Adaptive stochastic Galerkin FEM for lognormal coefficients in hierarchical tensor representations

Stochastic Galerkin methods for non-affine coefficient representations are known to cause major difficulties from theoretical and numerical points of view. In this work, an adaptive Galerkin FE method for linear parametric PDEs with lognormal coefficients discretized in Hermite chaos polynomials is derived. It employs problem-adapted function spaces to ensure solvability of the variational formulation. The inherently high computational complexity of the parametric operator is made tractable by using hierarchical tensor representations. For this, a new tensor train format of the lognormal coefficient is derived and verified numerically. The central novelty is the derivation of a reliable residual-based a posteriori error estimator. This can be regarded as a unique feature of stochastic Galerkin methods. It allows for an adaptive algorithm to steer the refinements of the physical mesh and the anisotropic Wiener chaos polynomial degrees. For the evaluation of the error estimator to become feasible, a numerically efficient tensor format discretization is developed. Benchmark examples with unbounded lognormal coefficient fields illustrate the performance of the proposed Galerkin discretization and the fully adaptive algorithm

Position control of an industrial robot using an optical measurement system for machining purposes

A series of mechanical properties and disturbances limit the accuracy achievable in robotic applications. External control of the end effector position is commonly known as being an appropriate mean to increase accuracy. This paper presents an approach for position control of industrial robots using the pass-through between an industrial CNC and servomotors. A CNC-controlled robot is used together with an external optical measurement system to close the feedback loop of robot end effector and robot controller in order to improve robot accuracy. For short cycle times and implementation reasons a PLC is used for signal processing and control implementation. The relevance of the approach is outlined in experiments. The robot behaviour in free space motion and in machining application is analysed with the optical measurement system and a CMM

A new method to determine multi-angular reflectance factor from lightweight multispectral cameras with sky sensor in a target-less workflow applicable to UAV

A new physically based method to estimate hemispheric-directional reflectance factor (HDRF) from lightweight multispectral cameras that have a downwelling irradiance sensor is presented. It combines radiometry with photogrammetric computer vision to derive geometrically and radiometrically accurate data purely from the images, without requiring reflectance targets or any other additional information apart from the imagery. The sky sensor orientation is initially computed using photogrammetric computer vision and revised with a non-linear regression comprising radiometric and photogrammetry-derived information. It works for both clear sky and overcast conditions. A ground-based test acquisition of a Spectralon target observed from different viewing directions and with different sun positions using a typical multispectral sensor configuration for clear sky and overcast showed that both the overall value and the directionality of the reflectance factor as reported in the literature were well retrieved. An RMSE of 3% for clear sky and up to 5% for overcast sky was observed