Prior design for tomographic volume fraction estimation in pneumatic conveying systems from capacitive data

Abstract

Pneumatic conveying systems have become a standard technique for the transport of bulk materials such as powdery or granulates. The spatial dependence of the material density and the stream velocity in such transport systems require a volumetric measurement principle for flow measurement. In this paper we analyse the capability to estimate the volume fraction from capacitive sensing data using electrical capacitance tomography (ECT). In particular, we investigate the capability of back-projection type imaging algorithms. The ill-posed nature of the imaging problem of ECT require the incorporation of prior knowledge in the design of the estimator. We analyse the different flow profiles in pneumatic conveying in order to generate specific sample-based prior information to improve the estimation performance and robustness. We discuss the construction of different linear image reconstruction algorithms and present a framework, which allows a detailed statistical analysis of the estimator performance. Simulation studies show the estimation behaviour of different algorithms with respect to the incorporated prior information. We demonstrate, that the incorporation of specific prior knowledge leads to an improved estimator behaviour; for example, reduced variance and unbiased estimates. We implemented laboratory experiments in order to analyse the presented approach for the application in real pneumatic conveying processes. We demonstrate the improved robust estimation behaviour by means of comparative reconstruction results obtained with different algorithms and priors. Furthermore, the uncertainty of the estimated volume fraction is analysed in steady state conveying processes. Hereby, it is demonstrated, that appropriate prior information improves the estimation performance also for measurements coming from real pneumatic conveying processes, making ECT a suitable tool for the volume fraction estimation in such transport systems.