Foundation-Specific Hybrid Models for Expansive Soil Deformation Prediction and Early Warning

Abstract

Foundation deformation prediction on expansive soils involves complex soil-structure interactions and environmental variability. This study develops foundation-specific hybrid modeling approaches for temporal deformation prediction using 974 days of monitoring data from four foundations on medium-expansive soil. Four hybrid architectures were evaluated—Residual-Clustering Hybrid, Elastic Net Fusion, Residual Correction, and Enhanced Robust Huber—optimized through Ridge regression-based feature selection and validated against seven baseline methods. Systematic feature engineering with optimal selection identified foundation-specific complexity requirements. Statistical validation employed bootstrap resampling, temporal cross-validation, and Bonferroni correction for multiple comparisons. Results demonstrated foundation-specific effectiveness with distinct hybrid model performance: Residual-Clustering Hybrid achieved optimal performance for Foundation F1 (R² = 0.945), Elastic Net Fusion performed best for Foundation F2 (R² = 0.947), Residual Correction excelled for Foundation F3 (R² = 0.963), and Enhanced Robust Huber showed strongest results for Foundation F4 (R² = 0.881). Statistical significance was achieved in 35.7% of comparisons with effect sizes of Cohen’s d = 0.259–1.805. Time series forecasting achieved R² = 0.881–0.963 with uncertainty intervals of ±0.654–0.977 mm. Feature analysis revealed temporal variables as primary predictors, while domain-specific features provided complementary contributions. The early warning system achieved F1-scores of 0.900–0.982 using statistically derived thresholds. Foundation deformation processes exhibit strong autoregressive characteristics, providing enhanced prediction accuracy and quantified uncertainty bounds for operational infrastructure monitoring.

1. Introduction

Foundation monitoring in expansive soils represents a significant challenge in geotechnical engineering, with considerable annual infrastructure damage due to soil volume changes induced by moisture variations [1,2,3]. These soils undergo swelling and shrinkage cycles that generate differential settlements, structural cracking, and premature infrastructure deterioration, necessitating continuous monitoring systems to prevent failures and optimize maintenance strategies [1,2,4]. This investigation focuses specifically on static foundation deformation prediction under quasi-static moisture-induced volume changes, excluding dynamic loading conditions, seismic response, and cyclic behavior that involve additional soil dynamics and inertial parameters.

Environmental factors including moisture content fluctuations, matric suction variations, temperature cycles, and precipitation patterns operate across multiple temporal scales—daily, seasonal, and annual—creating complex soil-structure interaction mechanisms [5,6]. These factors substantially compromise soil mechanical properties, facilitate water infiltration pathways, and trigger failure mechanisms that are difficult to predict using conventional approaches [7,8]. The heterogeneous nature of expansive soils further complicates monitoring, as spatial variations in clay mineralogy, plasticity characteristics, and moisture distribution create foundation-specific behavioral patterns requiring individualized assessment protocols [9,10,11,12,13].

Traditional monitoring approaches face limitations including sparse spatial and temporal resolution, expensive laboratory testing requirements, and time-intensive field instrumentation [14,15]. Conventional empirical models, primarily developed for cohesionless soils, demonstrate limited applicability to expansive clay behavior, while theoretical approaches often fail to capture the complex nonlinear relationships between environmental drivers and foundation response [7,16]. Furthermore, existing monitoring systems typically lack integrated early warning capabilities and foundation-specific calibration, reducing their effectiveness for proactive infrastructure management [17,18,19].

Machine learning (ML) approaches have emerged as promising alternatives for foundation monitoring applications. Recent studies report the application of various algorithms including Artificial Neural Networks, Support Vector Machines, Random Forest, and Gradient Boosting, ensemble methods such as XGBoost, and hybrid approaches combining multiple techniques [5,7,9,15,16,17,20,21,22,23]. Comparative analyses generally indicate that ensemble and hybrid methods outperform individual base models, though the magnitude of improvement and its practical significance remain underexplored [7,16].

The selection of appropriate ML techniques must balance predictive accuracy with engineering interpretability to address practical implementation concerns in geotechnical applications. Hybrid approaches combining multiple methodologies offer potential solutions to the “black-box” limitations inherent in complex ML models [24]. The systematic evaluation frameworks incorporating multiple performance indices enable comprehensive assessment of model reliability, allowing practitioners to understand decision-making processes while achieving robust forecasting capabilities.

Despite these advances, current research exhibits limitations that constrain practical implementation. Most studies rely on short-term monitoring periods (typically <100 days) [12], insufficient for capturing complete seasonal cycles and long-term soil behavior patterns [5,17,20,25]. Comparative analyses of hybrid versus baseline models lack statistical rigor, with absent multiple testing corrections, effect size reporting, and confidence interval estimation for practical significance assessment [7,15,16,20]. Foundation-specific behavioral differences remain under-explored, as most studies assume uniform soil response across monitoring locations [10,11,13]. Additionally, practical early warning systems lack comprehensive validation frameworks [19], including precision/recall analysis and threshold optimization for operational deployment [17,18,19].

This study addresses these research gaps through a comprehensive 974-day multi-foundation monitoring investigation that systematically evaluates baseline and hybrid ML approaches for expansive soil foundation behavior prediction. The research contributions include (1) long-term field monitoring of four isolated foundations with synchronized environmental data collection, capturing complete seasonal cycles and temporal dependencies; (2) comparative evaluation of seven baseline models against four hybrid approaches using statistical validation including bootstrap resampling, temporal cross-validation, and Bonferroni correction for multiple comparisons; (3) foundation-specific feature analysis revealing spatial heterogeneity in soil-structure interaction patterns and feature importance hierarchies through systematic ablation studies; and (4) development and validation of an integrated early warning system with precision/recall metrics and uncertainty quantification for operational risk assessment. The study provides empirical evidence for hybrid model effectiveness while establishing statistical frameworks for practical significance evaluation in geotechnical ML applications.

Table 1. Representative ML Studies for Geotechnical Deformation Prediction.

Study	ML Methods	Dataset	Feature Categories	Target Variable	Best R2	Key Contribution
Hu & Li [5]	Baseline: XGBoost, RF, LS-SVM; Hybrid: XGBoost-SHAP	Long-term monitoring, 4-year series	canal water level components, groundwater level components, time dependent effect, displacement increment of previous month data, lag features, VMD trend/periodic decomposition, atmospheric precipitation, evaporation,	Slope deformation	0.908–0.993	Interpretable ML with actionable reinforcement insights
Chen et al. [7]	Baseline: XGBoost, RF, ANN, SVM, MARS; Hybrid: Stacked Generalization	Manual collection, 125 records	dry density, water content, matric suction, unconfined compressive strength, failure compressive/tensile strains	Uniaxial tensile strength	0.88	Ensemble approach outperforming individual models
Habib et al. [9]	Baseline: SGD, DT, RF, AB, GB; Hybrid: ERT, XGB	Laboratory testing, 210 samples	dry unit weight, liquid limit, plasticity index, clay content, initial moisture content, etc.	Soil swelling potential	0.97	~49% error reduction over baseline methods
Davar et al. [13]	Baseline: ANN-BR; Hybrid: PSO-ANN, BOA-ANN	Real-time monitoring, 13,690 hourly points	volumetric soil moisture content, 18-month hourly time series, air temperature, soil temperature, rainfall	Soil matric suction	0.9949	Hybrid optimization achieving temporal prediction
Eyo et al. [15]	Baseline: BLR, REG, LR, ANN, SVM, RDF, BDT; Hybrid: Voting/Stacking ensembles	Literature compilation, 517 records	void ratio, unit weight, liquid limit, plasticity index, clay content, maximum dry unit weight, coarse content, cation exchange capacity, activity, moisture content	Soil expansion	0.94	Meta-heuristic ensembles with 2–10 fold improvement
Zhou et al. [17]	Baseline: SVR, BPNN, RBFNN, LSTM; Hybrid: PSO-VMD-LSTM	MEMS sensors, 7-day hourly	cumulative displacement, lag features 8–24 h, temporal dependencies, rainfall, water level, tide height	Vertical deformation	>0.90	Time series decomposition for tidal environments
Nguyen et al. [26]	Baseline: GP, MLP, ANN, SVM; Hybrid: Bagging-MLP	Field collection, 214 samples	gravel content, coarse/fine sand content, silt clay content, liquid/plastic limits, plasticity index, maximum dry density, organic content, optimum water content	Swelling potential	0.90	Bootstrap aggregation for variance reduction
Present study, 2025	Baseline: LR, Ridge, Lasso, EN, Huber, BR, RF; Hybrid: Residual-Clustering, Elastic Net Fusion, Residual Correction, Enhanced Robust Huber	Foundation monitoring, 974 days, 4 foundations	raw monitoring variables, physics-based features (swelling/deformation potentials), statistical transformations (normalized and nonlinear terms), temporal features, seasonal encodings, and lag variables	Foundation deformation	0.881–0.963	Foundation-specific modeling with statistical validation and early warning

summarizes representative studies focusing on geotechnical deformation prediction and soil behavior modeling, highlighting the diversity of methodological approaches and performance achievements.

2. Methodology

2.1. Data Characteristics and Preprocessing

The monitoring dataset comprised 140 temporal observations collected over 974-day field monitoring program conducted at Salahaddin University-Erbil, where a reinforced concrete frame supported by four isolated footings was constructed on medium-expansive clay [6]. The experimental design monitored four variables: vertical deformation, daily temperature, weekly rainfall, and soil moisture at 60 cm depth. Vertical displacements were measured using dial gauges (0.01 mm precision) with cross-validation through Bosch line lasers and LEICA digital levels, while meteorological data were obtained from government agencies.

For temporal validation consistent with operational forecasting conditions, the dataset was partitioned chronologically into training (112 observations, 80%) and testing (28 observations, 20%) subsets, maintaining temporal ordering to prevent data leakage in time series analysis.

2.1.1. Environmental Conditions and Spatial Variability

Environmental conditions (Figure 1a,

Table 2. Basic statistical analysis of monitoring data (derived from raw dataset, 140 observations per variable).

Variable Group	Variable	N	Mean	Std	Min	25%	Median	75%	Max	Range	Skewness	Kurtosis	CV (%)	Missing
Deformation (mm)	F1	140	−1.01	1.39	−3.99	−1.83	−1.34	0.35	1.67	5.66	0.09	−0.77	−137.64	0
	F2	140	0.72	1.84	−2.83	−0.55	0.98	1.95	4.86	7.69	−0.23	−0.56	255.35	0
	F3	140	−0.80	1.21	−3.38	−1.70	−0.65	0.04	2.89	6.27	0.17	0.06	−150.66	0
	F4	140	0.70	2.61	−3.15	−1.23	0.12	1.51	7.43	10.58	0.93	0.20	370.74	0
Soil Moisture (%)	F1	140	9.79	1.68	6.07	8.26	10.05	10.86	14.64	8.57	0.18	−0.20	17.11	0
	F2	140	11.96	2.49	6.46	9.59	11.88	13.29	18.60	12.14	0.53	0.39	20.84	0
	F3	140	8.33	2.03	4.49	7.10	8.28	9.39	13.65	9.16	0.47	0.04	24.39	0
	F4	140	8.63	3.22	3.24	7.58	8.40	9.87	16.48	13.24	0.28	0.11	37.29	0
Environmental	Temp (°C)	140	22.48	10.02	3.30	13.40	21.55	32.65	39.40	36.10	0.11	−1.35	44.56	0
	Rainfall (mm)	140	7.66	18.29	0.00	0.00	0.00	5.20	146.30	146.30	4.25	23.96	238.77	0

) exhibited distinct seasonal patterns with spatial heterogeneity across monitoring locations. Temperature ranged from 3.3 °C to 39.4 °C (mean = 22.48 °C, CV = 44.56%) following regular annual cycles. Rainfall demonstrated episodic behavior (mean = 7.66 mm, skewness = 4.25, maximum = 146.3 mm) with extended dry periods punctuated by intense precipitation events.

Soil moisture response (Figure 1b, Table 2) demonstrated spatial heterogeneity across the four monitoring locations. F2 recorded the highest mean moisture content (11.96% ± 2.49%), while F4 exhibited the greatest temporal variability (CV = 37.29%). F1 and F3 maintained lower baseline moisture levels (9.79% and 8.33%, respectively), consistent with their settlement-dominated behavior patterns.

2.1.2. Foundation Deformation Patterns and Measurement Validation

The monitoring structure consists of a reinforced concrete frame (430 cm × 430 cm base, 342 cm height) with four vertical columns connected by horizontal beams, where each column rests on isolated footings (125 cm × 125 cm). Foundation deformations (Figure 1c, Table 2) exhibited differential responses reflecting localized soil-foundation interaction mechanisms, where ‘soil-foundation interaction’ refers specifically to the geotechnical response of expansive soil to moisture-induced volume changes and the resulting vertical displacement of individual footings, without incorporating superstructure load distribution or dynamic structural characteristics. Temporal analysis revealed systematic movement patterns: F2 and F4 experienced net upward displacement (+1.52 mm and +3.36 mm), while F1 and F3 underwent sustained downward movement (−3.99 mm and −3.38 mm). Foundation F4 displayed the largest deformation magnitude and variability (standard deviation = 2.61 mm, range = 10.58 mm), consistent with its position in the most moisture-sensitive soil zone.

Measurement validation through independent dial gauge monitoring (Figure 1d,

Table 3. Summary statistics for long-term monitoring (974 days, Salahaddin University-Erbil).

Category	Variable	Foundation	Mean	Std	Min	Max	Trend/Net Change	Status	Notes (From Figure 1)
Environmental	Temperature (°C)	–	22.48	10.02	3.30	39.40	–	–	Seasonal cycles
	Rainfall (mm)	–	7.66	18.29	0.00	146.30	5 extreme events	–	Episodic spikes
Soil Moisture (%)	Moisture	F1	9.79	1.68	6.07	14.64	Decreasing	–	Matches settlement
		F2	11.96	2.49	6.46	18.60	Increasing	–	Matches heave
		F3	8.33	2.03	4.49	13.65	Decreasing	–	Matches settlement
		F4	8.63	3.22	3.24	16.48	Increasing	–	Matches heave
Deformation (mm)	Vertical disp.	F1	−1.01	1.39	−3.99	1.67	−3.99	Settlement	Long-term decline
		F2	0.72	1.84	−2.83	4.86	+1.52	Heave	Episodic rise
		F3	−0.80	1.21	−3.38	2.89	−3.38	Settlement	Sustained decline
		F4	0.70	2.61	−3.15	7.43	+3.36	Heave	Strong episodic rise
Dial Gauge (mm)	Position	F1	5.32	1.40	2.34	8.00	−3.99	–	Corroborates disp.
		F2	5.06	1.85	1.51	9.20	−1.52	–	–
		F3	3.95	1.21	1.37	7.64	−3.38	–	–
		F4	5.35	2.62	1.50	12.08	+3.36	–	–

) confirmed deformation patterns with high consistency. Absolute gauge readings tracked relative foundation movements across all locations, with maximum recorded positions of 12.08 mm (F4) and 9.20 mm (F2).

2.1.3. Statistical Analysis and Data Quality Assessment

Statistical analysis (Table 2) confirmed complete data coverage with zero missing values across all 140 observations per variable. Distribution characteristics revealed approximate normality for F1 and F3 deformations (|skewness| < 0.5), while F4 exhibited positive skewness (0.93) reflecting episodic upward movements during moisture expansion events. All environmental and geotechnical variables demonstrated stable measurement characteristics suitable for predictive modeling.

2.1.4. Feature Categorization Framework

The feature engineering framework distinguishes between physics-based approaches (embedding domain knowledge) and derived statistical approaches (optimizing predictive patterns through mathematical transformations). To support subsequent ablation analysis, engineered features were systematically categorized into three domain-specific groups based on geotechnical principles: physics-based features (moisture derivatives, swelling potentials, deformation potentials, and quadratic transformations including Moist²_Fi reflecting nonlinear moisture-deformation coupling in medium-expansive clay with PI = 21% and swelling index Cs = 0.016 as characterized [6]. Temporal features (lagged variables, seasonal encodings, and autoregressive terms capturing time-dependent responses), and Environmental features (temperature, rainfall, and their transformations representing external driving forces). This categorization framework enabled systematic evaluation of feature group contributions to predictive performance while maintaining physical interpretability.

2.1.5. Foundation-Specific Feature Selection Methodology

Given the training sample size constraints (112 observations), optimal feature selection employed foundation-specific optimization balancing predictive performance with model parsimony following established bias-variance trade-off principles [27,28]. The methodology operationalized parsimony through information criteria evaluation and partial F-tests for statistical significance assessment [29].

For correlation analysis presentation, the most influential features for each foundation were systematically identified and ranked based on correlation magnitude with deformation responses. This selective approach was guided by the feature-to-sample ratio of 10–15:1 to maintain statistical power while mitigating overfitting risks in subsequent modeling stages [30].

The feature selection process determined optimal complexity levels through: (1) elbow method analysis identifying performance plateaus, (2) partial F-tests evaluating incremental feature significance, and (3) information criteria (AIC/BIC) assessment, with BIC providing formal balance between model fit and complexity through parameter penalization [31]. Rather than enforcing uniform feature counts, the methodology determined optimal numbers for each foundation reflecting local soil-moisture interaction patterns under constant structural loading. The methodology does not incorporate variable structural characteristics or loading conditions, limiting applicability to similar foundation types under comparable load configurations.

2.1.6. Correlation Analysis with Statistical Validation and Feature Derivation Effects

Foundation-specific correlation patterns were analyzed using feature sets optimized for each foundation’s characteristics under the constant loading conditions of the reinforced concrete monitoring frame to identify primary predictive relationships within this specific structural context (Figure 2,

Table 4. Foundation-specific correlation analysis: relationship between deformation and primary predictive variables.

Rank	Foundation F1			Foundation F2			Foundation F3			Foundation F4
	Variable	r	Sig.	Variable	r	Sig.	Variable	r	Sig.	Variable	r	Sig.
1	Target_lag1_F1	0.96	***	Target_lag1_F2	0.97	***	Target_lag1_F3	0.96	***	Target_lag1_F4	0.98	***
2	NormMoist_F1	0.41	***	Month_sin	0.65	***	Swell_F3	0.60	***	Moist2_F4	0.84	***
3	Swell_F1	0.41	***	TempLag1	−0.38	***	%moist_F3	0.60	***	NormMoistLag1_F4	0.78	***
4	DefPot_F1	0.41	***	Moist2_F2	0.38	***	NormMoist_F3	0.60	***	SwellLag1_F4	0.78	***
5	%moist_F1	0.41	***	Temp	−0.34	***	DefPot_F3	0.60	***	DefPotLag1_F4	0.78	***
6	Moist2_F1	0.39	***	%moist_F2	0.33	***	Moist2_F3	0.59	***	MoistLag1_F4	0.78	***
7	MoistLag1_F1	0.38	***	NormMoist_F2	0.33	***	TempLag1	−0.59	***	%moist_F4	0.78	***
8	Temp	−0.30	***	DefPot_F2	0.33	***	Temp	−0.58	***	Rain	0.30	***
9	Rain	0.16	NS	Rain	0.23	**	Rain	0.35	***	Temp	−0.17	*

Notes: Significance levels: *** p < 0.001, ** p < 0.01, * p < 0.05, NS = not significant.

). Statistical significance testing employed Pearson correlation coefficients with p-value calculation.

Temporal persistence dominated predictive relationships at all foundations, with one-step lagged deformation exhibiting very strong correlations (r = 0.96–0.98, all p < 0.001). This confirmed strong autoregressive behavior in foundation response, justifying temporal validation splitting and lag feature incorporation.

Identical correlation coefficients for multiple features within foundations (e.g., F3 moisture-derived features: r = 0.60; F4 lag features: r = 0.78) represent expected statistical behavior from systematic feature derivation. Features exhibiting identical correlations are linear transformations of core measurements, confirming the physics-based feature engineering validity. Complete feature specifications with mathematical definitions are provided in

Table A1. Complete Feature Engineering Specifications.

Feature Name	Feature Abbrev	Mathematical Definition	Physical Interpretation
deform_fi_mm	Target_Fi	Raw deformation measurement	Foundation vertical displacement
moisture_fi_percent	%moist_Fi	Raw moisture measurement	Soil moisture at foundation depth
temperature_celsius	Temp	Raw temperature measurement	Ambient temperature
rainfall_mm	Rain	Raw precipitation measurement	Daily precipitation
day	Day	Sequential day number	Cumulative day counter
date	Date	Timestamp	Date information (preprocessing only)
moisture_fi_normalized	NormMoist_Fi	(moisture_fi_percent − μ_train)/σ_train	Standardized moisture content
moisture_fi_squared	Moist2_Fi	(moisture_fi_percent)2	Nonlinear moisture effect
swelling_potential_fi	Swell_Fi	moisture_fi_percent × 0.016	Empirical swelling potential
deform_potential_fi	DefPot_Fi	(moisture_fi_percent − 8.0) × 0.1	Deformation potential
month	Month	date.dt.month	Calendar month (1–12)
month_sin	Month_sin	sin(2π × month/12)	Sinusoidal seasonal encoding
month_cos	Month_cos	cos(2π × month/12)	Cosinusoidal seasonal encoding
day_of_year	Day_yr	date.dt.dayofyear	Annual day position (1–365)
target_fi_lag1	Target_lag1_Fi	deform_fi_mm(t − 1)	Previous day foundation deformation
moisture_fi_percent_lag1	MoistLag1_Fi	moisture_fi_percent(t − 1)	Previous day moisture content
moisture_fi_normalized_lag1	NormMoistLag1_Fi	moisture_fi_normalized(t − 1)	Previous day normalized moisture
swelling_potential_fi_lag1	SwellLag1_Fi	swelling_potential_fi(t − 1)	Previous day swelling potential
deform_potential_fi_lag1	DefPotLag1_Fi	deform_potential_fi(t − 1)	Previous day deformation potential
rainfall_mm_lag1	Rain_lag1	rainfall_mm(t − 1)	Previous day precipitation
temperature_celsius_lag1	TempLag1	temperature_celsius(t − 1)	Previous day temperature

Notes: Index Notation: i = 1, 2, 3, 4 representing foundations F1, F2, F3, and F4, respectively.

.

Foundation-specific correlation hierarchies revealed distinct predictive signatures:

• F1 (Figure 2a): Moderate correlations across moisture-derived features (NormMoist_F1, Swell_F1, DefPot_F1, %moist_F1: all r = 0.41, with range r = 0.38–0.41, all p < 0.001), indicating systematic but constrained response mechanisms
• F2 (Figure 2b): Unique seasonal sensitivity (Month_sin: r = 0.65, p < 0.001) with significant temperature-related effects, reflecting annual cycle dependencies
• F3 (Figure 2c): Consistent strong correlations across moisture-related variables (Swell_F3, %moist_F3, NormMoist_F3, DefPot_F3: all r = 0.60, with range r = 0.59–0.60, all p < 0.001) with pronounced negative temperature effects (r = −0.58 to −0.59, p < 0.001)
• F4 (Figure 2d): Highest physics-based correlations with five moisture-derived features (NormMoistLag1_F4, SwellLag1_F4, DefPotLag1_F4, MoistLag1_F4, %moist_F4: all r = 0.78), consistent with pronounced moisture-expansion response characteristics.

Statistical validation revealed 35 of 36 tested correlations achieved significance (p < 0.05), with only rainfall correlation at F1 demonstrating non-significant association.

The correlation hierarchies reflect spatially heterogeneous soil-foundation response patterns under the specific loading conditions of the monitoring frame and informed subsequent optimal feature selection for hybrid model development. These structure-specific correlations limit direct generalizability to foundations with different structural configurations, necessitating model recalibration for applications involving different structural types or loading scenarios.

2.2. Baseline Model Selection Rationale

The selection of baseline models was guided by theoretical considerations and practical engineering requirements for foundation deformation prediction. Seven baseline algorithms were selected: Linear Regression (LR), Ridge, Lasso, Elastic net (EN), Huber Regressor (Huber), Bayesian Ridge (BR), and Random Forest (RF). Four hybrid approaches were developed: Residual-Clustering Hybrid (RCH), Elastic Net Fusion (ENF), Residual Correction (RC), and Enhanced Robust Huber (ERH).

Given the dataset size (140 observations), baseline selection followed principled methodological diversity while avoiding selection bias in small-sample conditions [32,33]. The algorithms represent core paradigms: linear methods (LR, Ridge, BR), regularized approaches (Lasso, EN), robust regression (Huber), and ensemble methods (RF), ensuring comprehensive algorithmic coverage while maintaining statistical reliability for comparative evaluation [34].

LR served as the fundamental baseline, representing ordinary least squares without regularization. Ridge and Lasso regression were included to address multicollinearity and feature selection challenges common in geotechnical monitoring data. Huber was selected for its robustness to outliers commonly encountered in field monitoring data, while BR was included for its uncertainty quantification capabilities—valuable for risk assessment in foundation monitoring. RF represented non-linear methodologies and industry-standard tree-based approaches.

This selection ensures representation across multiple regression paradigms (ordinary least squares, regularized, robust, Bayesian, and tree-based approaches), enabling comprehensive evaluation of proposed hybrid models against established methodologies. All models were implemented using scikit-learn with parameters specified in

Table A2. Model Parameter Specifications for Baseline and Hybrid Models.

Baseline Models			Hybrid Models
Model Name	Key Parameters	Parameter Setting	Model Name	Key Parameters	Parameter Setting
Linear Regression	fit_intercept	True	Residual-Clustering Hybrid	n_clusters	2
Ridge	alpha	10.0		cluster_model	BayesianRidge
Lasso	alpha	0.1		cluster_predictor_trees	50
Elastic Net	alpha	0.1	Elastic Net Fusion	alpha	0.1
	l1_ratio	0.5		l1_ratio	0.5
Huber Regressor	alpha	0.1		physics_weight	0.2
	epsilon	1.35	Residual Correction	base_model	LinearRegression
Bayesian Ridge	alpha_1	1 × 10−6		corrector	Ridge (α = 2.0)
	lambda_1	1 × 10−6		correction_strength	0.05–0.18 (optimized)
Random Forest	n_estimators	50	Enhanced Robust Huber	base_alpha	0.05
	max_depth	4		base_epsilon	1.2
	min_samples_split	10		enhancer_alpha	0.2
				enhancer_epsilon	1.5
				enhancement_weight	0.1

Note: Parameter settings combine empirical testing with systematic optimization. Baseline model parameters were selected through preliminary testing for stability across foundation types. Hybrid model parameters underwent foundation-specific tuning, with physics-based weights optimized through cross-validation to balance domain knowledge integration with predictive accuracy. The “optimized” designation indicates parameters determined through systematic grid search rather than fixed values. Enhancement weights were constrained to prevent overfitting while allowing meaningful correction contributions.

, ensuring reproducibility and fair comparison. Parameter selection balanced computational efficiency with predictive stability, with baseline model parameters following established best practices while hybrid model parameters underwent systematic optimization as detailed in the respective algorithmic specifications.

2.3. Hybrid Model Development Framework

The hybrid model development followed a systematic framework combining physical understanding with data-driven approaches, following established ensemble learning principles [35] and stacked generalization theory [36].

2.3.1. Residual-Clustering Hybrid

This approach addresses the multimodal nature of foundation responses by identifying distinct deformation regimes through residual clustering, as demonstrated in Algorithm 1. The model first identifies patterns in prediction errors using K-means clustering (k = 2), then applies cluster-specific corrections through Bayesian ridge regression. This architecture captures state-dependent deformation behavior.

Algorithm 1: Residual-Clustering Hybrid

Input: Training features X_train, targets y_train, test features X_test Output: Predictions y_pred 1: base_model ← HuberRegressor(α = 0.01, ε = 1.35).fit(X_train, y_train) 2: residuals ← y_train − base_model.predict(X_train) 3: clusters ← KMeans(k = 2).fit_predict(residuals.reshape(−1,1)) 4: cluster_models ← [BayesianRidge().fit(X_train[c], residuals[c]) for c in clusters] 5: cluster_predictor ← RandomForestClassifier(50).fit(X_train, clusters) 6: test_clusters ← cluster_predictor.predict(X_test) 7: corrections ← [cluster_models[c].predict(X_test[mask]) for c, mask in test_clusters] 8: y_pred ← base_model.predict(X_test) + corrections 9: return y_pred

2.3.2. Elastic Net Fusion

This model, as demonstrated in Algorithm 2, combines elastic net regularization with physics-based feature transformation. The algorithm simultaneously performs feature selection through L1 regularization and relationship preservation through L2 regularization, while incorporating domain knowledge through engineered features representing soil moisture dynamics and thermal effects on foundation behavior.

Algorithm 2: Elastic Net Fusion

Input: Training features X_train, targets y_train, test features X_test Output: Predictions y_pred 1: base_model ← ElasticNet(α = 0.1, l1 = 0.5).fit(X_train, y_train) 2: physics_features ← extract_physics_features(X_train) 3: residuals ← y_train − base_model.predict(X_train) 4: physics_corrector ← Ridge(α = 1.0).fit(physics_features, residuals) 5: correction ← physics_corrector.predict(X_test_physics) 6: y_pred ← base_model.predict(X_test) + 0.2 × correction 7: return y_pred

2.3.3. Residual Correction

This architecture integrates domain knowledge through physically motivated feature engineering while maintaining data-driven flexibility, as demonstrated in Algorithm 3. The model first estimates baseline deformation using conventional regression, then applies physics-based corrections to residuals using features derived from moisture-temperature interactions and soil mechanics principles. This approach maintains interpretability while capturing complex nonlinear relationships.

Algorithm 3: Residual Correction

Input: Training features X_train, targets y_train, test features X_test Output: Predictions y_pred 1: base_model ← LinearRegression().fit(X_train, y_train) 2: residuals ← y_train − base_model.predict(X_train) 3: physics_features ← extract_physics_features(X_train) 4: strength ← optimize([0.05, 0.08, 0.12, 0.15, 0.18], physics_features, residuals) 5: corrector ← Ridge(α = 2.0).fit(physics_features, residuals) 6: y_pred ← base_model.predict(X_test) + strength × corrector.predict(X_test_physics) 7: return y_pred

2.3.4. Enhanced Robust Huber

This model extends the classic Huber regressor with enhanced robustness to measurement outliers and environmental noise. The algorithm, as demonstrated in Algorithm 4, incorporates dual-stage robust processing with enhanced feature construction, providing systematic treatment to potentially unreliable measurements while maintaining sensitivity to genuine deformation signals.

Algorithm 4: Enhanced Robust Huber

Input: Training features X_train, targets y_train, test features X_test Output: Predictions y_pred 1: base_model ← HuberRegressor(α = 0.05, ε = 1.2).fit(X_train, y_train) 2: base_pred ← base_model.predict(X_train) 3: enhanced_features ← concatenate([X_train, base_pred.reshape(−1,1)]) 4: residuals ← y_train − base_pred 5: enhancer ← HuberRegressor(α = 0.2, ε = 1.5).fit(enhanced_features, residuals) 6: test_enhanced ← concatenate([X_test, base_model.predict(X_test).reshape(−1,1)]) 7: y_pred ← base_model.predict(X_test) + 0.1 × enhancer.predict(test_enhanced) 8: return y_pred

All hybrid models were implemented in Python using scikit-learn as the foundation, with custom modifications to incorporate physical constraints and specialized architectures. The development process followed rigorous validation protocols including temporal cross-validation and bootstrap resampling to ensure generalizability beyond the training dataset.

2.4. Feature Engineering and Selection Protocol

The feature engineering framework incorporated domain-specific transformations guided by established geotechnical principles for expansive soil behavior [2,4], ensuring statistical robustness and physical interpretability. The ablation study empirically validates this integration by quantifying how physics-based domain knowledge and derived statistical optimization contribute through their respective operational categories, demonstrating their complementary roles in the hybrid modeling framework.

Initial feature creation included quadratic and interaction terms for moisture-temperature relationships based on unsaturated soil mechanics principles [4], logarithmic transformations for rainfall measurements to handle skewed distributions, and trigonometric encoding for temporal patterns through sine/cosine transformations. Physics-based features incorporated swelling potential relationships following established swell-shrinkage characterization methods [37]. Lagged variables incorporated first-order autoregressive terms for deformation measurements and environmental conditions to capture temporal dependencies.

The feature selection process employed Ridge regression as the primary analytical methodology, addressing multicollinearity through L2 regularization while identifying optimal feature subsets. This approach proceeded through systematic phases: computation of regularization paths across α values (10⁻⁴ to 10²) to identify stable features, k-fold temporal cross-validation to evaluate predictive performance across progressively expanded feature sets, and calculation of normalized Ridge coefficients for importance scoring. The elbow method combined with partial F-tests identified the point of diminishing returns where additional features provided statistically insignificant improvements (p > 0.05).

This methodology employed a systematic feature selection process to identify parsimonious optimal feature sets that effectively balance model complexity with predictive performance, ensuring all retained features demonstrated consistent predictive contributions across multiple regularization strengths.

2.5. Statistical Validation Methods

A multi-layered validation framework supported comprehensive performance assessment and mitigated overfitting risks. Temporal cross-validation employed a rolling-origin design with 5 folds, maintaining chronological data ordering to simulate operational forecasting conditions. Model performance evaluation utilized a comprehensive metric suite including R², adjusted R², RMSE, MAE, and MAPE, with primary emphasis on R² for model comparison due to its interpretability and domain standardization.

Statistical significance of performance differences was assessed through paired t-tests with Bonferroni correction for multiple comparisons, while effect sizes were calculated using Cohen’s d to distinguish statistical significance from practical significance. Bootstrap resampling with 1000 iterations provided confidence intervals for performance metrics [38], while temporal cross-validation employed rolling-origin design following time series validation best practices [39].

This validation approach specifically addressed temporal dependencies through time-series aware cross-validation and ensured that reported performance improvements represented genuine methodological advances rather than random variations or overfitting artifacts.

2.6. Early Warning System Design

The early warning system architecture employed statistically derived thresholds rather than arbitrary percentiles, ensuring scientific rigor in alert generation. Threshold determination utilized a parametric approach based on the distribution of historical deformation measurements, with warning levels at μ ± 1.5σ and critical levels at μ ± 2.5σ from training data means. This approach provided consistent probabilistic interpretation across all foundations while accommodating different deformation characteristics and operational monitoring capabilities within the observed range (−3.99 to +7.43 mm, Table 2). Engineering threshold validation requires comparison with established serviceability limits (10–15 mm), damage thresholds (15–25 mm), and ultimate failure criteria (30–50 mm) depending on structural type [1,2,40,41].

The system incorporated asymmetric thresholds for heave (positive deformation) and settlement (negative deformation) to reflect their different structural implications. Predictive uncertainty was quantified through bootstrap estimation of prediction intervals, providing probabilistic risk assessment capabilities for engineering decision-making [42], with alerts triggered when both the predicted value and its 95% confidence interval exceeded the statistical thresholds.

Performance validation included calculation of precision, recall, and F1 scores for both warning and critical alerts, with special attention to minimizing false negatives while maintaining manageable false positive rates. The system also incorporated temporal persistence requirements, requiring consecutive exceedances before issuing alerts, following established practices in foundation monitoring systems [43] to prevent transient fluctuations from triggering unnecessary warnings. This design provides statistically based threshold determination with operational alert capabilities, maintaining a systematic approach to foundation monitoring.

2.7. Implementation Details

All analyses were conducted using Python 3.10.13 on a Windows 10 platform with an Intel 8-core processor (4 physical cores) and 16 GB RAM. The computational framework utilized scikit-learn 1.7.1 for ML implementations, NumPy 1.26.4 and Pandas 2.2.3 for data manipulation, SciPy 1.15.3 for statistical computations, and statsmodels 0.14.4 for advanced statistical testing. Visualization was performed using Matplotlib 3.10.0 and Seaborn 0.13.2. GPU acceleration was available through NVIDIA GeForce GT 1030 (2 GB) for computationally intensive operations. All models were implemented with fixed random seeds (random_state = 42) to ensure reproducibility.

3. Results

3.1. Optimal Feature Selection Performance

The optimal feature selection employed Ridge regression analysis across four monitoring locations (Figure 3). Feature subsets ranging from 3 to 11 predictors were evaluated using training data (112 observations). Foundation F1 achieved Ridge regression test R² = 0.9260 with 4 features, Foundation F2 recorded R² = 0.9432 with 4 features, Foundation F3 obtained R² = 0.9515 with 8 features, and Foundation F4 achieved R² = 0.7966 with 4 features.

3.2. Comparative Model Performance

Comparative analysis evaluated four hybrid models against seven baseline regression techniques across all foundations (

Table A3. Comprehensive Model Performance Comparison Across Foundation Types.

Model	Train_R2	Train_RMSE	Train_MAE	Train_MAPE	Test_R2	Test_RMSE	Test_MAE	Test_MAPE	Over Fitting_Gap	BootstrapR2 (95%_CI)	CV_R2_Mean	Uncertainty_95CI	Train_Time	Test_Time	Total_Time
Foundation F1
RCH	0.987	0.144	0.081	10.14	0.945	0.381	0.308	41.93	0.042	(0.914, 0.973)	0.055	±0.6544	0.123	0.009	0.132
LR	0.976	0.198	0.129	15.2	0.926	0.44	0.349	54.07	0.049	(0.885, 0.960)	−0.402	±0.7792	0.002	0.002	0.004
BR	0.976	0.198	0.129	15.21	0.926	0.44	0.35	54.05	0.049	(0.885, 0.960)	−1.02	±0.7789	0.002	0.003	0.005
Huber	0.975	0.201	0.127	14.76	0.924	0.448	0.355	60.36	0.051	(0.873, 0.958)	−0.097	±0.8083	0.011	0.002	0.013
Lasso	0.957	0.261	0.2	22.65	0.897	0.52	0.456	55.71	0.060	(0.836, 0.930)	−5.485	±0.8629	0.002	0.002	0.004
EN	0.945	0.296	0.234	27.82	0.884	0.552	0.496	53.09	0.061	(0.823, 0.922)	−6.032	±0.8793	0.002	0.002	0.004
Ridge	0.940	0.311	0.248	31.1	0.882	0.556	0.502	51.23	0.057	(0.816, 0.922)	−9.21	±0.8474	0.002	0.002	0.004
Foundation F2
ENF	0.964	0.327	0.25	30.34	0.947	0.468	0.356	159.39	0.017	(0.897, 0.979)	−3.886	±0.9143	0.002	0.001	0.003
Lasso	0.968	0.312	0.228	30.38	0.946	0.472	0.36	163.15	0.021	(0.896, 0.979)	−2.756	±0.9238	0.002	0.005	0.008
EN	0.964	0.33	0.253	30.9	0.946	0.473	0.36	160.4	0.018	(0.892, 0.980)	−3.773	±0.9277	0.002	0.002	0.004
Huber	0.974	0.279	0.176	28.32	0.944	0.484	0.324	107.98	0.030	(0.888, 0.985)	0.274	±0.9360	0.01	0.002	0.012
BR	0.974	0.276	0.18	28.33	0.943	0.487	0.322	99.27	0.032	(0.890, 0.983)	−0.463	±0.9471	0.002	0.003	0.005
LR	0.974	0.276	0.18	28.35	0.943	0.487	0.322	99.33	0.032	(0.890, 0.983)	−0.244	±0.9483	0.002	0.002	0.003
Ridge	0.963	0.332	0.256	30.52	0.941	0.494	0.329	99.96	0.022	(0.875, 0.982)	−4.868	±0.9190	0.002	0.002	0.004
Foundation F3
RC	0.962	0.178	0.113	61.35	0.963	0.386	0.287	57.46	−0.001	(0.932, 0.983)	−0.124	±0.7409	0.008	0.001	0.008
LR	0.959	0.183	0.119	64.79	0.956	0.421	0.294	57.17	0.004	(0.920, 0.984)	−0.134	±0.8048	0.003	0.003	0.006
BR	0.959	0.183	0.119	65.43	0.954	0.428	0.307	56.43	0.005	(0.919, 0.982)	−0.263	±0.8045	0.002	0.002	0.004
Huber	0.95	0.203	0.107	54.93	0.951	0.444	0.354	55.08	−0.001	(0.924, 0.970)	0.402	±0.7231	0.014	0.002	0.016
Lasso	0.92	0.258	0.219	124.74	0.917	0.576	0.494	66.79	0.002	(0.884, 0.946)	−4.855	±1.0690	0.002	0.002	0.004
EN	0.909	0.275	0.238	132.22	0.84	0.802	0.703	61.37	0.069	(0.772, 0.879)	−3.8	±1.2196	0.002	0.002	0.004
Ridge	0.9	0.288	0.246	131.92	0.761	0.98	0.864	109.93	0.139	(0.642, 0.834)	−2.889	±1.2033	0.002	0.002	0.004
Foundation F4
ERH	0.944	0.326	0.19	56.67	0.881	0.522	0.319	8.12	0.063	(0.713, 0.940)	0.763	±0.9770	0.016	0	0.017
Huber	0.946	0.32	0.191	57.15	0.872	0.542	0.355	8.9	0.074	(0.698, 0.934)	0.767	±0.9893	0.01	0.002	0.011
LR	0.95	0.308	0.2	58.01	0.801	0.676	0.536	12.45	0.149	(0.591, 0.873)	0.776	±1.1731	0.002	0.002	0.004
BR	0.95	0.308	0.201	58.06	0.799	0.679	0.541	12.58	0.151	(0.589, 0.872)	0.771	±1.1688	0.002	0.002	0.004
Lasso	0.935	0.351	0.272	60.97	0.539	1.028	0.904	20.27	0.396	(0.266, 0.650)	−0.179	±1.0228	0.002	0.002	0.004
EN	0.923	0.382	0.308	63.62	0.326	1.243	1.13	24.78	0.597	(−0.079, 0.501)	−0.319	±1.0636	0.002	0.002	0.004
Ridge	0.916	0.398	0.32	67.25	0.218	1.339	1.248	27.18	0.698	(−0.284, 0.412)	−0.628	±0.9530	0.002	0.002	0.004

). Performance metrics included test R², RMSE, MAE, overfitting gaps, and 95% bootstrap confidence intervals. Residual-Clustering Hybrid achieved R² = 0.945 (F1), Elastic Net Fusion achieved R² = 0.947 (F2), Residual Correction achieved R² = 0.963 (F3), and Enhanced Robust Huber achieved R² = 0.881 (F4).

3.3. Statistical Significance Testing

Statistical hypothesis testing employed paired t-tests with Bonferroni correction across 28 model comparisons. Effect sizes were quantified using Cohen’s d (

Table 5. Statistically Significant Hybrid Model Improvements.

Foundation	Hybrid Model	Baseline Comparison	t-Statistic	p-Value	Cohen’s d	Effect Size	Performance Gain
F1	Residual-Clustering Hybrid	Ridge	5.366	0.001279 *	0.711	Medium	ΔR2 = +0.063
		EN	4.834	0.005326 *	0.669	Medium	ΔR2 = +0.061
F2	Elastic Net Fusion	(No significant improvements)	-	>0.05	<0.05	Negligible	-
F3	Residual Correction	Ridge	5.710	0.000510 *	1.507	Very Large	ΔR2 = +0.202
		EN	5.627	0.000636 *	1.135	Large	ΔR2 = +0.123
F4	Enhanced Robust Huber	Ridge	7.396	0.000007 *	1.494	Very Large	ΔR2 = +0.663
		EN	6.238	0.000127 *	1.201	Very Large	ΔR2 = +0.555
		RF	6.576	0.000053 *	1.805	Very Large	ΔR2 = +0.431
		Lasso	5.408	0.001141 *	0.854	Large	ΔR2 = +0.342
		LR	4.185	0.030339 *	0.259	Small	ΔR2 = +0.080
		BR	4.274	0.023901 *	0.264	Small	ΔR2 = +0.082

Note: 10 statistically significant improvements from 28 total comparisons (35.7% success rate). * Significant at α = 0.05 after Bonferroni correction for 28 multiple comparisons.

). Results showed 10 statistically significant improvements from 28 total comparisons (35.7% success rate), with effect sizes ranging from small to very large magnitudes (Cohen’s d = 0.259–1.805).

3.4. Time Series Forecasting Accuracy

Time series forecasting employed chronological train-test partitioning (80%/20%) maintaining temporal dependency integrity (Figure 4). Forecasting performance achieved R² values of 0.881–0.963 with RMSE ranging from 0.381 to 0.522 mm across the 28-day test period. Uncertainty intervals ranged from ±0.654 mm (F1) to ±0.977 mm (F4) using bootstrap resampling with 1000 iterations.

3.5. Feature Importance and Ablation Analysis

Feature importance analysis employed RF regression across four monitoring locations (Figure 5). Temporal persistence dominated predictive relationships, with one-step lagged target variables accounting for 93.5–97.4% of total feature importance across all foundations.

Systematic ablation study evaluated feature group contributions through controlled removal and model retraining (

Table 6. Feature Group Ablation Study Results.

Foundation	Full Model R2	−Physics Features	−Temporal Features	−Environmental Features	Critical Feature Group
F1	0.945	0.945 (0.000)	0.000 (−0.945)	0.855 (−0.090)	Temporal
F2	0.947	0.947 (0.000)	0.000 (−0.947)	0.897 (−0.050)	Temporal
F3	0.963	0.963 (0.000)	0.108 (−0.855)	0.913 (−0.050)	Temporal
F4	0.881	0.881 (0.000)	0.000 (−0.881)	0.843 (−0.038)	Temporal

Note: Values in parentheses show performance degradation. Physics features include moisture-based derived variables.

). Temporal feature removal resulted in catastrophic performance degradation (ΔR² = −0.855 to −0.947). Physics-based feature removal produced no measurable impact (ΔR² = 0.000 across all foundations). Environmental feature removal showed moderate impacts (ΔR² = −0.038 to −0.090).

3.6. Early Warning System Performance

Early warning system implementation employed statistically derived thresholds (μ ± 1.5σ for warnings, μ ± 2.5σ for critical alerts) from training data distributions (Figure 6,

Table 7. Early Warning System Performance Metrics.

Foundation	Model	Warning Events	Critical Events	Precision	Recall	F1-Score	Prediction Accuracy	Thresholds Used
F1	Residual-Clustering Hybrid	9/28 (32.1%)	7/28 (25.0%)	1.000	0.818	0.900	0.765	4
F2	Elastic Net Fusion	11/28 (39.3%)	6/28 (21.4%)	0.909	1.000	0.952	0.771	4
F3	Residual Correction	17/28 (60.7%)	13/28 (46.4%)	0.941	1.000	0.970	0.807	4
F4	Enhanced Robust Huber	27/28 (96.4%)	26/28 (92.9%)	1.000	0.964	0.982	0.655	4

Note: Warning thresholds determined by statistical analysis of training data (μ ± 1.5σ for warning, μ ± 2.5σ for critical). All models employed asymmetric thresholds for heave and settlement conditions.

). Performance metrics achieved F1-scores of 0.900–0.982, precision values of 0.909–1.000, and prediction accuracies of 0.655–0.807 across all foundations. Alert generation ranged from 32.1% (F1) to 96.4% (F4) for warning events.

4. Discussion

4.1. Temporal Dominance and Feature Hierarchy Implications

The overwhelming dominance of temporal features over physics-based variables indicates that foundation deformation processes exhibit stronger autoregressive characteristics than previously recognized in geotechnical modeling.

Temporal persistence emerged as the dominant predictor across all foundations, with one-step lagged target variables (target_lag1) accounting for 93.5–97.4% of total feature importance. Foundation F2 exhibited the highest temporal dependence (97.4%), indicating strong autoregressive characteristics in its deformation response, while Foundation F4 demonstrated relatively lower but still dominant temporal persistence (93.5%). This overwhelming dominance of lagged deformation measurements confirms the strong memory effects inherent in soil-structure interaction processes, consistent with established understanding of expansive soil behavior where moisture-induced volume changes exhibit pronounced temporal persistence [2].

Secondary feature importance patterns revealed distinct foundation-specific predictive signatures reflecting localized soil conditions and environmental sensitivities. Foundation F1 demonstrated the strongest dependence on contemporary soil moisture content (4.8% importance), suggesting direct moisture-deformation coupling mechanisms. In contrast, Foundation F2 exhibited minimal secondary feature contributions, with moisture content accounting for only 1.4% importance, reflecting its predominantly autoregressive behavior pattern.

Environmental variables displayed heterogeneous importance distributions across monitoring locations. Foundations F3 and F4 showed pronounced rainfall sensitivity (4.1% and 3.6% importance, respectively), indicating susceptibility to precipitation-driven moisture changes and subsequent deformation responses. Temperature effects varied systematically, ranging from minimal influence at Foundation F1 (0.2%) to highest contribution at Foundation F4 (1.1%), with Foundation F2 showing moderate sensitivity (0.9%) and Foundation F3 demonstrating intermediate response (1.0%), reflecting differential thermal expansion characteristics across the monitoring array.

Physics-based features demonstrated foundation-specific relevance patterns, with derived moisture variables showing measurable but limited individual contributions. Foundation F3 exhibited the most comprehensive physics-based feature representation, with moisture derivatives including squared terms, deformation potentials, normalized moisture, and swelling potentials collectively contributing approximately 0.8% importance across multiple engineered variables. However, individual physics-based features consistently ranked lower than environmental drivers, suggesting that while physically meaningful, their predictive contribution operates primarily through collective rather than individual mechanisms.

The feature importance hierarchy validated the multi-scale modeling approach, with temporal, environmental, and physics-based features providing complementary predictive contributions despite the overwhelming dominance of autoregressive terms. The systematic variation in secondary feature importance across foundations confirmed the necessity of foundation-specific feature selection protocols and supported the spatial heterogeneity observed in correlation analysis and deformation patterns.

The optimal feature selection analysis revealed foundation-specific complexity requirements, with three foundations (F1, F2, F4) achieving optimal performance using 4 features while Foundation F3 required 8 features for comparable accuracy. Environmental features provided moderate but consistent contributions, confirming their complementary role in foundation deformation modeling.

4.2. Foundation-Specific Modeling Requirements and Heterogeneity

The results advance geotechnical prediction theory by demonstrating foundation-specific modeling requirements that challenge conventional uniform approaches across different soil-structure interaction environments. The varying hybrid model effectiveness (ΔR² = +0.001 to +0.663) reflects genuine geotechnical complexity rather than algorithmic limitations, with statistical validation confirming that 35.7% of hybrid model comparisons achieved statistical significance with effect sizes ranging from small to very large magnitudes (Cohen’s d = 0.259–1.805).

The hybrid modeling framework demonstrates systematic integration of multiple prediction methodologies within foundation-specific optimization contexts. Each approach addressed distinct challenges: residual clustering (F1) captured multimodal deformation regimes, elastic net fusion (F2) achieved computational efficiency, residual correction (F3) provided the highest predictive performance, and enhanced robust Huber (F4) handled measurement outliers effectively.

Foundation F2 exhibited comparable performance between hybrid and baseline approaches, consistent with the No Free Lunch theorem [44]. The Elastic Net Fusion hybrid model achieved R² = 0.947 with RMSE = 0.468 mm, representing minimal improvement over the Lasso baseline (R² = 0.946, RMSE = 0.472 mm, ΔR² = +0.001). Despite the hybrid model’s computational efficiency advantages (training time: 0.003s vs. 0.008s for Lasso), the negligible performance improvement indicates that simpler baseline models should be preferred for operational deployment to reduce architectural complexity without sacrificing predictive capability.

The systematic variation in model effectiveness indicates that hybrid approaches provide greatest benefits for foundations exhibiting complex deformation patterns or requiring robust generalization, while foundations with predictable responses show minimal performance differentials. The consistent maintenance of forecasting accuracy across diverse foundation characteristics and environmental conditions demonstrates the operational viability of the hybrid modeling approach for foundation deformation monitoring with quantified uncertainty bounds.

4.3. Advanced Analysis and Model Extensions

The ablation analysis revealed overwhelming dependence on temporal features across all foundations, with complete elimination reducing test R² to effectively zero for Foundations F1, F2, and F4 (R² = 0.000), representing catastrophic performance degradations of −0.945, −0.947, and −0.881, respectively. Foundation F3 exhibited marginally better resilience (R² = 0.108), though still constituting severe degradation (−0.855). This universal collapse underscores the critical importance of autoregressive components in capturing foundation deformation dynamics and confirms that foundation responses exhibit pronounced memory effects that cannot be adequately modeled through instantaneous measurements alone.

Physics-based feature removal produced no measurable impact across all foundations (ΔR² = 0.000), indicating complete redundancy with information captured by temporal features. This finding suggests that domain knowledge integration requires careful consideration in temporal prediction contexts [45], where autoregressive signals can capture physics-based relationships. Environmental features demonstrated moderate but consistent importance, with removal resulting in performance degradations ranging from −0.038 (F4) to −0.090 (F1), providing complementary boundary condition information not captured by temporal features.

The ablation study revealed remarkably consistent feature group hierarchies across diverse foundation types and hybrid model architectures. Despite employing different hybrid modeling approaches—Residual-Clustering (F1), Elastic Net Fusion (F2), Residual Correction (F3), and Enhanced Robust Huber (F4)—all models exhibited identical feature group importance rankings: Temporal >> Environmental >> Physics-based.

This consistency suggests fundamental characteristics of the foundation deformation prediction problem rather than model-specific artifacts. The universal temporal dominance implies that foundation responses are inherently autoregressive processes where past deformation states provide the most informative predictive signals. The moderate environmental contribution indicates that external driving forces (temperature, rainfall) provide additional predictive value beyond historical patterns, while the absence of physics-based feature impact suggests that explicit domain knowledge integration may be less critical when strong temporal signals are available.

While domain knowledge-driven feature creation remains valuable for interpretability and physical understanding, the ablation analysis demonstrates that physics-based features contribute zero measurable predictive value (ΔR² = 0.000 across all foundations) when temporal information is available. In contrast, environmental features provide consistent modest contributions (ΔR² = −0.038 to −0.090 when removed), serving as essential boundary condition information that supports model reliability during extreme weather events when historical patterns may diverge from training conditions. This indicates that optimal predictive performance requires temporal persistence combined with environmental drivers, while physics-based features can be excluded without performance degradation.

While physics-based features demonstrated no incremental predictive value in the ablation analysis, their retention serves crucial interpretability functions in engineering practice. The identical correlation coefficients (Table 4) and mathematical relationships (Table A1) provide mechanistic understanding of moisture-deformation coupling, supporting engineering judgment and model validation. Future hybrid frameworks could implement physics-based features as interpretability layers while leveraging temporal features for predictive accuracy, maintaining the balance between operational performance and engineering insight.

Systematic evaluation of temporal lag dependencies was conducted to determine optimal lag orders for foundation-specific modeling (Figure 7). The analysis evaluated lag orders from 1 to 14 days using the same training/testing protocol as the comprehensive model comparison. Results demonstrate foundation-specific optimal lag characteristics, with 1-day lags consistently providing superior performance across all foundations (R² = 0.881–0.956). Performance degradation beyond 3-day lags indicates short-term memory characteristics in expansive soil systems, where immediate moisture-deformation coupling dominates longer-term seasonal patterns. The analysis validates the temporal feature selection approach while informing future research directions for lag order optimization in diverse soil conditions.

Transfer learning effectiveness was evaluated across foundation behavioral types to assess model adaptability and data requirement reduction (Figure 8). The analysis employed pre-training on source foundations followed by fine-tuning on target foundations using the same hybrid architectures. Results demonstrate foundation-type-specific transferability patterns, with 80% overall success rate (8/10 transfer scenarios achieving viable performance). Settlement-to-settlement transfers (F1 → F3: R² = 0.965) and cross-behavioral transfers (F1 → F2: R² = 0.920) showed strong effectiveness. Transfer learning to Foundation F4 exhibited limited success, reflecting F4’s inherently challenging deformation characteristics (lowest baseline R² = 0.881). The analysis indicates potential for reducing data requirements in foundation monitoring through strategic model transfer, particularly within similar behavioral categories.

4.4. Practical Implementation and Operational Considerations

The foundation-specific modeling approach provides practical capabilities for expansive soil foundation monitoring through quantified prediction accuracies and uncertainty bounds that support operational decision-making for infrastructure maintenance and risk management. The demonstrated performance metrics (F1-scores: 0.900–0.982, precision: 0.909–1.000, prediction accuracies: 0.655–0.807) establish baseline capabilities for integration into existing monitoring infrastructure.

The early warning system implementation employs statistically derived thresholds (μ ± 1.5σ for warnings, μ ± 2.5σ for critical alerts) providing consistent probabilistic interpretation across diverse foundation types while maintaining manageable false alarm rates. The operational effectiveness demonstrates foundation-specific calibration capabilities suitable for infrastructure monitoring applications.

The visualization reveals foundation-specific threshold calibration and alert generation patterns across diverse deformation behaviors. Foundation F1 (Figure 6a) exhibited conservative alert generation with warning and critical thresholds appropriately positioned to capture settlement progression without excessive false alarms. The Residual-Clustering Hybrid model’s predictions remained within confidence intervals while successfully triggering alerts during significant deformation events.

Foundation F2 (Figure 6b) demonstrated balanced threshold sensitivity through the Elastic Net Fusion model, with alert generation occurring during both heave and settlement phases. The warning thresholds captured intermediate deformation events while critical alerts were reserved for more severe movements. Foundation F3 (Figure 6c) showed the highest alert frequency, with the Residual Correction model generating numerous warning and critical alerts throughout the monitoring period, reflecting the foundation’s pronounced deformation activity and the system’s appropriate sensitivity calibration.

Foundation F4 (Figure 6d) exhibited the most active alert profile with the Enhanced Robust Huber model generating nearly continuous warning alerts and frequent critical alerts throughout the test period. The high alert frequency aligns with Foundation F4’s dynamic deformation characteristics and validates the system’s adaptation to high-variability conditions.

The visual evidence in Figure 6 demonstrates successful threshold positioning relative to actual deformation trajectories, validating the statistical approach to threshold calibration. The reported uncertainty intervals (±0.654 to ±0.977 mm) represent prediction confidence bounds significantly smaller than critical engineering thresholds, being approximately 15–20 times smaller than typical serviceability limits [40,41] and 40–60 times smaller than damage thresholds [1], providing substantial safety margins for operational decision-making.

The integrated framework contributes to advancing ML applications in geotechnical engineering while addressing specific challenges of expansive soil prediction through domain-informed feature engineering and quantified uncertainty bounds for operational risk assessment.

4.5. Methodological Insights and Statistical Validation

Statistical validation protocols incorporating bootstrap confidence intervals, cross-validation procedures, and multiple comparison corrections established rigorous evaluation standards for geotechnical prediction model assessment. The integration of uncertainty quantification through parametric threshold determination provided a framework for operational risk assessment in foundation monitoring applications, while temporal validation methodology ensures realistic performance assessment under operational forecasting conditions.

The feature engineering and selection protocols establish systematic approaches for optimizing predictive models within limited data environments common in geotechnical applications. The Ridge regression framework employed multiple evaluation criteria including adjusted R², BIC, and partial F-tests to balance predictive accuracy with model complexity, while the ablation study framework provides guidance for efficient feature utilization in resource-constrained monitoring scenarios.

Foundation-specific feature complexity analysis revealed systematic variation in modeling requirements, with BIC values ranging from 50.3 (F1) to 74.8 (F4) indicating prediction difficulty levels. The consistent 4-feature optimization for Foundations F1, F2, and F4 suggests similar fundamental deformation mechanisms, while Foundation F3’s requirement for 8 features indicates more complex soil-structure interaction patterns requiring enhanced feature representation. Foundation F3’s requirement for 8 features reflects genuine geotechnical complexity rather than overfitting, as evidenced by its superior generalization performance (R² = 0.963) and negative overfitting gap (−0.001), indicating slightly better test than training performance. The expanded feature requirement aligns with Foundation F3’s observed behavioral characteristics, including the most comprehensive physics-based feature correlations and sustained deformation patterns that required enhanced representational capacity for accurate prediction.

The statistical significance framework employed Bonferroni correction across 28 model comparisons, prioritizing Type I error control while ensuring reported improvements represent genuine rather than chance discoveries. The overall validation rate of 35.7% (10 significant improvements from 28 comparisons) reflects conservative testing standards while confirming performance advantages. Foundation-specific success rates varied dramatically: F4 achieved significance in 6 of 7 comparisons, F1 and F3 each achieved 2 of 7 significant results, while F2 achieved no significant improvements. This distribution indicates that hybrid model effectiveness exhibits strong foundation-specific characteristics, with benefits concentrated in challenging prediction environments characterized by complex soil-foundation interaction mechanisms under static loading conditions.

The statistical framework confirms that hybrid modeling approaches provide demonstrable and significant improvements over conventional methods for specific foundation types under static loading conditions, with validation concentrated in cases where baseline methods encounter fundamental limitations in capturing temporal soil-moisture interaction patterns.

4.6. Limitations and Future Research Directions

Several limitations constrain the generalizability of these findings. The findings and models presented in this study are based on data collected from a single site with medium-expansive soil under specific semi-arid climatic conditions. While the methodology may be transferable, direct application to significantly different soil types (e.g., high-plasticity clays) or climate regimes (e.g., monsoon regions) would require validation with site-specific data.

The higher feature complexity required to model F3’s deformation (8 features vs. 4 for other foundations) suggests more intricate soil-structure interaction at that location. While the exact cause (e.g., localized variation in soil composition, compaction, or micro-climatic effects) could not be determined from the current dataset, this finding highlights the value of future studies incorporating detailed spatial soil profiling and multi-depth moisture monitoring at each footing to explicitly guide feature engineering for complex foundations.

The 140-observation dataset represents a substantial temporal scope for geotechnical monitoring studies, spanning 974 days of continuous foundation behavior across complete seasonal cycles. This sample size exceeds minimum requirements for seasonal time series analysis [46] and provides adequate foundation-specific modeling capability with feature-to-sample ratios of 4–8 features per foundation using 112 training observations [30]. The temporal validation approach using chronological splitting ensures realistic assessment of forecasting performance under operational conditions [39], while bootstrap resampling with 1000 iterations provides robust confidence interval estimation despite the constrained sample size [38].

The training sample size of 112 observations constrained feature selection optimization and may limit model complexity in applications with larger datasets. The study’s deformation range (−3.99 to +7.43 mm, Table 2) represents early-stage foundation response well below established engineering failure thresholds, with future applications requiring validation against structure-specific serviceability limits and damage criteria [1,2,40,41].

The measurement validation approach employed cross-validation between dial gauges, Bosch line lasers, and LEICA digital levels [6]. However, comprehensive noise quantification protocols and outlier detection analyses were not extensively documented in the source study, representing a limitation that future research should address to enhance measurement reliability and model training stability.

The parametric threshold approach (μ ± 1.5σ, μ ± 2.5σ) provides consistent probabilistic interpretation but could be enhanced through precision-recall optimization for safety-critical applications. Future implementations should consider project-specific risk tolerance through ROC curve analysis and cost-weighted threshold selection, enabling dynamic calibration based on operational requirements. The demonstrated F1-scores (0.900–0.982) establish baseline performance for comparative evaluation of alternative threshold methodologies.

The demonstrated computational efficiency (training: 0.002–0.123 s per foundation) indicates potential for efficient multi-foundation applications based on the four-foundation framework tested. The hybrid architectures balance computational efficiency with predictive accuracy through parsimonious feature selection (4–8 features) and optimized algorithms. Future implementations could explore lightweight architectures including simplified neural networks or reduced-complexity ensemble methods to further enhance computational efficiency for expanded monitoring applications while maintaining comparable predictive performance.

Future research should extend the hybrid modeling framework to diverse soil classifications and multi-site validation across different geographical regions and climatic zones to enhance framework generalizability. Integration of additional sensor modalities, including ground-penetrating radar, distributed fiber optic sensing, and satellite-based monitoring, could provide enhanced spatial coverage and temporal resolution. This study used soil moisture data only at a depth of 60 cm due to data availability. Future work could incorporate multi-depth moisture sensors (e.g., at 30 cm, 60 cm, and 90 cm) to better capture moisture dynamics throughout the active zone, which may enhance the prediction of vertical deformation in expansive soils.

Advanced modeling approaches incorporating deep learning architectures and adaptive frameworks that automatically adjust to changing environmental conditions represent promising research directions for long-term monitoring applications. The framework addresses static foundation deformation under quasi-static environmental loading, with applicability limited to moisture-induced volume changes in expansive soils rather than dynamic or seismic loading scenarios.

5. Conclusions

This study developed foundation-specific hybrid modeling approaches for deformation prediction on expansive soils using 974 days of monitoring data. Key findings are as follows:

• Foundation-specific effectiveness: Hybrid models achieved superior performance with varying improvements (ΔR² = +0.001 to +0.663) across four foundations, with 35.7% achieving statistical significance
• Temporal dominance: Autoregressive features provided overwhelming predictive power (removing temporal features caused catastrophic failure: ΔR² = −0.855 to −0.947)
• Operational reliability: Early warning systems achieved F1-scores of 0.900–0.982 with quantified uncertainty bounds (±0.654–0.977 mm)
• Foundation-specific optimization: Different complexity requirements (4–8 features) reflect spatial heterogeneity in soil-structure interactions

The framework provides immediate value for infrastructure monitoring through enhanced prediction accuracy and statistically derived alert systems. The framework addresses static foundation deformation under quasi-static environmental loading, with applicability limited to moisture-induced volume changes in expansive soils rather than dynamic or seismic loading scenarios.

Future research should extend the methodology to diverse soil types and climatic conditions and incorporate multi-depth moisture monitoring to enhance spatial coverage and temporal resolution capabilities for long-term foundation behavior assessment.