Multi-level structure dynamics ATC optimization method and device based on target magnitude synchronization

Abstract

The invention discloses a multi-level structure dynamics ATC optimization method and device based on target magnitude synchronization. The method comprises the following steps: firstly, decomposing a multi-level structure dynamics optimization problem into a non-hierarchical ATC optimization model, initializing an external loop initial parameter, setting a design variable interval, and generating a self-adaptive agent model; setting an internal circulation initial parameter, and performing internal circulation step-by-step optimization of the multi-stage ATC optimization model; after the internal loop is finished, calculating an expansion consistency constraint; and finally, judging whether the round of outer circulation reaches a stop criterion, if so, completing optimization, and if not, updating the outer circulation parameters, and carrying out the next round of outer circulation. The device comprises an initialization / update module, an SML-ATC module, a design variable boundary setting / update module, a self-adaptive agent model construction module, a convergence judgment module and an output processing module. According to the method, the response value deviation information can be dynamically adjusted, the adaptability of the agent model is improved, the optimization time is saved, and the optimization efficiency is improved.

Description

Technical Field

[0001] The present invention relates to the technical field of multidisciplinary optimization design of structural dynamics, and in particular to a multi-level structural dynamics ATC optimization method and device based on target magnitude synchronization. Background Art

[0002] There are many strategies for multidisciplinary design optimization. Analytical Target Cascading (ATC) is an effective solution strategy for multi-level optimization systems of complex structural dynamics. However, the use of the ATC method to solve multi-level optimization of complex structural dynamics still faces the following problems: on the one hand, the coordination of multi-level targets with coupled variables is a very challenging problem; on the other hand, the analysis modules of each subsystem are usually composed of professional computing software or physical experiments, and numerical analysis or physical analysis with large computational complexity and long test cycle are not suitable for the requirements of multidisciplinary optimization.

[0003] For the coordination of multi-level objectives with coupled variables, the methods commonly used in ATC strategies include methods based on quadratic penalty functions and methods based on Lagrangian functions. The methods based on quadratic penalty functions include the quadratic penalty function method (QP) of system consistency constraints proposed by Bertsekas, the weight update method based on QP proposed by Michalek and Papalambros, and the coordination algorithm of ATC with quadratic penalty functions proposed by Michelena et al. The methods based on Lagrangian functions include the method using Lagrangian duality theory proposed by Lassiter et al. The method of improving the consistency relaxation function by ordinary Lagrangian function (OL), the method proposed by Kim et al. to update the multiplier estimate by Lagrangian relaxation and sub-gradient method, the method by Tosserams et al. to update the penalty weight by using augmented Lagrangian relaxation method and Bertsekas' augmented Lagrangian penalty function method and alternating direction method (AL-AD), the diagonal quadratic approximation method (DQA) proposed by Li et al. and the truncated diagonal quadratic approximation (TDQA) method proposed by Ruszcynski et al., etc., these methods effectively solve the problem of solving the multi-level optimization system of ATC. In addition, the augmented Lagrangian penalty function method proposed by Tosserams et al. further effectively solves the coordination problem of multi-level objectives with coupled variables.

[0004] For the problems of large computational complexity and long test cycle in subsystem analysis modules, surrogate models are very effective means. Common surrogate models include neural network surrogate models, polynomial response surface models, radial basis function models and Kriging models. Golovidov et al. used this method to establish surrogate models of aircraft range and three drag parameters in the multidisciplinary design optimization of high-speed aircraft (HSCT); Jin et al. systematically compared four methods including radial basis functions using 14 examples representing different types of problems and found that the radial basis function model is the most reliable when considering both model accuracy and robustness; Ginuta conducted a preliminary study on the application of the Kriging method in MDO and made a comparative analysis with the polynomial model.

[0005] It can be seen that in order to reduce the computational complexity and save computing time, the method of combining the surrogate model with the ATC is feasible. However, the use of the surrogate model for optimization has high requirements for the accuracy of the surrogate model, and the cost of training the surrogate model with high accuracy is also very large; and the core problem of the ATC strategy research is to solve the convergence problem of the inconsistency between the objectives and responses at all levels. In the numerical examples and engineering examples studied in the past, the orders of magnitude of the objectives and responses at all levels are basically the same. However, in the structural dynamics optimization problem, some response values ​​have large order of magnitude differences due to the non-uniform dimensions. The deviations that may be introduced in the direct calculation process will also make the order of magnitude abnormally small, which brings additional complexity to the optimization. Although the existing augmented Lagrangian penalty function method provides a certain solution to the coordination problem of multi-level objectives with coupled variables, it is not suitable for situations where there are deviations of too large or too small orders of magnitude. This order of magnitude data fluctuation makes it difficult for the existing method to control the convergence. Therefore, it is necessary to explore new and effective methods to deal with the order of magnitude solutions of response values ​​under different dimensions to achieve effective convergence of the multi-level objective cascade method with coupled variables. Summary of the invention

[0006] The purpose of the present invention is to provide a multi-level structural dynamics ATC optimization method and device based on target magnitude synchronization, which can solve the order of magnitude problem of response values ​​under different dimensions, dynamically adjust the response value deviation information, improve the adaptability of the proxy model, and save optimization time.

[0007] The technical solution to achieve the purpose of the present invention is: a multi-level structural dynamics ATC optimization method based on target magnitude synchronization, comprising the following steps:

[0008] Step 1: Decompose the multi-level structural dynamics optimization problem into a non-hierarchical ATC optimization model;

[0009] Step 2, initializing the initial parameters of the outer loop of the multi-level ATC optimization model;

[0010] Step 3: Set the design variable interval. For the first round of optimization, the design variable interval is set according to the upper and lower boundaries; for subsequent optimization, the design variable interval is updated according to the optimization results;

[0011] Step 4, generating an adaptive proxy model for the design variable interval;

[0012] Step 5: Set the initial parameters of the inner loop of the multi-level ATC optimization model;

[0013] Step 6: Optimize the inner loop of the multi-level ATC optimization model step by step;

[0014] Step 7: Determine whether the inner loop of this round has reached the stopping criteria. If so, it means that the inner loop has reached the convergence accuracy requirement, and then proceed to step 8. If not, update the inner loop parameters and return to step 6 to continue the inner loop.

[0015] Step 8: After the inner loop is completed, process the optimization results and calculate the extended consistency constraints;

[0016] Step 9: Determine whether the outer loop of this round reaches the stopping criterion. If so, the inconsistent information between system levels converges and the optimization is completed. If not, update the outer loop parameters according to the augmented Lagrangian penalty function method and return to step 3 to continue the outer loop.

[0017] Furthermore, the multi-level structural dynamics optimization problem described in step 1 is decomposed into a non-hierarchical ATC optimization model, as follows:

[0018] The expressions of the objective functions at all levels using Lagrange multipliers are:

[0019] The minimized objective function is:

[0020] The design variables are:

[0021] The constraint function is:

[0022]

[0023] in:

[0024]

[0025]

[0026]

[0027]

[0028]

[0029]

[0030] Where P ij is the optimization problem of the jth submodule at the i-th level obtained by decomposition, which is calculated by the adaptive agent model; ij is the design variable of the jth submodule at the i-th level, and the design boundary of the optimization model changes with the boundary of the adaptive proxy model; r ij is the system response value obtained by solving the analysis model at this level; a ij is the response analysis function; T U is the target value passed down from a higher level; T ik is the target value passed down from this level; is the response value passed up from the lower level; Y is the connection variable between the same levels; is the connection variable value passed down from a higher level; is the connection variable value passed up from the lower level; f ij is the optimization objective function; g ij is the constraint condition of the inequality; h ij is the equality constraint; is the penalty function weight vector of the higher-level response and target values; is the penalty function weight vector of the higher-level connection variables; is the penalty function weight vector of the k-th child response value and target value of the next level; is the penalty function weight vector of the connection variables associated with the k-th child of the next level; is a collection of child elements in a lower level, is the penalty function linear Grarangian multiplier vector of the higher level response and target values; is the penalty function linear Grarangian multiplier vector of the higher level connection variables; is the penalty function linear Grarangian multiplier vector with the response value and target value of the k-th child at the next level; is the penalty function linear Grarange multiplier vector of the connection variables associated with the kth child of the next level.

[0031] Furthermore, the initial parameters of the outer loop of the initialization multi-level ATC optimization model described in step 2 are as follows:

[0032] Set the initial value of the penalty function weight w; set the initial value of the Lagrange multiplier v = 0, the initial value of the penalty weight growth rate β, and the maximum number of iterations M Iter .

[0033] Furthermore, in step 3, the design variable interval is set according to the upper and lower boundaries for the first round of optimization; in subsequent optimizations, the design variable interval is updated according to the optimization results, and the specifics for the design variable x are as follows:

[0034] For the first round of optimization, the design variable interval is based on the boundary [x min ,x max ]set up;

[0035] In subsequent optimization, the design variable interval is updated according to the optimization results, and the update formula is:

[0036]

[0037] Among them, the shrinkage ratio α increases with the current number of iterations C Iter To the maximum number of iterations M Iter Approximation, using the cosine function to change from 1 to 0, that is, the degree of contraction of the design variable interval is positively correlated with the number of iterations; update width width to the boundary width (x max -x min ) multiplied by the shrinkage ratio α; upper and lower boundaries x max 、x min Updated value Cannot cross the original boundary value, x best is the optimization result of the design variable x in the previous round.

[0038] Furthermore, the adaptive proxy model for generating the design variable interval described in step 4 is specifically as follows:

[0039] Step 4.1, generate N sampling points in the design variable interval using the optimal super Latin sampling method, where N is determined by the number and complexity of the design variables of the model;

[0040] Step 4.2, constructing a surrogate model using a polynomial response surface model, a radial basis function model or a Kriging model modeling method;

[0041] Step 4.3: Determine the coefficient of determination R of the constructed proxy model 2 Does it satisfy R 2 >0.9. If not, adjust the parameters in the proxy model and rebuild it.

[0042] Furthermore, the setting of the initial parameters of the inner loop of the multi-level ATC optimization model described in step 5 is as follows:

[0043] Set the initial parameters of ATC at each level, including the boundary values ​​of the design variables of the optimization model and the parameters of the optimizer; if the optimizer uses a gradient optimizer, it is also necessary to set the initial values ​​of the system at each level, including the initial values ​​of the design variables and the target Tij The initial value of

[0044] The inner loop of the multi-level ATC optimization model is optimized step by step as described in step 6, as follows:

[0045] Starting from the top level of the system, after optimizing each system level, the target value T ij Pass it to the next level and calculate the response value r ij Then it will be updated to the previous level with the next inner cycle;

[0046] When the inconsistent information between the target value and the response value is calculated in ATC, the dimensions of the physical quantities in the target value and the response value are different. The ATC optimization based on synchronous improvement of magnitude, namely the SML-ATC method, is used to obtain the inconsistent information dT through logarithmic operation. ij -r ij |Order of magnitude optimization;

[0047] The ξ-th inconsistency information measure function The conversion formula is:

[0048]

[0049] Among them, T ij and r ij are the target and response of the jth submodule system at the i-th level, log 10 (|T ij -r ij |) is the order of magnitude of inconsistent information; ε is a very small value, ε is 1×10 -10 ; a is the proportionality coefficient, which is used to adjust the magnitude of the inconsistency index.

[0050] Furthermore, the stopping criteria described in step 7 are as follows:

[0051] The stopping criterion is that the error of the objective function for two consecutive inner loop iterations is less than the stopping tolerance ε in , as shown below:

[0052]

[0053] Among them, k represents the number of inner loop iterations, f ij is the optimization objective function; the inner loop stop tolerance ε in >0 and less than the outer loop termination tolerance.

[0054] Furthermore, after the inner loop described in step 8 is completed, the optimization results are processed and the extended consistency constraints are calculated, as follows:

[0055] Step 8.1, pass the design variables obtained in the previous round of optimization as new starting points to the inner loop, and update the optimization starting point;

[0056] Step 8.2: Calculate the inconsistency information c after each system is optimized ij , the formula is:

[0057]

[0058] where c ij It is the inconsistent information after the target value is passed downward or the response value is passed upward;

[0059] Step 8.3: The inconsistent information c ij Integrate into the extended consistency constraint q, the formula is:

[0060]

[0061] Furthermore, in step 9, it is determined whether the outer loop of the round reaches the stopping criterion. If the stopping criterion is reached, the inconsistent information between the system levels converges and the optimization is completed; if the stopping criterion is not reached, the outer loop parameters are updated according to the augmented Lagrangian penalty function method, and the outer loop is returned to step 3 to continue, as follows:

[0062] Step 9.1: When the bi-norm of all inconsistent information change values ​​after two consecutive ATC iterations is less than the convergence accuracy threshold ε out1 , and the two norms of all inconsistent information are less than the convergence accuracy threshold ε out2 When , the outer loop reaches the stopping criterion, the formula is:

[0063] ||q n -q n-1 || ∞ <ε out1

[0064] ||q n || ∞ <ε out2

[0065] Among them, n is the number of iterations, and the convergence accuracy threshold ε of the inconsistent information change value is out1 The value of is ε out1 =1×10 -4 , the convergence accuracy threshold ε of inconsistent information out2 The value of is ε out2 =1×10 -3 ;

[0066] Step 9.2: If the outer loop does not reach the stopping criterion, update the outer loop parameters according to the augmented Lagrange penalty function method and return to step 3 to continue the outer loop, as follows:

[0067] The Lagrange multiplier v of the n+1th round n+1 The vector update formula is:

[0068]

[0069] In the formula, v n is the linear Granger multiplier vector, w is the weight vector, q n is the extended consistency constraint at the end of the nth inner loop iteration, symbol stands for Hadamard multiplication, which is the term-by-term multiplication of two vectors;

[0070] The weight vector w update formula is:

[0071]

[0072] Where β and γ are weight vector update parameters, β>1,0<γ<1;

[0073] Step 9.3: If the number of iterations reaches the maximum number of iterations, that is, C Iter =M Iter If the above requirements are still not met, it means that the system cannot meet the accuracy requirements and the optimization fails and stops. Iter is the current iteration number, M Iter is the maximum number of iterations.

[0074] A multi-level structural dynamics ATC optimization device based on target magnitude synchronization, the device is used to implement the multi-level structural dynamics ATC optimization method based on target magnitude synchronization, the device includes an initialization / update module, an SML-ATC module, a design variable boundary setting / update module, an adaptive proxy model construction module, a convergence judgment module and an output processing module;

[0075] The initialization / update module is configured to be used for user initialization parameters, and drives the following units to perform the following initialization and subsequent parameter update steps: divide the subsystem unit to divide the subsystem optimization problem; the outer loop initialization / update unit sets the initial value v=0 of the Lagrange multiplier, the initial value of the weight w of the penalty function and the initial value of the growth rate β of the penalty weight, and updates the parameters of the Lagrange multiplier and the weight of the penalty function according to the augmented Lagrange penalty function method AL strategy; the inner loop initialization / update unit sets the boundaries of the design variables of the ATC optimization model at all levels, the starting points of the system optimizers at all levels, and the convergence accuracy threshold of the optimizer;

[0076] The SML-ATC module includes subsystem optimization solving units at all levels and magnitude synchronization calculation units, which are core calculation units used to solve the optimizers of each subsystem and belong to the inner loop calculation link, wherein:

[0077] The subsystem-level optimization solving unit drives the following units to execute the subsystem optimization steps: the subsystem solver setting unit configures the solver parameters for subsystem optimization solving; the subsystem objective function setting unit sets the objective function of the subsystem; the subsystem constraint condition setting unit sets the constraint conditions of the subsystem; the subsystem optimization convergence judgment unit determines whether the system meets the convergence accuracy requirements; the subsystem communication unit realizes the communication between the subsystem and other optimization modules and transmits data and information;

[0078] The synchronous computing unit adopts the optimization method based on SML-ATC and measures the function through the inconsistency information. Convert the inconsistent information between the target value and the response value to overcome the inconsistent information caused by the different dimensions of the physical quantity. ij -r ij |The order of magnitude is too small or too large, ultimately avoiding problems that affect the convergence of the system;

[0079] The design variable boundary setting / updating module drives the following units to execute the design variable boundary setting and updating of the proxy model module and the optimization solution module: the boundary setting unit sets the upper and lower boundaries of the design variable; the scaling coefficient calculation unit calculates the shrinkage ratio α so that the shrinkage degree of the design variable interval is positively correlated with the number of iterations, and adjusts the parameters or terminates the optimization process as needed; the boundary width calculation unit calculates the update width width; the boundary update unit updates the upper and lower boundary values;

[0080] The adaptive proxy model construction module drives the following units to generate an adaptive proxy model for the design variable interval: a sampling point setting unit, which sets N sampling points in the design variable interval; a proxy model parameter setting unit, which sets the parameters of the proxy model modeling method used; and a proxy model training unit, which trains the adaptive proxy model according to the proxy model modeling method used to determine the determination coefficient R. 2 Does it satisfy R 2 >0.9. If it does not meet the requirement, the parameters in the proxy model need to be adjusted and rebuilt;

[0081] The convergence judgment module drives the following units to judge whether the optimization process has reached the outer loop convergence standard: the judgment unit judges the current inner loop optimization to determine whether it has reached the preset outer loop convergence standard; the feedback unit feeds back the judgment result to the initialization / update module to adjust parameters or terminate the optimization process as needed;

[0082] The output processing module drives the following units to perform processing and output optimization results: a result processing unit processes the results of the optimization solution; and a result output unit outputs the final optimization result.

[0083] Compared with the prior art, the present invention has the following significant advantages: (1) It adopts a multi-level ATC optimization method with synchronized magnitudes. By designing an inconsistency information measurement function that is sensitive to the magnitude of the response value deviation, it can dynamically adjust the deviation information based on the excessive or insufficient magnitudes between the response values, thereby ensuring the coordination between the response values ​​during the optimization process; (2) It adopts a low-cost adaptive proxy model method, integrates the multi-level ATC optimization method with the adaptive proxy model technology, and constructs local high-precision proxy models layer by layer and one by one in the ATC outer loop, thereby improving the accuracy of small-magnitude response values; (3) It adopts a method of dynamically updating the boundaries of design variables according to the optimization results, integrates the multi-level ATC optimization with the adaptive proxy model technology, and adaptively adjusts the design boundaries of the optimization problem and the proxy model simultaneously during the optimization process, thereby improving the adaptability of the proxy model and saving optimization time. BRIEF DESCRIPTION OF THE DRAWINGS

[0084] Figure 1 It is a flow chart of the multi-level structural dynamics ATC optimization method based on target magnitude synchronization of the present invention.

[0085] Figure 2 It is a convergence curve diagram of the full trajectory dynamics optimization problem in an embodiment of the present invention.

[0086] Figure 3 It is an iterative curve diagram of the muzzle velocity of the internal ballistic subsystem in an embodiment of the present invention.

[0087] Figure 4 It is an iterative curve diagram of the range of the exterior ballistic subsystem in an embodiment of the present invention.

[0088] Figure 5 It is an iterative curve diagram of the killing area of ​​the endpoint effector system in an embodiment of the present invention.

[0089] Figure 6 It is a structural block diagram of the ATC device with level synchronization and multi-level optimization in an embodiment of the present invention.

[0090] Figure 7 4 is a structural block diagram of an outer loop initialization / update module in an embodiment of the present invention.

[0091] Figure 8 4 is a structural block diagram of an inner loop initialization / update module in an embodiment of the present invention.

[0092] Fig. 9 It is a structural block diagram of a subsystem-level optimization solution module in an embodiment of the present invention.

[0093] Fig.10 4 is a structural block diagram of a boundary setting / updating module in an embodiment of the present invention.

[0094] Fig.11 It is a structural block diagram of the adaptive agent model construction module in an embodiment of the present invention.

[0095] Fig.12 4 is a structural block diagram of a convergence judgment module in an embodiment of the present invention.

[0096] Fig.13 4 is a structural block diagram of an output processing module in an embodiment of the present invention.

[0097] Fig.14 4 is a structural block diagram of a module hardware device in an embodiment of the present invention. DETAILED DESCRIPTION

[0098] In order to make the above-mentioned purposes, features and advantages of the present invention more obvious and easy to understand, the specific implementation methods of the present invention are described in detail below in conjunction with the drawings of the specification. Obviously, the described embodiments are part of the embodiments of the present invention, but not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary persons in the art without creative work should fall within the scope of protection of the present invention.

[0099] In the following description, many specific details are set forth to facilitate a full understanding of the present invention, but the present invention may also be implemented in other ways different from those described herein, and those skilled in the art may make similar generalizations without violating the connotation of the present invention. Therefore, the present invention is not limited to the specific embodiments disclosed below.

[0100] It should be noted that, in the absence of conflict, the embodiments and features in the embodiments of the present application can be combined with each other. The present application will be described in detail below with reference to the accompanying drawings and in combination with the embodiments.

[0101] Combination Figure 1 The present invention discloses a multi-level structural dynamics ATC optimization method based on target magnitude synchronization, which decomposes the complex structural dynamics optimization problem into a non-hierarchical optimization model with m levels, each level having n sub-optimization models, coupling connection variables between models at different levels, target sending and response responses between upper and lower optimization models, connection variables between upper and lower optimization models and models at the same level, and the structural dynamics optimization problem is decomposed into a problem of minimizing the inconsistent information between the optimization target of the sub-optimization model and its target value and response value; the optimization problem P of the j-th submodule at the i-th level ij , optimize the design and iteration of the sub-optimization model in turn, and integrate the inconsistent information between the current level target and the response Inconsistency information of connection variables at this level Inconsistent information between superior and subordinate goals and responses Inconsistent information about variables in upper and lower level connections Coordinate to meet accuracy requirements, especially for inconsistent information |T ij -r ij | is too small or too large and needs to be processed based on the magnitude synchronization method. Then, the multi-level ATC optimization method is used to obtain the optimal solution for the entire structural dynamics optimization problem. The specific steps are as follows:

[0102] Step 1: Decompose the multi-level structural dynamics optimization problem into a non-hierarchical ATC optimization model as follows:

[0103] The expressions of the objective functions at all levels using Lagrange multipliers are:

[0104]

[0105] Where P ij is the optimization problem of the jth submodule at the i-th level obtained by decomposition, which is calculated by the adaptive agent model; ij is the design variable of the jth submodule at the i-th level, and the design boundary of the optimization model changes with the boundary of the adaptive proxy model; r ij is the system response value obtained by solving the analysis model at this level; a ij is the response analysis function, usually a “black box” function; T U is the target value passed down from a higher level; T ik is the target value passed down from this level; is the response value passed up from the lower level; Y is the connection variable between the same levels; is the connection variable value passed down from a higher level; is the connection variable value passed up from the lower level; f ij is the optimization objective function; g ij is the constraint condition of the inequality; h ij is the equality constraint; is the penalty function weight vector of the higher-level response and target values; is the penalty function weight vector of the higher-level connection variables; is the penalty function weight vector of the k-th child response value and target value of the next level; is the penalty function weight vector of the connection variables associated with the k-th child of the next level; is a collection of child elements in a lower level, is the penalty function linear Grarangian multiplier vector of the higher level response and target values; is the penalty function linear Grarangian multiplier vector of the higher level connection variables; is the penalty function linear Grarangian multiplier vector with the response value and target value of the k-th child at the next level; is the penalty function linear Grarange multiplier vector of the connection variables associated with the kth child of the next level.

[0106] Step 2: Initialize the initial parameters of the outer loop of the multi-level ATC optimization model, set the initial value of the weight w of the penalty function; set the initial value of the Lagrange multiplier v = 0, the initial value of the growth rate β of the penalty weight, and the maximum number of iterations M Iter .

[0107] Step 3: Set the design variable interval. For the first round of optimization, the design variable interval is set according to the upper and lower boundaries. For subsequent optimization, the design variable interval is updated according to the optimization results. Taking a design variable x as an example, the details are as follows:

[0108] For the first round of optimization, the design variable interval is based on the upper and lower boundaries [x min ,x max ]set up;

[0109] In subsequent optimization, the design variable interval is updated according to the optimization results, and the update formula is:

[0110]

[0111] Among them, the shrinkage ratio α increases with the current number of iterations C Iter To the maximum number of iterations M Iter Approximation, using the cosine function to change from 1 to 0, that is, the degree of contraction of the design variable interval is positively correlated with the number of iterations; update width width to the boundary width (x max -x min ) multiplied by the contraction ratio α; x best It is the optimization result of the design variable x in the previous round. The updated values ​​of the upper and lower boundaries cannot exceed the original boundary values.

[0112] Step 4: Generate an adaptive proxy model for the design variable interval, as follows:

[0113] Step 4.1, generate N sampling points in the design variable interval using the optimal super Latin sampling method, where N is determined by the number and complexity of the design variables of the model;

[0114] Step 4.2, constructing a surrogate model using a polynomial response surface model, a radial basis function model or a Kriging model modeling method;

[0115] Step 4.3: Determine the coefficient of determination R of the constructed proxy model 2 Does it satisfy R 2 >0.9. If not, adjust the parameters in the proxy model and rebuild it.

[0116] Step 5: Set the initial parameters of ATC at all levels, including the boundary values ​​of the design variables of the optimization model and the parameters of the optimizer; if the optimizer uses a gradient optimizer, it is also necessary to set the initial values ​​of the system at all levels, including the initial values ​​of the design variables and the target T ij The initial value of .

[0117] Step 6: Optimize the inner loop of the multi-level ATC optimization model step by step, as follows:

[0118] Starting from the top level of the system, after optimizing each system level, the target value T ij Pass it to the next level and calculate the response value r ij Then it will be updated to the previous level with the next inner cycle;

[0119] When the inconsistent information between the target value and the response value is calculated in ATC, the inconsistent information will be caused due to the different dimensions of the physical quantities in the target value and the response value in the optimization problem. ij -r ij The order of magnitude of | is too small or too large, which will eventually affect the convergence of the system. Therefore, the ATC optimization based on magnitude synchronization improvement, namely the SML-ATC method, is used to obtain the inconsistent information |T through logarithmic operation. ij -r ij | is optimized. When the difference order of magnitude is too small, it can capture subtle changes in inconsistent information. When the difference order of magnitude is too large, it can smooth large fluctuations, which helps the system converge to a more accurate solution.

[0120] The ξ-th inconsistency information measure function The conversion formula is:

[0121]

[0122] Among them, T ij and r ij are the target and response of the jth submodule system at the i-th level, log 10 (|T ij -r ij |) is the order of magnitude of inconsistent information; ε is a very small value, when |T ij -r ij When the logarithmic function is close to zero, a small positive number ε is set to avoid division by zero errors and ensure the stability of the calculation. ε is generally 1×10 -10 ; a is the proportional coefficient, which is used to adjust the magnitude of the inconsistency index to ensure that the inconsistency information measurement function can be coordinated with the target value or other parameters.

[0123] Step 7: Determine whether the inner loop of this round has reached the stopping criteria. If so, it means that the inner loop has reached the convergence accuracy requirement, and then proceed to step 8. If not, update the inner loop parameters and return to step 6 to continue the inner loop.

[0124] The stopping criteria are:

[0125] The stopping criterion is that the error of the objective function for two consecutive inner loop iterations is less than the stopping tolerance ε in , as shown below:

[0126]

[0127] Among them, k represents the number of inner loop iterations, f ij is the optimization objective function; the inner loop stop tolerance ε in >0 and less than the outer loop termination tolerance.

[0128] Step 8: After the inner loop is completed, process the optimization results and calculate the extended consistency constraints, as follows:

[0129] Step 8.1, pass the design variables obtained in the previous round of optimization as new starting points to the inner loop, and update the optimization starting point;

[0130] Step 8.2: Calculate the inconsistency information c after each system is optimized ij , the formula is:

[0131]

[0132] where c ij It is the inconsistent information after the target value is passed downward or the response value is passed upward;

[0133] Step 8.3: The inconsistent information c ij Integrate into the extended consistency constraint q, the formula is:

[0134]

[0135] Step 9: Determine whether the outer loop of this round reaches the stopping criterion. If the stopping criterion is reached, the inconsistent information between system levels converges and the optimization is completed; if the stopping criterion is not reached, the outer loop parameters are updated according to the augmented Lagrangian penalty function method, and return to step 3 to continue the outer loop, as follows:

[0136] Step 9.1: When the bi-norm of all inconsistent information change values ​​after two consecutive ATC iterations is less than the convergence accuracy threshold ε out1 , and the two norms of all inconsistent information are less than the convergence accuracy threshold ε out2 When , the outer loop reaches the stopping criterion, the formula is:

[0137] ||q n -q n-1 || ∞ <ε out1 (7)

[0138] ||q n || ∞ <ε out2 (8)

[0139] Among them, n is the number of iterations, and the convergence accuracy threshold ε of the inconsistent information change value is out1 The value of is ε out1 =1×10 -4 , the convergence accuracy threshold ε of inconsistent information out2 The value of is ε out2 =1×10 -3 ;

[0140] Step 9.2: If the outer loop does not reach the stopping criterion, update the outer loop parameters according to the augmented Lagrange penalty function method and return to step 3 to continue the outer loop, as follows:

[0141] The Lagrange multiplier v of the n+1th round n+1 The vector update formula is:

[0142]

[0143] In the formula, v n is the linear Granger multiplier vector, w is the weight vector, q n is the extended consistency constraint at the end of the nth inner loop iteration, symbol stands for Hadamard multiplication, which is the term-by-term multiplication of two vectors;

[0144] The weight vector w update formula is:

[0145]

[0146] Where β and γ are weight vector update parameters, β>1, 0<γ<1; the coordination efficiency depends on the selection of parameters β and γ, especially parameter β;

[0147] Step 9.3: If the number of iterations reaches the maximum number of iterations, that is, C Iter =M Iter If the above requirements are still not met, it means that the system cannot meet the accuracy requirements and the optimization fails and stops. Iter is the current iteration number, M Iter is the maximum number of iterations.

[0148] like Figure 6As shown, the present invention also provides a multi-level structural dynamics ATC optimization device based on target magnitude synchronization, including an initialization / update module, an SML-ATC module, a design variable boundary setting / update module, an adaptive agent model construction module, a convergence judgment module and an output processing module;

[0149] The initialization / update module is configured to be used for user initialization parameters, and drives the following units to perform the following initialization and subsequent parameter update steps: divide the subsystem unit to divide the subsystem optimization problem; the outer loop initialization / update unit sets the initial value v=0 of the Lagrange multiplier, the initial value of the weight w of the penalty function and the initial value of the growth rate β of the penalty weight, and updates the parameters of the Lagrange multiplier and the weight of the penalty function according to the augmented Lagrange penalty function method AL strategy; the inner loop initialization / update unit sets the boundaries of the design variables of the ATC optimization model at all levels, the starting points of the system optimizers at all levels, and the convergence accuracy threshold of the optimizer;

[0150] The SML-ATC module, including subsystem optimization solving units at all levels and magnitude synchronization calculation units, is the core calculation unit of the device, used to solve the optimizer of each subsystem, and belongs to the inner loop calculation link, wherein:

[0151] The subsystem-level optimization solving unit drives the following units to execute the subsystem optimization steps: the subsystem solver setting unit configures the solver parameters for subsystem optimization solving; the subsystem objective function setting unit sets the objective function of the subsystem; the subsystem constraint condition setting unit sets the constraint conditions of the subsystem; the subsystem optimization convergence judgment unit determines whether the system meets the convergence accuracy requirements; the subsystem communication unit realizes the communication between the subsystem and other optimization modules and transmits data and information;

[0152] The synchronous computing unit adopts the optimization method based on SML-ATC and measures the function through the inconsistency information. Convert the inconsistent information between the target value and the response value to overcome the inconsistent information caused by the different dimensions of the physical quantity. ij -r ij |The order of magnitude is too small or too large, ultimately avoiding problems that affect the convergence of the system;

[0153] The design variable boundary setting / updating module drives the following units to execute the design variable boundary setting and updating of the proxy model module and the optimization solution module: the boundary setting unit sets the upper and lower boundaries of the design variable; the scaling coefficient calculation unit calculates the shrinkage ratio α so that the shrinkage degree of the design variable interval is positively correlated with the number of iterations, and adjusts the parameters or terminates the optimization process as needed; the boundary width calculation unit calculates the update width width; the boundary update unit updates the upper and lower boundary values;

[0154] The adaptive proxy model construction module drives the following units to generate an adaptive proxy model for the design variable interval: a sampling point setting unit, which sets N sampling points in the design variable interval; a proxy model parameter setting unit, which sets the parameters of the proxy model modeling method used; and a proxy model training unit, which trains the adaptive proxy model according to the proxy model modeling method used to determine the proxy model determination coefficient R. 2 Does it satisfy R 2 >0.9. If it does not meet the requirement, the parameters in the proxy model need to be adjusted and rebuilt;

[0155] The convergence judgment module drives the following units to judge whether the optimization process has reached the outer loop convergence standard: the judgment unit judges the current inner loop optimization to determine whether it has reached the preset outer loop convergence standard; the feedback unit feeds back the judgment result to the initialization / update module to adjust parameters or terminate the optimization process as needed;

[0156] The output processing module drives the following units to perform processing and output optimization results: the result processing unit processes the results of the optimization solution; the result output unit outputs the final optimization result.

[0157] The present invention is further described in detail below with reference to the accompanying drawings and specific embodiments.

[0158] Example 1

[0159] This embodiment takes the artillery full trajectory launch dynamics optimization problem as an example to demonstrate the implementation process of the SML-ATC method.

[0160] The dynamic process of the entire ballistic launch of artillery can be decomposed into the dynamic process of the projectile in the bore, the external ballistic process of the projectile, and the terminal effect of the projectile at the target point, namely, the internal ballistics, external ballistics and terminal effect. The performance indicators of each ballistic stage in the entire process of artillery launch are interrelated and connected in series step by step. It is particularly appropriate to use the target cascade method ATC to optimize the design of different ballistic stages of the artillery system. Through the ATC method, the effective series connection of the performance response values ​​of each stage of the artillery can be achieved, thereby improving the overall shooting accuracy of the artillery system, expanding the range, and maximizing the combat effectiveness of the ammunition in the whole process. The disturbance amount after the projectile leaves the muzzle has a great influence on the accuracy of the strike. It is one of the targets and response values ​​that need to be transmitted and calculated in the ATC calculation. However, the horizontal and vertical swing angles of the projectile are of small magnitude, usually in the range of 1×10 -3 magnitude, making the inconsistent information between the target value and the response value |T ij -r ij The magnitude of | is too small, far below the accuracy of the stopping criterion, and the magnitude of the horizontal and vertical swing angles of the projectile is between 1×10-6 The order of magnitude of fluctuation between 20 and 20 is extremely large, and it is difficult to control the convergence using conventional data normalization methods. Therefore, the implementation process of the SML-ATC method is demonstrated for the full ballistic launch dynamics process of the artillery.

[0161] Step 1: According to the multi-level ATC optimization model establishment method with synchronous magnitude, under given constraints, the end point effect optimization system, the external ballistic optimization system, and the internal ballistic optimization system of the inner loop of the ATC optimization model are respectively established as shown in equations (11) to (13):

[0162] End point effect optimization system:

[0163]

[0164] Among them, the design variable l i (i=1,…,6) is the length of the projectile, t0 is the wall thickness of the projectile, q is the incident angle, v z is the terminal velocity; S A (x 11 ) is the killing area, S A * is the normalization coefficient of the killing area, which is 6797m 2 , and is the inconsistent information penalty term; the constraint condition is that the projectile mass m is between 44.5 and 47.5 kg; for the penalty term Where T vz is the terminal effect level terminal velocity target value, that is, v z ; r vz Terminal velocity of the external ballistic stage The incoming response value; T q is the target value of the incident angle q at the end effect level, r q is the external ballistic incident angle q * The incoming response value; T m is the target value of the terminal effect projectile mass m, r m is the external ballistic mass m * The incoming response value; T l is the terminal effect projectile length target, Calculated; r l is the length of the external ballistic projectile l * The response value of is the augmented Lagrangian operator term; Optimize weight coefficients for ATC;

[0165] Exoballistic Optimization System:

[0166]

[0167] Among them, the design variable is the projectile center of mass position x cg , m is the mass of the projectile, l is the length of the projectile, v0 is the initial velocity of the projectile, ur2 is the swing angle of the muzzle in the x direction, ur3 is the swing angle of the muzzle in the y direction, vr2 is the angular velocity of the muzzle in the x direction, and vr3 is the angular velocity of the muzzle in the y direction; objective function To maximize range, is the range normalization coefficient, take 30000m, and the rest is the inconsistent information penalty; for the penalty Among them, r vz is the terminal velocity response value of the external ballistic stage, that is, v z ; T vz The terminal speed target value of the terminal effect level r q is the external ballistic incident angle response value, i.e. q; T q is the target value of the incident angle at the end effect level q * ; r m is the external ballistic mass parameter, i.e. m; T m is the target value of the terminal effect projectile mass m * ; r l is the length parameter of the external ballistic projectile, i.e. l; T l is the target value of the terminal effect projectile length l * ; T v0 is the target value of the muzzle velocity at the external ballistic level, i.e. v0; r v0 is the muzzle response value of the internal ballistic level T ur2 is the target value of the muzzle swing angle in the x direction at the external ballistic level, i.e. ur2; r ur2 is the internal ballistic level muzzle x-direction swing angle response value T ur3 is the target value of the y-direction swing angle of the muzzle at the external ballistic stage, i.e. ur3; r ur3 is the y-direction swing angle response value of the internal ballistic level muzzle T vr2 is the target value of the angular velocity of the muzzle in the x direction at the external ballistic level, that is, vr2; r vr2 is the angular velocity response value of the muzzle in the x direction at the internal ballistic level T vr3 is the target value of the y-direction angular velocity of the muzzle at the external ballistic stage, that is, vr3; r vr3 is the angular velocity response value of the muzzle y-direction swing at the external ballistic stage v * R is the augmented Lagrangian operator term; Optimize weight coefficients for ATC;

[0168] Interior Ballistic Optimization System:

[0169]

[0170] Among them, l c is the mass eccentricity, rifling groove width b, rifling depth t, and belt position l RB , band width W g , the interval between the missile and the gun is l bd , arc thickness e, powder mass ω, chamber volume W0; objective function To maximize the projectile muzzle velocity, is the normalized parameter of muzzle velocity, which is 980 m / s; the constraint g1 is the constraint on chamber pressure, which is used to ensure the safety of firing; for the penalty term where r v0 is the muzzle response value of the internal ballistic level, that is, v0; T v0 is the target value of the muzzle velocity at the external ballistic level r ur2 is the internal ballistic level muzzle x-direction swing angle response value, that is, ur2; T ur2 is the target value of the muzzle swing angle in the x direction at the external ballistic level r ur3 is the y-direction swing angle response value of the internal ballistic level muzzle, i.e. ur3; T ur3 is the target value of the y-direction swing angle of the muzzle at the external ballistic stage r vr2 is the angular velocity response value of the muzzle in the x direction at the internal ballistic level, that is, vr2; T vr2 The target value of the angular velocity of the muzzle in the x direction at the external ballistic level r vr3 is the angular velocity response value of the muzzle y-direction swing at the external ballistic level, that is, vr3; T vr3 is the target value of the y-direction angular velocity of the muzzle at the external ballistic stage is the augmented Lagrangian operator term; Optimize weight coefficients for ATC.

[0171] Step 2: Initialize the initial parameters of the outer loop of the multi-level ATC optimization model. The initial value of the penalty function weight w is 0.01. Set the initial value of the Lagrange multiplier v to 0, and the growth rate of the penalty weight β = 1.3.

[0172] Step 3, set the design variable interval. Taking the endpoint effect as an example, in the first round of optimization, the design variable l1 interval is set according to the upper and lower boundaries [38.0, 42.0]; in the first round of optimization, the design variable l1 result is 40.44, then the design variable interval is updated according to formula (14), and α is calculated to be 0.99, the updated width width is 3.99, and the updated upper and lower boundaries are [39.94, 40.93]; in the subsequent optimization iteration process, the design variable interval is updated according to the optimization result according to formula (14), and the update formula is:

[0173]

[0174] Among them, the shrinkage ratio α increases with the current number of iterations C Iter To the maximum number of iterations M Iter Approximation, using the cosine function to change from 1 to 0, that is, the degree of contraction of the design variable interval is positively correlated with the number of iterations; update width width to the boundary width (x max -x min ) multiplied by the shrinkage ratio α; the updated values ​​of the upper and lower boundaries cannot exceed the original boundary values.

[0175] Step 4: Generate an adaptive surrogate model for the design variable interval, taking the endpoint effect as an example, as follows:

[0176] Step 4.1, generate 100 sampling points in the design variable interval using the optimal super Latin sampling method;

[0177] Step 4.2: Use the Kriging model method to build a surrogate model and obtain the determination coefficient R 2 It is 0.96>0.9.

[0178] Step 5: Set the initial parameters of the inner loop of the multi-level ATC optimization model, including the boundary values ​​of the parameters of the optimization model, as shown in Tables 1 to 3.

[0179] Table 1 End point effect design variable interval and starting point position

[0180] Design variables <![CDATA[Length l1 / mm]]> <![CDATA[Length l2 / mm]]> <![CDATA[Length l3 / mm]]> <![CDATA[Length l4 / mm]]> <![CDATA[Length l5 / mm]]> <![CDATA[Length l6 / mm]]> <![CDATA[Thickness t0 / mm]]> Upper Boundary 42.0 208.0 50.0 62.0 82.5 356.5 11.5 Lower Boundary 38.0 203.0 45.0 54.0 74.5 350.5 8.5 Starting point 40.0 205.5 47.5 56.0 78.5 353.5 8.5

[0181] Table 2 Exterior ballistic design variable range and starting point position

[0182] Design variables <![CDATA[The x-position of the projectile's centroid cg / mm]]> Projectile mass m / kg Projectile length l / mm Upper Boundary 700.0 47.5 801.0 Lower Boundary 400.0 44.5 765.0 Starting point 551.0 45.5 765.0

[0183] Table 3 Design variable range and starting point position of the in-bore firing process

[0184]

[0185] This embodiment uses Python to write an ATC solution framework with an inner and outer loop Lagrangian quadratic penalty function method. Each subsystem of the inner loop uses Scipy.slsqp as an optimization solver, which is a gradient optimizer that can handle constraint problems. The convergence accuracy threshold of the optimizer is 1×10 -8 , and give the initial values ​​of each level of the system, including the initial values ​​of the design variables and the target T ij The initial values ​​are listed in Table 4.

[0186] Table 4 Coordination target initial values ​​and boundaries between each ballistic subsystem

[0187]

[0188] Step 6: Perform in the inner loop Starting from the top level of the system, after optimizing each system level, the target value T ij Pass it to the next level and calculate the response value r ij Then it will be updated to the previous level with the next inner loop.

[0189] Among them, in the ballistic and internal ballistic subsystems, since the optimized values ​​of the projectile horizontal swing angle ur2 and the projectile vertical swing angle ur3 are relatively low, usually within 1×10 -3 Magnitude, inconsistent information between target value and response value |T ij -r ij | is too small, far below the accuracy of the stopping criterion, but at the same time, the values ​​of the projectile horizontal swing angle ur2 and the projectile vertical swing angle ur3 will be within 1×10 -6 The fluctuation range is extremely large, and it is difficult to control the convergence using the common data normalization method. Therefore, the two physical quantities of the projectile horizontal swing angle ur2 and the projectile vertical swing angle ur3 are measured using the inconsistency information function as shown in formula (15): Conversion, where ε is 1×10 -10 , set the proportional coefficient a = 1, the formula is:

[0190]

[0191] Among them, T ij and r ij are the target and response of the jth submodule system at the i-th level, log 10 (|T ij -r ij |) is the order of magnitude of inconsistent information; ε is a very small value, when |T ij -r ijWhen the logarithmic function is close to zero, a small positive number ε is set to avoid division by zero errors and ensure the stability of the calculation. ε is generally 1×10 -10 ; a is the proportional coefficient, which is used to adjust the magnitude of the inconsistency index to ensure that the inconsistency information measurement function can be coordinated with the target value or other parameters.

[0192] For example: the vertical swing angle target of the projectile in the internal ballistic system 4.03×10 -6 , the last iteration of the first round of the inner loop obtains the vertical swing angle response r of the projectile ur3 4.05×10 -6 , calculated by formula (15)

[0193] Step 7: Determine whether the objective function error of the end-point effect subsystem, the external ballistic subsystem, and the internal ballistic subsystem in the inner loop is less than the stop tolerance ε for two consecutive inner loop iterations. in The calculation method is shown in formula (16); if it is met, go to step 8; if the stop criterion is not met, return to step 6 to continue the inner loop;

[0194] The stopping criterion is that the error of the objective function for two consecutive inner loop iterations is less than the stopping tolerance ε in , as shown below:

[0195]

[0196] Among them, k represents the number of inner loop iterations, f ij is the optimization objective function; the inner loop stop tolerance ε in =1×10 -10 ; Taking the interior ballistic subsystem as an example, only the objective function f 31 , the inner loop gets the 55th cycle The 56th cycle yields Use formula (16) to calculate f ε =5.17×10 -12 <ε in , the stop condition is met, exit the inner loop and go to step 8;

[0197] Step 8: After the inner loop is completed, process the optimization results and calculate the extended consistency constraints, as follows:

[0198] Step 8.1, update the optimization starting points of the terminal effect subsystem, the external ballistic subsystem and the internal ballistic subsystem, and pass the design variables obtained in the previous round of optimization as new starting points to the inner loop;

[0199] Step 8.2 Optimized inconsistent information c ij , the formula is:

[0200]

[0201] where c ij It is the inconsistent information after the target value is transmitted downward or the response value is transmitted upward;

[0202] Taking the inconsistent information after one round of optimization as an example, c 11 Use formula (18) for calculation:

[0203] c 11 =[-1.86×10 -7 -0.022228.96×10 -6 8.44×10 -5 ]

[0204] Step 8.3: The inconsistent information c ij Integrate into the extended consistency constraint q, the formula is:

[0205]

[0206] The extended consistency constraint q after the first round of optimization 1 as follows:

[0207]

[0208] Step 9: Determine whether the outer loop of this round reaches the stopping criterion. If the stopping criterion is reached, the inconsistent information between system levels converges and the optimization is completed; if the stopping criterion is not reached, the outer loop parameters are updated according to the augmented Lagrangian penalty function method, and return to step 3 to continue the outer loop, as follows:

[0209] Step 9.1: When the bi-norm of all inconsistent information change values ​​after two consecutive ATC iterations is less than the convergence accuracy threshold ε out1 , and the two norms of all inconsistent information are less than the convergence accuracy threshold ε out2 When , the outer loop reaches the stopping criterion, the formula is:

[0210] ||q n -q n-1 || ∞ <ε out1 (20)

[0211] ||q n || ∞ <ε out2 (twenty one)

[0212] Among them, n is the number of iterations, and the convergence accuracy threshold ε of the inconsistent information change value isout1 The value of is ε out1 =1×10 -4 , the convergence accuracy threshold ε of inconsistent information out2 The value of is ε out2 =1×10 -3 ; For example, the q calculated in the second cycle is 2 for:

[0213]

[0214] Calculated by formula (20), ||q n -q n-1 || ∞ =2.235>ε out1 , formula (21) calculates ||q n || ∞ =0.064>ε out2 , the two stopping criteria of the outer loop do not meet the convergence accuracy threshold requirements, and go to step 9.2;

[0215] Step 9.2: If the outer loop does not reach the stopping criterion, update the outer loop parameters according to the augmented Lagrange penalty function method and return to step 3 to continue the outer loop, as follows:

[0216] The Lagrange multiplier v of the n+1th round n+1 The vector update formula is:

[0217]

[0218] In the formula, v n is the linear Granger multiplier vector, w is the weight vector, q n is the extended consistency constraint at the end of the nth inner loop iteration, symbol stands for Hadamard multiplication, which is the term-by-term multiplication of two vectors. stands for Hadamard multiplication, which is the term-by-term multiplication of two vectors, such as In the first round, v 1 is the initial value, that is

[0219]

[0220] At the same time, 1 In the first round, the initial value is used, that is:

[0221]

[0222] In the second round, according to formula (22), we get

[0223]

[0224] The weight vector w update formula is:

[0225]

[0226] Where β and γ are weight vector update parameters, β = 1.3 and γ = 0.4; w 11 For example, due to Apparently The initial value of the penalty function weight w is 0.01. Therefore, according to formula (23), after the first round of update,

[0227] Step 9.3: If the number of iterations reaches the maximum number of iterations, that is, C Iter =M Iter If the above requirements are still not met, it means that the system cannot meet the accuracy requirements and the optimization fails and stops. Iter is the current iteration number, M Iter is the maximum number of iterations.

[0228] Under the ATC strategy, the system meets the two given stopping criteria and completes convergence after 22 iterations, as shown in Figure 2 As shown in the optimization convergence curve, the accuracy of inconsistent information is controlled within 1×10 -3 Below, that is, the difference between each target value and the response value is within its own order of magnitude of 1×10 -3 the following.

[0229] After ATC, the target value and response value of each ballistic subsystem are coordinated and converged. First, the coordination process of the muzzle velocity target value and response value between the external ballistics and the firing process in the gun bore is as follows: Figure 3 As shown in Figure 2, the muzzle velocity, actual response value and target value continue to improve during the entire iteration process and tend to be stable after the fifth iteration. y and the target killing area S optimized for endpoint effect A The iterative process is as follows Figure 4 and Figure 5 Finally, the calculation results of the optimization targets of each ballistic subsystem are compared in Table 5. All key optimization targets have greatly improved performance compared with the initial parameters.

[0230] Table 5 Comparison of optimization targets at all levels before and after

[0231] Target value <![CDATA[Kill area S A / m 2 > <![CDATA[Range x y / m]]> <![CDATA[Initial muzzle velocity v0 of projectile / (m / s)]]> Initial value 6974.323 34993.11 989.84 After optimization 7600.702 35694.34 1002.63

[0232] In summary, under the initial conditions of optimal performance of each ballistic subsystem, the response values ​​of the ballistic subsystems are not consistent, and the physical performance cascade cannot be achieved between the ballistic subsystems. After the ATC solution framework, the targets of individual ballistic subsystems will decrease during the optimization process, but they are all improved compared to the initial values, and the coordination between the required target values ​​and the response values ​​of each ballistic subsystem is consistent, which satisfies the effective cascade of physical performance between the ballistic subsystems under the condition of consistent design parameters, and realizes the overall optimization design process of the entire ballistic performance.

[0233] Example 2

[0234] This embodiment provides a multi-level structural dynamics ATC optimization device based on target level synchronization. Figure 1 Corresponding to the method shown, the device can be specifically applied to electronic equipment.

[0235] like Figure 6 As shown, the multi-level structural dynamics ATC optimization device based on target magnitude synchronization provided in this embodiment includes the initialization / update module, the SML-ATC module, the design variable boundary setting / update module, the adaptive agent model construction module, the convergence judgment module and the output processing module;

[0236] The initialization / update module is configured to initialize parameters for the user, and drives the following units to perform the following initialization and subsequent parameter update steps: divide the subsystem units to divide the subsystem optimization problem; the outer loop initialization / update module, such as Figure 7 As shown, the initial value of the Lagrangian multiplier v=0, the initial value of the penalty function weight w and the initial value of the penalty weight growth rate β are set, and the parameters of the Lagrangian multiplier and the penalty function weight are updated according to the augmented Lagrangian penalty function method, namely the Augmented Lagrangian, referred to as the AL strategy; the inner loop initialization / update module, such as Figure 8 As shown, the boundaries of the design variables of the ATC optimization model at each level, the starting points of the system optimizers at each level, and the convergence accuracy threshold of the optimizer are set.

[0237] The SML-ATC module, including subsystem optimization solving units at all levels and magnitude synchronization calculation units, is the core calculation unit of the device, used to solve the optimizer of each subsystem, and belongs to the inner loop calculation link, wherein:

[0238] Subsystem level optimization solution module, such as Fig. 9As shown, the following units are driven to execute the subsystem optimization steps: a subsystem solver setting unit, which configures the solver parameters for subsystem optimization solution; a subsystem objective function setting unit, which sets the objective function of the subsystem; a subsystem constraint condition setting unit, which sets the constraint conditions of the subsystem; a subsystem optimization convergence judgment unit, which judges whether the system meets the convergence accuracy requirements; a subsystem communication unit, which realizes the communication between the subsystem and other optimization modules and transmits data and information;

[0239] The magnitude synchronization calculation unit adopts the ATC optimization method based on magnitude synchronization improvement, namely the SML-ATC method, through the inconsistency information measurement function Convert the inconsistent information between the target value and the response value to overcome the inconsistent information caused by the different dimensions of the physical quantity. ij -r ij |The order of magnitude is too small or too large, ultimately avoiding problems that affect the convergence of the system.

[0240] The design variable boundary setting / updating module, such as Fig.10 As shown, the following units are driven to execute the setting and updating of design variable boundaries of the proxy model module and the optimization solution module: the boundary setting unit sets the upper and lower boundaries of the design variables; the scaling coefficient calculation unit calculates the shrinkage ratio α so that the shrinkage degree of the design variable interval is positively correlated with the number of iterations; the parameters are adjusted or the optimization process is terminated as needed; the boundary width calculation unit calculates the update width width; the boundary update unit updates the upper and lower boundary values.

[0241] The adaptive agent model building module, such as Fig.11 As shown, the following units are driven to generate an adaptive proxy model for the design variable interval: a sampling point setting unit, which sets N sampling points in the design variable interval; a proxy model parameter setting unit, which sets the parameters of the proxy model modeling method used; a proxy model training unit, which trains the adaptive proxy model according to the proxy model modeling method used, and determines the proxy model determination coefficient R 2 Does it satisfy R 2 >0.9. If it is not satisfied, it is necessary to adjust the parameters in the proxy model and rebuild it.

[0242] The convergence judgment module is as follows: Fig.12 As shown, the following units are driven to execute the judgment on whether the optimization process reaches the outer loop convergence standard: the judgment unit judges the current inner loop optimization to determine whether the preset outer loop convergence standard is reached; the feedback unit feeds back the judgment result to the initialization / update module to adjust the parameters or terminate the optimization process as needed.

[0243] The output processing module, such as Fig.13As shown, the following units are driven to perform processing and output optimization results: result processing unit: processes the results of the optimization solution; result output unit, outputs the final optimization result.

[0244] Module hardware equipment such as Fig.14 As shown, the module may include at least one processor, such as a CPU, i.e., a Central Processing Unit, at least one user interface or output interface, a memory, and at least one communication bus. The communication bus is used to realize the connection and communication between the above components; the user interface may optionally include a display, a keyboard or a click device, such as a mouse, a trackball, a touchpad or a touch display screen; the memory may include a high-speed RAM, i.e., a Random Access Memory, and may also include a non-volatile memory, i.e., a non-volatile memory, such as at least one disk memory. In some implementations, the processor may include an initialization module, wherein the initialization module may set initialization parameters and subsequent parameter update rules through a user interface. The processor may also include an optimization solution module, which solves the optimization model by calling a calculator and a solver program in the memory. The processor may also include an output module, wherein the output module outputs the result obtained by the solution through an output interface. The memory may store a solver, a calculator, and a software program, so that the optimization solution module of the processor may call the solver and the calculator from the memory for optimization solution; the initialization module, the convergence judgment module, and the output module may implement their basic services through a software program. In some embodiments, the memory stores executable modules or data structures, or a subset thereof, or an extended set thereof.

[0245] The operating system contains various system programs used to implement various basic services and handle hardware-based tasks.

[0246] The application program includes various application programs for implementing various application services. Specifically, the application program may include an application program of the physical planning and enhanced collaborative optimization integration method of the present application, and the application program may be run under an operating system. Optionally, the memory may also include a cache unit, which may be used to store cache data and optimization results generated during the optimization process.

[0247] It is worth noting that the modules or units involved in the embodiments of the present application can be implemented by software or by hardware. The modules or units described can also be set in a processor, for example, it can be described as: a processor includes an initialization module, a physical planning module, an optimization solution module, a convergence judgment module and an output module. Among them, the names of these modules do not constitute a limitation on the module itself under certain circumstances. For example, the initialization module can also be described as a "module configured to initialize user parameters and update parameters". As another aspect, the present application also provides a computer-readable storage medium, which can be a computer-readable storage medium included in the device described in the above embodiment; or it can be a computer-readable storage medium that exists alone and is not assembled in a terminal. The computer-readable storage medium stores one or more programs, and the program is used by one or more processors to execute the physical planning and enhanced collaborative optimization integration method described in the present application. The above description is only a preferred embodiment of the present application and an explanation of the technical principles used. Those skilled in the art should understand that the scope of the invention involved in this application is not limited to the technical solutions formed by a specific combination of the above technical features, but should also cover other technical solutions formed by any combination of the above technical features or their equivalent features without departing from the inventive concept. For example, the above features are replaced with but not limited to the technical features with similar functions disclosed in this application.

[0248] The above are only preferred embodiments of the present invention. It should be pointed out that, for ordinary technicians in this technical field, several improvements and modifications can be made without departing from the principles of the present invention. These improvements and modifications should also be regarded as the scope of protection of the present invention.

Claims

1. A multi-level structural dynamics ATC optimization method based on target level synchronization, characterized in that: The following steps are involved: Step 1: Decompose the multi-level structural dynamics optimization problem into a non-hierarchical ATC optimization model; Step 2, initializing the initial parameters of the outer loop of the multi-level ATC optimization model; Step 3: Set the design variable interval. For the first round of optimization, the design variable interval is set according to the upper and lower boundaries; for subsequent optimization, the design variable interval is updated according to the optimization results; Step 4, generating an adaptive proxy model for the design variable interval; Step 5: Set the initial parameters of the inner loop of the multi-level ATC optimization model; Step 6: Optimize the inner loop of the multi-level ATC optimization model step by step; Step 7: Determine whether the inner loop of this round has reached the stopping criteria. If so, it means that the inner loop has reached the convergence accuracy requirement, and then proceed to step 8. If not, update the inner loop parameters and return to step 6 to continue the inner loop. Step 8: After the inner loop is completed, process the optimization results and calculate the extended consistency constraints; Step 9: Determine whether the outer loop of this round reaches the stopping criterion. If so, the inconsistent information between system levels converges and the optimization is completed. If not, update the outer loop parameters according to the augmented Lagrangian penalty function method and return to step 3 to continue the outer loop.

2. The multi-level structural dynamics ATC optimization method based on target magnitude synchronization according to claim 1 is characterized in that: The multi-level structural dynamics optimization problem described in step 1 is decomposed into a non-hierarchical ATC optimization model as follows: The expressions of the objective functions at all levels using Lagrange multipliers are: in: Where P ij is the optimization problem of the jth submodule at the i-th level obtained by decomposition, which is calculated by the adaptive agent model; ij is the design variable of the jth submodule at the i-th level, and the design boundary of the optimization model changes with the boundary of the adaptive proxy model; r ij is the system response value obtained by solving the analysis model at this level; a ij is the response analysis function; T U is the target value passed down from a higher level; T ik is the target value passed down from this level; is the response value passed up from the lower level; Y is the connection variable between the same levels; is the connection variable value passed down from a higher level; is the connection variable value passed up from the lower level; f ij is the optimization objective function; g ij is the constraint condition of the inequality; h ij is the equality constraint; is the penalty function weight vector of the higher-level response and target values; is the penalty function weight vector of the higher-level connection variables; is the penalty function weight vector of the k-th child response value and target value of the next level; is the penalty function weight vector of the connection variables associated with the k-th child of the next level; is a collection of child elements in a lower level, is the penalty function linear Grarangian multiplier vector of the higher level response and target values; is the penalty function linear Grarangian multiplier vector of the higher level connection variables; is the penalty function linear Grarangian multiplier vector with the response value and target value of the k-th child at the next level; is the penalty function linear Grarange multiplier vector of the connection variables associated with the kth child of the next level.

3. The multi-level structural dynamics ATC optimization method based on target magnitude synchronization according to claim 2 is characterized in that: The initial parameters of the outer loop of the initial multi-level ATC optimization model described in step 2 are as follows: Set the initial value of the penalty function weight w; set the initial value of the Lagrange multiplier v = 0, the initial value of the penalty weight growth rate β, and the maximum number of iterations M Iter .

4. The multi-level structural dynamics ATC optimization method based on target magnitude synchronization according to claim 3 is characterized in that: In step 3, the design variable interval is set according to the upper and lower boundaries for the first round of optimization; in subsequent optimizations, the design variable interval is updated according to the optimization results, and the specific details for the design variable x are as follows: For the first round of optimization, the design variable interval is based on the boundary [x min ,x max ]set up; In subsequent optimization, the design variable interval is updated according to the optimization results, and the update formula is: Among them, the shrinkage ratio α increases with the current number of iterations C Iter To the maximum number of iterations M Iter Approximation, using the cosine function to change from 1 to 0, that is, the degree of contraction of the design variable interval is positively correlated with the number of iterations; update width width to the boundary width (x max -x min ) multiplied by the shrinkage ratio α; upper and lower boundaries x max 、x min Updated value Cannot cross the original boundary value, x best is the optimization result of the design variable x in the previous round.

5. The multi-level structural dynamics ATC optimization method based on target magnitude synchronization according to claim 4 is characterized in that: The adaptive proxy model for generating the design variable interval described in step 4 is as follows: Step 4.1, generate N sampling points in the design variable interval using the optimal super Latin sampling method, where N is determined by the number and complexity of the design variables of the model; Step 4.2, constructing a surrogate model using a polynomial response surface model, a radial basis function model or a Kriging model modeling method; Step 4.3: Determine the coefficient of determination R of the constructed proxy model 2 Does it satisfy R 2 >0.

9. If not, adjust the parameters in the proxy model and rebuild it.

6. The multi-level structural dynamics ATC optimization method based on target magnitude synchronization according to claim 5 is characterized in that: The initial parameters of the inner loop of the multi-level ATC optimization model are set as described in step 5, as follows: Set the initial parameters of ATC at each level, including the boundary values ​​of the design variables of the optimization model and the parameters of the optimizer; if the optimizer uses a gradient optimizer, it is also necessary to set the initial values ​​of the system at each level, including the initial values ​​of the design variables and the target T ij The initial value of The inner loop of the multi-level ATC optimization model is optimized step by step as described in step 6, as follows: Starting from the top level of the system, after optimizing each system level, the target value T ij Pass it to the next level and calculate the response value r ij Then it will be updated to the previous level with the next inner cycle; When the inconsistent information between the target value and the response value is calculated in ATC, the dimensions of the physical quantities in the target value and the response value are different. The ATC optimization based on synchronous improvement of magnitude, namely the SML-ATC method, is used to obtain the inconsistent information by logarithmic operation|T ij -r ij |Order of magnitude optimization; The ξ-th inconsistency information measure function The conversion formula is: Among them, T ij and r ij are the target and response of the jth submodule system at the i-th level, log 10 (|T ij -r ij |) is the order of magnitude of inconsistent information; ε is a very small value, ε is 1×10 -10 ; a is the proportionality coefficient, which is used to adjust the magnitude of the inconsistency index.

7. The multi-level structural dynamics ATC optimization method based on target magnitude synchronization according to claim 6 is characterized in that: The stopping criteria described in step 7 are as follows: The stopping criterion is that the error of the objective function for two consecutive inner loop iterations is less than the stopping tolerance ε in , as shown below: Among them, k represents the number of inner loop iterations, f ij is the optimization objective function; the inner loop stop tolerance ε in >0 and less than the outer loop termination tolerance.

8. The multi-level structural dynamics ATC optimization method based on target magnitude synchronization according to claim 7 is characterized in that: After the inner loop described in step 8 is completed, the optimization results are processed and the extended consistency constraints are calculated as follows: Step 8.1, pass the design variables obtained in the previous round of optimization as new starting points to the inner loop, and update the optimization starting point; Step 8.2: Calculate the inconsistency information c after each system is optimized ij , the formula is: where c ij It is the inconsistent information after the target value is passed downward or the response value is passed upward; Step 8.3: The inconsistent information c ij Integrate into the extended consistency constraint q, the formula is:

9. The multi-level structural dynamics ATC optimization method based on target magnitude synchronization according to claim 8 is characterized in that: In step 9, it is determined whether the outer loop of the round has reached the stopping criterion. If the stopping criterion is reached, the inconsistent information between the system levels has reached convergence and the optimization is completed; if the stopping criterion is not reached, the outer loop parameters are updated according to the augmented Lagrangian penalty function method, and the outer loop is returned to step 3 to continue, as follows: Step 9.1: When the bi-norm of all inconsistent information change values ​​after two consecutive ATC iterations is less than the convergence accuracy threshold ε out1 , and the two norms of all inconsistent information are less than the convergence accuracy threshold ε out2 When , the outer loop reaches the stopping criterion, the formula is: ||q n -q n-1 || ∞ <ε out1 (7) ||q n || ∞ <e out2 (8) Among them, n is the number of iterations, and the convergence accuracy threshold ε of the inconsistent information change value is out1 The value of is ε out1 =1×10 -4 , the convergence accuracy threshold ε of inconsistent information out2 The value of is ε out2 =1×10 -3 ; Step 9.2: If the outer loop does not reach the stopping criterion, update the outer loop parameters according to the augmented Lagrange penalty function method and return to step 3 to continue the outer loop, as follows: The Lagrange multiplier v of the n+1th round n+1 The vector update formula is: In the formula, v n is the linear Granger multiplier vector, w is the weight vector, q n is the extended consistency constraint at the end of the nth inner loop iteration, symbol stands for Hadamard multiplication, which is the term-by-term multiplication of two vectors; The weight vector w update formula is: Where β and γ are weight vector update parameters, β>1,0<γ<1; Step 9.3: If the number of iterations reaches the maximum number of iterations, that is, C Iter =M Iter If the above requirements are still not met, it means that the system cannot meet the accuracy requirements and the optimization fails and stops. Iter is the current iteration number, M Iter is the maximum number of iterations.

10. A multi-level structural dynamics ATC optimization device based on target level synchronization, characterized in that: The device is used to implement the multi-level structural dynamics ATC optimization method based on target magnitude synchronization as described in any one of claims 1 to 9, and the device includes an initialization / update module, an SML-ATC module, a design variable boundary setting / update module, an adaptive agent model construction module, a convergence judgment module and an output processing module; The initialization / update module is configured to be used for user initialization parameters, and drives the following units to perform the following initialization and subsequent parameter update steps: divide the subsystem unit to divide the subsystem optimization problem; the outer loop initialization / update unit sets the Lagrange multiplier initial value v=0, the penalty function weight w initial value and the penalty weight growth rate β initial value, and updates the parameters Lagrange multiplier and the penalty function weight according to the augmented Lagrange penalty function method AL strategy; The inner loop initialization / update unit sets the boundaries of the design variables of the ATC optimization model at each level, the starting points of the system optimizers at each level, and the convergence accuracy threshold of the optimizer; The SML-ATC module includes subsystem optimization solving units at all levels and magnitude synchronization calculation units, which are core calculation units used to solve the optimizers of each subsystem and belong to the inner loop calculation link, wherein: The subsystem-level optimization solving unit drives the following units to execute the subsystem optimization steps: the subsystem solver setting unit configures the solver parameters for subsystem optimization solving; the subsystem objective function setting unit sets the objective function of the subsystem; the subsystem constraint condition setting unit sets the constraint conditions of the subsystem; the subsystem optimization convergence judgment unit determines whether the system meets the convergence accuracy requirements; the subsystem communication unit realizes the communication between the subsystem and other optimization modules and transmits data and information; The synchronous computing unit adopts the optimization method based on SML-ATC and measures the function through the inconsistency information. Convert the inconsistent information between the target value and the response value to overcome the inconsistent information caused by the different dimensions of the physical quantity. ij -r ij |The order of magnitude is too small or too large, ultimately avoiding problems that affect the convergence of the system; The design variable boundary setting / updating module drives the following units to execute the design variable boundary setting and updating of the proxy model module and the optimization solution module: the boundary setting unit sets the upper and lower boundaries of the design variable; the scaling coefficient calculation unit calculates the shrinkage ratio α so that the shrinkage degree of the design variable interval is positively correlated with the number of iterations, and adjusts the parameters or terminates the optimization process as needed; the boundary width calculation unit calculates the update width width; the boundary update unit updates the upper and lower boundary values; The adaptive proxy model construction module drives the following units to generate an adaptive proxy model for the design variable interval: a sampling point setting unit, which sets N sampling points in the design variable interval; a proxy model parameter setting unit, which sets the parameters of the proxy model modeling method used; and a proxy model training unit, which trains the adaptive proxy model according to the proxy model modeling method used to determine the determination coefficient R. 2 Does it satisfy R 2 >0.

9. If it does not meet the requirement, the parameters in the proxy model need to be adjusted and rebuilt; The convergence judgment module drives the following units to judge whether the optimization process has reached the outer loop convergence standard: the judgment unit judges the current inner loop optimization to determine whether it has reached the preset outer loop convergence standard; the feedback unit feeds back the judgment result to the initialization / update module to adjust parameters or terminate the optimization process as needed; The output processing module drives the following units to perform processing and output optimization results: a result processing unit processes the results of the optimization solution; and a result output unit outputs the final optimization result.

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