It is very important to acquire the proper instrument and sampling accessories as it directly affects the next stage involving NIR technology, which is calibration development. When using a NIR spectrometer, a large amount of time is initially spent turning the raw spectra into useful information. The ultimate goal is to be able to predict component concentrations in a matter of seconds or minutes, so the time spent performing wet chemical analysis of the calibration samples is well worth the effort.
THEORETICAL BASICS
When infrared radiation passes through a sample, some of the light is transmitted or reflected, without interacting with the molecules, and the remainder interacts with the molecules and is absorbed. The wavelengths at which the absorption will occur and how much light will be absorbed depend on a given substance. This is the basis of qualitative and quantitative analysis by spectroscopy, including NIR analysis. The amount of absorbed light is measured in absorbance. The absorbance, generally denoted as A, is defined as:
A = -log (Is/I0)
Where I0 is the light intensity before passing
through a sample
Is is the light intensity after passing
though the sample
Spectroscopic quantitative analysis is based on the Beer-Lambert law (also know as Beer’s law), which states that there is a linear relationship between the absorbance and concentration of absorbing molecules. Mathematically, Beer’s law can be written as:
A = ε C D
where A = Absorbance at a specific wavelength ε = absorption coefficient at a
given wavelength
C = concentration of absorbing molecules
D = pathlength
Since the pathlength D is often fixed, in practice the absorption coefficient and the pathlength are combined into one coefficient k. Equation (1) can be then simplified to:
A= kC (Equation 1)
Solid or slurry samples are often measured in diffuse reflectance mode, using the accessories shown in Figures 9 and 10. For reflectance measurements log (1/R) is used instead of absorbance, where R denotes reflectance. This is defined as:
log (1/R) = -log (Is/I0)
Where I0 is the light intensity measured from
a reference material
Is is the light intensity measured from
the sample
The reference material used in the NIR region is usually a material with uniform scattering properties and very little absorption over the entire NIR region. Two kinds of material are used
commercially. One is called Spectralon®, a
material made of a special type of Teflon®; the
other one is diffuse gold, a piece of metal with finely roughened surface coated with gold.
There are many theories regarding quantitative analysis in diffuse reflectance measurements. Empirically, log (1/R) is found to be fairly linear with the concentrations of chemical components in the NIR, hence,
log (1/R)= kC (Equation 2)
The similarities between equations 1 and 2 are apparent.
Quantitative analysis generally has two steps: calibration and prediction. During the calibration stage, NIR spectra of a set of samples will first be measured so that the absorbance values in
154 D. Livermore, Q. Wang and R.S. Jackson Equation (1) can be determined. The concen- trations of the chemical components can be analyzed with traditional lab methods such as wet chemical or HPLC methods. Once the absorbance values A and concentrations C are known, the values of the coefficients k can be determined by the least squares method. Once the coefficients are determined, the spectrometer is calibrated and ready to predict the concentrations of unknown samples. Equation 1 only works in a simple system where the absorption at a particular wavelength comes from only one component. Such a method is often called univariate calibration.
As described earlier, NIR spectra are highly overlapped, meaning that absorbance at a particular wavelength contains contributions from multiple chemical components in the sample. The univariate calibration can therefore rarely be applied to NIR applications. A more sophisticated multivariate analysis is usually required to build the calibration model. When multiple components are present, the total absorbance at a given wavelength is the summation of absorbances of each individual component. The absorbance at a given wavelength can then be expressed as follows:
A = ε1 C1 D + ε2 C2 D + …+ εn Cn D (2)
where
A = Total absorbance at a specific wavelength
ε1 = Absorption coefficient of component 1
C1 = Concentration of absorbing component 1
D = path length
ε2 = Absorption coefficient of component 2
C2 = Concentration of absorbing component 2
εn = Absorption coefficient of the n
th component
Cn = Concentration of absorbing component n
There are four multivariate methods used to build the calibration model, Classical Least Squares (CLS), Multiple Linear Regression (MLR), Principle Component Regression (PCR) and Partial Least Squares (PLS). How these methods work is beyond the scope of this chapter, but there are excellent review articles describing how all these methods work as well as the pros and cons of each (Haaland, 1988; Martens et al.,
1989). PLS is the most commonly used method for building multivariate quantitative models and is the method used in all data analysis presented in this chapter. This chapter will only deal with practical aspects of development of calibration models and how to interpret common terminology used in the PLS method.
CALIBRATION SAMPLE SET, NIR
MEASUREMENTS AND REFERENCE ANALYSIS
To build a quantitative calibration model using NIR data, the user must have a reference analysis method to determine the concentrations of the components of interest in a sample. The reference methods commonly used in QC laboratories in the distillery industry today are HPLC, GC, DMA and various wet chemical analyses. The accuracy and precision of a NIR calibration model is strongly affected by the quality of the reference analysis method. A few examples are given in the section of this chapter dealing with NIR applications in the distillery. The reference methods should be closely examined and understood so that the user does not have unrealistic expectations of NIR calibration models.
When building the calibration model, the reference analysis and NIR measurements should be performed as close to the same time as possible if samples are not stable. For example, live fermented mash samples taken from a fermentor are unstable. The longer a sample sits between the time of NIR measurement and the time of the reference measurement, the bigger the error to be expected.
Preferably, samples from production that span a period of time should be incorporated in the calibration model, with the goal of incorporating all possible variations in the production process. One must be cognizant of production parameters, and collect unique samples when they occur. For example, DDGS can vary in a whisky distillery with the many different mash bills, which can include grains such as rye, barley, wheat, and corn. The NIR user must recognize when different mash bills are being fermented and collect samples that do not occur very often and incorporate them into a calibration model. This means it may take an extended period of time to obtain a representative set of samples, but it is
important to do this because it makes a calibration model more robust, accurate, and precise. Another occasion when a user should incorporate unique samples is when processing equipment breaks down. Usually these are times when unique or extreme samples occur. For example, when a belt conveyer breaks while delivering corn to a pre-mix tank it can cause mash to be more dilute than usual. The user can collect the mash in these fermentors for analysis, collect the syrup in the evaporators, and collect the DDGS at the end, because the broken conveyer affects all of these processes. In that way, the next time the conveyer malfunctions the NIR user can quickly identify the source of the problem. To make the calibration model more robust, it is recommended that any odd samples be included at least three times in the calibration model (Williams and Norris, 2001). The calibration samples should also span the concentration range as smoothly as possible, avoiding large numbers of calibration samples at just a few concentrations. For example, refer to the calibration model for crude protein in DDGS in Figures 13a and Figure 13b. In Figure 13a there are not enough samples of DDGS with low (21 to 22%) and high crude protein (27 to 31%). To make a calibration model more robust and precise, the sample distribution should be similar to that of Figure 13b. This type of sample distribution, where samples are evenly distributed over the calibration set, is often described as a ‘boxcar’ effect (Williams, 2001). The calibration range should be larger than the specified range and not too small in view of the error of the reference method (EMEA 2003). If the required accuracy is greater than 0.1% by weight, generally it can be achieved with NIR. If the required accuracy is between 0.1 to 0.01% by weight, then the NIR application is likely to be feasible for a simple system with very few components, an accurate reference method, a wide enough concentration range, and a lot of samples. If the required accuracy is 0.01% wt to a few ppm, the application is unlikely to be feasible.
BUILDING CALIBRATION MODELS
After the calibration samples are collected, measured by a NIR spectrometer and analyzed
by the reference method, the user can then develop and validate the quantitative calibration models. Once the calibration model is validated, the user can finally enjoy the fruits of all this labor: the prediction of multiple parameters from a single NIR measurement in a matter of seconds to minutes. Validation is the key to the development of PLS models. Validation is used both to optimize many parameters during the development of the model, and to identify abnormal samples (outliers). There are two types of validation: cross validation and external validation or test-set validation.
External validation
External validation is sometimes referred to as test-set validation. The sample set used in external validation consists of samples with known reference data that were not used in the calibration set for the model development. The goal for the external validation is to test the predictive ability of the model. At the end of external validation, the NIR predicted values are compared with those from the reference method, often expressed in a plot of NIR predicted vs.
reference values. The value of R2 in this plot is
one of two important indicators for how good the model is. The other one is the Root Mean Square Error of Prediction (RMSEP), which is used as an indicator of the average error for NIR prediction on future unknown samples.
Cross validation
The advantage of external validation is that it is a true independent validation. The main disadvantage of external validation is that it wastes the valuable calibration data in order to check the predictive ability of the calibration models. When the number of available calibration samples is small, a procedure called cross validation is often used. In a cross validation, the first calibration sample is removed from the calibration set. PLS models are generated using the remaining calibration samples. The PLS models are then used to predict the first sample that is left out and the error of prediction for this sample is calculated. The first sample is then re-included into the calibration set and the next sample is removed from calibration. The whole process is repeated
156 D. Livermore, Q. Wang and R.S. Jackson
Crude protein in DDGS (%)
Number of samples
Non boxcar calibration model for protein in DDGS
20 21 22 23 24 25 26 27 28 29 30 31 0 1 2 3 4 5 6 7 8 9 10 11 Crude protein in DDGS (%) Number of samples
Boxcar calibration model for protein in DDGS
20 0 1 2 3 4 5 6 7 8 9 10 11 21 22 23 24 25 26 27 28 29 30 31
Figure 13a. A calibration set for protein prediction in DDGS.
Figure 13b. A calibration sample set for protein prediction in DDGS.
until the last sample is removed and analyzed. The number of samples left out can be just one sample or a small set of samples. At the end of cross validation, the Root Mean Squared Error of Cross Validation (RMSECV) is calculated and used as an indicator of the future predictive ability of the models.
Results of validation
As discussed earlier, the cross validation or
external validation result is often shown in a plot of NIR predicted values vs. reference method values. In an ideal situation, this plot should be
a 45o line, where the prediction should equal
the reference value. The closer the R2value is to
1 or 100%, the more accurate the model. Figures 14a and 14b show a PLS cross validation result and an external validation for prediction of ethanol concentrations in corn mash samples.
Errors exist in all measurements and cannot be avoided. It is important to identify the
Rank: 5 R2 = 99.86 RMSECV = 0.139 0 1 2 3 4 5 6 7 8 9 10 11 12 -1 0 1 2 3 4 5 6 7 8 9 10 11 12
Reference method value
NIR predicted value
Rank: 5 R2 = 99.86 RMSEP = 0.144 0 1 2 3 4 5 6 7 8 9 10 11 12 13 0 1 2 3 4 5 6 7 8 9 10 11 12 13
Reference method value
NIR predicted value
Figure 14a. Cross validation result for ethanol prediction in fermented corn mash samples. The values of R2 and RMSECV were 0.9986 and 0.139 % v/v, respectively. The number of samples in the calibration set is 111.
Figure 14b. External validation result for ethanol prediction in fermented corn mash samples. The values of R2 and RMSECV were 0.9986 and 0.144 % v/v, respectively. The number of samples in the validation set is 40.
accuracy that is needed for a plant to keep a process under control. For example in protein in DDGS, there is no need to strive for an error of 0.05% when an error of 0.5% is satisfactory for plant operations; however, a 0.05% error for determining alcohol strength in a finished blend can cost a company money in terms of ethanol losses and taxes.
How many samples in a calibration data set?
It is very important to include an adequate
number of samples in the calibration set. In general, one should incorporate as many as are available. Whether or not there are enough samples to build a stable calibration model can only be determined by performing validation tests with an independent validation set. As a rule of thumb, one should start with a minimum of 10 samples for each independent chemical component or other source of variation. ASTM provides guidelines that can be used to judge whether or not a calibration set contains sufficient samples (ASTM, 1997).
158 D. Livermore, Q. Wang and R.S. Jackson
Calibration model updating
When a calibration model is finished, it is good practice to check periodically to ensure the validity of the answers (Martens et al., 1989). The checks might be frequent when a calibration model is first used, but they will become more infrequent as the model becomes more robust over time. These routine checks are not only important in the maintenance of the calibration models, but also help build confidence in operators, technicians, and management, for whom NIR might be relatively new technology.