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Comparisons of prediction abilities of augmented classical least squares and partial least squares with realistic simulated data : effects of uncorrelated and correlated errors with nonlinearities

Proposed for publication in Applied Spectroscopy.

Melgaard, David K.; Melgaard, David K.; Haaland, David M.

A manuscript describing this work summarized below has been submitted to Applied Spectroscopy. Comparisons of prediction models from the new ACLS and PLS multivariate spectral analysis methods were conducted using simulated data with deviations from the idealized model. Simulated uncorrelated concentration errors, and uncorrelated and correlated spectral noise were included to evaluate the methods on situations representative of experimental data. The simulations were based on pure spectral components derived from real near-infrared spectra of multicomponent dilute aqueous solutions containing glucose, urea, ethanol, and NaCl in the concentration range from 0-500 mg/dL. The statistical significance of differences was evaluated using the Wilcoxon signed rank test. The prediction abilities with nonlinearities present were similar for both calibration methods although concentration noise, number of samples, and spectral noise distribution sometimes affected one method more than the other. In the case of ideal errors and in the presence of nonlinear spectral responses, the differences between the standard error of predictions of the two methods were sometimes statistically significant, but the differences were always small in magnitude. Importantly, SRACLS was found to be competitive with PLS when component concentrations were only known for a single component. Thus, SRACLS has a distinct advantage over standard CLS methods that require that all spectral components be included in the model. In contrast to simulations with ideal error, SRACLS often generated models with superior prediction performance relative to PLS when the simulations were more realistic and included either non-uniform errors and/or correlated errors. Since the generalized ACLS algorithm is compatible with the PACLS method that allows rapid updating of models during prediction, the powerful combination of PACLS with ACLS is very promising for rapidly maintaining and transferring models for system drift, spectrometer differences, and unmodeled components without the need for recalibration. The comparisons under different noise assumptions in the simulations obtained during this investigation emphasize the need to use realistic simulations when making comparisons between various multivariate calibration methods. Clearly, the conclusions of the relative performance of various methods were found to be dependent on how realistic the spectral errors were in the simulated data. Results demonstrating the simplicity and power of ACLS relative to PLS are presented in the following section.

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Optimal Estimation of Electrode Gap During Vacuum ARC Remelting

Metallurgical and Materials Transactions B

Williamson, Rodney L.; Melgaard, David K.

Electrode gap is a very important parameter for the safe and successful control of vacuum arc remelting (VAR), a process used extensively throughout the specialty metals industry for the production of nickel base alloys and aerospace titanium alloys. Optimal estimation theory has been applied to the problem of estimating electrode gap and a filter has been developed based on a model of the gap dynamics. Taking into account the uncertainty in the process inputs and noise in the measured process variables, the filter provides corrected estimates of electrode gap that have error variances two-to-three orders of magnitude less than estimates based solely on measurements for the sample times of interest. This is demonstrated through simulations and confined by tests on the VAR furnace at Sandia National Laboratories. Furthermore, the estimates are inherently stable against common process disturbances that affect electrode gap measurement and melting rate. This is not only important for preventing (or minimizing) the formation of solidification defects during VAR of nickel base alloys, but of importance for high current processing of titanium alloys where loss of gap control can lead to a catastrophic, explosive failure of the process.

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Calibration-free electrical conductivity measurements for highly conductive slags

Metallurgical Transactions B

Van Den Avyle, James A.; Melgaard, David K.; Van Den Avyle, James A.

This research involves the measurement of the electrical conductivity (K) for the ESR (electroslag remelting) slag (60 wt.% CaF{sub 2} - 20 wt.% CaO - 20 wt.% Al{sub 2}O{sub 3}) used in the decontamination of radioactive stainless steel. The electrical conductivity is measured with an improved high-accuracy-height-differential technique that requires no calibration. This method consists of making continuous AC impedance measurements over several successive depth increments of the coaxial cylindrical electrodes in the ESR slag. The electrical conductivity is then calculated from the slope of the plot of inverse impedance versus the depth of the electrodes in the slag. The improvements on the existing technique include an increased electrochemical cell geometry and the capability of measuring high precision depth increments and the associated impedances. These improvements allow this technique to be used for measuring the electrical conductivity of highly conductive slags such as the ESR slag. The volatilization rate and the volatile species of the ESR slag measured through thermogravimetric (TG) and mass spectroscopy analysis, respectively, reveal that the ESR slag composition essentially remains the same throughout the electrical conductivity experiments.

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New prediction-augmented classical least squares (PACLS) methods: Application to unmodeled interferents

Applied Spectroscopy

Haaland, David M.; Melgaard, David K.

A significant improvement to the classical least squares (CLS) multivariate analysis method has been developed. The new method, called prediction-augmented classical least squares (PACLS), removes the restriction for CLS that all interfering spectral species must be known and their concentrations included during the calibration. The authors demonstrate that PACLS can correct inadequate CLS models if spectral components left out of the calibration can be identified and if their spectral shapes can be derived and added during a PACLS prediction step. The new PACLS method is demonstrated for a system of dilute aqueous solutions containing urea, creatinine, and NaCl analytes with and without temperature variations. The authors demonstrate that if CLS calibrations are performed using only a single analyte's concentration, then there is little, if any, prediction ability. However, if pure-component spectra of analytes left out of the calibration are independently obtained and added during PACLS prediction, then the CLS prediction ability is corrected and predictions become comparable to that of a CLS calibration that contains all analyte concentrations. It is also demonstrated that constant-temperature CLS models can be used to predict variable-temperature data by employing the PACLS method augmented by the spectral shape of a temperature change of the water solvent. In this case, PACLS can also be used to predict sample temperature with a standard error of prediction of 0.07 C even though the calibration data did not contain temperature variations. The PACLS method is also shown to be capable of modeling system drift to maintain a calibration in the presence of spectrometer drift.

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Results 26–33 of 33
Results 26–33 of 33