Identification of transient boundary conditions with improved cuckoo search algorithm and polynomial approximation

The cuckoo search (CS) algorithm combined with Broyden-Fletcher-Goldfarb-Shanno (BFGS) algorithm (CS-BFGS) is proposed to identify time-dependent boundary conditions for 2-D transient heat conduction problems in functionally gradient materials. Firstly the dual reciprocity boundary element method (DRBEM) is used to solve the direct problem. Then taking the unknown boundary conditions as a polynomial function of coordinates with time-dependent coefficients, the CS-BFGS is applied to obtain the unknown coefficients of the polynomial. As a result, the transient boundary conditions are evaluated. The convergence speed of the CS-BFGS algorithm is faster than the CS algorithm. What's more, the effect of the polynomial degree is discussed. As the polynomial degree increases, the inverse results are more accurate but the iterative number and computation time also increase. Finally, the influences of the position and number of measurement points, and random errors on the inverse results are investigated. With the measurement points closer to the boundary, with the increase of measurement point number and with the decrease of measurement errors, the results are more accurate.