Comparing Predictive Maintenance Policies Under Rare Failures in Bridge and Infrastructure Systems

1. Research question and evidence scope

This article addresses a bounded methodological question for bridge maintenance: when failure-relevant events are rare, should policy comparison rely only on point predictions of deterioration, or should predictive uncertainty be propagated into the maintenance rule? Prior bridge studies support several ingredients needed for such a comparison. Inspection and monitoring can be fused for probabilistic deterioration assessment; remote-inspection and digital-twin research describes maintenance-oriented data workflows; image-based crack detection can provide upstream defect measurements; and conformal prediction provides distribution-free predictive bands for regression with finite-sample marginal coverage under exchangeability; serial and changing bridge records need separate empirical assessment. Building on those strands, this manuscript proposes, rather than validates, a bridge-focused protocol that compares maintenance policies under the same evidence inputs and safety constraint. The review scope is targeted and selective: it is used to justify specific protocol elements, not to claim exhaustive coverage of the literature. [1] [2] [3] [4]

The protocol is framed for bridges and for bridge components that can be represented by repeated measurements of defect severity, exposure, or monitoring-derived degradation summaries. It does not presume observed collapse events, and it does not require a fully calibrated physics model. Its central premise is a proposed design choice of this manuscript: maintenance policies should be compared against a probabilistic state estimate that makes predictive uncertainty explicit, rather than against a deterministic score alone. [3] [4]

2. Prior work and the specific gap addressed

Prior bridge research supports the separate building blocks of the proposed protocol. Hierarchical Bayesian fusion of inspection and monitoring data provides one example of probabilistic deterioration assessment with censored observations and time-varying crack information. Automated crack detection from UAV imagery can generate defect measurements such as crack extent and width. Remote bridge-inspection reviews describe how sensing, computer vision, predictive analysis, and visualization may be organized within maintenance workflows, including digital-twin architectures for high-value assets. The gap addressed here is therefore not the absence of condition models or inspection technology. It is the absence, within the cited bridge literature, of a single protocol that compares maintenance policies under rare failures using the same state estimate and an explicit uncertainty-sensitive decision rule. [1] [2] [3]

The methodological gap is narrower than a general lack of predictive modeling. Under rare failures, two policies can share similar mean risk scores yet differ in uncertainty calibration, intervention timing, and false-alarm burden. A retrospective comparison based only on fitted point predictions can therefore favor a policy whose apparent precision does not survive deployment. This manuscript proposes to place comparator policies on a common uncertainty scale. For continuous deterioration outcomes, that scale is a conformal prediction band around the future response, using the finite-sample marginal coverage result under exchangeability, which is not automatically available for serial bridge observations. For binary event outcomes, the protocol does not claim the same regression-band construction; instead it treats event prediction as a separate branch that must be evaluated with its own calibrated risk score and fixed action threshold. [4]

3. Proposed data structure and operational definitions

The analysis unit is a bridge component observed over discrete inspection times t = 1,...,T. For each component i, the protocol defines five variable classes. First, X_it denotes static descriptors such as span class, member type, age, geometric category, and exposure class. Second, M_it denotes monitoring summaries extracted from sensor streams, for example monthly crack-growth rate, vibration deviation, or displacement anomaly score. Third, V_it denotes defect-detection outputs from image-based inspection, such as crack presence, crack width, or segmentation-derived defect area. Fourth, A_it denotes maintenance actions, coded as none, minor repair, local strengthening, or replacement. Fifth, the protocol separates two outcome variables to avoid policy-dependent labeling. E_it is the exogenous safety event indicator for the prediction horizon H, where E_it = 1 only if a predeclared structural event or safety-boundary exceedance occurs within H independently of whether maintenance was scheduled, and E_it = 0 otherwise. Y_it denotes the observed label used in the binary branch after applying a fixed confirmation rule to E_it. Emergency intervention is therefore not part of the event definition; it is an action outcome generated by the policy or by external management and is evaluated in the cost function rather than embedded in the target label. The exogenous event definition and confirmation window are fixed before model fitting. [1] [2] [3]

The protocol allows two outcome formulations, but they are operationalized separately and compared only through common downstream policy outcomes. In the continuous branch, the target is a deterioration score D_it whose upper tail corresponds to elevated probability of the exogenous event E_it within horizon H. A base regressor predicts D_it, and split conformal inference is applied to produce a band B_it = [L_it, U_it] for the future score. In the binary branch, the target is Y_it, a horizon-H event label derived from E_it under the fixed confirmation rule. The model outputs a calibrated event-risk estimate p_it = P(Y_it = 1 | history). The default action rule in the continuous branch is to intervene if U_it > τ, where τ is a predeclared deterioration boundary. The default action rule in the binary branch is to intervene if p_it > r, where r is fixed ex ante. Cross-branch ranking is then based on a common estimand defined at the policy level, not at the prediction level: expected policy loss over the horizon under one shared cost schedule, reported jointly with safety compliance and failure miss rate. The two branches may therefore be evaluated in the same simulator without imposing one common prediction scale or a mixed trigger within a single policy definition. [4] [3]

4. Proposed methodology for policy comparison

The methodology has two stages. Stage 1 estimates the component state; Stage 2 maps that state to maintenance actions. Stage 1 has two admissible implementations, chosen before analysis. In the continuous-outcome implementation, a predictor f̂(X_it, M_it, V_it) estimates the future deterioration score D_it. The predictor may be a Weibull AFT model, a generalized additive model, a tree-based learner, or another estimator suited to the data structure, and it is then wrapped in split conformal inference to obtain a prediction band B_it = [L_it, U_it]. To make this construction operational, the default conformity score is the absolute residual |D_it - D̂_it| computed on a temporally ordered calibration block pooled across components within the same asset class; a sensitivity analysis may replace asset-class pooling with component-type pooling if sufficient calibration size exists. The nominal miscoverage level α is fixed before evaluation, and the upper endpoint is formed from the corresponding empirical calibration quantile. In the binary-outcome implementation, a classifier or survival-style event model estimates the horizon-specific event risk p_it; this branch uses a calibrated probability estimate rather than a regression prediction band. Missing predictors are handled by a prespecified rule: if a value is unavailable at decision time, the last observed value and a missingness flag are carried forward for one cycle, after which the record is excluded from decision simulation until a new observation arrives. Right-censoring and delayed event confirmation are handled by defining Y_it only when the full horizon H plus a fixed confirmation lag Δ has elapsed; otherwise the instance is withheld from scored evaluation. This separation avoids conflating regression conformal intervals with event-risk prediction while preserving a common Stage 2 policy simulator. [4] [1]

Stage 2 compares three mutually exclusive policy classes under an explicit priority order. Policy P1, the point-threshold policy, acts if the point prediction exceeds its fixed threshold: D̂_it > τ in the continuous branch or p_it > r in the binary branch. Policy P2, the interval-trigger policy, is defined only for the continuous branch and acts if U_it > τ. Policy P3, the uncertainty-aware policy, is also defined only for the continuous branch and follows one fixed rule: if U_it ≤ τ, do not intervene; if U_it > τ and the interval width U_it - L_it ≤ ω, intervene now; if U_it > τ and the interval width U_it - L_it > ω, schedule intensified inspection and defer intervention for one decision cycle only, after which intervention becomes mandatory if the updated upper bound still exceeds τ. Thus P3 is an independent comparator. The ambiguity limit ω is fixed in advance at the asset-class level by a preregistered rule on the calibration block: set ω to the 0.8 quantile of conformal interval widths among calibration instances with point predictions in the band [τ - ε, τ + ε], where ε is a prespecified local neighborhood around the action threshold. Sensitivity analysis then varies ω over the narrow fixed set {0.7, 0.8, 0.9} quantiles under the same definition. No component-specific retuning is allowed in the main analysis. [4] [3] [1]

If defect detection is available as an input stream, the protocol treats automated crack segmentation as a feature extractor rather than as a maintenance policy by itself. In that case, defect width, length, or area estimates are aggregated into V_it and fused with sensor summaries and static descriptors. This placement is important because defect detectors can improve state estimation while still inheriting image-quality limitations; they should not be equated with a complete maintenance decision framework. Likewise, if federated learning is used, the protocol allows distributed training of the Stage 1 predictor without transferring raw sensor data. Privacy-preserving aggregation is relevant where bridge data are held by different agencies or contractors, but it is auxiliary to the policy comparison and should not alter the definition of the maintenance outcome. [2] [5]

5. Comparator policies, outcome measures, and falsifiable propositions

The main outcome measures are policy loss, safety compliance, and decision error, defined separately and used for all cross-branch comparisons. Policy loss is the total cost over the study horizon under a fixed cost schedule shared by all policies, combining preventive maintenance, corrective repair, intensified inspection, and a penalty for confirmed exogenous events. Safety compliance is the proportion of evaluated component-time states that remain below the predeclared safety boundary over the horizon. Failure miss rate is the proportion of confirmed exogenous events E_it = 1 for which the policy did not intervene within the allowable lead time λ, where λ is fixed before analysis. Delayed confirmation is handled by scoring an event only after the full horizon and confirmation lag have elapsed. If an observation is right-censored before that point, it contributes to state-estimation diagnostics but not to lead-time-based miss-rate denominators. For the continuous branch, interval coverage and mean interval width are additional Stage 1 diagnostics. Outcomes are summarized per component and then by bridge asset class to avoid treating performance on one component mix as transportable to another. [3] [4] [1]

The protocol is designed to test three falsifiable propositions. First, relative to P1, policy P3 may lower the failure miss rate at equal safety threshold τ when the intensified-inspection option is used on cases with U_it > τ and interval width above ω; the proposition is rejected if miss rate does not decrease or if policy loss increases beyond a prespecified tolerance band. Second, if the continuous-branch intervals fail to attain their nominal marginal coverage on the forward test blocks or if mean interval width near τ exceeds a prespecified operational ceiling, then P3 is expected to increase inspection load without improving miss rate; this proposition is rejected if inspection load does not rise under those conditions. Third, if image-derived defect features are missing or noisy, then using them only through the Stage 1 predictor should yield lower decision volatility across adjacent decision times than using an unfiltered defect trigger; decision volatility is defined as the rate of action reversals across consecutive cycles for components without confirmed events. These are testable protocol statements, not empirical claims in this article. [4] [2] [1]

Conflicting evidence is expected at the boundary between inspection and monitoring. Bridge review literature emphasizes that digital twins can integrate prediction and visualization for maintenance planning, but also notes that implementation remains constrained by cost and complexity. That boundary condition matters for the present protocol: if a digital twin cannot be updated at the frequency needed for maintenance decisions, the policy comparison should fall back to a simpler state-update layer rather than assuming continuous synchronization. Likewise, when defect detection is performed under poor lighting, occlusion, or very narrow cracks, missed detections may propagate into the policy comparison as false reassurance. Such failures should be counted as input uncertainty, not ignored. [3] [2]

6. Prospective validation design

A detailed prospective evaluation can replace an empirical results section. The recommended design is rolling-origin validation on temporally ordered bridge records. Historical data are split into a training block, a calibration block for conformal intervals or probability calibration, and one or more forward test blocks. At each origin, the predictor is refit using only past data, the calibration quantities are recomputed on the calibration block, and the maintenance policy is simulated on future records without leakage. The protocol fixes a confirmation lag Δ for event labeling: a test instance at time t enters the scored set only when records through t + H + Δ are available to determine whether the exogenous event occurred within the horizon. Records censored before t + H + Δ are retained for state updating up to the censoring time but excluded from event-based scoring for that origin. Missing inspection or monitoring inputs are handled by the Stage 1 rule specified above and are logged so that evaluation can report the fraction of decisions made under carried-forward information. If multiple bridge agencies contribute data, one evaluation arm respects agency boundaries and a second arm respects temporal boundaries to distinguish within-network interpolation from cross-network transport. [4] [5] [1]

Validation includes two stress tests. The first is a label-sparsity stress test applied only to the training portion. A prespecified fraction ρ of positive event labels is masked and then treated as unlabeled rather than converted to negatives; the corresponding records remain available for predictor fitting only in the continuous branch, while in the binary branch they are excluded from supervised event-loss updates but retained as covariate histories. This defines the perturbation as training-label removal, not relabeling, and avoids changing positives into false negatives by construction. The purpose is to assess whether policy ranking changes when confirmed event information is scarce, not to estimate unbiased deployment performance under a population model. The second is a distribution-shift stress test in which one forward test block contains changed exposure patterns, maintenance history, or image-quality conditions. For both stresses, the protocol records policy loss, safety compliance, failure miss rate, inspection load, and, for the continuous branch, interval coverage and mean width. An additional audit reports the proportion of decisions triggered by D̂_it or p_it alone, by the upper bound U_it crossing τ, and by the defer-and-reinspect clause of P3. [4] [3] [5]

For comparability, the validation protocol should keep the maintenance cost structure fixed across policies and use the same observation window H. Hypothetical cost ratios may be explored in sensitivity analysis, but they must be labeled as illustrative rather than calibrated unless external engineering evidence is available. The protocol also recommends ablation tests: remove monitoring summaries, remove defect-detection features, or remove conformal calibration one at a time to determine which part of the pipeline contributes most to robust policy ranking. This is necessary because a maintenance policy may appear effective only because one input channel happens to dominate the decision rule. [1] [2] [4]

Temporal calibration and sparse threshold neighborhoods

At every forecast origin, form disjoint training and calibration blocks using only observations and confirmed labels available before that origin. Refit or retain the predictor according to a frozen schedule, then evaluate on the next untouched forward block. No future confirmation enters calibration. Serial dependence and distribution shift can violate exchangeability; consequently the reported temporal coverage is empirical, not an unconditional conformal guarantee. Require at least 30 eligible calibration intervals near tau before estimating omega. If fewer exist, the uncertainty-aware policy defers to engineering review and reports an unavailable calibrated threshold, rather than estimating an unstable quantile. This minimum is an illustrative protocol setting requiring sensitivity analysis. Continuous-score and binary-event branches are separate experiments; only policy losses expressed in the same registered monetary or utility units can be compared. Raw intervals and binary probabilities are never pooled. Training-label masking is a robustness experiment, not a semisupervised learning method, and the original confirmed test labels remain intact.

7. Failure cases, limits of generalization, and conclusion

Several failure cases delimit the use of the protocol. First, if the outcome definition mixes structural failure with routine maintenance backlog, the policy comparison will confound safety with administrative timing. Second, if defect detection is trained on a narrow image domain, the resulting features may not transfer to different lighting, surface texture, or camera geometry. Third, if federated learning is used across agencies with incompatible annotation standards, privacy-preserving training may still produce a pooled model whose labels are not comparable. Fourth, if conformal calibration is performed on data that already reflect a strong intervention regime, the resulting bands may encode historical practice rather than underlying deterioration. [2] [5] [4] [3]

The manuscript makes a bounded conceptual contribution for bridge maintenance under rare failures. It specifies a policy-comparison protocol with three linked layers: condition evidence, uncertainty characterization, and decision simulation; it distinguishes a continuous deterioration branch from a binary event branch; and it defines default comparator rules that can be simulated without ambiguity. The cited bridge literature supplies relevant inputs for these layers in separate forms, but this article's unified comparison design is a proposal rather than an empirical result. Whether the uncertainty-aware rule improves decisions relative to simpler threshold rules remains untested here and should be examined in a prospective, temporally ordered bridge study with preregistered thresholds, costs, and sensitivity analyses. [1] [2] [3] [4]

References

1. Wang, Benyu; Chen, Ke; Wang, Bingjian (2026). Hierarchical bayesian fusion of inspection and monitoring data for probabilistic bridge deterioration assessment. Scientific Reports. 16(1), 5965. doi:10.1038/s41598-026-36808-4.
2. Dong, Xuwei; Yu, Zhibing; Yuan, Jiashuo; Dai, Jinpeng (2026). Automatic bridge crack detections: A lightweight segmentation model for UAV inspection. PLOS One. 21(9), e0358865. doi:10.1371/journal.pone.0358865.
3. Ribeiro, Diogo; Rakoczy, Anna M.; Cabral, Rafael; Hoskere, Vedhus; Narazaki, Yasutaka; Santos, Ricardo; Tondo, Gledson; Gonzalez, Luis; et al. (2025). Methodologies for Remote Bridge Inspection—Review. Sensors. 25(18), 5708. doi:10.3390/s25185708.
4. Lei, Jing; G’Sell, Max; Rinaldo, Alessandro; Tibshirani, Ryan J.; Wasserman, Larry (2018). Distribution-Free Predictive Inference for Regression. Journal of the American Statistical Association. 113(523), 1094-1111. doi:10.1080/01621459.2017.1307116.
5. Yin, Huan; Chen, Congwen; Zhang, Jingyi; Yu, Dian; Liu, Shuanggen (2026). Privacy-Preserving and Poisoning-Robust Federated Learning for Industrial IoT. Sensors. 26(16), 5297. doi:10.3390/s26165297.