A quick sensitivity analysis method for launch vehicle stage separation model

Abstract

The application discloses a kind of launch vehicle first-second stage separation model sensitivity rapid analysis method, to efficiently, accurately analyze the influence of key parameters in the process of launch vehicle first-second stage separation on overall performance.The specific steps include: first, the Mworks software is used to establish launch vehicle first-second stage separation model, which includes launch vehicle first-second stage rigid body model, thrust model, separation mechanism model and multiple models;Second, by FMU interface, Mworks model is imported into MATLAB environment, and it is simulated by Simulink;Third, a plurality of key parameters (such as thrust change, mass center deviation, mass size etc.) in the process of first-second stage separation are parameterized;Fourth, simulation result is obtained by calling Simulink model;Finally, Sobol global sensitivity analysis method is used to analyze the sensitivity of different parameters to launch vehicle first-second stage separation result.The method not only improves the speed and accuracy of sensitivity analysis, but also simplifies the work process through the seamless integration of Mworks and MATLAB.In addition, the application also provides intuitive sensitivity analysis result visualization, which is convenient for designers to intuitively understand the influence of parameter change on separation process, thereby accelerating the design and iterative optimization process of launch vehicle.In summary, the application provides an efficient and accurate launch vehicle first-second stage separation model rapid sensitivity analysis method, which provides strong technical support for the design and performance optimization of launch vehicle.

Description

TECHNICAL FIELD

[0001] The present application relates to the field of aerospace engineering, and particularly relates to a rapid sensitivity analysis method for a launch vehicle first-second stage separation model. BACKGROUND

[0002] As the core carrier of space launch missions, the performance and reliability of a launch vehicle are directly related to the success of space missions. During the flight cycle of the rocket, the first-second stage separation phase is particularly critical, as it not only requires precise time control, but also ensures that both stages of the rocket maintain stable flight attitude and trajectory after separation. Therefore, accurate simulation and analysis of the first-second stage separation process of the launch vehicle become an important part of rocket design and optimization.

[0003] Traditional sensitivity analysis methods for launch vehicle first-second stage separation models often rely on complex mathematical formulas and large-scale computing resources, and are implemented through manual derivation or specific program writing. This method not only consumes time and effort, but also is difficult to comprehensively and efficiently evaluate the influence of each parameter on the separation process when facing a multi-parameter, multi-variable system. In addition, due to model simplification or computing capacity limitations, traditional methods may not accurately capture the nonlinear dynamic characteristics in the separation process, thereby affecting the accuracy of the analysis results.

[0004] Therefore, the development of a rapid sensitivity analysis method for a launch vehicle first-second stage separation model aims to efficiently and accurately analyze the influence of key parameters on the overall performance of the launch vehicle first-second stage separation process, and to achieve rapid and accurate evaluation of key parameters in the separation process, which is of great significance for improving the design efficiency and reliability of the rocket control system. SUMMARY

[0005] The purpose of the present application is to provide a rapid sensitivity analysis method for a launch vehicle first-second stage separation model.

[0006] The technical solution for achieving the purpose of the present application is as follows: a rapid sensitivity analysis method for a launch vehicle first-second stage separation model, comprising:

[0007] Step 1: First, build a launch vehicle first-second stage separation model in Mworks software. The model includes a launch vehicle first-second stage rigid body model, a first stage rocket afterburner thrust model, a launch vehicle first-second stage separation mechanism model, a positive and negative thrust small rocket thrust model, and a sway force model.

[0008] Step 2: Convert the launch vehicle first-second stage separation parameterized model into an FMU (Functional Mock-up Unit) file through the "Export FMU" function of Mworks software, import the FMU file through the "FMU Import" module in Simulink, and make necessary settings and configurations according to simulation requirements.

[0009] Step three, write a simulation script, set the range, distribution and sampling times of the launch vehicle first and second stage separation parameters required for analysis, and generate the corresponding sample value combination.

[0010] Step four, for each sample value combination, run the Simulink model and record the corresponding output results.

[0011] Step five, use Sobol method to calculate the sensitivity index of each input parameter, including first-order sensitivity index and total sensitivity index.

[0012] Further, the first and second stage rigid body model of the launch vehicle in step one includes design parameters such as mass center, mass, moment of inertia, length, diameter. The output of the first stage rocket afterburner thrust model is the force curve varying with time, the output of the positive and negative thrust small rocket thrust model is constant force, and the output of the sway force model is constant force.

[0013] Further, the constraint device model in step one is composed of a constraint device and a signal source, wherein the two ends of the constraint device are the action points of the entity frame, there is no relative motion and relative rotation between the first and second stages before separation, and the constraint equation is described as

[0014]

[0015] In the formula, r A , r B are the position vectors of the entity frame interfaces at the two ends of the rigid body to be connected, θ A , θ B are the attitude angles at the two ends of the rigid body to be connected, and the first and second order derivatives of the position vector and attitude angle with respect to time are calculated.

[0016]

[0017] This is used to constrain the relative position, velocity and attitude of the first and second stages, and to make the constraint device release the constraint when receiving the timing model signal.

[0018] Further, the rigid body model in step one is connected through a connector, wherein the connector includes flow variables and potential variables, and the sum of the flow variables is zero and the potential variables are equal.

[0019] According to the physical principle, force balance equation and moment balance equation of the launch vehicle full-process dynamics rapid simulation model, a mathematical model is established; Modelica model is adopted, code development and interface definition are carried out based on standard library; wherein the interface is used to transmit force, torque and attitude angle.

[0020] Furthermore, the output of the first and second stage separation model of the launch vehicle described in step one is the position, velocity, acceleration, attitude changes of the first and second stage rockets during separation, as well as the minimum separation gap information.

[0021] Furthermore, the parameters selected in step three are all random variables that follow a uniform distribution and are all uncorrelated.

[0022] Furthermore, in step four, the Simulink model is called N times, and the resulting output is used as a sample Y. t , t=1,2,3,…,N.

[0023] Furthermore, as described in step five, according to the formula:

[0024]

[0025] Calculate the sample output Y obtained above t The variance V(Y) and parameters X i The conditional expectation of Y is E(Y|X). i The variance V(E(Y|X)) i )).

[0026] Furthermore, as described in step five, according to the Sobol method formula:

[0027]

[0028] Calculate the first-order sensitivity exponent S of each parameter of the first and second stage separation model of the launch vehicle to the output result during the separation process. i and overall sensitivity index

[0029] Compared with the prior art, the significant advantages of this invention are:

[0030] 1) Significantly Improved Analysis Efficiency: By combining the modeling convenience of MWorks and the powerful computing capabilities of MATLAB, along with the global sensitivity analysis characteristics of the Sobol method, this invention enables rapid and comprehensive evaluation of the first and second stage separation processes of launch vehicles. This greatly shortens the analysis cycle and improves the work efficiency of the design team.

[0031] 2) Enhanced Analysis Accuracy: The Sobol method, as a global sensitivity analysis method, can comprehensively capture the interactions between parameters in a multi-parameter system and their impact on the output results. Combined with the precise modeling and computational capabilities of MWorks and MATLAB, this invention can more accurately assess the impact of key parameters on the first and second stage separation process of a launch vehicle, providing a reliable basis for optimizing the control system.

[0032] 3) Improve design flexibility: The method of the present application has high flexibility and scalability. Users can easily adjust model parameters and analysis range according to actual needs to adapt to the design requirements of different launch vehicles. This helps to improve the innovation ability of the design team and promote the continuous development of launch vehicle technology.

[0033] 4) Promote technology integration and innovation: The implementation of the present application promotes the integration and innovation of MWorks, MATLAB and Sobol method in the field of launch vehicle design and analysis. This not only provides new ideas and methods for the technological progress of the aerospace field, but also provides a reference solution for similar problems in other fields. BRIEF DESCRIPTION OF DRAWINGS

[0034] Figure 1 is a flow chart of the launch vehicle one-two stage separation model rapid sensitivity analysis method of the present application.

[0035] Figure 2 is a launch vehicle one-two stage separation model established in Mworks software of the present application.

[0036] Figure 3 is the FMU file export option of the present application.

[0037] Figure 4 is a launch vehicle one-two stage separation model imported in Simulink through FMU file of the present application.

[0038] Figure 5 is a case analysis sensitivity result graph of the present application. DETAILED DESCRIPTION

[0039] The launch vehicle one-two stage separation model sensitivity rapid analysis method of the present application comprises the following steps: step one, first construct a launch vehicle one-two stage separation model in Mworks software. The model includes a launch vehicle one-two stage rigid body model, a one-stage rocket aftereffect thrust model, a launch vehicle one-two stage separation mechanism model, a positive and negative thrust small rocket thrust model, and a sway force model.

[0040] Step two, convert the launch vehicle one-two stage separation parameterized model into an FMU (Functional Mock-up Unit) file through the "Export FMU" function of Mworks software. The exported FMU file has an FMI version of V3 version, an FMI type of Co-Simulation, and a platform of x64. Import the FMU file through the "FMU Import" module in Simulink, and make necessary settings and configurations according to simulation requirements.

[0041] Step three, write the simulation script, set the range, distribution mode and sampling times of the launch vehicle first and second stage separation parameters required for analysis, and generate the corresponding sample value combination.

[0042] Step four, for each sample value combination, run the Simulink model and record the corresponding output results.

[0043] Step five, use Sobol method to calculate the sensitivity index of each input parameter, including the main sensitivity index and the total sensitivity index.

[0044] The specific steps are as follows:

[0045] First, build the launch vehicle first and second stage separation model in Mworks software. The model includes launch vehicle first and second stage rigid body model, first stage rocket afterburner model, launch vehicle first and second stage separation mechanism model, positive and negative thrust small rocket thrust model, and sway force model;

[0046] Second, convert the launch vehicle first and second stage separation parameterized model into FMU file through the "export FMU" function of Mworks software. The FMI version of the exported FMU file is V3 version, the FMI type is Co-Simulation, and the platform is x64. Import the FMU file through the "FMU Import" module in Simulink, and make necessary settings and configurations according to the simulation requirements;

[0047] Third. Write the simulation script, assume that the launch vehicle first and second stage separation parameters required for analysis are all uniformly distributed and uncorrelated random variables, generate random samples X t (x1,x2,…,x i )(t=1,2,…,i) as sample input according to the range of each parameter value, and the sample size is N;

[0048] Fourth, call the Simulink model N times, and take the corresponding results as sample output Y t , t=1,2,3,…,N.

[0049] Fifth, according to the formula

[0050]

[0051] Calculate the variance V(Y) of the aforementioned sample output Y t and the variance V(E(Y|X i )) of the conditional expectation E(Y|X i ) of each parameter X i .

[0052] According to the Sobol method formula:

[0053]

[0054] The first-order sensitivity index and the overall sensitivity index of each parameter of a first-stage-second-stage separation model of a carrier rocket to an output result in a separation process are calculated.

[0055] Embodiment

[0056] The first-stage-second-stage separation model of a certain type of carrier rocket is described in detail as follows:

[0057] A rapid sensitivity analysis method for a first-stage-second-stage separation model of a carrier rocket has a flowchart as shown in Figure 1 , and specifically includes the following steps:

[0058] First, a first-stage-second-stage separation model of a carrier rocket is established in Mworks software according to specific parameters of a certain type of carrier rocket, with the x-axis as the axial direction of the rocket. The model includes a first-stage-second-stage rigid body model of the carrier rocket, a first-stage rocket afterburner thrust model, a first-stage-second-stage separation mechanism model of the carrier rocket, a positive thrust, a small rocket thrust model, and a sway force model, as shown in Figure 2 ;

[0059] Second, the model is exported as an FMU file, and the FMI version of the exported FMU file is V3, the FMI type is Co-Simulation, and the platform is x64, as shown in Figure 3 . The FMU file is imported through an “FMU Import” module in Simulink, and necessary settings and configurations are made according to simulation requirements, as shown in Figure 4 ;

[0060] Third, the parameters of the first-stage-second-stage separation model of the carrier rocket that need to be analyzed are selected. Here, the first-stage-second-stage mass (m1, m2), the center of mass offset (Δx1, Δy1, Δz1, Δx2, Δy2, Δz2), the positive thrust F p , the negative thrust F r , the afterburner thrust F C , and the sway force (F sy , F sz ) are selected as the model parameters, and the remaining parameters remain unchanged. It is assumed that each parameter is a random variable subject to a uniform distribution and is not correlated, and a Sobol sequence algorithm is used to generate a random sample X t (t = 1, 2, …, 5000) with a sample size of 5000.

[0061] Fourth, the Simulink model is called according to the sample combination, and the axial displacement of the first stage of the carrier rocket is taken as the output result.

[0062] Fifth, the formula

[0063]

[0064] The variance V(Y) of the aforementioned obtained sample output Y and each parameter X t The conditional expectation E(Y|X i ) of Y. i The variance V(E(Y|X i )).

[0065] According to the Sobol formula:

[0066]

[0067] The first-order sensitivity index S of each parameter of the launch vehicle first-second stage separation model to the output result in the separation process i and the total sensitivity index The calculation results are shown in Table 1.

[0068] Table 1 Sensitivity calculation results

[0069] Parameters F r ]]> F p ]]> [CAT] Δx1 [CAT] Δy1 ​ [Delta]x2 ​ ​ m1 m2 F sy ]]> F sz ]]> F C ]]> First order sensitivity index 0.207 -0.001 0 -0.001 0.003 0 0 0 0.004 0 0 0 0.818 Overall sensitivity index 0.171 0 0 0 0 0 0 0 0.001 0 0 0 0.827

[0070] For ease of analysis, a column chart is obtained as Figure 5 It can be concluded that the afterburning thrust has a significant impact on the axial displacement of the launch vehicle first stage in the separation process, followed by the retro-rocket thrust, and the remaining parameters have little effect on it.

[0071] The technical features of the above embodiments can be combined in any manner. To make the description concise, not all possible combinations of the technical features in the above embodiments are described, but as long as the combinations of the technical features do not contradict, they should be considered within the scope of the present disclosure.

[0072] The above-described embodiments only express several implementation manners of the present application, and the description is relatively specific and detailed, but it should not be understood as a limitation on the scope of the patent. It should be pointed out that for ordinary skilled in the art, without departing from the concept of the present application, a number of modifications and improvements can be made, which are within the scope of the present application. Therefore, the scope of the patent of the present application should be subject to the appended claims.

Claims

1. A method for rapid sensitivity analysis of a launch vehicle stage separation model, characterized in that, The method comprises the following steps: Step one, first build the launch vehicle first and second stage separation model in Mworks software; the model includes launch vehicle first and second stage rigid body model, first stage rocket afterburner thrust model, launch vehicle first and second stage separation mechanism model, positive and negative small rocket thrust model or sway force model; The launch vehicle first and second stage separation model in step one is composed of a constraint device, a signal source and a signal source, wherein the two ends of the constraint device are the action points of the entity frame, there is no relative motion and relative rotation between the first and second stages before separation, and the constraint equation is described as where r A , r B are position vectors of the frame interfaces at the ends of the rigid body to be connected, θ A , θ B are attitude angles at the ends of the rigid body to be connected, and the first and second order derivatives with respect to time are taken for the position vectors and the attitude angles. The relative position, velocity and attitude of the first and second stages are constrained, and the constraint device is released when receiving the signal of the timing model; Step two, convert the launch vehicle first and second stage separation parameterized model in Mworks software into FMU (Functional Mock-up Unit) file, import the FMU file into Simulink, and set and configure according to the simulation requirements; Step three, write a simulation script, set the range, distribution method and sampling number of the launch vehicle first and second stage separation parameters to be analyzed, and generate the corresponding sample value combination; Step four, for each sample value combination, run the Simulink model and record the corresponding output results; Step five, calculate the sensitivity index of each input parameter with respect to the above output results by Sobol method, including first order sensitivity index and total sensitivity index.

2. The launch vehicle stage separation model rapid sensitivity analysis method of claim 1, wherein: The first and second stage rigid body model of the launch vehicle in step one includes mass center, mass, moment of inertia, length, diameter design parameters.

3. The launch vehicle stage separation model rapid sensitivity analysis method of claim 1, wherein: The first stage rocket afterburner thrust model in step one outputs a force curve varying with time, and the positive and negative small rocket thrust model and the sway force model output a constant force.

4. The launch vehicle stage separation model rapid sensitivity analysis method of claim 1, wherein The rigid body models in step one are connected through connectors, wherein the connectors include flow variables and potential variables, and the sum of flow variables is zero and the potential variables are equal; According to the physical principle, force balance equation and moment balance equation of the launch vehicle first and second stage separation model, a mathematical model is established; Modelica model is adopted, code development and interface definition are carried out based on standard library; wherein the interface is used to transmit force, torque and attitude angle.

5. The launch vehicle stage separation model rapid sensitivity analysis method of claim 1, wherein The output of the launch vehicle first and second stage separation model in step one is the position, velocity, acceleration, attitude change and minimum gap information of the first and second stage rockets during separation.

6. The launch vehicle stage separation model rapid sensitivity analysis method of claim 1, wherein The parameters selected in step three are random variables obeying uniform distribution and are not correlated.

7. The launch vehicle stage separation model rapid sensitivity analysis method of claim 1, wherein Step four calls the Simulink model N times, and the resulting corresponding results are taken as sample outputs Y t , t = 1, 2, 3, …, N.

8. The launch vehicle stage separation model rapid sensitivity analysis method of claim 1, wherein, The calculation formula of Sobol method in step five is according to the formula: where V(Y) is the variance of the resulting sample output Y t , E(Y|X i ) is the conditional expectation of Y given X i , and each parameter X i , V(E(Y|X i )) is the variance of the conditional expectation of Y given X i ; Further, according to the Sobol method formula in step five: The first order sensitivity index S of each parameter of the launch vehicle first and second stage separation model to the output result in the separation process i and the overall sensitivity index

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