Error Analysis of Stored Grain Inventory Determination

Abstract

Estimation of the quantity of stored grain is important for crop insurance, financial statements, and inventory control. Traditionally, the height of grain has been measured using weighted tape measures, and the volume is subsequently computed using standard geometric shapes (cylinders and cones) along with visual correction of the grain surface. Field measurements by four trained USDA Farm Service Agency and crop insurance agents on older farm-sized bins (8.2 to 11.0Â m, or 27 to 36 ft, in diameter) resulted in standard deviations between 0.02 and 0.30 m for the equivalent height when the grain surface was not level. The largest errors were observed with off-center surface profiles. When the grain surface inside the bins was manually leveled, the standard deviation of the equivalent height varied between 0.02 and 0.18 m. Error propagation analysis was performed to evaluate the error in measuring the volume of stored grain caused by the uncertainty associated with measuring the bin diameter and grain height as a function of the ratio of equivalent level grain height to bin diameter (EH/D). The errors were examined using an assumed range of uncertainties to explore how each factor contributed to the error in different scenarios. The uncertainty increased as the EH/D ratio decreased, especially in small-diameter bins with shallow grain heights where the volume bounded by the surface profile of the grain represented a large percentage of the total volume within the structure. Therefore, any errors in defining the surface profile resulted in large errors in the total estimated volume of grain in small-diameter bins. Conversely, for large-diameter bins with large grain heights, the surface profile represented a very small percentage of the total volume of grain. Consequently, any errors in defining the profile produced much smaller errors in the total grain volume. For accurate measurements, defined as a standard deviation of 1.2 cm (0.04 ft) in the diameter and 7.6 cm (0.25 ft) in the equivalent level height, the overall uncertainty in the volume measurement never exceeded 5% for smaller bins (<10 m in diameter) and decreased to less than 1% for larger bins (>10 m in diameter). A sensitivity analysis was performed on the three most common methods used to convert the measured volume to a quantity of grain. In each method, the quantity of grain stored in a bin is the product of the volume measurement and the pack factor. With all three methods, the sensitivity of the pack factor determination resulted in an error of less than 1% in the estimated total quantity of stored grain. The volume measurement accounted for the majority of the error in the estimation of bin inventory. As a result, accurate measurement of the bin volume is critical for determining the quantity of stored grain.