CN116822240A - Solid engine thrust uncertainty modeling method based on maximum entropy method - Google Patents
Solid engine thrust uncertainty modeling method based on maximum entropy method Download PDFInfo
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Abstract
The method for modeling the thrust uncertainty of the solid engine based on the maximum entropy method is provided, based on the maximum entropy method and combined with an eigenvoice decomposition order reduction technology and a kriging agent model, the uncertainty of a thrust curve can be accurately quantified, the rapid and accurate prediction of the uncertainty of the thrust curve can be realized, and the analysis and calculation efficiency of the uncertainty of the solid engine can be improved; according to the invention, the curve is subjected to normalization processing according to the data characteristics before the thrust curve data is reduced, so that the precision of a reduced model can be effectively improved, errors generated by the reduction are reduced, and the number of modes is reduced; the rapid thrust curve uncertainty prediction model provided by the invention can be suitable for the prediction of the thrust uncertainty of solid rockets of various types of powder, can also be used for modeling the uncertainty of the grain mass change curve of the solid rockets, and has high model generalization capability.
Description
Technical Field
The invention belongs to the technical field of aerospace, and particularly relates to a solid engine thrust uncertainty modeling method based on a maximum entropy method.
Background
In the fine design of a solid engine, the influence of uncertainty of design variables on thrust performance is required to be considered, and a thrust curve considering the uncertainty has the problems of difficult description and difficult accurate prediction. At present, in order to perform uncertainty analysis, a conventional Monte Carlo method is only adopted to call a large amount of solid engine analysis models for calculation so as to obtain accurate thrust curve uncertainty distribution, and the calculation and analysis efficiency is low; however, when a solid engine pattern is selected, its thrust curve generally has similar rules that can be obtained using a reduced order model, thereby converting the uncertainty of the thrust curve into an uncertainty of a reduced parameter, which can be quantified using a maximum entropy method. Therefore, it is necessary and widely demanded to develop a field uncertainty modeling method based on the maximum entropy method.
Disclosure of Invention
The invention solves the technical problems that: the method for modeling the uncertainty of the thrust of the solid engine based on the maximum entropy method is provided, the uncertainty of the thrust curve can be accurately quantified based on the maximum entropy method by combining an eigenvoice orthogonal decomposition order reduction technology and a kriging agent model, the characteristics of the thrust curve of the solid engine are extracted, the accurate quantification of the uncertainty thrust curve is realized, the rapid and accurate prediction of the uncertainty thrust curve when the design variable is changed is realized, and the uncertainty analysis and calculation efficiency of the solid engine is improved.
The invention adopts the technical scheme that: the method for modeling the thrust uncertainty of the solid engine based on the maximum entropy method comprises the following steps:
1) Generating a thrust curve sample data set to be modeled, namely a thrust matrix; the method comprises the following specific steps:
1-1) selecting a solid engine thrust calculation analysis model and design variables, determining the design space of the design variables and the uncertainty of parameters, randomly sampling to obtain m input parameter samples, and taking the m input parameter samples as outer layer sampling data;
1-2) generating n parameter samples subjected to distribution as inner layer sampling data near each obtained input parameter sample according to the uncertainty type of the input parameter;
1-3) calculating the obtained n parameter samples, wherein the total operand is m multiplied by n, and thrust data with uncertainty is obtained;
1-4) extracting characteristic time nodes from thrust data corresponding to the modeling sample, and normalizing according to the time nodes to obtain a normalized thrust matrix;
2) Performing eigen orthogonal decomposition order reduction on a thrust matrix of the modeling sample, and calculating first four-order central statistical moment information after order reduction corresponding to each group of design variables;
3) Establishing a prediction model of the statistical moment information in the step 2) by using a kriging model;
4) Using the prediction model in the step 3) to obtain solid engine thrust data which contains uncertainty and is stored in a matrix form with the detection sample after the detection sample is used as input and predicting by using the prediction model, and then carrying out inverse normalization on the solid engine thrust data according to the normalization method of the step 1-4) to obtain a solid engine thrust curve containing uncertainty;
5) And (3) comparing the thrust curve directly calculated by the detection sample in the step (1-1) with the solid engine thrust curve corresponding to the detection sample in the step (4).
The specific steps of the step 2) are as follows:
2-1) reducing the thrust matrix obtained in the step 1-4) by using an eigenvoice orthogonal decomposition method, extracting a front L-order mode with the mode energy sum accounting for more than 99.9%, and obtaining a mode vector phi and L mode coefficients after the reduction;
2-2) calculating the first 4-order central statistical moment of the L modal coefficients after the reduction of each inner layer sampling data, and obtaining L multiplied by 0.9mmultiplied by 4 moment information in total.
In the step 4), the specific steps for determining the thrust curve of the solid engine are as follows:
4-1) predicting to obtain L×4 first 4-order moment predicted values in total of each modal coefficient by using the detection sample in step 1-1) and using the prediction model in step 3);
4-2) for each modal coefficient, calculating a probability density distribution function of each modal coefficient by using a maximum entropy method according to the first 4-order moment;
4-3) sampling the modal coefficient according to the probability density function obtained in the step 4-2);
4-4): multiplying the modal coefficient sampling result in the step 4-3) by the modal vector phi obtained in the step 2-1) to obtain solid engine thrust data which corresponds to the detection sample, contains uncertainty and is stored in a matrix form.
In step 1-1) above, 90% of the input parameter samples are used for modeling and 10% are used for detection.
5. The method for modeling the thrust uncertainty of the solid engine based on the maximum entropy method according to claim 1, wherein the method comprises the following steps of: in the above step 1-2), 3000 is taken as the parameter sample n of the intra-layer sample data.
In the step 3), the kriging model adopts a cubic spline kernel function.
Compared with the prior art, the invention has the advantages that:
1. according to the technical scheme, based on a maximum entropy method, by combining an eigenvoice orthogonal decomposition order reduction technology and a kriging proxy model, the uncertainty of a thrust curve can be accurately quantified, the characteristics of the thrust curve of the solid engine are extracted, the accurate quantification of the uncertainty thrust curve is realized, the rapid and accurate prediction of the uncertainty thrust curve when a design variable is changed is realized, and the uncertainty analysis and calculation efficiency of the solid engine is improved;
2. according to the technical scheme, the curve is normalized according to the data characteristics before the thrust curve data is reduced, so that the precision of a reduced model can be effectively improved, errors generated by the reduction are reduced, and the number of modes is reduced;
3. the rapid thrust curve uncertainty prediction model provided by the technical scheme can be suitable for predicting the thrust uncertainty of the solid rocket of each shaped charge, can also be used for modeling the uncertainty of the explosive column quality change curve of the solid rocket, and has high model generalization capability.
Drawings
FIG. 1 is a flow chart of a method for modeling the thrust uncertainty of a solid engine based on a maximum entropy method;
FIG. 2 is a schematic illustration of the geometry of a solid engine star-shaped charge according to the present invention;
FIG. 3 is a schematic illustration of the original thrust curve of the solid engine of the present invention;
FIG. 4 is a graph of thrust curves after an original curve normalization operation of a solid engine thrust curve in accordance with the present invention;
FIG. 5 is a graph showing a comparison of the uncertainty prediction results of the thrust curve according to the present invention;
FIG. 6 is a partial magnification of the thrust curve uncertainty prediction result in the present invention;
FIG. 7 is a graph comparing probability density distributions of predicted thrust at time 20s for a solid engine according to the present invention;
FIG. 8 is a graph comparing cumulative distribution function curves of predicted thrust at the moment of the solid engine 20s according to the present invention.
Detailed Description
The technical solutions in the embodiments of the present invention will be clearly and completely described in the following with reference to fig. 1 to 8 in the embodiments of the present invention, and it is obvious that the described embodiments are only some embodiments of the present invention, but not all embodiments. All other embodiments, which can be made by those skilled in the art based on the embodiments of the invention without making any inventive effort, are intended to be within the scope of the invention.
It should be noted that, in this document, the terms "comprises," "comprising," or any other variation thereof, are intended to cover a non-exclusive inclusion, such that a process, method, article, or apparatus that comprises a list of elements does not include only those elements but may include other elements not expressly listed or inherent to such process, method, article, or apparatus. Without further limitation. The inclusion of an element as defined by the phrase "comprising one does not exclude the presence of other like elements in a process, method, article, or apparatus that comprises an element.
Referring to FIGS. 1-5, embodiments of the invention are described in detail
The method for modeling the thrust uncertainty of the solid engine based on the maximum entropy method comprises the following steps:
1) Generating a thrust curve sample data set to be modeled, namely a thrust matrix; the method comprises the following specific steps:
1-1) selecting a solid engine thrust calculation analysis model and design variables, determining the design space of the design variables and the uncertainty of parameters, randomly sampling to obtain m input parameter samples, wherein the input parameter samples are used as outer layer sampling data, and the input parameter samples refer to input parameters of the solid engine analysis model, such as grain length, grain diameter and the like, and do not have specific requirements on the method; the number m of input parameter samples is related to the dimension of the design variable, 90% of m input parameter samples are used for modeling, 10% are used for detection, in this case, 6 design variables, 7 uncertainty parameters, and the number m=1000 of samples, wherein 900 are used as modeling samples, and 100 are used as detection samples;
1-2) generating n parameter samples subject to distribution as inner layer sampling data according to the uncertainty type of input parameters near each obtained input parameter sample (namely m input parameter samples); taking 3000 as a parameter sample n of inner layer sampling data, wherein the statistical moment calculated by sampling can be stably converged due to the law of large numbers; in the test case, in order to stabilize the statistical moment of the uncertainty distribution, the inner layer sampling number n=3000;
1-3) calculating the obtained n parameter samples, wherein the total operand is m multiplied by n, and thrust data with uncertainty is obtained;
1-4) extracting characteristic time nodes from thrust data corresponding to the modeling sample, and normalizing according to the time nodes to obtain a normalized thrust matrix; the time node is defined as: when the slope is less than 1×10 5 When N/s is reached, the thrust ascending section is considered to be ended; when the slope is smaller than-1×10 5 At N/s, the plateau of the thrust is considered to end; then until the thrust is zero, the thrust is the descending segment of the curve; the rising segment is described by 5-point average samplingThe method comprises the steps of carrying out a first treatment on the surface of the The plateau segment is described by 85 point average samples; the descent segment is described by 60 point average samples; obtaining normalized thrust matrixes, wherein each thrust curve is normalized to a vector of 1 multiplied by 150; as shown in fig. 3, the thrust curve (original curve) before normalization is shown, and as shown in fig. 4, the result after normalization is shown;
2) Performing eigen orthogonal decomposition order reduction on a thrust matrix of a modeling sample, and calculating the first four-order central statistical moment information after order reduction corresponding to each group of design variables, wherein the method comprises the following specific steps of:
2-1) reducing the thrust matrix obtained in the step 1-4) by using an eigenvoice orthogonal decomposition method, extracting a front L-order mode with the mode energy sum accounting for more than 99.9%, and obtaining a mode vector phi and L mode coefficients after the reduction;
2-2) calculating the first 4-order central statistical moment of the L modal coefficients after the reduction of each inner layer sampling data, and obtaining L multiplied by 0.9mmultiplied by 4 moment information in total.
3) Establishing a prediction model of the statistical moment information in the step 2) by using a kriging model; specifically, the kriging model adopts a cubic spline kernel function.
4) Using the prediction model in the step 3) to obtain solid engine thrust data which contains uncertainty and is stored in a matrix form with the detection sample after the detection sample is used as input and predicting by using the prediction model, and then carrying out inverse normalization on the solid engine thrust data according to the normalization method of the step 1-4) to obtain a solid engine thrust curve containing uncertainty; the specific steps for determining the thrust curve of the solid engine are as follows:
4-1) predicting to obtain L×4 first 4-order moment predicted values in total of each modal coefficient by using the detection sample in step 1-1) and using the prediction model in step 3);
4-2) for each modal coefficient, calculating a probability density distribution function of each modal coefficient by using a maximum entropy method according to the first 4-order moment; the maximum entropy method solves the probability density function and has five constraints, namely: the function integral in the function calculation domain is 1; calculating a first-order central moment to be 0 according to the obtained function; calculating a second order central moment equal to the second order central moment of the sample according to the obtained function; calculating third-order central moment equal to the third-order central moment of the sample according to the obtained function; calculating a fourth-order central moment equal to the fourth-order central moment of the sample according to the obtained function; converting constraint into optimization problem by using Lagrangian multiplier, wherein the coefficient initial value of each multiplier is 0; solving the optimization problem after conversion by using a steepest descent method;
4-3) sampling the modal coefficient according to the probability density function obtained in the step 4-2), wherein the sampling number in the test case is 1000;
4-4): multiplying the modal coefficient sampling result in the step 4-3) by the modal vector phi obtained in the step 2-1) to obtain solid engine thrust data which corresponds to the detection sample, contains uncertainty and is stored in a matrix form, as shown in fig. 5-6; the predicted thrust value data of the solid engine at the moment of 20s work is compared with the original data, and as shown in fig. 7, a probability density distribution comparison chart is shown, and as shown in fig. 8, an accumulated distribution function comparison chart is shown;
5) And (3) comparing the thrust curve directly calculated by the detection sample in the step (1-1) with the solid engine thrust curve corresponding to the detection sample in the step (4).
According to the technical scheme, the modeling of the thrust uncertainty of the solid engine is realized based on a maximum entropy method and a reduced order-prediction model, and compared with the prior art, the method is based on the maximum entropy method, combines an intrinsic orthogonal decomposition reduced order technology and a Kriging agent model, can accurately quantify the uncertainty of a thrust curve, can realize the rapid and accurate prediction of the uncertainty of the thrust curve, and improves the analysis and calculation efficiency of the uncertainty of the solid engine; according to the invention, the curve is subjected to normalization processing according to the data characteristics before the thrust curve data is reduced, so that the precision of a reduced model can be effectively improved, errors generated by the reduction are reduced, and the number of modes is reduced; the rapid thrust curve uncertainty prediction model provided by the invention can be suitable for the prediction of the thrust uncertainty of solid rockets of various types of powder, can also be used for modeling the uncertainty of the grain mass change curve of the solid rockets, and has high model generalization capability.
It will be evident to those skilled in the art that the invention is not limited to the details of the foregoing illustrative embodiments, and that the present invention may be embodied in other specific forms without departing from the spirit or essential characteristics thereof. The present embodiments are, therefore, to be considered in all respects as illustrative and not restrictive, the scope of the invention being indicated by the appended claims rather than by the foregoing description, and all changes which come within the meaning and range of equivalency of the claims are therefore intended to be embraced therein. Any reference sign in a claim should not be construed as limiting the claim concerned.
Furthermore, it should be understood that although the present disclosure describes embodiments, not every embodiment is provided with a separate embodiment, and that this description is provided for clarity only, and that the disclosure is not limited to the embodiments described in detail below, and that the embodiments described in the examples may be combined as appropriate to form other embodiments that will be apparent to those skilled in the art.
Claims (6)
1. The method for modeling the thrust uncertainty of the solid engine based on the maximum entropy method is characterized by comprising the following steps of:
1) Generating a thrust curve sample data set to be modeled, namely a thrust matrix; the method comprises the following specific steps:
1-1) selecting a solid engine thrust calculation analysis model and design variables, determining the design space of the design variables and the uncertainty of parameters, randomly sampling to obtain m input parameter samples as outer layer sampling data, wherein the m input parameter samples comprise modeling samples and detection samples;
1-2) generating n parameter samples subjected to distribution as inner layer sampling data near each obtained input parameter sample according to the uncertainty type of the input parameter;
1-3) calculating the obtained n parameter samples, wherein the total operand is m multiplied by n, and thrust data with uncertainty is obtained;
1-4) extracting characteristic time nodes from thrust data corresponding to the modeling sample, and normalizing according to the time nodes to obtain a normalized thrust matrix;
2) Performing eigen orthogonal decomposition order reduction on a thrust matrix of the modeling sample, and calculating first four-order central statistical moment information after order reduction corresponding to each group of design variables;
3) Establishing a prediction model of the statistical moment information in the step 2) by using a kriging model;
4) Using the prediction model in the step 3) to obtain solid engine thrust data which contains uncertainty and is stored in a matrix form with the detection sample after the detection sample is used as input and predicting by using the prediction model, and then carrying out inverse normalization on the solid engine thrust data according to the normalization method of the step 1-4) to obtain a solid engine thrust curve containing uncertainty;
5) And (3) comparing the thrust curve directly calculated by the detection sample in the step (1-1) with the solid engine thrust curve corresponding to the detection sample in the step (4).
2. The method for modeling the thrust uncertainty of the solid engine based on the maximum entropy method according to claim 1, wherein the method comprises the following steps of: the specific steps of the step 2) are as follows:
2-1) reducing the thrust matrix obtained in the step 1-4) by using an eigenvoice orthogonal decomposition method, extracting a front L-order mode with the mode energy sum accounting for more than 99.9%, and obtaining a mode vector phi and L mode coefficients after the reduction;
2-2) calculating the first 4-order central statistical moment of the L modal coefficients after the reduction of each inner layer sampling data, and obtaining L multiplied by 0.9mmultiplied by 4 moment information in total.
3. The method for modeling the thrust uncertainty of the solid engine based on the maximum entropy method according to claim 2, wherein the method comprises the following steps of: in the step 4), the specific steps for determining the thrust curve of the solid engine are as follows:
4-1) predicting to obtain L×4 first 4-order moment predicted values in total of each modal coefficient by using the detection sample in step 1-1) and using the prediction model in step 3);
4-2) for each modal coefficient, calculating a probability density distribution function of each modal coefficient by using a maximum entropy method according to the first 4-order moment;
4-3) sampling the modal coefficient according to the probability density function obtained in the step 4-2);
4-4): multiplying the modal coefficient sampling result in the step 4-3) by the modal vector phi obtained in the step 2-1) to obtain solid engine thrust data which corresponds to the detection sample, contains uncertainty and is stored in a matrix form.
4. The method for modeling the thrust uncertainty of the solid engine based on the maximum entropy method according to claim 1, wherein the method comprises the following steps of: in step 1-1) above, 90% of the input parameter samples are used for modeling and 10% are used for detection.
5. The method for modeling the thrust uncertainty of the solid engine based on the maximum entropy method according to claim 1, wherein the method comprises the following steps of: in the above step 1-2), 3000 is taken as the parameter sample n of the intra-layer sample data.
6. The method for modeling the thrust uncertainty of the solid engine based on the maximum entropy method according to claim 1, wherein the method comprises the following steps of: in the step 3), the kriging model adopts a cubic spline kernel function.
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| CN117077297A (en) * | 2023-10-17 | 2023-11-17 | 中国科学院工程热物理研究所 | Natural laminar flow nacelle pneumatic robust optimization design method based on double-layer proxy model |
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| CN117077297A (en) * | 2023-10-17 | 2023-11-17 | 中国科学院工程热物理研究所 | Natural laminar flow nacelle pneumatic robust optimization design method based on double-layer proxy model |
| CN117077297B (en) * | 2023-10-17 | 2024-01-02 | 中国科学院工程热物理研究所 | Natural laminar flow nacelle pneumatic robust optimization design method based on double-layer proxy model |
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