Periodicity and stochastic hierarchical orders of soil cutting force data detected by an "auto-regressive error distribution function" (AREF)

In this article, we describe a methodology to estimate typical soil properties such as moisture content and compactness using soil cutting force fluctuation information obtained by a conventional chisel. The data were obtained in a Yolo loam field under four different soil conditions: tilled dry (TD), tilled wet (TW), untilled dry (UD), and untilled wet (UW). In order to quantify the complexity of fluctuating patterns of soil cutting force and soil physical properties, we introduce a new time-series analysis technique, the auto-regressive error function (AREF). We found that the frequency distribution pattern of the modified time-series data with the time lag showed a very clear shift with change in the time lag. The AREF was developed to detect this pattern shift. The soil cutting force time-series data obtained using an instrumented chisel were analyzed using power spectrum and AREF techniques. The spatial power spectrum analysis detected periodicity under dry soil conditions. On the other hand, the AREF showed a very clear hierarchical order, which was caused by the existence of self-similarity in the fluctuating patterns of soil cutting forces under all four tested soil conditions. Two AREF parameters were found to be related to soil moisture content and cone index, but not bulk density.