稀疏偏最小二乘回归-多项式混沌展开代理模型方法EI北大核心CSCD

为解决传统多项式混沌展开方法在高维全局灵敏度和结构可靠度分析当中存在的维数灾难与多重共线性问题,该文提出一种稀疏偏最小二乘回归-多项式混沌展开代理模型方法。该方法首先采用偏最小二乘回归技术得到多项式混沌展开系数的初步估计,然后根据回归误差阈值允许下的最大稀疏度原则,采用带有惩罚的矩阵分解技术自适应地保留与结构响应相关性强的多项式,并采用偏最小二乘回归得到多项式混沌展开系数的更新估计。通过对展开系数进行简单后处理即可得到Sobol灵敏度指数。在此基础上保留重要输入变量并按新方法重新进行回归可实现对代理模型的精简,从而在不增加计算代价的情况下实现高精度结构可靠度分析。算例结果表明在保证精度的情况下,采用新方法进行全局灵敏度和结构可靠度分析比传统方法在计算效率方面有显著优势。     

稀疏偏最小二乘回归-多项式混沌展开代理模型方法

为解决传统多项式混沌展开方法在高维全局灵敏度和结构可靠度分析当中存在的维数灾难与多重共线性问题,该文提出一种稀疏偏最小二乘回归-多项式混沌展开代理模型方法。该方法首先采用偏最小二乘回归技术得到多项式混沌展开系数的初步估计,然后根据回归误差阈值允许下的最大稀疏度原则,采用带有惩罚的矩阵分解技术自适应地保留与结构响应相关性强的多项式,并采用偏最小二乘回归得到多项式混沌展开系数的更新估计。通过对展开系数进行简单后处理即可得到Sobol灵敏度指数。在此基础上保留重要输入变量并按新方法重新进行回归可实现对代理模型的精简,从而在不增加计算代价的情况下实现高精度结构可靠度分析。算例结果表明在保证精度的情况下,采用新方法进行全局灵敏度和结构可靠度分析比传统方法在计算效率方面有显著优势。     

结构可靠度分析的均匀设计响应面法

均匀设计和正交设计在试验次数相近的情况下,前者所选试验点均匀性更好,也更具代表性。该文将均匀设计与响应面法相结合,提出了结构可靠度的数值模拟新方法：基于均匀设计的响应面法、均匀设计响应面与蒙特卡罗抽样相结合的混合模拟法;介绍了利用均匀设计选取试验点构造响应面方程,求解可靠度的流程。结合一个门式框架的可靠度问题,基于AN...     

基于逆响应面法的有限元模型修正

基于响应面法（RSM）的有限元模型修正是以若干设计参数（如密度、弹性模量等）为自变量,以若干特征参数（如固有频率、振型等）为因变量,通过回归分析方法来拟合特征参数关于修正参数的显式表达式。提出的逆响应面法（IRSM）则是以特征参数作为自变量,设计参数作为因变量。利用此法的有限元模型修正可直接根据特征参数的目标值得到设计参数的修正量,而不需要经过迭代计算,有效地提高计算速度和精度。介绍逆响应面法及其应用,讨论使用响应面法和逆响应面法进行有限元模型修正的优缺点和适用范围,分析适合于逆响应面法的逆响应面函数、实验设计方案和回归精度检验的方法。利用逆响应面法对一简支梁进行有限元模型修正的结果表明,逆响应面法能高效准确地修正设计参数,对于输出变量少于输入变量的情况更能显著减少有限元计算次数,适用于复杂的工程结构。     

采用响应面法的复合板结构噪声优化设计

针对复合材料层合板结构出现的噪声问题,将响应面法RSM(Response Surface Method)与遗传优化算法相结合,提出一种降低复合材料层合板声压级的优化方法。该方法基于四边形复合材料层合板结构建立有限元分析模型,通过三因子试验设计点设计试验计划表,结合最小二乘法构建复合材料层合板声压级的2阶响应面近似模型。以影响层合板噪声的显著因子为设计变量,层合板的声压级为设计目标,采用遗传算法对响应面近似模型进行优化,结果表明,使用该方法对复合材料层合板的噪声特性进行分析,可明显提高优化效率并为工程实际提供参考。     

基于响应面法的结构动力学模型修正

为了获得精确的结构动力学模型,提出了响应面和优化相结合的方法。利用参数化模型和优化拉丁方试验设计获取样本点构造多项式响应面模型,最小二乘法确定多项式系数并检验响应面的拟合精度。用响应面计算结果与实验结果的误差构造目标函数,自适应模拟退火算法来优化修正响应面参数,将修正后的参数值带入有限元模型得到修正模型。以欧洲航空科技组织的基准模型GARTEUR飞机模型为算例,对比修正前后模态频率,结果表明修正后的模型在测试频段和预测频段具有良好的复现和预测能力,进而验证了基于响应面法与优化方法相结合的结构动力学有限元模型修正的有效性。     

基于响应面法的印制电路板组件有限元模型修正

在将印制电路板及元器件材料视为正交各向异性前提下,提出基于响应面法的印制电路板组件(Printed Circuit Board Assembly,PCBA)有限元模型修正法。利用相关性分析筛选出对PCBA模态频率影响较大参数作为修正参数;据修正参数数目选择合适的试验设计获取样本点,构造多项式响应面模型;通过最小二乘法确定多项式系数并检验响应面拟合精度;用响应面计算结果与模态试验结果误差绝对值构造目标函数;通过多目标遗传算法(MOGA)迭代计算获得优化修正参数并代入有限元模型获得修正模型。以某航空电子产品某PCBA为案例,对比修正前后各阶模态频率与试验值误差。结果表明,修正后模型各阶模态频率与试验值相对误差均明显减小,验证该方法对PCBA模型修正的有效性。     

关联因子裂区的响应曲面设计

裂区设计是处理工业试验设计中存在随机性约束的一种设计,针对现实的裂区设计中存在关联因子的问题,尝试提出将嵌套效应建模引入裂区试验设计的处理方法,通过对标准的面中心响应曲面的再构,为存在关联因子的裂区响应曲面设计提供了可行的方案.经过对标准裂区设计矩阵的改进,构造出存在关联因子裂区试验的二次项拟合模型,而且保证了普通最小二乘和广义最小二乘在模型拟合时的相等性,从而使得实验数据的分析更为简便.     

基于粗糙集与最小二乘支持向量回归的汽轮机主蒸汽流量预测

针对传统主蒸汽流量计算方法的不足,提出了一种新的主蒸汽流量预测方法,该方法综合了粗糙集理论与最小二乘支持向量回归算法的优点,利用ROSETTA V1.4.41研究实验平台中的遗传约简算法对输入变量的属性进行约简,再利用最小二乘支持向量回归算法建立主蒸汽流量的预测模型。实验表明,与未经粗糙集理论处理过的BP神经网络、支持向量回归算法和最小二乘支持向量回归算法所建模型相比,该方法具有更好的预测精度和泛化能力,且建模速度显著提高。     

液压千斤顶检定数据的处理

正千斤顶检定数据线性回归方程的拟合,其线性回归是利用数理统计中回归分析,来确定两种或两种以上变量间相互依赖的定量关系的一种统计分析方法,运用十分广泛。一般来说,线性回归都可以通过最小二乘法求出其方程,并计算出对于y=bx+a的直线。最小二乘法是实验数据处理中最重要的方法之一,公式如下:y=bx+a     

顾客满意度线性建模中多重共线性处理方法的模拟研究

多重共线性会给顾客满意度线性建模带来很大的危害。本文综述了四种处理多重共线性的方法,即逐步回归法、岭回归法、主成分回归法和偏最小二乘法,并使用蒙特卡罗方法,对这四种方法在建模可靠性、模型解释能力及模型预测能力方面进行了仿真比较。结果表明,存在多重共线性时,偏最小二乘法的建模效果最为理想。     

Optimized independent components for parameter regression

In this paper, a modified ICR algorithm is proposed for quality prediction purpose. The disadvantage of original Independent Component Regression (ICR) is that the extracted Independent Components (ICs) are not informative for quality prediction and interpretation. In the proposed method, to enhance the causal relationship between the extracted ICs and quality variables, a dual-objective optimization which combines the cost function w^TX^TYv in Partial Least Squares (PLS) and the approximations of negentropy in Independent Component Analysis (ICA) is constructed in the first step for feature extraction. It simultaneously considers both the quality-correlation and the independence, and then the ICR-MLR (Multiple Linear Regression) method is used to obtain the regression coefficients. The proposed method is applied to the quality prediction in continuous annealing process and Tennessee Eastman process. Applications indicate that the proposed approach effectively captures the relations in the process variables and use of proposed method instead of original PLS and ICR improves the regression matching and prediction ability.     

Least-squares approximation of a space distribution for a given covariance and latent sub-space

In this paper, a new method to approximate a data set by another data set with constrained covariance matrix is proposed. The method is termed Approximation of a DIstribution for a given COVariance (ADICOV). The approximation is solved in any projection subspace, including that of Principal Component Analysis (PCA) and Partial Least Squares (PLS). Given the direct relationship between covariance matrices and projection models, ADICOV is useful to test whether a data set satisfies the covariance structure in a projection model. This idea is broadly applicable in chemometrics. Also, ADICOV can be used to simulate data with a specific covariance structure and data distribution. Some applications are illustrated in an industrial case of study.     

基于近红外光谱分析技术的液态水性油墨印刷品 颜色预测模型

针对印刷品颜色离线检测存在滞后、检测不精准等问题,提出基于近红外光谱分析技术的液态水性油墨印刷品颜色预测模型。用多元散射校正（MSC） 、标准正态变换（SNV）和卷积平滑滤波器（SG）对原始光谱数据进行预处理,将原始光谱数据及预处理后的光谱数据分别与印刷品的Lab值建立偏最小二乘回归（PLSR）和主成分回归（PCR）两种预测模型。结果表明,基于MSC预处理的PLSR预测模型的预测精度最高,L、a、b值的R2分别高达0.9885, 0.9879和0.9938,预测颜色的平均色差约为0.71。液态水性油墨的近红外光谱可以精确预测印刷品颜色,为印刷品的在线检测提供了新思路。     

A new artificial neural network-based response surface method for structural reliability analysis

This paper presents a new artificial neural network-(ANN)based response surface method in conjunction with the uniform design method for predicting failure probability of structures. The method involves the selection of training datasets for establishing an ANN model by the uniform design method, approximation of the limit state function by the trained ANN model and estimation of the failure probability using first-order reliability method (FORM). In the proposed method, the use of the uniform design method can improve the quality of the selected training datasets, leading to a better performance of the ANN model. As a result, the ANN dramatically reduces the number of required trained datasets, and shows a good ability to approximate the limit state function and then provides a less rigorous formulation in the context of FORM. Results of three numerical examples involving both structural and non-structural problems indicate that the proposed method provides accurate and computationally efficient estimates of the probability of failure. Compared with the conventional ANN-based response surface method, the proposed method is much more economical to achieve reasonable accuracy when dealing with problems where closed-form failure functions are not available or the estimated failure probability is extremely small. Finally, several important parameters in the proposed method are discussed.     

Cost Prediction of a Turbofan Engine Using the Robust Partial Least Squares Method

In recent years,the cost of engines has become increasingly important to engine manufacturers,who are consistently faced with major problems on how to reduce cost to a minimum.Cost has become a decisive factor for aircraft design.To control the continual rapid increased cost,engine cost prediction is indispensable early in the design phase.But the cost data of an aircraft engine is small;we introduce the Robust Partial Least Squares Method in solving this problem,and reducing or removing the effect of outlying data points,which is different from the Classical PLS.We use the MATLAB software doing several simulations;results and analysis of a real turbofan engine data set show the effectiveness and robustness of the Robust PLS method.The Robust PLS method can effectively be used to estimate Turbofan Engine cost with reasonable accuracy.     

An integrated solution for reducing ill-conditioning and testing the results in non-linear 3D similarity transformations

To find 3D similarity transformation parameters (a scale, three rotational angles, and three translation elements) between two orthogonal coordinate systems in 3D is an ill-posed non-linear inverse problem by means of common points (their Cartesian components are known in the both systems). The problem can be solved via Linearized Least Squares (LLS) or Direct (non-iterative) Least Squares (DLS). Since the parameters in LLS take different quantities (and units) from each other, the condition problems can arise during the solution of normal equations. In this paper, we propose a combined solution to reducing ill-conditioning and to perform precision analysis and global outlier test in LLS accordingly. The way is based on column norming and uses the normalized unknowns instead of the original ones at the solution stage of the normal equations. While the global outlier test is fulfilled on the normalized unknowns, the original unknowns and their precisions obtained using the normalized matrix with linear transformation to the normalized unknowns and by the error propagation law to their variance-covariance matrix. A direct method (Direct Least Squares, DLS) is used to compute the initial values of LLS for reducing iteration number (to 1–3 cycles) with a 1.E-7 threshold in the paper. And, when the solution of 3D-ST having large rotational angles and uncertainties, it is also shown that DLS goes to a worse solution than LLS by means of a simulated transformation problem.     

基于自适应点估计和最大熵原理的结构体系多构件可靠度分析

准确而高效地求解结构体系中多个构件的可靠度水准对结构维护和优化具有重要意义,目前已有学者将蒙特卡洛法和响应面法用于此类可靠度分析。然而,蒙特卡洛法所需结构分析次数取决于失效概率的量级,通常计算成本较高。而响应面法的所需结构分析次数取决于杆件数量,当其数量较多时同样有较高的成本。鉴于此,该文提出了一种基于自适应点估计和最大熵原理的结构体系多构件可靠度分析方法,其所需的结构重分析次数上限与杆件数量无关,计算过程简便无需迭代。首先,通过引入自适应交叉项判定和双变量降维近似模型求解各杆件的前四阶矩;然后,根据各杆件的前四阶矩,采用最大熵原理求解各杆件的可靠度指标;最后,通过多个算例对比了蒙特卡洛法、响应面法和建议方法的精度和效率。结果表明建议方法所需的结构重分析次数远少于蒙特卡洛法和响应面法,实现过程简便,且精度能够满足工程要求。