TAILIEUCHUNG - Modeling of Combustion Systems A Practical Approach 12

Tham khảo tài liệu 'modeling of combustion systems a practical approach 12', kỹ thuật - công nghệ, cơ khí - chế tạo máy phục vụ nhu cầu học tập, nghiên cứu và làm việc hiệu quả | 4_ Analysis of Nonideal Data Chapter Overview In this chapter we show how to obtain information from less than ideal data. Thus far we have studied statistically cognizant experimental designs yielding balanced symmetrical data with ideal statistical properties. Statistical experimental design SED has great advantages and whenever we have an opportunity to use SED we should. However there will be many occasions when the data we receive are historical or from plant operating history or other nonideal sources with much less desirable statistical properties. But even poorly designed or nondesigned experiments usually contain recoverable information. On rarer occasions we may not be able to draw firm conclusions but even this is preferable to concluding falsehoods unawares. We begin our analysis with plant data. With the advent of the distributed control systems DCSs plant data are ubiquitous. However they almost certainly suffer from maladies that lead to correlated rather than independent errors. Also bias due to an improper experimental design or model can lead to nonrandom errors. In such cases a mechanical application of ANOVA and statistical tests will mislead F ratios will be incorrect coefficients will be biased. Since furnaces behave as integrators we look briefly at some features of moving average processes and lag plots for serial correlation as well as other residuals plots. The chapter shows how to orthogonalize certain kinds of data sets using source and target matrices and more importantly eigenvalues and eigenvectors. Additionally we discuss canonical forms for interpreting multidimensional data and overview a variety of helpful statistics to flag troubles. Such statistics include the coefficient of determination r2 the adjusted coefficient of determination rA2 the prediction sum of squares PRESS statistic and a derivative rP2 and variance inflation factors VIFs for multicollinear data. We also introduce the hat .

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