Balanced optimization method for multivariable complex aircraft system

Abstract

The invention discloses a balance optimization method for a multivariable complex aircraft system, relates to the technical field of complex aircraft systems, and aims to solve the problems that subsystems are mutually coupled, the convergence speed of the optimization process is low and the optimization calculation amount is large in the existing optimization process of the multivariable complex aircraft system. Comprising the following steps: step 1, taking the performance of an aircraft as an optimization target, determining constraint conditions according to the range of the aircraft and the cost of the aircraft, and determining a multivariable complex aircraft optimization model; 2, constructing a performance function of the aircraft system, and estimating the range of the aircraft system and the cost of the aircraft system; 3, performing system-by-system iterative optimization on the constructed multivariable complex aircraft optimization model, and solving decision variables; and 4, designing the aircraft by using the optimized aircraft system parameters so as to optimize the performance of the aircraft.

Description

Technical Field

[0001] The present invention relates to the technical field of complex aircraft systems, and in particular to a balanced optimization method for a complex aircraft system with multiple variables. Background Art

[0002] With the continuous development of science and technology, the capabilities of aircraft systems are gradually improving, and their systems are becoming more and more complex, making the optimization design of aircraft more and more difficult. Since there are multiple subsystems in the aircraft system, each subsystem has multiple optimization variables, and the subsystems and optimization variables are coupled and constrained with each other, this makes the overall optimization design of the aircraft system very difficult. At present, the optimization design methods for aircraft systems mostly adopt the idea of ​​multidisciplinary optimization. Some scholars combine the model-based system engineering method with the multidisciplinary optimization design method in the aircraft conceptual design process. In addition, there are some methods that use heuristic optimization algorithms to optimize the performance of aircraft, and some researchers use particle swarm optimization algorithms to optimize the control system of aircraft. Although there are currently optimization design methods for complex aircraft systems, it is difficult to solve the problem of mutual coupling among the subsystems of complex aircraft systems. There are still problems such as complex organization of the collaborative optimization process, difficult convergence, and large amount of calculation. Summary of the invention

[0003] The technical problems to be solved by the present invention are:

[0004] The existing optimization process of complex aircraft systems with multiple variables has problems such as mutual coupling of subsystems, slow convergence of the optimization process, and large amount of optimization calculations.

[0005] The present invention adopts the following technical solutions to solve the above technical problems:

[0006] The present invention provides a balanced optimization method for a complex aircraft system with multiple variables, comprising the following steps:

[0007] Step 1: Assume that the aircraft system to be optimized has N subsystems, each with M i variables, the parameter variable is x ij , i=1,2,…,N; j=1,2,…M i , taking system parameters as decision variables, aircraft performance as optimization goal, and determining constraints according to aircraft range and aircraft cost, a multivariable complex aircraft optimization model is determined;

[0008] Step 2: Assuming that the circular probability error of the aircraft landing point is only related to the parameters of the aircraft's guidance system and control system, the performance function of the aircraft system is constructed; the range of the aircraft is estimated by constructing the kinematic and dynamic equations corresponding to the aircraft and running the trajectory integration program. During the range estimation process, a 3-DOF model of the aircraft is established, and the aircraft state is recursively deduced by single-step integration and enlarged integration step length; the aircraft cost is estimated;

[0009] Step 3: Perform system-by-system iterative optimization on the constructed multivariable complex aircraft optimization model and solve the decision variables;

[0010] Step 4: Design the aircraft using the optimized aircraft system parameters to optimize the aircraft performance.

[0011] Furthermore, the multivariable complex aircraft optimization model in step 1 is:

[0012] max f(X)

[0013]

[0014] Where f(X) represents the performance measurement function of the aircraft, and X represents the optimization variable x ij A collection of represents the range function of the aircraft, L represents the minimum range value of the aircraft, represents the cost function of the aircraft, and C represents the maximum cost value of the aircraft.

[0015] Furthermore, the system parameter variables in step one include parameter variables of a power system, a guidance system and a control system.

[0016] Furthermore, in step 2, the performance of the aircraft system is evaluated by the aircraft's hit accuracy, and the objective function f(X) is constructed as:

[0017]

[0018] In the formula, K σ is a positive coefficient, σ p (X) is the circular error probability function of the aircraft landing point;

[0019] Assuming that the circular probability error of the aircraft landing point is only related to the parameters of the aircraft's guidance and control systems, we can construct σ p The estimation model for (X) is:

[0020]

[0021] In the formula, x I represents the accuracy coefficient of the aircraft inertial navigation system, xS represents the accuracy coefficient of the aircraft satellite navigation system, x G Represents the guidance accuracy coefficient of the aircraft seeker, represents the capacity coefficient of the i-th level actuator of the aircraft, represents the shortest actuation interval of the i-th stage actuator of the aircraft, K G , K M , K ΔT Respectively represent positive coefficients.

[0022] Furthermore, in step 2, the range of the aircraft is calculated by constructing the kinematic and dynamic equations corresponding to the aircraft and running the trajectory integration program. Make an estimate, specifically:

[0023] (1) Establish the 3-DOF model of the aircraft as follows:

[0024]

[0025] In the formula, s represents the position vector of the aircraft, v represents the velocity vector of the aircraft, and d(X) represents the acceleration calculation function of the aircraft;

[0026] (2) Use single-step integration to perform a long recursive derivation of the state of the aircraft, that is:

[0027]

[0028] In the formula, s(t) and s(t+1) represent the positions of the aircraft at time t and time t+1 respectively, v(t) and v(t+1) represent the velocities of the aircraft at time t and time t+1 respectively, and step represents the integration step size;

[0029] (3) Enlarge the integration step size and perform recursive calculation to obtain the trajectory of the aircraft.

[0030] Furthermore, in step 2 (3), the integration step after amplification is 0.5 s or 1 s.

[0031] Furthermore, in step 2, the cost C(X) of the aircraft system is estimated based on the costs incurred by the power system, the guidance system, and the control system; wherein the cost incurred by the power system is estimated in the following manner:

[0032]

[0033] Where P i represents the thrust of the i-th stage power system of the aircraft, represents the fuel mass of the i-th stage power system of the aircraft, represents the working time of the i-th level power system of the aircraft, and are positive coefficients respectively;

[0034] The cost of the guidance system is estimated as follows:

[0035]

[0036] In the formula, and are positive coefficients respectively;

[0037] The costs incurred by the control system are estimated in the following manner:

[0038]

[0039] In the formula, is a positive coefficient;

[0040] The estimated costs for the aircraft systems are:

[0041]

[0042] Furthermore, step three specifically includes the following steps:

[0043] Step 31: Optimize the system-wide variables included in the aircraft system to obtain the initial values ​​of the optimized variables of the aircraft system-wide;

[0044] Step 32: Based on step 31, keep the values ​​of other systems unchanged and optimize the variables of the power system, guidance system and control system in turn;

[0045] Step 33: Repeat step 31 to step 32 until the preset maximum number of iterative optimization times is reached.

[0046] Furthermore, in step 32, a genetic algorithm or a particle swarm algorithm is used to sequentially optimize the variables of the power system, the guidance system, and the control system.

[0047] Compared with the prior art, the present invention has the following beneficial effects:

[0048] The present invention provides a balanced optimization method for a complex aircraft system with multiple variables. By estimating the performance objective function of the aircraft and the range and cost constraints of the aircraft in the optimization model of the complex aircraft system, the amount of calculation in the optimization process can be effectively reduced and the operation speed of the optimization process can be improved. By using a system-by-system optimization method, the problem of severe coupling of subsystems in the complex aircraft system can be effectively reduced, the dimension of the optimization variables in the optimization problem can be reduced, and the speed of optimization convergence can be improved, which provides a new technical idea for the balanced optimization problem of the complex system. BRIEF DESCRIPTION OF THE DRAWINGS

[0049] Figure 1Schematic diagram of a system-by-system iterative optimization process of aircraft system variables in an embodiment of the present invention;

[0050] Figure 2 The values ​​of various parameters in the process of calculating the performance and constraint conditions of the aircraft in the embodiment of the present invention are obtained;

[0051] Figure 3 The aircraft performance index change curve during the iterative optimization process of the aircraft system in the embodiment of the present invention. DETAILED DESCRIPTION

[0052] In order to enable those skilled in the art to better understand the scheme of the present invention, exemplary implementations or embodiments of the present invention will be described below in conjunction with the accompanying drawings. Obviously, the described implementations or embodiments are only implementations or embodiments of a part of the present invention, not all of them. Based on the implementations or embodiments of the present invention, all other implementations or embodiments obtained by ordinary technicians in the field without creative work should fall within the scope of protection of the present invention.

[0053] In order to make the above-mentioned objects, features and advantages of the present invention more obvious and easy to understand, specific embodiments of the present invention are described in detail below with reference to the accompanying drawings.

[0054] like Figure 1 As shown, the present invention provides a balanced optimization method for a complex aircraft system with multiple variables, comprising the following steps:

[0055] Step 1: Assume that the aircraft system to be optimized has N subsystems, each with M i variables, the parameter variable is x ij , i=1,2,…,N; j=1,2,…M i , taking system parameters as decision variables, aircraft performance as optimization target, and determining constraints based on aircraft range and aircraft cost, a multivariable complex aircraft optimization model is determined:

[0056] max f(X)

[0057]

[0058] Where f(X) represents the performance measurement function of the aircraft, and X represents the optimization variable x ij A collection of parameters of the power system, guidance system, and control system. represents the range function of the aircraft, L represents the minimum range value of the aircraft, represents the cost function of the aircraft, and C represents the maximum cost value of the aircraft.

[0059] Step 2: Construct the performance function of the aircraft system and estimate the range and cost of the aircraft system. Specifically, evaluate the performance of the aircraft system based on the aircraft's hit accuracy and construct the objective function f(X) as follows:

[0060]

[0061] In the formula, K σ is a positive coefficient, σ p (X) is the circular error probability function of the aircraft landing point.

[0062] Due to σ p (X) It takes multiple runs of the aircraft trajectory integration program to calculate, which will result in multiple runs of the trajectory integration program at each optimization iteration step, thus slowing down the optimization process. In order to solve this problem, the present invention estimates the circular probability error of the aircraft landing point position.

[0063] Assuming that the circular probability error of the aircraft landing point is only related to the parameters of the aircraft's guidance system and control system, the estimation model of σp(X) is constructed as follows:

[0064]

[0065] In the formula, x I represents the accuracy coefficient of the aircraft inertial navigation system, x S Represents the accuracy coefficient of the aircraft satellite navigation system,

[0066] x G Represents the guidance accuracy coefficient of the aircraft seeker, represents the capacity coefficient of the i-th level actuator of the aircraft, represents the shortest actuation interval of the i-th stage actuator of the aircraft, K G , K M , K ΔT Respectively represent positive coefficients.

[0067] The range L(X) of the aircraft system is estimated. Specifically, the range of the aircraft is estimated by constructing the kinematic and dynamic equations corresponding to the aircraft and running the trajectory integral. In the integration process, three approaches are adopted to simplify the trajectory integral operation, namely:

[0068] (1) Establish the 3-DOF model of the aircraft as follows:

[0069]

[0070] Where s represents the position vector of the aircraft, v represents the velocity vector of the aircraft, and d(X) represents the acceleration calculation function of the aircraft, which is obtained by calculating the gravity, thrust, and aerodynamic force acting on the aircraft.

[0071] (2) Use single-step integration to perform a long recursive derivation of the state of the aircraft, that is:

[0072]

[0073] In the formula, s(t) and s(t+1) represent the positions of the aircraft at time t and time t+1 respectively, v(t) and v(t+1) represent the velocities of the aircraft at time t and time t+1 respectively, and step represents the integration step size;

[0074] (3) Enlarging the integration step size for recursive calculation, that is, taking a larger value for the integration step size step during the integration process, such as 0.5s, 1s.

[0075] The above three methods can effectively speed up the calculation of vehicle trajectory integral.

[0076] The cost function C(X) of an aircraft is closely related to each system of the aircraft, and its specific cost calculation process is very complicated. The present invention believes that the cost of an aircraft is mainly composed of the costs of the power system, the guidance system, and the control system. The cost of the power system is estimated in the following way:

[0077]

[0078] Where P i represents the thrust of the i-th stage power system of the aircraft, represents the fuel mass of the i-th stage power system of the aircraft, represents the working time of the i-th level power system of the aircraft, and are positive coefficients respectively;

[0079] The cost of the guidance system is estimated as follows:

[0080]

[0081] In the formula, and are positive coefficients respectively;

[0082] The costs incurred by the control system are estimated in the following manner:

[0083]

[0084] In the formula, is a positive coefficient;

[0085] Based on the above cost estimation methods for the power system, guidance system, and control system, the cost of the aircraft system is estimated to be:

[0086]

[0087] Step 3: Iteratively optimize the constructed multivariable complex aircraft optimization model system by system and solve the decision variables; including the following steps:

[0088] Step 31: Optimize the system-wide variables included in the aircraft system to obtain the initial values ​​of the optimized variables of the aircraft system-wide;

[0089] Step 32: On the basis of step 31, the values ​​of other systems are fixed and the variables of the power system, guidance system and control system are optimized in turn by using genetic algorithm, particle swarm and other algorithms;

[0090] Step 33: Repeat step 31 to step 32 until the preset maximum number of iterative optimization times is reached.

[0091] Step 4: Design the aircraft using the optimized aircraft system parameters to optimize the aircraft performance.

[0092] Embodiment 1, adopt the following embodiment to verify the beneficial effect of the present invention.

[0093] (1) Experimental environment

[0094] The correctness and rationality of the present invention are verified by digital simulation. In this embodiment, the optimization variables include 9 parameters of the power system, namely, the thrust size P of the i-th (i=1, 2, 3)-th level power system of the aircraft, i , the fuel mass of the i-th (i=1,2,3) stage power system of the aircraft Working time of the i-th (i=1,2,3) stage power system of the aircraft The three parameters of the guidance system are the accuracy coefficient x of the aircraft inertial navigation system I , the accuracy coefficient x of the aircraft satellite navigation system S and the guidance accuracy coefficient x of the aircraft seeker G , and the six parameters of the control system, namely the capacity coefficient of the i-th (i=1,2,3) level actuator of the aircraft and the shortest actuation interval of the i-th (i=1,2,3)-th level actuator of the aircraft There are 18 optimization variables in total. Without loss of generality, the maximum and minimum values ​​of each parameter in the aircraft system are used to normalize all parameter variables to between (0, 1), and the initial values ​​are all taken as 0.5; the integration step is 0.5s. In addition, the minimum range value and the maximum cost value of the aircraft are set to 1, that is, L = 1, C = 1. The parameters in the calculation process of aircraft performance and constraints are set as follows Figure 2 shown.

[0095] The simulation test software environment is Windows 10+Python3.7, and the hardware environment is AMD Ryzen 5 3550HCPU (2.10GHz) + 16.0GB (2400MHz) RAM.

[0096] (2) Experimental results and analysis

[0097] In the process of optimizing each parameter in the aircraft system, the particle swarm optimization algorithm (PSO) is used as the optimization benchmark algorithm. The population size in PSO is set to 200, the maximum number of iterations is 200, and the learning factor is set to c. 1 =c 2 =0.5, and the inertia factor is set to ω=0.8. For comparative analysis, the PSO algorithm is used to directly optimize all parameters in the aircraft system, without adopting the system-by-system optimization process proposed in the present invention. Figure 3 The figure shows the change curve of the aircraft performance index (i.e. the objective function in the optimization problem) during the iterative optimization process. Figure 3 It can be seen that compared with the method of directly optimizing the parameters of the entire system, the method of optimizing each system step by step proposed in the present invention can improve the speed of convergence of aircraft system parameter optimization and improve the final aircraft performance indicators. When all parameters of the aircraft system participate in the optimization process, each system parameter has a strong coupling effect on the performance indicators and constraints, so the optimization process is slow and it is difficult to obtain a good optimization result.

[0098] The system-by-system optimization method proposed in the present invention searches for the optimal system parameters that meet the set constraints. The dimension of the optimized parameters can be reduced in each iterative optimization process, so that the optimization process is more focused on the parameters of each system itself. This method can effectively solve the problem of parameter coupling of each system, and has a faster convergence speed and better optimization results than the whole system optimization method.

[0099] Although the present invention is disclosed as above, the protection scope of the present invention is not limited thereto. Those skilled in the art may make various changes and modifications without departing from the spirit and scope of the present invention, and these changes and modifications will fall within the protection scope of the present invention.

Claims

1. A balanced optimization method for a complex aircraft system with multiple variables, characterized in that: The following steps are involved: Step 1: Assume that the aircraft system to be optimized has N subsystems, each with M i variables, the parameter variable is x ij , i=1,2,…,N; j=1,2,…M i , taking system parameters as decision variables, aircraft performance as optimization target, and determining constraints according to aircraft range and aircraft cost, a multivariable complex aircraft optimization model is determined; Step 2: Assuming that the circular probability error of the aircraft landing point is only related to the parameters of the aircraft's guidance system and control system, the performance function of the aircraft system is constructed; the range of the aircraft is estimated by constructing the kinematic and dynamic equations corresponding to the aircraft and running the trajectory integration program. During the range estimation process, a 3-DOF model of the aircraft is established, and the aircraft state is recursively deduced by single-step integration and enlarged integration step length; the aircraft cost is estimated; Step 3: Perform system-by-system iterative optimization on the constructed multivariable complex aircraft optimization model and solve the decision variables; Step 4: Design the aircraft using the optimized aircraft system parameters to optimize the aircraft performance.

2. The method for balancing and optimizing a complex aircraft system with multiple variables according to claim 1, characterized in that: The multivariable complex aircraft optimization model described in step 1 is: max f(X) Where f(X) represents the performance measurement function of the aircraft, and X represents the optimization variable x ij A collection of represents the range function of the aircraft, L represents the minimum range value of the aircraft, represents the cost function of the aircraft, and C represents the maximum cost value of the aircraft.

3. The method for balancing and optimizing a complex aircraft system with multiple variables according to claim 2, characterized in that: The system parameter variables in step one include parameter variables of the power system, guidance system and control system.

4. The method for balancing and optimizing a complex aircraft system with multiple variables according to claim 3, characterized in that: In step 2, the performance of the aircraft system is evaluated by the aircraft's hit accuracy, and the objective function f(X) is constructed as: In the formula, K σ is a positive coefficient, σ p (X) is the circular error probability function of the aircraft landing point; Assuming that the circular probability error of the aircraft landing point is only related to the parameters of the aircraft's guidance and control systems, we can construct σ p The estimation model for (X) is: In the formula, x I represents the accuracy coefficient of the aircraft inertial navigation system, x S represents the accuracy coefficient of the aircraft satellite navigation system, x G Represents the guidance accuracy coefficient of the aircraft seeker, represents the capacity coefficient of the i-th level actuator of the aircraft, K represents the shortest actuation interval of the i-th stage actuator of the aircraft. G , K M , K ΔT Respectively represent positive coefficients.

5. The method for balancing and optimizing a complex aircraft system with multiple variables according to claim 4, characterized in that: In step 2, the range of the aircraft is calculated by constructing the kinematic and dynamic equations corresponding to the aircraft and running the trajectory integration program. Make an estimate, specifically: (1) Establish the 3-DOF model of the aircraft as follows: In the formula, s represents the position vector of the aircraft, v represents the velocity vector of the aircraft, and d(X) represents the acceleration calculation function of the aircraft; (2) Use single-step integration to perform a long recursive derivation of the state of the aircraft, that is: In the formula, s(t) and s(t+1) represent the positions of the aircraft at time t and time t+1 respectively, v(t) and v(t+1) represent the velocities of the aircraft at time t and time t+1 respectively, and step represents the integration step size; (3) Enlarge the integration step size and perform recursive calculation to obtain the trajectory of the aircraft.

6. The method for balancing and optimizing a complex aircraft system with multiple variables according to claim 5, characterized in that: The integration step after amplification in step 2 (3) is 0.5 s or 1 s.

7. The method for balancing and optimizing a complex aircraft system with multiple variables according to claim 5, characterized in that: In step 2, the cost of the aircraft system is calculated based on the cost of the power system, guidance system, and control system. The cost of the power system is estimated in the following way: Where P i represents the thrust of the i-th stage power system of the aircraft, represents the fuel mass of the i-th stage power system of the aircraft, represents the working time of the i-th level power system of the aircraft, and are positive coefficients respectively; The cost of the guidance system is estimated as follows: In the formula, and are positive coefficients respectively; The costs incurred by the control system are estimated in the following manner: In the formula, is a positive coefficient; The estimated costs for the aircraft systems are:

8. The method for balancing and optimizing a complex aircraft system with multiple variables according to claim 7, characterized in that: Step 3 specifically includes the following steps: Step 31: Optimize the system-wide variables included in the aircraft system to obtain the initial values ​​of the optimized variables of the aircraft system-wide; Step 32: Based on step 31, keep the values ​​of other systems unchanged and optimize the variables of the power system, guidance system and control system in turn; Step 33: Repeat step 31 to step 32 until the preset maximum number of iterative optimization times is reached.

9. The method for balancing and optimizing a complex aircraft system with multiple variables according to claim 8, characterized in that: In step 3.2, genetic algorithm or particle swarm algorithm is used to optimize the variables of the power system, guidance system and control system in turn.

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