基于表层数据的残余应力重构方法研究

doi:10.3901/JME.260543

摘要/Abstract

摘要： 基于表层测量数据重构残余应力，可在不破坏构件的同时获得全场残余应力分布。本征应变法能自然满足力学约束，是残余应力重构的主流方法之一。但随着构件结构复杂度的增加和测量数据量的减少，反演矩阵病态性加剧，影响重构可靠性。为此，提出一种改进的本征应变重构方法：采用基于有限元网格节点自适应生成径向基函数(Radial basis function，RBF)中心点，提升本征应变参数化的几何适应性；设计基于广义交叉验证法(Generalized cross-validation，GCV)粗筛-L曲线精调的正则化参数选取策略，抑制矩阵病态性。该方法可有效重构出四点弯曲件、球头压入件和淬火曲面件等二维和三维结构的残余应力场，重构值与ABAQUS模拟值的决定系数R²分别为0.943 5、0.903 7和0.939 6，分布趋势一致且重构的残余应力场平滑性更佳。进一步分析了基函数、形状偏差和输入数据对重构精度的影响，发现采用幂指数RBF并结合有限元网格节点的RBF中心点选取策略精度最优；形状偏差导致矩阵病态性加剧，但最终重构结果相差不大；当输入数据减少或引入噪声时，其重构结果与模拟值分布趋势仍基本一致，重构精度略有下降。表明提出的方法具有强鲁棒性。

关键词: 残余应力重构, 径向基函数, 本征应变法, 表层数据, 正则化

Abstract: Reconstructing residual stress based on surface measurement data enables obtaining the full-field residual stress distribution without damaging the component，providing a new approach for residual stress characterization. The eigenstrain method naturally satisfies mechanical constraints and is one of the mainstream methods for residual stress reconstruction. However，with the increase in component structural complexity and the decrease in the amount of measurement data，the ill-posedness of the inversion matrix intensifies，affecting the reliability of reconstruction. To address this，an improved eigenstrain reconstruction method is proposed：adaptive generation of radial basis function (Radial Basis Function，RBF) centers based on finite element mesh nodes is adopted to enhance the geometric adaptability of eigenstrain parameterization; a regularization parameter selection strategy based on GCV(Generalized Cross-Validation, GCV) rough screening-L curve fine-tuning is designed to suppress matrix ill-posedness. The residual stress fields of two-dimensional and three-dimensional components such as four-point bending components，ball-head indentation components，and quenched curved surface components are effectively reconstructed by this method. The coefficients of determination (R²) between the reconstructed values and ABAQUS simulation values are 0.943 5，0.903 7，and 0.939 6 respectively，with consistent distribution trends. Moreover，the reconstructed residual stress fields exhibit better smoothness and are closer to the continuous distribution characteristics of residual stress. Further，the effects of basis functions，shape deviations，and input data on reconstruction accuracy are analyzed. The results show that the power exponential RBF combined with the RBF center selection strategy based on finite element mesh nodes achieves the optimal accuracy; shape deviations exacerbate matrix ill-posedness，but the final reconstruction results differ slightly; when the input data is reduced or noise is introduced，the distribution trend of the reconstruction results is still basically consistent with the simulation values，with a slight decrease in reconstruction accuracy. These results indicate that the proposed method has strong robustness.

Key words: residual stress reconstruction, radial basis function, eigenstrain method, surface data, regularization

中图分类号:

TG306

王佳妮, 樊晓光, 詹梅, 俞扬镇, 曾祥屹, 王志军. 基于表层数据的残余应力重构方法研究[J]. 机械工程学报, 2026, 62(14): 231-240.

WANG Jiani, FAN Xiaoguang, ZHAN Mei, YU Yangzhen, ZENG Xiangyi, WANG Zhijun. Study on Residual Stress Reconstruction Method Based on Surface Data[J]. Journal of Mechanical Engineering, 2026, 62(14): 231-240.

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http://www.cjmenet.com.cn/CN/Y2026/V62/I14/231

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