ARMA Models to Measure the Scale of Fluctuation from CPT Data

Abstract

Objective: Spatial variability is one of the largest sources of uncertainty in geotechnical applications. This variability is primarily characterized by the scale of fluctuation, a parameter that describes the distance over which the parameters of a material are similar. Spatial variability is generally described with traditional methods of time series analysis. In statistics, the Auto-Regressive Moving Average (ARMA) model is commonly used to describe the relationship between two points in time. Instead of assuming an autocorrelation model, the ARMA model calculates the necessary auto-regressive components (AR), as well as a decaying Mean Structure (MA). The advantage of this method is that it is calculated for each specific field study, so that the data is not forced to fit into a fixed autocorrelation model (e.g. Markovian, Gaussian, etc). Methods: In this study, the ARMA model is introduced as a means of measuring scale of fluctuation, and two case studies and a simulation are used to compare the scale of fluctuation values from the ARMA model to the other estimates. Results: In the first case study, the ARMA model estimated a value of 0.26 m while the other methods ranged from 0.22-0.29 m. In the second case study, the ARMA model estimated a value of 0.40 m while the other methods ranged from 0.40-0.54 m. In the simulated example, where the true value was 5.0 m, the ARMA model estimated a value of 4.73 m while the other methods ranged from 3.24-3.51 m. Conclusion: This paper concludes that ARMA is a promising new method for estimating the scale of fluctuation but requires a considerable amount of research before it can become established in the geotechnical sphere.