ASTM D8321-22

Standard Practice for Development and Validation of Multivariate Analyses for Use in Predicting Properties of Petroleum Products, Liquid Fuels, and Lubricants based on Spectroscopic Measurements

SIGNIFICANCE AND USE
5.1 This practice can be used to establish the validity of the results obtained by an infrared (IR) spectrophotometer or Raman spectrometer at the time the calibration is developed. The ongoing validation of PPTMRs produced by analysis of unknown samples using the multivariate model is covered separately (see for example, Practice D6122).  
5.2 The multivariate calibration procedures define the range over which measurements are valid and demonstrate whether the accuracy and precision of the analysis outputs meet user requirements.  
5.3 This practice describes sampling procedures that must be followed to ensure that the sample which is analyzed by the spectrophotometer or spectrometer is the same as the sample analyzed by the PTM. The sampling procedures apply to analyses done on lab analyzers, at-line analyzers, and online analyzers.
SCOPE
1.1 This practice covers a guide for the multivariate calibration of infrared (IR) spectrophotometers and Raman spectrometers used in determining the physical, chemical, and performance properties of petroleum products, liquid fuels including biofuels, and lubricants. This practice is applicable to analyses conducted in the near infrared (NIR) spectral region (roughly 780 nm to 2500 nm) through the mid infrared (MIR) spectral region (roughly 4000 cm-1 to 40 cm-1). For Raman analyses, this practice is generally applied to Stokes shifted bands that occur roughly 400 cm-1 to 4000 cm-1 below the frequency of the excitation.
Note 1: While the practice described herein deals specifically with mid-infrared, near-infrared, and Raman analysis, much of the mathematical and procedural detail contained herein is also applicable for multivariate quantitative analysis done using other forms of spectroscopy. The user is cautioned that typical and best practices for multivariate quantitative analysis using other forms of spectroscopy may differ from the practice described herein for mid-infrared, near-infrared, and Raman spectroscopies.  
1.2 Procedures for collecting and treating data for developing IR and Raman calibrations are outlined. Definitions, terms, and calibration techniques are described. The calibration establishes a multivariate correlation between the spectral features and the properties to be predicted. This correlation is herein referred to as the multivariate model. Criteria for validating the performance of the multivariate model are described. The properties against which a multivariate model is calibrated and validated are measured by Primary Test Methods (PTMs) and the results of the PTM measurement are herein referred to as Primary Test Method Results (PTMR). The analysis of the spectra using the multivariate model produces a Predicted Primary Test Method Result (PPTMR).  
1.3 The implementation of this practice requires that the IR spectrophotometer or Raman spectrometer has been installed in compliance with the manufacturer's specifications. In addition, it assumes that, at the time of calibration, validation, and analysis, the analyzer is operating at the conditions specified by the manufacturer. The practice includes instrument performance tests which define the instrument performance at the time of calibration, and which qualify the instrument by demonstrating comparable performance during validation and analysis.  
1.4 This practice covers techniques that are routinely applied for online, at-line, and laboratory quantitative analysis. The practice outlined covers the general cases for liquids and solids that are single phase homogeneous samples when presented to the analyzers. Online application is limited by sample viscosity and the ability to introduce sample to the analyzer. All techniques covered require the use of a computer for data collection and analysis.  
1.5 This practice is most typically applied when the spectra and the PTMR against which the analysis is calibrated are measured on the same sample. However, for some applic...

General Information

• Status: Published
• Publication Date: 31-Mar-2022
• ICS: 75.080 - Petroleum products in general
• Technical Committee: D02 - Petroleum Products, Liquid Fuels, and Lubricants
• Drafting Committee: D02.25 - Performance Assessment and Validation of Process Stream Analyzer Systems

Relations

• Refers: ASTM D2699-24 - Standard Test Method for Research Octane Number of Spark-Ignition Engine Fuel
• Effective Date: 01-Mar-2024
• Refers: ASTM D4175-23a - Standard Terminology Relating to Petroleum Products, Liquid Fuels, and Lubricants
• Effective Date: 15-Dec-2023
• Refers: ASTM D1265-23a - Standard Practice for Sampling Liquefied Petroleum (LP) Gases, Manual Method
• Effective Date: 01-Dec-2023
• Refers: ASTM D6299-23a - Standard Practice for Applying Statistical Quality Assurance and Control Charting Techniques to Evaluate Analytical Measurement System Performance
• Effective Date: 01-Dec-2023
• Refers: ASTM D2699-23b - Standard Test Method for Research Octane Number of Spark-Ignition Engine Fuel
• Effective Date: 01-Nov-2023
• Refers: ASTM D6792-23c - Standard Practice for Quality Management Systems in Petroleum Products, Liquid Fuels, and Lubricants Testing Laboratories
• Effective Date: 01-Nov-2023
• Refers: ASTM D6792-23b - Standard Practice for Quality Management Systems in Petroleum Products, Liquid Fuels, and Lubricants Testing Laboratories
• Effective Date: 01-Oct-2023
• Refers: ASTM D5842-23 - Standard Practice for Sampling and Handling of Fuels for Volatility Measurement
• Effective Date: 01-Oct-2023
• Refers: ASTM D2699-23a - Standard Test Method for Research Octane Number of Spark-Ignition Engine Fuel
• Effective Date: 01-Oct-2023
• Refers: ASTM D4175-23e1 - Standard Terminology Relating to Petroleum Products, Liquid Fuels, and Lubricants
• Effective Date: 01-Jul-2023
• Refers: ASTM D6122-23 - Standard Practice for Validation of the Performance of Multivariate Online, At-Line, Field and Laboratory Infrared Spectrophotometer, and Raman Spectrometer Based Analyzer Systems
• Effective Date: 01-Jul-2023
• Refers: ASTM E456-13a(2022)e1 - Standard Terminology Relating to Quality and Statistics
• Effective Date: 01-Apr-2022
• Refers: ASTM D5842-19 - Standard Practice for Sampling and Handling of Fuels for Volatility Measurement
• Effective Date: 01-Nov-2019
• Refers: ASTM D6122-19b - Standard Practice for Validation of the Performance of Multivariate Online, At-Line, and Laboratory Infrared Spectrophotometer Based Analyzer Systems
• Effective Date: 01-Jun-2019
• Refers: ASTM D6122-19a - Standard Practice for Validation of the Performance of Multivariate Online, At-Line, and Laboratory Infrared Spectrophotometer Based Analyzer Systems
• Effective Date: 01-May-2019

Overview

ASTM D8321-22 is a standard practice established by ASTM International that provides guidelines for the development and validation of multivariate analyses used to predict properties of petroleum products, liquid fuels (including biofuels), and lubricants through spectroscopic measurements. This standard primarily applies to analyses using infrared (IR) and Raman spectroscopy within the near infrared (NIR) and mid infrared (MIR) spectral regions, as well as Raman Stokes shifted bands. The practice outlines essential procedures for calibrating and validating multivariate models to ensure accurate prediction of physical, chemical, and performance properties using spectral data.

Key Topics

• Scope of Application

  • Multivariate calibration of IR spectrophotometers and Raman spectrometers for the analysis of petroleum products, liquid fuels, and lubricants.
  • Applicability to both NIR (780 nm - 2500 nm) and MIR (4000 cm⁻¹ - 40 cm⁻¹) regions, as well as specific Raman spectral ranges.
  • Can be extended to other spectroscopic techniques with adaptations.

• Multivariate Calibration & Validation

  • Procedures for data collection, calibration sample selection, and treatment of spectral data.
  • Establishes mathematical correlations (multivariate models) linking spectral features to sample properties.
  • Criteria for validating model accuracy and precision against results from Primary Test Methods (PTMs).

• Sampling Procedures

  • Guidance to ensure the analyzed sample matches across spectroscopic and reference methods.
  • Applicable for laboratory, at-line, and online analyzer systems.

• Instrument Performance

  • Requires compliance with manufacturer specifications for IR or Raman instruments.
  • Includes performance qualification tests to demonstrate instrument reliability during calibration and application.

Applications

• Quality Control in Petroleum Industry

  • Enables rapid and non-destructive testing of key product attributes such as density, sulfur content, octane number, and more.
  • Supports real-time process control for refining and blending operations, improving efficiency and product consistency.

• Biofuel and Additive Analysis

  • Facilitates the validation of finished biofuel blends, blendstocks, and additized petroleum products.
  • Addresses scenarios where spectral analysis and primary test methods are performed on blends or constituent basestocks.

• Versatile Analysis Techniques

  • Standard practice suited for single-phase liquids and solids in both laboratory and process environments.
  • Techniques outlined are essential for online, at-line, and laboratory quantitative analysis regimes.
  • Requires computer-aided data collection and model computation.

• Model Validation and Compliance

  • Establishes protocols for confirming multivariate model reliability using independent validation samples.
  • Ensures predictive results from spectroscopic analysis align with established laboratory test methods.

Related Standards

ASTM D8321-22 references or connects with several key standards supporting best practices in sampling, measurement, quality assurance, and analyzer system validation, including:

• ASTM D6122 - Validation of performance for multivariate analyzer systems.
• ASTM D3764 - Performance assessment for process stream analyzer systems.
• ASTM D4057 / D4177 - Manual and automatic sampling of petroleum products.
• ASTM E1655 - Practices for infrared quantitative analysis.
• ASTM D5845, D6277 - Surrogate methods for components in fuels.
• ASTM D6792 - Quality management in petroleum testing laboratories.
• ASTM D8340 - Performance-based qualification of spectroscopic analyzer systems.

These references provide additional frameworks and terminology for implementing robust, validated spectroscopic analysis systems in the petroleum industry and related sectors.

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Keywords: ASTM D8321-22, multivariate analysis, petroleum products, infrared spectroscopy, Raman spectroscopy, calibration, validation, lubricants, liquid fuels, spectroscopic measurement, quality control, analyzer system, laboratory testing, process control, biofuels.

Standards Content (Sample)

This international standard was developed in accordance with internationally recognized principles on standardization established in the Decision on Principles for the
Development of International Standards, Guides and Recommendations issued by the World Trade Organization Technical Barriers to Trade (TBT) Committee.
Designation: D8321 − 22
Standard Practice for
Development and Validation of Multivariate Analyses for Use
in Predicting Properties of Petroleum Products, Liquid
Fuels, and Lubricants based on Spectroscopic
Measurements
This standard is issued under the fixed designation D8321; the number immediately following the designation indicates the year of
original adoption or, in the case of revision, the year of last revision.Anumber in parentheses indicates the year of last reapproval.A
superscript epsilon (´) indicates an editorial change since the last revision or reapproval.
1. Scope* 1.3 The implementation of this practice requires that the IR
spectrophotometerorRamanspectrometerhasbeeninstalledin
1.1 This practice covers a guide for the multivariate cali-
compliancewiththemanufacturer’sspecifications.Inaddition,
bration of infrared (IR) spectrophotometers and Raman spec-
it assumes that, at the time of calibration, validation, and
trometers used in determining the physical, chemical, and
analysis,theanalyzerisoperatingattheconditionsspecifiedby
performance properties of petroleum products, liquid fuels
the manufacturer. The practice includes instrument perfor-
includingbiofuels,andlubricants.Thispracticeisapplicableto
mance tests which define the instrument performance at the
analyses conducted in the near infrared (NIR) spectral region
(roughly 780nm to 2500nm) through the mid infrared (MIR) time of calibration, and which qualify the instrument by
-1 -1
spectral region (roughly 4000cm to 40 cm ). For Raman demonstrating comparable performance during validation and
analyses, this practice is generally applied to Stokes shifted
analysis.
-1 -1
bands that occur roughly 400cm to 4000cm below the
1.4 This practice covers techniques that are routinely ap-
frequency of the excitation.
plied for online, at-line, and laboratory quantitative analysis.
NOTE 1—While the practice described herein deals specifically with
The practice outlined covers the general cases for liquids and
mid-infrared, near-infrared, and Raman analysis, much of the mathemati-
solids that are single phase homogeneous samples when
cal and procedural detail contained herein is also applicable for multivari-
presented to the analyzers. Online application is limited by
ate quantitative analysis done using other forms of spectroscopy.The user
is cautioned that typical and best practices for multivariate quantitative sample viscosity and the ability to introduce sample to the
analysis using other forms of spectroscopy may differ from the practice
analyzer.All techniques covered require the use of a computer
described herein for mid-infrared, near-infrared, and Raman spectrosco-
for data collection and analysis.
pies.
1.2 Procedures for collecting and treating data for develop- 1.5 This practice is most typically applied when the spectra
ing IR and Raman calibrations are outlined. Definitions, terms, and the PTMR against which the analysis is calibrated are
and calibration techniques are described. The calibration es-
measuredonthesamesample.However,forsomeapplications,
tablishes a multivariate correlation between the spectral fea-
spectramaybemeasuredonabasestockandthePTMRmaybe
tures and the properties to be predicted. This correlation is
measured on the same basestock after constant level additiva-
herein referred to as the multivariate model. Criteria for
tion.
validating the performance of the multivariate model are
1.5.1 Biofuel applications will typically fall into three
described.Thepropertiesagainstwhichamultivariatemodelis
categories.
calibrated and validated are measured by Primary Test Meth-
1.5.1.1 The spectra and the PTM both measure the finished
ods(PTMs)andtheresultsofthePTMmeasurementareherein
biofuel blend.
referred to as Primary Test Method Results (PTMR). The
1.5.1.2 The spectra are measured on a petroleum derived
analysis of the spectra using the multivariate model produces a
blendstock, and the PTM measures the same blendstock after a
Predicted Primary Test Method Result (PPTMR).
constant level additivation with the biocomponent.
1.5.1.3 The spectra and PTM both measured the petroleum
This practice is under the jurisdiction ofASTM Committee D02 on Petroleum
derived blendstock, and the PPTMRs from the multivariate
Products, Liquid Fuels, and Lubricants and is the direct responsibility of Subcom-
mittee D02.25 on Performance Assessment and Validation of Process Stream
model are used as inputs into a second model which predicts
Analyzer Systems.
the results obtained when the PTM is applied to the analysis of
Current edition approved April 1, 2022. Published June 2022. Originally
the finished blended product. The practice described herein
approved in 2020. Last previous edition approved in 2021 as D8321–21. DOI:
10.1520/D8321-22. only applies to the first of these two models.
*A Summary of Changes section appears at the end of this standard
Copyright © ASTM International, 100 Barr Harbor Drive, PO Box C700, West Conshohocken, PA 19428-2959. United States
D8321 − 22
1.6 This practice includes a checklist in Annex A2 against D4175Terminology Relating to Petroleum Products, Liquid
which multivariate calibrations can be examined to determine Fuels, and Lubricants
if they conform to the requirements defined herein.
D4307Practice for Preparation of Liquid Blends for Use as
Analytical Standards
1.7 For some multivariate spectroscopic analyses, interfer-
D5769Test Method for Determination of Benzene,Toluene,
encesandmatrixeffectsaresufficientlysmallthatitispossible
and Total Aromatics in Finished Gasolines by Gas
to calibrate using mixtures that contain substantially fewer
Chromatography/Mass Spectrometry
chemical components than the samples that will ultimately be
D5842Practice for Sampling and Handling of Fuels for
analyzed. While these surrogate methods generally make use
Volatility Measurement
of the multivariate mathematics described herein, they do not
D5845Test Method for Determination of MTBE, ETBE,
conform to procedures described herein, specifically with
TAME, DIPE, Methanol, Ethanol and tert-Butanol in
respect to the handling of outliers. Surrogate methods may
Gasoline by Infrared Spectroscopy
indicate that they make use of the mathematics described
D6122Practice for Validation of the Performance of Multi-
herein, but they should not claim to follow the procedures
variate Online, At-Line, Field and Laboratory Infrared
described herein. Test Methods D5845 and D6277 are ex-
Spectrophotometer, and Raman Spectrometer BasedAna-
amples of surrogate methods.
lyzer Systems
1.8 Disclaimer of Liability as to Patented Inventions—
D6277Test Method for Determination of Benzene in Spark-
NeitherASTM International nor anASTM committee shall be
Ignition Engine Fuels Using Mid Infrared Spectroscopy
responsible for identifying all patents under which a license is
D6299Practice for Applying Statistical Quality Assurance
required in using this document.ASTM International takes no
and Control Charting Techniques to Evaluate Analytical
position respecting the validity of any patent rights asserted in
Measurement System Performance
connection with any item mentioned in this standard. Users of
D6792Practice for Quality Management Systems in Petro-
this standard are expressly advised that determination of the
leum Products, Liquid Fuels, and Lubricants Testing
validity of any such patent rights, and the risk of infringement
Laboratories
of such rights, are entirely their own responsibility.
D7278GuideforPredictionofAnalyzerSampleSystemLag
1.9 The values stated in SI units are to be regarded as
Times
standard. No other units of measurement are included in this
D7453Practice for Sampling of Petroleum Products for
standard.
Analysis by Process Stream Analyzers and for Process
1.10 This standard does not purport to address all of the
Stream Analyzer System Validation
safety concerns, if any, associated with its use. It is the
D7717Practice for Preparing Volumetric Blends of Dena-
responsibility of the user of this standard to establish appro-
tured Fuel Ethanol and Gasoline Blendstocks for Labora-
priate safety, health, and environmental practices and deter-
tory Analysis
mine the applicability of regulatory limitations prior to use.
D7915Practice for Application of Generalized Extreme
1.11 This international standard was developed in accor-
Studentized Deviate (GESD) Technique to Simultane-
dance with internationally recognized principles on standard-
ously Identify Multiple Outliers in a Data Set
ization established in the Decision on Principles for the
D8009Practice for Manual Piston Cylinder Sampling for
Development of International Standards, Guides and Recom-
Volatile Crude Oils, Condensates, and Liquid Petroleum
mendations issued by the World Trade Organization Technical
Products
Barriers to Trade (TBT) Committee.
D8340 Practice for Performance-Based Qualification of
Spectroscopic Analyzer Systems
2. Referenced Documents
E131Terminology Relating to Molecular Spectroscopy
2.1 ASTM Standards:
E456Terminology Relating to Quality and Statistics
D1265Practice for Sampling Liquefied Petroleum (LP)
E1655 Practices for Infrared Multivariate Quantitative
Gases, Manual Method
Analysis
D1319Test Method for HydrocarbonTypes in Liquid Petro-
E1866Guide for Establishing Spectrophotometer Perfor-
leum Products by Fluorescent Indicator Adsorption
mance Tests
D2699Test Method for Research Octane Number of Spark-
E2056Practice for Qualifying Spectrometers and Spectro-
Ignition Engine Fuel
photometers for Use in Multivariate Analyses, Calibrated
D3764PracticeforValidationofthePerformanceofProcess
Using Surrogate Mixtures
Stream Analyzer Systems
D4057Practice for Manual Sampling of Petroleum and
3. Terminology
Petroleum Products
D4177Practice for Automatic Sampling of Petroleum and
3.1 For terminology related to molecular spectroscopic
Petroleum Products
methods, refer to Terminology E131. For terminology relating
to quality and statistics, refer to Terminology E456. For
For referenced ASTM standards, visit the ASTM website, www.astm.org, or terminology relating to petroleum products, liquid fuels and
contact ASTM Customer Service at [e-mail]. For Annual Book of ASTM
lubricants, refer to Terminology D4175.
Standards volume information, refer to the standard’s Document Summary page on
the ASTM website. 3.2 Definitions:
D8321 − 22
3.2.1 absorptivity, n—theabsorbancedividedbytheproduct 3.2.11 fluorescence, n—the emission of radiant energy from
of the concentration of the substance and the sample anatom,molecule,orionresultingfromabsorptionofaphoton
pathlength, a =A/(bc). The units of b and c shall be specified. and a subsequent transition to the ground state without a
E131 change in total spin quantum number.
3.2.11.1 Discussion—The initial and final states of the
3.2.2 analysis, n—in multivariate spectroscopic
transition are usually both singlet states. The average time
measurement,theprocessofapplyingthemultivariatemodelto
interval between absorption and fluorescence is usually less
a spectrum, preprocessed as required, to predict a component
-6
than 10 s. E131
concentration value or property, the prediction being referred
tohereinasaPredictedPrimaryTestMethodResult(PPTMR). 3.2.12 inlier, n—see nearest neighbor distance inlier.
D6122
3.2.3 analyzer, n—see analyzer system.
3.2.13 inlier detection methods, n—statistical tests which
3.2.4 analyzer system, n—for equipment in the analysis of
are conducted to determine if a spectrum resides within a
liquid petroleum products and fuels, all piping, hardware,
region of the multivariate calibration space which is sparsely
computer, software, instrument, linear correlation or multivari-
populated. D6122
ate model required to analyze a process or product sample; the
3.2.14 instrument, n—for multivariate spectroscopic ana-
analyzer system may also be referred to as the analyzer, or the
lyzers used in used in the analysis of liquid petroleum products
total analyzer system. D3764
and fuels, the spectrometer or spectrophotometer, associated
3.2.4.1 Discussion—Online analyzers that utilize extractive
electronics and computer, spectrometer, or spectrophotometer
samplingincludesampleloop,sampleconditioningsystemand
cell, and if utilized, transfer optics. D6122
excesssamplereturnsystem(seeFig.1inD3764forexample).
Online analyzers that utilize insertion probes include fiber
3.2.15 instrument performance verification sample, n—for
optics and sample probes.
multivariate spectroscopic analyzers used in the analysis of
3.2.4.2 Discussion—At-line, field and laboratory analyzers liquid petroleum products and fuels, a material representative
include the instrument and all associated sample introduction of the product being analyzed which is adequately stored in
apparatuses. sufficient quantity to be used as a check on instrument
performance; instrument performance verification samples are
3.2.5 anti-Stokes line (band), n—a Raman line (band) that
used in instrument performance tests and as checks on calibra-
hasafrequencyhigherthanthatoftheincidentmonochromatic
tiontransfer,butthesamplesandtheirspectraaregenerallynot
beam. E131
reproducible long term. D6122
3.2.6 attenuated total reflection (ATR), n—reflection that
3.2.15.1 Discussion—In E1866 and previous versions of
occurs when an absorbing coupling mechanism acts in the
D6122 and this practice, an instrument performance verifica-
process of total internal reflection to make the reflectance less
tion samples were referred to as test samples.
than unity.
3.2.16 instrument qualification sample, n—for multivariate
3.2.6.1 Discussion—In this process, if an absorbing sample
spectroscopic analyzers used in the analysis of liquid petro-
is placed in contact with the reflecting surface, the reflectance
leum products and fuels, a single pure compound, or a known,
for total internal reflection will be attenuated to some value
reproducible mixture of compounds whose spectra is constant
between zero and unity (O overtimesuchthatitcanbeusedinaninstrumentperformance
where absorption of the radiant power can take place. E131
test. D6122
3.2.7 calibration, n—in multivariate spectroscopic
3.2.16.1 Discussion—In E1866 and previous versions of
measurement, a process for creating a multivariate model
D6122 and this practice, an instrument qualification sample
relating component concentrations or sample properties to
was referred to as a check sample.
spectra for a set of known samples, referred to as calibration
3.2.17 instrument standardization, n—a procedure for stan-
samples.
dardizing the response of multiple instruments such that a
3.2.8 calibration samples, n—in multivariate spectroscopic
common multivariate model is applicable for measurements
measurement, the set of samples with known (measured by the
conducted by these instruments, the standardization being
PTM) component concentrations or property values that are
accomplished by way of adjustment of the spectrophotometer
used for creating a multivariate model.
hardware or by way of mathematical treatment of the collected
spectra. D6122
3.2.9 calibration transfer, n—a method of applying a mul-
tivariatecalibrationdevelopedusingspectrafromone analyzer
3.2.18 liquid petroleum products and fuels, n—in relation to
for analysis of spectra collected on a second analyzer by
process analyzers, any single-phase liquid material that is
mathematically modifying the multivariate model or by instru-
produced at a facility in the petroleum and petrochemical
ment standardization. D6122
industries and will be in whole or in part of a petroleum
product; it is inclusive of biofuels, renewable fuels,
3.2.10 chemical property, n—a property of a material asso-
blendstocks, alternative blendstocks, and additives. D8340
ciated with its elemental or molecular composition.
3.2.10.1 Discussion—Examples of chemical properties 3.2.19 model degrees of freedom, (dof), n—thedimensionof
include, but are not limited to sulfur content, benzene content, the multivariate space defined by the number of calibration
and aromatics content. samplespectra,thenumberofmodelvariables,andthenumber
D8321 − 22
of variables used in defining the property level dependence of result, including correcting for temperature effects, adding a
the Standard Error of Calibration (SEC). D6122 meanpropertyvalueoftheanalyzercalibration,andconverting
3.2.19.1 Discussion—For a multivariate model that is not into appropriate units for reporting purposes. D6122
mean-centered, dof = n-k-c, where n is the number of calibra-
3.2.30 preprocessing, v—performing mathematical opera-
tion samples, k is the number of model variables, and c is 0, 1
tions on raw spectral data prior to multivariate analysis or
or 2 depending on whether SEC is level independent, has a
modeldevelopment,suchasselectingspectralregions,correct-
linear dependence on property level, or has a power depen-
ing for baseline, smoothing, differentiation, data
dence. For a mean-centered model, dof = n-k-c-1.
transformation, mean centering, and assigning weights to
3.2.20 model variables, n—the independent variables de-
certain spectral positions.
rived from the calibration spectra which are regressed against
3.2.31 predicted primary test method result(s) (PPTMR),
the calibration sample properties to produce the multivariate
n—result(s) from the analyzer system, after application of any
model. D6122
necessary correlation, that is interpreted as predictions of what
3.2.20.1 Discussion—For MLR, the model variables would
the primary test method results would have been, if it was
be the absorbance at the selected wavelengths or frequencies;
conducted on the same material. D3764
for PCR or PLS, the model variables are the Principal
3.2.32 primary analyzer, n—the analyzer(s) on which cali-
Components or latent variables.
bration spectra are collected for the purpose of building a
3.2.21 multivariate calibration, n—an analyzer calibration
multivariate model.
that relates the spectrum at multiple wavelengths or frequen-
3.2.33 primary test method (PTM), n—the analytical proce-
cies to the physical, chemical, or quality parameters. D6122
dure used to generate the reference values against which the
3.2.22 multivariate model, n—the mathematical expression
analyzer is both calibrated and validated. D3764
or the set of mathematical operations that relates component
3.2.34 primary test method result(s) (PTMR), n—test re-
concentrations or properties to spectra for a set of calibration
sult(s) produced from an ASTM or other established standard
samples.
test method that is accepted as the reference measure of a
3.2.22.1 Discussion—The multivariate model includes any
property. D3764
preprocessingdonetothespectraorconcentrationorproperties
priortothedevelopmentofthecorrelationbetweenspectraand 3.2.35 secondary analyzer, n—an analyzer not used in the
development of the multivariate model, but which will be used
properties, and any post-processing done to the initially pre-
dicted results. for analysis of new materials.
3.2.23 nearest neighbor distance inlier, n—the spectrum of 3.2.36 site precision (R'), n—the value below which the
a sample not used in the calibration which, when analyzed, absolutedifferencebetweentwoindividualtestresultsobtained
resides within a gap in the multivariate calibration space, and undersiteprecisionconditionsisexpectedtoexceedabout5%
for which the result is subject to possible interpolation error. of the time (one case in 20 in the long run) in the normal and
correct operation of the test method.
D6122
3.2.36.1 Discussion—It is defined as 2.77 times σ , the
3.2.24 outlier detection limits, n—the limiting value for R’
standard deviation of results obtained under site precision
application of an outlier detection method to a spectrum,
conditions. D6299
beyond which the spectrum represents an extrapolation of the
multivariate model. D6122 3.2.37 site precision conditions, n—conditions under which
test results are obtained by one or more operators in a single
3.2.25 outlier spectrum, n—a spectrum whose analysis by a
site location practicing the same test method on a single
multivariate model represents an extrapolation of the model.
measurement system which may comprise multiple
D6122
instruments, using test specimens taken at random from the
3.2.26 performance property, n—a property of a material
same sample of material over an extended period of time
whichmeasureshowwellthematerialfunctionsinitsintended
spanning at least a 15 day interval.
use.
3.2.37.1 Discussion—Site precision conditions should in-
3.2.26.1 Discussion—Examples of performance properties
clude all sources of variation that are typically encountered
include research and motor octane numbers.
during normal, long term operation of the measurement sys-
3.2.27 photometer, n—a device so designed that it furnishes
tem. Thus, all operators who are involved in the routine use of
the ratio or a function of the ratio, of the radiant power of two
the measurement system should contribute results to the site
electromagnetic beams. The two beams may be separated in
precision determination. In situations of high usage of a test
time, space, or both. E131
method where multiple QC results are obtained within a 24h
3.2.28 physical property, n—apropertyofmatternotinvolv- period, then only results separated by at least 4h to 8h,
ing in its manifestation a chemical change. depending on the absence of auto-correlation in the data, the
3.2.28.1 Discussion—Examples of physical properties nature of the test method/instrument, site requirements, or
include, but are not limited to density, melting point, boiling regulations, should be used in site precision calculations to
point, vapor pressure, flash point, cloud point, and pour point. reflect the longer term variation in the system. D6299
3.2.29 post-processing, v—performing a mathematical op- 3.2.38 spectral intensity, n—a generic term referring to
eration on an intermediate analyzer result to produce the final either infrared absorbance or Raman scattering intensity.
D8321 − 22
3.2.39 spectral position, n—a generic term referring to thatmoleculemakesatransitionfromtheground(v=0)tofirst
either wavelength or frequency position in spectrum. excited state (v=1), where v is the vibrational quantum
number.
3.2.40 spectrometer, n—an instrument for measuring some
3.3.5 homoscedastic, n—a condition where all the model
function of power, or other physical quantity, with respect to
errors have the same finite variance.
spectral position within a spectral range. E131
3.3.6 mean center, v—to scale a set of data by subtracting
3.2.41 spectrophotometer, n—a spectrometer with associ-
the mean value of the set.
ated equipment, so designed that it furnishes the ratio, or a
3.3.6.1 Discussion—To mean center spectra, calculate the
function of the ratio, of the radiant power of two beams as a
average spectrum, and then subtract this average from each
function of spectral position.The two beams may be separated
individual spectrum.
in time, space, or both. E131
3.3.7 model validation, n—the process of testing a multi-
3.2.42 standard error of calibration (SEC), n—ameasureof
variate model with validation samples to determine accuracy
the agreement between PPTMR and PTMR for the samples
and precision of the PPTMR produced by the model relative to
used in developing a multivariate model.
the PTMR.
3.2.42.1 Discussion—If the model error is level
3.3.8 model validation samples, n—a set of samples used in
n
validatingthemodelwhicharenotpartofthesetofcalibration
independent, then SEC5Π~PPTMR 2 PTMR ! , where
( i i
dof
i51
samples, and for which PTMRs are compared to PPTMRs.
dof is the model degrees of freedom and n is the number of
3.3.8.1 Discussion—This practice uses the phrase model
calibration samples.
validation samples to distinguish these from the validation
3.2.42.2 Discussion—If the model error is level dependent, samples defined in Practice D6122 used in validating analyzer
then SEC is expressed as a function of m which is the average
performance.
of PPTMR and PTMR, and SEC(m) is calculated using a
3.3.9 overtone band, n—in vibrational spectroscopy,aspec-
procedure described in Practice D6122 Annex A4 and in
tral band that occurs in the vibrational spectrum of a molecule
Practice D8321 Annex A2. D6122
when the molecule makes a transition from the ground state (v
= 0) to an excited state higher than the first excited state
3.2.43 Stokes line (band), n—aRamanline(band)thathasa
(v>1), where v is the vibrational quantum number.
frequency lower than that of the incident monochromatic
3.3.9.1 Discussion—Because of anharmonicity, the fre-
beam. E131
quency at which an overtone occurs will typically be less than
3.2.44 test performance index, n—an approximate measure
v–1 times the frequency of the fundamental vibration.
of a laboratory’s testing capability, defined as the ratio of test
3.3.9.2 Discussion—The intensity of overtones (absorbance
method reproducibility (R) to site precision (R'). D6792
or Raman scattering) decreases significantly as the vibrational
3.3 Definitions of Terms Specific to This Standard:
quantum number increases.
3.3.1 basestock, n—in the preparation of a biofuel, the
3.3.10 physical correction, n—a type of post-processing
petroleum derived blendstock to which a biocomponent is
where the correction made to the numerical value produced by
added.
the multivariate model is based on a separate physical mea-
surement of, for example, sample density, sample path length,
3.3.2 combination band, n—in vibrational spectroscopy,a
or particulate scattering. D6122
spectral band that are observed in the vibrational spectrum of
a molecule when two or more fundamental vibrations are
3.3.11 standard error of cross-validation, n—an estimate of
excited, or multiply excited simultaneously.
the performance of a multivariate model obtained using cross-
validation.
3.3.3 cross-validation, n—an exploratory data analysis tool
3.3.12 standard error of validation (SEV), n—a measure of
which provides an assessment the optimal number of variables
touseinamultivariatemodelandestimatesthemodel’sability theperformanceofamultivariatemodelobtainedbyanalyzing
a set of model validation samples and comparing the PPTMR
to predict new data not used in development of the model.
to PTMR measured on these samples.
3.3.3.1 Discussion—Cross-validation involves a repetitive
v
procedure in which a calibration sample set is partitioned into 1
3.3.12.1 Discussion—SEV5 PPTMR 2 PTMR
Π~ !
(
i i
v
two subsets, a training set which is used to develop a i51
where v is the number of model validation samples.
multivariate model, and a testing set which is analyzed using
thismodel.Theprocedurerepeatsusingdifferentpartitionsand 3.3.13 surrogate calibration, n—a multivariate calibration
the results are combined to estimate the model’s predictive
that is developed using a calibration set which consists of
performance. mixtures which contain substantially fewer chemical compo-
nents than the samples which will ultimately be analyzed.
3.3.3.2 Discussion—Cross-validation is a useful tool in
guidingthedevelopmentofthemultivariatemodel,butitisnot
3.3.14 surrogate method, n—a standard test method that is
asubstituteforvalidationofthemodelwithanindependentset
based on a surrogate calibration.
of validation samples.
3.3.15 vibrational spectroscopy, n—infrared and Raman
3.3.4 fundamental band, n—in vibrational spectroscopy,a spectroscopies which involve the measurement of vibrational
spectral band that occurs in the spectrum of a molecule when transitions in molecules.
D8321 − 22
3.3.16 X-block, n—the spectral data matrix used in the and the volumn of the sample that is illuminated by the laser
calibration or validation of a multivariate model. and visible to the collection optics.
3.3.17 Y-block, n—the component concentration or property
3.4.24 p—the number of properties being modeled.
data matrix using in the calibration or validation of a multi-
3.4.25 p—the f by 1 prediction vector.
variate model.
3.4.26 P—the f by p prediction matrix with p for individual
3.4 Symbols:
properties as columns.
3.4.1 Scalars are represented by italicized normal face
3.4.27 PRESS—the Predicted Residual Error Sum of
letters.Vectorsarerepresentedbyboldfaceitalicizedlowercase
Squares from cross-validation.
letters. Matrices are represented by boldface italicized upper-
case letters. Lower case i and j as subscripts are indices
3.4.28 r—number of replicate PTM measurements.
indicating specific samples, spectral positions, or model vari-
3.4.29 s—a single beam sample spectrum.
ables.
-1
3.4.2 — a minus 1 as a superscript indicates a matrix 3.4.30 t(λ)—the transmittance of a sample at wavelength λ.
inverse.
3.4.31 t—a transmittance spectrum equal to the ratio of s to
3.4.3 a(λ)—sample absorbance at wavelength λ.
b.
t
3.4.4 a(λ)—the absorptivity of the absorbing species at
3.4.32 —as a superscript, indicates a vector or matrix
wavelength λ.
transpose.
3.4.5 a—an absorbance spectrum.
3.4.33 σ —the Raman scattering cross section for the scat-
R
3.4.6 A—a c by f matrix with component spectra as rows,
tering species.
used in the matrix form of the Beer-Lambert Law.
3.4.34 v—a vibrational energy level quantum number.
3.4.7 b—the pathlength (sample thickness).
3.4.35 x —a1by frowvectorcontainingthespectrumofthe
i
th
3.4.8 b—a single beam background spectrum.
i sample.
3.4.9 B—an n by n diagonal matrix of pathlengths for the
3.4.36 x —a1by f row vector containing the spectrum of
unk
matrix form of the Beer-Lambert Law.
the unknown sample being analyzed.
3.4.10 c—the number of absorbing or scattering compo-
3.4.37 X—the spectral data matrix which contains the n
nents in a sample.
spectra as rows of length f, also referred to as the model
3.4.11 c—concentration of absorbing or scattering species.
X-Block.
3.4.12 C—an n by c matrix of component concentrations in
3.4.38 x¯—the average spectrum; the average down the
the matrix form of the Beer-Lambert Law.
columns of X.
3.4.13 e—an n by 1 vector of property prediction errors.
3.4.39 xˆ—the estimate of a spectrum based on the multi-
3.4.14 e —an n times l by 1 vector of property prediction variate model.
cv
errors produced during cross-validation when only one prop-
¯
3.4.40 X—an nby fmatrixwhereeachofthe nrowscontain
erty is modeled.
x¯ used in mean centering X.
3.4.15 E—an n by p matrix of property prediction errors.
th
3.4.41 y —the PTMR value for a single property for the i
i
3.4.16 E —an n times l by p vector of property prediction
cv sample.
errors produced during crossvalidation when multiple proper-
th
3.4.42 yˆ —the PPTMR value for a single property for the i
i
ties are modeled.
sample.
3.4.17 f—the number of spectral positions in the spectral
3.4.43 y—an n by 1 vector of PTMR values, also referred to
data used in a model.
as the modelY-Block;y contains the PTMR values for a single
3.4.18 I —in a Raman measurement, the power of the
o
property for all the samples defined in the X-Block.
incident laser.
3.4.44 y¯—The average of the values in y.
3.4.19 I —in a Raman measurement, the intensity of the
R
scattered light. 3.4.45 yˆ—an nby1vectorofPPTMRvalues;yˆ containsthe
PPTMRvaluesforasinglepropertyforallthesamplesdefined
3.4.20 l—during cross-validation, the number of times each
in the X-Block.
sample is left out of the model construction and analyzed.
3.4.46 yˆ —an n times l by 1 vector of estimated PPTMR
3.4.21 n—the number of calibration samples. cv
valuesproducedduringcrossvalidationwhenasingleproperty
3.4.22 k—the number of variables used in a model, where
is modeled.
variables may be, for example selected spectral data points for
3.4.47 Y—an n by p matrix of PTMR values, each column
MLR, Principal Components for PCR, or latent variables for
of which correspond to a y vector for a different property.
PLS.
ˆ
3.4.23 K—a term in the Raman scattering equation that 3.4.48 Y—an n by p matrix of PPTMR values, each column
includes the solid angle visible to the Raman collection optics, of which correspond to a yˆ vector for a different property.
D8321 − 22
ˆ
3.4.49 Y —an n time l by p matrix of estimated PPTMR employed to determine if the spectrum being analyzed falls in
cv
values produced during cross validation when multiple prop- a void in the multivariate space defined by the calibration
erties are modeled; each column of which correspond to a yˆ spectra.
cv
vector for a different property.
4.6 Statistical expressions for calculating the repeatability
3.4.50 z —the transform of m; z = max(m)– m. of the spectroscopic analysis and the expected agreement
i i i i i
between the spectroscopic analysis and the PTM are given.
3.4.51 z¯ —the transform of m¯ ; z¯ = max(m¯)– m.
j j j j
5. Significance and Use
4. Summary of Practice
5.1 This practice can be used to establish the validity of the
4.1 Multivariate mathematics is applied to correlate the
results obtained by an infrared (IR) spectrophotometer or
spectrameasuredforasetofcalibrationsamplestocomponent
Raman spectrometer at the time the calibration is developed.
concentrations or property values for the set of samples. The
The ongoing validation of PPTMRs produced by analysis of
resultant multivariate model is applied to the analysis of
unknown samples using the multivariate model is covered
spectra of unknown samples to predict the component concen-
separately (see for example, Practice D6122).
tration or property values for the unknown sample.
5.2 The multivariate calibration procedures define the range
4.1.1 This practice applies to both infrared and Raman
spectra. The infrared spectra are collected in the mid-infrared over which measurements are valid and demonstrate whether
the accuracy and precision of the analysis outputs meet user
spectral region, the near-infrared spectral region or, in some
requirements.
cases, in an extended region that covers part of both the mid-
and near-infrared.
5.3 This practice describes sampling procedures that must
4.1.2 The component concentrations and property values
be followed to ensure that the sample which is analyzed by the
which are used in establishing and validating the multivariate
spectrophotometer or spectrometer is the same as the sample
model are measured by a Primary Test Method (PTM),
analyzed by the PTM. The sampling procedures apply to
typicallyanASTMstandardtestmethod.Thevaluesareherein
analyses done on lab analyzers, at-line analyzers, and online
referred to as Primary Test Method Results (PTMR).
analyzers.
4.1.3 The predicted results produced by application of the
model for the analysis of a spectrum are referred to as
6. Vibrational Spectroscopies
Predicted Primary Test Method Results (PPTMR).
6.1 Both infrared and Raman spectroscopies measure sig-
4.2 Multilinear regression (MLR), principal components
nals associated with molecular vibrations. Various groups of
regression (PCR), partial least squares (PLS) and locally
bonded atoms in molecules give rise to vibrations that occur at
weighted regression (LWR) are examples of multivariate
characteristic frequencies. These groups of bonded atoms are
mathematical techniques that are commonly used for the
referred to as functional groups, and the characteristicfrequen-
development of the multivariate model. Other mathematical
cies as functional group frequencies. While each compound
techniques are also used, but may not detect outliers, and may
will have a unique spectrum, in complex mixtures such as
not be validated by the procedure described in this practice. It
petroleumsamples,theoverlapofthesespectraoftenprecludes
is the user’s responsibility to verify that the mathematics
identification of individual molecular components.
employed satisfy the requirements of this practice.
6.1.1 Infrared spectroscopy measures the absorption of
infrared light by molecules. Light from a broad band source is
4.3 Statistical tests are applied to detect outliers during the
incident on the sample being measured. As the light passes
development of the multivariate model. Outliers include high
through the sample, the intensity of the light at the functional
leverage samples (samples whose spectra contribute a statisti-
group frequencies is reduced, the amount of the reduction
cally significant fraction of one or more of the spectral
beingproportionaltotheconcentrationofthefunctionalgroup.
variables used in the model), samples with high spectral
Theabsorptionofthelightinducesvibrationalexcitationofthe
residuals (suggestive of unmodeled components) and samples
bonded atoms in the functional group.
whose PTMR values are inconsistent with the model.
6.1.1.1 Since the light incident on the sample cannot be
4.4 Validation of the multivariate model is performed by
directly measured, an infrared spectrum typically involves the
using the model to analyze a set of model validation samples
collection of two separate single-beam spectra, a background,
and statistically comparing the PPTMR values for the model
b,andasamplespectrum,s.Thebackgroundismeasuredwhen
validation samples to PTMR values measured for these
there is no sample present in the infrared beam. The single-
samples, to test for bias in the model and for the degree of
beam spectrum of the sample is ratioed (divided by) the
agreement of the model with the PTM.
single-beambackgroundtoproduceatransmissionspectrum,t.
The transmission spectrum is converted to an absorbance
4.5 Statistical tests are applied to detect when PPTMR
spectrum, a, using a negative logarithm base 10.
produced by application of the model represent extrapolation
of the calibration. A spectrum is labeled an outlier if its
t 5s⁄b (1)
leverage exceeds that of the calibration samples, or if the
a52log t (2)
spectrum produces high spectral residuals suggesting the
presence of components which were not in the calibration 6.1.2 Raman spectroscopy measures the inelastic scattering
samples. Optionally, a nearest neighbor outlier test may be of light by molecules. Raman uses a monochromatic light
D8321 − 22
source, typically a laser. The light interacts with molecular 6.3 Most fundamental bands occur in the mid-infrared
vibrationsresultinginthefrequencyofthescatteredlightbeing region. All bands in the near-infrared region are overtones or
shifted up or down by an amount corresponding to molecular combinationbands,butsomeovertonesandcombinationbands
vibration frequencies. also occur in the mid-infrared region.
-1 -1
6.1.2.1 Theinteractionmaytransferenergyfromthelightto
6.3.1 For example, the 910cm to 670cm region of the
the molecule, thereby reducing the frequency of the scattered mid-infrared contain many fundamental vibrations associated
light relative to the laser frequency (Stokes scattering), or it
with out-of-plane bending vibrations of aromatic C-H bonds.
may transfer energy from a molecule in a excited vibrational These bands are often too intense to measure in transmission
state to the scattered light, thereby increasing the frequency of
with cell pathlengths suitable for process analysis, and this
the scattered light relative to the laser frequency (anti-Stokes region is blocked by the absorption of some transmission cell
scattering). Since the number of molecules in an excited
window materials. Some overtones and combination bands of
-1
vibrationalstateisalwayslowerthanthenumberintheground these aromatic C-H vibrations occur between 2000cm and
-1
vibrational state, anti-Stokes Raman is always weaker in
1667cm and can be measured using 0.25mm to 0.5mm
intensity than Stokes Raman, the difference getting bigger as transmission cells
the frequency of the vibration increases. For this reason,
6.4 For overtones and combinations, as the excitation level
Raman analyzer applications typically use Stokes Raman
increases, the strength of the infrared absorbance (the absorp-
scattering.
tivity) decreases significantly. Thus, the pathlength necessary
6.1.2.2 Raman scattering is an inherently weak process.
tomeasurethespectrumasonemovesouttohigherandhigher
Only about 1 in 10 million of the scattered photons are
overtone/combinationbandlevelsincreasessignificantly.Table
scattered inelastically, most being scattered elastically with no
1 shows some example pathlengths for mid-infrared and
frequency change (Rayleigh scattering). Therefore, Raman
near-infraredmeasurementsofpetroleumproducts,liquidfuels
analysis is typically limited to materials that do not fluoresce
and lubricants. The pathlengths listed typically produce C-H
significantly when exposed to the monochromatic light.
aliphatic stretching vibration peaks with absorbance less than
6.2 Molecules exhibit a manifold of vibrational energy
1.0. Pathlengths used for specific applications may vary.
levels.
Pathlengthsshouldbeselectedtomaximizetheabsorbanceand
6.2.1 Fundamental vibrations occur when molecules are
thusspectralsignal-to-noisewithinthelinearresponserangeof
excited from the vibrational ground state (v=0) to the first
the instrument.
excited vibrational state (v=1), where v is the vibrational
quantum number. Raman spectroscopy typically deals with
7. Instrumentation
vibrational fundamentals. Vibrational fundamentals occur in
7.1 A complete description of all applicable types of infra-
the mid-infrared region. Bands due to aliphatic C-H vibrations
red and Raman analyzers is beyond the scope of this practice.
in petroleum are typically too strong to measure in transmis-
Only a general outline is given here. Instrumental performance
sionwithcellpathlengthssuitableforprocessanalyzersbutcan
criteria which are critical to successful multivariateapplication
bemeasuredusingattenuatedtotalreflection(ATR).ATRisnot
are discussed.
commonly used for process measurements.
7.2 The analyzers fall into two categories, including sys-
6.2.2 Overtone bands occur when a single vibration is
excited from the vibrational ground state (v=0) to a higher tems that acquire continuous spectral data over wavelength or
frequency ranges (spectrophotometers and spectrometers), and
vibrational level (v>1). The first overtone corresponds to a
th
transition from v=0 to v=2. The n overtone corresponds to a those that only examine one or several discrete wavelengths or
frequencies (photometers).
transitionfromv=0tov=n+1.Thefrequenciesoftheovertones
will be less than n+1 times the fundamental frequency, the 7.2.1 Photometers may have one or a series of wavelength
difference becoming larger as n increases. filters and a single detector. These filters are mounted on a
6.2.3 Combination bands occur when two or more vibra- turretwheelsothattheindividualwavelengthsarepresentedto
tions are excited simultaneously. Combination bands may a single detector sequentially. Continuously variable filters
involve multiple excitation of one or more of the combined may also be used in this fashion. These filters, either linear or
vibrations. circular, are moved past a slit to scan the wavelength being
TABLE 1 Example Pathlengths for MIR and NIR Measurements
Region Nominal Pathlength Measures Frequency / Wavelength
-1 -1
Mid-IR <10 microns Hydrocarbon Fundamentals 4000 cm to 400 cm
2.5 microns to 25 microns
-1 -1
Mid- and Near-IR 0.25 mm to 0.5 mm Hydrocarbon Overtones & Combination Bands, 5000 cm to 1000 cm
heteroatom fundamentals 2 microns to 10 microns
st -1 -1
Near-IR 2 mm Hydrocarbon 1 Overtones 6400 cm to 5000 cm
1562.5 nm to 2000 nm
nd -1 -1
Near-IR 1 cm Hydrocarbon 2 Overtones and Combination 9200 cm to 6400 cm
Bands 1087 nm to 1562.5 nm
rd -1 -1
Near-IR 10 cm Hydrocarbon 3 Overtones and Combination Bands 12000 cm to 9200 cm
833.3 nm to 1087 nm
D8321 − 22
measured.Alternatively, photometers may have several mono- 7.4 Spectral axis reproducibility is critical for successful
chromatic light sources, such as light-emitting diodes, that multivariate spectroscopic analyses. Multivariate modeling
sequentially turn on and off. procedures assume that a change in intensity at a certain
spectral position is always due to the same set of sample
7.2.1.1 For spectral data collected using photometers, the
molecularcomponents.Ifthecollectedspectramoveacrossthe
number of data points per spectrum is typically limited, and
spectral axis, then model performance is degraded.
models are typically built using MLR. Such models do
...

This document is not an ASTM standard and is intended only to provide the user of an ASTM standard an indication of what changes have been made to the previous version. Because
it may not be technically possible to adequately depict all changes accurately, ASTM recommends that users consult prior editions as appropriate. In all cases only the current version
of the standard as published by ASTM is to be considered the official document.
Designation: D8321 − 21 D8321 − 22
Standard Practice for
Development and Validation of Multivariate Analyses for Use
in Predicting Properties of Petroleum Products, Liquid
Fuels, and Lubricants based on Spectroscopic
Measurements
This standard is issued under the fixed designation D8321; the number immediately following the designation indicates the year of
original adoption or, in the case of revision, the year of last revision. A number in parentheses indicates the year of last reapproval. A
superscript epsilon (´) indicates an editorial change since the last revision or reapproval.
1. Scope*
1.1 This practice covers a guide for the multivariate calibration of infrared (IR) spectrophotometers and Raman spectrometers used
in determining the physical, chemical, and performance properties of petroleum products, liquid fuels including biofuels, and
lubricants. This practice is applicable to analyses conducted in the near infrared (NIR) spectral region (roughly 780 nm to 2500 nm)
-1 -1
through the mid infrared (MIR) spectral region (roughly 4000 cm to 40 cm ). For Raman analyses, this practice is generally
-1 -1
applied to Stokes shifted bands that occur roughly 400 cm to 4000 cm below the frequency of the excitation.
NOTE 1—While the practice described herein deals specifically with mid-infrared, near-infrared, and Raman analysis, much of the mathematical and
procedural detail contained herein is also applicable for multivariate quantitative analysis done using other forms of spectroscopy. The user is cautioned
that typical and best practices for multivariate quantitative analysis using other forms of spectroscopy may differ from the practice described herein for
mid-infrared, near-infrared, and Raman spectroscopies.
1.2 Procedures for collecting and treating data for developing IR and Raman calibrations are outlined. Definitions, terms, and
calibration techniques are described. The calibration establishes a multivariate correlation between the spectral features and the
properties to be predicted. This correlation is herein referred to as the multivariate model. Criteria for validating the performance
of the multivariate model are described. The properties against which a multivariate model is calibrated and validated are measured
by Primary Test Methods (PTMs) and the results of the PTM measurement are herein referred to as Primary Test Method Results
(PTMR). The analysis of the spectra using the multivariate model produces a Predicted Primary Test Method Result (PPTMR).
1.3 The implementation of this practice requires that the IR spectrophotometer or Raman spectrometer has been installed in
compliance with the manufacturer’s specifications. In addition, it assumes that, at the time of calibration, validation, and analysis,
the analyzer is operating at the conditions specified by the manufacturer. The practice includes instrument performance tests which
define the instrument performance at the time of calibration, and which qualify the instrument by demonstrating comparable
performance during validation and analysis.
1.4 This practice covers techniques that are routinely applied for online, at-line, and laboratory quantitative analysis. The practice
outlined covers the general cases for liquids and solids that are single phase homogeneous samples when presented to the analyzers.
Online application is limited by sample viscosity and the ability to introduce sample to the analyzer. All techniques covered require
the use of a computer for data collection and analysis.
This practice is under the jurisdiction of ASTM Committee D02 on Petroleum Products, Liquid Fuels, and Lubricants and is the direct responsibility of Subcommittee
D02.25 on Performance Assessment and Validation of Process Stream Analyzer Systems.
Current edition approved May 1, 2021April 1, 2022. Published July 2021June 2022. Originally approved in 2020. Last previous edition approved in 20202021 as
D8321 – 20.D8321 – 21. DOI: 10.1520/D8321-21.10.1520/D8321-22.
*A Summary of Changes section appears at the end of this standard
Copyright © ASTM International, 100 Barr Harbor Drive, PO Box C700, West Conshohocken, PA 19428-2959. United States
D8321 − 22
1.5 This practice is most typically applied when the spectra and the PTMR against which the analysis is calibrated are measured
on the same sample. However, for some applications, spectra may be measured on a basestock and the PTMR may be measured
on the same basestock after constant level additivation.
1.5.1 Biofuel applications will typically fall into three categories.
1.5.1.1 The spectra and the PTM both measure the finished biofuel blend.
1.5.1.2 The spectra are measured on a petroleum derived blendstock, and the PTM measures the same blendstock after a constant
level additivation with the biocomponent.
1.5.1.3 The spectra and PTM both measured the petroleum derived blendstock, and the PPTMRs from the multivariate model are
used as inputs into a second model which predicts the results obtained when the PTM is applied to the analysis of the finished
blended product. The practice described herein only applies to the first of these two models.
1.6 This practice includes a checklist in Annex A2 against which multivariate calibrations can be examined to determine if they
conform to the requirements defined herein.
1.7 For some multivariate spectroscopic analyses, interferences and matrix effects are sufficiently small that it is possible to
calibrate using mixtures that contain substantially fewer chemical components than the samples that will ultimately be analyzed.
While these surrogate methods generally make use of the multivariate mathematics described herein, they do not conform to
procedures described herein, specifically with respect to the handling of outliers. Surrogate methods may indicate that they make
use of the mathematics described herein, but they should not claim to follow the procedures described herein. Test Methods D5845
and D6277 are examples of surrogate methods.
1.8 Disclaimer of Liability as to Patented Inventions—Neither ASTM International nor an ASTM committee shall be responsible
for identifying all patents under which a license is required in using this document. ASTM International takes no position
respecting the validity of any patent rights asserted in connection with any item mentioned in this standard. Users of this standard
are expressly advised that determination of the validity of any such patent rights, and the risk of infringement of such rights, are
entirely their own responsibility.
1.9 The values stated in SI units are to be regarded as standard. No other units of measurement are included in this standard.
1.10 This standard does not purport to address all of the safety concerns, if any, associated with its use. It is the responsibility
of the user of this standard to establish appropriate safety, health, and environmental practices and determine the applicability of
regulatory limitations prior to use.
1.11 This international standard was developed in accordance with internationally recognized principles on standardization
established in the Decision on Principles for the Development of International Standards, Guides and Recommendations issued
by the World Trade Organization Technical Barriers to Trade (TBT) Committee.
2. Referenced Documents
2.1 ASTM Standards:
D1265 Practice for Sampling Liquefied Petroleum (LP) Gases, Manual Method
D1319 Test Method for Hydrocarbon Types in Liquid Petroleum Products by Fluorescent Indicator Adsorption
D2699 Test Method for Research Octane Number of Spark-Ignition Engine Fuel
D3764 Practice for Validation of the Performance of Process Stream Analyzer Systems
D4057 Practice for Manual Sampling of Petroleum and Petroleum Products
D4177 Practice for Automatic Sampling of Petroleum and Petroleum Products
D4175 Terminology Relating to Petroleum Products, Liquid Fuels, and Lubricants
D4307 Practice for Preparation of Liquid Blends for Use as Analytical Standards
D5769 Test Method for Determination of Benzene, Toluene, and Total Aromatics in Finished Gasolines by Gas
Chromatography/Mass Spectrometry
For referenced ASTM standards, visit the ASTM website, www.astm.org, or contact ASTM Customer Service at [e-mail]. For Annual Book of ASTM Standards
volume information, refer to the standard’s Document Summary page on the ASTM website.
D8321 − 22
D5842 Practice for Sampling and Handling of Fuels for Volatility Measurement
D5845 Test Method for Determination of MTBE, ETBE, TAME, DIPE, Methanol, Ethanol and tert-Butanol in Gasoline by
Infrared Spectroscopy
D6122 Practice for Validation of the Performance of Multivariate Online, At-Line, Field and Laboratory Infrared
Spectrophotometer, and Raman Spectrometer Based Analyzer Systems
D6277 Test Method for Determination of Benzene in Spark-Ignition Engine Fuels Using Mid Infrared Spectroscopy
D6299 Practice for Applying Statistical Quality Assurance and Control Charting Techniques to Evaluate Analytical Measure-
ment System Performance
D6792 Practice for Quality Management Systems in Petroleum Products, Liquid Fuels, and Lubricants Testing Laboratories
D7278 Guide for Prediction of Analyzer Sample System Lag Times
D7453 Practice for Sampling of Petroleum Products for Analysis by Process Stream Analyzers and for Process Stream Analyzer
System Validation
D7717 Practice for Preparing Volumetric Blends of Denatured Fuel Ethanol and Gasoline Blendstocks for Laboratory Analysis
D7915 Practice for Application of Generalized Extreme Studentized Deviate (GESD) Technique to Simultaneously Identify
Multiple Outliers in a Data Set
D8009 Practice for Manual Piston Cylinder Sampling for Volatile Crude Oils, Condensates, and Liquid Petroleum Products
D8340 Practice for Performance-Based Qualification of Spectroscopic Analyzer Systems
E131 Terminology Relating to Molecular Spectroscopy
E456 Terminology Relating to Quality and Statistics
E1655 Practices for Infrared Multivariate Quantitative Analysis
E1866 Guide for Establishing Spectrophotometer Performance Tests
E2056 Practice for Qualifying Spectrometers and Spectrophotometers for Use in Multivariate Analyses, Calibrated Using
Surrogate Mixtures
3. Terminology
3.1 For terminology related to molecular spectroscopic methods, refer to Terminology E131. For terminology relating to quality
and statistics, refer to Terminology E456. For terminology relating to petroleum products, liquid fuels and lubricants, refer to
Terminology D4175.
3.2 Definitions:
3.2.1 absorptivity, n—the absorbance divided by the product of the concentration of the substance and the sample pathlength, a
= A/(bc). The units of b and c shall be specified. E131
3.2.2 analysis, n—in multivariate spectroscopic measurement, the process of applying the multivariate model to a spectrum,
preprocessed as required, to predict a component concentration value or property, the prediction being referred to herein as a
Predicted Primary Test Method Result (PPTMR).
3.2.3 analyzer, n—see analyzer system.
3.2.4 analyzer system, n—for equipment in the analysis of liquid petroleum products and fuels, all piping, hardware, computer,
software, instrument, linear correlation or multivariate model required to analyze a process or product sample; the analyzer system
may also be referred to as the analyzer, or the total analyzer system. D3764
3.2.4.1 Discussion—
Online analyzers that utilize extractive sampling include sample loop, sample conditioning system and excess sample return system
(see Fig. 1 in D3764 for example). Online analyzers that utilize insertion probes include fiber optics and sample probes.
3.2.4.2 Discussion—
At-line, field and laboratory analyzers include the instrument and all associated sample introduction apparatuses.
3.2.5 anti-Stokes line (band), n—a Raman line (band) that has a frequency higher than that of the incident monochromatic beam.
E131
3.2.6 attenuated total reflection (ATR), n—reflection that occurs when an absorbing coupling mechanism acts in the process of
total internal reflection to make the reflectance less than unity.
3.2.6.1 Discussion—
In this process, if an absorbing sample is placed in contact with the reflecting surface, the reflectance for total internal reflection
D8321 − 22
will be attenuated to some value between zero and unity (O < R < 1) in regions of the spectrum where absorption of the radiant
power can take place. E131
3.2.7 calibration, n—in multivariate spectroscopic measurement, a process for creating a multivariate model relating component
concentrations or sample properties to spectra for a set of known samples, referred to as calibration samples.
3.2.8 calibration samples, n—in multivariate spectroscopic measurement, the set of samples with known (measured by the PTM)
component concentrations or property values that are used for creating a multivariate model.
3.2.9 calibration transfer, n—a method of applying a multivariate calibration developed using spectra from one analyzer for
analysis of spectra collected on a second analyzer by mathematically modifying the multivariate model or by instrument
standardization. D6122
3.2.10 chemical property, n—a property of a material associated with its elemental or molecular composition.
3.2.10.1 Discussion—
Examples of chemical properties include, but are not limited to sulfur content, benzene content, and aromatics content.
3.2.11 fluorescence, n—the emission of radiant energy from an atom, molecule, or ion resulting from absorption of a photon and
a subsequent transition to the ground state without a change in total spin quantum number.
3.2.11.1 Discussion—
The initial and final states of the transition are usually both singlet states. The average time interval between absorption and
-6
fluorescence is usually less than 10 s. E131
3.2.12 inlier, n—see nearest neighbor distance inlier. D6122
3.2.13 inlier detection methods, n—statistical tests which are conducted to determine if a spectrum resides within a region of the
multivariate calibration space which is sparsely populated. D6122
3.2.14 instrument, n—for multivariate spectroscopic analyzers used in used in the analysis of liquid petroleum products and fuels,
the spectrometer or spectrophotometer, associated electronics and computer, spectrometer, or spectrophotometer cell, and if
utilized, transfer optics. D6122
3.2.15 instrument performance verification sample, n—for multivariate spectroscopic analyzers used in the analysis of liquid
petroleum products and fuels, a material representative of the product being analyzed which is adequately stored in sufficient
quantity to be used as a check on instrument performance; instrument performance verification samples are used in instrument
performance tests and as checks on calibration transfer, but the samples and their spectra are generally not reproducible long term.
D6122
3.2.15.1 Discussion—
In E1866 and previous versions of D6122 and this practice, an instrument performance verification samples were referred to as
test samples.
3.2.16 instrument qualification sample, n—for multivariate spectroscopic analyzers used in the analysis of liquid petroleum
products and fuels, a single pure compound, or a known, reproducible mixture of compounds whose spectra is constant over time
such that it can be used in an instrument performance test. D6122
3.2.16.1 Discussion—
In E1866 and previous versions of D6122 and this practice, an instrument qualification sample was referred to as a check sample.
3.2.17 instrument standardization, n—a procedure for standardizing the response of multiple instruments such that a common
multivariate model is applicable for measurements conducted by these instruments, the standardization being accomplished by way
of adjustment of the spectrophotometer hardware or by way of mathematical treatment of the collected spectra. D6122
3.2.18 liquid petroleum products and fuels, n—in relation to process analyzers, any single-phase liquid material that is produced
at a facility in the petroleum and petrochemical industries and will be in whole or in part of a petroleum product; it is inclusive
of biofuels, renewable fuels, blendstocks, alternative blendstocks, and additives. D8340
D8321 − 22
3.2.19 model degrees of freedom, (dof), n—the dimension of the multivariate space defined by the number of calibration sample
spectra, the number of model variables, and the number of variables used in defining the property level dependence of the Standard
Error of Calibration (SEC). D6122
3.2.19.1 Discussion—
For a multivariate model that is not mean-centered, dof = n-k-c, where n is the number of calibration samples, k is the number of
model variables, and c is 0, 1 or 2 depending on whether SEC is level independent, has a linear dependence on property level, or
has a power dependence. For a mean-centered model, dof = n-k-c-1.
3.2.20 model variables, n—the independent variables derived from the calibration spectra which are regressed against the
calibration sample properties to produce the multivariate model. D6122
3.2.20.1 Discussion—
For MLR, the model variables would be the absorbance at the selected wavelengths or frequencies; for PCR or PLS, the model
variables are the Principal Components or latent variables.
3.2.21 multivariate calibration, n—an analyzer calibration that relates the spectrum at multiple wavelengths or frequencies to the
physical, chemical, or quality parameters. D6122
3.2.22 multivariate model, n—the mathematical expression or the set of mathematical operations that relates component
concentrations or properties to spectra for a set of calibration samples.
3.2.22.1 Discussion—
The multivariate model includes any preprocessing done to the spectra or concentration or properties prior to the development of
the correlation between spectra and properties, and any post-processing done to the initially predicted results.
3.2.23 nearest neighbor distance inlier, n—the spectrum of a sample not used in the calibration which, when analyzed, resides
within a gap in the multivariate calibration space, and for which the result is subject to possible interpolation error. D6122
3.2.24 outlier detection limits, n—the limiting value for application of an outlier detection method to a spectrum, beyond which
the spectrum represents an extrapolation of the multivariate model. D6122
3.2.25 outlier spectrum, n—a spectrum whose analysis by a multivariate model represents an extrapolation of the model. D6122
3.2.26 performance property, n—a property of a material which measures how well the material functions in its intended use.
3.2.26.1 Discussion—
Examples of performance properties include research and motor octane numbers.
3.2.27 photometer, n—a device so designed that it furnishes the ratio or a function of the ratio, of the radiant power of two
electromagnetic beams. The two beams may be separated in time, space, or both. E131
3.2.28 physical property, n—a property of matter not involving in its manifestation a chemical change.
3.2.28.1 Discussion—
Examples of physical properties include, but are not limited to density, melting point, boiling point, vapor pressure, flash point,
cloud point, and pour point.
3.2.29 post-processing, v—performing a mathematical operation on an intermediate analyzer result to produce the final result,
including correcting for temperature effects, adding a mean property value of the analyzer calibration, and converting into
appropriate units for reporting purposes. D6122
3.2.30 preprocessing, v—performing mathematical operations on raw spectral data prior to multivariate analysis or model
development, such as selecting spectral regions, correcting for baseline, smoothing, differentiation, data transformation, mean
centering, and assigning weights to certain spectral positions.
3.2.31 predicted primary test method result(s) (PPTMR), n—result(s) from the analyzer system, after application of any necessary
correlation, that is interpreted as predictions of what the primary test method results would have been, if it was conducted on the
same material. D3764
D8321 − 22
3.2.32 primary analyzer, n—the analyzer(s) on which calibration spectra are collected for the purpose of building a multivariate
model.
3.2.33 primary test method (PTM), n—the analytical procedure used to generate the reference values against which the analyzer
is both calibrated and validated. D3764
3.2.34 primary test method result(s) (PTMR), n—test result(s) produced from an ASTM or other established standard test method
that is accepted as the reference measure of a property. D3764
3.2.35 secondary analyzer, n—an analyzer not used in the development of the multivariate model, but which will be used for
analysis of new materials.
3.2.36 site precision (R'), n—the value below which the absolute difference between two individual test results obtained under site
precision conditions may be is expected to occur with a probability of approximately 0.95 (95 %). It is defined as 2.77 times the
standard deviation of results obtained under site precision conditions. exceed about 5 % of the time (one case in 20 in the long
run) in the normal and correct operation of the test method.
3.2.36.1 Discussion—
It is defined as 2.77 times σ , the standard deviation of results obtained under site precision conditions. D6299
R’
3.2.37 site precision conditions, n—conditions under which test results are obtained by one or more operators in a single site
location practicing the same test method on a single measurement system which may comprise multiple instruments, using test
specimens taken at random from the same sample of material over an extended period of time spanning at least a 15 day interval.
3.2.37.1 Discussion—
Site precision conditions should include all sources of variation that are typically encountered during normal, long term operation
of the measurement system. Thus, all operators who are involved in the routine use of the measurement system should contribute
results to the site precision determination. In situations of high usage of a test method where multiple QC results are obtained
within a 24 h period, then only results separated by at least 4 h to 8 h, depending on the absence of auto-correlation in the data,
the nature of the test method/instrument, site requirements, or regulations, should be used in site precision calculations to reflect
the longer term variation in the system. D6299
3.2.38 spectral intensity, n—a generic term referring to either infrared absorbance or Raman scattering intensity.
3.2.39 spectral position, n—a generic term referring to either wavelength or frequency position in spectrum.
3.2.40 spectrometer, n—an instrument for measuring some function of power, or other physical quantity, with respect to spectral
position within a spectral range. E131
3.2.41 spectrophotometer, n—a spectrometer with associated equipment, so designed that it furnishes the ratio, or a function of the
ratio, of the radiant power of two beams as a function of spectral position. The two beams may be separated in time, space, or both.
E131
3.2.42 standard error of calibration (SEC), n—a measure of the agreement between PPTMR and PTMR for the samples used in
developing a multivariate model.
3.2.42.1 Discussion—
n
If the model error is level independent, then SEC5Π~PPTMR 2 PTMR ! , where dof is the model degrees of freedom and
( i i
dof
i51
n is the number of calibration samples.
3.2.42.2 Discussion—
If the model error is level dependent, then SEC is expressed as a function of m which is the average of PPTMR and PTMR, and
SEC(m) is calculated using a procedure described in Practice D6122 Annex A4 and in Practice D8321 Annex A2. D6122
3.2.43 Stokes line (band), n—a Raman line (band) that has a frequency lower than that of the incident monochromatic beam. E131
D8321 − 22
3.2.44 test performance index, n—an approximate measure of a laboratory’s testing capability, defined as the ratio of test method
reproducibility (R) to site precision (R'). D6792
3.3 Definitions of Terms Specific to This Standard:
3.3.1 analysis, n—in the context of this practice, the process of applying the multivariate model to a spectrum, preprocessed as
required, to predict a component concentration value or property, the prediction being referred to herein as a Predicted Primary
Test Method Result (PPTMR).
3.3.1 basestock, n—in the preparation of a biofuel, the petroleum derived blendstock to which a biocomponent is added.
3.3.3 calibration, n—a process for creating a multivariate model relating component concentrations or sample properties to spectra
for a set of known samples, referred to as calibration samples.
3.3.4 calibration samples, n—the set of samples with known (measured by the PTM) component concentrations or property values
that are used for creating a multivariate model.
3.3.5 calibration transfer, n—a method of applying a multivariate calibration developed using spectra from one analyzer for
analysis of spectra collected on a second analyzer by mathematically modifying the multivariate model or by instrument
standardization.
3.3.6 check sample, n—in the context of this practice, a check sample is a material that is representative of the product being
analyzed which is adequately stored in sufficient quantity to be used as a long-term check on analyzer performance; check samples
are used for Level B instrument performance tests, and as checks on calibration transfer.
3.3.7 chemical property, n—a property of a material associated with its elemental or molecular composition.
3.3.7.1 Discussion—
Examples of chemical properties include, but are not limited to sulfur content, benzene content, and aromatics content.
3.3.2 combination band, n—in vibrational spectroscopy, a spectral band that are observed in the vibrational spectrum of a
molecule when two or more fundamental vibrations are excited, or multiply excited simultaneously.
3.3.3 cross-validation, n—an exploratory data analysis tool which provides an assessment the optimal number of variables to use
in a multivariate model and estimates the model’s ability to predict new data not used in development of the model.
3.3.3.1 Discussion—
Cross-validation involves a repetitive procedure in which a calibration sample set is partitioned into two subsets, a training set
which is used to develop a multivariate model, and a testing set which is analyzed using this model. The procedure repeats using
different partitions and the results are combined to estimate the model’s predictive performance.
3.3.3.2 Discussion—
Cross-validation is a useful tool in guiding the development of the multivariate model, but it is not a substitute for validation of
the model with an independent set of validation samples.
3.3.4 fundamental band, n—in vibrational spectroscopy, a spectral band that occurs in the spectrum of a molecule when that
molecule makes a transition from the ground (v = 0) to first excited state (v = 1), where v is the vibrational quantum number.
3.3.5 homoscedastic, n—a condition where all the model errors have the same finite variance.
3.3.12 inlier, n—see nearest neighbor distance inlier. D6122
3.3.13 inlier detection methods, n—statistical tests which are conducted to determine if a spectrum resides within a region of the
multivariate calibration space, which is sparsely populated. D6122
D8321 − 22
3.3.14 instrument, n—for the purpose of this practice, the word instrument will be used describe all parts of the analyzer system
that are associated with the spectral measurement but will exclude all parts of the analyzer associated with sampling and sample
conditioning.
3.3.15 instrument standardization, n—a procedure for standardizing the response of multiple instruments such that a common
multivariate model is applicable for measurements conducted by these instruments, the standardization being accomplished by way
of adjustment of the spectrophotometer hardware or by way of mathematical treatment of the collected spectra. D6122
3.3.6 mean center, v—to scale a set of data by subtracting the mean value of the set.
3.3.6.1 Discussion—
To mean center spectra, calculate the average spectrum, and then subtract this average from each individual spectrum.
3.3.17 model degrees of freedom, (dof), n—the number of calibration samples minus the number of model variables where the
mean counts as a variable for mean centered models.
3.3.18 model variables, n—the independent variables upon which a multivariate model is based.
3.3.18.1 Discussion—
The model variables may be spectral intensity at individual spectral positions for MLR, principle components for PCR, or latent
variables for PLS. D6122
3.3.7 model validation, n—the process of testing a multivariate model with validation samples to determine accuracy and precision
of the PPTMR produced by the model relative to the PTMR.
3.3.8 model validation samples, n—a set of samples used in validating the model which are not part of the set of calibration
samples, and for which PTMRs are compared to PPTMRs.
3.3.8.1 Discussion—
This practice uses the phrase model validation samples to distinguish these from the validation samples defined in Practice D6122
used in validating analyzer performance.
3.3.21 multivariate model, n—the mathematical expression or the set of mathematical operations that relates component
concentrations or properties to spectra for a set of calibration samples.
3.3.21.1 Discussion—
The multivariate model includes any preprocessing done to the spectra or concentration or properties prior to the development of
the correlation between spectra and properties, and any post-processing done to the initially predicted results.
3.3.22 nearest neighbor distance inlier, n—a spectrum residing within a gap in the multivariate calibration space, the result for
which is subject to possible interpolation error. D6122
3.3.23 outlier detection limits, n—the limiting value for application of an outlier detection method to a spectrum, beyond which
the spectrum represents an extrapolation of the multivariate model. D6122
3.3.24 outlier spectrum, n—a spectrum whose analysis by a multivariate model represents an extrapolation of the model. D6122
3.3.9 overtone band, n—in vibrational spectroscopy, a spectral band that occurs in the vibrational spectrum of a molecule when
the molecule makes a transition from the ground state (v = 0) to an excited state higher than the first excited state (v > 1), where
v is the vibrational quantum number.
3.3.9.1 Discussion—
Because of anharmonicity, the frequency at which an overtone occurs will typically be less than v–1 times the frequency of the
fundamental vibration.
3.3.9.2 Discussion—
The intensity of overtones (absorbance or Raman scattering) decreases significantly as the vibrational quantum number increases.
3.3.26 performance property, n—a property of a material which measures how well the material functions in its intended use.
D8321 − 22
3.3.26.1 Discussion—
Examples of performance properties include research and motor octane numbers.
3.3.10 physical correction, n—a type of post-processing where the correction made to the numerical value produced by the
multivariate model is based on a separate physical measurement of, for example, sample density, sample path length, or particulate
scattering. D6122
3.3.28 physical property, n—a property of matter not involving in its manifestation a chemical change.
3.3.28.1 Discussion—
Examples of physical properties include, but are not limited to density, melting point, boiling point, vapor pressure, flash point,
cloud point, and pour point.
3.3.29 pre-processing, v—performing mathematical operations on raw spectral data prior to multivariate analysis or model
development, such as selecting wave length regions, correcting for baseline, smoothing, differentiation, data transformation, mean
centering, and assigning weights to certain spectral positions. D6122
3.3.30 post-processing, v—performing a mathematical operation on an intermediate analyzer result to produce the final result,
including correcting for temperature effects, adding a mean property value of the analyzer calibration, and converting into
appropriate units for reporting purposes. D6122
3.3.31 predicted primary test method result (PPTMR), n—result from the analyzer system, after application of any necessary
correlation, that is interpreted as predictions of what the primary test method results would have been, if it was conducted on the
same material. D6122
3.3.32 primary instrument, n—the instrument(s) on which calibration spectra are collected for the purpose of building a
multivariate model.
3.3.33 primary test method (PTM), n—the analytical procedure used to generate the reference values against which the analyzer
is both calibrated and validated. D6122
3.3.34 primary test method result (PTMR), n—test result produced from an ASTM or other established standard test method that
is accepted as the reference measure of a property. D6122
3.3.35 secondary instrument, n—an instrument not used in the development of the multivariate model, but which will be used for
analysis of new materials.
3.3.36 spectral intensity, n—a generic term referring to either infrared absorbance or Raman scattering intensity.
3.3.37 spectral position, n—a generic term referring to either wavelength or frequency position in spectrum.
3.3.38 standard error of calibration (SEC), n—a measure of the agreement between PPTMR and PTMR for the samples used in
developing a multivariate model,
n
SEC5Π~PPTMR 2 PTMR ! , where dof is the model degrees of freedom and n is the number of calibration samples. D6122
(
i i
dof i51
3.3.11 standard error of cross-validation, n—an estimate of the performance of a multivariate model obtained using
cross-validation.
3.3.12 standard error of validation (SEV), n—a measure of the performance of a multivariate model obtained by analyzing a set
of model validation samples and comparing the PPTMR to PTMR measured on these samples.
3.3.12.1 Discussion—
v
SEV5 PPTMR 2 PTMR where v is the number of model validation samples.
Π~ !
( i i
v
i51
D8321 − 22
3.3.13 surrogate calibration, n—a multivariate calibration that is developed using a calibration set which consists of mixtures
which contain substantially fewer chemical components than the samples which will ultimately be analyzed.
3.3.14 surrogate method, n—a standard test method that is based on a surrogate calibration.
3.3.15 vibrational spectroscopy, n—infrared and Raman spectroscopies which involve the measurement of vibrational transitions
in molecules.
3.3.16 X-block, n—the spectral data matrix used in the calibration or validation of a multivariate model.
3.3.17 Y-block, n—the component concentration or property data matrix using in the calibration or validation of a multivariate
model.
3.4 Symbols:
3.4.1 Scalars are represented by italicized normal face letters. Vectors are represented by boldface italicized lowercase letters.
Matrices are represented by boldface italicized uppercase letters. Lower case i and j as subscripts are indices indicating specific
samples, spectral positions, or model variables.
-1
3.4.2 — a minus 1 as a superscript indicates a matrix inverse.
3.4.3 a(λ)—sample absorbance at wavelength λ.
3.4.4 a(λ)—the absorptivity of the absorbing species at wavelength λ.
3.4.5 a—an absorbance spectrum.
3.4.6 A—a c by f matrix with component spectra as rows, used in the matrix form of the Beer-Lambert Law.
3.4.7 b—the pathlength (sample thickness).
3.4.8 b—a single beam background spectrum.
3.4.9 B—an n by n diagonal matrix of pathlengths for the matrix form of the Beer-Lambert Law.
3.4.10 c—the number of absorbing or scattering components in a sample.
3.4.11 c—concentration of absorbing or scattering species.
3.4.12 C—an n by c matrix of component concentrations in the matrix form of the Beer-Lambert Law.
3.4.13 e—an n by 1 vector of property prediction errors.
3.4.14 e —an n times l by 1 vector of property prediction errors produced during cross-validation when only one property is
cv
modeled.
3.4.15 E—an n by p matrix of property prediction errors.
3.4.16 E —an n times l by p vector of property prediction errors produced during crossvalidation when multiple properties are
cv
modeled.
3.4.17 f—the number of spectral positions in the spectral data used in a model.
D8321 − 22
3.4.18 I —in a Raman measurement, the power of the incident laser.
o
3.4.19 I —in a Raman measurement, the intensity of the scattered light.
R
3.4.20 l—during cross-validation, the number of times each sample is left out of the model construction and analyzed.
3.4.21 n—the number of calibration samples.
3.4.22 k—the number of variables used in a model, where variables may be, for example selected spectral data points for MLR,
Principal Components for PCR, or latent variables for PLS.
3.4.23 K—a term in the Raman scattering equation that includes the solid angle visible to the Raman collection optics, and the
volumn of the sample that is illuminated by the laser and visible to the collection optics.
3.4.24 p—the number of properties being modeled.
3.4.25 p—the f by 1 prediction vector.
3.4.26 P—the f by p prediction matrix with p for individual properties as columns.
3.4.27 PRESS—the Predicted Residual Error Sum of Squares from cross-validation.
3.4.28 r—number of replicate PTM measurements.
3.4.29 s—a single beam sample spectrum.
3.4.30 t(λ)—the transmittance of a sample at wavelength λ.
3.4.31 t—a transmittance spectrum equal to the ratio of s to b.
t
3.4.32 —as a superscript, indicates a vector or matrix transpose.
3.4.33 σ —the Raman scattering cross section for the scattering species.
R
3.4.34 v—a vibrational energy level quantum number.
th
3.4.35 x —a 1 by f row vector containing the spectrum of the i sample.
i
3.4.36 x —a 1 by f row vector containing the spectrum of the unknown sample being analyzed.
unk
3.4.37 X—the spectral data matrix which contains the n spectra as rows of length f, also referred to as the model X-Block.
3.4.38 x¯—the average spectrum; the average down the columns of X.
3.4.39 xˆ—the estimate of a spectrum based on the multivariate model.
3.4.40 X¯—an n by f matrix where each of the n rows contain x¯ used in mean centering X.
th
3.4.41 y —the PTMR value for a single property for the i sample.
i
th
3.4.42 yˆ —the PPTMR value for a single property for the i sample.
i
D8321 − 22
3.4.43 y—an n by 1 vector of PTMR values, also referred to as the model Y-Block; y contains the PTMR values for a single
property for all the samples defined in the X-Block.
3.4.44 y¯—The average of the values in y.
3.4.45 yˆ—an n by 1 vector of PPTMR values; yˆ contains the PPTMR values for a single property for all the samples defined
in the X-Block.
3.4.46 yˆ —an n times l by 1 vector of estimated PPTMR values produced during cross validation when a single property is
cv
modeled.
3.4.47 Y—an n by p matrix of PTMR values, each column of which correspond to a y vector for a different property.
3.4.48 Yˆ—an n by p matrix of PPTMR values, each column of which correspond to a yˆ vector for a different property.
3.4.49 Yˆ —an n time l by p matrix of estimated PPTMR values produced during cross validation when multiple properties are
cv
modeled; each column of which correspond to a yˆ vector for a different property.
cv
3.4.50 z —the transform of m ; z = max(m ) – m .
i i i i i
3.4.51 z¯ —the transform of m¯ ; z¯ = max(m¯ ) – m.
j j j j
4. Summary of Practice
4.1 Multivariate mathematics is applied to correlate the spectra measured for a set of calibration samples to component
concentrations or property values for the set of samples. The resultant multivariate model is applied to the analysis of spectra of
unknown samples to predict the component concentration or property values for the unknown sample.
4.1.1 This practice applies to both infrared and Raman spectra. The infrared spectra are collected in the mid-infrared spectral
region, the near-infrared spectral region or, in some cases, in an extended region that covers part of both the mid- and near-infrared.
4.1.2 The component concentrations and property values which are used in establishing and validating the multivariate model are
measured by a Primary Test Method (PTM), typically an ASTM standard test method. The values are herein referred to as Primary
Test Method Results (PTMR).
4.1.3 The predicted results produced by application of the model for the analysis of a spectrum are referred to as Predicted Primary
Test Method Results (PPTMR).
4.2 Multilinear regression (MLR), principal components regression (PCR), partial least squares (PLS) and locally weighted
regression (LWR) are examples of multivariate mathematical techniques that are commonly used for the development of the
multivariate model. Other mathematical techniques are also used, but may not detect outliers, and may not be validated by the
procedure described in this practice. It is the user’s responsibility to verify that the mathematics employed satisfy the requirements
of this practice.
4.3 Statistical tests are applied to detect outliers during the development of the multivariate model. Outliers include high leverage
samples (samples whose spectra contribute a statistically significant fraction of one or more of the spectral variables used in the
model), samples with high spectral residuals (suggestive of unmodeled components) and samples whose PTMR values are
inconsistent with the model.
4.4 Validation of the multivariate model is performed by using the model to analyze a set of model validation samples and
statistically comparing the PPTMR values for the model validation samples to PTMR values measured for these samples, to test
for bias in the model and for the degree of agreement of the model with the PTM.
4.5 Statistical tests are applied to detect when PPTMR produced by application of the model represent extrapolation of the
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calibration. A spectrum is labeled an outlier if its leverage exceeds that of the calibration samples, or if the spectrum produces high
spectral residuals suggesting the presence of components which were not in the calibration samples. Optionally, a nearest neighbor
outlier test may be employed to determine if the spectrum being analyzed falls in a void in the multivariate space defined by the
calibration spectra.
4.6 Statistical expressions for calculating the repeatability of the spectroscopic analysis and the expected agreement between the
spectroscopic analysis and the PTM are given.
5. Significance and Use
5.1 This practice can be used to establish the validity of the results obtained by an infrared (IR) spectrophotometer or Raman
spectrometer at the time the calibration is developed. The ongoing validation of PPTMRs produced by analysis of unknown
samples using the multivariate model is covered separately (see for example, Practice D6122).
5.2 The multivariate calibration procedures define the range over which measurements are valid and demonstrate whether the
accuracy and precision of the analysis outputs meet user requirements.
5.3 This practice describes sampling procedures that must be followed to ensure that the sample which is analyzed by the
spectrophotometer or spectrometer is the same as the sample analyzed by the PTM. The sampling procedures apply to analyses
done on lab analyzers, at-line analyzers, and online analyzers.
6. Vibrational Spectroscopies
6.1 Both infrared and Raman spectroscopies measure signals associated with molecular vibrations. Various groups of bonded
atoms in molecules give rise to vibrations that occur at characteristic frequencies. These groups of bonded atoms are referred to
as functional groups, and the characteristic frequencies as functional group frequencies. While each compound will have a unique
spectrum, in complex mixtures such as petroleum samples, the overlap of these spectra often p
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