【作者】 成忠；

【导师】 陈德钊；

【作者基本信息】 浙江大学 ， 化学工程与技术， 2005， 博士

【摘要】 偏最小二乘回归（partial least squares regression,PLSR）作为一种基于因子分析的多变量校正方法,近年来广泛应用于化学、化工、经济、环境、食品、教育心理等领域。本文以PLSR方法的功能拓展和实际应用为主线,针对化学化工问题及其样本数据所具有的时变性、非线性、存在离群点及多因变量等特征,提出了拓展和改进PLSR功能的几个关键问题,使其能适应上述特性,满足实际需要,分别设计了加权分块递归偏最小二乘、模糊逻辑偏最小二乘、快速稳健偏最小二乘和基于极小极大估计的多因变量偏最小二乘等方法,并将这些方法应用于化学物质结构与性质间关系、化工生产过程等实际问题建模,效果显著。全文的主要内容可归结为以下五个部分,其中包括了研究工作所取得的主要成果。 1、系统回顾了偏最小二乘方法的发展历史、研究现状及应用领域;阐述偏最小二乘方法的基本原理及基本性质;简要介绍了偏最小二乘方法的诸多辅助分析技术。 2、为满足PLSR方法适于时变数据建模的要求,推导与构建了加权分块递归偏最小二乘回归方法。该方法基于相关多变量时变样本数据,采用偏最小二乘方法,以分块递归的方式,为过程变量建立软测量模型,并在分析时变数据特性的基础上,引入样本加权策略,以使模型具有跟踪过程变化的能力,同时提出选定加权函数相关参数的方法和步骤。将该法实际应用于某公司PTA装置溶剂脱水塔,为塔釜排出液H₂O含量建立软测量模型,与已有方法相比,它提高了建模效率,改进了模型预测性能,从而对确保生产过程稳定,有效控制产品质量具有重要意义。 3、提出模糊偏最小二乘（fuzzy PLS,FPLS）算法的新方案。该算法针对化学化工数据的非线性及PLS成分对的单输入单输出特性而构建的,同时它可克服高维变量系统模糊建模引起的规则“组合爆炸”以及变量间的耦合关系导致模型泛化能力较弱。其中成对PLS成分间的模糊模型,按因变量成分随自变量成分的变化剧烈程度（幅度和频度）和逼近精度要求自适应确定模糊规则总数和规则前件参数,由最小二乘方法确定规则后件参数。为更好实现每对成分间更多还原

【Abstract】 Partial least squares regression (PLSR), as a multivariate calibration method based on factor analysis, had been widely used in various kinds of fields, such as chemistry, chemical engineering, economy, environment, foodstuff, education psychology and etc. Now in this paper, to the questions of chemistry and chemical engineering data the time-series, nonlinearity, outliers and multivariate responses characteristics, we induced and constructed some novel PLSR algorithms and then applied them to solve the medicine molecule quantitative structure-activity relationship (QSAR) and chemical engineering process modeling respectively. The main work was as follow:1.The history, progress and application of PLSR had been first reviewed. Subsequently, we expatiated PLSR method the theory and its main property. In order to assess the performance and compare with some other methods, many kinds of its interrelated analysis technique were also introduced.2.A soft sensor model of a chemical process was established by PLSR method based on its time series data, and the model could be adjusted in the block-wise recursive way in the presence of new sample data. With a view to the data of time series characteristics, a strategy of allotting different weight coefficients to the time series data was introduced, and an approach of how to ascertain the weight coefficients was provided in the meantime. Subsequently, the weighted block-wise recursive partial least squares regression algorithm was developed and used to model the water content of solvent dehydration tower bottom drainage in a commerce purified terephthalic acid (PTA). The experimental result showed the algorithm was rapid and effective.3. A new nonlinear PLSR algorithm that embedded the adaptive fuzzy logic system into the regression framework of the PLSR method was proposed. The resulting model used Takagi-Sugeno fuzzy model to capture the nonlinearity andkept the projection to attain robust generalization property. At the same time, an adaptive learning algorithm for the fuzzy model was constructed to reduce the number of fuzzy rules. Subsequently, to increase partial least squares components interpretative capability, the error-based weights updating procedure was deduced and implemented in the fuzzy PLSR framework. Finally, application to the HIV-1 protease inhibitors QSAR modeling of the proposed fuzzy PLSR method was presented with comparison to some other methods. The Fuzzy PLSR method and its error-based method not only held on fine learning ability but also improved the model prediction performance and steady capability.4. In order to eliminate abnormal observations in the data set negative impact on the accuracy and reliability of the PLSR model, a new robust version of the simple partial least squares (SIMPLS) algorithm was constructed from a robust covariance matrix for. high-dimensional data and robust linear regression by embedding a simple multivariate outlier-detection procedure and a robust estimator into the SIMPLS regression framework. The multivariate outlier-detection procedure was based on the use of information obtained from projections onto the directions that maximize and minimize the kurtosis coefficient of the projected data. The proposed kurtosis-SIMPLS method application to the analysis of fish data near infrared spectroscopy was presented with comparison to the SIMPLS. The results showed that kurtosis-SIMPLS method not only found out the very outliers from the data set with less computational cost, but also held on better prediction performance and steady capability for the normal samples.5.In order to eliminate the correlation between predictor variables and make full use of information between the correlated responses in multi-input multi-output chemical process, a new partial least squares regression method called PLSR with mini-max estimator (PLS-Minimax) was introduced. It first implemented the PLSR algorithm with multiple responses to samples data to eliminate the predictor variables correlation and thus built a robust model. Then under the mini-max rule, a shrinkage matrix was calculated based on thecovariance matrix of the multiple responses errors between the PLS estimators and the responses to improve the model predictive precision by modifying the regression coefficient matrix. When the PLS-Minimax method was used to model a polymerization reaction process with four responses. The results showed that PLS-Minimax method not only gained a considerable improvement on predictive accuracy, but also held on high cross-validation correlative coefficient of the multiple responses.更多还原