Direct calibration model

A solvent free, fast and environmentally friendly near infrared-based methodology was developed for the determination and quality control of 11 pesticides in commercially available formulations. This methodology was based on the direct measurement of the diffuse reflectance spectra of solid samples inside glass vials and a multivariate calibration model to determine the active principle concentration in agrochemicals. The proposed PLS model was made using 11 known commercial and 22 doped samples (11 under and 11 over dosed) for calibration and 22 different formulations as the validation set. For Buprofezin, Chlorsulfuron, Cyromazine, Daminozide, Diuron and Iprodione determination, the information in the spectral range between 1618 and 2630 nm of the reflectance spectra was employed. On the other hand, for Bensulfuron, Fenoxycarb, Metalaxyl, Procymidone and Tricyclazole determination, the first order derivative spectra in the range between 1618 and 2630 nm was used. In both cases, a linear remove correction was applied. Mean accuracy errors between 0.5 and 3.1% were obtained for the validation set. 

In the direct standardization introduced by Wang et al. [42] one finds the transformation needed to transfer spectra from the child instrument to the parent instrument using a multivariate calibration model for the transformation matrix = ZgF. The transformation matrix F (qxq) translates spectra Zg that are actually measured on the child instrument B into spectra Z that appear as if they were measured on instrument A. Predictions are then obtained by applying the old calibration model to these simulated spectra Z ... 

In contrast to MLR, CLS is a direct calibration method that was designed specifically for use with spectroscopic data, and whose model formula is a reflection of the classical expression of the Beer-Lambert Law for a system with mnltiple analytes ... 

Although the CLS model can be considered rather rigid and limited in its scope of application, its advantages can be considerable in cases where it is applicable. Furthermore, recent work [47-51] has shown that extensions of the CLS model can reduce some of this rigidity , thus enabling the power of direct calibration methods to be applied to a wider scope of practical applications. Such extensions of CLS will be discussed in the following section. 

Standardizing the spectral response is mathematically more complex than standardizing the calibration models but provides better results as it allows slight spectral differences - the most common between very similar instruments - to be corrected via simple calculations. More marked differences can be accommodated with more complex and specific algorithms. This approach compares spectra recorded on different instruments, which are used to derive a mathematical equation, allowing their spectral response to be mutually correlated. The equation is then used to correct the new spectra recorded on the slave, which are thus made more similar to those obtained with the master. The simplest methods used in this context are of the univariate type, which correlate each wavelength in two spectra in a direct, simple manner. These methods, however, are only effective with very simple spectral differences. On the other hand, multivariate methods allow the construction of matrices correlating bodies of spectra recorded on different instruments for the above-described purpose. The most frequent choice in this context is piecewise direct standardization... 

Experience in this laboratory has shown that even with careful attention to detail, determination of coal mineralogy by classical least-squares analysis of FTIR data may have several limitations. Factor analysis and related techniques have the potential to remove or lessen some of these limitations. Calibration models based on partial least-squares or principal component regression may allow prediction of useful properties or empirical behavior directly from FTIR spectra of low-temperature ashes. Wider application of these techniques to coal mineralogical studies is recommended. 

In most cases, extensive overlap between spectral features associated with the analyte and individual matrix components precludes straightforward interpretation of the regression vector. Even with extensive spectral overlap, however, it is possible to determine the net analyte signal directly from the in vivo matrix and then compare this net analyte signal to the regression vector as direct evidence of analyte-specific information within the calibration model.40... 

The cost of the experiment (in this case preparation and analysis of 8 model solutions) is only slightly increased in comparison with the cost of direct calibration, so the described procedure can be used for routine water analysis. 

The equations for compound quantitation are shown in Appendix 22. Most of these equations apply to linear calibration models that rely on average response (calibration) factor for compound quantitation. Calibrations that use linear regression and non-linear polynomial equations read compound concentrations in the analyzed sample aliquot directly from the calibration curve. Once this concentration has been obtained, the final sample concentration can be calculated using the same rationale as for the linear concentration model. 

The goal of methods that standardize instrument response is to find a function that maps the response of the secondary instrument to match the response of the primary instrument. This concept is used in the statistical analysis procedure known as Procrustes analysis [97], One such method for standardizing instrument response is the piecewise direct standardization (PDS) method, first described in 1991 [98,100], PDS was designed to compensate for mismatches between spectroscopic instruments due to small differences in optical alignment, gratings, light sources, detectors, etc. The method has been demonstrated to work well in many NIR assays where PCR or PLS calibration models are used with a small number of factors. 

As previously noted, in a typical process analytical application, the measured data set might consist of spectral data recorded at a number of wavelengths much higher than the number of samples. The rank, R, of the measured matrix of spectra will be equal to or smaller than the number of the samples N. This causes rank deficiency in X, and the direct calculation of a regression or calibration model by use of the matrix inverse using Equation 8.85 and Equation 8.86 is problematic. 

To conduct a search for the E-optimal design directly to the NIR data, we need a methodology that is robust with respect to correlation between the variables (wavelengths). As previously noted, by using the principal component scores, it is possible to use the E-optimal approach to reduce the number of samples and minimize the number of time-consuming GC measurements while also improving the quality of the calibration model. 

There are different approaches to implementing the feedback concentration control for the direct design. Various schemes to implement the concentration control for direct design are described in the literature for cooling and antisolvent crystallizations. " The basic steps are as follows (i) the solution concentration is estimated from IR absorbances and temperature or solvent-antisolvent ratio using the calibration model that relates IR spectra to concentration and (ii) the temperature or antisolvent flow rate setpoint is calculated from the concentration, solubility curve, and the user-specified supersaturation setpoint. 

As direct spectral interpretation is limited in NIR spectroscopy, multivariate mathematical methods are used to obtain useful information. These techniques are used to develop mathematical models that correlate spectral features to properties of interest. For quantitative work, calibration models are needed that relate the concentration of a sample-analyte to spectral data. Information on developing calibration models and data analysis is provided elsewhere [128-132]. 

Linear calibration model Equation for the instrumental response which is directly proportional to the concentration (of the form y = a + bx). (Section 5.3)... 

The more common approach for sensor array calibration uses the direct regression model where the independent variables are the analyte concentrations and the dependent variables are the sensor responses. 

ILS methods (also known as P-matrix methods) differ in that the data are empirically modelled without using a direct physical model. These calibration methods are not restricted to the use of the same number of components as the individual components present in the spectral region being analysed. 

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