结构方程模型的约束最小二乘解与确定性算法

研究了结构方程模型（SEM）的约束最小二乘解（CLS）,从分析SEM的观测方程组入手,发现了这个不定方程组的结构变量与观测变量必须满足的最小二乘关系,在对结构变量有固定模长参数约束的条件下,求出它的一组模长约束最小二乘解（MCLS）,MCLS可以作为求解结构方程组的偏最小二乘（PLS）迭代初值,在求得MCLS以后,在观测方程组中改变结构变量的模长,使得每个结构变量所对应的与观测变量的路径系数满足配方条件,是更为合理的约束,它可以保证结构变量与所辖的观测变量同质,尽管观测方程组是不定方程组,但是根据误差平方和最小以及对路径系数的配方约束,使得MCLS求解为合理的确定性算法,然后再对结构方程组直接求解,也是确定性算法,这就解决了结构方程模型求解的唯一性问题。     

基于并行PLS算法的化学计量学软件研究

现有化学计量学软件普遍采用的偏最小二乘(PLS)算法均以单线程方式计算,建模速度缓慢,给应用带来较大的不便。随着多核处理器的普及,采用多线程并行计算技术可显著提高算法执行速度。本文将多线程并行计算技术引入化学计量学软件开发,提出并实现了PLS算法的并行化计算。利用标准数据集进行了性能对比实验,结果表明在四核计算机中多线程并行计算比单线程计算有大约3.1倍的速度提升。     

基于改进高效偏最小二乘的质量相关故障诊断

高效偏最小二乘(EPLS)作为偏最小二乘(PLS)的扩展算法之一, 在质量相关故障检测中取得了良好的应用 效果. 然而, 研究发现当系统中存在一些与产品质量无关的信息时会导致EPLS的检测率降低, 影响工业生产安全及 效益. 同时, 传统的基于贡献图的故障诊断方法在无故障时输入变量会对故障检测指标的贡献值不均等, 从而影响 故障诊断效果. 针对上述问题, 本文提出了一种改进高效偏最小二乘(IEPLS)的质量相关故障诊断方法. 所提方法首 先用正常数据建立IEPLS算法模型, 利用获得的模型参数对过程变量进行空间分解. 然后在分解后的空间中定义局 部信息增量均值和局部动态阈值, 结合故障判据进行故障检测. 当故障发生后, 利用每个变量的新息矩阵计算对故 障总体的新息贡献率, 根据各个变量新息贡献率大小实现对故障变量的定位. 最后, 使用田纳西伊士曼过程(TEP)对 算法性能进行了验证.     

非线性偏最小二乘建模方法及在近红外光谱建模上的应用

偏最小二乘算法(PLS)是常用的线性光谱建模方法。针对汽油在线调合中具有非线性特点的辛烷值、干点等属性应用PLS方法建立模型误差较大问题,本文提出了残差-递阶偏最小二乘的建模方法,该方法对已经提取成分后的自变量中剩余的信息再提取主成分,并将该主成分作为新的自变量参与回归建模。仿真验证结果表明:残差-递阶偏最小二乘方法建立的模型中验证集的样本数据误差均在正负0.2之间。残差-递阶偏最小二乘方法与偏最小二乘、递阶偏最小二乘叫-PLS)两种方法比较,残差-递阶偏最小二乘建立的模型有的更高的精度和模型适应性。     

年用电量预测的PLS-LSSVM模型

偏最小二乘法通过提取主成分能有效地消除变量间的多重共线性,最小二乘支持向量机能很好地逼近变量间的非线性关系。偏最小二乘与最小二乘支持向量机相结合用于年用电量的预测,充分发挥了两者的优点。对四川省1978～2007年的用电量进行了实证分析,与PLS模型和LSSV模型的预测成果进行了对比,结果表明年用电量预测的PLS-LSSVM模型有较高的精度。     

一种基于Cholesky分解的动态无偏LS-SVM学习算法

针对最小二乘支持向量机用于在线建模时存在的计算复杂性问题,提出一种动态无偏最小二乘支持向量回归模型.该模型通过改进标准最小二乘支持向量机结构风险的形式消除了偏置项.得到了无偏的最小二乘支持向量机,简化了回归系数的求解.根据模型动态变化过程中核函数矩阵的特点,设计了基于Cholesky分解的在线学习算法.该算法能充分利用历史训练结果,减少计算复杂性.仿真实验表明了所提出模型的有效性.     

修正Cp_EA-PLS用于多环芳烃光解半衰期QSAR的研究

文章讨论了多环芳烃光解半衰期的QSAR模型.运用量子化学软件包以B3LYP/6-311+C(d)方法计算13种PAHs的量子化学描述符,用修正CP统计量作目标函数并用进化算法(EA)选择变量,然后应用偏最小二乘(PLS)方法给13种PAHs的光降解活性进行建模,模型的相关系数为0.9719,比直接用PLS方法所得到的模型更优越.结果表明模型预测PAHs的光解半衰期有效.     

一种新型非线性偏最小二乘方法研究及应用--基于Chebyshev多项式改进的PLS方法

在实际生产过程中，过程变量之间往往存在大量相关关系，甚至非线性相关关系。过程变量间存在线性相关时，可采用偏最小二乘方法(Partial Least Squares，PLS)计算模型参数，但由于PLS方法采用线性关系来联系输入和输出因子，因而并不能有效地应用于非线性较强的过程。在这种情况下要对变量进行有效的压缩维数．需要采用非线性PLS方法。基于Chebyshev多项式改进的多元多项式PLS方法，是一种新的非线性PLS方法。该方法利用Chebyshev多项式的正交性质和递推性质，将过程输入变量正交化、线性化后，再应用PLS方法计算模型参数并还原，从而得到比较精确的模型。由于该方法综合考虑了输入变量的自相关和输入变量间的协相关关系。能够更有效地表达过程变量间的非线性关系，因此其对非线性过程的研究提供了新的思路。     

人工智能技术在电力系统状态估计的应用研究

为了有效地提高状态估计的计算精度和鲁棒性,将人工智能技术与电网数据相结合,提出了基于偏最小二乘(PLS)和极限学习(ELM)的电力系统状态估计方法。针对量测量之间的强相关性问题,采用偏最小二乘(PLS)对各量测量进行重要信息提取和变量选择,将得到的最优变量输入ELM模型,从而建立了状态量的PLS-ELM模型,然后,采用IEEE14节点系统数据样本和实际电网历史数据对所提方法进行了验证,并将该方法与其他方法进行对比。结果表明,所提状态估计方法降低了模型的复杂程度,能够有效地抵抗量测量中的不良数据,具有较高的估计精度和较强的鲁棒性。     

改进块式递推偏最小二乘建模方法及应用

针对传统偏最小二乘(PLS)模型的在线更新问题,提出了带有自适应遗忘因子的块式递推PLS建模方法.通过Hotelling-T2和Q统计量确定遗忘因子的大小,并且进行模型递推更新,确保模型跟踪过程特性的变化.将所提出的方法应用于管坯斜轧穿孔能耗过程,表现出较强的模型在线更新能力.测试结果表明,带有自适应遗忘因子的块式递推PLS方法的性能优于传统的迭代偏最小二乘方法的性能.     

On the relationships among latent variables and residuals in PLS path modeling: The formative-reflective scheme

A new approach for the estimation and the validation of a structural equation model with a formative-reflective scheme is presented. The basis of the paper is a proposal for overcoming a potential deficiency of PLS path modeling. In the PLS approach the reflective scheme assumed for the endogenous latent variables (LVs) is inverted; moreover, the model errors are not explicitly taken into account for the estimation of the endogenous LVs. The proposed approach utilizes all the relevant information in the formative manifest variables (MVs) providing solutions which respect the causal structure of the model. The estimation procedure is based on the optimization of the redundancy criterion. The new approach, entitled redundancy analysis approach to path modeling (RA-PM) is compared with both traditional PLS Path Modeling and LISREL methodology, on the basis of real and simulated data.     

On the relationships among latent variables and residuals in PLS path modeling: The formative-reflective scheme

A new approach for the estimation and the validation of a structural equation model with a formative-reflective scheme is presented. The basis of the paper is a proposal for overcoming a potential deficiency of PLS path modeling. In the PLS approach the reflective scheme assumed for the endogenous latent variables (LVs) is inverted; moreover, the model errors are not explicitly taken into account for the estimation of the endogenous LVs. The proposed approach utilizes all the relevant information in the formative manifest variables (MVs) providing solutions which respect the causal structure of the model. The estimation procedure is based on the optimization of the redundancy criterion. The new approach, entitled redundancy analysis approach to path modeling (RA-PM) is compared with both traditional PLS Path Modeling and LISREL methodology, on the basis of real and simulated data.     

From composites to factors: Bridging the gap between PLS and covariance‐based structural equation modelling

Partial least squares (PLS) methods possess desirable characteristics that have led to their extensive use in the field of information systems, as well as many other fields, for path analyses with latent variables. Such variables are typically conceptualized as factors in structural equation modelling (SEM). In spite of their desirable characteristics, PLS methods suffer from a fundamental problem: Unlike covariance‐based SEM, they do not deal with factors, but with composites, and as such do not fully account for measurement error. This leads to biased parameters, even as sample sizes grow to infinity. Anchored on a new conceptual foundation, we discuss a method that builds on the consistent PLS technique and that estimates factors, fully accounting for measurement error. We provide evidence that this new method shares the property of statistical consistency with covariance‐based SEM but, like classic PLS methods, has greater statistical power. Moreover, our method provides correlation‐preserving estimates of the factors, which can be used in a variety of other tests. For readers interested in trying it, the new method is implemented in the software WarpPLS. Our detailed discussion should facilitate the implementation of the method in any numeric computing environment, including open source environments such as R and GNU Octave.     

A modified PLS path modeling algorithm handling reflective categorical variables and a new model building strategy

Partial least squares (PLS) path modeling has found increased applications in customer satisfaction analysis thanks to its ability to handle complex models. A modified PLS path modeling algorithm together with a model building strategy are introduced and applied to customer satisfaction analysis at the French energy supplier Electricité de France. The modified PLS algorithm handles all kinds of scales (categorical or nominal variables) and is well suited when nominal or binary variables are involved. PLS path modeling and structural equation modeling are confirmatory approaches and thus need an initial conceptual model. A two-step model building strategy is presented; the first step is based on Bayesian networks structure learning to build the measurement model and the second step is based on partial correlation and hypothesis tests to build the structural model. Applications to customer satisfaction data are presented.     

基于T-PLS贡献图方法的故障诊断技术

多变量统计过程监控对于复杂工业过程是一种有效的故障检测和诊断技术. 最小二乘(或称潜空间投影)模型是多变量统计过程监控中常用的一种投影模型, 能够同时对过程数据和质量数据进行建模. 讨论了一种新的基于全潜空间投影模型的故障诊断技术. 全潜空间投影模型中有4个检测统计量. 提出了一种新的T2贡献图计算方法, 对于所有检测统计量, 得到了相应的贡献图算法. 为了确定一个变量是否发生了故障, 计算所有变量贡献图的控制限. 该技术可以将辨识到的故障变量分为与Y有关和与Y无关的两类. 基于Tennessee Eastman过程的案例研究表明了该技术的有效性.     

Sensitivity enhancing transformations for monitoring the process correlation structure

In this article we address the general problem of monitoring the process cross- and auto-correlation structure through the incorporation of information about its internal structure in a pre-processing stage, where sensitivity enhancing transformations are applied to collected data. We have found out that the sensitivity of the monitoring statistics based on partial or marginal correlations in detecting structural changes is directly related to the nominal levels of the correlation coefficients during normal operation conditions (NOC). The highest sensitivities are obtained when the process variables involved are uncorrelated, a situation that is hardly met in practice. However, not all transformations perform equally well in producing uncorrelated transformed variables with enhanced detection sensitivities. The most successful ones are based on the incorporation of the natural relationships connecting the process variables. In this context, a set of sensitivity enhancing transformations are proposed, which are based on a network reconstruction algorithm. These new transformations make use of fine structural information of the variables connectivity and therefore are able to improve the detection capability to local changes in correlation, leading to better performances when compared to current marginal-based methods, namely those based on latent variables models, such as PCA or PLS. Moreover, a novel monitoring statistic for the transformed variables variance proved to be very useful in the detection of structural changes resulting from model mismatch. This statistic allows for the detection of multiple structural changes within the same monitoring scheme and with higher detection performances when compared to the current methods.     

OpenMP多核技术在颗粒流体力学方法GHM中的应用

为了达到提高颗粒流体动力学方法 GHM计算效率的目标,分析了GHM模型的主要计算模块,抽取其中的可并行计算模块,基于多核计算机的硬件环境,应用OpenMP多线程并行计算模型,对采用数值积分方法求解颗粒运动方程的部分,实现求解过程的并行计算。最后通过多次实验验证程序的正确性及算法性能。实验结果表明,在Windows 7系统4核8线程处理器的计算机上,并行程序的并行加速比最高达到了2.5,说明OpenMP多核并行技术能较显著地提高GHM方法的计算性能。     

LDA-based path model construction process for structure equation modeling

This paper proposes a novel approach to generate and analyze path model by structure equation modeling (SEM). SEM is an important technique to carry out causal analysis based on path model. As such, constructing path models, which result in reliable analysis, are important in SEM. LSA-based method, which is used to build a path model from text data, is proposed. However, this method requires each document to belong to one topic; thus, the model cannot express natural variables and relationships. Therefore, this paper extends the existing approach to latent Dirichlet allocation (LDA) and generates a path model from the extracted topics by LDA. Experiments using review text data can confirm the feasibility and applicability of the proposed process.     

A virtual metrology model based on recursive canonical variate analysis with applications to sputtering process

In data driven process monitoring, soft-sensor, or virtual metrology (VM) model is often employed to predict product's quality variables using sensor variables of the manufacturing process. Partial least squares (PLS) are commonly used to achieve this purpose. However, PLS seeks the direction of maximum co-variation between process variables and quality variables. Hence, a PLS model may include the directions representing variations in the process sensor variables that are irrelevant to predicting quality variables. In this case, when direction of sensor variables’ variations most influential to quality variables is nearly orthogonal to direction of largest process variations, a PLS model will lack generalization capability. In contrast to PLS, canonical variate analysis (CVA) identifies a set of basis vector pairs which would maximize the correlation between input and output. Thus, it may uncover complex relationships that reflect the structure between quality variables and process sensor variables. In this work, an adaptive VM based on recursive CVA (RCVA) is proposed. Case study on a numerical example demonstrates the capability of CVA-based VM model compared to PLS-based VM model. Superiority of the proposed model is also presented when it applied to an industrial sputtering process.