Effects of Noise on Almost Collinear Systems
Abstract
We investigate the effects of noise on developing predictions of ill-conditioned systems from measurements. In particular we investigate collinearity between measurement devices. We assume the system is linear in the measurements taken, and that the measurement noise is uncorrelated both to the true measurements and to other measurement noises. The 'matrix' and 'vector' techniques (two stress transfer function techniques developed earlier) are analysed. The matrix technique produces better results, but requires external system information during calibration. On the other hand, the vector technique (based on least squares) is easily implemented (no knowledge of external information is required), but is sensitive to ill-conditioned configurations of measuring devices. The vector technique is shown to be the well-known errors-in-variable model, and hence unbiased but inconsistent, which explains the large errors it produces. Although a correction to the vector technique improves results, it is still not as accurate as the matrix technique. This vector correction additionally requires estimates of noise in the measuring devices, and suffers from sensitivity to noise estimation errors. The surrogate-matrix technique substitutes internal for external system information, circumventing the need for external system measurements. Simulation results involving a simple truss support all theoretical findings. The surrogate-matrix and vector techniques are recommended for ill- and well-conditioned systems respectively.
Document Details
- Document Type
- Technical Report
- Publication Date
- Mar 01, 2001
- Accession Number
- ADA390059
Entities
People
- Frank G. Polanco
Organizations
- Defence Science and Technology Group