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Updating/Filtering of Nonlinear Dynamical Systems for Structural Health Monitoring

用于结构健康监测的非线性动力系统的更新/过滤

基本信息

批准号：
11650494
负责人：
MARUYAMA Osamu
金额：
$ 0.83万
依托单位：
Musashi Institute of Technology
依托单位国家：
日本
项目类别：
Grant-in-Aid for Scientific Research (C)
财政年份：
1999
资助国家：
日本
起止时间：
1999 至 2001
项目状态：
已结题

项目摘要

Since civil engineering structures are involved in many uncertainties, they are often modeled as stochastic fields. Engineering knowledge and past data on a system or system of similar kinds are helpful to setting up the model, that is, a stochastic field. If observation is carried out on a system at site, then the model may be updated by the newly obtained information on the system. This procedure may be interpreted as a procedure of Bayesian updating or filtering of a prior model into a posterior model.This research will deal with a stochastic field, which is modeled as a discrete state vector equation.x_n = F(x_<n-1>,v_n) (1)and an observation vector equation which relates the state vector X_n to the observation vector byy_n = H(x_n)+w_n (2)where x_n = vector of k^*1 v_n = system noise vector of r^*1 with pdf q(v_n), y_n = observation vector of s^*1, w_n = observation noise vector of s^*1 with pdf r(w_n).For stochastic fields given by eqs(1) and (2), basic formulas are first discussed from which mathematical tools stem for updating/filtering of prior stochastic fields. In the past, Gaussian linear fields were successfully treated by, for example, the Kalman filter. However, engineering systems such as structural or soil foundation systems might be non-Gaussian and nonlinear in the nature and we might encounter with some difficulty due to the non-Gaussian and nonlinear properties in the dealing with probabilistic distributions. As a versatile tool to update such systems, Monte Carlo filter by Kitagawa is focused that is a sequential algorithm of generating a set of sample realizations of a predicted state vector and a filtered state vector respectively. In order to clarify the potential of this method, identification of dynamic parameters of a nonlinear system is first discussed, and stochastic interpolation of a non-Gaussian spatial random field is also demonstrated by using numerically simulated data.

由于土木工程结构中涉及到许多不确定性因素，因此常常将其建模为随机场。工程知识和过去关于系统或类似系统的数据有助于建立模型，即随机场。如果在现场对系统进行观测，则可以使用新获得的关于系统的信息来更新模型。这一过程可以解释为贝叶斯更新或过滤先验模型到后验模型的过程。本研究将处理一个被建模为离散状态向量方程的随机场。，v_n)(1)和将状态向量X_n与观测向量联系起来的观测向量方程y_n=H(X_N)+w_n(2)，其中x_n=k^*1v_n的向量，具有pdf q(V_N)的r^*1的系统噪声向量，y_n=S^*1的观测向量，w_n=具有pdf r(W_N)的S^*1的观测噪声向量。首先讨论了用于更新/过滤先前随机场的数学工具的基本公式。在过去，高斯线性场被成功地用例如卡尔曼滤波来处理。然而，结构或地基等工程系统在本质上可能是非高斯和非线性的，在处理概率分布时，由于非高斯和非线性的特性，我们可能会遇到一些困难。作为更新这类系统的通用工具，Kitagawa的蒙特卡罗过滤器是一种顺序算法，它分别生成预测状态向量和过滤状态向量的一组样本实现。为了阐明这种方法的潜力，首先讨论了非线性系统的动态参数辨识，并用数值模拟数据演示了非高斯空间随机场的随机内插。