Beyond Correlation: Mutual Information to Detect Damage in Nonlinear Systems

Analyzing and measuring the similarity between two signals is a common task in many vibration-based structural health monitoring applications. Coherence between input and response signals serves as a convenient indicator of damage, based on the premise that nonlinearity due to damage in a linear system manifests as a loss of coherence in specific frequency bands. Because input excitations in civil structures are difficult to measure, damage indicators based on the coherence between two response signals have been developed. These indicators have shown promise in detecting nonlinear behavior in structures that were initially linear. This paper proposes a new damage indicator based on Mutual Information, a nonlinear extension of the squared correlation coefficient, to quantify the similarity between two signals without making assumptions about the nature of their interactions or the underlying dynamics of the system. Mutual Information is distinguished from other nonlinear similarity metrics due to its ability to capture all types of nonlinear dependencies, its high computational efficiency, and its invariance to invertible transformations, such as scaling. The proposed approach is demonstrated using a standard dataset containing experimental data from a three-story aluminum frame structure under 17 different damage states. The results show that the proposed metric can detect deviations from the baseline state due to changes in mass, stiffness, or newly induced nonlinear behavior, suggesting its potential for monitoring changes in the structural system.