1. A multidisciplinary design optimization method for improving combination of target cascade and a Kriging model is characterized in that a method based on multiplier alternating direction updating is used for iteratively updating punishment parameters and weight coefficients in the optimization process, so that the optimization efficiency is improved, and the situation that the relatively optimal solution can be found only when the weight coefficients are too large is avoided. The specific optimization steps of updating by adopting a multiplier alternating direction method are as follows:

(1) defining evaluation values x for decomposition problems and initialization solutions⁰，r⁰，t⁰Setting the initial value of k to 0, defining the initial penalty parameter to v₁，w₁；

(2) Optimizing the decomposition problem by the inner loop, setting k as k +1 and punishing k with a punishment parameter v_k，w_kIs solved to obtain a new solution evaluation value x^k，r^k，t^k；

(3) Judging whether the optimized solution is converged, and if so, stopping optimization; if not, then the next step is carried out;

(4) the penalty parameter is updated by the outer loop, and the penalty parameter is updated to be v by using a penalty parameter updating formula_k+1，w_k+1Returning to the step (2), the penalty parameter is specifically updated according to the formula as follows:

w_k+1＝βw_k。

Background

With the modern engineering task design becoming more and more complex, the actual engineering system tasks and the subtasks of each system become more and more, and often, one engineering task involves the intersection of multiple disciplines, so that the mutual coupling relationship in the whole engineering design becomes more and more complex. In order to solve the difficulty, a Multidisciplinary Design Optimization (MDO) method is provided, a reasonable and efficient system operation framework is formulated by combining the mutual coupling relation among all the disciplines, and all the subsystems are coordinated and controlled, so that the whole engineering system is optimized, and finally the overall optimal solution of the system is obtained. Multidisciplinary design optimization has been successfully applied to the design of complex engineering systems such as aircraft, automobiles and mechanical equipment.

In the field of multidisciplinary design optimization, a design optimization method is divided into a single-stage design optimization method and a multi-stage design optimization method according to whether a design optimization process is hierarchical design. Compared with a single-stage MDO method, the multi-stage MDO method can better match the organizational structure of a complex engineering system, and is favorable for realizing concurrent design and distributed computation. The current multidisciplinary design optimization method comprises four multilevel methods which are respectively as follows: concurrent subspace optimization (CSSO), CO-optimization (CO), two-layer integrated system integration (BLISS), and Analytical Target Cascading (ATC). In contrast, the ATC method can divide a multitask complex system into multi-layer subsystems according to the complexity of the engineering system, and verify the convergence of the multi-layer subsystems. Provides a novel and effective method for solving large-scale complex engineering.

The augmented Lagrangian function is the most widely used coordination function at present, and represents the deviation between a problem target and a response, and the weighting coefficient is represented by an augmented Lagrangian multiplier. The specific formula is as follows:

the traditional inner-loop coordination strategy is to solve the problem in an inner-loop circularly, and a large weight is usually required to be set to obtain an accurate solution. The multiplier alternating direction method is a method for reducing the coordination calculation amount of subproblems, and ensures that each subproblem is solved once when the subproblems are solved optimally, whether convergence occurs or not is judged when all the subproblems are solved once, and the penalty parameters are updated once after the convergence does not occur. And finally solving the optimal solution of the engineering problem through an alternate optimization mode.

Disclosure of Invention

Aiming at the problem of coordination complexity of solving among decomposition problems in the existing analysis target cascade multidisciplinary design optimization method, the invention sets punishment weight values among the decomposition problems by introducing an augmented Lagrange function into an inner ring, thereby being beneficial to accurately solving the subproblems through smaller weight values. And then, each decomposition problem is optimized once in a cyclic optimization process by utilizing a multiplier alternating direction method, so that the coordination complexity in the optimization process among the sub-problems is reduced, and the solution calculation amount of the engineering problem is reduced.

The idea of the invention is as follows: according to the characteristics of hierarchical optimization of an Analysis Target Cascade (ATC) method, an augmented Lagrange coordination function is introduced to solve the problem of overhigh coordination complexity among subproblems, and a group of sample points are selected by a Latin Hypercube Sampling (LHS) method before the subproblems are optimized. And then analyzing each subsystem to obtain the response of all sampling points of the subsystem, and establishing a Kriging approximate model based on the sample points and the response of each subproblem. And evaluating the kriging model through error analysis, if the accuracy condition is not met, increasing the number of sample points, re-sampling the LHS, and establishing a new kriging model. And simultaneously optimizing each subsystem problem to obtain a corresponding response value. And finally, returning the optimized result of the subsystem to the system level for system level optimization. And after the optimization is finished, carrying out convergence judgment once, if the convergence is not finished, updating the punishment parameters, returning to the optimization stage of the subsystem, and repeating the operation. Until the final result converges.

The method comprises the following specific steps:

the first step is as follows: the complex engineering problem is decomposed into system-level and subsystem problems, and design variables and constraint conditions of the system and the subsystem are determined.

The second step is that: a set of sample points is selected for the design variables using the latin hypercube method (LHS) and each sample point is analyzed for a corresponding response value.

The third step: and establishing a Kriging model by using the sample points and the response obtained by LHS sampling. And evaluating the kriging model by using error analysis, returning to the previous step if the error precision is not met, adding a new sample point, and reestablishing the kriging model.

The fourth step: and on the basis of the created Kriging model, transmitting the initial variable values to the subsystem for subsystem optimization.

The fifth step: and transmitting the response value of the subsystem optimization back to the system level for system level optimization.

And a sixth step: and judging whether the optimization result is converged, if not, updating the punishment parameters v and w by using a punishment parameter updating formula, and returning to the fourth step to continuously optimize until the optimization result is converged.

The invention provides an improved analysis target cascade and kriging model combined multidisciplinary design optimization method, wherein an augmented Lagrange's day function and multiplier alternation method are introduced to solve the problems that a conventional method can obtain an accurate solution only under the condition of a large penalty weight and the problem of repeated circulation optimization of the neutron problem in internal circulation is solved. In complex engineering design optimization, a large number of high-precision simulation models are usually involved, and the simulation models greatly increase the calculation amount of system optimization. The MDO problem is processed by utilizing the characteristics of good comprehensive performance, high approximation precision, good robustness and the like of the Kriging model, so that the efficiency of the optimization process of the whole engineering complex problem can be improved, and the calculated amount is reduced.

Drawings

FIG. 1 is a flow chart of the steps involved in an embodiment of the present invention.

Fig. 2 is a technical diagram of a multiplier alternative direction method adopted in the embodiment of the invention.

FIG. 3 is a diagram of an exemplary optimization structure of a specific process engineering according to an embodiment of the present invention.

Detailed Description

The invention is a method of combining an improved target cascade multidisciplinary design optimization algorithm with a kriging approximation model method, and in the optimization iteration process, a penalty function is utilized to minimize inconsistency between a target variable and a response variable. The optimization model adopts an inner and outer loop nested model. In the inner ring, a fixed penalty weight is set by using an augmented Lagrange function to optimally solve the subproblem; in the outer ring, the weight value is updated by adopting a multiplier alternating direction method through the information of the inner ring. Then, the idea of the approximation model is introduced into the algorithm optimization. Based on the characteristics of higher approximation precision and robustness of the Kriging model, the error analysis is carried out on the system, and the approximation model is adopted for evaluation after each analysis and optimization of the subproblems, so that the solving precision and efficiency of the algorithm are improved.

The invention will be further elucidated by the following analysis with reference to figures 1 and 3 and the specific examples.

0≤x₁，x₂，x₃，x₄，x₅，x₆≤10

(12)

0≤x₇，x₈，x₉，x₁₀，x₁₁≤10

(13)

The first step is as follows: the method comprises the steps of firstly analyzing the problem of the given engineering example, decomposing the original problem into three parts, and determining the design variables and the constraints of each part. As follows:

(1) system level optimization model

g1，g2 (2)

h1，h2 (3)

(2) Subsystem 1 optimization model

g3，g4 (2)

h₃ (3)

X1＝{x₃，x₈，x₉，x₁₀，x₁₁} (4)

G1＝{g3，g4} (5)

(3) Subsystem 2 optimization model

g5，g6 (2)

h4 (3)

X2＝{x₆，x₁₁，x₁₂，x₁₃，x₁₄} (4)

G2＝{g5，g6} (5)

The second step is that:

selecting a group of sample points for each design variable by adopting a Latin Hypercube Sampling (LHS) method according to the value range of each design variable;

the third step:

the sample points obtained by the second step of sampling are brought into the subsystem 1 and the subsystem 2 for optimization analysis, and the response of all sampling points of each subsystem is obtained;

the fourth step:

establishing a corresponding Kriging model through the sample points of the subsystem obtained by sampling in the second step and the response of the subsystem obtained by analyzing in the third step;

the fifth step:

evaluating the Kriging model through error analysis; it is judged whether or not the accuracy is satisfied (here, an error evaluation function R is set²More than 0.9), if the precision condition is not met, returning to the second step to add a new sample point, and reestablishing a new Kriging model;

and a sixth step:

initializing all design variables, transmitting corresponding initial values to the subsystems as targets, and respectively optimizing each subsystem through a Kriging model established before;

the seventh step:

optimizing each subsystem, taking the optimized result as the response of the corresponding subproblem and transmitting the response back to the system for system-level optimization processing;

eighth step:

judging whether convergence occurs once after the system-level optimization processing is finished; and if not, jumping out of the loop and updating the weight coefficient. The updated weight coefficient is brought into the system again, namely the sixth step is returned;

the ninth step:

and converging to the optimal solution, and outputting an optimization result.