Solid engine charging multi-objective design optimization method

Abstract

The invention provides a solid engine charging multi-objective design optimization method, and relates to the technical field of solid engines, and the method comprises the steps: taking solid engine mass and solid engine impulse mass ratio as objective functions, and taking total impulse and working time as uncertainty constraint conditions; a solid engine charging multi-target uncertainty design optimization model is constructed; performing first-order inverse reliability analysis on the solid engine performance function at the design vector through an optimal chaos control strategy of an Armijo criterion to obtain a minimum performance target point vector, and inputting the minimum performance target point vector into a solid engine charging multi-target uncertainty design optimization model; the minimum mass of the solid engine and the maximum impulse mass ratio of the solid engine serve as optimization objectives, a Pareto optimal solution set is output through a multi-objective genetic algorithm to serve as a target design vector of a solid engine design variable, the charging performance reliability of the solid engine is remarkably improved, and mutual conflicts of the design objectives are effectively avoided.

Description

Technical Field

[0001] This application relates to the field of solid rocket motor technology, specifically to a multi-objective design optimization method for solid rocket motor propellant. Background Technology

[0002] Solid propulsion engines are chemical propulsion devices that use solid propellants. They possess numerous advantages, including simple structure, ease of use, and the ability to maintain long-term operational readiness, and are widely used in aerospace and other fields. The propellant grain is the engine's energy source, and its design level significantly impacts engine performance. However, on the one hand, solid propulsion engine propellant design parameters are numerous, and the operating environment is harsh. Uncertainties in geometric dimensions and material properties exist in the design and manufacturing stages, increasing the probability of propellant performance failures and significantly reducing reliability. On the other hand, multiple key design objectives, such as impulse-to-mass ratio and mass, conflict in propellant design, leading to suboptimal design results. Therefore, synergistic optimization of multiple objectives under uncertainty constraints is an effective way to improve the reliability and overall performance of solid propulsion engine propellants.

[0003] Currently, commonly used optimization methods for solid rocket motor propellant loading uncertainty design include single-objective uncertainty optimization methods and multi-objective uncertainty optimization methods based on modified chaotic control strategies. However, single-objective uncertainty optimization requires integrating multiple objectives into a single objective function through weight coefficients. The selection of weights is highly subjective, and different weights can lead to completely different "optimal solutions." The optimization results obtained heavily depend on the decision-maker's prior experience, which may result in a solution that is not applicable to the propellant loading design. On the other hand, multi-objective uncertainty optimization methods based on modified chaotic control strategies use a preset constant control factor, lacking adaptive adjustment capability. This may affect the stability and convergence of the optimization process, leading to poor convergence performance of multi-objective optimization algorithms based on modified chaotic control. When the chaotic control factor is set too large, the search point may deviate from the optimal solution range, even causing non-convergence; conversely, when the chaotic control factor is too small, the movement range of the search point is limited, potentially resulting in slow convergence.

[0004] The commonly used optimization design methods mentioned above face challenges in the optimization of solid rocket motor propellant design, such as parameter uncertainty leading to reduced propellant reliability, and the inability of single-objective optimization strategies to simultaneously resolve conflicts among multiple key performance design indicators. These issues severely affect the improvement of solid rocket motor propellant performance reliability and overall performance. Summary of the Invention

[0005] The purpose of this application is to address the above problems by providing a multi-objective design optimization method for solid rocket motor propellant, so as to achieve efficient design optimization of solid rocket motor propellant performance and improve the reliability and overall performance of solid rocket motor propellant.

[0006] This application provides a multi-objective design optimization method for solid rocket motor propellant charges, including: S1. Using the mass and impulse-mass ratio of the solid rocket motor as objective functions, the total impulse and operating time as uncertainty constraints, and the boundary values ​​of the solid rocket motor design variables as limiting constraints, a multi-objective uncertainty design optimization model for solid rocket motor propellant loading is constructed. S2. Construct the initial population matrix, population size, and function tolerance in the multi-objective optimization algorithm. Using the optimal chaotic control strategy based on the Armijo criterion, perform first-order inverse reliability analysis on each design vector of the solid rocket motor's function function in the initial population matrix to obtain the minimum performance target point vector of the solid rocket motor's function function at each design vector. The function function includes a total impulse constraint function function and a working time constraint function function. The minimum performance target point vector of the function function at each design vector includes the minimum performance target point vector of the total impulse constraint and the minimum performance target point vector of the working time constraint. S3. Input the minimum performance target point vector of the total impulse constraint and the minimum performance target point vector of the working time constraint into the multi-objective uncertainty design optimization model of the solid rocket motor. With the goal of minimizing the mass of the solid rocket motor and maximizing the impulse-mass ratio of the solid rocket motor, output the Pareto optimal solution set through the multi-objective genetic algorithm, and use the Pareto optimal solution set as the target design vector of the solid rocket motor design variables.

[0007] According to the technical solution provided in this application, step S2 includes: S2-1. Construct the initial population matrix, population size, and function tolerance in a multi-objective optimization algorithm; S2-2. Set the initial values ​​of the first-order inverse reliability analysis control parameters; wherein the optimized control parameters include at least the chaotic control step size, step size scaling factor, step size control parameter, and target reliability index. S2-3. Use the design vectors in the initial population matrix as the initial minimum performance target point vectors.

[0008] S2-4. Calculate the function response value and constraint gradient vector based on the initial minimum performance target point vector, and calculate the search direction based on the target reliability index and the constraint gradient vector; S2-5. Determine whether the constraint judgment condition is met based on the search direction, function response value, chaos control step size and constraint gradient vector. If so, proceed to step S2-6. S2-6-1. Based on the initial minimum performance target point vector, the target reliability index, and the chaos control step size, iterate the initial design vector to obtain the updated design vector; S2-7. If the updated minimum performance target vector satisfies the convergence criterion, then the updated minimum performance target vector is used as the minimum performance target vector; otherwise, the updated minimum performance target vector is used as the initial minimum performance target vector, and the process returns to step S2-4.

[0009] According to the technical solution provided in this application, step S2 further includes: S2-6-2. If the search direction, the chaotic control step size, and the constraint gradient vector judgment condition are used, the chaotic control step size is updated according to the Armijo criterion and the step size scaling factor, and then the process returns to step S2-4.

[0010] According to the technical solution provided in this application, step S2-4 includes: The initial minimum performance target point vector is spatially transformed to obtain the initial vector vector; The function response value and constraint gradient vector are calculated based on the initial vector, and the search direction is calculated based on the target reliability index and the constraint gradient vector.

[0011] According to the technical solution provided in this application, step S2-5 includes: If the following conditions are met: If so, then the constraint judgment condition is satisfied; in, For the first k The minimum performance target point vector in the next iteration; For the first k Chaos control step size for each iteration. For the search direction, For functional purposes, The gradient vector of the function. The target reliability index.

[0012] According to the technical solution provided in this application, step S2-6-1 includes: Calculate the gradient search direction based on the initial minimum performance target point vector, the target reliability index, the constraint gradient vector, and the chaos control step size; Based on the gradient search direction and the target reliability index, the updated minimum performance target point vector is iteratively calculated.

[0013] According to the technical solution provided in this application, step S2-7 includes: If satisfied Then the update The vectors satisfy the convergence criterion; where, Let X be the X-space vector corresponding to the updated minimum performance target point vector. Let X be the X-space vector corresponding to the initial design vector. This represents the convergence tolerance for first-order inverse reliability analysis.

[0014] Compared with the prior art, the beneficial effects of this application are as follows: The multi-objective design optimization method for solid rocket motor propellant provided by this application includes constructing a multi-objective uncertainty design optimization model for solid rocket motor propellant, with solid rocket motor mass and impulse-to-mass ratio as objective functions, total impulse and operating time as uncertainty constraints, and boundary values ​​of solid rocket motor design variables as limiting constraints; based on the function function and the optimal chaotic control strategy of the Armijo criterion, a first-order inverse reliability analysis is performed on each design vector of the solid rocket motor in the initial population matrix to obtain the minimum performance target point vector of the function function of the solid rocket motor; the function function includes a total impulse constraint function function and an operating time constraint function function, and correspondingly, the minimum performance target point vector includes a total impulse constraint reliable design vector and an operating time minimum performance target point vector; the total impulse constraint minimum performance target point vector and the operating time minimum performance target point vector are input into the multi-objective uncertainty design optimization model for solid rocket motor propellant, with the optimization objectives of minimizing solid rocket motor mass and maximizing solid rocket motor impulse-to-mass ratio, and a Pareto optimal solution set is output through a multi-objective genetic algorithm, and the Pareto optimal solution set is used as the target design vector of the solid rocket motor design variables. This method first constructs a multi-objective uncertainty design optimization model for propellant loading, with overall mass and impulse-to-mass ratio as objective functions and operating time and thrust as constraint functions. Second, it proposes an optimal chaotic control strategy based on the Armijo criterion to perform first-order inverse reliability analysis. This strategy enables optimal adaptive adjustment of chaotic control parameters, thus avoiding oscillations and chaos caused by fixed parameters. Finally, this optimal chaotic control strategy is integrated into the uncertainty design optimization framework to solve the established multi-objective uncertainty design optimization model for propellant loading. The inner layer uses an evolved optimal chaotic control strategy to perform reliability analysis, while the outer layer uses a multi-objective genetic algorithm to obtain the Pareto optimal solution set, thereby finding the globally optimal design under two objective functions and two uncertainty constraints. Compared to other implementation schemes, this invention achieves a synergistic optimization design of high reliability and comprehensive performance for solid rocket motor propellant loading, significantly improving the performance and reliability of solid rocket motor propellant loading. Attached Figure Description

[0015] To more clearly illustrate the technical solutions in this embodiment, the accompanying drawings used in the description of the embodiments will be briefly introduced below. Obviously, the accompanying drawings described below are only some embodiments of this application. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0016] Figure 1 A flowchart illustrating a multi-objective design optimization method for solid rocket motor propellant charges, provided in this application embodiment; Figure 2 A detailed flowchart of step S2 of a multi-objective design optimization method for solid rocket motor propellant provided in an embodiment of this application; Figure 3 This is a schematic diagram illustrating the convergence process of a multi-objective design optimization method for solid rocket motor propellant provided in an embodiment of this application. Detailed Implementation

[0017] To enable those skilled in the art to better understand the technical solutions of this application, the technical solutions in the embodiments of this application will be clearly and completely described below with reference to the accompanying drawings. The descriptions in this section are merely illustrative and explanatory, and should not be construed as limiting the scope of protection of this application. Specifically, the described embodiments are only some embodiments of this application, not all embodiments. All other embodiments obtained by those skilled in the art based on the embodiments of this application without creative effort should fall within the scope of protection of this application.

[0018] It should be noted that similar reference numerals and letters in the following figures denote similar items; therefore, once an item is defined in one figure, it does not need to be further defined and explained in subsequent figures. Furthermore, the terms "comprising" and "having," and any variations thereof, are intended to cover non-exclusive inclusion. For example, a process, method, system, product, or apparatus that comprises a series of steps or units is not necessarily limited to those steps or units explicitly listed, but may include other steps or units not explicitly listed or inherent to such process, method, product, or apparatus.

[0019] To make the technical solution of this application clearer and easier to understand, the multi-objective design optimization method for solid rocket motor propellant provided in the embodiments of this application is described below.

[0020] like Figure 1 As shown in the figure, this is a flowchart of a multi-objective design optimization method for solid rocket motor propellant provided in this embodiment. The method includes the following steps: S1. Using the mass and impulse-mass ratio of the solid rocket motor as objective functions, the total impulse and operating time as uncertainty constraints, and the boundary values ​​of the solid rocket motor design variables as limiting constraints, a multi-objective uncertainty design optimization model for solid rocket motor propellant loading is constructed. Specifically, the impulse-to-mass ratio of a solid rocket motor is a key indicator for measuring propulsion efficiency, while the mass of the solid rocket motor is a key indicator for measuring structural lightweighting. Solid rocket motor propellant design involves multiple parameters, including geometric dimensions (such as wing length and circumscribed circle diameter) and material properties (such as the reference burning rate of the propellant). These parameters inevitably fluctuate during the design and manufacturing stages, directly leading to an increased probability of failure in constraints related to propellant performance (thrust, operating time) and a significant decrease in reliability. Furthermore, there is an inherent contradiction between the key objectives of propellant design (maximizing the impulse-to-mass ratio and minimizing the mass), and single-objective optimization cannot simultaneously consider comprehensive performance, resulting in suboptimal design results. This invention constructs a multi-objective uncertainty design optimization model for solid rocket motor propellant, using solid rocket motor mass and impulse-to-mass ratio as objective functions, total impulse and operating time as uncertainty constraints, and boundary values ​​of solid rocket motor design variables as limiting constraints. The aim is to find the globally optimal design values ​​of solid rocket motor design variables within the boundary ranges of multiple design variables and while ensuring total impulse and operating time, so that the solid rocket motor mass is as small as possible and the impulse-to-mass ratio is as large as possible. The solid rocket motor design variables include wing length, wing width, wing tilt angle, circumscribed circle diameter, combustion chamber cylindrical section length, first-stage propellant reference burning rate, tail section inner bore length, aft end cap opening diameter, and forward end cap opening diameter. Other design parameters may also be included, which can be set and adjusted according to actual conditions; specific limitations are not specified here. Using total engine stroke and operating time as probabilistic constraints, a target reliability index of 99.87% is defined to ensure design feasibility under uncertainty conditions. The multi-objective uncertainty design optimization model for solid rocket motor propellant is as follows:

[0021] in, For the first i One solid rocket motor design variable n The number of design variables for solid rocket motors. for n A vector of solid rocket motor design variables consisting of individual solid rocket motor design variables. Let the mass function of the solid rocket motor be . For the mass-to-impulse ratio function of a solid rocket motor. This is for probability calculations; For target reliability indicators; For solid rocket motor final strike; For solid rocket motor operating time For the first i Lower limit values ​​of design variables for a solid rocket motor; For the first i The upper limit of the design variables for a solid rocket motor.

[0022] S2. Construct the initial population matrix, population size, and function tolerance in the multi-objective optimization algorithm. Using the optimal chaotic control strategy based on the Armijo criterion, perform first-order inverse reliability analysis on each design vector of the solid rocket motor's function function in the initial population matrix to obtain the minimum performance target point vector of the solid rocket motor's function function at each design vector. The function function includes a total impulse constraint function function and a working time constraint function function. The minimum performance target point vector of the function function at each design vector includes the minimum performance target point vector of the total impulse constraint and the minimum performance target point vector of the working time constraint. Specifically, see Figure 2 Step S2 includes: S2-1, constructing the initial population matrix, population size, and function tolerance in the multi-objective optimization algorithm; S2-2, setting the initial values ​​of the control parameters in the first-order inverse reliability analysis; wherein the control parameters of the first-order inverse reliability analysis include at least the chaotic control step size, step size scaling factor, step size control parameter, and target reliability index; S2-3, using the design vectors in the initial population matrix as initial minimum performance target point vectors; S2-4, calculating the function response value and constraint gradient vector based on the initial minimum performance target point vectors, and calculating the search direction based on the target reliability index and the constraint gradient vector; S2-5, based on the initial minimum performance target point vectors... The search direction, function response value, chaos control step size, and constraint gradient vector are used to determine whether the constraint judgment conditions are met. If so, step S2-6-1 is executed. S2-6-1: Based on the initial minimum performance target vector, the target reliability index, and the chaos control step size, the initial minimum performance target vector is iterated to obtain an updated minimum performance target vector. S2-6: If the updated minimum performance target vector satisfies the convergence criterion, it is used as the minimum performance target vector; otherwise, it is used as the initial minimum performance target vector, and the process returns to step S2-4. The function includes a total impulse constraint function and a working time constraint function. Correspondingly, the minimum performance target vector includes a total impulse constraint minimum performance target vector and a working time minimum performance target vector. During the execution of step S2, the total impulse constraint function and the working time constraint function are used as function functions respectively, and the above steps are executed to obtain the total impulse constraint minimum performance target vector and the working time minimum performance target vector respectively, to ensure total impulse reliability and working time reliability. It should be noted that the initial minimum performance target point vector can be set according to empirical values. For example, the average value of multiple solid rocket motor design variables can be used to form the initial design vector. It can also be adjusted according to the actual situation. No specific limitation is made here.

[0023] S3. Input the minimum performance target vector of the total impulse constraint and the minimum performance target vector of the working time constraint into the multi-objective uncertainty design optimization model of the solid rocket motor. With the goal of minimizing the mass of the solid rocket motor and maximizing the impulse-mass ratio of the solid rocket motor, output the Pareto optimal solution set through the multi-objective genetic algorithm, and use the Pareto optimal solution set as the target design vector of the solid rocket motor design variables.

[0024] Specifically, the minimum performance target vectors for total impulse constraint and operating time constraint, which have been verified for reliability, are input into the multi-objective uncertainty design optimization model for solid rocket motor propellant. The optimization objectives are to minimize the solid rocket motor mass and maximize its impulse-to-mass ratio. A multi-objective genetic algorithm outputs a Pareto optimal solution set, which is the target design vector for the solid rocket motor design variables. It is understood that this calculation process can be performed in Matlab software by inputting parameters as needed and executing the corresponding algorithm commands, allowing for direct call and output. The specific calculation process will not be elaborated here.

[0025] Furthermore, based on the above embodiments, step S2 includes: S2-1. Construct the initial population matrix, population size, and function tolerance in a multi-objective optimization algorithm; S2-2. Set the initial values ​​of the control parameters in the first-order inverse reliability analysis; wherein the first-order inverse reliability analysis control parameters include at least the chaos control step size, step size scaling factor, step size control parameter, and target reliability index. Specifically, the first-order inverse reliability analysis control parameters include at least the chaotic control step size (using...). This indicates that the initial step size is set to... ), step scaling factor (using It means that, among them, ) and step size control parameters (using It means that, among them, ) and target reliability index (using (Indicated). The optimized control parameters also include the mean values ​​of multiple solid rocket motor design variables (using... It means, that is, the first i The mean and upper limit of the design variables for each solid rocket motor (using...) It means, that is, the first i The upper limit and lower limit (using the design variables of a solid rocket motor) are the upper and lower limits. It means that the first i (Lower limit values ​​of design variables for a solid rocket motor).

[0026] S2-3. Use the design vectors in the initial population matrix as the initial minimum performance target point vectors.

[0027] S2-4. Calculate the function response value and constraint gradient vector based on the initial minimum performance target point vector, and calculate the search direction based on the target reliability index and the constraint gradient vector; Specifically, the initial minimum performance target point vector is first transformed from the X space to the U space to obtain the initial vector vector; then, the function response value and constraint gradient vector are calculated based on the initial vector vector, and the search direction is calculated based on the target reliability index and the constraint gradient vector.

[0028] S2-5. Determine whether the constraint judgment condition is met based on the search direction, function response value, chaos control step size and constraint gradient vector. If so, proceed to step S2-6-1. Specifically, the judgment is made if the following conditions are met: If so, then the constraint judgment condition is satisfied; in, For the first k Minimum performance target point vector in the next iteration; For the first k Chaos control step size for each iteration. For the search direction, For functional purposes, The gradient vector of the function. The target reliability index is defined as follows: If the above constraint conditions are met, it proves that the constraints are satisfied, and steps S2-3 are continued; otherwise, the chaotic control step size needs to be updated for iterative optimization. The function is defined as follows: Substitute the values ​​into the total stroke constraint function and the working time constraint function, respectively. The total stroke constraint function is as follows:

[0029] in, This is the response value of the total impulse constraint function. 5355 represents the total thrust of the solid rocket motor, and 5355 represents the design thrust requirement. The operating time constraint function is:

[0030] in, The response value of the function for the working time constraint. 33 represents the operating time of the solid rocket motor, and 33 represents the design requirement value for the operating time.

[0031] S2-6-1. Based on the initial minimum performance target point vector, the target reliability index, and the chaos control step size, iterate the initial minimum performance target point vector to obtain the updated minimum performance target point vector. Specifically, the gradient search direction is first calculated based on the initial minimum performance target point vector, the target reliability index, and the chaos control step size; then, the updated minimum performance target point vector is iteratively calculated based on the gradient search direction and the target reliability index.

[0032] S2-7. If the updated minimum performance target vector satisfies the convergence criterion, then the updated minimum performance target vector is used as the minimum performance target vector; otherwise, the updated minimum performance target vector is used as the initial minimum performance target vector, and the process returns to step S2-4.

[0033] Specifically, the updated minimum performance target point vector is transformed from U space back to X space to obtain the X space vector corresponding to the updated minimum performance target point vector, and then... This indicates that the X-space vector of the initial minimum performance target point vector is... It is indicated that the X-space vector corresponding to the updated minimum performance target point vector and the X-space vector of the initial design vector satisfy the following conditions: ,in, Let X be the X-space vector corresponding to the updated minimum performance target point vector. Let X be the X-space vector corresponding to the initial minimum performance target point vector. This is the convergence tolerance for the first-order inverse reliability analysis. If the condition is met, the updated minimum performance target vector satisfies the convergence criterion; the updated minimum performance target vector is then used as the reliable design vector. Otherwise, the updated minimum performance target vector is used as the minimum performance target design vector, and the process returns to step S2-2 to perform the first-order inverse reliability analysis again until the above convergence criterion is satisfied.

[0034] Furthermore, based on the above embodiments, step S2 further includes: S2-6-2. If the constraint judgment condition is not met according to the initial minimum performance target point vector and the chaotic control step size, then update the chaotic control step size according to the step size scaling factor based on the Armijo criterion, and then return to step S2-4.

[0035] Specifically, see Figure 2 If the initial minimum performance target point vector and the chaotic control step size determination do not satisfy the constraint determination conditions, then it is necessary to determine the following: Update the chaos control step size ,in, For the updated chaos control step size, This is the step size scaling factor. The step size for chaos control before the update.

[0036] It should be noted that the chaotic control parameters Adaptively selected according to the Armijo criterion, to ensure that the optimal step size is obtained in each iteration, it is required that... Conditions met:

[0037] in, For the first k The minimum performance target point vector obtained in the next iteration; Let be the chaotic control step size for the k-th iteration. For the search direction, For functional purposes, This represents the gradient vector of the function. When the search point approaches the reliability boundary, the step size automatically decreases to avoid overshoot; when the search point is far from the optimal range, the step size automatically increases to improve search efficiency. This completely solves the problems of "slow convergence" or "deviation from the optimal solution" caused by traditional fixed factors. Through dynamic adjustment of the step size, it adapts to the strong coupling relationship between total impulse / operating time and multiple design variables (e.g., the nonlinear effect of fuel rate variation on operating time). Wherein, the... Furthermore, based on the above embodiments, step S2-4 includes: The initial minimum performance target point vector is spatially transformed to obtain the initial vector vector; The function response value and constraint gradient vector are calculated based on the initial vector, and the search direction is calculated based on the target reliability index and the constraint gradient vector.

[0038] Specifically, the X-space vector of the initial minimum performance target point vector. According to the formula:

[0039] The X space will be transformed into the U space to obtain the initial vector. ;in, For the first k The X-space vector of the design vector, the initial minimum performance target point vector. Rosenblatt transforms the X space into the actual physical parameter space, and the U space into a normally distributed space. This spatial transformation aims to eliminate the dimensional differences between the parameters, providing a unified computational basis for reliability analysis. Then, the function response value and constraint gradient vector are calculated based on the initial vector. Finally, the target reliability index and the constraint gradient vector are used to apply the following formula:

[0040] Calculate the search direction; where, For the search direction, For the first k The minimum performance target point vector obtained in the next iteration. The gradient vector of the function. The target reliability index.

[0041] Furthermore, based on the above embodiments, step S2-5 includes: If the following conditions are met:

[0042] Then it is determined that the constraint conditions are met; where, For the first k The minimum performance target point vector obtained in the next iteration; For the first k Chaos control step size for each iteration. For the search direction, For functional purposes, The gradient vector of the function. The target reliability index.

[0043] Furthermore, based on the above embodiments, step S2-6-1 includes: Calculate the gradient search direction based on the initial minimum performance target point vector, the target reliability index, the constraint gradient vector, and the chaos control step size; Based on the gradient search direction and the target reliability index, the updated minimum performance point target vector is iteratively calculated.

[0044] Specifically, based on the initial minimum performance target point vector, the target reliability index, the constraint gradient vector, and the chaotic control step size, according to the formula:

[0045] Calculate the gradient search direction, where, For the search direction, For the first k Chaos control step size for each iteration. For functional purposes, The gradient vector of the function. As the target reliability index, To update the minimum performance point target vector, based on the gradient search direction and the target reliability index, according to the formula:

[0046] Iteratively calculate the updated minimum performance target point vector; wherein, the The gradient search direction is... To update the minimum performance target point vector, The target reliability index.

[0047] Furthermore, based on the above embodiments, step S2-5 includes: If satisfied Then the updated design vector satisfies the convergence criterion; where, The X-space vector corresponding to the updated design vector. Let X be the X-space vector corresponding to the initial design vector. Convergence tolerance for first-order inverse reliability analysis Specifically, using The minimum performance point target vector will be updated. From U space back to X space, according to Calculate the convergence parameters and compare them with the convergence tolerance of the first-order inverse reliability analysis. The size of the convergence parameter, if it is less than the convergence tolerance of the first-order inverse reliability analysis Then, it is determined that the updated design vector satisfies the convergence criterion; if the convergence parameter is greater than or equal to the first-order inverse reliability analysis convergence tolerance... If the updated design vector does not meet the convergence criterion, then it is determined that the updated design vector does not meet the convergence criterion.

[0048] Based on the above embodiments, the solid rocket motor design variables further include: wing length, wing width, wing tilt angle, circumscribed circle diameter, combustion chamber cylindrical section length, first-stage propellant reference burning rate, tail bore section length, rear end cap opening diameter, and front end cap opening diameter.

[0049] Specifically, for example, the design variables for a certain type of solid rocket motor are shown in Table 1. Table 1. Parameter information for solid rocket motor design variables

[0050] Based on the multi-objective design optimization method for solid rocket motor propellant provided in this application, the convergence optimization results of the impulse-to-mass ratio and mass of this solid rocket motor were successfully converged to the optimal solution for the solid rocket motor mass of 2639.8722 kg and the optimal solution for the impulse-to-mass ratio of 1901.0856 N·s / kg. 2 The specific convergence process is as follows: Figure 3 As shown.

[0051] In summary, the multi-objective design optimization method for solid rocket motor propellant provided in this application includes: constructing a multi-objective uncertainty design optimization model for solid rocket motor propellant, using solid rocket motor mass and impulse-to-mass ratio as objective functions, total impulse and operating time as uncertainty constraints, and boundary values ​​of solid rocket motor design variables as limiting constraints; performing first-order inverse reliability analysis on each design of the solid rocket motor in the initial population matrix based on the optimal chaotic control strategy using the Armijo criterion of the function function to obtain the minimum performance target point vector of the function function of the solid rocket motor; the function function includes a total impulse constraint function and an operating time constraint function, and correspondingly, the minimum performance target point vector includes a total impulse constraint minimum performance target point vector and an operating time minimum performance target point vector; inputting the total impulse constraint minimum performance target point vector and the operating time minimum performance target point vector into the multi-objective uncertainty design optimization model for solid rocket motor propellant, with the optimization objectives of minimizing solid rocket motor mass and maximizing solid rocket motor impulse-to-mass ratio, outputting a Pareto optimal solution set through a multi-objective genetic algorithm, and using the Pareto optimal solution set as the target design vector of the solid rocket motor design variables. This method first constructs a multi-objective uncertainty design optimization model for propellant loading, with overall mass and impulse-to-mass ratio as objective functions and operating time and thrust as constraint functions. Second, it proposes an optimal chaotic control strategy based on the Armijo criterion to perform first-order inverse reliability analysis. This strategy enables optimal adaptive adjustment of chaotic control parameters, thus avoiding oscillations and chaos caused by fixed parameters. Finally, this optimal chaotic control strategy is integrated into the uncertainty design optimization framework to solve the established multi-objective uncertainty design optimization model for propellant loading. The inner layer uses an evolved optimal chaotic control strategy to perform first-order reliability analysis, while the outer layer uses a multi-objective genetic algorithm to obtain the Pareto optimal solution set, thereby finding the globally optimal design under two objective functions and two uncertainty constraints. Compared to other implementation schemes, this invention achieves a synergistic optimization design of high reliability and comprehensive performance for solid rocket motor propellant loading, significantly improving the performance and reliability of solid rocket motor propellant loading.

[0052] This document uses specific examples to illustrate the principles and implementation methods of this application. The descriptions of the above embodiments are only for the purpose of helping to understand the methods and core ideas of this application. The above descriptions are only preferred embodiments of this application. It should be noted that due to the limitations of written expression, while there are objectively infinite specific structures, those skilled in the art can make several improvements, modifications, or changes without departing from the principles of this invention, and can also combine the above technical features in an appropriate manner. These improvements, modifications, changes, or combinations, or the direct application of the inventive concept and technical solution to other situations without modification, should all be considered within the scope of protection of this application.

Claims

1. A multi-objective design optimization method for solid rocket motor propellant, characterized in that, include: S1. Using the mass and impulse-mass ratio of the solid rocket motor as objective functions, the total impulse and operating time as uncertainty constraints, and the boundary values ​​of the solid rocket motor design variables as limiting constraints, a multi-objective uncertainty design optimization model for solid rocket motor propellant loading is constructed. S2. Construct the initial population matrix, population size, and function tolerance in the multi-objective optimization algorithm. Using the optimal chaotic control strategy based on the Armijo criterion, perform first-order inverse reliability analysis on each design vector of the solid rocket motor's function function in the initial population matrix to obtain the minimum performance target point vector of the solid rocket motor's function function at each design vector. The function function includes a total impulse constraint function function and a working time constraint function function. The minimum performance target point vector of the function function at each design vector includes the minimum performance target point vector of the total impulse constraint and the minimum performance target point vector of the working time constraint. S3. Input the minimum performance target point vector of the total impulse constraint and the minimum performance target point vector of the working time constraint into the solid rocket motor propellant multi-objective uncertainty design optimization model. With the objective of minimizing the solid rocket motor mass and maximizing the impulse-mass ratio of the solid rocket motor, output the Pareto optimal solution set through the multi-objective genetic algorithm, and use the Pareto optimal solution set as the target design vector of the solid rocket motor design variables.

2. The method according to claim 1, characterized in that, Step S2 includes: S2-1. Construct the initial population matrix, population size, and function tolerance in a multi-objective optimization algorithm; S2-2. Set the initial values ​​of the control parameters for the first-order inverse reliability analysis; wherein the control parameters include at least the chaos control step size, step size scaling factor, step size control parameter, and target reliability index. S2-3. Use the design vectors in the initial population matrix as the initial minimum performance target point vectors respectively; S2-4. Based on the initial minimum performance target point vector, calculate the function response value and constraint gradient vector, and calculate the search direction based on the target reliability index and the constraint gradient vector; S2-5. Determine whether the constraint judgment condition is met based on the search direction, function response value, chaos control step size and constraint gradient vector. If so, proceed to step S2-6-1. S2-6-1. Based on the initial minimum performance target vector, the target reliability index, and the chaos control step size, iterate the initial minimum performance target vector to obtain the updated minimum performance target vector. S2-7. If the updated minimum performance target vector satisfies the convergence criterion, then the updated minimum performance target vector is used as the minimum performance target vector; otherwise, the updated minimum performance target vector is used as the initial minimum performance target vector, and the process returns to step S2-4.

3. The method according to claim 2, characterized in that, Step S2 further includes: S2-6-2. If the constraint judgment condition is not met according to the search direction, the chaotic control step size and the constraint gradient vector, then update the chaotic control step size according to the step size scaling factor based on the Armijo criterion, and then return to step S2-4.

4. The method according to claim 2, characterized in that, Step S2-4 includes: The initial minimum performance target point vector is spatially transformed to obtain the initial vector vector; The function response value and constraint gradient vector are calculated based on the initial vector, and the search direction is calculated based on the target reliability index and the constraint gradient vector.

5. The method according to claim 2, characterized in that, Step S2-5 includes: If the following conditions are met: If so, then the constraint judgment condition is satisfied; in, For the first k The minimum performance target point vector in the next iteration; For the first k Chaos control step size for each iteration. For the search direction, For functional purposes, The gradient vector of the function. The target reliability index is .

6. The method according to claim 4, characterized in that, Step S2-6-1 includes: Calculate the gradient search direction based on the initial minimum performance point target vector, the target reliability index, the constraint gradient vector, and the chaos control step size; Based on the gradient search direction and the target reliability index, the updated minimum performance point target vector is iteratively calculated.

7. The method according to claim 2, characterized in that, Step S2-7 includes: If satisfied Then the updated minimum performance target point vector satisfies the convergence criterion; where, Let X be the X-space vector corresponding to the updated minimum performance target point vector. Let X be the X-space vector corresponding to the initial design vector. This represents the convergence tolerance for first-order inverse reliability analysis.

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