Dynamic load identification for uncertain structures based on interval analysis and regularization method

In this paper, an inverse method that combines the interval analysis with regularization is presented to stably identify the bounds of dynamic load acting on the uncertain structures. The uncertain parameters of the structure are treated as intervals and hence only their bounds are needed. Using the first-order Taylor expansion, the identified load can be approximated as a linear function of the uncertain parameters. In this function, it is assumed that the load at the midpoint of the uncertain parameters can be expressed as a series of impulse kernels. The finite element method (FEM) is used to obtain the response function of the impulse kernel and the response to the midpoint load is expressed in a form of convolution. In order to deal with the ill-posedness arising from the deconvolution, two regularization methods are adopted to provide the numerically efficient and stable solution of the desired unknown midpoint load. Then, a sensitivity analysis is suggested to calculate the first derivative of the identified load with respect to each uncertain parameter. Applying the interval extension in interval mathematics, the lower and upper bounds of identified load caused by the uncertainty can be finally determined. Numerical simulation demonstrates that the present method is effective and robust to stably determine the range of the load on the uncertain structures from the noisy measured response in time domain.