A two-stage thrust optimization method based on the down-hill simplex method

Abstract

The application provides a two-stage thrust optimization method based on a downhill simplex method, establishes a guided rocket trajectory dynamics model and a total impulse equation of a single-chamber double-thrust solid rocket engine, selects engine thrust search parameters, establishes a state constraint equation and an objective function, substitutes determined initial values of the search parameters into a downhill simplex optimization algorithm, substitutes optimal solutions of the search parameters into a first-stage average thrust equation and the total impulse equation of the engine, forms a two-stage thrust optimization scheme of the single-chamber double-thrust solid rocket engine, and effectively improves the range capability of the guided rocket under the conditions of a multi-state constraint trajectory and the index constraint requirements of the single-chamber double-thrust solid rocket engine, avoids excessively complex state equations caused by too many search parameters, and forms a multi-search parameter joint fast optimization method for the solid rocket engine.

Description

Technical Field

[0001] The present invention relates to the field of guided rockets, in particular to an optimization method for a single-chamber dual-thrust solid rocket engine of a high initial velocity and small disturbance guided rocket. Background Art

[0002] The thrust of a guided rocket engine is a significant factor influencing the rocket's trajectory and range. The thrust design of a solid rocket engine is a key factor in ensuring that a guided rocket meets its technical performance specifications. Compared to single-chamber, single-thrust solid rocket engines, single-chamber, dual-thrust solid rocket engines can meet more complex ballistic requirements and achieve more stringent range performance. Compared to dual-chamber, dual-thrust engines, single-chamber, dual-thrust engines offer advantages such as a simpler structure, no need to consider interstage separation issues, consistent aerodynamic shape across the entire stage, and low manufacturing costs. Therefore, they are widely used in various missile and rocket applications. Guided rockets, with their high initial velocity and low-disturbance launch characteristics, are more suitable for single-chamber, dual-thrust solid rocket engines.

[0003] When designing a single-chamber, dual-thrust solid rocket engine, a key challenge is how to utilize limited energy resources to achieve optimal ballistic performance and maximum range. Therefore, this study considered optimizing the thrust scheme for a single-chamber, dual-thrust engine, obtaining the optimal thrust solution with a reasonable thrust ratio and operating time. This approach maximizes engine performance within fixed parameters and improves the range capability of guided rockets.

[0004] The Downhill Simplex Algorithm (DSHLAM) algorithm, a non-differentiable algorithm for minimizing multidimensional state variable functions, can solve nonlinear optimization problems when the differential equations for the search variables are unknown. The algorithm uses the search variables to form a simplex Euclidean space, then uses the simplex algorithm to narrow the Euclidean space, repeatedly iterating to find the minimum in the space. Single-chamber, dual-thrust solid rocket engines have numerous state parameters, and some of these state parameters have undefined differential equations, making optimization of two-stage thrust schemes challenging. All engine state parameters affect the internal and external trajectory of the guided rocket. The joint optimization of these trajectories for a single-chamber, dual-thrust solid rocket engine presents a complex nonlinear optimization challenge characterized by multiple state constraints, multiple optimization parameters, and complex, sometimes unknown, state equations. The Downhill Simplex Algorithm (DSHLAM) method, utilizing simplex Euclidean space transformations, can solve the nonlinear optimization problem of two-stage thrust schemes for single-chamber, dual-thrust solid rocket engines. While the DSHLAM algorithm has not yet been applied in the field of guided rocket optimization design, this optimization method holds significant research significance and engineering value, addressing the performance characteristics of solid rocket engines, characterized by numerous state parameters and complex state coupling. Summary of the Invention

[0005] To overcome the shortcomings of the prior art, the present invention provides a two-stage thrust optimization method based on the Downhill Simplex Method. The present invention aims to provide a two-stage thrust optimization method for guided rockets with high initial velocity and small disturbance based on the Downhill Simplex Method. This method aims to effectively improve the range capability of guided rockets under multi-state constrained ballistic conditions and the performance constraints of single-chamber dual-thrust solid rocket engines.

[0006] The technical solution adopted by the present invention to solve the technical problem includes the following steps:

[0007] Step 1: According to the guided rocket index requirements and engine index requirements, the guided rocket ballistic dynamics model and the total impulse equation of the single-chamber dual-thrust solid rocket engine are established in sequence;

[0008] Step 2: Determine the two-stage thrust optimization scheme of the single-chamber dual-thrust solid rocket engine, that is, select the engine thrust search parameters;

[0009] Step 3: Establish state constraint equations and objective function;

[0010] The rocket engine optimization objective function is constructed as the rocket range R end , falling speed V end , angle of fall θ end The objective function is as follows:

[0011] minJ=f(R end V end ,θ end )

[0012] Step 4: Determine a set of initial values ​​for the engine search parameters based on the ballistic performance indicators of the guided rocket and the single-chamber dual-thrust engine index requirements, and substitute the determined initial values ​​of the search parameters into the downhill simplex optimization algorithm;

[0013] The engine charge design is performed based on the optimal solution of the two-stage thrust parameters of the engine obtained by the downhill simplex method optimization, and it is judged whether the charge design result meets the technical index requirements of the single-chamber dual-thrust solid engine. If it does not meet the index requirements, it is necessary to update the initial value of the search parameter and continue iterative optimization; if it meets the index requirements, it is judged whether the number of external iterations of the algorithm reaches the minimum number of iterations set by the downhill simplex algorithm; if the number of external iterations does not meet the requirements, the optimal solution is updated to the initial value of the engine search parameter; if the number of iterations meets the requirements, the optimal solution of the search parameter is output;

[0014] Step 5: Substitute the optimal solution of the search parameters into the average thrust and total impulse equation of the first stage of the engine to form the optimal solution for the two-stage thrust of the single-chamber, dual-thrust solid rocket engine. The optimal solution is the optimal value of the search parameters; the optimal two-stage thrust is the first and second stage thrust and thrust working time of the engine corresponding to the optimal solution of the search parameters.

[0015] The total impulse equation of the single-chamber dual-thrust solid rocket motor is as follows:

[0016]

[0017] Among them, I is the total impulse of the engine, F1 and F2 are the first-stage thrust and the second-stage thrust respectively, T is the total working time of the engine, t1 is the working time of the first-stage thrust, are the average thrust of the first stage and the average thrust of the second stage respectively, and the thrust ratio of the two stages is expressed as

[0018] In the second step, the average thrust of the engine stage is regarded as the thrust coefficient C F , the function of the combustion chamber working pressure P1 and the nozzle throat diameter A:

[0019]

[0020] The thrust coefficient, combustion chamber operating pressure, and nozzle throat diameter determine the two-stage thrust of a single-chamber, dual-thrust solid rocket engine when the total engine impulse is determined. Therefore, the four parameters of combustion chamber operating pressure, nozzle throat diameter, two-stage thrust ratio, and first-stage thrust operating time determine the performance of the single-chamber, dual-thrust engine. These four parameters are selected as engine search parameters and are iteratively optimized. The iteration is shown in step 4.

[0021] Therefore, the total impulse equation of the single-chamber dual-thrust solid rocket engine can be rewritten as:

[0022] c I=[C F P1AT+(K-1)C F P1At1] / K.

[0023] In step 3, the state constraint equation includes range constraint, terminal velocity constraint, and landing angle constraint, and its specific form is as follows:

[0024] R end min ≤R end ≤R end max ;

[0025] V end min ≤V end ≤V end max ;

[0026] θ end min ≤θ end ≤θ end max

[0027] Among them, V end min , R end min ,θ end min They represent the lower bounds of the rocket’s range, fall speed, and fall angle, respectively. V end max , R end max,θ end max They represent the upper bounds of the rocket's range, fall speed, and fall angle, respectively.

[0028] In the step four, the downhill simplex algorithm constructs the initial values ​​of the engine search parameters into a simplex polyhedron in the simplex Euclidean space, the simplex polyhedron performs objective function value calculation, and solves the optimized value of the engine search parameters through mapping, expansion, external contraction and internal contraction, and updates the optimized value of the engine search parameters to the initial values ​​of the search parameters to form a new simplex polyhedron, and iteratively maps, expands, externally contracts and internally contracts the new simplex polyhedron to obtain the minimum point of the engine search parameter state space, which is the optimal solution of the engine search parameters when the objective function is minimized.

[0029] The beneficial effect of the present invention lies in the simulation optimization of the downhill simplex algorithm for the design of the two-stage thrust scheme of a single-chamber, dual-thrust solid engine for a guided rocket. For guided rockets with high initial velocity and low disturbance characteristics, the optimization problem of the two-stage thrust scheme of the engine is solved under the conditions of a large number of search parameters, and the maximum range capability of the guided rocket is effectively improved under the main constraints such as engine mass, total operating time, and active segment overload. The downhill simplex optimization algorithm effectively solves the complex optimization problem of the joint optimization of the internal and external ballistics of the solid rocket engine. Compared with other optimization algorithms, it avoids the overly complex state equations caused by a large number of search parameters, forming a joint rapid optimization method for multiple search parameters of the solid rocket engine. BRIEF DESCRIPTION OF THE DRAWINGS

[0030] Figure 1 The present invention is a flow chart of a two-stage thrust optimization method for a guided rocket single-chamber dual-thrust engine based on the downhill simplex method. DETAILED DESCRIPTION

[0031] The present invention will be further described below with reference to the accompanying drawings and examples.

[0032] Figure 1 The embodiment of the two-stage thrust optimization method of the guided rocket engine based on the downhill simplex method is shown in FIG. Figure 1 As shown in Figure 2, the two-stage thrust optimization method based on the downhill simplex method includes:

[0033] Step 1: Establish a guided rocket trajectory dynamics model;

[0034] Step 2: Establish the total thrust equation of the two-stage active section. The specific total thrust equation of the rocket engine is as follows:

[0035] I=[C F P1AT+(K-1)C F P1At1] / K

[0036] Among them, C Fis the thrust coefficient, P1 is the working pressure of the combustion chamber, A is the nozzle throat diameter, T is the total working time of the engine, t1 is the first-stage thrust working time, and K is the two-stage thrust ratio.

[0037] Step 3: Select the rocket engine search parameter variable;

[0038] For a single-chamber, dual-thrust fixed rocket engine, its total operating time is fixed, and the thrust coefficient is determined by the performance of the propellant. The thrust and energy of the first and second stages of the engine are determined by parameters such as the nozzle throat diameter, combustion chamber operating pressure, the ratio of the first and second stages, and the first stage operating time. Therefore, this parameter is the search parameter for a single-chamber, dual-thrust solid rocket engine.

[0039] Step 4: Set the terminal trajectory constraints based on the overall mission requirements; set the expected trajectory range R K , expected falling speed V K , expected landing angle θ K ;

[0040] Step 5: Establish the guided rocket optimization objective function as follows:

[0041] minJ=c1|R end -R K |+c2|V K -V end | / V K +c3|θ K -θ end | / θ K

[0042] Among them, c1, c2, c3 are penalty function coefficients, V K , R K ,θ K where represents the desired fall velocity, desired ballistic range, and desired fall angle, respectively. The optimization objective function minJ represents the optimal minimum objective function value obtained when the guided rocket is given the desired range, rocket terminal fall velocity, and fall angle. The optimal single-chamber, dual-thrust solid rocket engine state indicators are obtained by optimizing the two-stage thrust parameters.

[0043] Step 6: Given the initial estimated values ​​of the rocket engine search parameters, set the engine index constraint equations based on the engine design requirements. These include engine operating time T, engine mass m, engine total length L, and guided rocket lateral overload n. x , normal overload n y etc. constraints.

[0044] Step 7: Use the Downhill Simplex Algorithm to search for the engine parameters that have the best range capability for the objective function. The Downhill Simplex Algorithm first sorts the objective function values ​​and then performs mapping, expansion, external contraction, and internal contraction algorithms, and then iterates within the algorithm.

[0045] Step 8: Design the charge based on the engine state parameter optimization results using the Downhill Simplex Method. If the engine charge design meets the interior ballistic performance and technical indicators, proceed to Step 9; otherwise, change the initial estimate and constraint form and return to Step 6.

[0046] Step 9: Determine the number of iterations. If it meets the requirements, output the engine parameter optimization results; otherwise, return to step 6 and update the initial values ​​of the optimization parameters.

[0047] This invention discloses a method for optimizing a high-initial-velocity, low-disturbance, two-stage thrust scheme for a single-chamber, dual-thrust, fixed rocket engine based on the Downhill Simplex method. By selecting engine state search parameters to form a multidimensional simplex Euclidean state space, the Downhill Simplex algorithm iteratively calculates the minimum value of the Euclidean state space, thereby optimizing the engine's two-stage thrust scheme while meeting the desired maximum range and trajectory terminal conditions.

Claims

1. A two-stage thrust optimization method based on the downhill simplex method, characterized by: Step 1: According to the guided rocket index requirements and engine index requirements, the guided rocket ballistic dynamics model and the total impulse equation of the single-chamber dual-thrust solid rocket engine are established in sequence; Step 2: Determine the two-stage thrust optimization scheme of the single-chamber dual-thrust solid rocket engine, that is, select the engine thrust search parameters; Step 3: Establish state constraint equations and objective function; The rocket engine optimization objective function is constructed as the rocket range R end , falling speed V end , angle of fall θ end The objective function is as follows: min J=f(R end ,V end ,the end ) Step 4: Determine a set of initial values ​​for the engine search parameters based on the ballistic performance indicators of the guided rocket and the single-chamber dual-thrust engine index requirements, and substitute the determined initial values ​​of the search parameters into the downhill simplex optimization algorithm; The engine charge design is performed based on the optimal solution of the two-stage thrust parameters of the engine obtained by the downhill simplex method. It is judged whether the charge design result meets the technical index requirements of the single-chamber dual-thrust solid engine. If it does not meet the index requirements, it is necessary to update the initial value of the search parameter and continue iterative optimization. If it meets the index requirements, it is judged whether the number of external iterations of the algorithm reaches the minimum number of iterations set by the downhill simplex algorithm. If the number of external iterations does not meet the requirements, the optimal solution is updated to the initial value of the engine search parameter. If the required number of iterations is reached, the optimal solution of the search parameters is output; Step 5: Substitute the optimal solution of the search parameters into the average thrust and total impulse equation of the first stage of the engine to form the optimal solution for the two-stage thrust of the single-chamber, dual-thrust solid rocket engine. The optimal solution is the optimal value of the search parameters; the optimal two-stage thrust is the first and second stage thrust and thrust working time of the engine corresponding to the optimal solution of the search parameters.

2. The two-stage thrust optimization method based on the downhill simplex method according to claim 1, characterized in that: The total impulse equation of the single-chamber dual-thrust solid rocket motor is as follows: Among them, I is the total impulse of the engine, F1 and F2 are the first-stage thrust and the second-stage thrust respectively, T is the total working time of the engine, t1 is the working time of the first-stage thrust, are the average thrust of the first stage and the average thrust of the second stage respectively, and the thrust ratio of the two stages is expressed as 3. The two-stage thrust optimization method based on the downhill simplex method according to claim 1, characterized in that: In the second step, the average thrust of the engine stage is regarded as the thrust coefficient C F , the function of the combustion chamber working pressure P1 and the nozzle throat diameter A: The thrust coefficient, combustion chamber operating pressure, and nozzle throat diameter determine the two-stage thrust of a single-chamber, dual-thrust solid rocket engine when the total engine impulse is determined. Therefore, the four parameters of combustion chamber operating pressure, nozzle throat diameter, two-stage thrust ratio, and first-stage thrust operating time determine the performance of the single-chamber, dual-thrust engine. These four parameters are selected as engine search parameters and are iteratively optimized. The iteration is shown in step 4. Therefore, the total impulse equation of the single-chamber dual-thrust solid rocket engine can be rewritten as: c I=[C F P1AT+(K-1)C F P1At1] / K。 4. The two-stage thrust optimization method based on the downhill simplex method according to claim 1, characterized in that: In step 3, the state constraint equation includes range constraint, terminal velocity constraint, and landing angle constraint, and its specific form is as follows: R endmin ≤R end ≤R end max ; In end min ≤V end ≤V end max ; i end min ≤θ end ≤θ end max Among them, V end min , R end min ,θ end min They represent the lower bounds of the rocket’s range, fall speed, and fall angle, respectively. V end max , R end max ,θ end max They represent the upper bounds of the rocket's range, fall speed, and fall angle, respectively.

5. The two-stage thrust optimization method based on the downhill simplex method according to claim 1, characterized in that: In the step four, the downhill simplex algorithm constructs the initial values ​​of the engine search parameters into a simplex polyhedron in the simplex Euclidean space, the simplex polyhedron performs objective function value calculation, and solves the optimized value of the engine search parameters through mapping, expansion, external contraction and internal contraction, and updates the optimized value of the engine search parameters to the initial values ​​of the search parameters to form a new simplex polyhedron, and iteratively maps, expands, externally contracts and internally contracts the new simplex polyhedron to obtain the minimum point of the engine search parameter state space, which is the optimal solution of the engine search parameters when the objective function is minimized.

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