CN104915478A - Product design model equivalent simplifying method based on multi-parameter uncertainty analysis - Google Patents

Product design model equivalent simplifying method based on multi-parameter uncertainty analysis Download PDF

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CN104915478A
CN104915478A CN201510267014.4A CN201510267014A CN104915478A CN 104915478 A CN104915478 A CN 104915478A CN 201510267014 A CN201510267014 A CN 201510267014A CN 104915478 A CN104915478 A CN 104915478A
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彭翔
刘振宇
谭建荣
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Zhejiang University ZJU
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Abstract

本发明公开了一种基于多参数不确定性分析的产品设计模型等效简化方法。使用优化拉丁方法选取采样点，构建Kriging等效简化模型；计算设计变量不确定性、系统参数不确定性和等效简化模型不确定性对性能的影响，构建性能目标的均值和标准差计算函数；基于性能预测区间进行新增设计变量采样点选取，并基于等效简化模型均方误差进行新增系统参数采样点选取，然后更新构建的Kriging等效简化模型。基于构建的最终等效简化模型，进行多参数不确定性的性能求解。本发明减少了各类参数不确定性对性能的影响，提高了设计结果的稳健性。

The invention discloses a product design model equivalent simplification method based on multi-parameter uncertainty analysis. Use the optimized Latin method to select sampling points and construct the Kriging equivalent simplified model; calculate the impact of design variable uncertainty, system parameter uncertainty and equivalent simplified model uncertainty on performance, and construct the mean and standard deviation calculation function of the performance target ; Select new design variable sampling points based on the performance prediction interval, and select new system parameter sampling points based on the mean square error of the equivalent simplified model, and then update the constructed Kriging equivalent simplified model. Based on the final equivalent simplified model constructed, the performance solution of multi-parameter uncertainty is performed. The invention reduces the influence of various parameter uncertainties on performance, and improves the robustness of design results.

Description

基于多参数不确定性分析的产品设计模型等效简化方法Equivalent simplification method of product design model based on multi-parameter uncertainty analysis

技术领域technical field

本发明涉及了一种产品模型简化方法，涉及一种基于多参数不确定性分析的产品设计模型等效简化方法。The invention relates to a product model simplification method, in particular to a product design model equivalent simplification method based on multi-parameter uncertainty analysis.

背景技术Background technique

仿真分析(有限元分析、计算流体分析等)是产品设计的有效方法。由于多种因素的影响，基于仿真分析的稳健设计中存在等效简化模型不确定性、设计变量不确定性和系统参数不确定性。为了减少各类不确定性因素对性能的影响，人们提出了一系列的方法。例如，Chen.W于2005年在《Journal ofMechanical Design》(127(2):184-195)的论文“Analytical variance-based globalsensitivity analysis in simulation-based design under uncertainty”中提出了一种用于稳健设计的有效而且精确的全局敏感度分析方法。Gu.X于2006年在《Journal ofMechanical Design》(128(4):1001-1013)的论文“Implicit uncertainty propagation forrobust collaborative optimization”中提出了考虑近似模型不确定性和变量不确定性的最坏可能不确定性传播分析方法。Yao.W于2011年在《Progress inAerospace Sciences》(47(6),450-479)的论文“Review of uncertainty-basedmultidisciplinary design optimization methods for aerospace vehicles”中提出了一种综合考虑近似模型不确定性和噪声参数不确定性的闭环不确定性分析方法。Zhang.S于2013年在《Structural and Multidisciplinary Design》(47(1),63-76)的论文“Concurrent treatment of parametric uncertainty and metamodeling uncertaintyin robust design”中提出了一种综合考虑模型不确定性和设计变量不确定性的稳健设计方法，并将该方法应用于汽车车壳的防撞性轻量化结构稳健设计。这些方法虽然提高了设计结果的稳健性，但都没有针对多参数不确定性因素构建等效简化模型，稳健设计结果与精确值间误差较大。Simulation analysis (finite element analysis, computational fluid analysis, etc.) is an effective method for product design. Due to the influence of many factors, there are equivalent simplified model uncertainties, design variable uncertainties and system parameter uncertainties in the robust design based on simulation analysis. In order to reduce the impact of various uncertain factors on performance, a series of methods have been proposed. For example, Chen.W proposed a method for robust design in the paper "Analytical variance-based global sensitivity analysis in simulation-based design under uncertainty" in "Journal of Mechanical Design" (127(2):184-195) in 2005. An effective and accurate global sensitivity analysis method. Gu.X proposed the worst possibility of considering approximate model uncertainty and variable uncertainty in the paper "Implicit uncertainty propagation for robust collaborative optimization" in "Journal of Mechanical Design" (128(4):1001-1013) in 2006 Uncertainty propagation analysis method. Yao.W proposed a comprehensive consideration of approximate model uncertainty and A Closed-Loop Uncertainty Analysis Method for Noise Parameter Uncertainty. Zhang.S proposed a comprehensive consideration of model uncertainty and design in the paper "Concurrent treatment of parametric uncertainty and metamodeling uncertainty in robust design" in "Structural and Multidisciplinary Design" (47(1),63-76) in 2013. Robust design method of variable uncertainty, and apply this method to the robust design of crashworthy lightweight structure of automobile body. Although these methods have improved the robustness of the design results, they have not constructed an equivalent simplified model for the multi-parameter uncertainty factors, and there is a large error between the robust design results and the exact values.

发明内容Contents of the invention

为了提高设计结果的准确性，本发明的目的在于提供一种基于多参数不确定性分析的产品设计模型等效简化方法，综合考虑了等效简化模型不确定性、设计变量不确定性和系统参数不确定性，减少多参数不确定性对性能的影响，提高设计结果的准确性。In order to improve the accuracy of the design results, the object of the present invention is to provide a product design model equivalent simplification method based on multi-parameter uncertainty analysis, which comprehensively considers the uncertainty of the equivalent simplified model, the uncertainty of design variables and the system Parameter uncertainty, reduce the impact of multi-parameter uncertainty on performance, and improve the accuracy of design results.

本发明采用的技术方案是包括以下步骤，如图1所示：The technical scheme that the present invention adopts is to comprise the following steps, as shown in Figure 1:

1)使用优化拉丁方法获取k个包含有设计变量X和系统参数W的初始采样点；1) Use the optimized Latin method to obtain k initial sampling points that include the design variable X and the system parameter W;

2)构建Kriging等效简化模型Gk(x,W)，k表示采样点数目；2) Construct the Kriging equivalent simplified model G k (x, W), where k represents the number of sampling points;

3)根据设计变量不确定性、系统参数不确定性和等效简化模型不确定性对性能目标y的影响，构建性能目标y的均值计算函数μ(x)和方差计算函数σ2(x)，计算得到基于Gk(x,W)的最优设计变量值xmin,k；3) According to the impact of design variable uncertainty, system parameter uncertainty and equivalent simplified model uncertainty on performance target y, construct the mean value calculation function μ(x) and variance calculation function σ 2 (x) of performance target y , calculate the optimal design variable value x min,k based on G k (x,W);

4)建立性能预测区间，增加新的设计变量采样点xk+1；4) Establish a performance prediction interval and add a new design variable sampling point x k+1 ;

5)计算模型均方误差，增加新的系统参数采样点Wk+1；5) Calculate the mean square error of the model and add a new system parameter sampling point W k+1 ;

6)重复步骤2)～5)进行迭代计算，每一次计算中根据已有采样点和新增的采样点(xk+1,Wk+1)构建新的等效简化模型Gk+1(x,W)，直到采样点数量和相邻迭代计算得到的等效简化模型之间的误差满足终止判定条件为止；6) Repeat steps 2) to 5) for iterative calculations, constructing a new equivalent simplified model G k+1 based on existing sampling points and newly added sampling points (x k+1 , W k+1 ) in each calculation (x, W), until the error between the number of sampling points and the equivalent simplified model calculated by adjacent iterations meets the termination judgment condition;

7)将最后一次计算得到的等效简化模型作为最佳等效简化模型，实现产品设计模型的简化。7) The equivalent simplified model obtained from the last calculation is used as the best equivalent simplified model to realize the simplification of the product design model.

所述的步骤3)的计算采用以下步骤：The calculation of described step 3) adopts the following steps:

3.1)将设计变量X分解为确定性部分x和表征变量波动的不确定性部分d，设计变量X的分解如公式1所示：3.1) Decompose the design variable X into a deterministic part x and an uncertain part d that characterizes the fluctuation of the variable. The decomposition of the design variable X is shown in Formula 1:

X＝x+d  (1)X＝x+d (1)

采样点中第i个设计变量Xi的不确定性部分di服从正态分布其中表示di和Xi的方差；采样点中第i个系统参数Wi服从正态分布其中i表示采样点中设计变量的序数，wi和分别是Wi的均值和方差；The uncertainty part d i of the i-th design variable X i in the sampling point obeys the normal distribution in Indicates the variance of d i and Xi; the i -th system parameter W i in the sampling point obeys the normal distribution where i represents the ordinal number of the design variable in the sampling point, w i and are the mean and variance of W i respectively;

3.2)建立以下公式2和公式3分别表示的性能目标y的预测均值函数μ(x)和性能目标y的预测方差函数σ2(x)，并进行计算：3.2) Establish the predicted mean function μ(x) of the performance target y and the predicted variance function σ 2 (x) of the performance target y represented by the following formula 2 and formula 3 respectively, and calculate:

μμ (( xx )) == ∫∫ WW ∫∫ dd ythe y GG kk (( Xx ,, WW )) pp (( dd )) pp (( WW )) dd dd dd WW -- -- -- (( 22 ))

σσ 22 (( xx )) == ∫∫ WW ∫∫ dd [[ ythe y GG kk (( Xx ,, WW )) ]] 22 pp (( dd )) pp (( WW )) dd dd dd WW -- [[ ∫∫ WW ∫∫ dd [[ ythe y GG kk (( Xx ,, WW )) ]] 22 pp (( dd )) pp (( WW )) dd dd dd WW ]] 22 ++ ∫∫ WW ∫∫ dd [[ ϵϵ ythe y (( Xx ,, WW )) ]] 22 pp (( dd )) pp (( WW )) dd dd dd WW ++ 22 ∫∫ WW ∫∫ dd [[ ythe y GG kk (( Xx ,, WW )) ×× ϵϵ ythe y (( Xx ,, WW )) ]] 22 pp (( dd )) pp (( WW )) dd dd dd WW -- -- -- (( 33 ))

其中，p(d)为设计变量X的不确定性部分d的概率密度分布函数，p(W)为系统参数W的概率密度分布函数，εy(X,W)为Kriging等效简化模型Gk(x,W)的模型方差函数的预测均值，为使用Kriging等效简化模型Gk(x,W)计算得到的性能目标y的预测值。Among them, p(d) is the probability density distribution function of the uncertainty part d of the design variable X, p(W) is the probability density distribution function of the system parameter W, ε y (X, W) is the Kriging equivalent simplified model G Model variance function for k (x,W) the predicted mean of is the predicted value of the performance target y calculated using the Kriging equivalent simplified model G k (x, W).

3.3)构建以下公式4表示的稳健设计函数进行性能目标y的最小化设计：3.3) construct the robust design function represented by the following formula 4 Minimize design of performance target y:

f(x)＝μ(x)+cσ(x)  (4)f(x)＝μ(x)+cσ(x) (4)

其中，c表示稳健度常量，μ(x)表示性能目标y的预测均值，σ(x)表示性能目标y的预测标准差。Among them, c represents the robustness constant, μ(x) represents the predicted mean of performance target y, and σ(x) represents the predicted standard deviation of performance target y.

3.4)以稳健设计函数f(x)为目标采用优化方法对设计变量X进行最优设计，得到基于Kriging等效简化模型Gk(x,W)计算得到的最优设计变量值xmin,k。3.4) With the robust design function f(x) as the goal, use the optimization method to optimally design the design variable X, and obtain the optimal design variable value x min,k calculated based on the Kriging equivalent simplified model G k (x,W) .

所述的步骤3.4)中的优化方法采用遗传算法、蚁群算法、粒子群算法等优化方法。The optimization method in the step 3.4) adopts genetic algorithm, ant colony algorithm, particle swarm algorithm and other optimization methods.

所述的步骤4)具体包括：Described step 4) specifically comprises:

4.1)根据步骤3)得到的性能目标y的预测均值μ(x)和性能目标y的预测标准差σ(x)，建立性能目标y的预测区间[μ(x)-cσ(x),μ(x)+cσ(x)]；4.1) According to the predicted mean value μ(x) of the performance target y obtained in step 3) and the predicted standard deviation σ(x) of the performance target y, establish the prediction interval of the performance target y [μ(x)-cσ(x), μ (x)+cσ(x)];

4.2)构建以下公式5表示的预测区间函数h1(x)，以预测区间函数h1(x)取最大值时对应的设计变量值x作为新的设计变量采样点xk+1增加到已有的设计变量采样点中：4.2) Construct the prediction interval function h 1 (x) represented by the following formula 5, and use the design variable value x corresponding to the maximum value of the prediction interval function h 1 (x) as the new design variable sampling point x k+1 to increase to the existing Some design variable sampling points:

h1(x)＝(μ(xmin,k)+cσ(xmin,k))-(μ(x)-cσ(x))  (5)h 1 (x) = (μ(x min,k )+cσ(x min,k ))-(μ(x)-cσ(x)) (5)

其中，μ(xmin,k)、σ(xmin,k)分别表示性能目标y在最优设计变量值xmin,k处的均值和标准差。Among them, μ( xmin,k ) and σ( xmin,k ) represent the mean and standard deviation of the performance target y at the optimal design variable value x min,k , respectively.

所述的步骤5)具体包括：Described step 5) specifically comprises:

5.1)根据步骤2)得到的Kriging等效简化模型Gk(x,W)，计算该模型的均方误差 5.1) Calculate the mean square error of the model according to the Kriging equivalent simplified model G k (x, W) obtained in step 2)

5.2)构建以下公式6表示的采样点选取函数h2(W)，以采样点选取函数h2(W)取最大值时对应的系统参数值W作为新的系统参数采样点Wk+1，增加到已有的系统参数采样点中：5.2) Construct the sampling point selection function h 2 (W) represented by the following formula 6, and take the corresponding system parameter value W when the sampling point selection function h 2 (W) takes the maximum value as the new system parameter sampling point W k+1 , Add to the existing system parameter sampling points:

hh 22 (( WW )) == σσ GG kk (( xx kk ++ 11 ,, WW )) pp (( WW )) -- -- -- (( 66 ))

其中，p(W)为系统参数值W的概率密度分布函数。Among them, p(W) is the probability density distribution function of the system parameter value W.

所述的步骤6)中采样点数量和相邻迭代计算得到的等效简化模型之间的误差满足终止判定条件的计算与判断采用以下方式：The error between the number of sampling points and the equivalent simplified model obtained by adjacent iterative calculations in the step 6) satisfies the calculation and judgment of the termination judgment condition in the following manner:

6.1)采用以下公式7计算得到包含k个采样点的等效简化模型yk(x,W)和包含k+1个采样点的等效简化模型yk+1(x,W)的两个模型之间的误差函数h3(x,W)：6.1) The following formula 7 is used to calculate the equivalent simplified model y k (x, W) containing k sampling points and the equivalent simplified model y k+1 (x, W) containing k+1 sampling points. The error function h 3 (x,W) between the models:

h3(x,W)＝yk+1(x,W)-yk(x,W)  (7)h 3 (x,W)=y k+1 (x,W)-y k (x,W) (7)

6.2)再采用以下公式8计算包含k个采样点的等效简化模型和包含k+1个采样点的等效简化模型之间的差距函数Z(x)；6.2) Then use the following formula 8 to calculate the gap function Z(x) between the equivalent simplified model comprising k sampling points and the equivalent simplified model comprising k+1 sampling points;

Z(x)＝∫wh3(x,W)p(W)dW  (8)Z(x)＝∫ w h 3 (x,W)p(W)dW (8)

6.3)当采样点数量k满足k<kmax且差距函数Z(x)的预测均值E(Z(x))满足E(Z(x))≤Emax的情况下，kmax表示采样点数量最大值，则重复步骤2)～5)；6.3) When the number of sampling points k satisfies k<k max and the predicted mean E(Z(x)) of the gap function Z(x) satisfies E(Z(x))≤E max , k max represents the number of sampling points maximum value, repeat steps 2) to 5);

当采样点数量k满足k＝kmax或者差距函数Z(x)的预测均值E(Z(x))满足E(Z(x))>Emax的情况下，Emax表示误差阈值，则停止迭代计算。When the number of sampling points k satisfies k=k max or the predicted mean E(Z(x)) of the gap function Z(x) satisfies E(Z(x))>E max , E max represents the error threshold, then stop Iterative calculation.

所述的步骤7)最终得到最佳等效简化模型用于产品的性能稳健设计，计算得到满足多参数不确定性要求的最优设计变量值。The step 7) finally obtains the best equivalent simplified model for robust design of product performance, and calculates the optimal design variable values that meet the multi-parameter uncertainty requirements.

本发明具有的有益效果是：The beneficial effects that the present invention has are:

1、计算了设计变量不确定性、系统参数不确定性和等效简化模型不确定性对性能不确定性的影响，构建了考虑多参数不确定性的性能目标不确定性表征函数。1. The influence of design variable uncertainty, system parameter uncertainty and equivalent simplified model uncertainty on performance uncertainty is calculated, and a performance target uncertainty characterization function considering multi-parameter uncertainty is constructed.

2、提出了基于性能目标预测区间和模型均方误差的非均匀采样点选取方法，进行了等效简化模型构建，减少了构建的等效简化模型的不确定性，提高了性能度量的精确性。2. A non-uniform sampling point selection method based on performance target prediction interval and model mean square error is proposed, and an equivalent simplified model is constructed, which reduces the uncertainty of the constructed equivalent simplified model and improves the accuracy of performance measurement .

3、将构建的等效简化模型应用于复杂产品的性能求解，减少了多参数不确定性对性能的影响，提高了设计结果的稳健性。3. Apply the constructed equivalent simplified model to solve the performance of complex products, which reduces the impact of multi-parameter uncertainty on performance and improves the robustness of design results.

附图说明Description of drawings

图1是本发明的流程图。Figure 1 is a flow chart of the present invention.

图2是实施例1中设计目标与设计变量、系统参数之间的真实响应模型。Fig. 2 is the real response model between design target and design variable, system parameter in embodiment 1.

图3是实施例1中初始Kriging等效简化模型的预测均值。Fig. 3 is the predicted mean value of the initial Kriging equivalent simplified model in Example 1.

图4是实施例1中初始Kriging等效简化模型的预测均方误差。Fig. 4 is the prediction mean square error of the initial Kriging equivalent simplified model in Example 1.

图5是实施例1中考虑多参数不确定性的稳健设计函数。Fig. 5 is a robust design function considering multi-parameter uncertainty in Example 1.

图6是实施例1中最终等效简化模型的预测均值。FIG. 6 is the predicted mean value of the final equivalent simplified model in Example 1.

图7是实施例1中最终等效简化模型的预测均方误差。Fig. 7 is the prediction mean square error of the final equivalent simplified model in Example 1.

图8是实施例1中评价函数随采样点数量的变化过程。FIG. 8 is the change process of the evaluation function with the number of sampling points in Embodiment 1.

图9是实施例1中考虑多参数不确定性的稳健设计函数。FIG. 9 is a robust design function considering multi-parameter uncertainty in Example 1.

具体实施方式Detailed ways

下面结合具体实施例和附图对本发明作进一步解释和说明。The present invention will be further explained and illustrated below in conjunction with specific embodiments and accompanying drawings.

本发明方法如图1所示，具体实施例如下：The inventive method as shown in Figure 1, specific embodiments are as follows:

该设计模型为最小化y(x,w)＝80x-2+2xw+x2w。设计变量x的设计空间为x∈[0.8,2.5]，设计变量不确定性为x～N(x,0.072)；系统参数为w＝10，其不确定性符合正态分布w～N(10,2)。本实施例中，设计目标y与设计变量x、系统参数w之间的真实响应模型采用如图2所示的多边形曲面。The design model is to minimize y(x,w)=80x −2 +2xw+x 2 w. The design space of the design variable x is x∈[0.8,2.5], the uncertainty of the design variable is x～N(x,0.07 2 ); the system parameter is w=10, and its uncertainty conforms to the normal distribution w～N( 10,2). In this embodiment, the real response model between the design target y, the design variable x, and the system parameter w adopts a polygonal surface as shown in FIG. 2 .

本发明具体步骤为：Concrete steps of the present invention are:

1)使用优化拉丁超立方法选取15个采样点，基于这15个采样点的仿真分析结果构建初始Kriging简化模型。该初始Kriging简化模型在每一设计点处的均值如图3所示，均方误差如图4所示。1) Select 15 sampling points by using the optimized Latin hypercube method, and construct the initial Kriging simplified model based on the simulation analysis results of these 15 sampling points. The mean value of the initial Kriging simplified model at each design point is shown in Figure 3, and the mean square error is shown in Figure 4.

2)在初始Kriging简化模型基础上，构建综合考虑设计变量不确定性、系统参数不确定性和等效简化模型不确定性的性能稳健设计函数，如图5所示，计算得到的最优设计变量值为x＝1.4511。2) On the basis of the initial Kriging simplified model, construct a performance robust design function that comprehensively considers the uncertainty of design variables, system parameters and the uncertainty of the equivalent simplified model, as shown in Figure 5, the calculated optimal design The variable value is x=1.4511.

3)进行设计变量和系统参数采样点选取。最终的等效简化模型包含29个采样点，该简化模型的均值如图6所示，模型预测方差如图7所示。简化模型构建过程中，随着采样点的增加，Z(x)的均值变化过程如图8所示。基于最终的简化模型，构建的性能求解设计函数如图9所示，得到的最优设计变量值为x＝1.4239。3) Select sampling points for design variables and system parameters. The final equivalent simplified model contains 29 sampling points, the mean value of the simplified model is shown in Figure 6, and the model prediction variance is shown in Figure 7. In the simplified model construction process, with the increase of sampling points, the mean value change process of Z(x) is shown in Figure 8. Based on the final simplified model, the constructed performance solution design function is shown in Figure 9, and the obtained optimal design variable value is x=1.4239.

使用传统的简化模型得到的最优设计变量值为x＝1.5072。该实例的真实最优设计值为x＝1.3542。本发明的计算结果与已有方法的计算结果、精确计算结果对比如表1所示，对比结果显示本发明的计算结果更接近真实值。The optimal design variable value obtained by using the traditional simplified model is x=1.5072. The actual optimal design value of this example is x=1.3542. The calculation result of the present invention is compared with the calculation result of the existing method and the accurate calculation result as shown in Table 1, and the comparison result shows that the calculation result of the present invention is closer to the real value.

表1Table 1

本发明结果Results of the invention 已有方法结果Existing method results 精确值The exact value 稳健目标值Robust target value 113.05113.05 115.99115.99 109.10109.10 性能平均值performance average 88.4288.42 94.3694.36 88.1688.16 性能标准差值performance standard deviation 8.218.21 7.217.21 6.986.98 最优设计变量值Optimal Design Variable Values 1.42391.4239 1.50721.5072 1.35421.3542

由此可见，本发明通过性能目标不确定性表征函数等方式等效简化了产品模型，减少了构建的等效简化模型的不确定性，提高了性能度量的精确性以及产品设计结果的稳健性。It can be seen that the present invention equivalently simplifies the product model by means of performance target uncertainty characterization functions, etc., reduces the uncertainty of the constructed equivalent simplified model, improves the accuracy of performance measurement and the robustness of product design results .

Claims (7)

1., based on a product design model equivalent-simplification method for multiparameter uncertainty analysis, it is characterized in that comprising the following steps:
1) the initial samples point optimized Latin method acquisition k and include design variable X and systematic parameter W is used;
2) Kriging equivalent simplified model G is built k(x, W), k represents sampled point number;
3) uncertain according to design variable, systematic parameter is uncertain and the uncertain impact on performance objective y of equivalent simplified model, builds mean value computation function mu (x) and the variance computing function σ of performance objective y 2x (), calculates based on G kthe optimal design variate-value x of (x, W) min, k;
4) set up performance prediction interval, increase new design variable sampled point x k+1;
5) computation model square error, increases new systematic parameter sampled point W k+1;
6) step 2 is repeated) ~ 5) carry out iterative computation, according to existing sampled point and newly-increased sampled point (x in calculating each time k+1, W k+1) build new equivalent simplified model G k+1(x, W), until the error between the equivalent simplified model that obtains of sampled point quantity and adjacent iterative computation meets stop technology condition;
7) using the equivalent simplified model that calculates for the last time as best equivalence simplified model, realize the simplification of product design model.
2. a kind of product design model equivalent-simplification method based on multiparameter uncertainty analysis according to claim 1, is characterized in that:
Described step 3) calculating adopt following steps:
3.1) design variable X be decomposed into determinacy part x and characterize the uncertain part d of variable perturbations, the decomposition of design variable X as shown in Equation 1:
X＝x+d (1)
I-th design variable X in sampled point iuncertain part d inormal Distribution wherein represent d iand X ivariance; I-th systematic parameter W in sampled point inormal Distribution wherein i represents the ordinal number of design variable in sampled point, w iwith w respectively iaverage and variance;
3.2) prediction mean value function μ (x) of performance objective y and the prediction variance function σ of performance objective y that following formula 2 and formula 3 represent respectively is set up 2(x), and calculate:
Wherein, the probability density function of the uncertain part d that p (d) is design variable X, the probability density function that p (W) is systematic parameter W, ε y(X, W) is Kriging equivalent simplified model G kthe model variance function of (x, W) prediction average, for using Kriging equivalent simplified model G kthe predicted value of the performance objective y that (x, W) calculates;
3.3) the based Robust Design function that following formula 4 represents is built carry out the miniaturized design of performance objective y:
f(x)＝μ(x)+cσ(x) (4)
Wherein, c represents and steadily and surely spends constant, and μ (x) represents the prediction average of performance objective y, and σ (x) represents the prediction standard deviation of performance objective y;
3.4) adopt optimization method to carry out optimal design to design variable X with based Robust Design function f (x) for target, obtain based on Kriging equivalent simplified model G kthe optimal design variate-value x that (x, W) calculates min, k.
3. a kind of product design model equivalent-simplification method based on multiparameter uncertainty analysis according to claim 1, is characterized in that: described step 3.4) in optimization method adopt the optimization method of genetic algorithm, ant group algorithm or particle cluster algorithm.
4. a kind of product design model equivalent-simplification method based on multiparameter uncertainty analysis according to claim 1, is characterized in that: described step 4) specifically comprise:
4.1) according to step 3) prediction average μ (x) of performance objective y that obtains and prediction standard deviation sigma (x) of performance objective y, set up the forecast interval [μ (x)-c σ (x), μ (x)+c σ (x)] of performance objective y;
4.2) the forecast interval function h that following formula 5 represents is built 1x (), with forecast interval function h 1design variable value x corresponding when () gets maximal value is x as new design variable sampled point x k+1be increased in existing design variable sampled point:
h 1(x)＝(μ(x min,k)+cσ(x min,k))-(μ(x)-cσ(x)) (5)
Wherein, μ (x min, k), σ (x min, k) represent that performance objective y is at optimal design variate-value x respectively min, kthe average at place and standard deviation.
5. a kind of product design model equivalent-simplification method based on multiparameter uncertainty analysis according to claim 1, is characterized in that: described step 5) specifically comprise:
5.1) according to step 2) the Kriging equivalent simplified model G that obtains k(x, W), calculates the square error of this model
5.2) the sampled point Selection of Function h that following formula 6 represents is built 2(W), with sampled point Selection of Function h 2(W) system parameter values W corresponding when getting maximal value is as new systematic parameter sampled point W k+1, be increased in existing systematic parameter sampled point:
Wherein, p (W) probability density function that is system parameter values W.
6. a kind of product design model equivalent-simplification method based on multiparameter uncertainty analysis according to claim 1, is characterized in that: described step 6) in the calculating that meets stop technology condition of error between the equivalent simplified model that obtains of sampled point quantity and adjacent iterative computation with judge in the following ways:
6.1) following formula 7 is adopted to calculate the equivalent simplified model y comprising k sampled point k(x, W) and comprise the equivalent simplified model y of k+1 sampled point k+1error function h between two models of (x, W) 3(x, W):
h 3(x,W)＝y k+1(x,W)-y k(x,W) (7)
6.2) following formula 8 is adopted to calculate gap function Z (x) comprised between the equivalent simplified model of k sampled point and the equivalent simplified model comprising k+1 sampled point again;
Z(x) ＝∫ wh 3(x,W)p(W)dW (8)
6.3) when sampled point quantity k meets k<k maxand the prediction average E (Z (x)) of gap function Z (x) meets E (Z (x))≤E maxwhen, k maxrepresent sampled point quantity maximal value, then repeat step 2) ~ 5);
When sampled point quantity k meets k=k maxor the prediction average E (Z (x)) of gap function Z (x) meets E (Z (x)) >E maxwhen, E maxrepresent error threshold, then stop iterative computation.
7. a kind of product design model equivalent-simplification method based on multiparameter uncertainty analysis according to claim 1, it is characterized in that: described step 7) finally obtain best equivalence simplified model and design for the Robust Performance of product, for calculating the optimal design variate-value meeting multiparameter uncertainty and require.
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Cited By (5)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN109358589A (en) * 2018-11-07 2019-02-19 惠科股份有限公司 Method and device for controlling quantifiable optical characteristics and readable storage medium
CN110442974A (en) * 2019-08-07 2019-11-12 广东工业大学 Horse shoe flame regenerator chamber of glass kiln performance optimization method and device
CN110852605A (en) * 2019-11-08 2020-02-28 北京理工大学 A method and system for determining product design decisions based on information efficiency
CN111189699A (en) * 2019-12-12 2020-05-22 大连理工大学 A realization method of inversion and identification of crystal plastic material parameters based on nanoindentation experiment
CN113194366A (en) * 2021-04-23 2021-07-30 烽火通信科技股份有限公司 Service configuration rationality checking method and device based on closed-loop constraint

Citations (2)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN102867083A (en) * 2012-08-30 2013-01-09 浙江大学 High-rigidity and light-weight design method considering uncertainty of slide block mechanism of press machine
CN104636563A (en) * 2015-02-14 2015-05-20 浙江大学 Reliability design method for upper crossbeam of high-speed pressure machine

Patent Citations (2)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN102867083A (en) * 2012-08-30 2013-01-09 浙江大学 High-rigidity and light-weight design method considering uncertainty of slide block mechanism of press machine
CN104636563A (en) * 2015-02-14 2015-05-20 浙江大学 Reliability design method for upper crossbeam of high-speed pressure machine

Non-Patent Citations (2)

* Cited by examiner, † Cited by third party
Title
SILIANG ZHANG等: "Concurrent treatment of parametric uncertainty and metamodeling uncertainty in robust design", 《STRUCTURAL AND MULTIDISCIPLINARY OPTIMIZATION》 *
李小刚等: "基于双层更新Kriging模型的机械结构动态特性稳健优化设计", 《机械工程学报》 *

Cited By (10)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN109358589A (en) * 2018-11-07 2019-02-19 惠科股份有限公司 Method and device for controlling quantifiable optical characteristics and readable storage medium
CN109358589B (en) * 2018-11-07 2021-07-02 惠科股份有限公司 Method and device for controlling quantifiable optical characteristics and readable storage medium
CN110442974A (en) * 2019-08-07 2019-11-12 广东工业大学 Horse shoe flame regenerator chamber of glass kiln performance optimization method and device
CN110442974B (en) * 2019-08-07 2022-11-11 广东工业大学 Method and device for optimizing performance of regenerative chamber of horseshoe flame glass kiln
CN110852605A (en) * 2019-11-08 2020-02-28 北京理工大学 A method and system for determining product design decisions based on information efficiency
CN110852605B (en) * 2019-11-08 2022-05-27 北京理工大学 Product design decision determining method and system based on information efficiency
CN111189699A (en) * 2019-12-12 2020-05-22 大连理工大学 A realization method of inversion and identification of crystal plastic material parameters based on nanoindentation experiment
CN111189699B (en) * 2019-12-12 2021-05-18 大连理工大学 A realization method of inversion and identification of crystal plastic material parameters based on nanoindentation experiment
CN113194366A (en) * 2021-04-23 2021-07-30 烽火通信科技股份有限公司 Service configuration rationality checking method and device based on closed-loop constraint
CN113194366B (en) * 2021-04-23 2022-06-03 烽火通信科技股份有限公司 Service configuration rationality checking method and device based on closed-loop constraint

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