Abstract
Foundation settlement prediction often requires repeated numerical simulation, sparse field observations, and frequent recalibration as soil and loading conditions evolve. This protocol proposes a transferable calibration framework for surrogate models of foundation settlement that combines comparative surrogate assessment, metaheuristic feature and hyperparameter optimization, and digital-twin data fusion for iterative updating. The research question is whether a calibrated surrogate can approximate settlement responses with sufficient fidelity for design-space exploration while retaining explicit uncertainty and failure checks under limited, heterogeneous, and time-dependent measurements. The evidence scope is a targeted narrative synthesis of methodological findings from surrogate-based building optimization, ML task–algorithm mapping, digital-twin architectures for real-time simulation, geospatial calibration for flood dynamics, directed spatiotemporal dependence modeling, and ML calibration studies for sensor systems. These sources motivate the selection of BPNN and SVR as comparator surrogates, the use of wrapper-based feature selection and metaheuristic tuning, and the structuring of a foundation settlement digital twin around synchronized geometry, soil parameters, load history, and observation streams. The proposed protocol defines variables, operational rules, a calibration objective, model-selection criteria, and a validation sequence using blocked temporal and spatial splits. A direct operational rule is introduced for calibration: a surrogate is accepted only if it reduces both holdout error and systematic residual structure relative to a physics baseline, with residual autocorrelation explicitly tested rather than assumed absent. The manuscript establishes a reproducible methodological foundation and delineates what remains untested: empirical performance on a specific foundation class, site, or sensor regime.
1. Introduction
Foundation settlement is a calibration problem rather than a single prediction task. The target variable is not only the vertical displacement of a foundation at a given time, but the relation between observed settlement, load history, soil state, drainage condition, and model error. In practice, settlement forecasts are often generated by numerical models that are expensive to rerun across large parameter grids. A surrogate model is therefore useful only if it can approximate the response surface, quantify its own limits, and be recalibrated when new observations arrive. This protocol is designed for that purpose and does not claim completed empirical validation.
The methodological need for task-specific algorithm choice is supported by prior ML mapping work in indoor air quality, where model families were related to dataset structure, temporal dependence, computational cost, and interpretability, and where the authors concluded that no universal algorithm exists for IAQ. That framing is transferable here only at the level of method selection under heterogeneous data conditions. It supports a disciplined comparison of linear, kernel-based, and neural surrogate families for settlement calibration rather than assuming that one model class is intrinsically adequate. [1]
2. Evidence scope and research question
This manuscript uses a targeted narrative synthesis, not a systematic review. The evidence scope is limited to prior work that offers reusable procedures for surrogate construction, comparative assessment, optimization, digital-twin data fusion, and directed dependence modeling. Unrelated application domains are excluded unless they provide a transferable calibration or validation method. On that basis, the most relevant evidence comes from building retrofit optimization with BPNN and SVR surrogates, digital twins for traffic and flood simulation, a metaheuristic feature-selection framework for house-price prediction, ML task–algorithm mapping for sensor calibration, and a spatiotemporal dependence model that extracts directed pathways from finite sequences. [2] [3] [4] [1] [5]
The research question is: how should a foundation settlement surrogate be calibrated when observations arrive from multiple sources with different temporal resolutions, while the underlying soil-structure system may change over time? The answer proposed here is a protocol that couples a baseline physics simulator with a data-assimilating digital twin, compares BPNN and SVR as candidate surrogates, and uses explicit residual diagnostics to decide whether the surrogate is admissible for further use. Other nonlinear surrogate families are excluded by design in order to keep the comparison interpretable and implementable in a first protocol. The scope is therefore narrow: calibration for settlement prediction and update, not full constitutive discovery or general geotechnical automation.
Prior work suggests three transferable lessons. First, surrogate models can replace expensive simulations in optimization loops, but model comparison should be explicit; in the building-retrofit study, BPNN and SVR were both used as surrogates, BPNN showed better predictive performance in that application, and the selected surrogate was then carried forward into optimization. Second, feature selection and hyperparameter tuning can materially affect model behavior, as illustrated by the house-price framework that combined wrapper-based feature selection with metaheuristic hyperparameter search. Third, digital twins are structurally clearer when data ingestion, simulation, and feedback are separated into layers, as in the traffic and flood studies. These lessons motivate a settlement-specific architecture with separate data, model, and decision layers. [2] [6] [3] [4]
3. Conceptual basis for settlement surrogate calibration
A foundation settlement surrogate approximates the mapping f: X -> y, where X contains design, loading, soil, and environmental variables and y is settlement at a specified location and time. For a footing, mat, or pile cap, X may include average applied pressure, contact stress distribution, footing width, embedment depth, soil layer thicknesses, elastic moduli, compression indices, groundwater level, consolidation coefficient, and elapsed time since loading. The output y should be operationally defined as vertical settlement at a fixed reference point or as a settlement vector across multiple gauges. If a time series is used, the target should be indexed as y(t), not aggregated prematurely.
The calibration problem requires distinguishing the reference signal, the surrogate prediction, and the residual. Let y_ref denote the calibration target. In one use-case, y_ref is measured settlement from field instrumentation. In a second use-case, y_ref is settlement generated by a previously verified high-fidelity numerical model for emulator construction. These use-cases should not be pooled in one loss calculation because the reference uncertainty and the interpretation of residuals differ. Let y_hat denote the surrogate prediction and e = y_ref - y_hat the residual. In this protocol, low average error is necessary but not sufficient. Residual structure is treated as a diagnostic quantity that may reveal omitted load-history or drainage-state information. The directed dependence literature is relevant at this level of modeling logic: finite-length spatiotemporal systems can contain directional, sequence-dependent relations rather than only contemporaneous association. By analogy, settlement calibration may require explicit lagged predictors and state variables when loading and drainage history is expected to influence later response. [5]
The flood-dynamics digital-twin study is a useful application analogue because it combines geospatial data, historical flood events, and scenario modeling into a virtual replica for operational analysis. The settlement twin proposed here adopts the same logic at a smaller physical scale: static geometry, dynamic loading, and monitoring streams are fused into a live representation that supports recalibration after each observation update. The traffic digital twin adds a second transferable idea: a layered architecture that separates system construction, data acquisition, and model generation. That separation is useful for settlement calibration because it keeps prediction routines linked to measurement provenance and update rules. [4] [3]
4. Proposed methodology: variables, model classes, and decision sequence
The protocol defines four variable groups. Group A comprises geometry variables: footing width, length, thickness, embedment depth, pile length if present, and layer interfaces beneath the foundation. Group B comprises soil-state variables: unit weight, void ratio, preconsolidation stress, undrained shear strength, elastic modulus, compression index, permeability, and consolidation coefficient. Group C comprises load-history variables: static service load, cyclic load amplitude, loading rate, unloading history, and duration. Group D comprises observation variables: settlement gauge readings, pore pressure, tilt, temperature when used only as a sensor-correction covariate, and timestamps. Temperature enters the predictor set only if a preregistered sensor audit shows a non-negligible association between raw settlement readings and temperature after controlling for load and time; otherwise it is excluded. The default target for this protocol is point settlement y(t) at a fixed gauge and time index. Settlement-field prediction is treated as an extension that requires vector-valued loss functions and is not the default calibration task here.
The candidate surrogate set consists of BPNN and SVR as primary comparators, with a linear baseline retained for transparency. This choice is grounded in prior comparative surrogate work in which BPNN and SVR were both used to approximate nonlinear building-performance relationships and were compared on predictive performance. For the present protocol, BPNN and SVR are treated as contrasting regression strategies rather than as methods with predetermined superiority. The working assumption for implementation is that BPNN may be advantageous when interactions are strongly nonlinear, whereas SVR may remain competitive under limited sample sizes; this assumption is to be tested within the blocked validation design rather than accepted a priori. [2]
A metaheuristic feature and hyperparameter routine is included because the settlement predictor will rarely be well specified by default settings. The proposed routine uses a two-stage search: Stage 1 selects features by minimizing validation loss under sparsity pressure; Stage 2 tunes model parameters. For BPNN, the tuned parameters are hidden-layer width, activation, learning rate, batch size, and early-stopping patience. For SVR, the tuned parameters are C, epsilon, and kernel width. The house-price study supports this kind of optimization logic by combining wrapper-based feature selection with metaheuristic search for hyperparameters, while the building-retrofit study supports the broader practice of comparing surrogate families before embedding them into an optimization loop. [6] [2]
Exact operational rule: let the baseline be a calibrated physics model of the same foundation, evaluated on the same inputs, boundary conditions, and observation times as the surrogate. Acceptance is based on blocked holdout mean absolute error on the original settlement scale, not on mean absolute percentage error, because settlement values may be zero, near zero, or sign-changing. Before analysis, the investigator preregisters two quantities on that same scale: a minimum improvement margin delta_MAE >= 0 and a bias tolerance tau_bias >= 0 for the absolute holdout residual mean. The primary residual-dependence test is Ljung-Box on holdout residuals at lag 1, applied only when the ordered holdout block contains at least 20 observations; lag-1 sample autocorrelation may be reported descriptively but is not a separate acceptance test. Under the default rule, a surrogate is accepted for operational updating only if all three conditions hold simultaneously: holdout MAE is lower than the baseline by at least delta_MAE, the absolute residual mean does not exceed tau_bias, and the lag-1 Ljung-Box test is not significant at the preregistered alpha level. If MAE improves but either diagnostic fails, the surrogate is retained only for diagnostic comparison and the physics baseline remains the operational model. This is a protocol choice, not an empirical claim about all settlement surrogates.
Algorithmic sequence. Step 1: ingest geometry, soil, load, and observation data into a synchronized table with explicit time stamps. Step 2: define the physics baseline class before surrogate training, calibrate that baseline only on the training portion, and require that baseline and surrogate be compared on identical inputs and boundary conditions. Step 3: perform leakage-free preprocessing using only training-fold statistics. Step 4: generate candidate feature subsets using a wrapper search with an explicit penalty on feature count. Step 5: train BPNN, SVR, and a linear baseline on blocked folds. Step 6: compute mean absolute error, root mean squared error, bias, and residual diagnostics on the holdout block. Step 7: apply the acceptance rule; if no surrogate is accepted, retain the physics baseline for operational use. Step 8: update the digital-twin state only after model selection, then archive model version, feature set, split definition, and residual diagnostics for auditability.
5. Digital-twin architecture for settlement calibration
The digital-twin architecture is organized into three layers. The system-construction layer stores geometry, stratigraphy, and boundary conditions in a versioned foundation model. The data-acquisition layer synchronizes settlement gauges, inclinometers, pore-pressure sensors, and load-monitoring devices, with explicit handling of missingness and clock drift. The model-generation layer hosts the surrogate and the physics baseline, enabling rapid prediction and recalibration. This design mirrors the traffic twin’s separation of construction, acquisition, and concept generation, but it is adapted here to geotechnical observables rather than traffic flow. [3]
The flood twin provides a relevant geospatial analogy for calibration because it integrates terrain, infrastructure, and historical flood events into a dynamic replica that is validated with historical events and used for scenario modeling. For foundation settlement, the counterpart is a site twin that incorporates soil layering, groundwater variations, and construction sequence. The protocol therefore treats each monitoring event as a state update, not merely as a fresh data point. This state-based formulation is adopted as a modeling assumption because settlement response may depend on prior loading and hydraulic conditions; if later data do not support lagged effects, the state representation should be simplified. [4]
A directed dependence structure is used only when the observation sequence is long enough to justify lagged analysis. Operationally, the twin stores a state vector s_t that includes current settlement, cumulative load, elapsed time since loading, and any selected soil or pore-pressure indicators, and then predicts s_t+1 or y(t+1) from current and lagged states. If lagged modeling is activated, candidate lags are fixed in advance and ranked by a directional information criterion such as transfer-entropy-based contribution rather than by simple correlation alone. The rationale comes from finite-length directed-spillover modeling, which distinguishes origin and reception in ordered sequences. In the present protocol, that logic is used only as a prospective estimator choice for ordered loading and drainage histories. [5]
6. Prospective validation design and outcome measures
Validation should be prospective in structure, even if the protocol is later applied retrospectively for implementation testing. The default design is blocked temporal validation with at least three non-overlapping ordered blocks: an initial training block, one tuning block, and one final holdout block. To keep the search procedure estimable, the training plus tuning portion should contain at least 50 observations for single-output calibration; if fewer are available, the metaheuristic search is suspended and only the linear baseline and a minimally tuned SVR are compared. The final holdout block should contain at least 20 ordered observations if the lag-1 residual-dependence test is to be used; otherwise acceptance is based only on MAE and bias, and the missing residual test is reported as a protocol deviation. The temporal gap between adjacent blocks should be at least one dominant observation interval of the monitoring system, and should be increased when engineering judgment indicates delayed consolidation effects that would otherwise leak information across the split. If multiple foundations or soil zones are available, one zone is held out only if it contains enough observations to support the same outcome metrics; the default rule is to hold out the zone with the latest start date so that transfer is tested without mixing early and late monitoring regimes. Random splits alone are not sufficient because they can leak temporal dependence and produce optimistic error estimates.
Primary outcome measures are mean absolute error and root mean squared error on the original physical settlement scale, with mean bias error reported alongside them. Mean absolute percentage error is excluded from the default decision rule because it is unstable when observed settlement is zero, near zero, or changes sign. Secondary diagnostics are residual autocorrelation at preregistered lags, calibration slope when observed and predicted values can be regressed on the holdout block, and prediction-interval coverage if uncertainty intervals are produced. A model is operationally weak if it meets average-error targets but fails either the bias tolerance or the preregistered residual-dependence test. The validation set should also include one stress block that differs from the modal training regime, such as a higher service load or altered groundwater conditions. Any numeric acceptance threshold remains hypothetical until local data support it.
The comparator is a physics baseline, not an arbitrary machine-learning baseline. This is important because surrogate calibration is meant to improve or accelerate a mechanistic model, not merely compete with a generic regressor. The BPNN versus SVR comparison is then nested inside the broader question of whether the surrogate faithfully reproduces the mechanistic output or field observation under the same input conditions. The building-retrofit literature supports this nested comparison structure because surrogate selection preceded optimization, rather than being conflated with the optimization target itself. [2]
To examine robustness, the protocol includes two ablation checks. First, remove the metaheuristic feature search and retest model stability. Second, freeze the digital-twin update and test static versus dynamically updated inputs. Both ablations are evaluated on the same blocked splits, with the same preprocessing rules, outcome metrics, and acceptance logic as the main protocol, so that the estimand remains comparable. For each ablation, the primary estimand is the change in holdout mean absolute error relative to the full protocol, supplemented by the change in absolute residual mean and the lag-1 residual-dependence test when available. Before analysis, the investigator preregisters a materiality threshold delta_ablate on the original settlement scale; deterioration is judged substantial only when the ablated version worsens MAE by more than delta_ablate or newly fails a diagnostic that the full protocol passed. This is a proposed test, not an established result.
Where directed dependence is plausible, an additional validation step estimates whether lagged variables improve forecast fidelity relative to contemporaneous-only inputs. The question is not only whether lagged variables lower error, but whether they reduce residual dependence over time. This is the practical settlement analogue of modeling directional spillover pathways in finite-length spatiotemporal systems. [5]
7. Failure cases and limits of generalization
Three failure cases are anticipated. First, if the foundation response is governed by abrupt regime changes such as localized shear failure or construction defects, the surrogate may interpolate poorly even when average error is low. Second, if sensor drift or missingness is severe, the twin may learn instrumentation artifacts rather than soil response. Third, if the data window is too short, directed lag structure cannot be estimated reliably and the model should be simplified rather than forced into a temporal architecture.
Generalization is limited by soil diversity, foundation type, and boundary condition differences. A surrogate calibrated on shallow footings in one geological setting should not be assumed valid for pile groups, mat foundations, or expansive clays without revalidation. The indoor air quality study is relevant here because it explicitly notes that no universal algorithm exists and that sensor, metadata, and preprocessing differences require careful comparison. That caution applies directly to settlement calibration, where differences in field instrumentation and soil characterization can invalidate cross-site transfer. [1]
The protocol also recognizes that surrogate superiority can be conditional. In the industrial-building study, BPNN and SVR were compared as alternative surrogates and the selected model depended on predictive performance in that application. This manuscript therefore does not claim that BPNN is generally preferable for settlement. It proposes BPNN and SVR as a bounded comparator pair for a first settlement-calibration protocol because they represent distinct nonlinear regression strategies, have precedent as surrogates in another simulation-intensive setting, and keep the protocol narrow enough for transparent testing. [2]
8. Conclusion
This manuscript proposes a conceptual and procedural basis for calibrating foundation settlement surrogate models within a digital-twin framework. The main contribution is a specific protocol: define point settlement as a time-indexed response, compare BPNN and SVR against a calibrated physics baseline under identical inputs, apply wrapper-based feature selection and hyperparameter tuning, and accept a surrogate only when holdout error, bias, and residual dependence jointly satisfy preregistered criteria. The architecture is modular so that data acquisition, model training, and state updating can be audited separately.
What remains untested is empirical performance in any specific foundation class, soil profile, or sensor network. The proposed thresholds are hypothetical until established against local data, and the value of directed dependence modeling must be confirmed under real settlement sequences rather than assumed from analogy. The protocol therefore offers a bounded methodological contribution: it clarifies how calibration should be organized for foundation settlement surrogates, while leaving open the quantitative question of which implementation performs best in a particular site.
Contribution and availability
This manuscript proposes a bounded, reusable protocol for calibrating foundation settlement surrogate models within a digital-twin architecture. It specifies operational variables, comparator surrogates (BPNN and SVR), a metaheuristic feature/hyperparameter search, a residual-based acceptance rule, and a prospective validation design that tests both error reduction and temporal dependence control. The contribution is methodological rather than empirical: it synthesizes transferable procedures from surrogate-based optimization, digital twins, and directed spatiotemporal modeling into a settlement-specific calibration workflow.
Funding: Roman Vlasov’s own funds. Editorial responsibility and competing interests: Roman Vlasov is the founder and Editor-in-Chief of Smart World Journal and the creator of the BILDRY construction-planning platform. Other competing interests have not been declared.
This conceptual study reports no newly collected empirical data. Its proposed procedures require the prospective validation described above.
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