Chaos and complexity in mine grade distribution series detected by nonlinear approaches

Abstract

In this article, the underlying dynamics of treating grade distribution is interpreted as a chaotic system instead of a stochastic system for a better understanding. Here, we study the behavior of grade distribution spatial series acquired at the Chadormalu mine in Bafgh city of Iran to distinguish the possible existence of low‐dimensional deterministic chaos. This work applies a variety of nonlinear techniques for detecting the chaotic nature of the grade distribution spatial series and adopts a nonlinear prediction method for predicting the future of the grade distributions. First, the delay time dimension is computed using auto mutual information function to reconstruct the strange attractors. Then, the dimensionality of the trajectories is obtained using Cao's method and, correspondingly, the correlation dimension method is adopted to quantify the embedding dimension. The low embedding dimensions achieved from these methods show the existence of low dimensional chaos in the mining data. Next, the high sensitivity to initial conditions is evaluated using the maximal Lyapunov exponent criterion. Positive Lyapunov exponents obtained demonstrate the exponential divergence of the trajectories and hence the unpredictability of the data. Afterward, the nonlinear surrogate data test is done to further verify the nonlinear structure of the grade distribution series. This analysis provides considerable evidence for the being of low‐dimensional chaotic dynamics underlying the mining spatial series. Lastly, a nonlinear prediction scheme is carried out to predict the grade distribution series. Some computer simulations are presented to illustrate the efficiency of the applied nonlinear tools. © 2016 Wiley Periodicals, Inc. Complexity 21: 355–369, 2016