Displacement identification of oil storage tank and calibration of tank capacity table model based on indicator function integral

Qinghua Liu; Jing Wang; Keying Song; Qinghua Liu; Jing Wang; Keying Song

doi:10.3934/mbe.2024082

Mathematical Biosciences and Engineering

2024, Volume 21, Issue 2: 1872-1883. doi: 10.3934/mbe.2024082

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Displacement identification of oil storage tank and calibration of tank capacity table model based on indicator function integral

Basic Education School, Beijing Information Technology College, Beijing 100070, China

Academic Editor: Yang Kuang

Received: 17 September 2023 Revised: 04 December 2023 Accepted: 21 December 2023 Published: 04 January 2024

Based on the indicator function integral, this paper identifies the displacement of oil storage tank and calibrates the tank capacity table model. The displacement parameters of a cylinder oil tank with spherical caps at both ends are deduced by establishing an appropriate rectangular coordinate system while cross-section analysis, coordinate transformation, and the functional relationship between oil reserves and oil level height are used as well. Furthermore, the displacement parameters are determined by the least square method and alternating contraction search method to verify the data, which improves the accuracy of the calculation. This research simplifies the integral operation and can be extended to other types of liquid containers of arbitrary shape as a generally applicable method, which shows significant application value for further research on the integral method of indicator function.
- calibration of tank capacity table,
- coordinate transformation,
- indicator function integral,
- least square method
Citation: Qinghua Liu, Jing Wang, Keying Song. Displacement identification of oil storage tank and calibration of tank capacity table model based on indicator function integral[J]. Mathematical Biosciences and Engineering, 2024, 21(2): 1872-1883. doi: 10.3934/mbe.2024082

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Abstract

Based on the indicator function integral, this paper identifies the displacement of oil storage tank and calibrates the tank capacity table model. The displacement parameters of a cylinder oil tank with spherical caps at both ends are deduced by establishing an appropriate rectangular coordinate system while cross-section analysis, coordinate transformation, and the functional relationship between oil reserves and oil level height are used as well. Furthermore, the displacement parameters are determined by the least square method and alternating contraction search method to verify the data, which improves the accuracy of the calculation. This research simplifies the integral operation and can be extended to other types of liquid containers of arbitrary shape as a generally applicable method, which shows significant application value for further research on the integral method of indicator function.

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