Evaluation of undetectable perturbations of peak parameters estimated by the least square curve fitting of analytical signal consisting of overlapping peaks (original) (raw)
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Based on the concept of Big Data Modeling, the errors in determining peak parameters of noisy Gaussian quartets using nonlinear least squares curve fitting have been evaluated. The probability that the relative error in estimating each model parameter is not greater than a priory given limit for a given fitting error has been found. Obtained results showed that small fitting error does not guarantee that the fitting algorithm does converge to the correct peak parameters. It was found that the mean probability is a useful measure of the effectiveness of the curve fitting procedure.
Based on the concept of Big Data Modeling, the errors in determining peak parameters of noisy Gaussian quartets using nonlinear least squares curve fitting have been evaluated. The probability that the relative error in estimating each model parameter is not greater than a priory given limit for a given fitting error has been found. Obtained results showed that small fitting error does not guarantee that the fitting algorithm does converge to the correct peak parameters. It was found that the mean probability is a useful measure of the effectiveness of the curve fitting procedure.
Talanta, 1986
The resolving power of multicomponent spectra analysis and the computation reliability of the stability constants and molar absorptivities determined for nine variously protonated anions of three sulphonephthaleins and an impurity, by analysis of data for a mixture by programs SQUAD(84) and PSEQUAD(83), has been examined by use of synthetic and experimentally measured spectra containing severely overlapping spectral bands. The model mixture of Bromocresol Green, Phenol Red, Thymol Blue and azoxine as impurity, with five yellow, three blue and one red species in the pH range from 2 to 10, was used to examine the influence of precision of spectral data and of use of the spectra of the individual components, on the precision and accuracy of the estimated parameters when the chemical model is known. An efficient computation strategy has been found and both programs were shown to lead to the same values and reliability of the parametric estimates. Of the various diagnostics considered, the goodness-of-fit achieved is used as the criterion of whether the parameters found adequately represent the data.
Parabolic-Lorentzian modified Gaussian model for describing and deconvolving chromatographic peaks
… of Chromatography A, 2002
A new mathematical model for characterising skewed chromatographic peaks, which improves the previously reported polynomially modified Gaussian (PMG) model, is proposed. The model is a Gaussian based equation whose variance is a combined parabolic-Lorentzian function. The parabola accounts for the non-Gaussian shaped peak, whereas the Lorentzian function cancels the variance growth out of the elution region, which gives rise to a problematic baseline increase in the PMG model. The proposed parabolic-Lorentzian modified Gaussian (PLMG) model makes a correct description of peaks showing a wide range of asymmetry with positive and / or negative skewness. The new model is shown to give better fittingś than other models as the Li, log-normal or Pap-Papai models, which have a different mathematical basis. The model parameters are also related to peak properties as the skewness and kurtosis. The PLMG model is applied to the deconvolution of peaks in binary mixtures of structurally related compounds that are highly overlapped (retention times in min): oxytetracycline (9.00)-tetracycline (10.20), sulfathiazole (3.67)-sulfachloropyridazine (3.93), and sulfisoxazole (5.14)-sulfapyridine (5.24). The use of non-linear least-squares calibration in combination with the PLMG model gave superior results than the classical multiple linear least-squares and partial least-squares regressions. The proposed method takes into account run to run changes in retention time that occur along the injection of standards and samples, and the possible interactions that exist between the coeluting compounds. This decreases significantly the quantitation errors.
Journal of Chromatography A, 2001
The problem of the appropriate choice of the function that describes a chromatographic peak is examined in combination with the deconvolution of overlapped peaks by means of the non-linear least-squares method. It is shown that the majority of the functions proposed in the literature to describe chromatographic peaks are not suitable for this purpose. Only the polynomial modified Gaussian function can describe almost every peak but it is mathematically incorrect unless it is redefined properly. Two new functions are proposed and discussed. It is also shown that the deconvolution of an overlapping peak can be done with high accuracy using a non-linear least-squares procedure, like Microsoft Solver, but this target is attained only if we use as fitted parameters the position of the peak maximum and the peak area (or height) of every component in the unresolved chromatographic peak. In case we use as fitted parameters all the parameters that describe each single peak enclosed in the multi-component peak, then Solver leads to better fits, which though do not correspond to the best deconvolution of the peak. Finally, it is found that Solver gives much better results than those of modern methods, like the immune and genetic algorithms.
Chromatographic Peak Shape Analysis and Modeling
1990
Various aspects of chromatographic peak quantitation and shape characterization are investigated in detail for single and overlapping chromatographic peaks. From the viewpoint of providing better quantitation of real chromatographic data while minimizing computational complexity, the results presented should be easily incorporated into existing routine chromatographic data analysis regimes. Three topics applicable to modem chromatographic data analysis are considered. First, progress in the application of the exponentially modified Gaussian (EMG) function to chromatography is reviewed. The review covers the following areas: (1) equations derived from the model, (2) studies of inherent errors in the quantitation of chromatographic peaks via use of the EMG model, (3) chromatographic applications since 1983 and (4) applications to flow injection analysis. The information discussed and the references included in this review should provide a valuable resource for those researchers consid...
Separations
Selectivity in separation science is defined as the extent to which a method can determine the target analyte free of interference. It is the backbone of any method and can be enhanced at various steps, including sample preparation, separation optimization and detection. Significant improvement in selectivity can also be achieved in the data analysis step with the mathematical treatment of the signals. In this manuscript, we present a new approach that uses mathematical functions to model chromatographic peaks. However, unlike classical peak fitting approaches where the fitting parameters are optimized with a single profile (one-way data), the parameters are optimized over multiple profiles (two-way data). Thus, it allows high confidence and robustness. Furthermore, an iterative approach where the number of peaks is increased at each step until convergence is developed in this manuscript. It is demonstrated with simulated and real data that this algorithm is: (1) capable of mathemat...