A geometrical approach for the measurement of the volume of masses of granular material through grid-layout sensor networks Cristiano Bocci a , Ada Fort a , Alessandro Pozzebon a,⇑ , Duccio Bertoni b a Department of Information Engineering and Mathematics, University of Siena, Via Roma 56, 53100 Siena, Italy b Department of Earth Sciences, University of Pisa, Via S. Maria 53, 56126 Pisa, Italy article info Article history: Received 18 April 2019 Received in revised form 10 August 2019 Accepted 24 September 2019 Available online 5 October 2019 Keywords: Volume Granular Material Sensor networks Grid-layout networks Geometry abstract In this paper, the authors propose a novel methodology to measure the volume of masses of granular material by means of wired or wireless sensor networks. The proposed technological framework exploits a grid of sensor nodes, each of them in charge of measuring the level of a layer of granular material in a specific point. Since this layout allows to subdivide an area in grid of squares, 4 sensor nodes are expected to sit at the corners of each square, where they will be able to punctually measure the level of the layer. This paper proposes a geometrical approach to calculate the volume of the material in the area covered by the sensors using these data sets. Thanks to the proposed calculation methodology, the volume can be estimated by means of simple geometrical calculations that can be easily performed on a resource- constrained device like a microcontroller. Ó 2019 Elsevier Ltd. All rights reserved. 1. Introduction The measurement of the volume of masses of granular material is of great importance in a wide range of possible application sce- narios, from environmental monitoring to warehouse manage- ment. Granular materials include all those materials composed by a conglomerate of solid particles whose size does not allow them to be subject to thermal motion fluctuations. The lower bound for the dimensions of a single particle to be considered part of a granular material is 0.1 lm: according to the dimensions of the particle, granular materials are sub-divided in ultra-fine powders (0.1–1 lm), superfine powders (1–10 lm), granular powders (10–100 lm), granular solids (100 lm–3 mm) and broken solids [1]. They include a wide range of very common materials like snow, cereals, sand, minerals, seeds and many others, that can be found in nature but can be also stored, transported and used for manufacturing or sold in shops. The definition of a simple and fast measurement methodology for volume and volume variations of these materials can be of great importance in several application scenarios. Such a system may be useful for storable materials like cereals or minerals to calculate their quantity and variations: examples may include the amount of cereals stored in a warehouse or the quantity of coal accumu- lated in a powerhouse. Such a measurement system may also be employed in outdoor scenarios: examples may be the measure- ment of ice volume in glaciers or snow volume in the mountains. It may also be useful to evaluate mountain slopes used as quarry dump deposits: these deposits are frequently unstable and it is not easy to understand how long they can be increasingly filled. An interesting application in the outdoor scenario, foreseeing the use of such a system for the measurement of variations of sand vol- ume in sand dunes, will be described in Section 3. Nevertheless, many other applications may be envisaged in several other scenarios. While some techniques currently exist to measure or estimate granular materials volume (see Section 2), the most part of them is based on the use of expensive instrumentation like cameras or satellites. Moreover, these methodologies require powerful com- putation instruments and do not allow real-time, remote monitor- ing. The aim of this paper is to propose a novel methodology exploiting data collected by grid-layout sensor networks: by means of the proposed geometrical approach, data concerning the level of the material can be processed with a very low compu- tational load, and the volume calculated in real time. The proposed calculation method is independent of the type of sensor and node architecture, as described in Section 4, and can be performed even on resource-constrained devices as microcontrollers, thus imple- menting the paradigm of Edge Computing. The rest of the paper is structured as follows: in Section 2 a state of the art describing existing techniques for volume measurement is provided. Section 3 is devoted to the description of a possible https://doi.org/10.1016/j.measurement.2019.107102 0263-2241/Ó 2019 Elsevier Ltd. All rights reserved. ⇑ Corresponding author. E-mail address: alessandro.pozzebon@unisi.it (A. Pozzebon). Measurement 151 (2020) 107102 Contents lists available at ScienceDirect Measurement journal homepage: www.elsevier.com/locate/measurement