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Digital Twin of a Photoacoustic Trace Gas Sensor for Monitoring Methane in Complex Gas Compositions
(2022)
The digitalization of industrial processes requires smart sensor systems. Photoacoustic spectroscopy is well suited for this purpose as it allows for small-sized and low-cost trace gas analysis. However, the method is susceptible to changes in measurement conditions and standard calibration routines often fail to correct for all changes. We therefore created a Digital Twin (DT) of a photoacoustic trace gas sensor for methane and evaluated it regarding variations in gas composition (CH4, N2, O2, CO2, H2O), temperature and pressure. With a mean absolute percentage error of 0.8 % the accuracy of the sensor after DT compensation significantly exceeds the 24 % achieved based on standard calibration in nitrogen. For the first time, we can fully analytically compute the photoacoustic signal under moderate ambient conditions with an error in the ppbV range by taking a holistic approach. Assuming knowledge of the underlying energy transfer processes, the model of this Digital Twin can be adapted to any microphone based photoacoustic sensor for monitoring any analyte species.
The characteristic feature of inverse problems is their instability with respect to data perturbations. In order to stabilize the inversion process, regularization methods have to be developed and applied. In this work we introduce and analyze the concept of filtered diagonal frame decomposition which extends the standard filtered singular value decomposition to the frame case. Frames as generalized singular system allows to better adapt to a given class of potential solutions. In this paper, we show that filtered diagonal frame decomposition yield a convergent regularization method. Moreover, we derive convergence rates under source type conditions and prove order optimality under the assumption that the considered frame is a Riesz-basis.
A basic task in the design of an industrial robot application
is the relative placement of robot and workpiece. Process points are defined in Cartesian coordinates relative to the workpiece coordinate system, and the workpiece has to be located such that the robot can reach all points. Finding such a location is still an iterative procedure based on the developers' intuition. One difficulty is the choice of one of the several solutions of the backward transform of a typical 6R robot.
We present a novel algorithm that simultaneously optimizes the workpiece location and the robot configuration at all process points using higher order optimization algorithms. A key ingredient is the extension of the robot with a virtual prismatic axis. The practical feasibility of the approach is shown with an example using a commercial industrial robot.