WO2021217975A1 - Efficient automobile side collision safety and reliability design optimization method - Google Patents

Abstract

An efficient automobile side collision safety and reliability design optimization method, relating to the technical field of automobile reliability design optimization. The reliability analysis and deterministic optimization in the method are performed in sequence. The method comprises: calculating first four-order moments of a response by using a univariate dimension reduction method, and calculating a PDF of the response according to the maximum entropy principle; then performing deterministic optimization, calculating a translation distance by using a function moving method based on a response PDF, constructing an equivalent deterministic optimization model and calculating, and obtaining a new optimal solution; taking the new optimal solution as input, repeatedly performing the reliability analysis and deterministic optimization processes till convergence conditions are satisfied, and finally obtaining the optimal solution of the original optimization model. According to the method, the reliability analysis and the optimization design are decoupled by utilizing the proposed function moving method based on the response PDF, so that the efficiency is improved; reliability analysis uses information of the first four-order moments of the response, higher precision can be obtained, and the method has the dual characteristics of high precision and high efficiency.

Description

An Efficient Method for Optimizing the Safety and Reliability Design of Vehicle Side Impact Technical field

The invention relates to the technical field of automobile reliability design optimization, in particular to an efficient automobile side collision safety and reliability design optimization method.

Background technique

With the advent of high-performance computers, the automotive industry has used multidisciplinary optimization and crashworthiness simulation to solve the safety problems of vehicle side collisions, thereby reducing the cost and time of new vehicle development. However, simulation-based optimization is usually a deterministic optimization design, which usually adopts the limits of the design constraint boundary. In actual engineering, there are a large number of uncertain factors such as material properties, geometric characteristics, and collision environment in the entire vehicle structure, which directly affect the reliability of the vehicle in a side collision. Reliability-based design optimization (RBDO) can not only obtain the best design plan, but also fully consider the influence of these uncertain factors, which can effectively balance the best design goals and reliability. RBDO has become one of the most powerful methods to solve complex problems in engineering design, and many advanced theories and methods have been developed. Traditional RBDO solutions are usually divided into three categories. (1) Double loop method. Reliability analysis of this kind of method is nested inside the design optimization. Reliability analysis needs to be performed every time a new point in the design space is iterated through the optimization algorithm. The double-cycle method is very inefficient and cannot meet the requirements of engineering applications. (2) Single loop method. This kind of method adopts approximate technique or Karush-Kuhn-Tucker (KKT) optimality condition instead of reliability analysis, so as to transform the nested double loop into a single loop problem. It has a very high computational efficiency, but may not converge when the function function is highly non-linear. (3) Sequence optimization method. This type of method decouples reliability analysis and design optimization, and the two are executed sequentially until convergence. The sequence optimization method is one of the most effective RBDO methods, which has the characteristics of high precision, high precision and strong stability.

The above-mentioned traditional RBDO solution method basically uses the first-order reliability analysis method, which requires iterative calculation of MPP points, which may result in reduced efficiency or insufficient accuracy when dealing with high-dimensional and highly nonlinear problems. Considering that the car side collision problem has the characteristics of high complexity, extreme working conditions (environment), and high degree of nonlinearity, traditional methods cannot effectively solve this problem. The above methods cannot integrate many advanced reliability analysis methods, such as dimensionality reduction integration method (DRM), sparse grid integration (SGI) and so on. Compared with the reliability analysis methods based on MPP, these methods do not need to calculate the derivative of the functional function, do not perform an iterative solution process, and in some cases, the calculation efficiency is higher. If these advanced methods are integrated into the sequence optimization method, it is hoped that an efficient and high-precision RBDO solution method will be developed, which will be of great significance to the research of the reliability optimization design problem of automobile side impact.

For example, Chinese Patent Announcement No. CN 104036100 B, the authorization announcement date 20170510, discloses an optimization method for automobile reliability design based on Bayesian deviation correction under uncertainty, which belongs to the technical field of automobile reliability design optimization. The method includes the following steps: Step 1: Define the reliability-based design optimization (RBDO) problem; Step 2: Build a design of experiment (DOE) matrix for the Bayesian inference deviation model and the initial response surface model; Step 3: Use the second step The deviation model corrects the initial response surface model and quantifies the uncertainty from repeated experiments and CAE simulation; Step 4: Run the RBDO optimization program to find the best and most reliable solution; Step 5: Perform Monte Carlo simulation (MCS) Verify the reliability of the obtained solution. This method has many operations, takes a long time, and is low in efficiency.

Summary of the invention

The technical problem to be solved by the present invention is that when the optimization target is completed, for example, the optimization target is set to minimize the weight of the entire vehicle under the premise of ensuring the performance of side collisions, further reduce the number of calculations, and maintain higher accuracy. Save optimization design time and improve optimization design efficiency.

In order to solve the above problems, a high-performance automotive crash safety reliability design optimization method is adopted. The reliability analysis and deterministic optimization of the method are executed in order. First, the first four moments of the response are obtained by the univariate dimensionality reduction method. According to the principle of maximum entropy, the PDF of the response is obtained. Then the deterministic optimization is performed, and the translation distance is calculated by the functional function movement method based on the response PDF, and an equivalent deterministic optimization model is constructed and solved to obtain a new optimal solution. Taking the new optimal solution as input, repeat the reliability analysis and deterministic optimization process until the convergence condition is met, and finally the optimal solution of the original optimization model is obtained.

Specific steps are as follows:

The first step: According to the requirements of reliability design optimization for car side collision safety, define the mathematical optimization model, and define the mathematical optimization model including determining the deterministic design variables, random design variables and random parameters of the system, according to the probability of random variables and parameters The statistical characteristics obtain the probability distribution; at the same time, the objective function should be determined, the system function function should be established, and the target reliability should be set;

Step 2: Set the number of iterations k = 1, the moving distance of the function function PDF

a=1,2,...,n _g , the initial point

Set the allowable error ε (a small positive number), and set a=1 to record the function function number;

The third step: Introduce the univariate dimensionality reduction method to decompose the system function into a single random parameter subsystem, which is used to convert the high-dimensional integral calculating the response origin moment into the one-dimensional integral Q _ij ;

Step 4: Calculate the one-dimensional integral Q _ij using the Gauss series numerical integration method, and use the binomial theorem combination Q _{ij to} calculate the origin moment ma _,l .

Step 5: Assume that the probability density function of the response y to be estimated is

Use the maximum entropy method to find

To give ρ _a (y) analytical formula, y is the response obtained after PDFρ (y), is calculated by the constraint of [rho] (y) by integrating reliability R _a;

Step Six: Let a = a + 1, the third to five steps is repeated until all the functions determined probability function density function ρ _a response and reliability _{R a (a = 1,2, ...} , n g);

Step 7: Calculate the movement distance using the function function movement method based on the response PDF

Step 8: Build a deterministic optimization model and solve it to get the optimal solution for the kth iteration

And minimum objective function value

Step 9: Judgment

Whether it is established, if it is established, perform the tenth step; if it is not established, set k=k+1, a=1, and repeat the third to ninth steps.

Step 10: Output the optimal solution

And minimum objective function value

Finish.

As a further improvement of the present invention, in the first step, the mathematical model of reliability design optimization is:

Among them, C(d,μ _X ) is the objective function, P{g _a (d,X,P)≥0} is the reliability of the a-th functional function, and g _a (d,X,P) is the a-th Function function, d is a deterministic design variable, X is a random design variable, P is a random parameter, μ _X and μ _P are the mean values of X and P respectively,

Is the target reliability, d ^L ,d ^U ,

Is the upper and lower bounds of the respective mean values of the deterministic design variable d and the random design variable X. Z=(X,P) represents all random variables/parameters, then g _a (d, X, P) is abbreviated as g _a (d, Z); Since d is unchanged during uncertainty analysis, g _a (d, Z) _{can be abbreviated as g a} (Z).

As a further improvement of the present invention, in the first step, when the optimization goal is to minimize the weight of the vehicle under the premise of ensuring the performance of side collision, adopt the side impact test standard of the European Enhanced Vehicle Safety Committee, then the reliability design is optimized The mathematical model is:

stP (abdominal load: F _Abdom ≤1.0kN)≥R ^t

P (rib deformation (upper/middle/lower): Def _{rib_l/rib_m/rib_u} ≤32mm)≥R ^t

P (stickiness standard ( _{upper/middle/lower} ): VC upper/middle/lower ≤0.32m/s)≥R ^t

P(Comprehensive power of pubic bone: Force _pubic ≤4.0kN)≥R ^t

P(B-pillar midpoint velocity: Vel _B-pillar ≤9.9mm/ms)≥R ^t

P(B-pillar speed at the front door: Vel _door ≤15.7mm/ms)≥R ^t

μ _X ∈R ⁹

As a further improvement of the present invention, the best Latin hypercube sampling and secondary reverse stepwise regression are used to establish _weight , F Abdom, Def _{rib_l} , Def _{rib_m} , Def _{rib_u} , VC _upper , VC _middle , VC _lower , Force _pubic , Vel The global response surface model of _B-pillar and Vel _door.

In addition, in the above technical solution, the random design variable X includes X ₁ : thickness of the inner wall of the B-pillar, X ₂ : thickness of the reinforcement of the B-pillar, X ₃ : thickness of the inner wall of the side of the floor, X ₄ : thickness of the beam, X ₅ : The thickness of the door beam, X ₆ : the thickness of the door belt line reinforcement, X ₇ : the thickness of the roof rail, X ₈ : the material of the inner wall of the B-pillar and X ₉ : the material of the inner wall of the floor side; the random parameter P includes X ₁₀ : Moving barrier height and X ₁₁ : impact position.

A further improvement of the present invention, particularly the third step the steps of: calculating a function of a function g _a (Z) before the order origin moment l m _{a, l, l} = 1,2,3,4 expression for:

In the formula, E{·} represents the mathematical expectation operator;

Perform additive decomposition on the functional function y=g _a (Z):

Where μ _i represents the mean of a random variable Z _i, N is the number of random variables;

After using the univariate dimensionality reduction method, the first-order origin moment formula of the response y:

Expand equation (4) using the binomial theorem to get:

Make the following definitions:

Equation (4) can be simplified to:

Above style

It can be found by the following recursive formula:

Through formulas (3)～(8), high-dimensional integral can be transformed into solving mathematical expectation

This is a one-dimensional integral; for the convenience of description, use Q _{ij to} denote this integral, then:

Where

Z _i is the probability density function.

As a further improvement of the present invention, the specific steps of the fourth step are:

The numerical integration formula of Gauss series is:

In the formula, ω _i,m represents the weight, vi _,h represents the integration node, and m represents the number of integration nodes.

_{Calculate all Q ij} by Gaussian series numerical integration, and combine equations (7)～(8) to find the origin moment ma _,l . Each one-dimensional integral uses m integration nodes. For the N-dimensional function function, The number of points to be integrated is m×N+1, that is, it is necessary to calculate the function function m×N+1 times.

As a further improvement of the present invention, the specific steps of the fifth step are:

Suppose the probability density function of the response y to be estimated is

Then the formula for calculating Shannong's entropy is:

Use the maximum entropy method (MEM) to find

It can be described as the following optimization problem:

Using Lagrangian multiplier method to solve, construct the Lagrangian function as follows:

When the partial derivative of the Lagrangian function with respect to the probability density function is equal to 0, formula (9) takes the extreme value, and _{the analytical formula of ρ a} (y) is obtained as follows:

After calculating the Lagrangian multiplier λ _l (l=0,1,2,3,4) and obtaining the PDFρ(y) of the response y, the reliability R of the constraint can be calculated by integrating ρ(y) _a :

As a further improvement of the present invention, the specific steps of the seventh step are:

Rewrite the reliability optimization model as:

Where

The PDF representing the response of the a-th functional function. For each set of trial points (d, μ _X ) in the optimization process, the response PDF can be obtained by the third to fifth steps, so

Is a function of design variables, which can be expressed as

The basic idea of the function function movement method based on response PDF is: Generally, the reliability requirement in reliability design (≥0.90) is usually much higher than the reliability achieved by deterministic design (≈0.5), that is, the probability constraint ratio is deterministic The constraints are stricter. Geometrically, when the target reliability R ^t >0.5, the feasible region of probabilistic design optimization is narrower than that of deterministic optimization. The key to establishing an equivalent deterministic optimization model is the conversion from probability constraints to deterministic constraints. It is necessary to calculate the translation distance from the boundary of the deterministic constraint to the boundary of the probability constraint. Through translation, the actual constraint boundary is moved from the deterministic constraint boundary to the probability constraint boundary, thereby improving the reliability of the constraint.

Hypothesis

with

Are the PDFs of the responses obtained in the kth and (k+1)th iterations, respectively,

Represents the best point of the kth time, (d, μ _X ) represents the trial point of the (k+1)th iteration;

The relationship between the PDF of the kth and k+1th iteration response is:

Where

Represents design variables from

When it becomes (d, μ _X ), _{the moving distance of ρ a} (y|d, μ _X ), this distance is equal to the difference of the function function value:

In order to ensure that the probability constraints are met, the constraint reliability of the current iteration step needs to be greater than or equal to the target reliability:

Substituting formula (17) into formula (19), we get:

Because at the kth iteration

The expression has been calculated, so the size of the left term of the inequality sign in equation (20) is only the same as

Is related to the value of and can be defined as

The function:

Equation (20) can be rewritten as:

By solving the above equation, the translation distance can be obtained

In the formula, arch represents the inverse function of the function h, and substituting formula (18) into formula (23) to obtain:

Considering that the inequality signs of the deterministic optimization constraint and the probability constraint are the same, equation (24) can take the equal sign, and finally the formula for the translation distance is:

As a further improvement of the present invention, the specific steps of the eighth step are:

The formula of the k-th iterative deterministic optimization model is:

Solve the deterministic optimization model and get the optimal solution for the kth iteration

And minimum objective function value

The advantages and beneficial effects of the present invention lie in the following points:

1. The method of the present invention decomposes the reliability design optimization into a sequential solution process executed by reliability evaluation and deterministic optimization in turn, avoiding a two-layer nested solution process; passing conflicting constraints through a function function based on the response PDF The moving method moves to the reliable area to ensure that the optimal solution that satisfies the probability constraint is found. This method has the dual advantages of high precision and high efficiency.

2. The method of the present invention uses the first four-order statistical moments of the functional function response in the reliability analysis. Compared with the traditional first-order reliability method that only uses the first-order and second-order moments, it uses more information; although Both of them require less calculation, but the method of the present invention can obtain more accurate calculation results relatively.

3. The method of the present invention can integrate many advanced reliability analysis methods, such as two-variable (or multi-variable) dimensionality reduction integration method, polynomial chaotic expansion method, sparse grid numerical integration method, etc., not only can obtain higher accuracy, but also It can expand the scope of application and solve engineering problems with higher complexity and stronger nonlinearity.

Description of the drawings

Figure 1 is a flow chart of the method of the present invention.

Figure 2 is a finite element (FEM) model of a car's side impact.

Fig. 3 is a schematic diagram of a function function moving method based on response PDF.

Figure 4 is an approximate schematic diagram of the PDF deformation of the response of two consecutive iterations.

Figure 5 shows the change of the objective function with respect to the number of calculations of the functional function.

Detailed ways

The present invention will be further described in detail below in conjunction with the accompanying drawings and specific examples, using a method of comparison with Monte Carlo simulation (MCS). Obviously, the described embodiments are only a part of the embodiments of the present invention, rather than all of them. Based on the embodiments of the present invention, all other embodiments obtained by those of ordinary skill in the art without creative work shall fall within the protection scope of the present invention.

The first step: Define the mathematical model according to the requirements of the reliability design optimization of the lightweight design of the automobile. This step needs to determine the deterministic design variables, random design variables and random parameters of the system, and obtain the probability distribution according to the probability and statistics characteristics of the random variables and parameters. At the same time, the objective function should be determined, the system function function should be established, and the target reliability should be set.

To deal with side impact protection, vehicle design must meet the requirements of the government and the automotive industry on side impact protection. At present, there are three main side collision protection standards that are referenced or used in China: (1) Chinese national standard "Occupant Protection in Car Side Column Collision" (GB/T37337-2019); (2) U.S. Highway Traffic Safety Administration Safety standard side impact test standard (FMVSS); (3) European Enhanced Vehicle Safety Committee (EEVC) side impact test standard. In this example, the side impact test standard of the European Enhanced Vehicle Safety Committee (EEVC) is adopted. The main indicators of the dummy's response to the side impact research. The EEVC standard stipulates the dummy's response mainly including abdominal peak force (Abdomen Load), rib deformation (Rib Deflection), viscosity index (VC: viscous criteria), pubic symphysis (Pubic symphysis) force) and head injury index (HIC: Head injury criterion) five parts. In addition, since the midpoint speed of the B-pillar and the speed of the B-pillar at the front door are also two indicators that have received great attention, these two indicators will also be used in this example. Table 1 is the detailed information of this standard.

Table 1 European Enhanced Vehicle Safety Committee (EEVC) side impact test standards

The optimization goal of this example is to minimize the weight of the whole vehicle under the premise of ensuring the performance of side collision, and the target reliability is R ^t =0.99. According to the safety standards shown in Table 1 and the standards for the two indicators of the midpoint speed of the B-pillar and the speed of the B-pillar at the front door, the RBDO problem formula of this example is:

The system model includes the finite element model of the whole vehicle, the virtual finite element model of side collision and the model of side moving barrier. Figure 2 is a finite element model of the entire vehicle, which contains 85941 shell elements and 96122 nodes. In the finite element simulation of the side collision accident, the initial speed of the moving barrier is set to 49.89km/h. On the SGI Origin 2000 computer, it takes about 20 hours to perform a finite element simulation. In view of the high computational cost of the finite element method, in order to facilitate the calculation, this example uses optimal Latin Hypercube Sampling and quadratic backward-stepwise regression to establish a global response surface model. The response surface formula established in this example is:

Weight=1.98+4.90x ₁ +6.67x ₂ +6.98x ₃ +4.01x ₄ +1.78x ₅ +2.73x ₇

F _Abdom = 1.16-0.3717x ₂ x ₄ -0.00931x ₂ x ₁₀ -0.484x ₃ x ₉ +0.01343x ₆ x ₁₀

Def _{rib_l} = 46.36-9.9x ₂ -12.9x ₁ x ₈ +0.1107x ₃ x ₁₀

Def _{rib_m} = 33.86+2.95x ₃ +0.1792x ₁₀ +5.057x ₁ x ₂ -11.0x ₂ x ₈ -0.0215x ₅ x ₁₀ -9.98x ₇ x ₈ +22.0x ₈ x ₉

Def _{rib_u} = 28.98+3.818x ₃ -4.2x ₁ x ₂ +0.0207x ₅ x ₁₀ +6.63x ₆ x ₉ -7.7x ₇ x ₈ +0.32x ₉ x ₁₀

VC _upper ＝0.261-0.0159x ₁ x ₂ -0.188x ₁ x ₈ -0.019x ₂ x ₇ +0.0144x ₃ x ₅ +0.0008757x ₅ x ₁₀ +0.08045x ₆ x ₉ +0.00139x ₈ x ₁₁ +0.00001575x ₁₀ x ₁₁

Vel _B-pillar = 10.85-0.674x ₁ x ₂ -1.95x ₂ x ₈ +0.02054x ₃ x ₁ 0-0.0198x ₄ x ₁₀ +0.028x ₆ x ₁₀

This example has 10 probability constraints, including 11 random design variables and parameters such as geometric dimensions, material properties of key parts, height of moving barriers and impact position. There are 0 deterministic design variables, 9 random design variables (X ₁ ～X ₉ ) and 2 random parameters (X ₁₀ , X ₁₁ ). The names of random design variables and parameters, distribution types and parameters, and the range of changes in the mean are shown in Table 2.

Table 2 Characteristics of random design variables and parameters

Step 2: Set the number of iterations k=1, the initial point of the design variables (μ ₁ ,μ ₂ ,…,μ ₉ )=(1,1,1,1,1,1,1,0.3,0.3), random The parameter mean value (μ ₁₀ ,μ ₁₁ )=(10,10) Set the allowable error ε=0.01, the moving distance of the function function PDF

Let a=1 to record the function number.

The third step: Introduce the univariate dimensionality reduction method to decompose the system function into a single random parameter subsystem, so that the high-dimensional integral that calculates the moment of response to the origin is converted into a one-dimensional integral. Calculate the first l-order origin moment ma _,l (l=1, 2, 3, 4) of the a-th functional function g _{a (Z) and the expression is:}

In the formula, E{·} represents the mathematical expectation operator.

Perform additive decomposition on the functional function y=g _{a (Z)}

In the formula, μ _j represents the mean value of the random variable Z _j , and N represents the number of random variables.

The first-order origin moment formula of response y after using univariate dimensionality reduction method

Expand equation (4) using the binomial theorem to get:

Make the following definitions:

Equation (4) can be simplified to:

Above style

It can be found by the following recursive formula:

Through formulas (3)～(8), high-dimensional integral can be transformed into solving mathematical expectation

This is a one-dimensional integral. For the convenience of description, use Q _ij (i=1,...,N,j=1,...,l) to represent the integral, then:

Where

Z _i is the probability density function.

Step 4: Calculate the one-dimensional integral Q _ij using the Gauss series numerical integration method, and use the binomial theorem combination Q _{ij to} calculate the origin moment ma _,l . The numerical integration formula of Gauss series is:

In the formula, ω _i,m represents the weight, vi _,h represents the integration node, and m represents the number of integration nodes.

_{Calculate all Q ij} by Gaussian series numerical integration, and combine equations (7) to (8) to obtain the origin moment ma _,l (l=1, 2, 3, 4). Each one-dimensional integration uses 4 integration nodes. The model has a total of 10 functional functions, and the number of integration nodes is shown in Table 3:

Table 3 Calculation times of each function function

Step 5: Assume that the probability density function of the response y to be estimated is

Then the formula for calculating Shannong's entropy is:

Use the maximum entropy method (MEM) to find

It can be described as the following optimization problem:

Using Lagrangian multiplier method to solve, construct the Lagrangian function as follows:

When the partial derivative of the Lagrangian function with respect to the probability density function is equal to 0, formula (9) takes the extreme value, and _{the analytical formula of ρ a} (y) is obtained as follows:

After calculating the Lagrangian multiplier λ _l (l=0,1,2,3,4) and obtaining the PDFρ(y) of the response y, the reliability of the constraint can be calculated by integrating ρ(y):

Step Six: Let a = a + 1, the third to five steps is repeated until all the functions determined response function ρ _a probability density function and reliability _{R a (a = 1,2, ...} , 10).

Step 7: Calculate the movement distance using the function function movement method based on the response PDF

(a=1,2,...,10).

Rewrite the reliability optimization model as:

Where

Represents the PDF of the response of the a-th functional function. For each set of trial points (d, μ _X ) in the optimization process, the third to fifth steps can be used to obtain the response PDF, so

Is a function of design variables, which can be expressed as

The basic idea of the function function movement method based on response PDF is: Generally, the reliability requirement in reliability design (≥0.90) is usually much higher than the reliability achieved by deterministic design (≈0.5), that is, the probability constraint ratio is deterministic The constraints are stricter. Geometrically, when the target reliability R ^t >0.5, the feasible region of probabilistic design optimization is narrower than that of deterministic optimization. The key to establishing an equivalent deterministic optimization model is the conversion from probability constraints to deterministic constraints. It is necessary to calculate the translation distance from the boundary of the deterministic constraint to the boundary of the probability constraint. Through translation, the deterministic constraint boundary that does not satisfy the reliability condition moves to the probability constraint boundary, thereby improving the reliability of the constraint.

Take the probability constraint P{g(X ₁ ,X ₂ )≥0}=R ^t as an example, it has two random design variables. As shown in Figure 3, there are two coordinate systems in the figure: one is the design space, which is determined by the design variables

with

Composition; the other is a random space, which is composed of random variables X ₁ and X ₂ . The curved surface represented by the innermost dashed line is the constraint boundary g(X ₁ , X ₂ )=0 in the deterministic design. After translation, the constraint boundary of the actual design scheme represented by the thin solid line in the middle is obtained. The surface is closer to the outermost probability constraint boundary, and the corresponding reliability is also higher. After several translations, the boundary of the actual design scheme coincides with the boundary of the probability design, and a design scheme that satisfies the constraints is obtained.

Hypothesis

with

These are the PDFs of the responses obtained at the kth and (k+1)th iterations, respectively.

Represents the best point of the kth time, and (d, μ _X ) represents the trial point of the (k+1)th iteration. Generally speaking, as shown in Figure 4,

with

At the same time, there are two kinds of deformations: telescopic and translation. For telescopic deformation, the PDF curve is shown as stretching or shrinking along the vertical axis; while the translational deformation is the PDF curve showing parallel movement along the horizontal axis.

Introduce an approximation:

with

There is only translational deformation but no telescopic deformation, as shown in FIG. 4. Since the candidate design points obtained in two consecutive iterations are usually located in a small neighborhood, especially when the optimized design is close to convergence, in this case, the shape of the response PDF is very close, and the difference between the two can be regarded as There is only translational deformation, so it is reasonable to make such an approximation. Based on this approximation, the relationship between the PDF of the k-th and k+1-th iteration response is:

Where

Represents design variables from

When it becomes (d, μ _X ), _{the moving distance of ρ a} (y|d, μ _X ), this distance is equal to the difference of the function function value:

In order to ensure that the probability constraints are met, the constraint reliability of the current iteration step needs to be greater than or equal to the target reliability:

Substituting formula (17) into formula (19), we get:

Because at the kth iteration

The expression has been calculated, so the size of the left term of the inequality sign in equation (20) is only the same as

Is related to the value of and can be defined as

The function

Equation (20) can be rewritten as:

By solving the above equation, the translation distance can be obtained

Where arch represents the inverse function of the function h. Substituting formula (18) into formula (23) to obtain:

Considering that the inequality signs of deterministic optimization constraints and probability constraints are the same, equation (24) can take the equal sign. The final formula for the translation distance is:

Step 8: Build a deterministic optimization model and solve it to get the optimal solution for the kth iteration

The formula of the k-th iterative deterministic optimization model is:

Solve the deterministic optimization model and get the optimal solution for the kth iteration

And minimum objective function value

Step 9: Judgment

Whether it is established, if it is established, execute the eleventh step; if it is not established, set k=k+1, a=1, and repeat the third to ninth steps.

Step 10: Output the optimal solution

And minimum objective function value

Finish.

Using the above steps, convergence is reached after three iterations, and the optimal solution, minimum objective function value, and function function calculation times obtained in each iteration are shown in Table 4. In order to compare the efficiency, the double loop method is used to solve this example. The reliability analysis of the double loop method is the same as the method of the present invention. Table 5 is a comparison of the results of the two methods. It can be seen from Table 4 that the proposed method only needs 2118 performance function evaluations to converge, and each cycle requires 706 evaluations on average. Compared with the double-loop method, the calculation amount of the method of the present invention is less than 1/15 of it, showing a very high efficiency. At the same time, the minimum objective function value obtained by this method is very close to the double loop method (the error is 0.9%), indicating that the accuracy of this method is similar to that of the double loop method. Table 6 shows the reliability of each function function during convergence. It can be seen that the reliability of the eighth constraint is slightly smaller than the target reliability R ^t =0.99 (the difference is only 0.04%), and the reliability of other function functions are very close or exceed The target reliability once again shows that the method of the present invention has very high accuracy. Fig. 5 describes the convergence process of the objective function value with respect to the calculation order function in the optimization process. In the figure, each iteration cycle is clearly distinguished from each other. In each cycle, a reliability evaluation is performed before deterministic optimization is performed. In summary, the method of the present invention has the dual characteristics of high precision and high efficiency, and is worthy of popularization.

Table 4 Reliability design optimization iteration process

Table 5 Comparison of the two methods

Table 6 Probability constraint reliability

Function function	g 1	g 2	g 3	g 4	g 5	g 6	g 7	g 8	g 9	g 10
Reliability	1.0	0.9901	1.0	1.0	1.0	1.0	1.0	0.9896	0.9997	0.9903

The present invention first defines the reliability design optimization mathematical optimization model for the safety of automobile side collision, obtains the probability distribution characteristics of random design variables and parameters by means of probability statistics and other means, and establishes the response surface model of the function function of the automobile side collision system ; Then, develop a functional function movement method based on the response PDF to decouple the traditional nested reliability optimization design into reliability analysis and deterministic optimization sequence execution, that is, use the univariate dimensionality reduction method to solve the PDF of the response for reliability analysis, And calculate the function function movement amount to construct equivalent deterministic optimization to obtain better design variables. The above process is repeated until the convergence condition is met to obtain the optimal solution of the problem; finally, the above is verified by a specific car side collision safety analysis example The feasibility and efficiency of the method.

The present invention combines the function function movement method based on the response PDF, the univariate dimensionality reduction method (UDRM) and the maximum entropy method (MEM), and proposes an efficient reliability design optimization method for automobile side collision safety. The difference between the method of the present invention and the traditional method is: using the proposed method of function function movement based on the response PDF, the reliability analysis and the optimization design are decoupled, and the efficiency is improved; the reliability analysis uses the first fourth moment of the response Information, higher accuracy can be obtained, and it has the dual characteristics of high accuracy and high efficiency.

The above content is a further detailed description of the present invention in combination with specific preferred embodiments, and it cannot be considered that the specific implementation of the present invention is limited to these descriptions. For those skilled in the art to which the present invention belongs, without departing from the concept of the present invention, several equivalent substitutions or obvious modifications can be made, and the same performance or use should be regarded as falling within the protection scope of the present invention. Inside

Claims (10)

1. An efficient method for designing and optimizing vehicle side collision safety and reliability, which is characterized in that it specifically includes the following steps:

   The first step: According to the requirements of reliability design optimization for car side collision safety, define the mathematical optimization model, and define the mathematical optimization model including determining the deterministic design variables, random design variables and random parameters of the system, according to the probability of random variables and parameters The statistical characteristics obtain the probability distribution; at the same time, the objective function should be determined, the system function function should be established, and the target reliability should be set;

   Step 2: Set the number of iterations k = 1, the moving distance of the function function PDF

   

   a=1,2,...,n _g , the initial point

   

   Set the allowable error ε, let a=1 to record the function number;

   The third step: Introduce the univariate dimensionality reduction method to decompose the system function into a single random parameter subsystem, which is used to convert the high-dimensional integral calculating the response origin moment into the one-dimensional integral Q _ij ;

   Step 4: Calculate the one-dimensional integral Q _ij using the Gaussian series numerical integration method, and use the binomial theorem combination Q _{ij to} calculate the origin moment ma _,l ;

   Step 5: Assume that the probability density function of the response y to be estimated is

   

   Use the maximum entropy method to find

   

   To give ρ _a (y) analytical formula, y is the response obtained after PDFρ (y), is calculated by the constraint of [rho] (y) by integrating reliability R _a;

   Step Six: Let a = a + 1, the third to five steps is repeated until all the functions determined probability function density function ρ _a response and reliability _{R a (a = 1,2, ...} , n g);

   Step 7: Calculate the movement distance using the function function movement method based on the response PDF

   

   Step 8: Build a deterministic optimization model and solve it to get the optimal solution for the kth iteration

   

   And minimum objective function value

   

   Step 9: Judgment

   

   Whether it is established, if it is established, perform the tenth step; if it is not established, set k=k+1, a=1, and repeat the third to ninth steps;

   Step 10: Output the optimal solution

   

   And minimum objective function value

   

   Finish.
2. An efficient method for designing and optimizing car side collision safety and reliability according to claim 1, characterized in that, in the first step, the mathematical model of reliability design optimization is:

   

   Among them, C(d,μ _X ) is the objective function, P{g _a (d,X,P)≥0} is the reliability of the a-th functional function, and g _a (d,X,P) is the a-th Function function, d is a deterministic design variable, X is a random design variable, P is a random parameter, μ _X and μ _P are the mean values of X and P respectively,

   

   Target reliability, d ^L ,d ^U ,

   

   Is the upper and lower bounds of the respective mean values of the deterministic design variable d and the random design variable X. Z=(X,P) represents all random variables/parameters, then g _a (d, X, P) is abbreviated as g _a (d, Z); Since d is unchanged during uncertainty analysis, g _a (d, Z) _{can be abbreviated as g a} (Z).
3. An efficient method for designing and optimizing vehicle side collision safety and reliability according to claim 2, characterized in that, in the first step, when the optimization goal is to minimize the weight of the vehicle under the premise of ensuring the performance of side collision, Using the European Enhanced Vehicle Safety Committee’s side impact test standards, the mathematical model for reliability design optimization is:

   
4. As claimed in claim 3, an efficient method for designing and optimizing the safety and reliability of automobile side collision safety and reliability is characterized in that the optimal Latin hypercube sampling and secondary reverse stepwise regression are adopted to establish the method including Weight, F _Abdom , Def _{rib_l} , Def The global response surface model of _{rib_m} , Def _{rib_u} , VC _upper , VC _middle , VC _lower , Force _pubic , Vel _B-pillar and Vel _door.
5. An efficient method for designing and optimizing the safety and reliability of automobile side collision safety and reliability according to claim 2, wherein the random design variables X include X ₁ : thickness of the inner wall of the B-pillar, X ₂ : thickness of the reinforcement of the B-pillar, and X ₃ : side of the floor The thickness of the inner wall, X ₄ : the thickness of the beam, X ₅ : the thickness of the door beam, X ₆ : the thickness of the door strip line reinforcement, X ₇ : the thickness of the roof rail, X ₈ : the inner wall material of the B-pillar, and X ₉ : the floor Side inner wall material; the random parameter P includes X ₁₀ : the height of the moving barrier and X ₁₁ : the impact position.
6. An efficient method for designing and optimizing car side collision safety and reliability according to claim 2, wherein the specific steps of the third step are:

   Calculate the first-order origin moment ma _{,l of} the a-th functional function g _a (Z), and the expression for l=1, 2, 3, 4 is:

   

   In the formula, E{·} represents the mathematical expectation operator;

   Perform additive decomposition on the functional function y=g _a (Z):

   

   Where μ _i represents the mean of a random variable Z _i, N is the number of random variables;

   After using the univariate dimensionality reduction method, the first-order origin moment formula of the response y:

   

   Expand equation (4) using the binomial theorem to get:

   

   Make the following definitions:

   

   Equation (4) can be simplified to:

   

   Above style

   

   It can be found by the following recursive formula:

   

   

   Through formulas (3)～(8), high-dimensional integral can be transformed into solving mathematical expectation

   

   This is a one-dimensional integral; use Q _{ij to} express the integral, then:

   

   Where f _Zi (z _i) is the probability density function of Z _i.
7. An efficient method for designing and optimizing automobile side collision safety and reliability according to claim 6, wherein the specific steps of the fourth step are:

   The numerical integration formula of Gauss series is:

   

   In the formula, ω _i,m represents the weight, v _i,h represents the integration node, and m represents the number of the integration node;

   _{Calculate all Q ij} by Gaussian series numerical integration, and combine equations (7)～(8) to find the origin moment ma _,l . Each one-dimensional integral uses m integration nodes. For the N-dimensional function function, The number of points to be integrated is m×N+1, that is, it is necessary to calculate the function function m×N+1 times.
8. An efficient method for designing and optimizing automobile side collision safety and reliability according to claim 7, wherein the specific steps of the fifth step are:

   Suppose the probability density function of the response y to be estimated is

   

   Then the formula for calculating Shannong's entropy is:

   

   Use the maximum entropy method to find

   

   It can be described as the following optimization problem:

   

   Using Lagrangian multiplier method to solve, construct the Lagrangian function as follows:

   

   When the partial derivative of the Lagrangian function with respect to the probability density function is equal to 0, formula (9) takes the extreme value, and _{the analytical formula of ρ a} (y) is obtained as follows:

   

   After calculating the Lagrangian multiplier λ _l (l=0,1,2,3,4) and obtaining the PDFρ(y) of the response y, the reliability R of the constraint can be calculated by integrating ρ(y) _a :

   
9. An efficient method for designing and optimizing automobile side collision safety and reliability according to claim 1, wherein the specific steps of the seventh step are:

   Rewrite the reliability optimization model as:

   

   Where

   

   The PDF representing the response of the a-th functional function. For each set of trial points (d, μ _X ) in the optimization process, the response PDF can be obtained by the third to fifth steps, so

   

   Is a function of design variables, which can be expressed as

   

   Hypothesis

   

   Are the PDFs of the responses obtained in the kth and (k+1)th iterations, respectively,

   

   Represents the best point of the kth time, (d, μ _X ) represents the trial point of the (k+1)th iteration;

   The relationship between the PDF of the kth and k+1th iteration response is:

   

   Where

   

   Represents design variables from

   

   When it becomes (d, μ _X ), _{the moving distance of ρ a} (y|d, μ _X ), this distance is equal to the difference of the function function value:

   

   In order to ensure that the probability constraints are met, the constraint reliability of the current iteration step needs to be greater than or equal to the target reliability:

   

   Substituting formula (17) into formula (19), we get:

   

   Because at the kth iteration

   

   The expression has been calculated, so the size of the left term of the equal sign in equation (20) is only the same as

   

   Is related to the value of and can be defined as

   

   The function:

   

   Equation (20) can be rewritten as:

   

   By solving the above equation, the translation distance can be obtained

   

   

   In the formula, arch represents the inverse function of the function h, and substituting formula (18) into formula (23) to obtain:

   

   Considering that the inequality signs of the deterministic optimization constraint and the probability constraint are the same, equation (24) can take the equal sign, and finally the formula for the translation distance is:

   
10. An efficient method for designing and optimizing automobile side collision safety and reliability according to claim 1, wherein the specific steps of the eighth step are:

    The formula of the k-th iterative deterministic optimization model is:

    

    Solve the deterministic optimization model and get the optimal solution for the kth iteration

    

    And minimum objective function value

    

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