the sample points added to the sample point set are all relatively small, after multiple updates, most of the sample points in the sample point set correspond to relatively small learning function values. Updating the Kriging model with such sample points allows the Kriging model to calculate the maximum strain response value and standard deviation corresponding to the sample points more accurately.

[0056] S3-2: Calculate the maximum strain corresponding to all sample points in the sample point set to obtain multiple second maximum strains; in this embodiment, Abaqus software is also used for finite element simulation to obtain the strains.

[0057] S3-3: Based on the sample point set and multiple second maximum strains, an iterative kriging model is constructed. The specific method is the same as described above.

[0058] Specifically, the above steps can be performed by using a learning function to filter the remaining sample points, adding the remaining sample points with the smallest learning function value to the sample point set. This updates the sample point set, and the updated sample point set is then used to reconstruct the kriging model, resulting in an iterative kriging model. Repeating the above process completes the iterative updating of the kriging model.

[0059] S4: Based on the current iterative kriging model and the reference kriging model, determine whether the current iterative kriging model meets the accuracy requirements; Specifically, it includes: Input the remaining sample points corresponding to the minimum learning function value into the current iteration of the Kriging model and calculate the first iteration standard deviation; Input the remaining sample points corresponding to the minimum learning function value into the reference Kriging model and calculate the standard deviation of the second iteration. If the absolute value of the difference between the first iteration standard deviation and the second iteration standard deviation is less than or equal to the set threshold, it is determined that the accuracy requirement is met; otherwise, it is determined that the accuracy requirement is not met.

[0060] In this embodiment, a multiplier is set as a relative tolerance to control the stopping threshold of the iterative update process. The core idea is that when the prediction uncertainty (i.e., standard deviation) of the newly constructed iterative kriging model at the most critical sample point (i.e., the sample point with the smallest current learning function value) compared to the reference model changes sufficiently, the model is considered to have met the accuracy requirements for engineering applications. For example, the multiplier is set to 0.01.

[0061] Specifically, a convergence criterion is used to determine whether the accuracy requirement is met; the convergence criterion is expressed by the following formula:

[0062] in, This represents the standard deviation of the sample points in the newly added sample point set during the current iteration of the Kriging model (i.e., the sample points corresponding to the minimum learning function value among the remaining sample points from the previous iteration). Let S be the standard deviation of the sample point with the maximum strain among teammates in the sample point set. i This represents the current iteration number.

[0063] If the accuracy requirement is not met in this iteration of the Kriging model, then repeat steps S2-S4. If the kriging model obtained in this iteration meets the accuracy requirements, then the kriging model obtained in this iteration will be used as the optimized kriging model, and step S5 will be performed. Based on the above scheme, the Kriging model can be gradually optimized, so that the first-order sensitivity index and total effect index of the drug column parameters can be calculated using the optimized Kriging model to obtain more accurate results.

[0064] S5: Based on the optimized Kriging model, the first-order sensitivity index and the total effect index are calculated.

[0065] The process of calculating the first-order sensitivity index and the total effect index includes: S5-1: Generate the first and second sample points according to the distribution of sample points in the total sample data set; S5-2: Replace the column in the matrix corresponding to the first sample point that has not been replaced with a column in the matrix corresponding to the second sample point to obtain the third sample point; one column of the third sample point is the same as one column of the second sample point, and the remaining columns are the same as the remaining columns of the first sample point. S5-3: Repeat step S5-2 to obtain multiple third sample points; S5-4: Input the first sample point, the second sample point, and multiple third sample points into the optimized Kriging model, and calculate the maximum strain response value of the first sample point, the maximum strain response value of the second sample point, the multiple maximum strain response values ​​of the multiple third sample points, as well as the standard deviation of the first sample point, the standard deviation of the second sample point, and the multiple standard deviations of the multiple third sample points. S5-5: The first-order sensitivity index and the total effect index are calculated based on the maximum strain response value of the first sample point, the maximum strain response value of the second sample point, the multiple maximum strain response values ​​of multiple third sample points, and the standard deviations of the first sample point, the second sample point, and the multiple standard deviations of multiple third sample points.

[0066] The variance is the square of the standard deviation. Taking the square of the standard deviation gives the variance. Furthermore, based on the maximum strain response values ​​of the first sample point, the second sample point, and multiple third sample points, the following calculations can be performed:

[0067]

[0068] in, Indicates parameters x i The variances corresponding to (the first sample point, the second sample point, and multiple third sample points) Indicates parameters x i Self and x i The variance corresponding to the interaction with other parameters, N represents the number of third sample points, which in this embodiment is equal to the total number of parameter types included in the drug column parameters. This represents the maximum strain response value at the first sample point. This represents the maximum strain response value at the second sample point. This represents the maximum strain response value of the i-th third sample point.

[0069] The first-order sensitivity exponent satisfies the following formula:

[0070] in, This represents the first-order sensitivity exponent of the i-th drug column parameter among the first sample point, the second sample point, and multiple third sample points; This represents the matrix composed of the maximum strain response values ​​of the first sample point. The matrix represents the maximum strain response values ​​of the second sample points. express and The variance of the sum.

[0071] The total effect index is calculated using the following formula:

[0072] in, It represents the total effect index of the i-th drug column parameter corresponding to the first sample point, the second sample point, and multiple third sample points.

[0073] After obtaining the first-order sensitivity index and the total effect index, it is as follows: Figure 2 As shown in Table 1, which contains the design parameters for solid rocket motor propellant grains.

[0074] Table 1 Design Parameters of Solid Propellant Glue

[0075] Taking the data in Table 1 as an example, the sensitivity analysis results are based on the parameters of this case. Figure 2 As shown, S represents the first-order sensitivity index, and ST represents the total effect index. Figure 3 The maximum strain analysis results for a single parameter variation are given; where the horizontal axis number represents the sample number and the vertical axis strain represents the strain value.

[0076] The results show that the sensitivity analysis method based on the learning function kriging model has sufficient confidence.

[0077] In this embodiment, the finite element simulation was called only 28 times during actual implementation, a reduction of 97.1% compared to the 1,000 calls required by the MCS method. In the calculation process for engine propellant sensitivity analysis, this invention improves both computational efficiency and ensures computational accuracy.

[0078] The present invention provides an electronic device, including a memory, a processor, and a computer program stored in the memory and executable on the processor. When the processor executes the computer program, it implements the steps of a global sensitivity analysis method for solid rocket motor propellant grain parameters as described in the above embodiments.

[0079] Among them, such as Figure 4 As shown, the electronic device 500 includes a CPU 501, which can perform various appropriate actions and processes according to a program stored in ROM 502 or a program loaded from a storage portion into RAM 503.

[0080] RAM 503 also stores various programs and data required for system operation. CPU 501, ROM 502, and RAM 503 are interconnected via bus 504. I / O interface 505 is also connected to bus 504.

[0081] The following components are connected to I / O interface 505: an input section 506 including a keyboard, mouse, etc.; an output section 507 including a cathode ray tube (CRT), liquid crystal display (LCD), etc., and speakers, etc.; a storage section 508 including a hard disk, etc.; and a communication section 509 including a network interface card such as a LAN card, modem, etc. The communication section 509 performs communication processing via a network such as the Internet. A drive is also connected to I / O interface 505 as needed. A removable medium 511, such as a disk, optical disk, magneto-optical disk, semiconductor memory, etc., is installed on drive 510 as needed so that computer programs read from it can be installed into storage section 508 as needed.

[0082] In particular, according to embodiments of the present invention, the above-described reference process Figure 1 The described process can be implemented as a computer software program.

[0083] For example, the present invention includes a computer program product comprising a computer program carried on a computer-readable medium, the computer program containing program code for performing the methods shown in the flowchart. In such an embodiment, the computer program can be downloaded and installed from a network via a communication component, and / or installed from a removable medium. When the computer program is executed by CPU 501, it performs the functions defined above in the system of the present invention.

[0084] It should be noted that the computer-readable medium shown in this invention can be a computer-readable signal medium or a computer-readable storage medium, or any combination thereof. The computer-readable storage medium can be, for example,—but not limited to—an electrical, magnetic, optical, electromagnetic, infrared, or semiconductor system, apparatus, or device, or any combination thereof. More specific examples of the computer-readable storage medium may include, but are not limited to: an electrical connection having one or more wires, a portable computer disk, a hard disk, RAM (random access memory), ROM (read-only memory), erasable programmable read-only memory (EPROM or flash memory), optical fiber, portable compact disk read-only memory (CD-ROM), optical storage device, magnetic storage device, or any suitable combination thereof.

[0085] In this invention, a computer-readable storage medium can be any tangible medium containing or storing a program that can be used by or in connection with an instruction execution system, apparatus, or device. In this invention, a computer-readable signal medium can include a data signal propagated in baseband or as part of a carrier wave, carrying computer-readable program code. Such propagated data signals can take various forms, including but not limited to electromagnetic signals, optical signals, or any suitable combination thereof. A computer-readable signal medium can also be any computer-readable medium other than a computer-readable storage medium, which can send, propagate, or transmit a program for use by or in connection with an instruction execution system, apparatus, or device. The program code contained on the computer-readable medium can be transmitted using any suitable medium, including but not limited to: wireless, wireline, optical fiber, RF, etc., or any suitable combination thereof.

[0086] The flowcharts and block diagrams in the accompanying drawings illustrate the architecture, functionality, and operation of possible implementations of systems, methods, and computer program products according to various embodiments of the present invention. In this regard, each block in a flowchart or block diagram may represent a module, segment, or portion of code, which contains one or more executable instructions for implementing a specified logical function.

[0087] It should also be noted that in some alternative implementations, the functions marked in the boxes may occur in a different order than those shown in the accompanying drawings. For example, two consecutively indicated boxes may actually be executed in substantially parallel order, or sometimes in reverse order, depending on the functions involved. It should also be noted that each box in a block diagram or flowchart, and combinations of boxes in a block diagram or flowchart, can be implemented using a dedicated hardware-based system to perform the specified functions or operations, or using a combination of dedicated hardware and computer instructions.

[0088] The units described in the embodiments of the present invention can be implemented in software or hardware, and can also be located in a processor. The names of these units do not necessarily limit the specific unit itself. The described units or modules can also be located in a processor.

[0089] The present invention also provides a computer-readable storage medium, which may be included in the electronic device described in the above embodiments; or it may exist independently and not assembled into the electronic device. The computer-readable medium carries one or more programs, which, when executed by the electronic device, cause the electronic device to implement a global sensitivity analysis method for solid rocket motor propellant grain parameters as described in the above embodiments.

[0090] 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 global sensitivity analysis of solid rocket motor grain parameters, characterized in that, The application relates to a method for constructing a Kriging model of a solid rocket engine grain, comprising the following steps: S1, constructing an initial Kriging model of the solid rocket engine grain; S2, constructing a learning function; S3, screening a remaining sample point corresponding to a minimum learning function value from a total sample data set by using the learning function, adding the remaining sample point to a sample point set, and updating a reference Kriging model to obtain an iterative Kriging model; S4, judging whether the iterative Kriging model meets accuracy requirements; S5, if the iterative Kriging model does not meet the accuracy requirements, repeating steps S2-S4; if the iterative Kriging model meets the accuracy requirements, taking the Kriging model obtained in the iteration as an optimized Kriging model, and performing step S5; and S5, calculating a first-order sensitivity index and a total effect index based on the optimized Kriging model, wherein the first-order sensitivity index and the total effect index are used for reflecting the influence degree of each parameter of the grain on the maximum strain. The application relates to a method for constructing a Kriging model of a solid rocket engine grain, comprising the following steps: S1, constructing an initial Kriging model of the solid rocket engine grain; S2, constructing a learning function; S3, screening a remaining sample point corresponding to a minimum learning function value from a total sample data set by using the learning function, adding the remaining sample point to a sample point set, and updating a reference Kriging model to obtain an iterative Kriging model; S4, judging whether the iterative Kriging model meets accuracy requirements; S5, if the iterative Kriging model does not meet the accuracy requirements, repeating steps S2-S4; if the iterative Kriging model meets the accuracy requirements, taking the Kriging model obtained in the iteration as an optimized Kriging model, and performing step S5; and S5, calculating a first-order sensitivity index and a total effect index based on the optimized Kriging model, wherein the first-order sensitivity index and the total effect index are used for reflecting the influence degree of each parameter of the grain on the maximum strain. The method comprises the following steps: S1-1, constructing a total sample data set; S1-2, randomly selecting part of sample points in the total sample data set to form a sample point set; S1-3, calculating the maximum strain corresponding to all sample points in the sample point set to obtain a plurality of first maximum strains; and S1-4, constructing an initial Kriging model based on the sample point set and the plurality of first maximum strains. The method comprises the following steps: S2-1, obtaining an initial learning function; S2-2, inputting remaining sample points in the total sample data set which are not added to the sample point set into the initial Kriging model to calculate the maximum strain response value and the corresponding standard deviation of each remaining sample point; and S2-3, constructing a learning function of the Kriging model based on the maximum strain response value and the corresponding standard deviation of each remaining sample point. ​ ​ ​ ​ ​ ​ 2. The method of claim 1, wherein, ​ ​ ​ ​ ​ 3. The method of claim 2, wherein the method is characterized by, ​ ​ ​ ​ 4. The method of claim 3, wherein the method is characterized by, The initial learning function has a distance adjustment factor for avoiding excessive aggregation of sample points. The initial learning function is obtained by: constructing an active learning function; updating the distance adjustment factor according to the current iteration number; and constructing the initial learning function according to the distance adjustment factor and the active learning function.

5. The method of claim 3, wherein the method is characterized by, The learning function is used to screen the remaining sample points corresponding to the minimum learning function value, and the remaining sample points corresponding to the minimum learning function value are added to the sample point set. The reference Kriging model is updated by using the updated sample point set to obtain an iterative Kriging model, including: updating the sample point set according to the learning function; calculating the maximum strain corresponding to all sample points in the sample point set to obtain a plurality of second maximum strains; and constructing an iterative Kriging model based on the sample point set and the plurality of second maximum strains.

6. The method of claim 5, wherein, The sample point set is updated according to the learning function, including: inputting the maximum strain response value of each remaining sample point and the corresponding standard deviation into the learning function to obtain a plurality of learning function values; and adding the remaining sample points corresponding to the minimum learning function value to the sample point set.

7. The method of claim 5, wherein the method is characterized by, The iterative Kriging model is determined whether to meet the accuracy requirement, including: inputting the remaining sample points corresponding to the minimum learning function value into the iterative Kriging model to calculate the first iteration standard deviation; inputting the remaining sample points corresponding to the minimum learning function value into the reference Kriging model to calculate the second iteration standard deviation; if the absolute value of the difference between the first iteration standard deviation and the second iteration standard deviation is less than or equal to the set multiple of the second iteration standard deviation, it is determined that the accuracy requirement is met; otherwise, it is determined that the accuracy requirement is not met.

8. The method of claim 2, wherein, Based on the optimized Kriging model, the first-order sensitivity index and the total effect index are calculated, including: S5-1: generating a first sample point and a second sample point according to the distribution of sample points in the sample data set; S5-2: replacing a column in the matrix corresponding to the first sample point with a column in the matrix corresponding to the second sample point to obtain a third sample point; one column of the third sample point is the same as one column of the second sample point, and the remaining columns are the same as the remaining columns of the first sample point; S5-3: repeating step S5-2 to obtain a plurality of third sample points; S5-4: inputting the first sample point, the second sample point, and the plurality of third sample points into the optimized Kriging model to calculate the maximum strain response value of the first sample point, the maximum strain response value of the second sample point, the plurality of maximum strain response values of the plurality of third sample points, and the standard deviation of the first sample point, the standard deviation of the second sample point, and the plurality of standard deviations of the plurality of third sample points, respectively; S5-5: calculating the first-order sensitivity index and the total effect index according to the maximum strain response value of the first sample point, the maximum strain response value of the second sample point, the plurality of maximum strain response values of the plurality of third sample points, and the standard deviation of the first sample point, the standard deviation of the second sample point, and the plurality of standard deviations of the plurality of third sample points.

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