The determination of the regularization parameter based on signal-to-noise ratio in load identification

Tikhonov regularization is frequently used to solve the ill-conditioned inverse problem in load identification, and the regularization parameter which plays a significant role in Tikhonov regularization is usually determined by L-curve method. However, two corners appear on the L-curve at some situations, which cause the L-curve method to fail to determine a proper regularization parameter. To improve the accuracy of load identification, a new form of regularization parameter which is based on the largest singular value of the impulse response function matrix and signal-to-noise ratio is developed, and a modified L-curve is plotted. When the norm of the solution and the norm of the residual are balanced, a proper regularization parameter is determined through the modified L-curve. Both simulation and experimental results show that the identified load by the modified L-curve is closer to the actual load than L-curve. It also reveals that the modified L-curve is reasonable and the new regularization parameter is correct, and the accuracy of load identification is improved effectively.