基于高精度曲面建模的物体表面形变监测

道路、隧道、桥梁等物体表面形变监测是质量安全保障的重要前提。针对其表面监测问题，提出一种基于激光栅格化采样和高精度曲面建模的物体表面监测方法。该方法对监测物体表面利用栅格化采样进行高精度曲面建模和插值，通过多项式空间插值估计监测点的真实值和曲面第一、二基本量，对物体表面沉降和曲率半径参数变化角度进行监测。为验证该方法的有效性，在两组不同复杂程度的已知曲面上随机选取100个测试点，针对采样密度和插值密度分别进行数值仿真实验，并利用实物模型构建模拟形变实验，进而对测试点处的沉降变化和曲率半径变化进行监测。实验结果表明：在仿真实验中，高栅格化采样密度和插值密度能够大幅提高曲面重构精度，并降低物体表面不同复杂程度对监测精度的影响；在实物模拟形变实验中，沉降测量精度可达98.41%，曲率半径变化检测精度可达81.82%。

Object surface deformation monitoring using high accuracy surface modeling

Surface deformation monitoring of roads, tunnels, bridges, etc. is an important prerequisite for quality and safety. Aiming at the surface monitoring problem, we propose an object surface monitoring method based on laser rasterization sampling and high precision surface modeling. Utilizing rasterized sampling, the method can carry out high-precision surface modeling and interpolation on the surface of the monitored object. Then through the polynomial spatial interpolation method, the true value of the monitored points and the first and second basic quantities of the surface are estimated. Lastly, the surface settlement of the object and the change of the curvature radius parameters are monitored. In order to verify the effectiveness of the proposed method, we randomly selected 100 test points on two known surfaces of different complexity levels. On different conditions of the sampling density and interpolation density, we carried out numerical simulation experiments separately. Meanwhile, a simulated deformation experiment was constructed by a physical model. Then we monitored changes of settlement and curvature radius at the test points. The experimental results are as follow. In the simulation experiment, high rasterized sampling density and interpolation density can greatly improve surface reconstruction accuracy and reduce the impact of different complexity of the object surface on the monitoring accuracy. In the physical simulation deformation experiment, the settlement monitoring accuracy can reach 98.41%, and the curvature radius change monitoring accuracy can reach 81.82%.