Abstract
We consider an industrial problem brought to the Mathematics in Industry New Zealand study group in 2016, where items pass briefly over load cells resulting in a noisy oscillatory signal, from which the mass of the item is to be computed. We compare results obtained using a single load cell for one piece of fruit, with results from passing over two load cells in tandem or in succession with fruit on multiple keys. We develop mathematical models to assist with the computation of total load mass, considering both deterministic and statistical approaches. The fitting of simple harmonic motion plus a step function exhibits the possibility of rapid estimates of load mass. We find that using multiple keys to measure the weight of a fruit provides more accurate results than using the single-key method. References minz-2004, Case Study Compac. http://www.minz.org.nz/assets/downloads/Case-Study-Compac.pdf Kesilmis, Z., and Baran, T. (2016). A Geometric Approach to Beam Type Load Cell Response for Fast Weighing. doi:10.1007/s12647-016-0168-2 K. Levenberg, A method for the solution of certain non-linear problems in least squares. Quarterly of applied mathematics , 2(1944), pp. 164–168. http://www.jstor.org/stable/43633451 D. W. Marquardt, An algorithm for least-squares estimation of nonlinear parameters. Journal of the society for Industrial and Applied Mathematics , 11(1963), pp. 431–441. doi:10.1137/0111030
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