Examining the Data

When data from a process or experiment are used for the development of a black box model, it first has to undergo a thorough examination. Much attention should be given to the data set, because it will determine how the final model will look like. Erroneous data could lead to a model that has poor prediction capability and bad generalization properties. Therefore the data set has to meet the following conditions  

This means that the data set needs to be examined carefully and calculations should be made for suspicious data points that might be the result of bad measurements. This is explained further in the following sections. 

To ensure that the data in the set gives an accurate representation of the process, the entire set has to be examined. This examination has to be made in person, because no software is available to achieve this. The data set should comply with the following guidehnes  

The entire range of values that the process measmement can assnme, should be present within the data set. Although some black box models have reasonable generalization ca-pabihties, no risk should be taken. The maximum as well as the minimum values of the process measurements should be present, together with a wide variety of other process states. 

Process Dynamics and Control Modeling for Control and Prediction. Brian Roffel and Ben Betlem. 

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This prediction can be tested by examining the data given in Table 37 for the equilibrium... 

Numerical simulations. Locate one research publication that makes use of the kinsim program, by tracing Ref. 30 in Science Citation Index. Examine the data to check the match between experiment and model. In particular, study the differences between the results and those expected for a simpler kinetic system to ascertain why the complex treatment was needed. Report on how well the proposed model accounts for the complications. 

The kinetic information is obtained by monitoring over time a property, such as absorbance or conductivity, that can be related to the incremental change in concentration. The experiment is designed so that the shift from one equilibrium position to another is not very large. On the one hand, the small size of the concentration adjustment requires sensitive detection. On the other, it produces a significant simplification in the mathematics, in that the re-equilibration of a single-step reaction will follow first-order kinetics regardless of the form of the kinetic equation. We shall shortly examine the data workup for this and for more complex kinetic schemes. 

To understand the mechanism of flame quenching in narrow channels in detail, one should first examine the data of flames in mixtures of constant composition, but in charmels of different sizes (Figure 6.1.2). The measured propagation velocities in stoichiometric propane/ air mixture are shown in Figure 6.1.2a. For channel widths slightly larger than the quenching distance, the... 

Simplifying, 1.0 = (10) how can this be We can treat this mathematically, but examining the data also gives the result. Changing the concentration of NO2 F has no effect on the initial rate, so the rate is independent of [NO2 F]. This means that [NO2 F] does not appear in the rate law. Mathematically, we set Z = 0. The reaction is zero order in NO2 F, and the rate law is as follows ... 

Some data from corrosion-monitoring probes do not measure corrosion rate, but rather give other useful information about the system. For example, suppose conditions change dramatically during a process upset. An ejq)erienced corrosion engineer can examine the data and correlate it with the upset conditions. Such analysis can provide insight into the process and help to improve performance and extend equipment lifetime. Changes in simple parameters such as pH, ion content, and temperature may lead to detection of a process upset. Without careful analysis, process upsets can reduce the corrosion lifetime of equipment and even cause a system failure. 

We examined the data in a number of ways. One was to use the classification system established by the APA to categorize levels of depression. The APA system, which was also adopted by NICE, divides scores on the Hamilton depression scale into the following five categories ... 

In the next chapter I examine the data behind the chemical-imbalance theory. Others have argued that these data provide only weak support for this conventional view.381 go a step further. I do not think the data are weak at all. They are in fact rather strong. But rather than supporting the chemical-imbalance theory of depression, they contradict it. It now seems beyond question that the traditional account of depression as a chemical imbalance in the brain is simply wrong. 

Upon examining the data for the reactions of all four butene isomers (Fig. 37), the most striking observation is that the data for all four isomers are quite similar, except that there is no YH2 formed from isobutene. In addition, the branching ratios for each isomer are similar, except that 4>ych2 OyCiHe, is approximately a factor of two greater for isobutene than for the other isomers, and for propene, YCH2 is a much more important channel than is YH2 (Fig. 40), a situation that is exactly the opposite to that for the butene reactions (Fig. 37). 

To obtain more information on this point, let us examine the data given in Table 3.6<42-47> for some substituted benzophenones. The data in Table 3.6 indicate that benzophenone derivatives having lowest triplet states of n->TT character undergo very efficient photoreduction in isopropyl alcohol. Those derivatives having a lowest it- -it triplet, on the other hand, are only poorly photoreduced, while those having lowest triplets of the charge-transfer type are the least reactive toward photoreduction. In additon, in some cases photoreduction is more efficient in the nonpolar solvent cyclohexane than in isopropanol. This arises from the solvent effect on the transition energies for -> , ir- , and CT transitions discussed in Chapter 1 (see also Table 3.7). 

I know of no experienced practitioner of chemometrics who would blindly use the full spectrum when applying PLS or PCR. In the book Chemometrics by Beebe, Pell and Seasholtz, the first step they suggest is to examine the data. Likewise, Kramer in his new book has two essential conditions The data must have information content and the information in the data must have some relationship with the property or properties which we are trying to predict. Likewise, in the course I teach at Union Carbide, I begin by saying that no modeling technique, no matter how complex, can produce good predictions from bad data. ... 

Even experienced practitioners can be misled, however. As was pointed out, real data contains various types and amounts of variations in both the X and Y variables. Furthermore, in the usual case, neither the constituent values nor the optical readings are spaced at nice, even, uniform intervals. Under such circumstances, it is extremely difficult to pick out the various effects that are operative at the different wavelengths, and even when the data analyst does examine the data, it may not always be clear which phenomena are affecting the spectra at each particular wavelength. 

Let us examine the data of the third measurement on the metallized wafer. There are two contributions to the heat capacity, a linear contribution and a spurious one. The spurious contribution may be interpreted as the high temperature side of a Schottky anomaly. In this hypothesis, the heat capacity per unit volume of the metallized wafer may be... 

We have discussed individual analyses and the demands to achieve optimization of instrumentation. However, an analytical laboratory must deal with series of samples and we must consider another factor if we want to optimize complete workflows cycle time optimization. Cycle time is defined as the time from finishing the analysis of one sample to the time the next sample is finished. This can be easily determined on Microsoft Windows -based operating systems by examining the data file creation time stamps of two consecutive samples. A better way is calculating the average of a reasonable number of samples. 

Next examine the data for U versus wt in the context of Figure 2.6. For a reasonable range of wt the pattern is similar to curve D in Equation (3) where... 

Positive Slope The mL and mole ratio for equivalency is 4 NaClO to 1 Na2S203 (see 1 above). In examining the data table, it can be seen that the Na2S203 is in excess, with the NaClO being the limiting reactant for example, in Trial 7, for 30 mL of 0.500 M NaClO,... 

Negative Slope In examining the data table, it can be seen that the NaCIO is in excess and that the Na2S203 is the limiting reactant. 

Many studies on the modelling of esterification, melt polycondensation, or solid-state polycondensation refer to the reaction scheme and kinetic data published by Ravindranath and co-workers. Therefore, we will examine the data sources they have used over the years. The first paper concerned with reactor modelling of PET production was published by Ravindranath el al. in 1981 [88], The reaction scheme was taken from Ank and Mellichamps [89] and from Dijkman and Duvekot [90], The kinetics for DEG formation are based on data published by Hovenkamp and Munting [60], while the kinetics for esterification were deduced... 

Examining the data used to create Fig. 6 in comparison with known experimental values, we conclude that ... 

More subtle factors that might affect k will be the sites structures, their relative orientation and the nature of the intervening medium. That these are important is obvious if one examines the data for the two copper proteins plastocyanin and azurin. Despite very similar separation of the redox sites and the driving force (Table 5.12), the electron transfer rate constant within plastocyanin is very much the lesser (it may be zero). See Prob. 16. In striking contrast, small oxidants are able to attach to surface patches on plastocyanin which are more favorably disposed with respect to electron transfer to and from the Cu, which is about 14 A distant. It can be assessed that internal electron transfer rate constants are =30s for Co(phen)3+, >5 x 10 s for Ru(NH3)jimid and 3.0 x 10 s for Ru(bpy)3 , Refs. 119 and 129. In the last case the excited state Ru(bpy)3 is believed to bind about 10-12 A from the Cu center. Electron transfer occurs both from this remote site as well as by attack of Ru(bpy)j+ adjacent to the Cu site. At high protein concentration, electron transfer occurs solely through the remote pathway. 

The results obtained with NaCl at 25°C and with KCl at 25°, 35° and 45°C in Eastman Kodak 398-3 cellulose acetate are listed in Table I. When examining the data it should be remembered that the fixed charge capacity measured here is that effective in electro-kinetic properties of the membrane it is not a quantity of analytical chemistry. Nevertheless, because NaCl and KCl are very similar in their electrochemical properties, one would expect the apparent number of moles of fixed charges per unit mass of dry... 

For the SIMCA analyses, the individual PCB isomer concentrations were normalized to sum 100. We examined the data by using the SIMCA-3B program to calculate principal components and to plot sample scores in a manner identical to that discussed for the Aroclor mixtures. The plot of sample data illustrates that the geographic locations have different residue profiles (Figure 5). 

The result of the paradox is that many useful observations remain uninterpreted. Pattern recognition techniques have been used to enhance the interpretation of large data bases. This paper describes how these techniques were used to examine a large water quality monitoring data base. The paper describes how pattern recognition techniques were used to examine the data quality, identify outliers, and describe underground water chemistries. 

Environmental studies are often characterized by large numbers of variables measured on many samples. When poor understanding of the system exists one tends to rely upon the "measure everything and hope that the obvious will appear" approach. The problem is that in complex chemical systems significant patterns in the data are not always obvious when one examines the data one variable at a time. Interactions among the measured chemical variables tend to dominate the data and this useful information is not extracted by univariate approaches. 

The two pattern recognition techniques used In this work are among those usually used for unsupervised learning. The results will be examined for the clusters which arise from the analysis of the data. On the other hand, the number of classes and a rule for assigning compounds to each had already been determined by the requirements of the mixture analysis problem. One might suppose that a supervised approach would be more suitable. In our case, this Is not so because our aim Is not to develop a classifier. Instead, we wish to examine the data base of FTIR spectra and the metric to see If they are adequate to help solve a more difficult problem, that of analyzing complex mixtures by class. 

An objective description of results allows readers to examine the data unbiased by interpretation. Results are sometimes viewed as a glimpse at the truth alternatively, interpretations are educated opinions that are likely to change over... 

Dendi ogrmi Without Class Labels (Sample Diagnostic) Even if class information iSJEffailable, it is advisable to examine the data first without the class labels to redme bias in the interpretation. The dendrogram for this example is shown in Fi c 4.15- The sample identities (indicated for now by X) are listed on the left-hmd side of the graph, and the vertical lines indicate which samples constiti a cluster. 

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