Load spectra

In the polyethylene example, the first and second PC loadings spectra are shown in Figure 8.30. Note that these loadings spectra, unlike conventional spectra, have both positive and negative peaks and seem rather cryptic to interpret. This is mainly due to two factors ... 

Figure 8.30 Loadings spectra of the first (solid line) and second (dotted line) rotated PCs obtained from PCA analysis of the NIR spectra of HDPE/LDPE blend films shown in Figure 8.27.

Figure 4.3 Left - 10 three-component spectra having a single Gaussian band for each component. Right - First four loading spectra produced from 20 two-component spectra.

The SIMPLISMA method was recently modified so that principal components (loading spectra) could be used instead of the original spectra.16,17 The modified method referred to as interactive principal component analysis (IPCA) consolidates the spectral information into few loadings and reduces the overall noise. It makes it somewhat easier to deal with noise in regions that lack absorptions. Otherwise, SIMPLISMA and IPCA produce very similar results. 

Figure 8.4 Principal component loading spectra and corresponding score images representative of starch, oil and water components on two different flavored chips.

Since the rows of L and the columns of L are orthonormal, the product (L L) = I (Identity Matrix). Thus the scores in each row of the S matrix are the dot products of the corresponding original spectrum in the R matrix with each of the loading spectra in the L matrix. The dot product is the sum over all frequencies of the products of intensities for two spectra. 

Figure 5-8 Left Raman spectra of synthetic mixtures of GA in water. Right, top First two principal component (loading) spectra from PCA. Right, bottom Raman spectra of pure components.

Going from the CU/HT923 to the CU/HT1173 sample, the bands due to chemisorbed CO exhibited a smaller half-width, evidencing a lower dispersion of the metal phase, in agreement with the decreased specific surface area of the support. At variance, the effect of the pre-calcination temperature of the support could not be evidenced in the case of Pt/HT samples, possibly due to the low Pt loading (spectra not reported). 

If the stress amplitude is constant and Paris equation (Equation (7.15)) is valid, i.e. f(AK) = C (AK) , Equation (7.18) can be integrated analytically. With other load spectra and deviation from Paris equation, a numerical integration is necessary. 

Residual stiffness degradation models have proved capable of estimating the cumulative damage in composite laminates under constant amplitude loading. In a recent publication Lee et al. [51] extended such a model, so that service load spectra could also be predicted. 

L J Lee, K E Fu and J N Young, Prediction of fatigue damage and life for composite laminates under service loading spectra . Compos Sci Technol 1996 56 635-648. 

The study had three objectives first, changes in NIR spectra were correlated to the time aspirin tablets spent in the hydrator (the calibration had a correlation coefficient of 0.95 and SEE of 18.8 h) second, a calibration was developed for the prediction of tablet salicylic acid content (the researchers ensured that prediction of salicylic acid was based on changes in salicylic acid concentration, and not some related process, such as absorption of moisture, by evaluation of loadings spectra from principal component analysis of the data. The HPLC-determined salicylic acid levels ranged from 0.36 to 1.66 mg, and the NIR method allowed prediction of the degradant with a standard error of 144 mg) and third, the mass of water absorbed by the tablets was determined by NIR spectroscopy. 

The second level of capability is introduced through Zencrack Professional and provides a facility for 3D non-planar crack growth prediction for cases of fatigue and time-dependent loading. This includes several options for crack growth data definition and a flexible load system approach for defining complex load spectra. 

The data set is broken down into loadings, which are analogous to abstract spectra, and scores, which describe the amount of each loading associated with each sample and are similar to abstract concentrations. Some of the loading spectra will describe noise or minor components and will not be relevant to the model and can be rejected. Determining which principal components can be rejected affects the robustness of the model. 

Fig. 8.9 Different types of load spectra (modified from [2])...

---