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• A model for wafers surface topography prediction in the ultra-precision grinding considering volumetric errors is proposed. • An HTM-based volumetric error model is optimized considering Abbe and Bryan errors induced while measuring errors. • On-machine measurement of translational axes' geometric errors is realized using an author's group developed system. • The predicted and experimental wafer surface topographies are in reasonable agreement with each other. Ultra-precision grinding machine is widely used for thinning silicon wafers. The wafer surface quality is considerably affected by volumetric errors at the functional point of the ultra-precision grinding machine. Therefore, a volumetric error model is established based on the homogeneous transformation matrix (HTM) method. The model is, then, optimized by considering Abbe and Bryan errors induced volumetric errors during the error measurements process. A prediction model for the wafer surface topography is established by combining the manufacturing mechanism of the ultra-precision grinding and the optimized volumetric error model of the ultra-precision grinding machine. Volumetric errors are detected using an author's group developed laser measurement system and a commercial spindle error analyzer. The model enables to predict the topography and total thickness variation (TTV) of the wafer surface. A group of grinding experiments are performed to verify the effectiveness of the proposed models. [ABSTRACT FROM AUTHOR]

This paper presents a systematic approach for selecting the optimal moving order (MO) in a multi-axis precise motion system (MPMS). According to the proposed procedure, an optimal high-efficiency MO selection approach for high-efficiency and high-accuracy requirement is introduced. First, the characteristics of the giving MPMS are analysed, and the error model is established. The orthogonal test method is used to evaluate the influence on the MO caused by different MPMS configurations. Second, the number of possible MOs can be narrowed to limited and satisfied MO types. By calculating the deviations after each step, all directional movements can be arranged. Third, considering that both the accuracy and efficiency are important indexes, a series of systematic formulations are developed to select the optimal MO to balance accuracy and efficiency. A case for which a six-axis precise platform is adopted in an optoelectronic packaging system is implemented, and the methods of high-quality MO selection are verified by performing a series of experiments, and the methods are shown to be useful and effective. To balance the proportion of efficiency and accuracy, the formula and corresponding model are proposed to select the MO. The approach is not only beneficial to the accuracy improvement and trajectory planning of MPMS, but also helpful in terms of reducing the computational processing for the following algorithm. For the engineers using in precise industry area, the proposed approach can significantly improve the operative precision of MPMS with an optimal MO. This methodology of MO can also be the basis of references to error-related analyses on MPMS. • This paper introduced a novel moving order selection approach for a multi-axis precise motion platform by searching the minimum deviation DOF-by-DOF. • The approach provides corresponding formulas for balancing the efficiency and accuracy with different requirement. • A case indicates that the approach can save the computational volume greatly in moving order finding. [ABSTRACT FROM AUTHOR]

Through the computational modelling and experimental verification of a stereo-photogrammetry system, the expanded uncertainty on form measurement was estimated and was found to be 32 μ m , 12 μ m and 29 μ m for a 95% confidence interval (coverage factors of k = 3.2, 2.0 and 2.0 respectively) in the x, y and z axis respectively. The contribution of systematic offsets in the system properties was also investigated, demonstrating the complex distortions of the measurement volume that result from these systematic errors. Additionally, a traceable method of applying a scale factor to the reconstruction was demonstrated using a laser interferometer and gauge block. The relative standard uncertainty on the size of the measurements was estimated to be 0.007% corresponding to length measurement uncertainties of around 7 μ m over a 100 mm range. Finally, the residuals from a linear fit of the scale factor were found to exhibit behaviour that would be expected to result from small offsets in the system properties. The outcome of this work is a better understanding of the propagation of uncertainty through the stereo-photogrammetry system as well as highlighting key influence factors that must be addressed in future work. • Monte Carlo simulation of a stereo-photogrammetry system. • Traceable calibration of stereo-photogrammetry measurements. • Effect of Systematic errors on stereo-photogrammetry is demonstrated and verified. [ABSTRACT FROM AUTHOR]

The inherent uncertainties of a manipulator, including manufacturing tolerances, input errors and joint clearances, cause deviations between the actual motion and the expected motion, leading to a motion reliability problem. This paper focuses on the motion reliability of a planar 3- R RR parallel manipulator with multiple uncertainties. First, the error model of the manipulator is built. Then, an analytical method is presented to verify its validation and accuracy. To address the complexity of the motion in a journal-bearing joint, the joint clearance parameters are modelled as interval variables while other parameters are treated as random variables. A new hybrid approach to motion reliability analysis based on the first order second moment (FOSM) method and the Monte Carlo simulation (MCS) method is developed for the manipulator with both random and interval variables. This method has an easier simulation process than that of the conventional MCS method using direct kinematics. Compared to the probability method with random variables, the proposed hybrid method has a higher confidence estimate of motion reliability for the manipulator with joint clearances. [ABSTRACT FROM AUTHOR]

Abstract: Time-of-flight range camera data are prone to the scattering bias caused by multiple internal reflections of light received from a highly reflective object in the camera’s foreground that induce a phase shift in the light received from background targets. The corresponding range bias can have serious implications on the quality of data of captured scenes as well as the geometric self-calibration of range cameras. In order to minimise the impact of the scattering range biases, the calibration must be performed over a planar target field rather than a more desirable 3D target field. This significantly impacts the quality of the rangefinder offset parameter estimation due to its high correlation with the camera perspective centre position. In this contribution a new model to compensate for scattering-induced range errors is proposed that allows range camera self-calibration to be conducted over a 3D target field. Developed from experimental observations of scattering behaviour under specific scene conditions, it comprises four new additional parameters that are estimated in the self-calibrating bundle adjustment. The results of experiments conducted on five range camera datasets demonstrate the model’s efficacy in compensating for the scattering error without compromising model fidelity. It is further demonstrated that it actually reduces the rangefinder offset-perspective centre correlation and its use with a 3D target field is the preferred method for calibrating narrow field-of-view range cameras. [Copyright &y& Elsevier]

• A new error model to propagate uncertainty for ensemble streamflow forecasts. • Suitable for ephemeral and perennial rivers. • We compare it to an existing error model. • The new model produces more reliable ensembles to long (>150 h) lead times. • The new model better propagates uncertainty downstream for nested gauges. We propose a revised version of the ERRIS (error reduction and representation in stages) error model capable of reliably propagating hydrological uncertainty to long lead times (>150 time steps). ERRIS employs four stages: a transformation to handle heteroscedasticity, a moving average bias-correction, an autoregressive model and two mixture Gaussian distributions. To propagate uncertainty through multiple lead times, ERRIS makes use of a technique termed 'stochastic updating'. Ensemble spread at long lead times is partly controlled by the interplay of the autoregression coefficient ρ and the width of the error distribution. When ρ approaches 1 and the error distribution is wide, this causes over-wide ensemble distributions at long lead times. We control this interplay with the moving average bias-correction, which reduces the value of ρ and the width of the error distribution, resulting in reliable ensembles at long lead times. An additional control on the width of the ensemble at longer lead times is a restriction applied to the autoregressive model. This restriction guards against large overcorrections, which can lead to very poor forecasts. Applying the restriction when parameters are inferred can result in over-wide residual distributions. We propose the simple expedient of applying the restriction only when forecasts are generated, not when parameters are inferred. We show through a comparison with an earlier version of ERRIS that this produces more reliable ensemble distributions at long lead times, whilst still guarding against overcorrection. The resulting error model is simple and computationally efficient, and thus suitable for deployment in operational streamflow forecasting systems. [ABSTRACT FROM AUTHOR]

Abstract: This paper presents research showing how random errors in a fine toposcale digital elevation model (DEM) are propagated to DEM-based surface derivatives. The focus was on two constrained derivatives, slope and aspect, and one unconstrained derivative, drainage basin delineation. The error propagation was explored by using numerical and analytical methods, and in both approaches the DEM error was modelled as a second-order stationary Gaussian random process. The results were summarised in the case study, in which 32 realistic scenarios of DEM error models were used. The scenarios were based on exponential and Gaussian spatial autocorrelation models with four sills (0.0625, 0.25, 1.00, and 4.00m2) and practical ranges (0, 30, 60, and 120m). We found that, as expected, increase in DEM error increased the error in surface derivatives. However, contrary to expectations, the spatial autocorrelation model appears to have varying effects on the error propagation analysis depending on the application. In constrained surface derivatives, such as slope and aspect, the maximum error in results appeared to exist when the practical range of the error''s spatial autocorrelation was roughly equal to the size of the surface derivative''s calculation window. In unconstrained terrain analysis, such as drainage basin delineation, the variance of the results appeared to increase while the spatial autocorrelation range increases. Until now, the use of spatially uncorrelated DEM error models have been considered as a ‘worst-case scenario’, but this opinion may now be challenged because none of the DEM derivatives investigated in the study had maximum variation with spatially uncorrelated random error. In addition, the study revealed that the role of the appropriate shape of the spatial autocorrelation model, either exponential or Gaussian, was not as important as the choice of appropriate autocorrelation parameters: practical range and sill. However, the shape of the spatial autocorrelation model appeared to have more influence on the calculation of slope and aspect than on the drainage basin delineation. For error propagation analysis purposes an analytical approach appears to be more useful for constrained derivatives, while the Monte Carlo method is appropriate for analysing both constrained and unconstrained derivatives. [Copyright &y& Elsevier]