Nonlinear structural damage detection based on cascade of Hammerstein models

• Structural damages result in nonlinear signatures that enhance their detection.
• A damage detection approach based on cascade of Hammerstein models is proposed.
• The model is estimated by the Exponential Sine Sweep Method from one measurement.
• Linear and nonlinear output parts are estimated and two damage indexes are built.
• The method is validated numerically and experimentally in the presence of noise.

Structural damages result in nonlinear dynamical signatures that can significantly enhance their detection. An original nonlinear damage detection approach is proposed that is based on a cascade of Hammerstein models representation of the structure. This model is estimated by means of the Exponential Sine Sweep Method from only one measurement. On the basis of this estimated model, the linear and nonlinear parts of the outputs are estimated, and two damage indexes (DIs) are proposed. The first DI is built as the ratio of the energy contained in the nonlinear part of an output versus the energy contained in its linear part. The second DI is the angle between the subspaces obtained from the nonlinear parts of two sets of outputs after a principal component analysis. The sensitivity of the proposed DIs to the presence of damages as well as their robustness to noise is assessed numerically on spring–mass–damper structures and experimentally on composite plates with surface-mounted PZT-elements. Results demonstrate the effectiveness of the proposed method to detect a damage in nonlinear structures and in the presence of noise.