2001 Fiscal Year Final Research Report Summary
Updating/Filtering of Nonlinear Dynamical Systems for Structural Health Monitoring
| Project/Area Number |
11650494
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| Research Category |
Grant-in-Aid for Scientific Research (C)
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| Allocation Type | Single-year Grants |
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| Section | 一般 |
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| Research Field |
構造工学・地震工学
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| Research Institution | Musashi Institute of Technology |
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Principal Investigator |
MARUYAMA Osamu Musashi Inst. Of Tech., Dept. of Civil Engrg., Assistant Professor, 工学部, 助教授 (50209699)
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| Co-Investigator(Kenkyū-buntansha) |
HOSHIYA Masaru Musashi Inst. Of Tech., Dept. of Civil Engrg., Professor, 工学部, 教授 (30061518)
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| Project Period (FY) |
1999 – 2001
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| Keywords | Kalman Filter / Bootstrap Filter / Monte Carlo Filter / Health Monitoring |
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| Research Abstract |
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 by
y_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.
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