A nonprobabilistic structural damage identification approach based on orthogonal polynomial expansion and interval mathematics

In this study, a nonprobabilistic structural damage identification approach based on orthogonal polynomial expansion and interval mathematics is proposed for uncertainty-oriented damage identification with insufficient parametric information. A deterministic damage identification method is firstly reviewed. By means of a nonnegative least squares algorithm that combines truncated singular value decomposition and the L-curve method, the ill-posed damage equation is then solved, and the damage index is simultaneously obtained. In terms of the uncertainty quantification issue, the material elastic modulus and density in structural models herein are described as unknown-but-bounded interval numbers. On the basis of orthogonal polynomial expansion and interval mathematics, the set collocation methodology is presented to determine the upper and lower bounds of the damage index. The interval bounds can provide supports for structural health diagnosis under uncertain conditions. A nonprobabilistic identification using the first-order Taylor series expansion is also proposed for comparison's purpose. Two numerical applications and one test are finally given under single damage and multidamage scenarios with different uncertainty degree. Results suggest that the presented nonprobabilistic structural damage identification approach can identify the damage location and degree with consideration of uncertainties.