An evaluation of Mahalanobis Distance and grey relational analysis for crack pattern in concrete structures

Mahalanobis Distance (MD) and grey relational grade (GRG) are useful methods for analyzing patterns in multivariate cases. Developed in this paper is the application of MD and GRG for crack pattern recognition in concrete structure. In case of small data sizes, the sample group covariance matrices used in MD analysis are singular. This paper uses the pooled covariance matrix as an alternative estimate for the sample group covariance matrix to solve this kind problem. The results show that MD and GRG are capable of classifying the distinction among the data sets in time domain and thus identify the type of crack developed in concrete structure. Finally, learning vector quantization (LVQ) artificial neural network is introduced and used to be compared with MD and GRG.