Damage Identification with Linear Discriminant Operators

This paper explores the application of statistical pattern recognition and machine learning techniques to vibration-based damage detection. First, the damage detection process is described in terms of a problem in statistical pattern recognition. Next, a specific example of a statistical-pattern-recognition-based damage detection process using a linear discriminant operator, ''Fisher's Discriminant'', is applied to the problem of identifying structural damage in a physical system. Accelerometer time histories are recorded from sensors attached to the system as that system is excited using a measured input. Linear Prediction Coding (LPC) coefficients are utilized to convert the accelerometer time-series data into multi-dimensional samples representing the resonances of the system during a brief segment of the time series. Fisher's discriminant is then used to find the linear projection of the LPC data distributions that best separates data from undamaged and damaged systems. The method i s applied to data from concrete bridge columns as the columns are progressively damaged. For this case, the method captures a clear distinction between undamaged and damaged vibration profiles. Further, the method assigns a probability of damage that can be used to rank systems in order of priority for inspection.