Inverse Dyanmic Problems
Key words: Inverse dynamic problems, dynamic programming
filter, regularization, measurement error, measurement type, empirical data
processing, element dynamic programming filter, dual reciprocity BEM (DRBEM),
elastodynamics, heat conduction
Inverse problems are concerned with the estimations of
system properties or input forcing terms from system behaviours. Reversely,
classical direct problems involve the analysis of the behaviours from the input
forcing terms and system properties. In recent years inverse dynamic
problems have received increasing attention due to a broad range of
engineering necessity. In general, the solution of the inverse dynamic problem
is far more difficult than the direct problem due to some degree of
noise in the measurement data. In other words, the inverse solution is
extremely sensitive to measurement errors, namely, the ill-posed
nature of the inverse problem. In compared with direct problems, research of
inverse dynamic problems is much less reported in literature, especially for
inverse elastodynamic problem. There are several methods available now to
stabilize and estimate the inverse solutions of dynamic problem. Among them, the
dynamic programming filter (DPF) with regularization, introduced
recently by
#1:
The coupling application of the dual reciprocity BEM (DRBEM) and
dynamic programming filter with regularization was first presented to
solve inverse elastodynamic problems. The affect of noise level,
regularization parameter, and measurement and input force
types on the estimation was investigated. The study showed that the combined
method is accurate, robust and generally applicable. It was found that the
strategy is insensitive to measurement errors and can give good
estimate even using heavily noisy data. To our knowledge, this is the
first attempt to use the DRBEM combined with dynamic programming filter to
handle the inverse problems.
#2:
One of the key shortcomings in the existing dynamic programming filter is
to require high computational effort for large systems over a long history.
Recently, we proposed an element (sequent) dynamic programming filter to
considerably reduce computational cost without the loss of accuracy in general.
#3:
It was found that element dynamic programming filter performs very well
in smoothing and differentiating empirical data with great reduction in
computing effort. Further numerical experiments are still under way.
Related Publications
Journals
- M. Tanaka and W. Chen, Dual
reciprocity BEM and dynamic programming filter for inverse elastodynamic
problems, Transactions of the Japan Society for Computational
Engineering and Science, 2, 2000.
- W. Chen and M. Tanaka, "Reducing computing
effort in dynamic programming filter for inverse problem", (in
preparation).
Proceedings
- M. Tanaka and W. Chen, "Identification of
elastodynamic load using DRBEM and dynamic programming filter",
International Symposium on Inverse Problems in Engineering Mechanics
2000, Mar. 2000,
- M. Tanaka and W. Chen, "DRBEM and dynamic
programming filter for inverse elastodynamic problems", Proceedings of
- M. Tanaka and W. Chen, "Dual reciprocity
BEM solution of an inverse heat conduction boundary problem", JSME
conference on thermoelastic dynamic problems, August. 2000,
- W. Chen and M. Tanaka, Solution of some
inverse heat conduction problems by the dynamic programming filter and
BEM, International Symposium on Inverse Problems in Engineering
Mechanics 2001, 23-28, Feb. 2001,
Projects
- JSPS (
[
DQ-type methods ||
Modeling || BEM || Inverse analysis
|| RBF || Wavelet || Patent ]
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