Long-term monitoring of bridges records slowly varying displacement and strain signals in which daily and seasonal temperature cycles dominate and mask the small signatures of structural damage. Hu, Liu, Deng and Luo (2024) proposed the Adaptive Bandwidth Filter Algorithm (ABFA), which passes measured response and temperature signals through band-pass filters centered on the day and year temperature frequencies, tunes the filter bandwidths by particle swarm optimization, regresses the filtered response linearly on the filtered temperature, and subtracts the fitted temperature effect; in simulation, injected damage becomes visible in the residuals. The field part of that study, on a 160 m concrete-filled steel tube arch bridge, validated only temperature separation — because deliberate damage on an in-service bridge is infeasible — and the method needs multi-year records to resolve the annual temperature band as well as co-measured temperature, with no criterion for when a day-cycle-only fallback suffices. The problem left open is to establish, on real monitoring data from structures that actually incurred damage, whether temperature-separated residuals enable reliable damage detection, and to quantify and relax the data-length and temperature-sensing requirements.

Background

Long-term structural health monitoring (SHM) of bridges records quasi-static responses — slowly varying strain and vertical-displacement signals sampled at intervals of minutes to hours — in which the dominant variation usually has nothing to do with damage. A measured static response is conventionally modeled as a sum of effects: the temperature effect, the traffic-loading effect, concrete shrinkage and creep, the structural-damage effect, and measurement error. Because daily and seasonal temperature cycles move bridge responses far more than early damage does, the temperature contribution masks the small signatures that damage detection seeks. A large literature therefore removes environmental effects before flagging anomalies, using regression, principal component analysis (PCA — a linear statistical technique that projects data onto the directions of largest variance so that the dominant temperature-driven component can be discarded), cointegration, and similar tools. Celebrated validations on real structures include the Z24 Bridge benchmark (a real bridge subjected to a progressive damage campaign before demolition) and the retrofitted KW51 railway bridge, where natural frequencies tracked over years had to be cleaned of temperature influence before the genuine structural change became statistically visible.

Hu, Liu, Deng and Luo (2024) approached this removal in the frequency domain for quasi-static monitoring data. They decomposed the temperature effect into a day-temperature effect (DTE, driven by the day–night cycle, corresponding in the amplitude spectrum to a center frequency of one cycle per day, about 1.16e-5 Hz), an abrupt-temperature-drop effect, and a year-temperature effect (YTE, driven by the seasons, center frequency of one cycle per year, about 3.2e-8 Hz). These fixed time scales fix the center frequencies at which the corresponding response components concentrate. Their Adaptive Bandwidth Filter Algorithm (ABFA) passes the measured displacement and temperature signals through band-pass filter groups centered on the day and year frequencies, with the filter bandwidths — difficult to choose by hand under measurement noise — tuned automatically by particle swarm optimization (PSO, a population-based stochastic optimization heuristic). An Integrated Assessment Index (IAI), the product of the average distance of the filtered points to the regression line and the absolute correlation between the residual signal and temperature, scores candidate bandwidths. The filtered displacement is then linearly regressed on the filtered temperature at each time scale, and the fitted temperature effect is subtracted, leaving residuals attributed to traffic, measurement error, and damage. In simulation (one-year span, with instantaneous and cumulative damage injected at a known time), damage invisible in the raw signal becomes visible in the ABFA residuals precisely because its frequency content lies outside the day/year temperature bands. On field data from a 160 m concrete-filled steel tube arch bridge with eight displacement stations and one temperature sensor, only the separation itself was validated: after ABFA extraction the displacement–temperature correlation improves and the residual is essentially uncorrelated with temperature.

Three practical gaps remain open. First, damage detection from ABFA residuals has never been tested against real damage, because deliberate damage on an in-service bridge is infeasible; the validation is simulation-only. Second, separating the YTE band requires a frequency resolution attainable only from multi-year records (the paper states that 'several year reference periods are needed at least'), which for deteriorated bridges is so long that 'collapse accidents may not be prevented timely'; the authors advise falling back on DTE-only regression when long records are missing but give no criterion for when that simplification is safe. Third, the regression needs co-measured temperature at the monitored section; the authors note that such data are usually accessible because temperature sensors are installed in most long-term monitoring systems, but how much temperature instrumentation the regression actually requires, and what separation quality survives when instrumentation is sparse or thermally lagged, has not been quantified. Meanwhile, alternative temperature-separation methods for static signals keep appearing — chirp-mode decomposition combined with PCA and blind source separation for bridge strain, statistical-learning removal of seasonal and thermal-inertia effects from static inclinometer and displacement signals, and PSO-tuned variational mode decomposition for bridge deflection — but, like ABFA, all of them are validated only for separation quality on undamaged bridges.

Problem Statement

The problem is to establish whether temperature-effect separation by adaptive-bandwidth filtering of quasi-static (static displacement and strain type) monitoring data enables reliable damage detection under real field conditions, and to relax the data-length and sensing requirements under which this is possible. Three linked questions remain open after Hu et al. (2024): (1) Field validation of damage detection — apply ABFA-style separation (band-pass filter groups centered on the day and year temperature frequencies with automatically optimized bandwidths, followed by per-scale linear regression of filtered response on filtered temperature) to real monitoring records from a structure that has actually incurred damage (progressive-damage benchmark data, a retrofit, or opportunistic field damage), and quantify whether the separation residuals reveal the damage — detection success, false-alarm behavior, and timeliness relative to a pre-damage baseline — including the case of slow cumulative damage whose signature may overlap the day/year temperature frequency bands on which the filtering relies. (2) Data-length requirement — quantify how separation and detection performance degrade as the reference period shortens, and provide a criterion that decides when the day-temperature-only simplification suffices, i.e. one that can be evaluated on records too short to resolve the annual cycle. (3) Sensing requirement — determine how many temperature measurements the regression actually needs, and what separation and detection quality survives when temperature instrumentation is sparse or thermally lagged. All three components serve one overarching objective: determining the practical operating envelope — which damages are detectable, from how much data, and with what temperature sensing — of temperature-separation-based damage detection for quasi-static structural monitoring. All three sub-questions are jointly posed: each requires the quantified quantity named in it.

References

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