The study, published in Frontiers in Future Transportation, tackles a deceptively simple problem. Vehicle speed and axle spacing are fundamental inputs for virtually every downstream model that tries to interpret pavement behavior, from estimating axle loads to detecting hidden voids beneath the road surface. But obtaining those parameters usually requires a separate sensing system, such as video cameras or lidar, that is vulnerable to weather, illumination changes, and occlusion. Worse, external systems and embedded pavement monitors typically run on different clocks, so the time-synchronization error between them undermines any attempt to jointly interpret traffic data and structural response. Estimating speed and axle spacing directly from the pavement vibration signal eliminates both problems, allowing a single embedded system to interpret traffic information and structural state in one closed loop.

For the field test, the researchers embedded two MEMS accelerometers inside an asphalt pavement in Zhaotong, Yunnan Province, China. The sensors were installed in slots cut into the binder course during paving, fixed with emulsified asphalt and asphalt mortar, and covered with a thin surface layer. They sit two and a half meters apart along the driving direction, directly beneath the wheel path, and sample vibration at 1000 hertz, providing millisecond time resolution. A four-axle heavy dump truck with a total wheelbase of 7750 millimeters, and axle spacings of 2100, 4300, and 1350 millimeters, then passed over the section twelve times, carrying gross weights from 25.00 to 55.62 tonnes at speeds of roughly 40, 50, and 60 kilometers per hour.

Raw pavement vibration is messy. It is non-stationary, multi-scale, and contaminated by noise, baseline drift, and broadband tire-pavement disturbances. To clean it up, the team applied complete ensemble empirical mode decomposition with adaptive noise, or CEEMDAN, a signal-processing technique that repeatedly adds controlled white-noise realizations to the signal and decomposes it into intrinsic mode functions, each capturing a distinct frequency component. The decomposition yielded ten modes. One high-frequency mode near 370 hertz turned out to be broadband tire-pavement noise, while several low-frequency modes below 2 hertz reflected sensor drift and environmental trends. By screening modes for dominant frequencies between 2 and 200 hertz, the researchers retained components strongly correlated with actual axle impacts and reconstructed a signal in which the vibration energy is sharply concentrated where it matters.

The heart of the method lies in what happens next. The reconstructed signal is analyzed with the continuous wavelet transform using a complex Morlet wavelet, which excels at capturing transient impacts in non-stationary signals. Squaring the wavelet coefficients and summing them across all scales produces an instantaneous total-energy curve, essentially a timeline of how much vibration energy the pavement carries at each moment. Each passing axle stamps a prominent peak onto this curve. Because the dual-tire rear axles of the test truck strike the sensor with wide wheel-path coverage, their peaks are stable and prominent, while the single-tire steering axles can deviate from the sensor and produce weaker responses. The algorithm therefore anchors its estimates on the reliable rear-axle peaks.

Speed estimation follows from a simple geometric insight. The two embedded sensors are a known 2.5 meters apart, and their energy curves have identical shapes shifted in time. By pairing the first rear-axle peak across the two sensors and measuring the time shift, the researchers compute the vehicle speed directly. With speed known, the total wheelbase follows from the interval between the first and last axle peaks at a single sensor. A cross-sensor consistency check, comparing candidate four-peak combinations against the known axle-spacing template, guards against mismatches, and a fallback criterion using the rear-axle pair handles cases where the front-axle peaks are too weak. In one illustrative case, a 55.62-tonne truck at 60 kilometers per hour produced a speed estimate of 54.5 kilometers per hour and a wheelbase estimate of 7227 millimeters, a 6.7 percent error against the true 7750 millimeters.

To benchmark the approach, the team ran a time-domain envelope peak method under identical criteria on the same data. The envelope method, the generic form of most published two-sensor estimators, simply rectifies the raw signal and smooths it with a moving average, then detects axle peaks on the resulting amplitude envelope. Both methods succeeded in all twelve field cases, and their median errors over the ten total-wheelbase cases were nearly identical at 6.5 and 6.8 percent. The differences emerged in the tails of the error distribution. The wavelet energy method achieved a mean error of 6.2 percent against 8.8 percent for the envelope, a narrower interquartile range of 3.3 versus 4.8 percentage points, and a maximum error of 10.5 percent versus a striking 33.8 percent. In the two cases judged against the 1350-millimeter rear-axle spacing, errors ranged from 2.8 to 4.5 percent.

The envelope method’s worst failure is instructive. For the lightest and slowest pass, the 25-tonne truck at 40 kilometers per hour, the axle peaks were weakest and the raw signal contained an isolated noise spike roughly one-third the size of an axle peak. The 30-millisecond envelope could not suppress the spike, which formed a spurious packet that fooled the peak-matching algorithm into underestimating the wheelbase at 5129 millimeters, a 33.8 percent error. The continuous wavelet transform, acting as a band-limited filter, suppressed the same disturbance easily and delivered a 6.5 percent error in that case. The envelope method also suffers from a subtle circular dependency: its optimal smoothing window drifts with vehicle speed, yet speed is precisely the quantity being estimated. At a 10-millisecond window the mean error rose to 14.5 percent with a maximum of 46 percent, while at 60 milliseconds the high-speed cases deteriorated to a 17.4 percent mean error as adjacent axle peaks merged. The energy method, by contrast, uses fixed parameters for every case and proved insensitive to its frequency band, its wavelet scale grid, and the CEEMDAN noise settings.

Sensitivity analysis showed the method is robust across its configuration space. Varying the number of noise realizations from 100 to 500, altering the noise standard deviation, or changing random seeds left the median error between 6.4 and 6.5 percent for the total-wheelbase cases. Only a very coarse wavelet scale grid or missing energy-curve smoothing degraded results noticeably; without the five-millisecond smoothing the maximum error climbed to 21.4 percent. First-order error propagation confirmed that the one-millisecond sampling quantisation contributes at most about 0.7 percent to speed and wheelbase uncertainty, meaning the observed errors stem mainly from energy-packet crest localisation, particularly when wheel paths deviate from the sensors and signal amplitudes drop.

The implications reach beyond a single truck on a single highway. The CEEMDAN-reconstructed signal preserves the waveform and spectral character of the original vibration, with a mean correlation of 0.84 and roughly 74 percent of its energy retained, and its instantaneous time-frequency energy distribution can feed directly into downstream models for axle-load estimation and hidden-void detection. That makes one buried accelerometer array do the work of several systems: it yields traffic parameters and structural response on a shared time base, unaffected by darkness, rain, or fog. The method does carry limitations. It was validated on one four-axle vehicle up to 60 kilometers per hour, above which the rear-axle energy packets begin to merge, and it relies on known axle-spacing templates that must be matched with vehicle classification in mixed traffic. Still, as MEMS sensors grow cheaper, smaller, and better suited to edge computing and wireless communication, roads that hear their own traffic may soon become a practical foundation for the smart highways of the coming decade.

Subject of Research: Estimation of vehicle speed and axle spacing from embedded pavement vibration sensors for intelligent transportation infrastructure

Article Title: Pavement vibration-based estimation of vehicle speed and axle spacing for intelligent transportation infrastructure

Article References: Li, W., Chen, D., Ye, Z., Yang, S., Li, P., Zhang, H., & Wang, L. (2026). Pavement vibration-based estimation of vehicle speed and axle spacing for intelligent transportation infrastructure. Frontiers in Future Transportation, 7, Article 1918909. https://doi.org/10.3389/ffutr.2026.1918909

Image Credits: AI Generated

DOI: 10.3389/ffutr.2026.1918909

Keywords: smart roads, pavement vibration, MEMS accelerometers, CEEMDAN, continuous wavelet transform, vehicle speed estimation, axle spacing, weigh-in-motion, intelligent transportation, structural health monitoring, signal processing, embedded sensing