Optimization of Transducer Array for Cross-Sectional Velocity Field Reconstruction in Acoustic Tomography

As a part of industrial process tomography, acoustic tomography (AT) is a promising method for high-quality velocity field measurement, which is widely utilized in the monitoring of multiphase flow, atmospheric environment, and so on. However, subjected to the safety and reliability requirements of furnaces or industrial pipes, the number of installed transducers is restricted, which results in sparse valid data, and, thus, ill-posed and rank-deficient limited-data linear AT. Therefore, special attention should be given to the transducer arrangement in the framework construction module to maximize the reconstruction accuracy. Unlike methods that minimize relative reconstruction error including true value of interesting field, finding an alternative prior knowledge-based predictor that maps the reconstruction error is more practical and preferred. In this work, based on the prior information that the linear independence of vectors incorporates maximum measurement information, a linear independence degree (LID) metric is proposed to optimize the transducer array. It contains no prior information about flow velocity fields, which enables the procedure to be performed in an off-line mode. A covariance matrix adaptation evolution strategy (CMA-ES) algorithm is employed to solve this minimization problem. Proof-of-concept demonstrations, including representative synthetic vortical flow fields with a biased single vortex or with double vortices and experimental data-based velocity field, are performed by comparison with existing representative optimization strategies. Qualitative and quantitative results show the feasibility and robustness of the LID metric in improving imaging accuracy of arbitrary practical velocity fields based on AT. This prior metric is expected to provide guidance for better diagnosis of multiphase flow and optimization of industrial flow process.