基于贝叶斯傅里叶动态模型的桥梁极值应力预测

Bridge Extreme Stress Prediction Based on Bayesian Fourier Dynamic Models

研究了基于健康监测应力数据的桥梁极值应力动态预测.考虑到监测应力的周期性、随机性和动态性等特点,首先初次建立了桥梁监测极值应力的傅里叶动态非线性模型(Fourier Dynamic Nonlinear Model,FDNM),结合Taylor级数展开技术,将FDNM近似转化为傅里叶动态线性模型(Fourier Dynamic Linear Model,FDLM);然后采用贝叶斯方法,基于动态监测极值应力数据,建立了无先验信息的贝叶斯傅里叶动态线性模型(Bayesian Fourier Dynamic Linear Model: BFDLM),进而对监测极值应力的一步向前预测分布参数和后验应力状态分布参数进行了预测分析;最后通过实际桥梁监测极值应力数据对本文所建模型和方法的合理性及适用性进行了验证分析,结果表明本文所建BFDLM能够反映桥梁极值应力的周期性、随机性以及动态性等特点.研究成果将为桥梁监测极值应力预测提供理论基础和应用方法.

The dynamic prediction of bridge extreme stress based on health monitoring stress data was studied. Considering the monitored stresses’ periodicity, randomness, dynamic characteristics and so forth,firstly,the Fourier Dynamic Nonlinear Model(FDNM) of bridge monitored extreme stress was built,and, with Taylor series expansion technology, FDNM was approximately transferred into the Fourier Dynamic Linear Model(FDLM);secondly, with Bayes method, the Bayesian FDLM(BFDLM) was built based on the monitored extreme stress data,and the one-step forward prediction distribution parameters of monitored extreme stress and distribution parameters of poserior stress state were dynamically predicted;finally, the monitored extreme stress data of an actual bridge was provided to illustrate the application and feasibility of the proposed models and methods. The results show that the proposed BFDLM can reflect bridge extreme stresses' periodicity, randomness, dynamics and so forth,which can provide the theoretical foundation and application approach for bridge monitoring extreme stress prediction.