Machine learning-based Graphical User Interface for predicting high-performance concrete compressive strength: Comparative analysis of Gradient Boosting Machine, Random Forest, and Deep Neural Network Models

Abstract

The research investigates ensemble machine learning techniques to forecast high-performance concrete (HPC) compressive strength through analysis of Gradient Boosting Machines (GBM) together with Random Forest (RF) and Deep Neural Network (DNN) performances. Previous experiment data served as model inputs for the machine learning systems that comprised cement, fly ash, blast furnace slag, water, superplasticizer, coarse aggregate, and fine aggregate for HPC compressive strength prediction. The research study utilizes input parameters and direct bypassing of dimensionality reduction to evaluate the performance of models that capture intricate nonlinear patterns from concrete compressive strength data. RF produced the most accurate results during training by establishing 0.9650 R² measurements and 0.0798 RMSE indicators, thus demonstrating exceptional accuracy at a minimal error level. In testing, RF maintained its lead with an R² of 0.9399, followed closely by GBM, while DNN showed slightly higher error rates. A comprehensive ranking analysis across multiple statistical metrics highlighted RF as the most dependable concrete compressive strength prediction model. Further, Regression Error Characteristic (REC) curves visually assessed model performance relative to error tolerance, revealing RF and GBM’s reliable accuracy across different thresholds. A Graphical User Interface (GUI) with user-oriented features connected to the prediction models was created for smooth system usage. The results indicate that RF provides accurate predictions for concrete compressive strength because of the effectiveness of ML models, according to this study. Predictions of tensile strength, modulus of elasticity, and fracture energy parameters in concrete materials become possible when categorized based on their compressive strength values. This approach significantly enhances structural analysis by reducing both cost and time requirements.

Graphical abstract

Keywords

HPC / compressive strength prediction / REC curve / GUI / model performance evaluation

1 Introduction

Conventional concrete is commonly applied in traditional construction projects, while high-performance concrete (HPC) has gained popularity in industrial construction due to its enhanced strength and durability. HPC is a composite material engineered to achieve high-strength properties, making it suitable for demanding structures like bridges, skyscrapers, tunnels, and pavements that must withstand severe environmental conditions [1–3]. To achieve these properties, HPC incorporates supplementary cementitious materials (SCMs) such as fly ash (Fa) and blast furnace slag (SB), along with chemical admixtures, in addition to the core components of conventional concrete: Portland cement, water-to-cement ratio, and fine and coarse aggregates [4]. The strength of HPC is affected by different parameters such as SCMs, water-to-binder (w/b) ratio, fiber types, aggregate quality, and curing method [5]. SCMs improve the strength but reduce the early strength, which is solved by adding admixtures like nano-silica. The flexural and tensile strength was enhanced by adding fibers, and the overall strength was found to increase by strong aggregate and reducing the w/b ratio [6]. According to the ASTM C39 and AASHTO T 22 Standards, HPC is classified by an early compressive strength of 20 to 28 MPa, which gains within the first three days [7].

The composition of HPC is mainly different from that of conventional concrete, as it contains significant amounts of additional ingredients such as Fa, slag, and silica fume (SF) [8]. Additionally, superplasticizers are used to attain a low water-to-cement ratio, usually in the range of 0.22 to 0.35, and minimize the maximum aggregate size. These changes boost resistance to severe environmental conditions, decrease microcracking, improve density, and strengthen the material [9]. In HPC, polypropylene (PP) fibers and air-entraining admixture (AEA) are used to enhance fire performance and lower the chance of spalling [10]. The probability of spalling was considerably reduced by PP fibers, particularly when combined with AEA [11,12]. The low water-to-cement ratio in HPC makes the concrete prone to shrinkage and micro-cracking. An internal curing method was used to reduce autogenous shrinkage by incorporating recycled ceramic waste with varying replacement ratios [13]. Autogenous shrinkage occurs when water hydrates cement particles, resulting in a volume contraction and the formation of voids, which create tensile stresses. HPC produces tiny capillaries that may increase tensile stresses after hydration, making this shrinking more noticeable [14]. The higher porosity of the recycled ceramic waste enhances shrinkage control, while lower replacement ratios improve the strength of HPC [15]. Water absorption, particle size, and replacement ratio of water-retaining materials that support continued cement hydration were parameters that affected the performance of HPC in terms of strength, shrinkage, and durability [16].

Traditional methods like slump and slump flow tests are insufficient for evaluating the workability of HPC because they are not sensitive enough to its fluid consistency. It was discovered that increasing the mortar content improved the flowability [17]. Yield stress and plastic viscosity are essential for slump and workability, and these characteristics are influenced by particle friction and packing density; superplasticizers enhance flow and lower water demand. Compressive and tensile strengths are related to the water-cement ratio and aggregate distribution. Stability depends on consistent grading to prevent segregation and bleeding [18]. The densified mixture design algorithm produces the HPC, while the water-to-solid ratio influences the concrete’s volume stability, strength, and durability. Incorporating pozzolanic components improves the rheology of HPC and reduces problems like bleeding and segregation [19].

HPC is highly suitable for harsh environments when properly cured since it resists the penetration of aggressive chemicals. HPC is still a safe material, and its dense matrix makes it a long-lasting concrete technology innovation by significantly extending the service life of structures [14]. HPC offers several benefits in severe conditions, including decreased porosity, improved carbonation resistance, reduced water sorptivity, and decreased chloride permeability. These characteristics are essential for delaying the onset of corrosion in steel reinforcement, especially in harsh environments. Incorporating Pozzolanic products results in a dense microstructure that increases strength and reduces permeability [20].

Predicting HPC performance is challenging with traditional approaches, so researchers have increasingly turned to soft computing methods to estimate concrete compressive strength (CCS) and analyze input variables. For instance, Khashman and Akpinar [21] developed an artificial neural network (ANN) model to accurately forecast and classify CCS for different types of concrete, highlighting the strong predictive capability of ANN. Similarly, Yeh [4] applied ANN to predict the CCS of HPC and found its superiority over linear regression for modeling accuracy. Khademi et al. [22] explored CCS predictions in recycled aggregate concrete (RAC) using ANN, multiple linear regression (MLR), and adaptive neuro-fuzzy inference systems (ANFIS), concluding that the performance of ANN and ANFIS models was better than MLR.

Other researchers have employed diverse machine-learning approaches to predict CCS. Gholampour et al. [23,24] used models like multivariate adaptive regression splines (MARS), M5 model tree, gene expression programming (GEP), and least squares support vector regression (LSSVR) to assess mechanical properties of RAC, showing positive results for CCS prediction. Chou et al. [2] compared various models, including ANN, support vector machine (SVM), MLR, multiple additive regression tree (MART), and bagging regression trees, determining MART to be highly effective for CCS prediction. Cheng et al. [25] developed the Evolutionary Fuzzy Support Vector Machine Inference Model for Time Series Data (EFSIMT) by combining fuzzy logic and SVM, which performed better than ANN and SVM in CCS prediction for HPC. Recent reviews by Yucel and Namlı [24] highlight various machine-learning models, including HPC-specific CCS prediction approaches. Hoang et al. [1] have advocated for models like Gaussian Process Regression (GPR) over other methods like Least Squares Support Vector Machines (LSSVM) and ANNs. Several research papers have implemented machine learning methods for solving partial differential equations as well as material fracture analysis through energy-based or physics-informed approaches [26–28] yet the usage of ensemble models Random Forest (RF) and Gradient Boosting for predicting HPC compressive strength remains scarce.

Numerous input variables are analyzed for their impact on the CCS of HPC. These include cement (C), Fa, SB, water (W), superplasticizer (SP), coarse aggregate in varying sizes (CA, CAm, CAs), fine aggregate (FA), SF, concrete age (Age), mix grade (MG), specimen dimensions (SS), curing methods and duration (TC), maximum temperature (T), relative humidity and air velocity (HV), and strength period (S). While several studies highlight the water-to-cement ratio and age as particularly significant factors in CCS prediction [4,29,30], others used all available variables without distinguishing their contributions [1,2,31,32]. DeRousseau et al. [33] identified emerging approaches in concrete property modeling. It emphasized that prediction models should consider factors such as cost-effectiveness, durability, strength, workability, and sustainability in concrete design.

1.1 Research gap

Research about CCS prediction previously used models that included ANNs, SVMs, and MARS. Few research efforts have explored the combination of Gradient Boosting Machine (GBM) and RF ensemble models and their effectiveness in predicting the CCS of HPC. Research has not examined predictive performance measurements and optimal input parameter selection for HPC CCS prediction through advanced machine learning model applications.

1.2 Novelty of the present work

The research makes substantial progress toward predicting HPC compressive strength through advanced methods, which include GBM, RF, and Deep Neural Network (DNN). This research employs GBM, RF, and DNN models instead of ANN and SVM because these advanced methods better handle the complex nonlinear relationships between HPC CCS and its various influencing variables. The production of HPC requires a mixture of C, Fa, SB, W, SP, CA, and FA. Additionally, the study enhances model precision and efficiency, eliminating unnecessary data inputs by carefully selecting input parameters. The study assesses these models’ predictive accuracy and generalization, delivering essential insights into model performance and identifying the most reliable options. The resulting generalizable framework for CCS prediction of HPC is adaptable to different types of concrete performance, offering the construction industry a reliable tool. This work advances the prediction of CCS for HPC by focusing on accuracy, efficiency, and adaptability. Thus, it establishes a solid foundation for future machine-learning applications for HPC and other construction problems.

2 Data collection and computational modeling

Research data consisting of 200 standard-tested samples from ordinary Portland cement mixed with different additives underwent standard curing under various conditions and came from multiple university research laboratories [2,4]. Chou et al. [2] specified the CCS by cylinder specimens with dimensions of 15 cm and 30 cm, which were prepared following established procedures, with data sourced from Yang et al. [31]. The seven elements used to forecast HPC CCS are illustrated in Tab.1 through C, Fa, SB, W, SP, CA, and FA. The data set presents CCS values with a minimum of 2.3 MPa, maximum of 82 MPa, and average at 34.9 MPa, setting the computational model’s validity range. It is important to note that predictions may not be reliable for parameter values outside these boundaries.

The frequency histogram in Fig.1 reveals vital information about four input variables as part of exploratory data analysis to identify fundamental data features such as distribution type and range, central tendencies and variations, and skewness and outlier patterns. Fig.2 demonstrates how Pearson correlation coefficient heatmap matrices allow users to view inter-relationships between parameters. Data quality analysis requires these correlation coefficients because high parameter correlation signifies redundant variables, while low or zero correlation indicates independent variables. Blood pressure training processes heavily depend on recognizing relationships between variables to acquire data that depicts needed model interactions effectively. The matrix shows how particular variables exhibit strong relationships with each other. A high correlation between variables suggests that these variables are dependent on others, such as cement and water content. Conversely, a low correlation indicates minimal or no interdependence between the parameters.

2.1 Machine learning description and data preprocessing

The choice of a machine learning model becomes essential because data features and analytic goals determine the selection. The way to model time-history data such as soil shear stress and pore water pressure ratio is crucial [34]. Effective models that identify and capture changes in order require immediate development. The sequences of information require Recurrent Neural Network-based models, including Long Short-Term Memory (LSTM) and Bi-directional Long Short-Term Memory (BiLSTM) alongside Gated Recurrent Unit (GRU) to tackle these applications effectively [35]. Convolutional Neural Networks (CNNs) are the best approach to processing spatial data consisting of images or grid-based structures because these models demonstrate exceptional capability for pattern recognition and feature extraction [36]. Users should apply neural networks and ensemble techniques, including Extreme Gradient Boosting (XGBoost) and RF, to process tabular data that contains non-sequential features [37].

Again, the compressive strength prediction for HPC utilized GBM RF and DNN models to process non-sequential tabular data featuring complex non-spatial relationships. These models were selected because they better handled intricate data structures that eventually produced accurate predictions. The results support the “no free lunch” theorem, demonstrating that any single algorithm lacks effectiveness on every problem type. The following sections present details on DNN, GBM, and RF models and their parameters, while Fig.3 shows the implemented model design. In data analysis, statistical normalization is crucial in ensuring that variables are aligned for fair comparison across various data sets. This process adjusts numerical distributions, often standardizing scales or following statistical norms, using techniques like min-max scaling. The reliability of statistical outcomes strengthens when data normalization occurs because it provides better interpretability of results, eliminates outlier effects, and promotes equal variable participation throughout analysis [38,39]. Data normalization is defined as follows:

(1)V_{\mathrm{n}\mathrm{o}\mathrm{r}\mathrm{m}}= \frac{V_{\mathrm{a}\mathrm{c}\mathrm{t}}-V_{\mathrm{m}\mathrm{i}\mathrm{n}}}{V_{\mathrm{m}\mathrm{a}\mathrm{x}}-V_{\mathrm{m}\mathrm{i}\mathrm{n}}},

where V_max and V_min represent a parameter’s maximum and minimum values, while V_act and V_norm denote the actual and normalized parameter values, respectively. Following normalization, the data set is randomly divided into training and testing subsets.

According to this study, the data set is partitioned into training and testing portions with proportions of 70:30. The model development occurs inside the training set. In contrast, the testing set preserves its performance evaluation function after completion of training. The experimental design enables an objective evaluation demonstrating both predictive power on new information and identifying unnecessary overlapping between training and testing. Only at the model evaluation phase is the testing set utilized once because it differs from validation sets.

The examination of training and testing set distributions utilized density plots following data normalization and split partitioning. It is essential to examine distribution patterns of data sets before model training to ensure both groups match in terms of representation and are comparable since significant discrepancies may produce flawed predictive power and weaken generalization effectiveness. To assess this, we employed the Kolmogorov–Smirnov (KS) test [40], a non-parametric statistical method to determine the significant difference between two sample distributions. The test evaluates two empirical cumulative distribution functions from data sets while returning statistical values to express differences between the sets. When the p-value reaches a level higher than 0.05, the distributions show no statistical variations between them. The analysis employs density plots to show variable distributions through Kernel Density Estimate (KDE) plots, which use kernel density estimation as the non-parametric method for estimating probability density functions. Through KDE plots, users can view data distribution continuously, allowing them to grasp their data set’s characteristics intuitively throughout different subsets. It is evident from the results of KS test in Fig.4 that training and testing set distributions remain identical with a split ratio of 70:30, as shown in density plots. This figure illustrates the normalized distributions of eight variables used in the compressive strength prediction model, comparing the training and testing data sets. Each subplot shows histogram-based density plots with overlaid KDE curves for visual assessment. The key variables include C, SB, Fa, W, SP, CG, FA, and Compressive Strength. To statistically validate the similarity between the training and testing distributions, the KS test was performed.

2.2 Computational model

2.2.1 Gradient Boosting Machine

Gradient Boosting Regression is one of the families of the Machine Learning Model of Supervised Learning and works by using ensemble learning. Where base models are added together to provide a composite model, several simple models are combined without altering the trees used earlier. This approach is known as an additive model, as each additional model adds to the overall accuracy of the model. In Gradient boosting, we decrease the loss specifically using coordinate descent, which is the first-order optimization method using gradient descent. In this technique, decision trees are weak learners using a squared error loss function. The model sets the weak learner into identifying and predicting the features of the expected residuals, which are used in conjunction with the current model inputs to steer the model in the right direction. Applying the same process step by step enhances the model’s accuracy in terms of prediction [41,42].

GBMs, also known as “gradient boosted tree ensembles”, is a powerful machine learning technique proven effective in numerous real-world applications. GBMs excel in tackling complex problems with highly nonlinear relationships as they learn hierarchical patterns within the data. This method builds models sequentially, enhancing the accuracy of the response variable estimate with each iteration. The basic idea of GBMs is to create each new model to give maximum correlation between the model and the overall negative gradient of the loss function from the prior ensemble. However, GBMs are prone to overfitting, especially when the tree depth and the number of boosting iterations is high, potentially leading to an inflated sense of model accuracy. Regularization techniques such as limiting the number of boosting iterations, constraining tree depth, and tuning other hyperparameters can be applied to address overfitting.

2.2.2 Random Forest

RFs are also appreciated in academic research for their applicability to actual problems of classification and regression, as these are the algorithms of ensemble learning based on the divide-and-conquer method. They combine prediction from several unpruned classifiers, and each is created through bootstrap samples. Random Forest Regressor (RFR) forms a bagged set of decision trees within a limited range of randomness. Random selection is critical when the model is being trained. For each node, a set of M variables is produced. Of course, the selection of diverse variables minimizes variation between decision trees, whereby each tree is supposed to create a different decision for the same instance within the forest. A majority vote across all trees determines the final result.

Previous studies provide an in-depth overview of the RF methodology [43,44]. RF is a collective learning technique that merges numerous independent simulation models to generate more precise predictions. This method constructs multiple randomized, unpruned decision trees and combines their outputs to produce a final forecast. Each tree is a standard classification and regression tree (CART), utilizing the Gini impurity criterion for splitting data. To introduce randomness and prevent overfitting, the features used to build each tree are randomly selected, and not all attributes are considered.

Bootstrap sampling is employed to select training data, further randomly diversifying the trees. This process can be efficiently parallelized as each tree can be constructed independently. Model creation involves feature selection, sample selection, and tree combination. Each tree is built using a random subset of features to avoid overfitting. Bootstrap sampling is used to create training sets, with the remaining data (out-of-bag data) serving as a validation set. The error of each tree is estimated using its out-of-bag data. The final RF prediction is determined by averaging the outcomes of all decision trees. Breiman [45] introduced the RF algorithm, an advanced ensemble learning method that combines multiple decision trees for prediction. RF models excel due to their independence from feature scaling, effective handling of complex relationships, and reduced parameter count. This leads to a significantly lower risk of overfitting. The core of RF regression is based on decision trees. The algorithm generates numerous decision tree models by utilizing different training data and feature sets. The mathematical representation of the RF regression algorithm is expressed in Eq. (2) as follows:

(2)Y\left(x\right)=\frac{1}{n} \sum _{i=1}^k{h}_i\left(x\right),

where (x) signifies the final output of the RF regression model, and h(x) represents the output of the ith decision tree.

2.2.3 Deep Neural Network

A DNN is an architecture of neural networks that utilizes numerous hidden layers positioned between its input and output sections. The wide adoption of DNN models occurs because they excel at detecting intricate connections between nonlinear data relationships and vector-based data structures [46]. DNNs represent ANN constructions that derive their concepts from brain structures through interconnected layers of brain cells. The system finds sophisticated data relationships through forward propagation, activation functions, and repetitive training protocols. The training period enables networks to improve their internal processing, which enhances their ability to forecast new data. The initial input layer handles unprocessed data before the hidden layers develop a hierarchy until the output layer uses this learned data to make predictions. Forward propagation in the DNN processes input data through the input layer before activating it with nonlinear functions. The training process requires adjustments to weight values and bias terms to reduce prediction errors from actual results. DNN performance depends heavily on the network’s depth and size, which needs extensive testing to achieve optimal operational results.

Before starting its operations, the Restricted Boltzmann Machine (RBM) applies contrastive divergence to adjust connections in both directions. The trained structure of the RBM operates similarly to a simple neural network layer by layer, and several RBMs connected build a neural network architecture. A RBM training sequence begins with applying input data to an initial RBM model (RBM1) before directing its hidden layer outputs to the subsequent RBM model (RBM2). The training sequence moves from RBM1 to additional RBMs (such as RBM3) without requiring target outputs because this process occurs under unsupervised conditions. The training procedure helps the model extract relevant information from the input data and learn variable relationships but cannot execute practical operations by itself. A subsequent backpropagation process enables supervised DNN training after initial training, simplifying the model into operating like an extensive ANN.

2.2.4 Building of models

The research employed a GBM and RF besides a DNN for HPC compressive strength prediction after tuning parameters to enhance model performance along with training efficiency. Hidden layers in the DNN model detected complex data patterns, resulting in generalization abilities that directly depended on their configured number and dimensions. The selection of neuron numbers in individual layers required a strike between accuracy improvement and overfitting avoidance because more neurons improve accuracy but may cause overfitting when unchecked. The frequency of weight updates depended directly on the batch size, which played a crucial role during training. The training accuracy improved with smaller batch sizes, although they required longer training duration. Larger batch sizes accelerated training but decreased reliability. Both stochastic gradient descent and adaptive moment estimation were essential optimizers for updating model weight parameters because each selection offered different trade-offs between performance speed and weight stability success. Mean squared error (MSE) operated as the loss function to evaluate accuracy, guiding the optimizer’s weight adjustment. The learning rate adjusted how substantially weights transformed while maintaining training stability through proper speed control. The key purpose of activation functions is to introduce nonlinear elements in DNN architectures so they can identify complex data patterns. The model used regressions in its output layer to generate estimates of compressive strength as its final output. The hyperparameters involving several trees and learning rate for GBM and depth of trees for RF were optimized independently so predictions could improve without producing overfitting results. Complete parameter optimization was conducted on all three model types, DNN, GBM, and RF, and reliable predictions were created according to the information in Tab.2.

Understanding how epochs relate to loss is essential in machine learning training. One epoch consists of processing the training data set fully during model training. The model starts with high loss during its first epoch since the randomly selected parameters yield suboptimal results. As the training model completes successive epochs, its loss value decreases because the model boosts its prediction accuracy by nearing the actual values. The training process should aim to reduce losses until they achieve their smallest possible value. However, special attention must be paid to this because long training runs may result in both overtraining and overfitting issues that prevent the effective generalization of new data. The ability of an overfitted model to achieve top performance on training data results in weak performance when tested on new data in validation or testing data sets [47]. Early stopping serves as a regularization technique that helps prevent overfitting. The model monitoring system known as early stopping tracks validation set performance to stop training when performance improvement reaches a threshold defined by the patience parameter within consecutive epochs. According to this study’s patient parameter, training stops when there is no performance improvement within ten epochs.

2.2.5 Performance matrices

The final and essential part of machine learning modeling requires a performance assessment achieved by statistical indices. Three statistical metrics from eight assess the trend patterns by using the coefficient of determination (R²), expanded uncertainty (U₉₅), and global performance indicator (GPI), but root mean square error (RMSE) and mean absolute error (MAE) and mean bias error (MBE) and mean absolute deviation (MAD). Weighted mean absolute percentage error (WMAPE) evaluates model errors [48–50]. Additional evaluation methods for regression analysis include actual vs. predicted plots and rank analysis alongside Taylor diagrams, error matrices, Regression Error Characteristic (REC) curves, loss vs. epoch curves, residual plots, and Williams plots [51]. Model assessment needs extensive examination since individual statistical indices reveal distinct information despite their particular constraints. R² functions widely as a fit evaluation tool, although it remains sensitive to data points outside the main distribution while failing to detect prediction distortions. Average prediction bias emerges as the main output of MBE yet the model does not present information regarding its overall predictive accuracy. Model performance evaluations become efficient by choosing metrics that match the research goals and applicable data patterns. The evaluation benefits from multiple performance measures which deliver an in-depth understanding about model results. Tab.3 shows optimal values for the performance indices that better model results correspond to nearer numbers.

The equations contain parameters that function according to the specifications presented in Eqs. (3) to (10) as follows.

(3)R^2= \frac{{\displaystyle \sum _{i=1}^n(d_i-d_{\mathrm{m}\mathrm{e}\mathrm{a}\mathrm{n}}{)}^2-{\displaystyle \sum _{i=1}^n(d_i-y_i{)}^2}}}{{\displaystyle \sum _{i=1}^n(d_i-d_{\mathrm{m}\mathrm{e}\mathrm{a}\mathrm{n}}{)}^2}},

(4)RMSE= \sqrt{\frac{{\displaystyle \sum _{i=1}^n(d_i-y_i{)}^2}}{N}},

(5)U_{95}= 1.96{\left(RMS{E}^2+S{D}^2\right)}^{1/2},

(6)LMI=1 -\left(\frac{{\displaystyle \sum _{i=1}^N|d_i-y_i|}}{{\displaystyle \sum _{i=1}^N|d_i-d_{\mathrm{m}\mathrm{e}\mathrm{a}\mathrm{n}}|}}\right),

(7)WI=1- \left[\frac{{\displaystyle \sum _{i=1}^N(d_i-y_i)}}{{\displaystyle \sum _{i=1}^N\left(\right|y_i-d_{\mathrm{m}\mathrm{e}\mathrm{a}\mathrm{n}}|+|d_i-d_{\mathrm{m}\mathrm{e}\mathrm{a}\mathrm{n}}|{)}^2}}\right],

(8)NSE=1 -\frac{{\displaystyle \sum _{i=1}^N(d_i-y_i{)}^2}}{{\displaystyle \sum _{i=1}^N(d_i-d_{\mathrm{m}\mathrm{e}\mathrm{a}\mathrm{n}}{)}^2}},

(9)MAE=\frac{{\displaystyle \sum _{i=1}^n\left|\left(y_i-d_i\right)\right|}}{N},

(10)WMAPE =\frac{{\displaystyle \sum _{i=1}^n\left|{\displaystyle \frac{d_i-y_i}{d_i}}\right|\times d_i}}{{\displaystyle \sum _{i=1}^n{d}_i}},

where d_i = observed ith value, d_mean = average of the observed values, y_i = predicted ith value, N = the number of sample data points, SD is standard deviation, LMI is Legates and MacCabe’s Index, WI is Willmott’s Index of Agreement, and NSE is Nash-Sutcliffe Efficiency.

3 Results and discussion

The evaluation performance metrics of the researched models appear in Tab.4 and Tab.5 for the training and testing phases. All studied models demonstrate reliable capability in estimating and testing CCS relationships during training. The RF model achieved higher accuracy during training through its fitness metrics (R² = 0.9650, RMSE = 0.0798) than other models and was followed by GBM and DNN. The actual and predicted CCS values match closely, as shown in Fig.5, indicating the robust training performance of these models. During testing, the RF model displayed excellent performance because it achieved an R² value of 0.9399, which the GBM model followed closely with an R² value of 0.9282. The DNN model showed a lower correlation than both RF and GBM, according to Fig.6. A reduction in error values determined the performance strength of each model. Tab.6 shows the multiple model rankings in summary form. The RMSE and SD, together with Pearson’s correlation coefficient (PCC) between observed and predicted values, are provided in the Taylor diagram presented in Fig.7.

3.1 Rank analysis

Machine learning models generally show inconsistent results when testing rather than training data sets. A standard rank analysis is an effective tool for determining the general performance quality of Machine learning models across all statistical metrics. The evaluation method was used to assess all three model performances. The evaluation score for every model depended on its prediction accuracy throughout training and testing data sets. Each data set received its error-based ranking with the lowest error, obtaining a score of 1, and the others received rising ranks accordingly. The performance evaluation of all models was calculated by adding their assigned ranks across each data set. The final model ranking stemmed from combining scores from splitting the data into multiple sections. The image in Fig.8 represents the ranking outcomes achieved from this assessment.

3.2 Regression error characteristics curve

REC curves extend the concept of receiver operating characteristic (ROC) curves to regression analysis [52], providing a valuable tool for visualizing and comparing classification outcomes [53]. The regression explanation to non-professionals becomes easier with REC curves. REC curves use error tolerance as the X-axis scale and proportion of accurate predictions as the Y-axis scale. Error tolerance appears in REC curves through two formats: absolute deviations and squared residuals, indicating how accuracy levels relate to error tolerance limits. This error evaluation tool depicts the total distribution of differences between predictions and observations, enabling researchers to distinguish model performances when various models exhibit small or significant variations. The REC curve is an effective method to evaluate regression model effectiveness because it analyzes prediction error distributions at different thresholds [54]. A single benefit distinguishes REC from ROC since ROC services classification models, but REC analyzes regression model accuracy by measuring predicted value correspondence to actual measurements. The visualization depicts how prediction or absolute errors accumulate against predicted values through the cumulative distribution shape, demonstrating error distribution across the whole range of predictions. This visual representation facilitates evaluating the model’s performance across different data segments. Through analysis of the REC curve, practitioners can interpret the accuracy of the regression model because it demonstrates prediction success frequencies across various error ranges. The graphical representation demonstrates which percentage of predictions stay within an error interval that measures ten percent of actual values. The performance consistency of a model becomes evident through the REC analysis because it shows where errors become significantly large. The distribution information provides essential knowledge for applications that require precise measurements because it helps identify model weaknesses. The REC curve proves essential for evaluating and selecting between different regression models. Researcher assessment becomes easier through the side-by-side graph comparison of different models’ REC curves which helps identify superior error distribution performance. Models which show consistent lower cumulative error quantities at each threshold level earn the classification of precision. A comparative analysis enables one to pick the most suitable model for a regression task since it yields crucial insights about model prediction reliability and stability. The figures in Fig.9 present the REC curves for the three models during training and testing sessions.

3.3 Graphical User Interface (GUI)

A GUI is an interactive platform that enhances user accessibility by visually interacting with software applications. In this study, a user-friendly GUI was designed to predict the CCS of HPC, as shown in Fig.10. Built upon advanced machine learning models, the GUI leverages sophisticated algorithms to analyze data and generate reliable strength predictions, making it a valuable resource for researchers and professionals alike. This tool allows users to input significant parameters that quickly and accurately predict the CCS of HPC. Thus, structural engineers save the time, labor work, and cost required to conduct the traditional laboratory methods. The intuitive interface of this tool simplifies the data entry process estimate CCS of HPC without needing specialized expertise in machine learning. This GUI promotes efficiency and enables more frequent and widespread testing by streamlining the estimation process, supporting data-driven decision-making in the construction industry. Overall, it represents a practical and accessible solution, empowering users to harness the power of machine learning for rapid, non-destructive assessment of concrete properties.

4 Conclusions

Different machine learning models enable this research to maximize the reliability and accuracy of HPC CCS prediction. GBM joins RF and DNN among the models utilized in this research. This analysis comprehensively analyses how the models function independently during training and testing periods for maximum predictive ability. Seven parameters of C, Fa, SB, W, SP, CA, and FA were chosen for the study since avoiding dimensionality reduction allows direct model performance assessment. A complex evaluation system analyzed the fundamental data relationships in CCS data for all models to enhance prediction capabilities. The bootstrap method employed an RF algorithm, demonstrating the best learning outcomes for CCS data relationships during training with 0.9650 R² value and 0.0798 RMSE compared to GBM (R² = 0.9352) and DNN (R² = 0.9098). The performance ranking stands as RF shows maximum results while GBM follows, with DNN trailing behind. During testing, R² values reached 0.9399 for RF while GBM obtained 0.9282 and DNN established 0.9349. The experiment phase performed best with RF, demonstrating superior results to GBM and DNN. The best-measured model performance confirms it can provide stable results on untested data sets. A complete ranking metric review showed RF outperforming GBM and DNN in all statistical evaluation criteria, including R², RMSE, U₉₅, LMI, WI, NSE, MAE, and WMAPE. RF obtained the highest rankings for all metrics when evaluating performance against GBM and DNN models. The predictive performance superiority of RF becomes evident from the Taylor diagram, which displays RMSE, standard deviation, and Pearson correlation coefficient values. The visual model performance assessment tool used REC curves.

The REC evaluation showed that RF and GBM produced more promising error patterns than DNN, demonstrating increased total errors within different tolerance ranges. Developing a user-friendly GUI enabled easy performance of CCS on HPC predictions. The various metrics and data sets during model evaluation confirm that RF effectively handles the complex interactions in CCS data. Studies should explore optimization methods for prediction models, including combination algorithms or dimensionality reductions, to boost the predictive quality. The presented work demonstrates how machine learning methods help improve concrete strength evaluation with practical benefits for the construction sector’s data-based decision-making process.

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