【摘要】 由于引起变形的原因错综复杂性，经典的回归模型难以适应变形呈现出非线性和动态性的特征，对标准高斯过程回归(GPR)理论进行扩展研究，解决GPR用于变形分析面临在线自学习，特征自适应的问题。首先通过训练样本集优化，样本和超参数在线同步更新来改进GPR在线学习能力，提升GPR处理实时数据流的计算性能；然后通过分析残差序列的非线性特征并应用傅里叶变换技术提取周期性特征，实现在线自适应生成与变形特征相匹配的特征核函数。数值模拟和工程应用结果表明，自适应生成特征核函数较标准的核函数能更好提取非线性变形特征并保留了周期性特征。研究成果可用于自动化变形监测系统的变形特征在线分析，保障监测数据分析的近实时性和分析结果的可靠性。更多还原

【Abstract】 Due to the intricate nature of deformation-causing factors, classic regression models struggle to accommodate the nonlinearity and dynamism presented by deformations. This paper extends the theory of standard Gaussian Process Regression(GPR) to address the challenges faced by GPR in deformation analysis, specifically in online self-learning and adaptive feature presentation. Firstly, by optimizing the training sample set and synchronously updating samples and hyperparameters online, the online learning capability of GPR is enhanced, thereby improving its computational performance in handling real-time data streams. Secondly, by analyzing the nonlinear characteristics of residual sequences and applying Fourier transform techniques to extract periodic features, an online adaptive generation of feature kernel functions matching the deformation features is achieved. The results of simulation experiment and engineering applications indicated that the adaptively generated feature kernel functions outperform standard kernel functions in extracting nonlinear deformation features while retaining periodic features. The research findings can be applied to the online analysis of deformation features in automated deformation monitoring systems, ensuring the near real-time analysis of monitoring data and the reliability of analysis results.更多还原