EP0801737A1 - Methode d'analyse infrarouge non lineaire a plusieurs variables - Google Patents

Methode d'analyse infrarouge non lineaire a plusieurs variables

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Publication number
EP0801737A1
EP0801737A1 EP95943410A EP95943410A EP0801737A1 EP 0801737 A1 EP0801737 A1 EP 0801737A1 EP 95943410 A EP95943410 A EP 95943410A EP 95943410 A EP95943410 A EP 95943410A EP 0801737 A1 EP0801737 A1 EP 0801737A1
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EP
European Patent Office
Prior art keywords
linear
property
ron
estimate
composition data
Prior art date
Legal status (The legal status is an assumption and is not a legal conclusion. Google has not performed a legal analysis and makes no representation as to the accuracy of the status listed.)
Withdrawn
Application number
EP95943410A
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German (de)
English (en)
Other versions
EP0801737A4 (fr
Inventor
Bruce N. Perry
James M. Brown
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ExxonMobil Technology and Engineering Co
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Exxon Research and Engineering Co
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Publication date
Priority claimed from US08/567,613 external-priority patent/US5641962A/en
Application filed by Exxon Research and Engineering Co filed Critical Exxon Research and Engineering Co
Publication of EP0801737A1 publication Critical patent/EP0801737A1/fr
Publication of EP0801737A4 publication Critical patent/EP0801737A4/fr
Withdrawn legal-status Critical Current

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Classifications

    • G—PHYSICS
    • G01—MEASURING; TESTING
    • G01N—INVESTIGATING OR ANALYSING MATERIALS BY DETERMINING THEIR CHEMICAL OR PHYSICAL PROPERTIES
    • G01N21/00—Investigating or analysing materials by the use of optical means, i.e. using sub-millimetre waves, infrared, visible or ultraviolet light
    • G01N21/17—Systems in which incident light is modified in accordance with the properties of the material investigated
    • G01N21/25—Colour; Spectral properties, i.e. comparison of effect of material on the light at two or more different wavelengths or wavelength bands
    • G01N21/31—Investigating relative effect of material at wavelengths characteristic of specific elements or molecules, e.g. atomic absorption spectrometry
    • G01N21/35—Investigating relative effect of material at wavelengths characteristic of specific elements or molecules, e.g. atomic absorption spectrometry using infrared light
    • G01N21/3577—Investigating relative effect of material at wavelengths characteristic of specific elements or molecules, e.g. atomic absorption spectrometry using infrared light for analysing liquids, e.g. polluted water

Definitions

  • This invention relates generally to a method for determining physical or chemical properties of materials using infra-red analysis and more specifically to a method for improving the estimation of properties of interest in samples of materials based on non linear correlations to their infra-red spectra.
  • a particular use of the method is to obtain an improved estimation of octane number of gasolines by infra-red analysis.
  • Physical or chemical properties such as octane number, cetane number, and aromatics content can be usefully correlated to infrared spectra for appropriate sample sets.
  • Linear techniques such as PLS, PCR, and extensions such as CPSA (Constrained Principal Spectra Analysis, J.M. Brown, U.S. Patent 5,121,337) and the method of DiForggio, U.S. Patent 5,397,899, provide workable correlations in many circumstances.
  • the object of the correlations is to calibrate the infrared analyzer so that it can be employed to estimate the physical or chemical properties of future unknown samples on the basis of their infrared spectra.
  • An important consideration in the implementation of these analyzers is their ability to statistically detect outlier samples, i.e. samples whose analysis represents an extrapolation of the predictive model.
  • linear correlation techniques such as PLS, PCR and CPSA do not provide calibrations that predict physical or chemical properties with sufficient accuracy. Inaccurate calibrations can be an indication that the property being estimated depends in a nonlinear manner on sample composition.
  • Various techniques have been suggested for addressing this problems including localized linear regression, MARS, and Neural Nets, but such techniques generally require large numbers of coefficients to be fit, and generally do not provide the statistical guidance available from linear techniques.
  • a variety of linear calibrations are in use in estimating property and component concentrations.
  • Hieftje, Honigs and Hirschfeld (US. Patent 4,800,279) discussed linear methods for evaluation of physical properties of hydrocarbons.
  • Lambert and Martens (EP 0 285 251) described a linear method for estimating octane numbers.
  • Maggard discussed linear methods for estimating octane numbers (US. Patent 4,963,745) and for estimating aromatics in hydrocarbons (US. Patent 5,145,785).
  • Brown US. Patent 5,121,337) discusses linear methods based on Constrained Principal Spectra Analysis (CPSA) and gives various examples.
  • CPSA Constrained Principal Spectra Analysis
  • Espinosa, et al. (EP 0 305 090 Bl and EP 0 304 232 A2) describe methods for direct determination of physical properties of hydrocarbons.
  • Espinosa, et al. include linear terms (absorption at selected frequencies), quadratic terms (products between absorptions at different frequencies) and homographic terms (quotients between absorptions at different frequencies) in their equations. While the equations presented in their examples generally contain only a few nonlinear terms, these quadratic and homographic terms were chosen either arbitrarily or statistically from among a large number of possible nonlinear terms.
  • Nonlinear multivariate calibration methods have been reviewed by Sekulic, et al. (Analytical Chemistry, 65 (1993) 835A-845A). Locally weighted regression (LWR), Projection Pursuit Regression (PPR), Alternating Condition Expectations (ACE), Multivariate Adaptive Splines (MARS), Neural Networks, nonlinear Principal Components Regression (NLPCR) and nonlinear Partial Least Squares (NLPLS) are discussed. All these techniques are much more computationally difficult than the nonlinear postprocessing method of the current invention.
  • the present invention is a method to significantly improve the performance of spectrometer-based analyzers which are used to measure test samples and provide sample property or composition data for process or analytical applications.
  • the method determines property or composition data of a test sample from a nonlinear correlation between the spectrum of the test sample and the value of that property or composition data of the test sample.
  • the method involves the following steps:
  • the nonlinear calibration is used to determine the property or composition data for the tests sample by:
  • step (3) the application of the linear correlation determined in step (3) to the spectrum to obtain a linear estimate of the property or composition data
  • step (8) the application of the nonlinear correction determined in step (5) to the linear estimate in step (7) to estimate the property or composition data of the test sample;
  • the estimate of the property or composition data for the test sample in step (8) involves substituting the linear estimate from step (7) into the nonlinear correction equation from step (5).
  • the estimate of the property or composition data for the test sample in step (8) involves substituting the linear estimate from step (7) into the nonlinear correction equation from step (5), and adding the resultant nonlinear correction to the linear estimate from step (7) to produce the final estimate.
  • the linear correlation in step (3) involves a linear multivariate calibration developed by regressing the reference property data against variables derived from the spectral data.
  • the spectral variables may be absorbance values at specific wavelengths and the regression method Multilinear Regression (MLR).
  • MLR regression method Multilinear Regression
  • PCR Principal Components Regression
  • PLS Partial Least Squares
  • CPSA Constrained Principal Spectra Analysis
  • the residual i.e. the difference between the actual reference property value and the value predicted by the linear model, is obtained for each sample in the calibration set.
  • the property residuals are then fit as a nonlinear function (e.g. quadratic or cubic function) of the linearly predicted values.
  • the actual reference values can be fit directly as a nonlinear function of the linearly predicted values.
  • the method can result in significantly improved calibration accuracy and performance of spectrometer-based analyzers, while maintaining the outlier detection capabilities of linear methods.
  • Figure 1 shows a plot of engine measured Research Octane Number (RON) versus RON estimated via Linear CPSA calibration in Example 1. Circles represent data for 365 Powerformate samples in calibration dataset. Lines are ASTM 95% reproducibiuty limits for RON Engine measurements calculated relative to linearly estimated RON.
  • Figure 2 shows a plot of residuals (RON Estimated via linear CPSA calibration minus RON measured by engine) versus RON estimated via linear CPSA calibration for dataset in Example 1. Circles represent residual values for 365 Powerformate samples in calibration dataset. The line is the cubic polynomial function of the linearly estimated RON which best fits the residuals.
  • Figure 3 shows a plot of engine measured Research Octane Number (RON) versus RON estimated via Nonlinear Post-Processing of the Linear CPSA calibration in Example 1. Circles represent data for 365 Powerformate samples in calibration dataset. Lines are ASTM 95% reproducibiuty limits for RON Engine measurements calculated relative to nonlinearly estimated RON.
  • Figure 4 shows a plot of engine measured Research Octane Number (RON) versus RON estimated via Linear CPSA calibration in Example 2. Circles represent data for 385 blended gasoline samples in calibration dataset. The line represents the cubic polynomial funtion of the linearly estimated RON that is the best fit of the engine RON values.
  • Figure 5 shows a plot of engine measured Research Octane Number (RON) versus RON estimated via Linear CPSA calibration for test dataset in Example 2.
  • Diamonds represent data for 238 blended gasoline samples in test dataset. Lines are ASTM 95% reproducibility limits for RON Engine measurements calculated relative to linearly estimated RON.
  • Figure 6 shows a plot of residuals (RON Estimated via linear CPSA calibration minus RON measured by engine) versus RON estimated via linear CPSA calibration for dataset in Example 2. Circles represent residual values for 385 blended gasoline samples in calibration dataset. The line is the cubic polynomial function of the linearly estimated RON which best fits the residuals.
  • Figure 7 shows a plot of residuals (RON Estimated via linear CPSA calibration minus RON measured by engine) versus RON estimated via linear CPSA calibration for the test dataset in Example 2. Circles represent residual values for 238 blended gasoline samples in the test dataset. The line is the cubic polynomial function of the linearly estimated RON which was derived from the calibration set.
  • Figure 8 shows a plot of engine measured Research Octane Number (RON) versus RON estimated via Nonlinear Post-Processing of the Linear CPSA calibration for the test dataset in Example 2.
  • Diamonds represent data for 238 blended gasoline samples in test dataset. Lines are ASTM 95% reproducibility limits for RON Engine measurements calculated relative to Nonlinearly estimated RON.
  • Figure 9 shows a plot of engine measured Research Octane Number (RON) versus RON estimated via Linear MLR calibration for the test dataset in Example 3. Circles represent data for 238 blended gasoline samples in test dataset. Lines are ASTM 95% reproducibility limits for RON Engine measurements calculated relative to linearly estimated RON.
  • Figure 10 shows a plot of engine measured Research Octane Number (RON) versus RON estimated via Linear MLR calibration in Example 3. Squares represent data for 385 blended gasoline samples in calibration dataset. The line represents the cubic polynomial function of the linearly estimated RON that is the best fit of the engine RON values.
  • Figure 11 shows a plot of engine measured Research Octane Number (RON) versus RON estimated via Nonlinear Post-Processing of the Linear MLR calibration for the test dataset in Example 3. Circles represent data for 238 blended gasoline samples in test dataset. Lines are ASTM 95% reproducibility limits for RON Engine measurements calculated relative to nonlinearly estimated RON. DESCRIPTION OF THE PREFERRED EMBODIMENT
  • Linear calibration methods have been used to relate spectral measurements to chemical compositions, physical properties, and performance properties.
  • the linear methods are calibrated or trained using a set of samples with known compositions or properties, i.e. samples whose composition or property has been measured by a reference technique.
  • the calibration is then validated by applying it for the analysis of a separate test set, and comparing the predicted results to the results produced by the reference method.
  • the calibrated analyzer is used to analyze unknowns to predict composition or property data.
  • the spectra of the calibration samples form the columns of a matrix X, which is of dimension /by //, where/ is the number of individual data points (frequencies or wavelengths) in a spectrum, and n is the number of calibration samples. If the vector y contains the composition/property data for the n calibration samples, then the linear model is built by solving for p in the equation
  • Equation [1] cannot be solved directly.
  • Three approaches are typically employed. For MLR, k individual rows of X (individual frequencies or wavelengths) are chosen such that k ⁇ n, and X is replaced by the smaller matrix X* containing only the k rows, p is then obtained by calculating the pseudo inverse of the X k matrix.
  • the matrix X is decomposed into the product of three matrices, U (the loadings matrix of dimension /by k), ⁇ (the singular value matrix of dimension k by k), and V (the scores matrix of dimension n by k)
  • the scores are then regressed against the property vector y to form the model.
  • PLS involves a similar decomposition of X into orthogonal matrices and regression of y against a scores matrix.
  • y is the estimated property or component concentration for the linear model, and is given by
  • the post-processing can take one of two forms. Either the residuals, r,, or the property/composition values, y, are regressed as a nonlinear function of the linearly estimated properties, y, .
  • /(y,) stands for the nonlinear function of the linearly estimated property/component values.
  • the nonlinear function is preferably a polynomial in powers of the linearly estimated property/component.
  • the post-processing is quadratic, and if m is 3, the post-processing is cubic.
  • the choice of m is made based on the ability of the post-processing function to fit the structure observed in the residuals. If the residuals are fit as a linear function of the linearly estimated properties using [5] or [7], then the nonlinear estimate for the component/property is obtained by summing the linear estimate, and the nonlinearly estimated residual
  • r is the nonlinear estimate for the residual obtained by applying [5] or [7] to the linearly estimated property. If [6] or [8] are used, the nonlinear estimate for the component/property is obtained directly.
  • the spectral matrix X can be preprocessed prior to the model development by, for instance, mean centering, baseline correction, numerical derivatives, or orthogonalization to baseline and correction spectra (e.g. use of the CPSA algorithm).
  • a single set of calibration spectra can be used to develop models for multiple properties, each of which can be separately post-processed.
  • Components that are predicted can include individual chemical species (e.g. benzene), lumped chemical species (e.g. olefins or aromatics), physical properties (e.g. refractive index, specific gravity), chemical properties (e.g. stability) or performance properties (e.g. octane and cetane numbers).
  • individual chemical species e.g. benzene
  • lumped chemical species e.g. olefins or aromatics
  • physical properties e.g. refractive index, specific gravity
  • chemical properties e.g. stability
  • performance properties e.g. octane and cetane numbers
  • Absorbances in the 7000-5300.392 cm" 1 range are too weak to contribute signigicantly to the correlation.
  • the frequency ranges from 3150.151- 2599.573 cm" 1 and from 1649.804 - 400 cm' 1 are excluded since they contain absorbances that exceed the dynamic response range of the FT-IR instrumentation.
  • the frequency range from 2445.296 - 2274.627 cm -1 is excluded to avoid interferences from atmospheric carbon dioxide.
  • Two sets of polynomial corrections are employed in the CPSA calibration to compensate for baseline variations, one set covering the range from 5300.392 - 3150.151 cm" 1 , and the second set covering the range from 2599.573 - 1649.804 cm” 1 .
  • Water vapor corrections are also employed in the CPSA calibration to minimize the effects of variations in instrument purge on the estimated values.
  • Five constrained principal components were used in developing the RON calibration. The coefficients for the five constrained principal components were determined using a PRESS based step- wise regression. A plot of the linearly predicted RON value versus the reference (engine) value is shown in Figure 1. The standard error of estimate of the data in Figure 1 is 0.54 RON numbers.
  • the RON residuals (FT-IR linearly predicted RON minus Engine RON) were regressed against a quadratic function of the linearly-predicted RON.
  • a plot of the RON residuals versus linearly-predicted RON value is shown in Figure 2, together with a quadratic fit to the residuals.
  • Figure 3 shows the result of the model obtained by applying the quadratic correction of Figure 2 to the data of Figure 1. This is equivalent to fitting the reference (engine) RON value as a quadratic function of the linearly predicted RON.
  • the standard error of estimate for Figure 2 is 0.41 RON numbers.
  • nonlinear post-processing method described herein results in a 24% improvement in the RON estimation over the linear method previously used, but requires that only three additional coefficients be determined beyond the five coefficients for the original linear correlation.
  • the frequency ranges from 3150.151- 2400 cm” 1 and from 1634.376 - 400 cm” 1 are excluded since they contain absorbances that exceed the dynamic response range of the FT-IR instrumentation.
  • the frequency range from 2400 - 2200.381 cm” 1 is excluded to avoid interferences from atmospheric carbon dioxide.
  • Two sets of polynomial corrections are employed in the CPSA calibration to compensate for baseline variations, one cubic set covering the range from 5300.392 - 3150.151 cm" 1 , and the second quadratic set covering the range from 2599.573 - 1649.804 cm” 1 .
  • Water vapor corrections are also employed in the CPSA calibration to minimize the effects of variations in instrument purge on the estimated values. Fourteen constrained principal components were used in developing the RON calibration.
  • the coefficients for the fourteen constrained principal components were determined using a PRESS based step-wise regression.
  • a plot of the linearly predicted RON value versus the reference (engine) value is shown in Figure 4.
  • the Standard Error of Calibration for the linear CPSA model is 0.411.
  • the linear model shown in Figure 4 was applied for the analysis of 238 Blended Gasoline samples (314 individual engine determinations) which were not in the set of used in the development of the model.
  • the predictions obtained from the linear model for these test samples are shown in Figure 5.
  • the Standard Error of Validation for the test samples is 0.569 , and only 84% of the samples have predicted values that agree with the reference engine values to within the ASTM engine reproducibility limit.
  • the RON residuals (FT-IR linearly predicted RON minus Engine RON) for the 385 samples in the calibration set were regressed against a cubic function of the linearly-predicted RON.
  • a plot of the RON residuals versus linearly-predicted RON value is shown in Fig. 6, together with a cubic fit to the residuals. With the cubic post ⁇ processing of the linearly estimated RON values, the Standard Error of Calibration is reduced to 0.327.
  • Figure 7 shows the RON residuals (FT-IR linearly predicted RON minus Engine RON) for the 238 samples in the test set, plotted against a cubic curve generated using the coefficients derived from the fit of the calibration samples.
  • Figure 8 shows Engine RON for the test set plotted against the RON values estimated by cubic post ⁇ processing of the linearly estimated RON values. With the cubic post-processing, the Standard Error of Validation is reduced to 0.397, and 95% of the estimated RON values agree with the reference engine values to within the ASTM reproducibility of the RON engine.
  • the nonlinear post-processing method results in a 30% improvement in the RON estimate for the test set, but requires that only 4 additional coefficients be determined beyond those used in the original linear calibration.
  • ASTM tests such as the D2699 RON test, measurements made by two different operators in two different laboratories are expected to be within the quoted reproducibility 95% of the time.
  • the IR RON estimates agree with D2699 RON test data to within the reproducibility 95% of the time demonstrating that the IR estimate is equivalent to the engine determination.
  • Example 2 The same set of 385 Blended Gasoline sample spectra described in Example 2 were used to generate a Multiple Linear Regression (MLR) model according to the method described by Lambert and Martens (EP 0 285 251 Bl, Aug. 28, 1991).
  • the absorbances at the frequencies closest to the 15 frequencies given by Lambert and Martens (Table 1) were corrected by subtracting the absorbance at the baseline point, and then were regressed against engine RON values to obtain the coefficients in Table 2.
  • the Standard Error of Estimate for the linear MLR model was 0.459.
  • the MLR model was used to analyze the same set of 238 Blended gasoline test sample spectra. The MLR estimates were compared to the 314 engine determinations for the test set. The predictions from the linear MLR model are shown in Figure 9. For the linear MLR model, the Standard Error of Validation for the test samples is 0.457, and only 81% of the samples are predicted to within the ASTM engine reproducibility limit.
  • the cubic post-processing was applied to the linear MLR estimates for the test set of 238 blended gasolines.
  • the Nonlinear Post -Processed MLR estimates are compared to the 314 individual engine measurements in Figure 11.
  • the Standard Error of Validation for the test set is 0.406, and 91% of the samples are estimated to within the reproducibility limits of the ASTM RON test.
  • the cubic Nonlinear Post-processing method results in an improvement of 11% over the linear MLR calibration, but requires only 4 additional coefficients to be determined beyond those used in the linear MLR calibration.

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Abstract

On obtient un indice d'octane recherche (IOR) d'un échantillon de test, ainsi que la définition d'autres propriétés physiques ou chimiques ou de données relatives à sa composition, par une analyse spectrale infrarouge dudit échantillon de test et d'un ensemble d'échantillons d'étalonnage. On obtient une meilleure définition des propriétés susmentionnées grâce à l'aide du spectre de l'échantillon de test et d'un modèle de prédiction linéaire sur lequel on effectue une correction non linéaire.
EP95943410A 1994-12-13 1995-12-13 Methode d'analyse infrarouge non lineaire a plusieurs variables Withdrawn EP0801737A4 (fr)

Applications Claiming Priority (5)

Application Number Priority Date Filing Date Title
US35497694A 1994-12-13 1994-12-13
US354976 1994-12-13
US08/567,613 US5641962A (en) 1995-12-05 1995-12-05 Non linear multivariate infrared analysis method (LAW362)
US567613 1995-12-05
PCT/US1995/016129 WO1996018881A1 (fr) 1994-12-13 1995-12-13 Methode d'analyse infrarouge non lineaire a plusieurs variables

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EP0801737A1 true EP0801737A1 (fr) 1997-10-22
EP0801737A4 EP0801737A4 (fr) 1999-03-31

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JP (1) JP3671241B2 (fr)
AU (1) AU689016B2 (fr)
CA (1) CA2208216C (fr)
WO (1) WO1996018881A1 (fr)

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JP3706437B2 (ja) * 1996-07-13 2005-10-12 株式会社堀場製作所 多成分水溶液の分析方法
JP3992188B2 (ja) * 2002-10-15 2007-10-17 株式会社キャンパスクリエイト 性状予測方法
WO2005111583A1 (fr) * 2004-05-17 2005-11-24 The New Industry Research Organization Procede et dispositif pour examiner de maniere non destructive un constituant de legume ou similaire par spectroscopie proche infrarouge
CN100425975C (zh) * 2004-07-29 2008-10-15 中国石油化工股份有限公司 由近红外光谱测定汽油性质数据的方法
US8017910B2 (en) * 2008-10-20 2011-09-13 Nalco Company Method for predicting hydrocarbon process stream stability using near infrared spectra
CN103134767B (zh) * 2013-01-30 2015-04-01 华中科技大学 一种红外光谱校正鉴定白酒品质的方法
JP6725928B1 (ja) * 2020-02-13 2020-07-22 東洋インキＳｃホールディングス株式会社 回帰モデル作成方法、回帰モデル作成装置、及び、回帰モデル作成プログラム
CN112683816B (zh) * 2020-12-25 2021-08-06 中船重工安谱（湖北）仪器有限公司 一种光谱模型传递的光谱识别方法

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EP0305090A2 (fr) * 1987-08-18 1989-03-01 Bp Oil International Limited Méthode pour la détermination directe de propriétés physiques de produits hydrocarbures
US5337140A (en) * 1991-07-30 1994-08-09 Horiba, Ltd. Optical detecting system wtih self-correction

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US4800279A (en) * 1985-09-13 1989-01-24 Indiana University Foundation Methods and devices for near-infrared evaluation of physical properties of samples
US5349188A (en) * 1990-04-09 1994-09-20 Ashland Oil, Inc. Near infrared analysis of piano constituents and octane number of hydrocarbons
US5223714A (en) * 1991-11-26 1993-06-29 Ashland Oil, Inc. Process for predicting properties of multi-component fluid blends

Patent Citations (2)

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Publication number Priority date Publication date Assignee Title
EP0305090A2 (fr) * 1987-08-18 1989-03-01 Bp Oil International Limited Méthode pour la détermination directe de propriétés physiques de produits hydrocarbures
US5337140A (en) * 1991-07-30 1994-08-09 Horiba, Ltd. Optical detecting system wtih self-correction

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Title
See also references of WO9618881A1 *

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Publication number Publication date
AU4468596A (en) 1996-07-03
JPH10512667A (ja) 1998-12-02
WO1996018881A1 (fr) 1996-06-20
CA2208216A1 (fr) 1996-06-20
AU689016B2 (en) 1998-03-19
EP0801737A4 (fr) 1999-03-31
CA2208216C (fr) 2007-03-13
JP3671241B2 (ja) 2005-07-13

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