Correlation redefinition and analysis for monitoring data-based operational bridge evaluation

Abstract

This study is dedicated to propose a new correlation coefficient to cope with the limitations of the traditional Pearson correlation coefficient, Spearman correlation coefficient and Kendall correlation coefficient in specific scenarios such as in-service bridge monitoring. Firstly, the scope, essential meaning and differences of these three traditional correlation coefficients are systematically analyzed and compared. The characteristics of the bridge monitoring data were then further analyzed and a new correlation coefficient was designed, taking into account the local slope and distance, to capture the dynamic characteristics between data points. Finally, the independence tests of the newly proposed correlation coefficients and three traditional correlation coefficients are carried out considering three working conditions, namely, bridge measured data, very strong correlation data, and very weak correlation data, in order to validate and explore the actual performance of the new correlation coefficients. Study shows that, First, when the sample size of the very strong correlation data is large enough, the value of the newly proposed correlation coefficient reaches 0.8376, which is close to 1. This indicates that it is effective in capturing strong correlations between variables in very strong linear relationships. Second, The value of the new correlation coefficient is 0.002 when the sample size of very weakly correlated data is sufficient, which proves the excellence of the new correlation coefficient in accurately measuring the true correlation even when the correlation between the variables is not obvious. Third, When the number of samples of the measured bridge monitoring data is large enough, the value of the new correlation coefficient reaches 0.7378, which is obviously larger than the three traditional correlation coefficients, reflecting the potential advantage of the new correlation coefficient in dealing with the abnormal data in the real environment. However, it is worth noting that, upon further verification, the new correlation coefficient still has limitations when reflecting non-monotonic relationships between variables (as evidenced in this study by quadratic dependencies in distributions symmetric about zero). The correlation coefficient formula proposed in this study can provide a new expectation for the analysis of long-term monitoring data of bridges, and the applicability of the coefficient can also be verified through the analysis in other fields, so that the study of the correlation coefficient can be more perfect.