Reweighted L1 Minimization for Networkwide Weak Spot Detection from Traffic Speed Deflectometer Measurements

Abstract

The traffic speed deflectometer (TSD) can collect network-level deflection data in a cost-effective and timely manner. However, an automated feature extraction method is needed to interpret such large amounts of data. Basis pursuit (BP) is one such technique: BP can sparsely decompose TSD measurements over a given basis or set of bases of the signal vector space that can represent a particular signal feature. For instance, the TSD surface deflection estimates can be reconstructed as a combination of wavelets, which represent continuously varying features like changes in pavement properties, plus pulses representing the response from structurally weak spots. Yet, the denoised measurements estimated by BP may either be riddled with several false positives (spikes that mismatch real weak spots) or be constructed out of true positive features with damped amplitude. This paper presents reweighed L1 minimization (RWL1), an enhancement to BP to both correct the dampening and discard false positives. This paper introduces RWL1 with examples from simulated data to show its advantage over vanilla BP denoising, plus a demonstration featuring real TSD measurements from a networkwide survey to demonstrate RWL1’s potential as an exploratory analysis tool to detect structurally weak locations within the pavement network worthy of further investigation at the project level.