Investigating quality inconsistencies in the ultra-high performance concrete manufacturing process using a search-space constrained non-dominated sorting genetic algorithm II

2.1 Predicting concrete mechanical properties

Predicting the compressive strength (CS) of concrete, particularly its 28-day CS, has traditionally relied on empirical relationships [8] and, more recently, machine learning techniques [9], [10]. The initial obstacle to adopting machine learning techniques in concrete research is the scarcity of comprehensive, high-quality datasets. The datasets on Compressive Strength [11] and Slump Flow Test [12], collected by Yeh from diverse research sources, are commonly used [13], [14]. These generally focus on the impact of mixing proportions on high-performance concrete. Since the datasets are compiled from diverse sources, they are susceptible to inherent redundancies and inconsistencies.

Nguyen et al. [15] employed the XGB algorithm to predict CS of UHPC using a dataset of 931 mix formulations derived from both laboratory experiments and the existing literature. However, the dataset does not incorporate potential uncertainties in material quality, dosing, and environmental conditions.

Aylas-Paredes et al. [16] built a 1,300-entry UHPC dataset from more than 55 studies and trained a random forest (RF) and a three-layer artificial neural network (ANN) to predict the 28-day strength. Hyperparameters were tuned by 10-fold cross-validation (CV), but accuracy came from a single 75 %/25 % train–test split, risking sampling and initialization bias. Undocumented mixing, curing and storage differences across labs further threaten generalizability.

Wakjira et al. [17] trimmed Abellán-García’s 931-mix UHPC [18] archive to 540 mixes by deleting entries with missing data and keeping only 10 compositional variables, omitting all processing details (e.g. curing and batching temperature). They trained decision-tree, GBM and XGB models and stacked them with a linear-SVR meta learner, but validated the system on just one random 80 %/20 % train–test split with no repeated initializations. Consequently, both the reported accuracy and the multiobjective Pareto fronts may vary with a different split, and ensemble diversity is limited because each base learner is tree-based [19].

Designing a pipeline for the concrete production process with sparse data has been seldom addressed [20]. Recently, Golafshani et al. [21] proposed a pipeline for modeling concrete production and optimizing mixtures that investigates a framework for the low-carbon mix design of recycled aggregate concrete with supplementary cementitious materials using machine learning.

Despite progress in predicting concrete mechanical properties, notable challenges persist [22]. These include limited data coverage of material quality, measurement errors, and mixing and curing conditions – factors that necessitate a holistic perspective on the production process. Even minor variations in these variables can lead to inconsistencies in UHPC quality, despite using identical recipes [23]. Additional hurdles include systematic data generation, feature selection methods that fail under high dimensionality and limited sample sizes, inadequate training-testing strategies, and a narrow range of investigated algorithms. To address these gaps, this study investigates the effects of material quality, uncertainties in material dosing and particle size distribution, as well as mixing and environmental conditions on final mechanical properties. By leveraging the developed multiobjective feature selection method and a diverse set of 10 machine learning algorithms and employing a leave-one-out cross-validation (LOOCV) [24] training-testing strategy – coupled with multiple initializations – the proposed methodology ensures reliable predictions of UHPC mechanical properties.

2.2 Evolutionary multiobjective feature selection

Feature selection (FS) is crucial in machine learning, particularly for high-dimensional datasets with small sample sizes. It enhances model interpretability, mitigates overfitting, and improves prediction accuracy by discarding irrelevant or redundant features. Traditionally, FS methods – filter, wrapper, and embedded – may select redundant features, exhibit nesting effects, or become trapped in local optima, especially in complex, high-dimensional domains [5], [6].

Evolutionary multiobjective feature selection (EMOFS) has been studied for several decades [25]. It excels in global optimization and can handle high-dimensional data; however, it generally requires large datasets. For complex, sparse datasets, the intrinsic randomness of evolutionary processes often leads to unstable outcomes. As a result, EMOFS has primarily been employed for large-scale classification tasks [26], [27], [28], [29]. One way to address this challenge is incorporating prior knowledge into the FS process [30]. EMOFS methodologies can integrate domain expertise at multiple design stages, including solution representation, evaluation metrics, initialization strategies, offspring generation methods, environmental selection, and decision-making [6]. Kropp et al. [31] propose a Sparse Population Sampling technique, seeding the population with sparse initial solutions and thus leveraging a form of prior knowledge. Xu et al. [32] employ duplication analysis to simplify FS by exploiting patterns of feature redundancy. Song et al. [33] group features based on correlations before using particle swarm optimization, thereby harnessing prior knowledge of feature relationships. Ren et al. [34] develop an algorithm for sparse optimization that indirectly integrates domain insights by emphasizing the distribution of non-zero elements. Likewise, Wang et al. [35] apply multiobjective differential evolution to balance feature minimization and classification performance, implying an indirect use of domain-specific feature importance. Vatolkin et al. [25] apply EMOFS, optimizing trade-offs between classification error and the number of features. Follow-up studies [36] further generalized this approach to multiple objective pairs and scenarios. These works show the efficacy of EMOFS in complex domains. Moreover, biased or informed initialization has been proposed as a means to inject domain knowledge into the evolutionary search. For instance, seeding the initial population with high-quality or sparse solutions can guide the algorithm towards better optima.

Yet, no existing approach explicitly utilizes predefined features as prior knowledge or directly tackles problems marked by both high dimensionality and small sample size. A gap remains in achieving stable EMOFS outcomes under these constraints. This work addresses this gap by partially initializing the populations with domain-specific knowledge and tuning the mutation probabilities to balance exploration and exploitation.

3.1 Key factors and characteristics in the UHPC production process

To collect data for the UHPC dataset ( X ∈ R 19 × 150 ) [3], a fixed reference UHPC recipe with constant material amounts is used. However, as summarized in Table 1, UHPC quality can be influenced by small variations in multiple factors during production. In addition to mechanical tests, properties such as temperature, electrical conductivity, air content, slump flow [37], and funnel runtime are measured for fresh concrete.

In the first stage, the effects of material quality, storage environment, and silica fume impurities are examined by varying delivery batch time (DB), cement reactivity (CR), ingredient moisture (IM), ingredient temperature (IT), and graphite content (GRP). Even materials supplied by the same manufacturer but at different times (labeled as DB1 or DB2) can exhibit subtle differences that affect the microstructure. Cement reactivity can be altered by changes in chemical composition and environmental factors during storage. Variations in moisture content may also impact UHPC quality. Additionally, raw materials stored outside can experience fluctuations in temperature and humidity. Consequently, the temperature of raw materials is artificially adjusted, and extra water is added to simulate humidity. A crucial characteristic of UHPC is its low water content; thus, impurities that absorb water (e.g. GRP content) can significantly affect workability and, ultimately, compressive strength.

The recipe formulation (e.g. ratios of aggregates, superplasticizer, and silica fume) is critical for UHPC strength and durability. Small measurement errors or variations in particle size distribution can lead to significant differences in final properties. Various fresh concrete properties – temperature (FCT), electrical conductivity (EC), air content (AC), slump flow (SF), and funnel runtime (FR) – serve as indicators of homogeneity, workability, and potential structural integrity. To capture real-world variability, different curing conditions are implemented in two phases [23]. During the first 24 h, the UHPC transitions from paste to a minimally hardened state. It is either stored in a humidity-controlled cabinet at 90 % relative humidity and 20 °C or covered with plastic film at 20–40 °C. After demolding at 24 h, the specimens are either maintained under plastic film at 20 °C or submerged in water at 20–40 °C until day 28.

3.2 Data preprocessing

The data preprocessing stage consists of four main steps (Figure 2). First, data are normalized to the range [0, 1]. Second, iterative imputation manages missing data, which constitutes approximately 4 % of the dataset [3]. Simple methods like mean or median imputation can produce biased estimates [38]. Iterative imputation [39], implemented via scikit-learn’s IterativeImputer [40], treats each feature with missing values as a function of other features in a sequential modeling process. Thirdly, Pearson’s correlation coefficient [41] is used to detect and remove highly correlated inputs, preventing multicollinearity. The correlation analysis, detailed in Section 4.1, leads to the removal of three inputs, further reducing the dimensionality of the dataset from 19 to 16 [3]. Finally, based on expert analysis [3], the removal of 11 outliers yields a refined dataset X ∈ R 16 × 139 for the subsequent investigations.

3.3 Ensemble-based feature importance determination

In this study, the ensemble-based feature importance determination (E-FID) framework [2] is employed to identify predefined features as prior knowledge for incorporation into the next step (see Figure 2). Unlike single-model approaches, the ensemble method combines insights from multiple predictive algorithms, mitigating bias and variance issues. This strategy is particularly advantageous in high-dimensional, limited-data settings, where ensembles enhance generalization and reduce the risk of overfitting [19], [42].

E-FID utilizes 16 different feature importance determination methods as base learners (BLs), ranging from filter and wrapper to embedded approaches, to provide diverse perspectives for data analysis. Diversity among the BLs is measured using Pearson’s correlation analysis; highly correlated BLs are removed to eliminate redundancies. Finally, an averaging aggregate method is applied to combine the outcomes into the final result [2].

3.4 Search-space constrained evolutionary multiobjective feature and algorithm selection framework

3.4.2 Search-space constrained non-dominated sorting genetic algorithm II

To address the challenges of EMOFS methods in high-dimensional datasets with small sizes, this study developed the search-space constrained non-dominated sorting genetic algorithm II (NSGA-II), as shown in Figure 3. The search-space constrained NSGA-II serves as an optimization process that selects the optimal features (i.e., dimensionality reduction) for modeling while simultaneously optimizing the hyperparameters of the chosen model. In the search-space constrained NSGA-II, an individual is represented by a vector.

(3) x = [ x 1 , x 2 , … , x n , h 1 , h 2 , … , h k ] T ,

where each x _i ∈ {0, 1} indicates whether the i-th feature is absent (0) or present (1), and each h j ∈ R is a real-valued hyperparameter of the machine learning algorithm [44]. The number of features is n, and the number of hyperparameters is k. The search-space constraint is realized by a specific population initialization in NSGA-II, where predefined features identified by the E-FID framework are integrated as prior knowledge to constrain the search space.

Figure 3:

Overview of the search-space constrained NSGA-II process. Each generation selects parents (p _c ) from the current population (P _t ) for crossover and mutation, producing offspring (o _c ) in (Q _t ). After G generations, the final solutions comprise the predefined feature set (F _predef), the non-predefined feature set (F _rest), and the optimal hyperparameters (H _yper). By enforcing features in (F _predef) to be 1, NSGA-II narrows the search space, focusing on how other features (F _rest) interact with F _predef. (f _i (x): Objective function, F _i : Pareto solution).

Let S ⊆{1, 2, …, d} be the set of indices corresponding to these predefined features. During population initialization, crossover, and mutation, for each predefined feature index i ∈ S is enforced by setting x _i = 1 (Figure 3). In the initialization phase, a population P _t is created, each retaining the predefined feature set F predef = [ x 1 , x 2 , … , x d ] T and a random selection of additional features F rest = [ x d + 1 , … , x n ] T , along with randomly assigned values for the corresponding hyperparameters H yper = [ h 1 , h 2 , … , h k ] T :

(4) x = [ x 1 , x 2 , … , x d , x d + 1 , … , x n , h 1 , h 2 , … , h k ] T .

During initialization, each individual has its predefined feature bits set to 1. For features not in the predefined set, bits are randomly chosen (0 or 1 with equal probability):

(5) x i = 1 ,   if  i ∈ S , randint { 0,1 } ,   if  i ∉ S .

In the crossover step, two parents exchange bits for non-predefined features with probability α = 0.5. However, predefined feature bits (i ∈ S) are never swapped, so they remain 1 in each offspring (Figure 3).

In the mutation step, predefined feature bits are never flipped. For non-predefined features, each bit can flip with a small probability (μ = 0.05):

(6) x i ′ = x i ,   if  i ∈ S , 1 − x i ,   w.p.  μ ,  if  i ∉ S , x i ,   w.p.  ( 1 − μ ) ,  if  i ∉ S .

A uniform re-sampling mutation is applied to the hyperparameter genes: each hyperparameter is given an independent 5 % probability of being mutated, and, when mutation occurs, a new random value is drawn across its full valid range (a continuous uniform distribution for the real-valued and discrete uniform distributions for integer hyperparameters). In this way, each mutated value is kept admissible, fresh genetic material is injected at each generation, and the real-valued parameters are allowed to evolve jointly with the feature subset [45].

The fitness of each individual is evaluated as follows [43], [46]:

(7) X * = arg max x ∈ X f 1 ( x ) , − f 2 ( x ) ,

where f ₁(x) = R ²(x) represents the model’s predictive accuracy, and f 2 ( x ) = ∑ i = 1 n x i measures its complexity by summing up the selected features. The dual objectives are to achieve high accuracy and to minimize the size of the feature set [43], [46] while enforcing the predefined features.

An alternative strategy to the proposed population initialization methodology is to integrate the predefined features directly into the fitness function – first applying NSGA-II only on non-predefined features and then combining them with the predefined ones – but this approach incurs extra computational overhead due to the repeated concatenation and separation of features. In contrast, the search-space constrained NSGA-II incorporates the predefined features from the initialization stage, ensuring they remain fixed during crossover and mutation for a more straightforward and efficient implementation.

3.4.3 Parameter settings and evaluation framework

In this study, both the search-space constrained and standard NSGA-II algorithms are implemented as sequential, single-threaded processes. The overall crossover probability is set to 0.7, meaning that 70 % of selected parent pairs undergo recombination. Within each crossover event, a gene-level probability of 0.5 is applied to swap features between individuals. Similarly, mutation is executed with an overall probability of 0.3, whereby each eligible gene has a 0.05 chance of being flipped.

In a nested modeling, validation, and evaluation loop, one test data point is held out at the start of the SEM-FAS framework using LOOCV for the final evaluation phase. Then, 10-fold cross-validation is performed on the remaining training data to train and validate each algorithm, thereby identifying the best features and hyperparameters for the chosen model via the search-space constrained NSGA-II. After finalizing the model and its optimal settings, the unseen test point is used for evaluation. These steps are repeated across multiple LOOCV folds, each with a different initialization, and the average prediction performance and frequency of feature selection are recorded. This entire procedure is then repeated for all 10 machine learning algorithms.

Considering the two objectives – prediction accuracy and feature count – the final solution selected from the Pareto front is the one that uses no more than 12 features while achieving the highest accuracy, as illustrated in Figure 4.

Figure 4:

An illustration of the final solution selection strategy from a Pareto front for a maximization – minimization problem [47]. The chosen solution is the one that does not exceed 12 features while achieving the highest accuracy. (f _i (x): Objective function).

3.5 UHPC manufacturing process modeling

In the final layer of the proposed pipeline, the ranked features and the best-performing model (including optimal hyperparameters) identified by the SEM-FAS framework are employed (see Figure 2). This final stage implements a cumulative LOOCV procedure, in which features are cumulatively added to the previous feature subset in order of their importance, allowing an iterative assessment of how each additional feature and its interaction with others contribute to the final model’s performance (Alg. 1).

The cumulative LOOCV procedure systematically evaluates the incremental contribution of each feature based on its predefined ranking (from most important to least important), continuing until all features have been evaluated. The process is intentionally continued even if performance degrades at intermediate steps, because the goal is to provide comprehensive insights into the influence of each feature. The optimal number of features is thus clearly indicated by the resulting performance trajectory. Moreover, because each feature is evaluated in combination with all previously added features, interaction effects are implicitly captured and reflected in the predictive performance at each step.

4.1 Correlation patterns in studied factors

The correlation analysis, presented in the heatmap in Figure 5, reveals strong linear correlations in specific variable pairs: SAI and SAII, FLI and FLII, and IT and FCT. Due to these high correlations, SAII, FLII, and FCT are removed, reducing the factor pool from 19 to 16 dimensions.

Figure 5:

The Pearson correlation matrix of the 16 candidate input variables with a companion bar that displays the redundancy index ∑ ρ for each feature is shown on the right. The aim is to identify pairs whose high collinearity could distort subsequent modeling. To mitigate redundancy and improve numerical conditioning, FLII, SAII, and FCT are removed from the feature set. For a detailed explanation of the variables and their abbreviations used in this heatmap, see Table 1. (ρ: Pearson correlation coefficient).

4.2 Gaining insights into feature importance for UHPC mechanical properties using E-FID

The feature importance analysis for CS28 (Figure 6) underscores the pivotal role of CT28, emphasizing the influence of environmental conditions during the second curing phase. Interestingly, CT1 on the first day of curing also emerges as significant, albeit less impactful than CT28. This finding suggests that conditions on the first day establish foundational strength, which is then further enhanced between days 2 and 28. It also reinforces the well-known principle that higher temperatures accelerate cement hydration, although ensuring adequate moisture in such environments remains vital.

Figure 6:

Feature importance for compressive strength (CS28) and flexural strength (FS28) at day 28. The figure highlights the dominance of curing temperatures and the varied impacts of material and environmental factors on these strengths. Feature relevances shown here are computed using the ensemble-based feature importance determination (E-FID) framework [2] by the aggregate averaging method described in Section 3.3. For definitions of the variables, refer to Table 1.

IM exerts a critical influence on final compressive strength, highlighting the importance of raw material moisture content. Likewise, while APW is not directly controllable, it serves as an informative indicator of energy input during mixing – reflecting UHPC paste rheology – and thus aids in predicting final compressive strength. Additionally, GRP and CC28 play notable roles. The presence of graphite (as an impurity in silica fume) can significantly absorb water in the mixture – an especially critical factor in UHPC given its low water content.

For FS28, as shown in Figure 6, CT28 remains paramount, reinforcing the overall impact of curing conditions. However, in a notable departure from compressive strength findings, CC28 emerges as the second most critical factor for flexural strength. This distinction underlines how environmental conditions influence the material’s resistance to bending stress.

IM and CT1 retain their importance across both compressive and flexural strengths, again emphasizing the role of moisture content and early-age curing. Notably, AC provides more predictive value for FS28 than for CS28, likely due to its effect on pore structure and distribution, which is especially relevant for flexural properties.

Based on these insights, the most important features are identified to form predefined feature vectors, serving as prior knowledge for the SEM-FAS framework. For CS28, the predefined features are CT28, CT1, IM, APW, GRP, and CC28. For FS28, the selected features are CT28, CC28, IM, CT1, AC, and DB.

4.3 Enhanced predictive modeling of UHPC mechanical properties by constraining the search-space of NSGA-II

4.3.2 Impact on solution stability and interpretability in the FS process

From Table 2, it is evident that models trained with search-space constrained NSGA-II can achieve higher predictive performance than those using standard NSGA-II. In this section, we examine how population initialization by injecting predefined features into NSGA-II affects solution stability and interpretability in the feature selection process for CS28 and FS28 (Figure 7). Figure 7 presents four heatmaps: for each mechanical property, one using I-FS and one using T-FS . In both scenarios, 139 runs are performed in a LOOCV train-test configuration across 10 models, and feature selection frequencies are recorded for each model.

Figure 7:

A comparative analysis of feature selection frequencies across the 16 candidate variables in I-FS and T-FS when predicting compressive and flexural strength at 28 days (CS28 and FS28) is presented. For each LOOCV fold, the feature subset on the Pareto front that achieves the highest predictive accuracy while using no more than 12 variables is selected. This yields final solutions whose number of selected features ranges from 6 to 12 under I-FS and from 1 to 12 under T-FS. See Table 1 for variable definitions. (a) Heatmap illustrating the frequency of feature selection in models employing I-FS for CS28. Under I-FS, models achieve greater solution stability and interpretability. (b) Heatmap displaying the frequency of feature selection in models using T-FS for CS28, showing higher variability in selected features. (c) Heatmap illustrating the frequency of feature selection using I-FS across all models for FS28, showing greater stability and interpretability. (d) Heatmap displaying the frequency of feature selection using T-FS for FS28, highlighting greater variability without domain-specific guidance.

Figure 7a (I-FS for CS28) shows that the six features predefined as the most critical are consistently chosen (139 times) across all models. In contrast, the T-FS scenario (Figure 7b), without predefined feature guidance, still identifies the same six features as most frequently selected, but with lower overall selection frequency. This consistency underscores the accuracy of the initial feature importance assessment by the E-FID method.

A notable difference between I-FS and T-FS lies in the stability of feature selection. I-FS consistently selects the predefined features in each model iteration, signifying enhanced stability, interpretability, and reliability in the selection process. By contrast, T-FS demonstrates higher selection variability, indicating potential instability in model performance without the injection of prior knowledge.

Additionally, features such as SAI, IT, and DB show substantially higher selection frequencies under I-FS, suggesting that the algorithm not only reinforces predefined features but also identifies and promotes other relevant factors based on intrinsic data characteristics. Conversely, features like SPP and CC1, which appear infrequently or not at all under I-FS, illustrate the capacity of I-FS to deprioritize less impactful features. This selective refinement by I-FS enhances both model interpretability and simplicity by clearly indicating which features provide consistent value for predicting CS28, while simultaneously ensuring stable solutions.

For FS28, Figure 7c shows that the predefined features CT28, CC28, IM, CT1, AC, and DB are each selected 139 times under I-FS. In contrast, the T-FS scenario (Figure 7d) displays more variability in feature selection. While features such as IM, CT1, AC, and DB remain frequently chosen, they appear with lower frequency than in the I-FS case. Moreover, I-FS reveals that APW, although significant under T-FS, is emphasized less when evaluated alongside the predefined features. Conversely, GRP and particularly EC, which T-FS deems less important, exhibit stronger interactions with predefined features under I-FS.

A broader comparison of feature selection frequencies (Figure 7) for both CS28 and FS28 shows that I-FS often assigns a frequency of zero to certain features, resulting in a clearer distinction between selected and non-selected features. This leads to more stable solutions, higher predictive accuracy, and improved interpretability.

As discussed in Section 4.3.1, MLR is the chosen algorithm for CS28 under I-FS, while SVR is selected for FS28. As shown in Figure 7a, the MLR model consistently selects CT28, CT1, IM, APW, GRP, CC28, SAI, IT, EC, FR, and FLI as the most critical features. Likewise, as shown in Figure 7c, the SVR model prioritizes CT28, CT1, IM, APW, GRP, CC28, SAI, IT, DB, SPP, SF, FR, FLI, and EC, reflecting their pivotal roles in the subsequent analysis phase.

4.4 Assessment of UHPC manufacturing process modeling

The results of the final modeling and evaluation of the selected models on unseen data are shown in Figure 8. The modeling process (Algorithm 1) for CS28 uses MLR and begins by adding the most influential factor, CT28 (Figure 8a). Using CT28 as a single predictor yields an R ² value of 57.10 %, underscoring the predominant role of this curing temperature in explaining CS28 variance. Next, incorporating CT1 (the first 24 h of curing temperature) significantly enhances model performance, increasing R ² to 66.61 %. This improvement suggests that CT1 provides additional variance information not captured by CT28. Adding IM raises R ² to 70.53 %, and introducing APW increases it further to 71.16 %. Subsequently, including GRP and CC28 refines the model, lifting R ² to 75.40 %. Although additional features such as SAI and IT only marginally increase R ² to 75.77 %, they are retained based on domain expertise, reflecting their potential practical importance. Ultimately, the model achieves its highest R adj 2 (74.28 %) with a core subset of six predictors: CT28, CT1, IM, APW, GRP, and CC28. This subset strikes a balance between model accuracy and computational efficiency while highlighting the key variables for optimal CS28 prediction.

Figure 8:

Comparative performance evaluation of MLR (multiple linear regression) and SVR (support vector regression) in the test phase. This figure shows how adding features affects the prediction metrics for CS28 and FS28. For CS28, Sub8 comprises CT28, CT1, IM, APW, GRP, CC28, SAI, and IT. For FS28, Sub7 includes CT28, CC28, IM, CT1, AC, DB, and IT. Variable definitions are in Table 1. (a) Prediction performance of MLR for CS28: Average R ², R adj 2 , and MAE in the test phase as the number of features increases. (Sub1: CT28, Sub2: Sub1 & CT1, Sub3: Sub2 & IM, Sub4: Sub3 & APW, Sub5: Sub4 & GRP, Sub6: Sub5 & CC28, Sub7: Sub6 & SAI, Sub8: Sub7 & IT, Sub9: Sub8 & EC, Sub10: Sub9 & FR, Sub11: Sub10 & FLI). (b) Prediction performance of SVR for FS28: Average R ², R adj 2 , and MAE in the test phase as the number of features increases. (Sub1: CT28, Sub2: Sub1 & CT1, Sub3: Sub2 & IM, Sub4: Sub3 & APW, Sub5: Sub4 & GRP, Sub6: Sub5 & CC28, Sub7: Sub6 & SAI, Sub8: Sub7 & IT, Sub9: Sub8 & DB, Sub10: Sub9 & SPP, Sub11: Sub10 & SF, Sub12: Sub11 & FR, Sub13: Sub12 & FLI, Sub14: Sub13 & EC).

For FS28 modeling with SVR (Figure 8b), starting with CT28 alone yields an average R ² of 46.23 %. Adding CC28 significantly enhances performance (to 74.32 %), underlining the importance of the curing conditions from day 2 to day 28. Incorporating additional variables such as IM, CT1, and AC leads to fluctuations in model accuracy; for instance, IM slightly lowers R ² to 74.02 %, and CT1 plus AC reduce it further to 71.51 %. These variations suggest that while some factors add valuable information, others can introduce complexity without significantly improving predictive power. The model achieves its highest average R ² of 78.89 % by also including DB and IT.

These findings (Figure 8) emphasize the critical role of curing conditions in optimizing the mechanical properties of UHPC. Additionally, factors related to material storage and delivery, which affect temperature and moisture content, significantly influence overall UHPC quality. Measurement errors in dosing key materials such as sand, along with impurities in silica fume (simulated as graphite content), substantially impact UHPC performance. These results illustrate why, in real-world scenarios, achieving the same final UHPC quality – even with an identical recipe – can be challenging if raw material storage conditions, silica fume impurities, dosing errors, and curing conditions (e.g., seasonal effects) are not properly managed.