Optimization algorithm for calibration of elastic membrane binding force and instrument comprehensive deformation based on Python
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摘要: 旁压试验是岩土工程勘察中重要的原位测试方法，其中弹性膜约束力和仪器综合变形两个率定试验十分重要。然而，传统的率定方法依赖人工操作，并借助一些猜测模型，存在诸多局限性。基于Python语言对旁压试验两个率定算法优化，构建了仪器综合变形率定的最小二乘法线性模型和弹性膜约束力率定的三次多项式最小二乘法非线性模型。通过分析认为，仪器综合变形率定模型斜率计算合理，残差分布良好；三次多项式模型对弹性膜约束力率定拟合效果好，且引入正则化避免过拟合。研究表明，Python语言在旁压试验数据处理中优势明显，能通过优化算法来提高旁压试验结果的准确性。Abstract: Pressuremeter test is an important in-situ testing method in geotechnical engineering investigation, while the two calibration tests of elastic membrane binding force and instrument comprehensive deformation are very important. However, traditional calibration methods rely on manual operations and use inaccurate empirical models, which have many limitations. Based on Python, this study optimizes the calibration algorithms for the two tests of pressuremeter test, constructing a linear least squares model for instrument comprehensive deformation calibration and a nonlinear cubic polynomial least squares model for elastic membrane binding force calibration. The analysis shows that the slope calculation of the instrument comprehensive deformation calibration model is reasonable, with uniformly distributed residuals; the cubic polynomial model has an excellent fitting effect on elastic membrane binding force calibration, and regularization is introduced to mitigate overfitting. The research indicates that Python has obvious advantages in pressuremeter test data processing, and the accuracy of pressuremeter test results can be improved using the optimized algorithms.
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图 1 仪器综合变形率定曲线和残差分布图
Figure 1. Calibration curve and residual distribution diagram of instrument comprehensive deformation
图 2 不同函数拟合弹性膜约束力率定曲线
Figure 2. Calibration curves of elastic membrane binding force fitted by different functions
图 3 不同拟合曲线方程计算的Pi值对比
Figure 3. Comparison of Pi values calculated by different fitting curve equations
图 4 不同拟合曲线方程与目测Pi数值绝对误差分析
Figure 4. Absolute error analysis of Pi values between different fitting curve equations and visual measurements
图 5 不同拟合曲线方程与目测Pi数值相对误差分析
Figure 5. Relative error analysis of Pi values between different fitting curve equations and visual measurements
图 6 三次多项式模型正则化参数与平均均方误差的关系
Figure 6. Relationship between regularization parameters and mean squared error of cubic polynomial model
表 1 测管水位位移值sm（cm）与对应的弹性膜约束力Pi（kPa）
Table 1. Measured pipe water level displacement values sm (cm) and corresponding elastic membrane binding force Pi (kPa)
点号 sm Pi Pia Pib Pic Pid 1 2.9 27.8 34.8 34.5 26.5 27.7 2 7.0 45.2 46.4 46.6 45.7 45.3 3 10.1 52.8 52.4 52.3 53.1 52.8 4 11.7 56 54.9 54.7 56 55.8 5 12.7 57.6 56.4 56.2 57.5 57.5 6 13.7 59 57.9 57.6 59 59 7 14.7 60.3 59.2 58.9 60.4 60.4 8 15.7 61.5 60.5 60.2 61.7 61.7 9 16.8 62.9 61.9 61.5 63 63.1 10 18.2 64.5 63.5 63.1 64.6 64.7 11 20.5 67 66 65.7 67 67.2 12 23.8 70.1 69.3 69.1 70 70.2 13 28.2 73.4 73.3 73.2 73.6 73.7 14 33.7 77.3 77.7 77.9 77.5 77.5 
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