Development of an expression for the volume of off-centered conical pile inside a cylindrical silo Enes Yigit Department of Electrical and Electronics Engineering, Engineering Faculty, Karamanoglu Mehmetbey University, 70100 Karaman, Turkey article info Article history: Received 7 March 2019 Received in revised form 18 June 2019 Accepted 8 July 2019 Available online 11 July 2019 Keywords: Conical grain pile Grain level measurement Particle swarm optimization algorithm abstract In this study, both analytical and empirical formula that expresses volume of off-centered conical pile inside a cylindrical structure are proposed. The total of 1050 off-centered cones including three param- eters of dimension are acquired by computer aided design software. A volume expression enclosing con- ical pile parameters associated with variables of optimization is derived. Then the volume expression is obtained by substituting the variables determined by particle swarm optimization algorithm. The mean absolute percentage error between calculated and designed volumes of 1050 data are found as 0.0017% and 0.0299% for analytical and empirical expressions, respectively. Proposed calculations are also com- pared with another empirical formula existing in literature. In addition, two different small-scale case study are performed and the proposed formulations are verified experimentally. Results demonstrate that volume of the off-centered conical pile inside a cylindrical structure can be easily calculated with the help of empirically developed expression, without using complex mathematics. Ó 2019 Elsevier Ltd. All rights reserved. 1. Introduction The most valuable production and consumption material of the food industry are grain. Due to political and commercial concerns, the grain must be stored for a long time [24]. In cases of war or famine, nations can take measures according to the amount of the stored grain. Therefore, it is important to know the amount of grain in stock. On the other hand, the adjusters should regularly measure the amount of stored grain for insurance compensation and the amount of collateral for loans. In addition, grain proces- sors, elevators and grain dealers need to make periodical inspec- tions to guarantee that sufficient grain is stored to fulfill their financial and physical responsibilities [20]. Therefore, maintaining the right grain inventory is crucial for both commercial and social concerns. Grain is weighed in buying and selling, but it is not practical to measure the mass of grain after it has been stored in the grain storage areas, such as silos, stakes and warehouses. Therefore, to determine the amount of the stored grain, many methods have been presented [8,19,1,2,21]. In these presented methods, the volume of grain inside the silo should be measured by the operator. Thus, the amount of the stored grain is estimated by multiplying the measured factor and the density factor corre- sponding to the grain type. The most important process of quan- tity estimation is to accurate measurement of the volume of the grain. For this purpose, different systems and methods have been developed [13]. These systems can be classified as destructive (pressure diaphragms, slope switches and rotary wings) and non-destructive level-meters (Lasers, stereovision, ultrasound and radars). Among these, the non-destructive level measurement systems which have become popular in recent years are provide more information about the level of the pile [13,25,23]. Especially, laser and radar based methods provide valuable information about the surface pattern of the grain pile [20,24]. If the pile is occurred as a levelled or centered conical shape, basic geometric calculations can be used to obtain the volume information of such a pile. If the pile is off-centered, complex mathematics and com- puter aided software’s are required to calculate the volume from the surface pattern information. However, an analytical formula- tion which expresses the volume of the off-centered conical pile inside a cylindrical structure has not yet been presented in the lit- erature, except for an empirical formula [7]. Although the existing formulation (given in [7]) provides an approximate volume value, it cannot be used in sensitive processes (such as insurance com- pensation or amount of collateral for loans) due to the high error margin. On the other hand, by the help of computer-aided design (CAD) software [3] which gives the volume of the irregular shapes, the volume of the off-centered conical pile can be obtained. How- ever, since it is not practical to recreate the solid model and achieve its volume for each structure, alternative approaches are needed. Meta-heuristic optimization algorithms which are successfully applied for the solution of nonlinear engineering problems can https://doi.org/10.1016/j.measurement.2019.07.036 0263-2241/Ó 2019 Elsevier Ltd. All rights reserved. Measurement 146 (2019) 903–911 Contents lists available at ScienceDirect Measurement journal homepage: www.elsevier.com/locate/measurement