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2015 | Buch

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Statistics for Chemical and Process Engineers

A Modern Approach

verfasst von: Yuri A.W. Shardt

Verlag: Springer International Publishing

Enthalten in: Springer Professional "Wirtschaft+Technik" , Springer Professional "Technik" , Springer Professional "Wirtschaft"

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Über dieses Buch

A coherent, concise and comprehensive course in the statistics needed for a modern career in chemical engineering; covers all of the concepts required for the American Fundamentals of Engineering examination.

This book shows the reader how to develop and test models, design experiments and analyse data in ways easily applicable through readily available software tools like MS Excel® and MATLAB®. Generalized methods that can be applied irrespective of the tool at hand are a key feature of the text.

The reader is given a detailed framework for statistical procedures covering:

· data visualization;

· probability;

· linear and nonlinear regression;

· experimental design (including factorial and fractional factorial designs); and

· dynamic process identification.

Main concepts are illustrated with chemical- and process-engineering-relevant examples that can also serve as the bases for checking any subsequent real implementations. Questions are provided (with solutions available for instructors) to confirm the correct use of numerical techniques, and templates for use in MS Excel and MATLAB can also be downloaded from extras.springer.com.

With its integrative approach to system identification, regression and statistical theory, Statistics for Chemical and Process Engineers provides an excellent means of revision and self-study for chemical and process engineers working in experimental analysis and design in petrochemicals, ceramics, oil and gas, automotive and similar industries and invaluable instruction to advanced undergraduate and graduate students looking to begin a career in the process industries.

Inhaltsverzeichnis

Frontmatter

Chapter 1. Introduction to Statistics and Data Visualisation

Abstract

This chapter introduces the reader to the fundamentals of descriptive statistics and data visualisation. Descriptive statistics focus on the development of methods for describing a given data set. They can be divided into two main groups: measures of central tendency, which examine the average behaviour of the data set, and measures of dispersion, which examine the spread of the data set. Measures of central tendency, such as the mean, mode, and median, are introduced, while measures of dispersion considered include the range, standard deviation, variance, median absolute difference, and skew. Also, quantiles and outliers are introduced as ways to describe a data set. Data visualisation focuses on developing a set of rules for effectively displaying data visually. Common data visualisation methods such as bar charts, histograms, pie charts, line charts, time series plots, box-and-whisker plots, scatter plots, probability plots, tables, and sparkplots are explained with detailed examples and methods of construction. The different approaches are illustrated with suitable examples, including a comprehensive analysis of a data set from a friction factor experiment. By the end of this chapter, the reader should be able to apply the principles of data description and visualisation to meaningfully portray the key properties of a given data set.

Yuri A. W. Shardt

Chapter 2. Theoretical Foundation for Statistical Analysis

Abstract

This chapter introduces the reader to the theoretical foundations of statistical analysis by presenting a rigorous, multivariate, set-based approach to probability and statistical theory. The foundation is laid with consideration of the key statistical axioms and definitions, which formalise many of the concepts introduced in Chapter 1. Probability density functions, sample space, moments, the expectation operator, and various marginal functions are examined. Next, the most common statistical distributions, including the normal, Student’s t-, χ²-, F-, binomial, and Poisson distributions, are described by providing their key mathematical properties and computational implementation. Using these ideas, the subject of parameter estimation, that is, determining unknown values given a data set and an assumed model, is considered. Key topics include method of moments estimation, likelihood estimation, and regression estimation. Finally, the ability to compare two statistical variables using hypothesis testing and confidence intervals is introduced for many different commonly encountered cases, including means, variances, ratios, and paired values. Detailed examples are provided for all of the key concepts using simple, but relevant, examples. By the end of the chapter, the reader should have a strong understanding of the mathematical framework of statistics. As well, the ability to estimate parameters for a given situation and conduct appropriate hypothesis testing should be understood.

Yuri A. W. Shardt

Chapter 3. Regression

Abstract

This chapter introduces the reader to the concepts of data modelling using least-squares, regression analysis through a simplified framework consisting of three iterative steps, model selection, parameter estimation, and model validation, which forms the foundation for all subsequent chapters. Model selection focuses on selecting an appropriate description of the data set given both physical and mathematical constraints. This chapter focuses on deterministic models, while subsequent chapters focus on stochastic or more complex models. Parameter estimations seeks to determine the values of the parameter for the given model and data set. Different approaches, including ordinary, linear regression; weighted, linear regression; and nonlinear regression, are examined in detail. Theoretical results are provided as necessary to illustrate the need for some of the components of the analysis. Also, detailed summaries listing all the required formulae are provided after each section. Finally, model validation, which consists of two components, residual testing and model adequacy testing, is explained in detail. Suggestions for corrective actions are also provided for commonly encountered issues in model validation. Detailed examples are provided to illustrate the different methods and approaches. By the end of the chapter, the reader should be familiar with the regression analysis framework and be able to apply it to complex, real-life examples.

Yuri A. W. Shardt

Chapter 4. Design of Experiments

Abstract

This chapter presents the framework for the design and analysis of experiments. First, the general principles of design, including confounding, signal-to-noise ratio, randomisation, and blocking, are considered. Next, the commonly encountered factorial and fractional factorial designs are analysed in detail. Both analysis and design of such experiments, including the topics of model determination, replicates, confounding patterns, and resolution, are explored. Appropriate methods, including the development of orthogonal and orthonormal bases, for the analysis of such experiments using computers are presented. Although the results focus on 2-factorial design, higher-order design experiments are also considered, and the procedure for their analysis is explained. Detailed examples and cases are given. Third, methods for analysis of curvature, or quadratic terms, in a model are examined using factorial design with centre point replicates. Finally, the idea behind response surface methodologies, such as central composite design and optimal design, is briefly explored. Examples drawn from a wide range of different examples are considered. By the end of this chapter, the reader should be able to design and analyse factorial and fractional factorial experiments and curvature experiments and perform basic response surface methodologies using appropriate computational assistance.

Yuri A. W. Shardt

Chapter 5. Modelling Stochastic Processes with Time Series Analysis

Abstract

This chapter introduces the reader to the concept of time series analysis using transfer functions, state-space models, and spectral decomposition. Time series analysis is used to develop stochastic, or probabilistic, models. First, the theoretical properties of different model types, including standard autoregressive moving-average models, integrating models, and seasonal models, are examined and compared in both the time and frequency domains. The results obtained here can then be used to determine the appropriate model structure for a given data set. Spectral methods are also introduced at this point to assist in explaining various seasonal or periodic components in the data set. Next, the topic of parameter estimation is considered, and results are obtained for different methods and approaches, including the Yule–Walker for autoregressive models, the log-likelihood method for generalised autoregressive moving-average models, and the Kalman filter for state-space models. Finally, appropriate model validation methods are presented for time series analysis. Throughout this chapter, the Edmonton temperature data series is used to illustrate the concepts involved in time series analysis. By the end of the chapter, the reader should have a thorough understanding of the principles of time series analysis, including model structure determination, parameter estimation, and model validation.

Yuri A. W. Shardt

Chapter 6. Modelling Dynamic Processes Using System Identification Methods

Abstract

This chapter introduces the reader to the topic of system identification. System identification seeks to develop a generalised framework for the development of deterministic and stochastic models for complex chemical processes for application to control. First, the most common linear models, including the prediction error model with its simplifications and the impulse response model, are examined theoretically. Next, the prediction error method is developed for open-loop system identification. It is shown that the method provides unbiased and consistent parameter estimates. Furthermore, model validation is presented for open-loop models to assess not only the standard regression results but also such concepts as linearity, time delay, and time invariance. Then, the open-loop approach is extended to closed-loop system identification, and appropriate changes in the estimation and validation approaches are noted. Three different methods are considered: indirect, direct, and joint closed-loop identification. Finally, nonlinear system identification is briefly introduced and examined. All examples in this chapter are drawn from a single experiment to determine the water level in a four-tank system. By the end of the chapter, the reader should have a good understanding of the theoretical underpinning of system identification and be able to apply its results to develop complex models for industrial applications.

Yuri A. W. Shardt

Chapter 7. Using MATLAB® for Statistical Analysis

Abstract

This chapter introduces the reader to the application of MATLAB^® to solving statistical problems. Appropriate MATLAB functions for visualising data, performing regression analysis, design and analysis of experiments, time series analysis, and system identification are presented drawn from the available toolboxes, including the statistical, system identification, and econometric toolboxes. MATLAB code that can create periodograms, autocorrelation plots, correlation plots, and cross-correlation plots is provided. Three detailed examples, covering linear regression, nonlinear regression, and system identification are presented to provide the reader with appropriate code and an approach to these problems in MATLAB. By the end of this chapter, the reader should be comfortable in using MATLAB to solve any of the problems presented in this book and be able to prepare properly labelled figures.

Yuri A. W. Shardt

Chapter 8. Using Excel® to Do Statistical Analysis

Abstract

This chapter introduces the reader to the application of Excel^® to solving statistical problems with an emphasis on regression. Required Excel functions are described, including array functions that allow for the manipulation of matrices in Excel. Writing your own Excel code to extend its functionality and the resulting issues from Excel security are also considered. Finally, the Data Analysis and Solver add-ins are described in detail. Ready-to-use Excel templates are provided for constructing normal probability plots, box-and-whisker plots, and periodograms, as well as linear regression, nonlinear regression, and factorial design analysis. This chapter concludes with three examples: one focusing on linear regression and one on nonlinear regression, and the last one is a collection of factorial design experiments solved using the factorial design template. By the end of this chapter, the reader should be comfortable in using Excel to perform linear regression and factorial design for any level of problem complexity. The reader should also be able to use the appropriate templates and functions to speed up the analysis of a given data set.

Yuri A. W. Shardt

Backmatter

Titel: Statistics for Chemical and Process Engineers
verfasst von: Yuri A.W. Shardt
Verlag: Springer International Publishing
Electronic ISBN: 978-3-319-21509-9
Print ISBN: 978-3-319-21508-2
DOI: https://doi.org/10.1007/978-3-319-21509-9