Distribution Of Observation Points Research Articles

Machine-Tool Error Observer Design With Application to Thermal Error Tracking

Abstract A parameter identification procedure for identifying the parameters of a volumetric error model of a large machine tool requires hundreds of random volumetric error components in its workspace and thus takes hours of measurement time. It causes thermal errors of a large machine difficult to be tracked and compensated periodically. This paper demonstrates the application of the optimal observation design theories to volumetric error model parameter identification of a large five-axis machine. Optimal designs maximize the amount of information carried in the observations. In this paper, K-optimal designs are applied for the construction of machine-tool error observers by determining locations in the workspace at which 80 components of volumetric errors to be measured so that the model parameters can be identified in 5% of an 8-h shift. Many of optimal designs tend to localize observations at the boundary of the workspace. This leaves large volumes of the workspace inadequately represented, making the identified model inadequate. Therefore, the constrained optimization algorithms that force the distribution of observation points in the machine’s workspace are developed. Optimal designs reduce the number of observations in the identification procedure. This opens up the possibility of tracking thermal variations of the volumetric error model with periodic measurements. The design, implementation, and performance of a constrained K-optimal in tracking the thermal variations of the volumetric error over a 400-min period of operation are also reported. About 70–80% of machine-tool error can be explained using the proposed thermal error modeling methodology.

Calibration Method for Mapping Camera Based on a Precise Grouped Approach Method

This paper introduces a new calibration method for the mapping camera called Precise Grouped Approach Method (PGAM). The conventional calibration method for the mapping camera is the exact measuring angle method. The accuracy of this method can be reduced by theoretical uncertainties and the number and distribution of observation points. PGAM is able to overcome these disadvantages and improve the accuracy. Firstly, we reduce the theoretical uncertainties by means of a grouped approach method, which rectifies the high-precision rotation stage to zero position. Secondly, a weighted theory is applied to eliminate the effect of the number and distribution of observation points. Finally, the accuracy of PGAM is analyzed. The experiment result shows that the calibration accuracy is significantly improved when using the proposed PGAM algorithm, compared to the conventional one under the identical experimental condition.

Error evaluation in acoustic positioning of a single transponder for seafloor crustal deformation measurements

The observation of seafloor crustal deformation is very important to understand plate motions, nucleation processes and mechanisms of great interplate earthquakes as well as the activities of submarine volcanoes. We have been developing an observation system for seafloor crustal deformation. This system consists of two main components; (1) kinematic GPS positioning of an observation vessel and (2) accurate acoustic measurements of distances between a transponder attached on the side of the vessel (onboard station) and one located on the ocean bottom (seafloor station). In this study, we performed numerical simulations to estimate measurement errors with acoustic positioning assuming acoustic velocities in the sea water and the distribution of observation points around the single seafloor station. We found that the position of the seafloor station which we can obtain by analyzing travel-time data might have around 18-cm discrepancy with respect to its “true” position. Colombo et al. (2001) reported that the position of the vessel can be determined with about 10-cm error by kinematic GPS positioning. These results indicate that the system should be able to detect seafloor crustal deformation much larger than 28 cm, including pre-, co-, and post-seismic slips due to the large earthquakes at subduction zones, slow and silent earthquakes, etc. Therefore, we emphasize the importance of continuous observations with a nationwide geodetic observational network for seafloor crustal deformation.

A multiscale, statistically based inversion scheme for linearized inverse scattering problems

The application of multiscale and stochastic techniques to the solution of a linearized inverse scattering problem is presented. This approach allows for the explicit and easy handling of many difficulties associated with problems of this type. Regularization is accomplished via the use of a multiscale prior stochastic model which offers considerable flexibility for the incorporation of prior knowledge and constraints. the authors use the relative error covariance matrix (RECM), introduced by E.L. Miller et al. (1995), as a tool for quantitatively evaluating the manner in which data contribute to the structure of a reconstruction. Given a set of scattering experiments, the RECM is used for understanding and analyzing the process of data fusion and allows the authors to define the space-varying optimal scale for reconstruction as a function of the nature (resolution, quality, and distribution of observation points) of the available measurement sets. Examples of the authors' multiscale inversion algorithm are presented using the Born approximation of an inverse electrical conductivity problem formulated so as to illustrate many of the features associated with inverse scattering problems arising in fields such as geophysical prospecting and medical imaging.

Gravimetric interpolation of the deflection of the vertical

Abstract The horizontal gravity anomaly vector h, and hence the components of the deflection of the vertical, is interpolated from the surrounding discrete observations of gravity anomaly g j lying within a limited radius. If the observation points lie at distances p i , azimuths θ j , and heights ζ j with respect to the interpolation point, and represent areas a j , then h is found by a linear summation The weighting function incorporates Gaussian smoothing of the observed anomalies with a frequency response of exp(-ν2/ω2) where ν is the frequency of the observed anomaly, and ω a frequency parameter which must be chosen with regard to the spacing of the observation points. The linear summation formula is modified to correct for irregularities in the distribution of observation points. The method has been developed for the interpolation of local variations in the deflcxtion components between astrogeodetic points.