Nonlinear Acoustic Tomography for Measuring the Temperature and Velocity Fields by Using the Covariance Matrix Adaptation Evolution Strategy Algorithm

Accurate measurement of temperature and velocity fields in combustion and flow diagnostic plays an important role in analyzing the heat transfer mechanism and ensuring the safe operation of equipment. In this work, considering the refraction effect of sound waves, temperature and velocity fields are reconstructed simultaneously based on the nonlinear acoustic tomography (NAT) by using the covariance matrix adaptation evolution strategy (CMA-ES) algorithm. In the forward problem, the fast two-point ray-tracing algorithm is introduced to track curved sound waves more efficiently. Due to the sparse measurement signals caused by the limited space and curved acoustic paths, Tikhonov regularization is introduced as the constraint of smoothing prior information to reduce the ill-posedness of the problem. The influence of the velocity regularization parameter and temperature regularization parameter on simultaneously visualizing the temperature and corresponding velocity fields are investigated, respectively. Then the selection strategies of these two regularization parameters are given, which are proved to have high selection efficiency. On this basis, inhomogeneous temperature and velocity fields are reconstructed simultaneously by using the CMA-ES algorithm, simulated annealing, and genetic algorithms. By solving the inverse problem of the NAT, which is highly nonlinear and ill-posed, the feasibility and effectiveness of the CMA-ES algorithm in the simultaneous reconstruction of velocity and temperature fields are confirmed. The proposed method for visualizing the temperature and velocity fields will supply key feedback for the combustion process control.