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Porosity prediction using Fuzzy SVR and FCM SVR from well logs of an oil field in south of Iran

Moosavi Nastaran, Bagheri Majid, Nabi-Bidhendi Majid, Heidari Reza

Acta Geophysica

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2023

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Vol. 71, no. 2

769--782

EN

Identification of petrophysical parameters including porosity plays an important role to evaluate hydrocarbon reservoirs. A precise prediction of porosity in oil and gas reservoirs may prevent lots of costs before drilling operations. Porosity obtained from core analysis in laboratory is the most reliable one, while they are very expensive and not always accessible. Inappropriate or missing data in under-survey locations are a key challenge for reservoir engineers. In this paper, support vector regression (SVR) is used to estimate porosity in one of the oil fields in south of Iran. SVR creates models due to structural risk minimization methods which help us to produce models with better generalization and less risk of overfitting. Definitely, measured data are always contaminated with noise. One of the common methods to reduce noise and outliers in data is to process them before using them to train the algorithm; during processing, outliers and some noisy data can be suppressed from data, while it is not always easy to distinguish real data from noise. In this paper, we modified SVR to Fuzzy SVR and Fuzzy C Means (FCM) SVR, which are used to decrease effect of noise on model, and then by adding artificial noise including random noise and outliers to data we investigated how these two methods respond to presence of noise. The results show the presence of noise and outliers in data can alter the center locations and distribution of data points in clusters in FCM SVR. Similarly, it can change the variance of Gaussian membership function we used for Fuzzy SVR, but overall, the results show Fuzzy SVR model is notably more robust against noise compared to FCM SVR. Correlation coefficient (CC) calculated between model and core data decreased from 78 to 67% after noise added to data in FCM SVR model, however, calculated CC for Fuzzy SVR remained almost steady altering from 87 to 86%. Subsequently, calculated root mean square error (RMSE) between models and core data increased from 0.0376 to 0.03827 for Fuzzy SVR, while RMSE jumped from 0.0448 to 0.0517 for FCM SVR.

2

Probabilities of discrepancy between minima of cross-validation, Vapnik bounds and true risks

Klęsk P.

International Journal of Applied Mathematics and Computer Science

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2010

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Vol. 20, no 3

525-544

EN

Two known approaches to complexity selection are taken under consideration: n-fold cross-validation and structural risk minimization. Obviously, in either approach, a discrepancy between the indicated optimal complexity (indicated as the minimum of a generalization error estimate or a bound) and the genuine minimum of unknown true risks is possible. In the paper, this problem is posed in a novel quantitative way. We state and prove theorems demonstrating how one can calculate pessimistic probabilities of discrepancy between these minima for given for given conditions of an experiment. The probabilities are calculated in terms of all relevant constants: the sample size, the number of cross-validation folds, the capacity of the set of approximating functions and bounds on this set. We report experiments carried out to validate the results.

3

Rüschendorf, Adaptive estimation of hazard functions

Döhler S., Rüschendorf L.

Probability and Mathematical Statistics

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2002

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Vol. 22, Fasc. 2

355--379

EN

In this paper we obtain convergence rates for sieved maximum-likelihood estimators of the log-hazard function in a censoring model. We also establish convergence results for an adaptive version of the estimator based on the method of structural risk-minimization. Applications are discussed to tensor product spline estimators as well as to neural net and radial basis function sieves. We obtain simplified bounds in comparison to the known literature. This allows us to derive several new classes of estimators and to obtain improved estimation rates. Our results extend to a more general class of estimation problems and estimation methods (minimum contrast estimators).