Rapid sensitivity analysis method for first-stage and second-stage separation model of carrier rocket

Abstract

The invention discloses a rapid analysis method for the sensitivity of a carrier rocket first-stage and second-stage separation model, and aims to efficiently and accurately analyze the influence of key parameters on the overall performance in the carrier rocket first-stage and second-stage separation process. The method comprises the following specific steps: firstly, establishing a carrier rocket first-stage and second-stage separation model by utilizing Mworks software, wherein the model comprises a plurality of models such as a carrier rocket first-stage rigid body model, a carrier rocket second-stage rigid body model, a thrust model and a separation mechanism model; secondly, through an FMU interface, the Mworks model is imported into an MATLAB environment, and simulation setting is carried out on the Mworks model through Simulink; thirdly, performing parameter setting on a plurality of key parameters (such as thrust change, centroid offset, mass size and the like) in the first-stage and second-stage separation process; fourthly, calling a Simulink model to obtain a simulation result; and finally, analyzing the sensitivity of different parameters to the first-stage and second-stage separation results of the carrier rocket through a Sobol global sensitivity analysis method. The method not only improves the speed and precision of sensitivity analysis, but also simplifies the working process through seamless integration of Mworks and MATLAB. In addition, the invention also provides visual sensitivity analysis result visualization, so that designers can visually understand the influence of parameter change on the separation process, thereby accelerating the design and iterative optimization process of the carrier rocket. In conclusion, the rapid sensitivity analysis method for the first-stage and second-stage separation model of the carrier rocket is efficient and accurate, and powerful technical support is provided for design and performance optimization of the carrier rocket.

Description

Technical Field

[0001] The invention relates to the field of aerospace engineering, and in particular to a rapid sensitivity analysis method for a primary and secondary separation model of a carrier rocket. Background Art

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

[0003] Traditional methods for sensitivity analysis of the first and second stage separation model of launch vehicles often rely on complex mathematical formulas and large-scale computing resources, and are implemented by manual derivation or writing specific programs. This method is not only time-consuming and laborious, but also difficult to comprehensively and efficiently evaluate the impact of each parameter on the separation process when faced with multi-parameter and multi-variable systems. In addition, due to model simplification or computing power limitations, traditional methods may not be able to accurately capture the nonlinear dynamic characteristics of the separation process, thus affecting the accuracy of the analysis results.

[0004] Therefore, a rapid sensitivity analysis method for the launch vehicle's first- and second-stage separation model is developed to efficiently and accurately analyze the impact of key parameters in the launch vehicle's first- and second-stage separation process on the overall performance, 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 of the invention

[0005] The purpose of the present invention is to provide a rapid sensitivity analysis method for a primary and secondary separation model of a launch vehicle.

[0006] The technical solution to achieve the purpose of the present invention is: a rapid sensitivity analysis method for a launch vehicle primary and secondary separation model, comprising:

[0007] Step 1: First, build a launch vehicle first-stage and second-stage separation model in Mworks software. The model includes the first-stage and second-stage rigid body models of the launch vehicle, the first-stage rocket aftereffect thrust model, the first-stage and second-stage separation mechanism model of the launch vehicle, the forward and reverse thrust small rocket thrust models, and the shaking force model.

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

[0009] Step 3: Write a simulation script to set the range, distribution method and sampling times of the first and second stage separation parameters of the launch vehicle to be analyzed, and generate the corresponding sample value combination.

[0010] Step 4: For each sample value combination, run the Simulink model and record the corresponding output results.

[0011] Step 5: Use the Sobol method to calculate the sensitivity index of each input parameter, including the first-order sensitivity index and the overall sensitivity index.

[0012] Furthermore, the rigid body models of the first and second sub-stages of the launch vehicle described in step 1 include design parameters such as center of mass, mass, moment of inertia, length, and diameter. The output of the after-effect thrust model of the first sub-stage rocket is a force curve that changes with time, and the output of the forward thrust, reverse thrust small rocket thrust model and the sway force model is a constant force.

[0013] Furthermore, the constraint device model in step 1 is composed of a constraint device, a signal generator, and a signal generator, wherein the two ends of the constraint device are the action points of the entity frame, and there is no relative motion and relative rotation between the first and second sub-stages before separation. The constraint equation is described as

[0014]

[0015] Where r A 、r B is the position vector of the entity frame interface at both ends of the rigid body to be connected, θ A ,θ B For the attitude angles at both ends of the rigid body to be connected, calculate the first and second order derivatives of the position vector and attitude angle with respect to time;

[0016]

[0017] This is used to constrain the relative position, speed and posture of the first and second sub-stages, and enables the constraint device to release the constraint when receiving the signal of the timing model.

[0018] Furthermore, the rigid body models described in step 1 are connected by 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] A mathematical model is established based on the physical principles, force balance equations and torque balance equations of the full-process dynamics rapid simulation model of the launch vehicle; a Modelica model is adopted, and code development and interface definition are performed based on a standard library; wherein the interface is used to transmit force, torque and attitude angle.

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

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

[0022] Furthermore, the Simulink model is called N times as described in step 4, and the corresponding results generated are used as sample output Y t , t=1,2,3,…,N.

[0023] Further, as described in step 5, according to the formula:

[0024]

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

[0026] Further, as described in step 5, according to the Sobol method formula:

[0027]

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

[0029] Compared with the prior art, the present invention has the following significant advantages:

[0030] 1) Significantly improve analysis efficiency: By combining the modeling convenience of MWorks and the powerful computing power of MATLAB, as well as the global sensitivity analysis characteristics of the Sobol method, the present invention achieves a rapid and comprehensive evaluation of the first and second stage separation process of the launch vehicle. This greatly shortens the analysis cycle and improves the work efficiency of the design team.

[0031] 2) Enhanced analysis accuracy: As a global sensitivity analysis method, the Sobol method can fully capture the interaction between parameters in a multi-parameter system and their impact on the output results. Combining the precise modeling and computing capabilities of MWorks and MATLAB, the present invention can more accurately evaluate the impact of key parameters on the primary and secondary separation process of the launch vehicle, providing a reliable basis for optimizing the control system.

[0032] 3) Improve design flexibility: The method of the present invention is highly flexible and scalable. Users can easily adjust model parameters and analysis scope 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 sustainable development of launch vehicle technology.

[0033] 4) Promote technology integration and innovation: The implementation of this invention promotes the integration and innovation of three advanced technologies, MWorks, MATLAB and Sobol method, in the field of launch vehicle design and analysis. This not only provides new ideas and methods for technological progress in the aerospace field, but also provides solutions that can be used as reference for similar problems in other fields. BRIEF DESCRIPTION OF THE DRAWINGS

[0034] Figure 1 The present invention is a flow chart of a rapid sensitivity analysis method for a primary and secondary separation model of a carrier rocket.

[0035] Figure 2 The invention discloses a primary and secondary separation model of a launch vehicle established in the Mworks software.

[0036] Figure 3 It is an FMU file export option of the present invention.

[0037] Figure 4 The invention discloses a primary and secondary separation model of a launch vehicle which is imported into Simulink through an FMU file.

[0038] Figure 5 It is a sensitivity result diagram of the case analysis of the present invention. DETAILED DESCRIPTION

[0039] The invention discloses a method for rapid sensitivity analysis of a launch vehicle primary and secondary separation model, comprising the following steps: Step 1, firstly constructing a launch vehicle primary and secondary separation model in Mworks software. The model comprises a launch vehicle primary and secondary rigid body model, a primary rocket aftereffect thrust model, a launch vehicle primary and secondary separation mechanism model, a forward thrust and reverse thrust small rocket thrust model, and a sloshing force model.

[0040] Step 2: Use the "Export FMU" function of the Mworks software to convert the launch vehicle's first and second stage separation parameterized model into an FMU (Functional Mock-up Unit) file. The exported FMU file has an FMI version of V3, an FMI type of Co-Simulation, and a platform of x64. Import the FMU file through the "FMU Import" module in Simulink, and perform necessary settings and configurations according to simulation requirements.

[0041] Step 3: Write a simulation script to set the range, distribution method and sampling times of the first and second stage separation parameters of the launch vehicle to be analyzed, and generate the corresponding sample value combination.

[0042] Step 4: For each sample value combination, run the Simulink model and record the corresponding output results.

[0043] Step 5: Use the 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, a launch vehicle first-stage and second-stage separation model was constructed in Mworks software. The model includes the first-stage and second-stage rigid body models of the launch vehicle, the first-stage rocket aftereffect thrust model, the first-stage and second-stage separation mechanism model of the launch vehicle, the forward and reverse thrust small rocket thrust models, and the shaking force model;

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

[0047] Third, write a simulation script, assuming that the first and second stage separation parameters of the launch vehicle to be analyzed are uniformly distributed and unrelated random variables, and generate a random sample X with a sample size of N according to the range of each parameter value. t (x1,x2,…,x i )(t=1,2,…,i) as sample input;

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

[0049] Fifth, according to the formula

[0050]

[0051] Calculate the sample output Y obtained above t The variance V(Y) and the parameters X i The conditional expectation E(Y|X i ) is the variance of V(E(Y|X i )).

[0052] According to the Sobol formula:

[0053]

[0054] The first-order sensitivity index and overall sensitivity index of each parameter of the launch vehicle's first- and second-stage separation model to the output results during the separation process are calculated.

[0055] Example

[0056] The following is a detailed description of the first and second stage separation model of a certain type of launch vehicle:

[0057] A rapid sensitivity analysis method for the first and second stage separation model of a launch vehicle, the flow chart of which is as follows: Figure 1 As shown, the specific steps include:

[0058] First, according to the specific parameters of a certain type of launch vehicle, a launch vehicle first-stage and second-stage separation model is established in Mworks software, with the x-axis as the axial direction of the rocket. The model includes the first and second stage rigid body models of the launch vehicle, the first stage rocket aftereffect thrust model, the first and second stage separation mechanism model of the launch vehicle, the forward and reverse thrust small rocket thrust models, and the shaking force model, such as Figure 2 As shown;

[0059] Secondly, export the model as an FMU file. The FMI version of the exported FMU file is V3, the FMI type is Co-Simulation, and the platform is x64. Figure 3 Import the FMU file through the "FMU Import" module in Simulink, and perform necessary settings and configurations according to simulation requirements, such as Figure 4 As shown;

[0060] Third, select the parameters of the launch vehicle first and second stage separation model to be analyzed. Here, the first and second stage mass (m1, m2), center of mass offset (Δx1, Δy1, Δz1, Δx2, Δy2, Δz2), and positive thrust F p , reverse thrust F r , aftereffect thrust F C , Shaking force (F sy , F sz ) as the model parameter, and the other parameters remain unchanged. Assuming that each parameter is a random variable that obeys a uniform distribution and is uncorrelated, the Sobol sequence algorithm is used to generate a random sample X with a sample size of 5000. t (t=1,2,…,5000);

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

[0062] Fifth, according to the formula

[0063]

[0064] Calculate the sample output Y obtained above t The variance V(Y) and the parameters X i The conditional expectation E(Y|X i ) is the variance of V(E(Y|X i )).

[0065] According to the Sobol formula:

[0066]

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

[0068] Table 1 Sensitivity calculation results

[0069] parameter <![CDATA[F r ]]> <![CDATA[F p ]]> <![CDATA[Δx1]]> <![CDATA[Δy1]]> <![CDATA[Δz1]]> <![CDATA[Δx2]]> <![CDATA[Δy2]]> <![CDATA[Δz2]]> <![CDATA[m1]]> <![CDATA[m2]]> <![CDATA[F sy ]]> <![CDATA[F sz ]]> <![CDATA[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] To facilitate the analysis of the bar chart, Figure 5 It can be concluded that the after-effect thrust has a significant effect on the axial displacement of the first stage of the launch vehicle during separation, followed by the reverse thrust, while the other parameters have almost no effect on it.

[0071] The technical features of the above embodiments may be combined arbitrarily. To make the description concise, not all possible combinations of the technical features in the above embodiments are described. However, as long as there is no contradiction in the combination of these technical features, they should be considered to be within the scope of this specification.

[0072] The above-mentioned embodiments only express several implementation methods of the present application, and the descriptions thereof are relatively specific and detailed, but they cannot be understood as limiting the scope of the invention patent. It should be pointed out that, for a person of ordinary skill in the art, several variations and improvements can be made without departing from the concept of the present application, and these all belong to the protection scope of the present application. Therefore, the protection scope of the patent of the present application shall be subject to the attached claims.

Claims

1. A rapid sensitivity analysis method for a launch vehicle primary and secondary separation model, characterized in that: The following steps are involved: Step 1: First, build a launch vehicle one-stage and two-stage separation model in Mworks software; the model includes the launch vehicle one-stage and two-stage rigid body models, the one-stage rocket aftereffect thrust model, the launch vehicle one-stage and two-stage separation mechanism model, the forward thrust and reverse thrust small rocket thrust model or the shaking force model; Step 2: Convert the launch vehicle primary and secondary separation parameterized model in Mworks software into an FMU (Functional Mock-up Unit) file, import the FMU file into Simulink, and perform necessary settings and configurations according to simulation requirements; Step 3: Write a simulation script to set the range, distribution mode and sampling times of the launch vehicle primary and secondary separation parameters to be analyzed, and generate corresponding sample value combinations; Step 4: For each sample value combination, run the Simulink model and record the corresponding output results. Step 5: Use the Sobol method to calculate the sensitivity index of each input parameter relative to the above output results, including the first-order sensitivity index and the overall sensitivity index.

2. The rapid sensitivity analysis method for the primary and secondary separation model of a launch vehicle according to claim 1 is characterized in that: The first and second stage rigid body models of the launch vehicle described in step 1 include design parameters such as center of mass, mass, moment of inertia, length, and diameter.

3. The rapid sensitivity analysis method for the primary and secondary separation model of a launch vehicle according to claim 1 is characterized in that: The output of the after-effect thrust model of a sub-stage rocket described in step one is a force curve that changes with time, and the output of the forward thrust, reverse thrust small rocket thrust model and the sway force model is a constant force.

4. The rapid sensitivity analysis method for the primary and secondary separation model of a launch vehicle according to claim 1, characterized in that: Step 1: The launch vehicle first and second stage separation model is composed of a constraint device, a signal generator, and a signal generator. The two ends of the constraint device are the action points of the entity frame. There is no relative motion or rotation between the first and second stages before separation. The constraint equation is described as Where r A 、r B is the position vector of the entity frame interface at both ends of the rigid body to be connected, θ A ,θ B For the attitude angles at both ends of the rigid body to be connected, calculate the first and second order derivatives of the position vector and attitude angle with respect to time; This is used to constrain the relative position, velocity and posture of the first and second sub-level rigid bodies, and enables the constraint device to release the constraint when receiving the signal of the timing model.

5. The rapid sensitivity analysis method for the primary and secondary separation model of a launch vehicle according to claim 1, characterized in that: The rigid body models described in step 1 are connected by 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; A mathematical model is established based on the physical principles, force balance equations and torque balance equations of the primary and secondary separation model of the launch vehicle; a Modelica model is adopted, and code development and interface definition are performed based on a standard library; wherein the interface is used to transmit force, torque and attitude angle.

6. The rapid sensitivity analysis method for the primary and secondary separation model of a launch vehicle according to claim 1, characterized in that: The output of the launch vehicle first-stage and second-stage separation model described in step one is the position, velocity, acceleration, attitude change and minimum separation gap information of the first-stage and second-stage rockets during separation.

7. The rapid sensitivity analysis method for the primary and secondary separation model of a launch vehicle according to claim 1 is characterized in that: The parameters selected in step 3 are all random variables that obey uniform distribution and are uncorrelated.

8. The rapid sensitivity analysis method for the primary and secondary separation model of a launch vehicle according to claim 1, characterized in that: Step 4 calls the Simulink model N times and uses the corresponding results as sample output Y t , t=1,2,3,…,N.

9. The rapid sensitivity analysis method for the primary and secondary separation model of a launch vehicle according to claim 1, characterized in that: The calculation formula of the Sobol method described in step 5 is based on the formula: Where V(Y) is the sample output Y obtained above t The variance of E(Y|X i ) is V(Y) and each parameter X i The conditional expectation E(Y|X i ), V(E(Y|X i )) is the conditional expectation E(Y|X i )’s variance. Further, as described in step 5, according to the Sobol method formula: Calculate the first-order sensitivity index S of each parameter of the launch vehicle's first- and second-stage separation model to the output results during the separation process i and overall sensitivity index

Images