Extract Characteristic Parameters of FID Signal Combining Autocorrelation Function with the Least Absolute Value

2012 ◽  
Vol 239-240 ◽  
pp. 1108-1112
Author(s):  
Hui Cui Hao ◽  
Jun Lin ◽  
Bao Feng Tian ◽  
Qi Wan
Keyword(s):  
Autocorrelation Function ◽  
Least Squares Method ◽  
Measurement Data ◽  
Characteristic Parameters ◽  
Absolute Value ◽  
Nonlinear Fitting ◽  
Least Absolute Value ◽  
Function Fitting ◽  
Parameters Extraction ◽  
Fitting Method

FID signal is the envelope of magnetic resonance signal, and the extraction accuracy of characteristic parameters directly influence the accuracy of the hydrogeologic parameters of the inverse interpretation. In order to improve the accuracy of characteristic parameters extraction, made simulation and study combined the autocorrelation function fitting with the least absolute value nonlinear fitting method in different SNR and different noise in this paper. The simulation results showed that, the characteristic parameters fitting error using this method was smaller than that using linear, nonlinear fitting method or the autocorrelation function with the least squares method, within 7% in lower SNR. The field measurement data and inversion results verified the method validity.

Calibration and Uncertainty Quantification of Gas Turbine Performance Models

2015 ◽  
Author(s):  
Manuel Arias Chao ◽  
Darrel S. Lilley ◽  
Peter Mathé ◽  
Volker Schloßhauer
Keyword(s):  
Uncertainty Quantification ◽  
Gas Turbine ◽  
Bayesian Approach ◽  
Least Squares Method ◽  
Measurement Data ◽  
Operating Conditions ◽  
Performance Models ◽  
Regression Problem ◽  
Calibration Problem ◽  
Calibration Parameters

Calibration and uncertainty quantification for gas turbine (GT) performance models is a key activity for GT manufacturers. The adjustment between the numerical model and measured GT data is obtained with a calibration technique. Since both, the calibration parameters and the measurement data are uncertain the calibration process is intrinsically stochastic. Traditional approaches for calibration of a numerical GT model are deterministic. Therefore, quantification of the remaining uncertainty of the calibrated GT model is not clearly derived. However, there is the business need to provide the probability of the GT performance predictions at tested or untested conditions. Furthermore, a GT performance prediction might be required for a new GT model when no test data for this model are available yet. In this case, quantification of the uncertainty of the baseline GT, upon which the new development is based on, and propagation of the design uncertainty for the new GT is required for risk assessment and decision making reasons. By using as a benchmark a GT model, the calibration problem is discussed and several possible model calibration methodologies are presented. Uncertainty quantification based on both a conventional least squares method and a Bayesian approach will be presented and discussed. For the general nonlinear model a fully Bayesian approach is conducted, and the posterior of the calibration problem is computed based on a Markov Chain Monte Carlo simulation using a Metropolis-Hastings sampling scheme. When considering the calibration parameters dependent on operating conditions, a novel formulation of the GT calibration problem is presented in terms of a Gaussian process regression problem.

scholarly journals Flux control coefficients determined by inhibitor titration: the design and analysis of experiments to minimize errors

1993 ◽  
Vol 296 (2) ◽  
pp. 423-433 ◽  
Author(s):  
J R Small
Keyword(s):  
Random Errors ◽  
Flux Control ◽  
Graph Method ◽  
Function Fitting ◽  
Fitting Method ◽  
Simple Extrapolation ◽  
Experimental Errors ◽  
Flux Control Coefficients ◽  
Fitted Function ◽  
Control Coefficients

This paper is a study into the effects of experimental error on the estimated values of flux control coefficients obtained using specific inhibitors. Two possible techniques for analysing the experimental data are compared: a simple extrapolation method (the so-called graph method) and a non-linear function fitting method. For these techniques, the sources of systematic errors are identified and the effects of systematic and random errors are quantified, using both statistical analysis and numerical computation. It is shown that the graph method is very sensitive to random errors and, under all conditions studied, that the fitting method, even under conditions where the assumptions underlying the fitted function do not hold, outperformed the graph method. Possible ways of designing experiments to minimize the effects of experimental errors are analysed and discussed.

scholarly journals Methods for Fitting the Limit State Function of the Residual Strength of Damaged Ships

2022 ◽  
Vol 10 (1) ◽  
pp. 102
Author(s):  
Zhiyao Zhu ◽  
Huilong Ren ◽  
Xiuhuan Wang ◽  
Nan Zhao ◽  
Chenfeng Li
Keyword(s):  
Least Squares ◽  
Residual Strength ◽  
Least Squares Method ◽  
Limit State ◽  
Nonlinear Least Squares ◽  
State Function ◽  
Limit State Function ◽  
Distribution Models ◽  
Sample Distribution ◽  
Fitting Method

The limit state function is important for the assessment of the longitudinal strength of damaged ships under combined bending moments in severe waves. As the limit state function cannot be obtained directly, the common approach is to calculate the results for the residual strength and approximate the limit state function by fitting, for which various methods have been proposed. In this study, four commonly used fitting methods are investigated: namely, the least-squares method, the moving least-squares method, the radial basis function neural network method, and the weighted piecewise fitting method. These fitting methods are adopted to fit the limit state functions of four typically sample distribution models as well as a damaged tanker and damaged bulk carrier. The residual strength of a damaged ship is obtained by an improved Smith method that accounts for the rotation of the neutral axis. Analysis of the results shows the accuracy of the linear least-squares method and nonlinear least-squares method, which are most commonly used by researchers, is relatively poor, while the weighted piecewise fitting method is the better choice for all investigated combined-bending conditions.

scholarly journals Robust and Fast State Estimation for Poorly-Observable Low Voltage Distribution Networks Based on the Kalman Filter Algorithm

Energies ◽  
2019 ◽  
Vol 12 (23) ◽  
pp. 4457 ◽  
Author(s):  
Antončič ◽  
Papič ◽  
Blažič
Keyword(s):  
Kalman Filter ◽  
State Estimation ◽  
Low Voltage ◽  
Least Squares Method ◽  
Weighted Least Squares ◽  
Measurement Data ◽  
Estimation Algorithm ◽  
Distribution Networks ◽  
Voltage Distribution ◽  
State Estimator

This paper presents a novel approach for the state estimation of poorly-observable low voltage distribution networks, characterized by intermittent and erroneous measurements. The developed state estimation algorithm is based on the Extended Kalman filter, where we have modified the execution of the filtering process. Namely, we have fixed the Kalman gain and Jacobian matrices to constant matrices; their values change only after a larger disturbance in the network. This allows for a fast and robust estimation of the network state. The performance of the proposed state-estimation algorithm is validated by means of simulations of an actual low-voltage network with actual field measurement data. Two different cases are presented. The results of the developed state estimator are compared to a classical estimator based on the weighted least squares method. The comparison shows that the developed state estimator outperforms the classical one in terms of calculation speed and, in case of spurious measurements errors, also in terms of accuracy.

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