Advanced hybrid machine learning models for estimating chloride penetration resistance of concrete structures for durability assessment: optimization and hyperparameter tuning

The database comprises 843 data points that capture D _nssm values across various types of concrete. This database is collected from two channels: i) academic research projects [36], and ii) publications in international journals [21], 27], [37], [38], [39], [40], [41], [42]. The D _nssm values serve as indicators for evaluating concrete’s ability to withstand chloride ion infiltration, as illustrated in Figure 1.

Figure 1:

Chloride penetration resistance.

The dataset comprises diverse concrete classifications, including conventional, lightweight, enhanced-strength, advanced-performance, and self-consolidating concrete. These concrete mixes are characterized by eight attributes that detail the components and their proportions: water-to-binder ratio, quantities of binders (slag, cement, silica fume, lime filler, and fly ash) measured in kg/m³, amounts of fine and coarse aggregates in kg/m³, and levels of chemical additives (air-entraining agents, superplasticizers, and plasticizers) as a percentage of the binder’s weight.

The database encompasses various cement varieties documented in diverse standards as experimental data has been gathered from numerous regions of the world. To ensure uniformity, all cement types are standardized based on the European standard EN 197-1. This standard classifies cement into 27 unique types, organized into five main categories, as depicted in Figure 2. Within the database, there are 15 cement types representing the four primary cement groups as illustrated in Figure 3. Around 57 % of the experiments conducted incorporate supplementary cementitious materials. The water-to-binder ratio spans from 0.19 to 0.65. Within the dataset, admixtures consist of numerous compounds, including superplasticizers containing polycarboxylate ether, naphthalene, melamine sulfonate, and lignosulfonate, as well as air-entraining agents composed of vinsol resin, synthetic surfactants, and fatty acid soap. The statistical distribution of the features is given in Table 1. Further, box plots of the features and D _nssm are depicted in Figure 4.

Figure 2:

Cement groups (EN 197-1).

Figure 3:

Cement types utilized in the database.

Figure 4:

Statistical distribution of the features and label.

Correlation heatmaps were utilized to evaluate multicollinearity issues. In the Spearman correlation matrix (Figure 5), a notable correlation exists between D _nssm and the water-to-binder ratio (W/B), with a coefficient of 0.57. This correlation is followed by water (0.45), fine aggregate (FA, 0.12), and coarse aggregate (CA, 0.07). Additionally, there are negative correlations of −0.36, −0.32, −0.21, −0.14, −0.13, and −0.12 with silica fume (SF), migration test age (MT Age), slag, total aggregate (TA), superplasticizer (SP), and fine aggregate (FA), respectively. Likewise, in the Pearson correlation matrix (Figure 6), W/B exhibits the strongest linear association, with a correlation coefficient of 0.38, followed by CA (0.10) and TA (0.03). Conversely, there are negative correlations of −0.27 and −0.22 with SP and MT Age, respectively. As all features have correlation coefficients below 0.8, multicollinearity is not present.

Figure 5:

Spearman correlation heatmap.

Figure 6:

Pearson correlation heatmap.

The dataset consisted of 843 data points collected from academic journals and research projects, covering a wide range of concrete mixes. To ensure data quality, errors and duplicates were removed, and missing values were handled using manual and naïve imputation [43], 44]. Box plots were used to detect and remove outliers. Some features, like water, cement, and slag, had highly skewed distributions. Although log transformations were considered to correct this, standardizing the data with StandardScaler was enough to handle the skewness without changing the original meaning of the features.

All input features were scaled to have zero mean and unit variance to improve model stability and performance. Correlation analysis using Pearson and Spearman methods confirmed that all variables had correlation coefficients below 0.8, indicating low multicollinearity. The dataset had a high data-to-variable ratio (76.6), exceeding the recommended minimum and reducing the risk of overfitting [45], 46]. Additionally, 30 % of the data was reserved for testing and validation. For the hybrid models, parameter values for the metaheuristic algorithms (GWO, GTO, FFA, and PSO) were initially based on literature. A preliminary sensitivity analysis was also performed to fine-tune the parameters and ensure good optimization performance for the SVR models.

The optimization techniques PSO, GWO, FFA, and GTO were utilized to enhance the predictive performance of the SVR model in determining the D _nssm. An overview of the model development process is presented in Figure 7. The key SVR parameters include the radial basis function (RBF) kernel width (g) and penalty factor (C), each constrained within the range of 0.01–100. The parameter configurations for the ML models are as follows: In FFA, the absorption coefficient (α) is set to 0.2, the randomization parameter (rand) is 0.93, the initial attractiveness coefficient (β ₀) is 2, and the light intensity absorption coefficient (γ) is 1. For GWO, the control variable (a) reduces in a linear fashion from an initial value of 2 down to 0. In PSO, the maximum velocity (V _max) is defined as 6, while the minimum (w _min) and maximum (w _max) inertia weights are 0.2 and 0.8, respectively. Additionally, the cognitive coefficient (c ₁) and social coefficient (c ₂) are assigned values of 1.6 and 1.8, respectively, to regulate swarm behaviour during optimization. The GTO algorithm utilizes 20 candidate solutions per iteration, with a maximum of 50 optimization iterations. A reproducibility seed of 42 ensures consistency in results, while the perturbation range is set at ±0.1. The candidate solution adjustment follows a random uniform perturbation mechanism based on both exploitation and exploration strategies. These optimized parameter settings enhance the efficiency of the SVR model in predicting the response parameter.

Figure 7:

Overview of hybrid model development.

Every model is subjected to a comprehensive assessment procedure, which involves computing a range of performance indicators to evaluate its effectiveness (Figure 8). The mathematical formulations for these statistical indices are provided in Eqs. (1–6). (1) R 2 = ∑ i = 1 i = n P i − P ‾ i Q i − Q ‾ i 2 ∑ i = 1 i = n P i − P ‾ i 2 ∑ i = 1 i = n Q i − Q ‾ i 2 $${R}^{2}=\frac{{\left[\sum _{i=1}^{i=n}\left({P}_{i}-{\bar{P}}_{i}\right)\left({Q}_{i}-{\bar{Q}}_{i}\right)\right]}^{2}}{\sum _{i=1}^{i=n}{\left({P}_{i}-{\bar{P}}_{i}\right)}^{2}\sum _{i=1}^{i=n}{\left({Q}_{i}-{\bar{Q}}_{i}\right)}^{2}}$$ (2) Adj R 2 = 1 − 1 − R 2 N − 1 N − K n − 1 $$\text{Adj\,}{R}^{2}=1-\frac{\left(1-{R}^{2}\right)\left(N-1\right)}{N-{K}_{{n}^{-1}}}$$ (3) RMSE = 1 N ∑ i = 1 i = n P I − Q i 2 $$\text{RMSE}=\sqrt{\frac{1}{N}\sum _{i=1}^{i=n}{\left({P}_{I}-{Q}_{i}\right)}^{2}}$$ (4) MAE = 1 N ∑ i = 1 i = n P i − Q i $$\text{MAE}=\frac{1}{N}\sum _{i=1}^{i=n}\left\vert {P}_{i}-{\mathrm{Q}}_{i}\right\vert $$ (5) a 10 − index = R 10 N $$a10-\text{index}=\frac{R10}{N}$$ (6) a 20 − index = R 20 N $$a20-\text{index}=\frac{R20}{N}$$ Where P _i depicts the actual value, while Q _i represents the anticipated value, where N refers to the total observations, and K _n represents the number of predictors. The letter with a bar on top represents the average values. R20 denotes the anticipated number of values falling within the ratio range of 0.90–1.20 for experimental-to-predicted values, whereas R10 represents the count of values within the range of 0.80–1.10.

Figure 8:

Performance indicators for assessing model efficacy.

Regression analysis is crucial for evaluating the predictive accuracy of ML models by quantifying the alignment between predicted and observed values (Figure 9). A regression coefficient close to 1, particularly above 0.8, demonstrates the model’s effectiveness in capturing complex relationships [47], 48]. The obtained regression slopes validate the performance of the suggested SVR-based hybrid models (Figure 10). During the training phase, SVR-GTO exhibited the highest slope (0.93), followed by SVR-GWO (0.92), while SVR-PSO and SVR-FFA both achieved a slope of 0.85. In the testing phase, the regression slopes further improved, with SVR-GTO increasing to 0.96, SVR-GWO reaching 0.93, SVR-PSO attaining 0.91, and SVR-FFA maintaining a strong slope of 0.88. These results confirm the robustness of the models in estimating chloride penetration resistance in concrete, ensuring minimal deviation from experimental values and reinforcing their applicability in engineering practices. Additionally, Figure 11 presents an evaluation of the prediction accuracy by comparing actual and predicted values, along with the corresponding relative errors.

Figure 9:

Scatter plots comparing predicted and actual values.

Figure 10:

Regression analysis of the developed models.

Figure 11:

Evaluation of prediction accuracy using actual, predicted, and relative error values.

The statistical assessment of the ML models was conducted utilizing key performance indicators for both the training and testing phases (Table 2). In the training phase, SVR-GTO achieved the highest accuracy with an R ² of 0.95 and an RMSE of 2.95, followed closely by SVR-GWO (R ² = 0.94, RMSE = 3.12). SVR-PSO and SVR-FFA demonstrated slightly lower performance, with R ² values of 0.92 and 0.90, and RMSE values of 3.45 and 3.56, respectively.

In the testing phase, SVR-GTO again outperformed other models, attaining the highest R ² of 0.97 and the lowest RMSE of 0.93, indicating strong generalization. SVR-GWO maintained solid performance (R ²  = 0.92, RMSE = 1.55), while SVR-PSO and SVR-FFA yielded R ² values of 0.91 and 0.89, and RMSE values of 1.67 and 2.13, respectively. These findings confirm the superior accuracy and reliability of the SVR-GTO model in predicting chloride penetration resistance (Figure 12). The superior performance of SVR-GTO can be attributed to the unique exploration–exploitation balance of the GTO algorithm. GTO simulates the complex social behavior and dynamic movement patterns of gorilla troops, enabling it to effectively avoid local optima and explore the solution space more thoroughly. Its adaptive strategy and strong global search capability make it particularly suitable for high-dimensional, nonlinear problems such as predicting chloride diffusion in concrete.

Figure 12:

Spider plots of statistical indicator scores.

The relative importance of input features in predicting D _nssm is illustrated in Figure 13 through SHAP analysis. The W/B exhibited the highest mean SHAP value (+3.8), underscoring its dominant influence on model predictions. MT Age followed with a mean value of +2.6, indicating its strong contribution to chloride resistance. TA and SP also demonstrated notable impacts, with SHAP values of +0.8 and slightly lower, respectively. Furthermore, fly ash and slag each contributed with a value of +0.6, while CA, cement, and SF showed smaller but meaningful effects, with SHAP values of 0.5, 0.3, and 0.2, respectively. These findings highlight the critical roles of mixture composition and curing age in determining chloride ingress behavior in concrete.

Figure 13:

Mean SHAP plot: assessing feature’s significance.

A rise in the W/B ratio is associated with a positive SHAP value of approximately +35, indicating that higher W/B ratios contribute positively to D _nssm (Figure 14). Conversely, a decrease in the W/B ratio depicts a negative SHAP value (around −10), suggesting a detrimental effect on D _nssm. The MT Age also plays a significant role, with higher durations showing negative SHAP values (around −8) and shorter durations exhibiting positive SHAP values (around +48). This implies that longer curing periods negatively impact D _nssm, while shorter durations have a positive influence. Similarly, higher FA quantities show negative SHAP values (−5), indicating adverse effects on D _nssm prediction, while lower FA amounts exhibit positive SHAP values (+3), implying beneficial impacts.

Figure 14:

Impact of variables: SHAP summary visualization.

D _nssm shows contrasting trends with CA and TA content. Specifically, increasing CA content leads to a decrease in D _nssm, indicating improved resistance to chloride penetration. This occurs because larger, well-graded coarse aggregates disrupt the continuity of the cement paste, increasing the tortuosity of the diffusion path and effectively reducing the permeability of the concrete [49]. In contrast, while moderate increases in TA, which includes both fine and coarse aggregates, can improve the concrete matrix, very high TA levels lead to an increase in D _nssm. This rise may be attributed to the excessive volume of fine aggregates within the total aggregate fraction, which increases the interfacial transition zones (ITZs). Since ITZs are more porous than bulk paste, their expansion at very high TA contents can create easier pathways for chloride ions, thereby increasing chloride diffusivity. Hence, while coarse aggregate contributes positively to durability by blocking ion transport, an overly large total aggregate content, largely influenced by fine aggregate and the associated ITZ volume, can counteract this benefit and increase chloride permeability. This highlights the importance of optimizing both aggregate grading and overall aggregate volume to balance tortuosity effects with ITZ-induced permeability for enhanced concrete durability.

The D _nssm of concrete exhibits diverse trends across different material parameters (Figure 15). Initially, D _nssm increases with higher W/B ratios but only for a limited range, after which it stabilizes until approximately 0.44. Subsequently, there is a rapid increase in D _nssm from 0.44 to 0.49, maintaining a constant value up to 0.55. Similarly, D _nssm remains consistent up to 102 kg/m³ of cement, beyond which it experiences a slight decrease until approximately 145 kg/m³, remaining relatively constant thereafter. Additionally, D _nssm remains constant up to 225 kg/m³ and then slightly decreases. Furthermore, D _nssm shows a slight decrease up to 90 kg/m³, followed by a more significant decrease up to 100 kg/m³, after which it remains constant. D _nssm almost remains constant with an increase in SF but decreases around 112 kg/m³. It also decreases slightly up to 18 kg/m³of FA, then shows a slight rise and decreases again. With an increase in CA content, D _nssm remains almost constant and slightly decreases initially but remains constant up to 980 kg/m³, after which it increases. Moreover, D _nssm initially experiences a rapid fall with a rise in MT age and continues to decrease with further increases in MT age. The PDP analysis reveals that D _nssm rises sharply when the TA content exceeds approximately 1,100 kg/m³, consistent with the SHAP findings.

Figure 15:

PDP analysis.

The results of this study offer clear guidance for optimizing concrete mix designs to enhance durability against chloride ingress. Maintaining a low W/B ratio, ideally below 0.44, is a key factor in minimizing chloride diffusivity. A moderate cement content, around 102–145 kg/m³, appears sufficient for maintaining strength without increasing permeability. Incorporating SF up to 112 kg/m³ improves matrix densification, thereby reducing D _nssm. Increasing CA content up to 980 kg/m³ is beneficial, as it enhances tortuosity and obstructs ion transport pathways. However, care must be taken with TA content. When TA exceeds 1,100 kg/m³, D _nssm may increase due to a larger volume of ITZs, which are more porous and facilitate chloride movement. Additionally, extending the MT age shows that prolonged curing significantly improves chloride resistance. By carefully adjusting these key parameters, engineers can design concrete mixes with better long-term performance in chloride-rich environments.