Robust Regression And Its Application In Spectral Analysis

In order to guarantee product quality and to reduce energy consumption, production costs as well as environmental pollution, quality monitoring need to be paid more attention in modern industries. Quality analysis mainly consists of chemical analysis and instrumental analysis. The instrumental analysis has become mainstream. Due to the advantages of spectral analysis, such as fast, non-destructive, easy to operate, etc., it has recently been used in many different fields. The principle of spectral analysis is demonstrated as follows:first, an analytical model is constructed based on a training data set with known compositions or properties and the spectra; then the compositions or properties of a testing sample can be calculated based on the model and its spectrum.However, in industrial applications, because of environmental factors, instrumental bias, human operation mistake and other reasons, there may be some outliers in the training samples; these outliers may greatly influence on the reliability and accuracy of the calibration model. How to avoid or reduce the influence of outliers has become an urgent problem. In this thesis, a series of robust regression algorithms have been proposed and applied in spectral quantitative analysis, which can be summarized as follows:1. In order to address the disadvantages of existing robust Partial Least Squares (PLS) algorithms, a novel robust PLS with outlier detection is proposed. New algorithm can automatically eliminate outliers based on the confidence interval, which is determined by PLS regression errors. Meanwhile, a robust local Principle Component Regression (PCR) algorithm is also proposed. In this algorithm, two steps of PCR, i.e., principle component analysis and multivariate linear regression, are both improved to enhance model robustness. Besides, a local regression method has been introduced to multivariate linear regression. The above two algorithms are applied in near infrared spectral analysis of gasoline octane number. Experimental results show that they perform better than other linear robust algorithms.2. To improve the robustness of Least Squares Support Vector Machine (LS-SVM), a novel robust LS-SVM algorithm is developed. In this algorithm, the confidence interval of the residual distribution is applied iteratively to detect outliers and select normal samples, and then the LS-SVM model is developed based on the selected subset which has no outliers. In order to reduce the computing time, the corresponding fast algorithm is also proposed. The novel robust LS-SVM is applied in a Raman analyzer to predict gasoline properties. Application results show it can detect outliers effectively; the predictive accuracy of the analyzer is suitable for industrial applications. 3. A robust iterative algorithm of Weighted Least Squares Support Vector Machine (WLS-SVM) is proposed to address shortcomings of the original WLS-SVM in convergence and robustness. In this algorithm, the calculation formula for regression residual in the original WLS-SVM algorithm is revised to ensure the iterative convergence; another formula to compute weighted value is also improved to enhance the robustness of WLS-SVM, in which the median value of regression error is selected as a criterion to compute weighted value.4. In order to further improve the robustness of WLS-SVM, a new robust LS-SVM algorithm based on M-estimator (MLS-SVM) is proposed. The residual in M-estimator firstly replaces the least squares residual in the LS-SVM objective function; then an iterative algorithm is used to solve the improved optimization problem. The MLS-SVM is applied to an infrared spectral analysis example. The result shows that MLS-SVM is more robust and accurate than WLS-SVM and other traditional SVMs; besides, the computation time of MLS-SVM is close to that of LS-SVM, which means MLS-SVM can be used in online analysis.5. A generalized LS-SVM (GLS-SVM) is proposed, in which a general decreasing residual even function is used to replace the sum of residuals squares in LS-SVM objective function. An iterative algorithm is proposed to solve the corresponding optimization problem, in which only a weighted function of the residuals is required to construct. Some typical weighted functions are also proposed. GLS-SVM is applied in the NIR spectral analysis of tobacco properties. Experimental results show its advantages on both robustness and accuracy when a proper weighted function is chosen.Finally, conclusions and future issues about robust regression are illustrated.