Christer Albano

Multivariate Data Analysis in Chemistry

Any data table produced in a chemical investigation can be analysed by bilinear projection methods, i. e. principal components and factor analysis and their extensions. Representing the table rows (objects) as points in a p-dimensional space, these methods project the point swarm of the data set or parts of it down on a F-dimensional subspace (plane or hyperplane). Different questions put to the data table correspond to different projections.

Four levels of pattern recognition

Abstract Problems of pattern recognition in chemistry and other subjects can be divided conveniently into four different types depending on the level of scope of the problem. (1) Classification into one of a number of defined classes. As an example blood samples taken from persons known to be either controls or welders are considered. The problem is whether trace element concentrations in these samples contain information on whether or not a person is a welder. (2) Level 1 plus the possibility that an object is an outlier, i.e. does not belong to any of the defined classes. As an example, the use of 13C-n.m.r. data to decide whether 2-substituted norbornanes have the exo or endo structure is discussed. (2A) Level 2, asymmetric. This situation occurs when one class does not have a systematic structure, but another class is homogeneous and can be described by a level 2 model. This occurs in the classification of materials or compounds as good or bad, active or inactive, and in binary classifications. As an example the use of trace element data to classify steel samples as having good or poor properties of strength is discussed. (3) Level 2 plus the ability to relate the variables measured to external properties of continuous character. As an example, the classification of a series of chemical compounds as β -receptor blockers, β -receptor stimulants, or neither, on the basis of their structural variables is discussed. In addition, relations between these structural variables and the measured biological activity are sought within each of the two classes. (4) Level 3 with the difference that several external property variables in the objects are measured. It may be desirable to use variables of the objects both for classification and for relations to several property variables: such examples are numerous in analytical chemistry.

Multivariate process and quality monitoring applied to an electrolysis process. : Part II - Multivariate time-series analysis of lagged latent variables

Abstract Multivariate time series analysis is applied to understand and model the dynamics of an electrolytic process manufacturing copper. Here, eight metal impurities were measured, twice daily, over a period of one year, to characterize the quality of the copper. In the data analysis, these eight variables were summarized by means of principal component analysis (PCA). Two principal component (PC) scores were sufficient to well summarize the eight measured variables ( R 2 =0.67). Subsequently, the dynamics of these PC-scores (latent variables) were investigated using multivariate time series analysis, i.e., partial least squares (PLS) modelling of the lagged latent variables. Stochastic models of the auto-regressive moving average (ARMA) family were appropriate for both PC-scores. Hence, the dynamics of both scores make the exponentially weighted moving average (EWMA) control chart suitable for process monitoring.

Principal components analysis of complex n.m.r. spectra from heterogeneous material

Abstract Principal components (PC) analysis is applied to raw data profiles of solid state 13 C CP/MAS n.m.r. spectra of heterogeneous organic material. Information about various peat classes is obtained from component scores plots, where similar types of samples ( Carex or Sphagnum peat) group together. Substructures in these groups that correspond to directions of increased decomposition are found. Component loadings are used to estimate spectra from peat constituents e.g. bitumen/humic substances and carbohydrates are uncovered in the first two loadings. This may be a good method to use in combination with other techniques, such as deconvolution and synthesis of spectra.

Optimization of a mechanical peat dewatering process by using multivariate data analysis

Abstract A new experimental design (nearly orthogonal experimental design) was used for a dewatering study under laboratory conditions with two type of peats. This design was able to test more levels for each design variable with considerably fewer experiments than the usual factorial or fractional factorial designs. The process under study is dependent on many variables and instead of a mechanistic model, an empirical model based on multivariate data analysis was chosen. The way of expressing the relation is by regression coefficients obtained from partial least square regression. For accommodating the possibility of detecting and describing nonlinearities, the design variables were augmented with their square and interaction terms. User-friendly response surface methodology was used to study the relationship between the design and the response variables. Results presented are response surfaces for different response variables. Performing the experiments under the nearly orthogonal experimental design conditions and analysing the data by using a multivariate data analysis system, fundamental mechanisms underlying the mechanically peat dewatering process can be understood. The models generated using the PLS method predicted the outcome from new experiments within reasonable limits. With relatively few experiments, information can be collected to predict the results.

Determination of water content and calorific value of peat by near i.r. spectroscopy

Abstract Near infrared reflectance (n.i.r.) spectroscopy is used for the determination of water and calorific value in peat. Partial least squares modelling in latent variables (PLS) has been used to correlate n.i.r. spectra to water content and calorific value. Separate calibrations for water and calorific value have been compared with the simultaneous calibration for both properties. The result of the simultaneous calibration for water is better than the result obtained in the separate calibration. This indicates that the inclusion of an extra meaningful variable will stabilize the calibration.

Developing an empirical model for dewatering — And its application to peat

This paper contains two main topics: a strategy for finding optima in general experimentation and examples of using this strategy for the dewatering of peat. For optimising experimental conditions of industrial processes, the relation between design variables and response variables has been studied. For accommodating the possibility of detecting and describing nonlinearities, the design variables have been augmented with their square and interaction terms. Use is made of response surface methodology. The way of expressing the relation is by regression coefficients obtained from partial least square regression. The design uses more levels than the usual factorial or fractional factorial ones. This requires the use of almost-orthogonal designs in the designs variables (instead of the usual orthogonal ones) in order to limit the number of experiments. A computer program was developed to allow the construction of design with minimal correlation. The response surfaces were validated using extra experiments, and the results of this were satisfying, showing the validity of the surface obtained. The strategy was tried for dewatering of peat by filtration of a slurry followed by pressing the filter cake. Here, the traditional deterministic laws for filtration were replaced by an empirical approach resulting in parameters obtained from experiments.

CHARACTERIZATION AND CLASSIFICATION BASED ON MULTIVARIATE DATA ANALYSIS

Abstract The characterization of chemical or biological samples by multidimensional data followed by an appropriate data analysis provides a means for the quantitative classification of new samples. Data analytic problems and ways to solve them are discussed using two examples. The first concerns the classification of micro-organisms (fungi) on the basis of pyrolysis-gaschromatography data. The second concerns the determination of the chemical structure of organic compounds on the basis of C-13 NMR data.

Empirical modelling of a dewatering process using multivariate data analysis

Abstract A method is described for relating operating variables and dewatering parameters of Thunes disc filters, in the LKAB pelletizing plant at Malmberget in Sweden, via empirical mathematical models. Near orthogonal experimental design was used: all independent variables were allowed to span their domain of variation and pseudorandomly distributed among the experiments. The dewatering parameters are dependent on many variables and an empirical model based on multivariate data analysis was chosen rather than a traditional mechanistic model. The relationships are expressed by regression coefficients obtained from partial least square regression. Two empirical models were generated. The models were validated and parameters were related to design variables by experiment. Userfriendly response surface methodology was used to determine the optimal conditions.

Multivariate analysis of solvolysis kinetic data; an empirical classification paralleling charge delocalization in the transition state

A multivariate data analysis of solvolysis rate constants measured for a range of solvents of different ionization power provides a pattern parallel to the degree of charge delocalization in the transition state. In this way direct evidence is obtained for a difference in kinetic behaviour between exo- and endo-norbornyl solvolyses.