Data Processing Protocol for Regression of Geothermal Times Series with Uneven Intervals

TL;DR

This paper investigates how selecting different subsets of unevenly spaced geothermal time series data affects regression model accuracy, proposing schemes to optimize data points for better model fitness without losing data features.

Contribution

It introduces six novel data processing schemes for selecting data points in regression analysis of uneven time series, improving model fitness without sacrificing data features.

Findings

Number of data points has negligible effect on model fit depending on the scheme

Proposed schemes are ranked based on R2 and NRMSE metrics

Optimal data selection can enhance model accuracy without increasing data size

Abstract

Regression of data generated in simulations or experiments has important implications in sensitivity studies, uncertainty analysis, and prediction accuracy. Depending on the nature of the physical model, data points may not be evenly distributed. It is not often practical to choose all points for regression of a model because it doesn't always guarantee a better fit. Fitness of the model is highly dependent on the number of data points and the distribution of the data along the curve. In this study, the effect of the number of points selected for regression is investigated and various schemes aimed to process regression data points are explored. Time series data i.e., output varying with time, is our prime interest mainly the temperature profile from enhanced geothermal system. The objective of the research is to find a better scheme for choosing a fraction of data points from the entire set to find a better fitness of the model without losing any features or trends in the data. A workflow is provided to summarize the entire protocol of data preprocessing, regression of mathematical model using training data, model testing, and error analysis. Six different schemes are developed to process data by setting criteria such as equal spacing along axes (X and Y), equal distance between two consecutive points on the curve, constraint in the angle of curvature, etc. As an example for the application of the proposed schemes, 1 to 20% of the data generated from the temperature change of a typical geothermal system is chosen from a total of 9939 points. It is shown that the number of data points, to a degree, has negligible effect on the fitted model depending on the scheme. The proposed data processing schemes are ranked in terms of R2 and NRMSE values.