基于振动传递率统计特性的桥梁结构参数识别方法研究

System identification is of primary importance in the studies of catastrophism mechanism and structural health monitoring for bridge engineering. Unfortunately, most of the system identification approaches available require measuring the system input precisely or assuming that the input is white noise. Measurement of the input seriously hinders its implementation, while the white noise assumption cannot be strictly satisfied in real applications.To avoid measuring system input and assuming white noise simultaneously, this project aims to utilize the unique property of dynamic transmissibility which is independent of the input as well as the advantage of Bayes' theorem in quantifying the uncertainties so that multiple uncertainties such as measurement noise and modelling error existing in system identification can be well accommodated. Issues of theoretical, computational and practical realization natures with computer are investigated deeply, drawing experiences from theoretical, numerical and experimental studies. The project is expected to prove the principle of statistical inference for random vector composed of ratio random variables, based on which the probability density function of dynamic transmissibility can be derived analytically. Then the Bayesian system identification approach driven by the statistical properties of dynamic transmissibility will be proposed. Also, efficient algorithms will be developed to obtain the optimal values of the physical parameters as well as their standard deviations and coefficients of variance. The project is expected to provide solid foundations for structural health monitoring and catastrophism analysis of bridge engineering, which is of theoretical significance and practical values in real applications.

参数识别是研究桥梁结构灾变机理和健康监测的基础。现有的参数识别方法通常需要“精确测量系统输入”或者 “假定未知输入为白噪声”，前者给应用带来了极大不便，而后者本质上难以严格满足。项目充分利用“振动传递率能有效消除荷载影响的特性”以及“贝叶斯理论在不确定性定量方面的优势”，以避免测量系统输入和白噪声假定为出发点，以考虑测试噪音和建模误差等多源不确定性因素的影响为突破口，从理论分析、数值模拟和试验验证三方面，对桥梁结构统计参数识别理论、算法和计算机实现进行深入研究。项目将着重从数学上严格证明复数域比例随机向量的统计推断原理，推导出振动传递率的概率密度函数解析表达式，建立振动传递率统计特性驱动的贝叶斯参数识别框架，并开发高效算法求解特征参数的最优值、标准差以及变异系数。项目成果可为桥梁动力灾变分析和健康监测提供依据，具有较大的理论意义和工程实用价值。

在研究桥梁动力灾变机理、健康监测和安全评估时，一个首先需要解决的关健问题就是正确地识别或监测结构的动力特性或参数，这些桥梁的结构参数是研究重大桥梁灾变机理、健康监测和安全评估的基础和依据。现有的参数识别方法通常需要精确测量系统输入或者假定未知输入为白噪声，精确测量系统输入给应用带来了极大不便，而未知输入的白噪声假定本质上难以严格满足。项目充分利用振动传递比能有效消除荷载影响的特性，以避免测量系统输入和白噪声假定为出发点，对基于传递比函数的结构参数识别理论、算法和应用进行了深入研究，项目取得的主要成果包括：（1）从数学上严格证明了复数域比例随机向量的统计推断定理，该定理提供了复数域比例随机向量概率密度函数的一般求解方法；（2）基于复数域比例随机向量的统计推断定理推导出了振动传递比的概率密度函数解析表达式，并得到了传递比函数实部、虚部、模和相位的边缘概率密度函数解析表达式，并通过大型土木工程结构的监测数据分析验证了振动传递比概率模型的鲁棒性；（3）基于振动传递比解析概率模型，建立了振动传递比函数驱动的贝叶斯参数识别框架，开发了高效算法求解特征参数的最优值、标准差以及变异系数；（4）建立了基于功率谱传递比矩阵奇异值分解的最小二乘复频域算法，通过参数化拟合的思路识别结构的模态参数并绘制稳定图剔除虚假模态；（5）项目在国内外期刊上发表论文14篇，其中SCI收录11篇，三篇论文以连载的形式(Part I/II/III)发表于振动信号处理领域著名期刊Mechanical Systems and Signal Processing。项目成果可为桥梁工程动力灾变分析和健康监测提供依据，具有较大的理论意义和工程实用价值。