SeisRank-Ord: Governance-aware ordinal learning for seismic damage recognition and policy simulation

2.1 Seismic building damage recognition

Research on seismic building damage recognition has moved from generic multi class recognition toward grade aware recognition that reflects practical response needs (Wen et al., 2025). Typical settings define four damage grades and also consider regrouped tasks such as binary and three class variants. Most works train standard convolutional backbones with cross entropy and report overall accuracy and kappa. While this line of work has improved nominal accuracy, two structural difficulties persist (Jiang et al., 2024). First, damage grades are ordered, yet ordinary multi class training treats them as independent categories. Second, mistakes are not equally harmful, since underestimation of severe or collapsed states is more costly than overestimation. These gaps motivate objectives that encode order and asymmetric cost while remaining compatible with the evaluation protocol used in practice, namely overall accuracy, kappa, and mean squared error.

2.2 Ordinal and cost-sensitive objectives

Ordinal methods enforce consistency with the natural order of labels (Cai et al., 2024). Representative strategies include cumulative link style formulations, binary threshold decompositions as in CORAL and CORN, and objectives that penalize the distance between predicted and true grades using soft labels or earth mover distance. These methods reduce label swapping between adjacent grades and often improve mean squared error (Walczyna and Piotrowski, 2024). However, they usually assume symmetric penalties around the true grade and do not reflect the higher consequence of underestimating severe cases. They also do not concentrate learning pressure near the decision threshold that selects limited-service slots. As a result, their gains in order fidelity do not necessarily translate into higher kappa under capacity constrained dispatch.

2.3 Cost sensitivity and class imbalance

Cost sensitive learning addresses unequal error consequences and class imbalance by reweighting losses, adjusting sampling, or shaping the loss surface with functions such as class balanced cross entropy and focal variants (Peykani et al., 2025). These approaches can raise overall accuracy in skewed data and can discourage specific error types. Yet they do not encode the ordinal structure of damage grades, so improvements in overall accuracy may coexist with unnecessary grade hopping that inflates mean squared error. Moreover, uniform reweighting across the score range does not target the threshold neighborhood where operational decisions occur, which limits their effect on agreement measured by kappa.

2.4 Learning to rank and differentiable selection

Learning to rank introduces pairwise and listwise surrogates that shape relative ordering, while differentiable sorting and differentiable top K provide smooth proxies for selection (Wild et al., 2025). These advances enable gradient based optimization for ranking objectives. Nevertheless, generic surrogates spread gradients over the entire score spectrum and do not align the strongest learning signal with the specific threshold that implements a daily capacity limit (Chen et al., 2024). They also address ranking without explicitly modeling ordinal distances or asymmetric costs. In contrast, our objective concentrates separation near the operational threshold, preserves grade order, and encodes higher penalties for underestimation. This joint treatment aims to convert classifier gains into improvements in kappa and reductions in mean squared error while keeping overall accuracy at a comparable level.

3.1 Governance-driven motivation

Earthquake damage recognition differs fundamentally from conventional image classification. Building states are annotated on a four-grade ordinal scale: L0 (intact), L1 (slightly damaged), L2 (severely damaged), and L3 (collapsed). In operational settings, responders cannot process all cases simultaneously; instead, they must allocate limited resources cycle by cycle, guided by predicted risk scores. This capacity constraint implies that optimizing for overall classification accuracy is insufficient. Three governance-driven principles emerge:

Respect for ordinal structure (L0 < L1 < L2 < L3), avoiding unrealistic “grade hopping.”

Asymmetric treatment of errors, since underestimating severe or collapsed buildings is far more damaging than overestimating.

Prioritization near operational thresholds, because decisions hinge on which buildings rank at the top of the risk distribution, not on uniform accuracy across all classes.

Our method, SeisRank-Ord, instantiates these principles by defining a governance risk functional. Although this functional can be decomposed into four complementary mechanisms, it is designed as a unified optimization objective tailored for post-disaster triage.

From a decision-theoretic perspective, the unified governance-aware objective in SeisRank-Ord can be understood as minimizing an expected societal cost rather than a purely statistical error rate. Conventional ordinal models typically treat all misclassifications as interchangeable deviations between predicted and true labels. In contrast, post-earthquake governance is shaped by strongly asymmetric consequences: delaying service to severely damaged or collapsed buildings generates far greater social and political costs than over-serving mildly affected sites. SeisRank-Ord therefore re-weights prediction errors according to their governance relevance and explicitly encourages locally consistent rankings along the damage continuum. In practical terms, the model learns risk scores that are calibrated to the priorities of triage, so that optimization directly targets earlier service for high-severity cases and more equitable coverage under capacity constraints. This governance-weighted view of risk provides a coherent conceptual foundation for the composite loss, linking the design of the learning objective to the downstream behavior of allocation policies.

3.2 Ordinal alignment mechanism

The first mechanism ensures predictions preserve the ordinal nature of labels. Let the predicted probability vector be $p_i=(p_{i,0},\dots ,p_{i,3})$. Define cumulative probabilities $s_{i,k}=\sum _{c=0}^k{p}_{i,c}$ and thresholds $t_{i,k}=1[y_i\le k]$.

We penalize deviations via cumulative cross-entropy and enforce monotonicity with a soft constraint Eq (1):

This mechanism discourages unrealistic large jumps, such as predicting L3 as L0, thereby improving mean-squared error and maintaining the integrity of the ordinal taxonomy. Although $s_k$ represents cumulative probabilities, the monotonicity term does not vanish because it acts as a soft regularizer that tolerates small violations of the cumulative constraint. These residual gradients stabilize the optimization process and prevent degenerate cases where all cumulative probabilities collapse to identical values.

3.3 Risk-sensitive adjustment

From a governance perspective, underestimation of severe damage is intolerable, while overestimation primarily incurs redundant inspections. To encode this asymmetry, we define a weighted penaltyEqs (2 and 3)

with weights

When c is smaller than y, the apparent negative difference (c – y) is compensated by the weighting coefficient α, which guarantees that all penalty values remain non-negative. This design amplifies the cost of underestimation while keeping the overall optimization landscape stable and interpretable. As a result, severe or collapsed categories receive stronger corrective gradients, aligning the learning process with governance priorities.

3.4 Triage prioritization

In post-disaster operations, what matters is whether the most critical buildings are ranked above others, since only the top fraction can be served in each cycle. Let the severe-risk score be defined as Eq (4):

We enforce ranking separation between positives $(P=\{i|y_i\in \{2,3\left\}\right\})$ and negatives ($N=\left\{j\right|y_j\in \{0,1\}\}$) with a pairwise margin Eq (5):

This ensures that severely damaged and collapsed structures consistently appear higher in the risk ranking, making predictions actionable for triage under capacity limits.

3.5 Stability enhancement

Disaster datasets are typically small and imbalanced, often leading to overconfident or unstable predictions. Such instability undermines threshold-based decisions in field operations. To mitigate this, we introduce a calibration-inspired term Eq (6):

This regularizer smooths probabilities and reduces variance, improving reliability when the model is applied to novel disaster events. Although secondary, it enhances operational robustness, ensuring decision rules remain stable.

3.6 Unified governance risk functional

The mechanisms introduced above are not independent add-ons but natural instantiations of a single governance risk functional. Conceptually, this functional formalizes the real-world costs of misallocation under post-earthquake capacity constraints. Its decomposition into four terms is purely analytic, designed to clarify the operational priorities encoded within. Formally, the complete functional isEqs (7 and 8):

The overall training objective is then:

Unlike prior methods that combine multiple objectives in an ad-hoc manner, SeisRank-Ord is unified by design. Each mechanism directly operationalizes a corresponding governance principle: ordinal alignment, asymmetric conservatism, triage readiness, and stability. The formulation should therefore be interpreted not as a sum of heterogeneous losses, but as a governance-driven framework whose decomposition provides interpretability rather than construction. To better illustrate the governance-driven design of our proposed objective, we provide a schematic overview of the SeisRank-Ord framework in Fig. 1. The framework depicts the end-to-end process: post-earthquake aerial images are first processed by a CNN backbone, followed by the unified governance risk functional that integrates ordinal alignment, asymmetric risk-sensitive adjustment, triage prioritization, and stability enhancement. The resulting prediction scores are then linked to policy simulation modules, demonstrating how technical improvements translate into governance outcomes in terms of efficiency and fairness.

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Fig. 1.

Overall framework of SeisRank-Ord: governance-aware ordinal learning for seismic damage recognition and policy simulation.

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3.7 Practical interpretation

From a governance perspective, SeisRank-Ord can be viewed as translating machine learning outputs into decision rules that resonate with emergency operations.

Ordinal alignment ensures predictions reflect the physical continuum of structural damage, supporting engineering interpretability and credible communication to stakeholders.

Asymmetric conservatism embodies the ethical imperative of “erring on the side of caution,” reducing the likelihood that collapsed buildings are overlooked in triage.

Threshold-focused ranking ensures that scarce resources are allocated where they are most needed, improving response equity by pushing high-risk cases consistently to the top of the priority list.

Stability enhancement reduces the variance of predictions under small, imbalanced datasets, ensuring that governance decisions are robust and transparent rather than brittle or arbitrary.

In short, SeisRank-Ord is not merely an accuracy-optimizing classifier, but a governance-aligned recognition framework. It operationalizes its governance risk functional through several complementary mechanisms—ensuring ordinal consistency across damage grades, penalizing underestimation of severe cases more heavily, and enforcing stable rankings near decision thresholds. By embedding fairness, caution, and operational relevance directly into training, it bridges the gap between computational modeling and disaster governance, ensuring that recognition outputs are both technically reliable and policy-actionable.

4.1 Datasets

We employ two post-earthquake datasets, Yushu and Ludian, both consisting of high-resolution building image chips annotated into four ordered damage grades: L0 (intact), L1 (slightly damaged), L2 (severely damaged), and L3 (collapsed). These labels are consistently regarded as ordinal, with higher indices denoting more severe structural damage. The Yushu dataset contains post-earthquake aerial images collected after the 7.1-magnitude earthquake that struck Yushu County, Qinghai Province, China, on 14 April 2010. The Ludian dataset comprises post-earthquake aerial images captured following the 6.5-magnitude earthquake that occurred on 3 August 2014 in Ludian County, Yunnan Province, China. Both datasets are publicly available and can be accessed through open repositories, ensuring transparency and reproducibility of research. The per-grade image counts for each event are summarized in Table 1.

To reflect different operational requirements, we regroup these four labels into three evaluation settings. Set 1 merges L0 and L1 as the non-severe class and L2 and L3 as the severe class, corresponding to a binary triage scenario under resource-constrained emergencies. Set 2 retains L0 as intact, keeps L1 as slightly damaged, and combines L2 and L3 as the high-risk category, providing a balanced three-class view that isolates intact stock and mild damage while consolidating the most critical cases. Set 3 preserves the original four grades, offering the most detailed ordinal taxonomy. Together, these settings enable systematic evaluation across different decision granularities.

We evaluate performance using Overall accuracy (OA), Cohen’s kappa, and Mean squared error (MSE). OA measures the proportion of correctly classified samples, kappa adjusts for chance agreement to reflect categorical consistency, and MSE penalizes predictions farther from the ground truth, thereby quantifying ordinal fidelity. These three metrics provide complementary perspectives on correctness, reliability, and severity awareness.

We benchmark five representative convolutional backbones: ResNet-50 (Wen et al., 2025), DenseNet (Ilmak et al., 2024), ResNet-18 (Wang et al., 2024), MobileNet (Nguyen et al., 2025), and ShuffleNet (Cui and Jiang, 2022). These models span from lightweight architectures (MobileNet, ShuffleNet) suitable for rapid on-device inference to deeper networks (ResNet-50, DenseNet) with stronger representational capacity, ensuring robustness across diverse deployment scenarios.

All images are resized to 128x128 pixels and normalized using ImageNet statistics. To ensure fairness, no data augmentation is applied, so that improvements can be attributed directly to the proposed loss design. For each dataset, samples are stratified by grade and split into 70% training, 10% validation, and 20% testing. Models are trained with AdamW using an initial learning rate of 1e-3, weight decay of 1e-4, cosine learning rate decay with a warmup of 5 epochs, and gradient clipping at 1.0. Training runs for 100 epochs with a batch size of 128, and the checkpoint with the best validation kappa (averaged over the last five epochs) is selected. All experiments are conducted on an NVIDIA RTX 3090 GPU (24 GB) with PyTorch 1.7.0.

4.2 Evaluation

Tables 2 and 3 report the results on both datasets under the three evaluation settings. Several consistent trends can be observed.

First, across all settings and backbones, SeisRank-Ord outperforms the CE baseline in OA, kappa, and MSE. The gains are particularly pronounced on Yushu, where data sparsity makes ordinal alignment and asymmetric penalties more critical. This confirms that embedding governance-oriented principles into the loss design improves robustness under real-world data constraints.

Second, the relative benefits vary across operational settings. In Set 1 (binary triage), SeisRank-Ord achieves substantial improvements in kappa, reflecting its ability to correctly prioritize severe (L2-L3) cases. This aligns with the governance imperative of minimizing missed detections in emergency allocation. In Set 2 (three-class), the method demonstrates balanced improvements across all metrics, showing its utility for intermediate decision-making that separates intact stock, mild damage, and high-risk categories. In Set 3 (four-class), improvements in MSE highlight the value of ordinal consistency, ensuring that predictions reflect the natural progression of structural failure rather than arbitrary categorical jumps.

Third, performance is stable across backbones, with both lightweight models (MobileNet, ShuffleNet) and deeper ones (ResNet, DenseNet) benefiting from the proposed objective. This indicates that SeisRank-Ord is architecture-agnostic and can be deployed flexibly, from edge devices to large-scale servers.

The results illustrate a broader point: evaluating disaster recognition methods solely on overall accuracy overlooks operational nuances. While OA remains important, kappa and MSE reveal whether predictions are reliable and severity-aware. The consistent gains across all three metrics suggest that SeisRank-Ord not only improves recognition accuracy but also produces outputs that are more actionable for governance.

4.3 Ablation study

To evaluate the contribution of each governance-aware mechanism, we conduct ablation experiments on the Yushu dataset under the Set-3 protocol, which preserves the complete four-level taxonomy (L0–L3). The backbone is fixed to ResNet-50, identified as the best-performing architecture on Yushu. All settings, including data splits, preprocessing, optimization schedule, and selection criteria, are kept identical to the main experiments to ensure strict comparability. Each ablation removes one component from the unified SeisRank-Ord functional: (i) w/o Ordinal alignment removes cumulative encoding and order constraints, reducing the objective to nominal classification; (ii) w/o Asymmetry disables conservative weighting, treating underestimation and overestimation symmetrically; (iii) w/o Ranking eliminates the top-K ranking term, weakening sensitivity near the triage threshold; and (iv) w/o Regularizer drops the probabilistic stabilizer, potentially impairing calibration under data imbalance.

Table 4 reports the quantitative results, and Figs. 2 and 3 provide visualizations of absolute performance and relative changes, respectively. Several consistent trends emerge. First, removing ordinal alignment produces the largest increase in MSE (0.460 → 0.487), reflecting more severe ordinal jumps such as confusing intact with collapse. This confirms that enforcing a cumulative probability structure is indispensable for severity fidelity. Second, disabling asymmetric weighting leads to a substantial decline in Kappa (0.540 → 0.512), indicating that the model misses more high-risk cases when underestimation is not penalized more strongly. This directly aligns with the governance motivation of avoiding critical misses. Third, removing the ranking term causes the most severe degradation overall (Kappa: 0.540 → 0.505; MSE: 0.460 → 0.480), demonstrating that triage prioritization is critical for decision-making accuracy around operational thresholds. Finally, excluding the regularizer results in smaller but consistent declines, highlighting its role in stabilizing training and improving calibration under imbalance.

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Fig. 2.

Ablation study on the Yushu dataset under Set-3 with a ResNet-50 backbone. (a) Kappa scores for different ablation settings. (b) MSE values for different ablation settings.

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Fig. 3.

Relative performance changes with respect to the full model on the Yushu dataset under Set-3 with a ResNet-50 backbone. (a) Relative change in Kappa. (b) Relative change in MSE.

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Overall, the ablation study confirms that SeisRank-Ord is not merely an additive combination of loss functions but a governance-driven framework in which each mechanism addresses a distinct failure mode. The systematic degradations across Kappa and MSE validate both the coherence of the design and the necessity of integrating all four mechanisms to achieve robust, governance-aware ordinal learning for seismic damage recognition.

5.1 Efficiency outcomes

Table 5 summarizes efficiency-oriented results. Across all policies, SeisRank-Ord consistently outperforms the CE baseline. Under severity-first (Policy A), SeisRank-Ord reduces the AUC from 130,800.0 to 122,359.7 and advances the median response (T₅₀) from day 22 to day 19, indicating that critical buildings are typically served three days earlier. The tail coverage (T₉₀) also improves substantially (51→47), showing that even the hardest-to-reach cases are addressed sooner.

Under egalitarian allocation (Policy B), which does not explicitly leverage severity predictions, SeisRank-Ord still provides clear benefits: AUC drops from 205,900.0 to 198,156.0, and T₉₀ improves from 67 to 65. The two-day gain at the tail highlights that improved recognition accuracy positively impacts resource distribution, even when allocation is evenly enforced.

For quota + threshold (Policy C), the governance-aware model again demonstrates consistent advantages. SeisRank-Ord reduces AUC from 188,900.0 to 182,396.6 and shortens both the median response day (29→27) and the tail response (69→66). These improvements confirm that calibrated risk scores are particularly valuable in constrained regimes where both quotas and thresholds govern daily allocation. Fig. 4 (cumulative coverage curves) illustrates these efficiency gains: Policy A achieves the fastest coverage, Policy B is the slowest, while Policy C provides a balanced trade-off between responsiveness and quota fairness. Fig. 4 illustrates the cumulative coverage curves that characterize efficiency gains across the three allocation policies. Policy A achieves the fastest coverage, Policy B is the slowest, while Policy C provides a balanced trade-off between responsiveness and quota fairness. Baseline comparisons are summarized in Table 5.

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Fig. 4.

Cumulative coverage curves of SeisRank-Ord under three allocation policies.

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5.2 Fairness outcomes

Having established efficiency improvements, we next examine fairness metrics. Table 6 highlights fairness-oriented results. Under Policy A, SeisRank-Ord advances the top-20% median response by one day (9 → 8) while slightly reducing inequality (Gini 0.760 → 0.754). This shows that severity-driven prioritization not only improves efficiency but also maintains fairness.

Policy B demonstrates the largest fairness improvement: the Gini index drops from 0.700 to 0.685, and top-20% high-risk buildings are reached three days earlier (39 →36). Even under egalitarian allocation, governance-aware objectives reduce response inequality and ensure that the most critical cases are not delayed.

In Policy C, SeisRank-Ord outperforms the baseline across both fairness metrics. The most critical 20% of buildings are served earlier (14 → 11), and the Gini index is reduced from 0.760 to 0.752. These improvements are significant because quota systems are frequently adopted in practice, and ensuring equitable allocation under such constraints directly strengthens governance legitimacy. Fig. 5 further highlights the fairness–efficiency trade-offs by showing the uncovered-damage trajectories across the three allocation policies. SeisRank-Ord consistently lowers residual damage throughout the response period, especially in the high-risk tail.

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Fig. 5.

Uncovered-damage trajectories of SeisRank-Ord under three allocation policies.

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The simulations demonstrate that SeisRank-Ord delivers consistent benefits across all policies, advancing both efficiency (earlier median and tail coverage, lower uncovered-damage AUC) and fairness (lower Gini, earlier top-20% service). While Tables 5 and 6 provide detailed numerical comparisons against the CE baseline, Figs. 4 and 5 focus exclusively on SeisRank-Ord to clearly illustrate efficiency and fairness dynamics. Specifically, cumulative coverage curves (Fig. 4) emphasize improvements in median and tail response times, while uncovered-damage trajectories (Fig. 5) highlight systematic reductions in long-tail risk. Crucially, these gains emerge from aligning model training with governance principles rather than simply optimizing nominal accuracy, underscoring that governance-aware objectives can directly improve disaster response by serving high-risk structures earlier and distributing aid more equitably.

5.3 Governance insights

The policy simulations offer several actionable insights for earthquake disaster governance. First, severity-first prioritization proves most effective in accelerating the service of critically unsafe buildings. With SeisRank-Ord, the median response to high-risk structures is advanced by three days compared to the baseline, and the long-tail coverage is shortened by four days. In operational terms, this implies that search-and-rescue teams could identify and stabilize severely damaged or collapsed buildings earlier, reducing secondary casualties and enabling faster triage of affected communities. Second, even under egalitarian allocation, governance-aware modeling enhances equity without sacrificing responsiveness. Although resources are distributed broadly in this regime, SeisRank-Ord lowers inequality (Gini reduced by 0.015) and reaches the top 20% of high-risk cases three days earlier. This indicates that fairer allocation does not necessarily conflict with efficiency when prediction models are aligned with governance priorities. In practice, such improvements could support more transparent and publicly accepted disaster response strategies, particularly in regions where equity concerns are politically salient. Third, quota-based allocation benefits from calibrated severity scores. Many real-world disaster response systems impose quotas or thresholds due to logistical constraints. In our simulations, SeisRank-Ord improves both responsiveness and equity under these conditions: high-risk buildings are reached three days earlier, and the distribution of service becomes more equitable (Gini reduced by 0.008). These improvements are especially relevant to earthquake-prone developing regions where limited capacity amplifies the consequences of misallocation. By complementing institutional mechanisms, governance-aware recognition ensures that quota rules do not inadvertently disadvantage the most vulnerable groups. Taken together, these findings emphasize that technical refinements in recognition models can translate directly into governance outcomes. By embedding operational principles into the learning objective, SeisRank-Ord enables disaster response systems to become not only more accurate but also more just, transparent, and aligned with societal priorities. These findings underscore that efficiency–fairness trade-offs are not merely numerical differences but policy choices. In real emergency response, prioritizing speed may reduce residual damage, while prioritizing fairness may strengthen institutional legitimacy and social stability. SeisRank-Ord thus serves as a bridge between algorithmic recognition and governance strategy, supporting more transparent and accountable disaster management decisions.