Error analysis of an inclinometer based on numerical analysis
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摘要:
测斜仪在边坡深部位移监测中应用比较广泛，但其监测结果存在一定误差。已有测斜仪监测误差研究多是针对系统误差进行，缺少针对测斜仪监测数据计算原理引起的误差进行的研究。基于测斜仪监测数据计算方法原理与数值分析中常微分方程Euler解法的一致性，讨论了造成测斜仪监测误差的原因。分析结果表明：测斜仪监测误差与测斜仪监测初始值、测量分段长度和位移变形曲线形状有关；测斜仪监测初始值变化将给监测带来误差；测斜仪测量段长与监测误差呈线性关系，误差随测量段长减小而变小；当位移变形曲线为直线时，误差为0；当位移变形曲线为单-凸曲线或凹曲线时，监测误差随曲线变形程度和孔口变形位移增大而变大；测斜仪位移变形监测误差为累积误差，孔口误差大于孔底误差。在使用测斜仪监测时，为了减少监测误差，建议将每次监测初始值设为固定值，并尽可能减少测量段长。
Abstract:Inclinometer is widely used in slope deep displacement monitoring, and the error of an inclinometer is an issue of concern. The existing research on the inclinometer error is based on the system error, and the error caused by the calculation principle of inclinometer monitoring data was seldom examined. Based on the consistency between the calculation principle of inclinometer monitoring data and the Euler solution of the ordinary differential equation in numerical analysis, this paper discusses the monitoring error of inclinometer according to the principle of numerical analysis method. The analysis results show that the monitoring error of an inclinometer is related to the initial value of the inclinometer, the length of the measurement section and the shape of the displacement deformation curve. Among them, the change of the initial value of inclinometer monitoring will bring errors to the monitoring. The length of the measuring section of the inclinometer has a linear relationship with the monitoring errors, and the errors decrease with the decrease of the measuring section length. When the displacement deformation curve is straight, the errors are zero; when the displacement deformation curve is a single convex curve or concave curve, the monitoring errors increase with the increase of the curve deformation degree and the orifice deformation displacement. The error of displacement deformation monitoring is the cumulative error, and the error of orifice is larger than that of the bottom. When using an inclinometer for monitoring, in order to reduce the monitoring error of the inclinometer, the initial value of each monitoring should be fixed, and the length of the measuring section should be reduced as much as possible.
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Key words:
- slope /
- deep displacement /
- monitoring /
- numerical analysis /
- Euler method /
- error analysis
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表 1 不同孔口水平位移下的计算误差
Table 1. Errors under different orifice displacement
孔口水平位移/m 0.5 0.4 0.3 0.2 0.1 误差/mm 二次曲线 5.0 4.0 3.0 2.0 1.0 三次曲线 15.0 12.0 9.0 6.0 3.0 
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表 2 不同测量分段长度下的计算误差
Table 2. Errors under different length of the measuring section with conic curve
测量段长/m 0.5 1.0 2.0 3.0 4.0 误差/mm 二次曲线 5 10 20 30 40 三次曲线 15 30 60 90 120
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