Optimal Averaging and Localized Weak Spot Identification of Traffic Speed Deflectometer Measurements

One of the main difficulties that arise during the analysis of continuous deflection measurements is the reduction of measurement variability (noise) without smoothing out important features or adversely affecting the true spatial variability, and no objective method has been available. The use of the smoothing spline determined through minimization of the generalized cross-validation criteria is proposed for denoising traffic speed deflectometer (TSD) deflection slope measurements. The generalized cross-validation criteria find the optimal trade-off between variance and bias so that the estimated smoothing spline gives the best smoothing fit (weighted moving average fit) for minimum mean square error with respect to the true deflection slope values. The smoothing spline fit allows the construction of a confidence interval for the true deflection slope as well as the use of outlier detection methods for identifying localized weak spots, such as those caused by cracks or weak joints in jointed concrete sections. In each case, the distribution and standard deviation of the measurement error is needed. It is shown that TSD measurement error distribution is well represented by a normal distribution, and an outlier robust method is used to evaluate the standard deviation. Example data analysis uses computer-generated data to simulate a smoothly varying deflection slope profile as well as a homogeneous profile with localized weak spots and uses actual TSD deflection slope measurements. The results show that smoothing spline denoising can significantly improve the interpretation of TSD deflection slope measurements.