Abstract Summary
In many structural health monitoring applications, different types of sensors monitor the same structure. Measured vibration response can include accelerations, velocities, displacements, and strains. It is important that all available information is utilized in damage detection for an early warning. Although displacement, velocity and acceleration are related (via time differentiation), their signals are not directly correlated. This makes it difficult to utilize all available sensor data in damage detection. Damage detection in the time domain includes certain advantages over feature-domain methods: (1) system identification is not needed, and (2) the number of data points is large, and the dimensionality is relatively low, resulting in higher statistical reliability. Some challenges of using measured response data directly in the time domain are: (1) The signal-to-noise ratio (SNR) may be too low to detect small damage. (2) The number of sensors must be larger than the number of active modes. (3) Different measured quantities are not directly correlated, as mentioned before. A possible solution to handle heterogeneous response data in the time domain for damage detection is to use autocovariance function (ACF) estimates instead of direct sensor data. If the excitation is stationary random, the ACFs have the same form as a free decay of the system. In particular, different response quantities yield functionally similar ACFs, which can be utilized in centralized sensor fusion. However, phase differences exist between the ACFs of different quantities, so that applying only spatial correlation between different ACFs is insufficient. However, spatiotemporal correlation between different ACFs exists and should be used. Spatiotemporal correlation makes it also possible to have a smaller number of sensors than the number of active modes. The SNR can be controlled by adjusting the measurement period. In the proposed method, a spatiotemporal covariance matrix is estimated from the ACFs of the training data from the undamaged structure under different environmental or operational conditions. Using novelty detection techniques, an extreme value statistics control chart is designed to detect damage. A numerical experiment was performed by simulating vibration measurements of a bridge deck under stationary random excitation and variable environmental conditions. Neither excitation nor environmental variables were measured. Damage was a crack in a steel girder. Noisy response was measured with displacement, velocity, acceleration, and strain sensors at different locations of the deck. Assuming ergodicity, ACFs were estimated and used in time-domain data analysis to detect damage.
