Quantitative modelling, chemometrics used

This section discusses common methods for building quantitative chemometric models in PAC. In this field, the user most often desires to build a model that converts values generated by an analytical instrument into values of properties or concentrations of interest for use in process control, quality control, industrial hygiene, safety, or other value-adding purposes. There are several chemometric techniques that can be used to build quantitative models, each of which has distinct advantages and disadvantages. 

As a chemometric quantitative modeling technique, ANN stands far apart from all of the regression methods mentioned previously, for several reasons. First of all, the model structure cannot be easily shown using a simple mathematical expression, but rather requires a map of the network architecture. A simplified example of a feed-forward neural network architecture is shown in Figure 8.17. Such a network structure basically consists of three layers, each of which represent a set of data values and possibly data processing instructions. The input layer contains the inputs to the model (11-14). 

Chemometrics uses multivariate, multidimensional data to generate product specific models. These models are the basis against which future data can be compared to allow both qualitative and quantitative predications to be made. 

For many applications, quantitative band shape analysis is difficult to apply. Bands may be numerous or may overlap, the optical transmission properties of the film or host matrix may distort features, and features may be indistinct. If one can prepare samples of known properties and collect the FTIR spectra, then it is possible to produce a calibration matrix that can be used to assist in predicting these properties in unknown samples. Statistical, chemometric techniques, such as PLS (partial least-squares) and PCR (principle components of regression), may be applied to this matrix. Chemometric methods permit much larger segments of the spectra to be comprehended in developing an analysis model than is usually the case for simple band shape analyses. 

Multivariate calibration has the aim to develop mathematical models (latent variables) for an optimal prediction of a property y from the variables xi,..., jcm. Most used method in chemometrics is partial least squares regression, PLS (Section 4.7). An important application is for instance the development of quantitative structure—property/activity relationships (QSPR/QSAR). 

As a result, it is very important to evaluate process samples in real time for their appropriateness of use with the empirical model. Historically, this task has been often overlooked. This is very unfortunate not only because it is relatively easy to do, but also because it can effectively prevent the misuse of quantitative results obtained from a multivariate model. I would go so far as to say that it is irresponsible to implement a chemometric model without prediction outlier detection. 

Thousands of chemical compounds have been identified in oils and fats, although only a few hundred are used in authentication. This means that each object (food sample) may have a unique position in an abstract n-dimensional hyperspace. A concept that is difficult to interpret by analysts as a data matrix exceeding three features already poses a problem. The art of extracting chemically relevant information from data produced in chemical experiments by means of statistical and mathematical tools is called chemometrics. It is an indirect approach to the study of the effects of multivariate factors (or variables) and hidden patterns in complex sets of data. Chemometrics is routinely used for (a) exploring patterns of association in data, and (b) preparing and using multivariate classification models. The arrival of chemometrics techniques has allowed the quantitative as well as qualitative analysis of multivariate data and, in consequence, it has allowed the analysis and modelling of many different types of experiments. 

The use of mathematical and statistical modeling methods to relate chemical data sets to the state of the chemical system is referred to as chemometrics. A key figure in the development of chemometrics and its application to industrial problems has been B.R. Kowalski [18, 147, 319] who led the Center for Process Analytical Chemistry (CPAC) that was established in 1984. To aid qualitative and quantitative analysis of chemical data, Eigenvector Technologies Inc., a developer of independent commercial software, has provided a number of software solutions, primarily as a Matlab Toolbox [328]. 

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