Evaluation of Compressive Strength of Expanded Polystyrene Concrete Based on Broad Learning System

Abstract

Expanded polystyrene (EPS) concrete, with excellent properties such as light weight, thermal insulation, and soundproofing, is widely applied in construction engineering. However, its complex heterogeneous internal structure makes it difficult to quickly and accurately assess compressive strength. Existing testing methods struggle to meet the real-time demands of on-site quality control in terms of both operational efficiency and accuracy. To address this, the present study proposes a method for predicting the compressive strength of EPS concrete based on image processing and Deep Convolutional Neural Networks (DCNN). By constructing a dataset consisting of 5600 preprocessed concrete slice images and addressing the issue of parameter redundancy in fully connected layers, the Broad Learning System (BLS) was employed to reconstruct and optimize the network architecture, thereby improving computational efficiency and enhancing prediction accuracy. The experimental results indicate that after introducing the BLS and related training optimization mechanisms, the training time was reduced by approximately 15%. Among all models, the BLS-Xception model performed the best, requiring only 1.9 s per training image. The coefficient of determination (R²) on the test set reached 0.95, representing an 18.7% improvement over traditional models. The study also indicates that the appropriate incorporation of coal ash, silica fume, and mineral powder significantly enhances the compressive strength of EPS concrete, with smaller EPS particles contributing more substantially to strength improvement. The model demonstrates excellent accuracy and reliability in predictions, providing an effective method for the rapid, non-destructive evaluation of the compressive strength of EPS concrete on construction sites.

1. Introduction

Expanded polystyrene (EPS) concrete has gained increasing attention in contemporary construction owing to its advantages of low density, favorable thermal insulation, and sound absorption performance [1]. In practical engineering applications, the reliable assessment of compressive strength is essential for construction quality control, structural safety evaluation, and the subsequent optimization of design schemes [2]. Nevertheless, the accurate strength evaluation of EPS concrete remains challenging. The difficulty mainly arises from its highly heterogeneous composition and pronounced porous microstructure [3,4]. Conventional destructive testing methods, such as standard cube compression tests, are unsuitable for in situ applications due to their intrusive nature. Core drilling techniques, although commonly used, are strongly influenced by the nonuniform distribution of EPS particles and voids, which often leads to large variability and poor repeatability of test results. In addition, commonly adopted nondestructive testing (NDT) approaches, including rebound hammer and ultrasonic pulse velocity methods, exhibit limited reliability when applied to EPS concrete. The inherently low strength, high porosity, and structural discontinuity of EPS concrete significantly distort signal propagation and surface response, thereby reducing measurement accuracy and restricting their applicability for on-site strength evaluation [5,6]. Consequently, these traditional methods are impractical for in situ compressive strength assessment of EPS concrete in real-world engineering applications, hindering timely quality control. Therefore, a reliable method for accurately predicting the compressive strength of EPS concrete needs to be established in advance.

Developing efficient and intelligent methods for compressive strength evaluation of EPS concrete is crucial for rapid on-site assessment, accuracy improvement, and cost reduction in engineering practice. In recent years, related studies have been conducted in the manufacturing and machining domain. Oguzhan developed a multi-output prediction framework using process parameters as inputs to model and predict multiple quality responses, such as surface roughness, kerf width, and the heat-affected zone, demonstrating that data-driven approaches can effectively support quality assessment and process optimization [7]. Various non-destructive and vision-based inspection techniques have been explored for concrete and cement-based materials, aiming to replace conventional intrusive testing methods and enhance efficiency in engineering practice [8,9]. Early studies introduced three-dimensional laser scanning techniques for surface quality inspection of precast concrete components, demonstrating their potential in geometric measurement and defect detection [10,11]. Subsequently, mirror-assisted scanning strategies were proposed to address accuracy degradation and occlusion issues in ground-based laser scanning, enabling the more precise and efficient evaluation of concrete surface flatness [12]. To further improve data processing efficiency, some studies transformed three-dimensional laser scanning data into two-dimensional images and combined image processing with machine learning algorithms, such as radial basis nearest neighbor methods, to accelerate segmentation of large-scale scanning datasets [13]. In addition, slice-based mapping approaches were developed to reconstruct three-dimensional as-built models at prefabricated construction sites, effectively mitigating local detail loss and noise interference in quality inspection processes [14]. Despite the progress achieved by these approaches, their practical application in engineering environments remains constrained by several factors. In addition to the large data volume and high computational cost associated with laser-based scanning, many advanced sensing techniques require specialized equipment, complex data acquisition procedures, and strict site conditions, which limit their efficiency and scalability in routine construction practice [15]. Moreover, the complexity of data processing and the demand for high-performance computing resources further hinder their widespread adoption for rapid on-site assessment. In comparison, image-based data acquisition provides a more accessible and flexible alternative. Images can be obtained with minimal equipment requirements and lower data-processing overhead, while recent advances in image analysis and object detection enable efficient extraction of structurally relevant information.

In recent years, continuous advances in computer vision and image processing technologies have promoted the increasing adoption of image-based approaches in engineering applications, including industrial monitoring [16], structural safety assessment [17], and damage evaluation of concrete materials [18]. Yu et al. provided the first systematic review of non-contact tool condition monitoring in machining based on computer vision, highlighting that the analysis of tool-surface images can extract key features related to wear severity and cutting-edge degradation, thereby enabling effective characterization and assessment of the tool’s real-time condition [19]. Başyiğit studies demonstrated that compressive strength can be effectively estimated by extracting morphological features from sliced concrete surfaces under controlled lighting conditions using conventional image processing techniques [20]. Subsequently, image processing methods were combined with artificial neural networks to analyze surface texture characteristics, achieving prediction accuracies exceeding 90 percent and further confirming the feasibility of image driven strength prediction models [21]. However, many of these approaches still rely on manually designed image features or relatively shallow learning frameworks. As a result, their capability to fully represent the complex spatial variability and multiscale heterogeneity inherent in EPS concrete images remains limited.

To address these limitations, deep convolutional neural networks have been increasingly adopted because of their strong ability to automatically learn hierarchical image features through convolutional layers [22]. These features range from low level edges and textures to higher level structural patterns, enabling more accurate modeling of heterogeneous materials such as EPS concrete [23,24,25]. Owing to the parameter sharing mechanism of sliding convolutional kernels, DCNNs can significantly reduce the number of trainable parameters while improving training efficiency when processing high dimensional image data [26]. Moreover, advanced network architectures such as VGG and ResNet facilitate deeper feature abstraction and enhanced generalization performance in complex prediction tasks [27,28]. Previous studies have confirmed the superior performance of DCNNs in compressive strength prediction. High resolution image-based investigations have shown that DCNN models outperform traditional artificial neural networks in prediction accuracy [29].

Traditional deep convolutional neural networks often suffer from parameter redundancy, particularly in fully connected layers, which increases computational complexity and reduces training efficiency. This limitation restricts their applicability in scenarios requiring fast or near real-time prediction. To overcome this issue, Chen [30] proposed the Broad Learning System (BLS), a shallow yet efficient learning framework based on incremental learning and lateral network expansion. By replacing deep hierarchical structures with wide feature and enhancement node mappings, BLS significantly improves computational efficiency while retaining strong representation capability. Subsequently, a regularized and robust version of BLS was developed to enhance model stability and robustness against outliers and noisy data [31]. This improvement enables BLS to effectively handle incomplete or contaminated datasets, leading to notable gains in both prediction accuracy and computational performance. Further extensions of BLS have demonstrated its effectiveness in nonparametric spatial modeling, where it overcomes the limitations of traditional methods in capturing complex spatial relationships and improves generalization performance [32,33]. Moreover, the introduction of advanced feature mapping strategies and adaptive node selection mechanisms further strengthens the flexibility and learning capacity of BLS. These enhancements allow the model to efficiently process complex nonlinear data while maintaining high computational efficiency, making BLS particularly suitable for engineering applications involving high-dimensional and heterogeneous data. Although considerable efforts have been made to reduce parameter redundancy in conventional convolutional neural networks, existing studies rarely address the efficient and accurate analysis of multivariate image datasets involving material-related variables, such as cementitious material replacement levels, EPS particle content, and particle size distribution. This limitation restricts the applicability of current deep learning models in complex material systems encountered in engineering practice.

In this study, the feature mapping and representation mechanisms of convolutional neural networks were systematically optimized to enhance the accurate extraction of local image features. At the same time, the consistency and integrity of feature information were improved during the feature-sharing process. By strengthening feature interaction and improving information flow efficiency, the overall representation capability and prediction accuracy of the model were further enhanced. On this basis, a novel modeling framework was developed to enable reliable prediction of the compressive strength of EPS concrete. The main contributions of this study are summarized as follows:

• A novel model named BLS-Xception was proposed, which integrates the feature extraction capability of deep convolutional networks with the efficient learning mechanism of the BLS. The proposed model effectively alleviates feature redundancy and improves learning efficiency when dealing with heterogeneous image data, demonstrating enhanced robustness in compressive strength prediction of EPS concrete.
• A dedicated image dataset of EPS concrete slices was established, consisting of 5600 high-quality cross-sectional images obtained through standardized cutting, background removal, cropping, and normalization procedures. This dataset provides a reliable visual basis for learning the intrinsic relationships between mesoscale structural characteristics and compressive strength.
• Comprehensive experimental investigations were conducted to validate the proposed model, systematically examining the effects of cementitious material replacement ratios, EPS particle contents, and particle sizes on the compressive strength of EPS concrete. The experimental results confirm the effectiveness of the BLS-Xception model in capturing strength-related features under varying material compositions.

2. Experimental Setup and Dataset Acquisition

2.1. Sample Preparation

The thermal insulation performance and mechanical strength of EPS concrete are jointly governed by EPS particles and the cementitious matrix. As a lightweight filler, the content and particle size of EPS directly affect the packing mode of the paste–particle system and the pore structure, thereby influencing material compactness and mechanical performance. On this basis, this study designs mix proportions by coordinating EPS parameters with the binder system and introduces different mineral admixtures to achieve controlled replacement and optimization of cementitious materials.

The materials used in this study include 42.5 R ordinary Portland cement produced by Xinjiang Tianshan Cement Plant, whose properties were tested according to the Chinese standard Common Portland Cement (GB 175-2007) [34], EPS particles supplied by Xinjian Tengda Thermal Insulation Materials Co., Ltd. (Fukang, China), fly ash from Xinjiang Tianshan Electric Power Manas Power Plant, S75-grade ground granulated blast-furnace slag from Xinjiang Shengyuan Co., Ltd., Tulufan, China, and silica fume produced by Jinrun New Materials Co., Ltd., Zhengzhou, China. The experimental variables include EPS particle content, EPS particle size, type of mineral admixture, and mineral admixture replacement ratio. The EPS volume fractions were set at 85%, 80%, 75%, and 70%. Two EPS particle size ranges were adopted: 1.18–2.36 mm and 4.75–6.3 mm. The replacement ratios of mineral admixtures were set at 10% and 20%. The main physical properties of cement are listed in

Table 1. Physical performance of Portland cement.

Grade	Specific Gravity (g/cm3)	Blaine Surface Area (m2/kg)	Setting Time (min)		Flexural Strength (MPa)		Compressive Strength (MPa)
			Initial	Final	3 d	28 d	3 d	28 d
42.5 R	3.18	339	147	179	5.3	7.7	27.4	49.8

, the main chemical compositions of mineral admixtures are given in

Table 2. Specifications of the cement, coal ash, silica fume and mineral powder.

Chemical Composition (%)	Cement	Silica Fume	Coal Ash	Mineral Powder
Silica	21.57	91.17	45.1	27.85
Aluminum oxide	4.91	0.19	24.2	12.93
Iron oxide	3.56	0.12	3	0.31
Loss on ignition	0.92	3.92	2.8	2.3

, and the detailed mix proportions are presented in

Table 3. Mix Proportion Details.

Label	Cement Percentage of Quality	Coal Ash Percentage of Quality	Silica Fume Percentage of Quality	Mineral Powder Percentage of Quality	EPS Percentage of Volume
100-C-85	100%	0	0	0	85%
100-C-80					80%
100-C-75					75%
100-C-70					70%
10-CA-85	90%	10%	0	0	85%
10-CA-80					80%
10-CA-75					75%
10-CA-70					70%
20-CA-85	80%	20%	0	0	85%
20-CA-80					80%
20-CA-75					75%
20-CA-70					70%
10-SF-85	90%	0	10%	0	85%
10-SF-80					80%
10-SF-75					75%
10-SF-70					70%
20-SF-85	80%	0	20%	0	85%
20-SF-80					80%
20-SF-75					75%
20-SF-70					70%
10-MP-85	90%	0	0	10%	85%
10-MP-80					80%
10-MP-75					75%
10-MP-70					70%
20-MP-85	80%	0	0	20%	85%
20-MP-80					80%
20-MP-75					75%
20-MP-70					70%

.

EPS concrete specimens were prepared in the Urumqi Metallurgical Group factory. The fresh mixtures were cast into 150 mm × 150 mm × 150 mm cubic molds and vibrated to ensure uniform distribution. After standard curing for 28 days, compressive strength tests, specimen cutting, slicing, and image acquisition were carried out in sequence. A total of 952 EPS concrete specimens were produced, among which 168 specimens were used for compressive strength testing [35], while the remaining 784 specimens were used for slice preparation and image data acquisition.

2.2. Sample Sectioning Procedure

Due to the lack of publicly available image datasets for EPS concrete, this study constructed an in-house dataset of EPS concrete cross-sectional images using the remaining 784 specimens. Each specimen was cut along the height direction into four slices with a thickness of approximately 37 mm. Both the top and bottom surfaces of each slice were photographed, resulting in eight cross-sectional images per specimen and a total of 784 × 8 = 6272 raw images. After image quality control and screening, 5600 valid images were retained in the final dataset. This multi-surface acquisition strategy was adopted to reduce the representation bias caused by EPS particle flotation when using a single cross-section. If only the top surface of the specimen were used, particle flotation could lead to distorted distribution features and consequently reduce the reliability of compressive strength prediction. In contrast, multi-slice and multi-surface images provide a more comprehensive representation of key features related to compressive strength, including paste morphology, pore structure, and the spatial distribution of EPS particles. Figure 1 illustrates the slicing scheme of EPS concrete specimens.

2.3. Compressive Strength Test

The compressive strength test was conducted in accordance with the relevant provisions of Standard for Test Methods of Physical and Mechanical Properties of Concrete (GB/T 50081-2019) [35]. A YES-2000 testing machine was used, with a loading rate of 0.2–0.3 MPa/s. The final compressive strength value was taken as the average of three specimens.

2.4. Image Acquisition

To ensure image quality and reproducibility, a dedicated imaging setup was established in a controlled environment to minimize the influence of ambient light variations and shadows [36,37].

• A box-type enclosure was built indoors using black blackout cloth (inner dimensions: 50 cm × 80 cm × 120 cm) with a 30 cm × 50 cm front opening; non-reflective covering was used to block ambient light and suppress specular reflections.
• The slice was placed at the center of the enclosure bottom and cleaned with an air blower; wet surfaces were air-dried to prevent glare.
• Two 15 W LED lamps (emitting area: 8 cm × 60 cm) were fixed on the side walls near the bottom (5 cm above the bottom plane and ~30 cm from the specimen edge), and the illuminance at the specimen center was calibrated to ~2000 lx (±5%).
• Images were acquired using a Canon EOS 3000D mounted on a rigid stand through a top opening, with the optical axis perpendicular to the slice surface and a fixed working distance of 60 cm (lens front to slice surface), at a resolution of 6000 × 4000 pixels.

A limitation of this study is that all specimens and images were collected from a single production center, which may restrict strict cross-factory generalizability to elements produced under different material sources and manufacturing conditions.

2.5. Image Preprocessing

Image quality and consistency directly affect the performance of compressive strength prediction models for EPS concrete. Therefore, targeted preprocessing was applied to all acquired images in this study. The core principle is to exploit the pronounced grayscale contrast between the EPS concrete cross-section and the black background to automatically remove background regions. Specifically, each image was first partitioned into regular pixel blocks, and the average grayscale value (0–255) of each block was calculated. Based on grayscale intensity discrimination, blocks with brightness significantly higher than the background were identified as concrete regions, while blocks with grayscale values close to black were classified as background and set to 0 (black). This procedure is equivalent to extracting the largest high-intensity region at the block level, thereby retaining only the core information associated with the EPS concrete cross-section. The overall processing workflow is illustrated in Figure 2. This approach effectively reduces the interference of background and edge noise during feature extraction.

After specimen regions were extracted, all processed images were resized to 224 × 224 pixels to meet the input requirements of the deep convolutional neural network. In addition, to mitigate the influence of illumination conditions and imaging variability, pixel values were normalized by linearly scaling them to the range of 0–1. This normalization improves training stability and accelerates model convergence. After preprocessing, the images were fed into the model in batches for subsequent training and analysis. The overall flowchart of the experiment is shown in Figure 3.

3. Model Architecture Design and Optimization

In this study, to improve the training efficiency and optimize the predictive performance of the model, pretrained convolutional neural networks (such as VGG19, ResNet101, and InceptionV3) were used as base models. A key improvement mechanism, the BLS, was introduced, along with three optimization strategies: ReduceLROnPlateau, freezing convolutional layers [38,39,40]. By monitoring the validation set loss, ReduceLROnPlateau automatically reduces the learning rate when the validation loss stops decreasing. This dynamic adjustment mechanism helps the model avoid becoming trapped in local optima during training, thereby enhancing convergence; this aspect is especially critical in complex datasets. By adjusting the learning rate in a timely 1 manner, the model can find the global optimum more quickly.

3.1. DCNN

In recent years, deep convolutional neural networks (DCNNs) have demonstrated remarkable advantages in image classification tasks, processing image data by extracting specific features from multiple arrays. Unlike traditional methods that primarily address data distortions caused by translation, scaling, and noise, DCNNs excel in learning hierarchical features through a sequence of convolutional, pooling, and fully connected layers. The convolutional layers capture local features, such as edges and textures, while deeper layers progressively learn more abstract representations. Pooling layers reduce spatial dimensions, enhancing computational efficiency and preventing overfitting. Finally, fully connected layers integrate these features for classification or regression, enabling DCNNs to achieve high accuracy and robustness in predictive tasks. The network architecture diagram of the DCNN is shown in Figure 4.

However, EPS concrete presents significant challenges in compressive strength prediction due to its internal heterogeneity, complex microstructure, and highly variable mechanical properties. While DCNNs have shown success in general image processing, they struggle to capture the fine-grained structural features inherent in EPS concrete, leading to suboptimal performance in strength estimation. To overcome these limitations, this study introduces a novel hybrid architecture, BLS-DCNN. By combining the strengths of BLS with the feature extraction capabilities of DCNN, the BLS-DCNN model is designed to enhance predictive accuracy and generalization ability, enabling more accurate and robust estimation of EPS concrete’s compressive strength.

3.2. BLS Basic Network

Traditional shallow neural networks often struggle to accurately capture the pore morphology, EPS particle distribution, and the interface transition zone—microscopic structural features that are rich in discriminative details—when processing EPS concrete images. This limitation in feature representation hampers their accuracy and generalization ability in predicting the mechanical properties of materials. To overcome these challenges, this study introduces a structure-enhanced Broad Learning System (BLS) network, incorporating a pre-trained deep convolutional neural network (DCNN) as the backbone feature extractor. This hybrid model effectively captures the multi-scale, high-dimensional structural information inherent in EPS concrete. To further improve predictive accuracy, BLS is integrated on top of the DCNN. Unlike traditional deep learning approaches that primarily rely on increasing network depth, BLS enhances data representation by expanding the feature space horizontally. In the BLS framework, input data are first processed through a mapping layer to generate initial feature maps, which are then expanded through enhancement nodes. This horizontal expansion enables the model to capture more complex feature relationships, making it well-suited for nonlinear and complex data. Furthermore, this approach enhances computational efficiency, providing a robust solution for modeling the heterogeneous structure of EPS concrete. A diagram of the BLS architecture is shown in Figure 5.

The input is assumed to have N samples and each sample has an M dimensional feature vector (L). The feature vector is mapped to feature nodes by random weights:

$$Z_i=\varphi (X{W}_{ei}+{\beta }_{ei}),i=1,...,n$$

(1)

where $Z_i$ is the $i$-th feature node, $W_{ei}$ and ${\beta }_{ei}$ are random weights and bias.

Denote $Z^n=[Z^1,\dots ,Z^n]$, the $m$-th enhancement node is defined:

$$H_m\equiv \xi (Z_n{W}_{h_m}+{\beta }_{h_m})$$

(2)

where $W_m$ and ${\beta }_m$ are random weights and bias.

Therefore, the model is given by:

$$\begin{array}{cc}{f}_c& =\left[Z_1,...,Z_n\mid \mathit{\xi }\left(Z_n{W}_{h_1}+{\mathit{\beta }}_{h_1}\right),...,\mathit{\xi }\left(Z^n{W}_{h_m}+{\mathit{\beta }}_{h_m}\right)\right]W^m\\ & =\left[\begin{array}{c}{Z}_1,...,Z_n\mid H_1,...,H_m\end{array}\right]W^m\\ & =\left[Z^n\mid H^m\right]W^m\end{array}$$

(3)

where $W^n=[{Z^n\mid H^m]}^{+}$, $f_c$ is the weight to be determined, and $[{Z^n\mid H^m]}^{+}$ is the pseudo-inverse of $[Z^n\mid H^m]$.

When the dataset contains many training samples, the cost of direct computation of the pseudo-inverse is high. However, it can be approximated by using ridge regression:

$${\left[Z^n\mid H^m\right]}^{+}={\left(\lambda I+\left[Z^n\mid H^m\right]{\left[Z^n\mid H^m\right]}^T\right)}^{-1}{\left[Z^n\mid H^m\right]}^T$$

(4)

where $\lambda$ is the regularization parameter.

In BLS, the number of enhancement nodes is a hyperparameter ($N_3$) but the number of feature nodes is a product of two hyperparameters: the number of feature windows ($N_1$) and the number of nodes in each feature window ($N_2$). In this paper, we utilized Bayesian optimization to find the optimal hyperparameters for the model. This can be executed by using the Hyperopt package, which makes use of the Tree-Parzen estimator to perform Bayesian optimization.

3.3. Optimization Mechanisms

Freezing convolutional layers is another critical aspect of model design. When pretrained models are used, freezing the convolutional layers preserves the low-level and mid-level features learned from large-scale datasets. These features prove effective in processing images of EPS concrete slices. Thus, freezing the convolutional layers not only reduces the number of parameters that need to be trained but also significantly shortens the training time and mitigates the risk of overfitting. In this scenario, only the last few fully connected layers are trained to learn high-level features tailored to the specific needs of predicting compressive strength. This approach effectively leverages the advantages of pretrained models while enhancing training efficiency.

To align with the specific task of this study, the output layer of the model was designed as a regression output layer, enabling the direct prediction of the compressive strength values of EPS concrete. This structure ensures that the model focuses on producing precise continuous numerical outputs tailored to experimental objectives. Additionally, a global average pooling (GAP) layer was incorporated to replace fully connected layers, significantly reducing the number of trainable parameters while maintaining model performance. By aggregating spatial information from feature maps, the GAP layer not only enhances computational efficiency but also minimizes the risk of overfitting, making the model more robust and suitable for the given dataset.

3.4. Model Construction and Training

3.4.1. Model Construction

In this study, several pretrained convolutional neural networks (CNNs), including VGG19, ResNet101, InceptionV3, Inception-ResNet V2, and Xception, were employed as baseline models. These architectures exhibit distinct structural characteristics and advantages. VGG19 [41] is a 19-layer CNN that adopts small convolutional kernels to effectively capture fine-grained image details; however, its large number of parameters results in relatively high computational complexity. ResNet101 introduces residual connections to alleviate the vanishing gradient problem, enabling the training of deeper networks with improved performance [42,43]. InceptionV3 and Inception-ResNet V2 combine inception modules with residual connections to efficiently extract multi-scale features, achieving a favorable balance between prediction accuracy and computational cost [44]. Xception employs depthwise separable convolutions, which significantly enhance computational efficiency while maintaining high classification accuracy [45].

3.4.2. Training Process

All experiments in this study were conducted on a Windows 11 platform using the PyTorch 2.0.0 framework (Torch 2.0.0 and torchvision 0.15.1). The workstation was equipped with a 13th-generation Intel^® Core™ i7-13700HX CPU (5.00 GHz) and an NVIDIA GeForce RTX 4090 GPU, with CUDA version 11.7 enabled for acceleration. To ensure consistency and comparability, all models were trained under identical hardware conditions, software environments, and hyperparameter settings. The dataset was split into training, validation, and testing sets with a ratio of 70% (3920 images) for training, 20% (1120 images) for validation, and 10% (560 images) for testing. This ratio was chosen to provide sufficient data for both training the models and evaluating their generalization ability on unseen data. To avoid potential data leakage and overestimation of performance due to multiple images from the same specimen appearing in both the training and test sets, the dataset partitioning in this study is performed at the specimen level, rather than the image level. Specifically, each EPS concrete specimen is treated as an independent grouping unit: all cross-sectional images extracted from the same specimen are assigned to only one subset—either the training set, validation set, or test set—ensuring that images from the same specimen do not appear in multiple subsets. As a result, during the model testing phase, the test data consists of specimens that were not seen during training, ensuring the objectivity and reproducibility of the performance evaluation.

To evaluate the performance of different DCNN models, this study employs MAPE, MAE, and RMSE as the primary evaluation metrics [46,47]. MAPE represents the Mean Absolute Percentage Error, where a value closer to 0 indicates better performance. RMSE represents the Root Mean Square Error, with smaller values indicating higher prediction accuracy. Additionally, R², the coefficient of determination, measures how well the model explains the fluctuations in the data, with a value closer to 1 suggesting better model performance. The coefficients of R², MAPE, and RMSE are defined as follows:

$${\mathrm{R}}^2=1-{\displaystyle \frac{\sum _{i=1}^n(y_i-{\widehat{y}}_i)}{\sum _{i=1}^n(y_i-{\stackrel{-}{y}}_i)}}$$

(5)

$$\mathrm{M}\mathrm{A}\mathrm{P}\mathrm{E}={\displaystyle \frac{1}{n}}\sum _{i=1}^n\left|{\displaystyle \frac{y_i-{\widehat{y}}_i}{y_i}}\right|\times 100\%$$

(6)

$$\mathrm{R}\mathrm{M}\mathrm{S}\mathrm{E}=\sqrt{{\displaystyle \frac{1}{n}}\sum _{i=1}^n(y_i-{\widehat{y}}_i{)}^2}$$

(7)

$$MAE={\displaystyle \frac{1}{n}}\sum _{i=1}^n\left|y_i-{\widehat{y}}_i\right|$$

(8)

$$MPE={\displaystyle \frac{1}{n}}\sum _{i=1}^n\left({\displaystyle \frac{y_i-{\widehat{y}}_i}{y_i}}\right)\times 100\%$$

(9)

where $y_i$ and ${\widehat{y}}_i$ represent the actual and predicted compressive strengths, ${\stackrel{-}{y}}_i$ is the mean of the actual compressive strengths, and $n$ denotes the total number of data samples.

4. Result

4.1. Analysis and Experimental Results of Compressive Strength of EPS Concrete

In this study, the compressive strength of EPS concrete was experimentally determined, and the influences of cementitious material replacement levels, polystyrene particle size, and EPS content on compressive strength were systematically investigated. The objective was to clarify the interactions among these parameters and to assess their combined effects on the mechanical performance of EPS concrete. For each mixture group, three specimens were tested to ensure data reliability, and the mean compressive strength was adopted to reduce the influence of random variability and potential outliers. The experimental results, together with the corresponding variation trends, are summarized in Figure 6.

Overall, the compressive strength of EPS concrete shows a general increasing trend as the EPS content decreases, although the degree of enhancement varies depending on the type of cementitious material used. For EPS concrete with particle sizes ranging from 1.18 to 2.36 mm, when the EPS content is 80%, the compressive strength of 100-C is 4.7 MPa. With the addition of 10% silica fume (10-SF), coal ash (10-CA), and mineral powder (10-MP), the strengths are 5.1 MPa, 5.7 MPa, and 5.8 MPa, respectively, representing relative increases of 8.5%, 21.3%, and 23.4%. At a 20% replacement level, the compressive strengths of 20-SF, 20-CA, and 20-MP are 4.8 MPa, 5.4 MPa, and 6.7 MPa, with mineral powder showing the most significant improvement, increasing by 42.6%. These results clearly demonstrate that mineral powder provides the most pronounced enhancement, followed by coal ash, and silica fume, especially at higher replacement levels, where the advantages of mineral powder become even more evident. The effect of reducing EPS content on compressive strength enhancement gradually weakens. When the EPS dosage decreases from 85% to 80%, the strength increases by 17.9%. However, when the EPS content further decreases from 80% to 75%, the strength improvement is only 9.2%, and from 75% to 70%, the increase is just 8.6%. This trend shows that as the EPS content decreases, the effect on strength enhancement becomes progressively weaker.

The overall compressive strength for the 4.75–6.3 mm group, shown in the right graph, is lower than that for the 1.18–2.36 mm group, reflecting the negative impact of larger EPS particles on the integrity and load-bearing capacity of the concrete structure. As smaller particles achieve a better distribution within the concrete matrix and form a more beneficial bond with the paste. The incorporation of supplementary cementitious materials still enhances the compressive strength of EPS concrete, with silica fume demonstrating the best overall performance, particularly at higher replacement levels (20%). This is consistent with its known micro-filling and pozzolanic effects, which improve the bonding strength and internal cohesion of the concrete [48], especially in mixtures containing larger EPS particles. Furthermore, the reduction in EPS content leads to a lower overall strength improvement compared to the small-particle EPS group, with the maximum average strength increase limited to just 11.6%.

Figure 7a illustrates the effects of different cementitious material types and replacement ratios on the compressive strength of EPS concrete at an EPS content of 70% and a particle size range of 1.18–2.36 mm. The compressive strength of the 100-C is 5.5 MPa, which serves as the reference level. After the incorporation of mineral admixtures, the compressive strength of EPS concrete increases to varying extents. Among them, MP exhibits the most pronounced strengthening effect: the compressive strength increases to 7.2 MPa at a 10% replacement ratio and further rises to 7.5 MPa at a 20% replacement ratio, representing the highest value under this condition. In comparison, CA shows a relatively limited enhancement effect, with compressive strengths of 6.9 MPa and 6.1 MPa at replacement ratios of 10% and 20%, respectively, both higher than that of plain cement but lower than those of the MP system. SF also provides a certain degree of strength improvement at this particle size, yielding a compressive strength of 6.2 MPa at a 10% replacement ratio; however, a slight reduction is observed when the replacement ratio increases to 20% (5.9 MPa).

Figure 7b presents the compressive strength results of EPS concrete incorporating different cementitious material systems when the EPS particle size increases to 4.75–6.3 mm. Overall, the compressive strength under this particle size condition is generally lower than that of the fine-particle group, indicating the adverse effect of larger EPS particles on matrix continuity and load-bearing capacity. The compressive strength of the 100-C is 4.1 MPa. After the incorporation of mineral admixtures, varying degrees of strength improvement are still observed. Among them, SF exhibits the most pronounced enhancement effect under this particle size condition: the compressive strength reaches 5.1 MPa at a 10% replacement ratio and further increases to 6.2 MPa at a 20% replacement ratio, which is significantly higher than those of the other cementitious systems. In contrast, the strengthening effects of MP and CA are relatively moderate. The compressive strengths of the MP system are 4.9 MPa and 5.3 MPa at replacement ratios of 10% and 20%, respectively, while those of the CA system are 4.9 MPa and 4.7 MPa, indicating limited improvement. A combined analysis of Figure 7 demonstrates that EPS particle size plays a significant role in regulating the strengthening effectiveness of cementitious materials. Under smaller particle size conditions (1.18–2.36 mm), slag powder provides the most evident enhancement in compressive strength, with a continuously increasing trend as the replacement ratio increases. In contrast, under larger particle size conditions (4.75–6.3 mm), silica fume exhibits a more pronounced advantage, as its high reactivity and micro-filling effect are more effective in improving the interfacial structure of EPS concrete containing larger EPS particles.

In summary, SF, CA, and MP exhibit distinct influences on the compressive strength of EPS concrete when used as partial cement replacements. At both 10% and 20% replacement levels, these mineral admixtures improve compressive strength compared with plain cement mixtures. Among them, MP shows the most pronounced strengthening effect, and its contribution increases with replacement rate. The highest compressive strength is achieved at 20% MP replacement, indicating that MP provides the greatest improvement within the investigated range. SF and CA also enhance strength, but their overall gains are less significant than those obtained with MP. A clear matching trend is observed between EPS particle size and the optimal cementitious system. For mixtures with smaller EPS particles, MP delivers the strongest and most stable strength enhancement, and 20% MP is the preferred option for maximizing compressive strength. In contrast, for mixtures with larger EPS particles, SF becomes more effective and shows a more pronounced strength benefit than MP and CA, indicating that SF is better suited for strength improvement when larger EPS particles are used. Therefore, 20% MP is recommended for EPS concrete with smaller EPS particles, whereas SF is the preferred choice for mixtures incorporating larger EPS particles; CA offers a moderate improvement across both cases.

4.2. Performance of the BLS-DCNN Model for EPS Concrete Prediction

In this study, five optimized convolutional neural network models—VGG19, ResNet101, InceptionV3 (InV3), Inception-ResNet V2 (InRNV2), and Xception—were employed to predict the compressive strength of EPS concrete. The experimental samples were prepared with different replacement rates of cementitious materials, varying EPS particle contents, and distinct EPS particle sizes. The measured compressive strength values ranged from 3.6 MPa to 7.44 MPa. To further improve training efficiency and prediction accuracy, several optimization strategies were introduced, including BLS integration, ReduceLROnPlateau, partial freezing of convolutional layers.

Figure 8 presents a comparison of the predicted and true compressive strength values of EPS concrete for various DCNN models. As shown, the BLS-DCNN models consistently outperformed their baseline counterparts, with a clear improvement in the coefficient of determination (R²), indicating better prediction accuracy. In particular, the BLS-Xception model exhibited the highest R² value of 0.95, significantly outperforming the other models in terms of fitting accuracy. The baseline Xception model, in contrast, had an R² value of 0.92. The addition of the BLS architecture led to a marked improvement in prediction performance, confirming the benefits of incorporating BLS to enhance feature representation and regression capability. The VGG19 model demonstrated a considerable improvement as well, with its R² value increasing from 0.88 to 0.91 after incorporating BLS. Similarly, the ResNet101 model showed an increase from 0.80 to 0.87, and the InceptionV3 and InceptionResNetV2 models both showed noticeable improvements in their R² values after the BLS enhancement (from 0.86 to 0.88 and from 0.87 to 0.89, respectively). These results highlight the effectiveness of the BLS architecture in improving the predictive performance of DCNN models, especially for more complex architectures. By providing a mechanism for better feature extraction and enhanced regression capacity, the BLS-DCNN models offer a powerful tool for predicting the compressive strength of EPS concrete with greater accuracy and robustness. In summary, incorporating the BLS architecture into various DCNN models significantly boosts their prediction capabilities. The BLS-Xception model, in particular, stands out as the best performer, making it an ideal choice for compressive strength prediction tasks in EPS concrete analysis. The consistent improvement across models suggests that BLS can be a valuable technique for strengthening deep learning models, particularly in cases of complex and heterogeneous materials like EPS concrete.

Figure 9 presents a comprehensive error analysis of the baseline DCNN models and their corresponding BLS-optimized versions. The prediction performance is evaluated using multiple metrics, including R², MAE, MAPE, RMSE, and MSE. Overall, the incorporation of the BLS architecture leads to consistent performance improvements across all models, as evidenced by increased R² values and simultaneous reductions in all error-related metrics. Compared with the baseline models, the BLS-enhanced models exhibit lower MAE, MAPE, RMSE, and MSE, indicating improved prediction accuracy and stability. However, the magnitude of improvement varies among different network architectures. This variation is mainly attributed to differences in network depth, parameter scale, and inherent feature extraction capability, which influence how effectively the BLS structure can enhance high-level representations. Among all evaluated models, the BLS-Xception framework demonstrates the most superior overall performance. Its R² value shows the most pronounced increase, while its MAPE decreases to approximately 6%, accompanied by the lowest RMSE and MSE among all models. The radar charts further reveal that BLS-Xception achieves the smallest enclosed area associated with error metrics and the largest expansion along the R² dimension, reflecting strong fitting capability and minimal prediction error. The superior performance of the BLS-Xception model can be attributed to the combination of deep convolutional feature extraction, depthwise separable convolutions, and the BLS-based enhancement mechanism. This integrated structure effectively captures multilevel image features related to the compressive strength of EPS concrete, while mitigating overfitting through cross-layer information fusion. Overall, these results indicate that the BLS-Xception model can effectively support the prediction of EPS concrete compressive strength based on image information, providing a practical tool for engineering applications.

In addition, to evaluate the stability and reproducibility of the results, we conducted five repeated runs with different random seeds for all models. As shown in Figure 10, the performance of all baseline CNNs and their BLS-augmented counterparts remains stable across five random seeds. For each model, the fluctuations of R², RMSE, and MAPE are small, indicating limited sensitivity to random initialization and data shuffling. Notably, the BLS-augmented variants generally maintain comparable or improved accuracy while exhibiting similarly low variability, suggesting that the proposed hybrid framework provides robust and reproducible predictions under different random settings. The stability is further confirmed by the statistics in

Table 4. Mean and standard deviation of performance metrics across random seeds for baseline models and BLS-augmented variants.

Model	R2-Mean	R2-Std	RMSE-Mean	RMSE-Std	MAPE-Mean (%)	MAPE-Std (%)
VGG19	0.890	0.012	0.695	0.018	7.65	0.18
ResNet101	0.808	0.014	0.791	0.021	7.84	0.42
InV3	0.857	0.008	0.705	0.012	7.45	0.39
InRNV2	0.854	0.018	0.696	0.026	7.29	0.32
Xception	0.908	0.013	0.622	0.020	6.92	0.31
BLS-VGG	0.900	0.018	0.649	0.028	6.10	0.24
BLS-ResNet	0.865	0.011	0.713	0.016	7.41	0.28
BLS-InV3	0.881	0.018	0.682	0.028	6.36	0.35
BLS-InRNV2	0.884	0.015	0.681	0.023	6.07	0.71
BLS-Xception	0.938	0.018	0.593	0.027	5.69	0.40

. Across five random seeds, all models exhibit small dispersions (R²-Std = 0.008–0.018, RMSE-Std = 0.012–0.028, and MAPE-Std = 0.18–0.71), indicating that the reported performance is not driven by a particular initialization. Among all candidates, BLS-Xception achieves the best overall accuracy with R² = 0.938 ± 0.018, RMSE = 0.593 ± 0.027, and MAPE = 5.69% ± 0.40%, while the baseline Xception reports R² = 0.908 ± 0.013, RMSE = 0.622 ± 0.020, and MAPE = 6.92% ± 0.31%. These results suggest that introducing BLS consistently improves predictive accuracy while maintaining stable performance across different random seeds. Nevertheless, a limitation of this study is that the model was trained and validated primarily on EPS concrete cross-sectional images acquired under controlled conditions; its robustness and cross-scenario generalization under low-quality, uncontrolled imaging conditions (e.g., smartphone capture with blur, noise, illumination fluctuations, and compression artifacts) have not yet been systematically evaluated. In future work, we will address this limitation by systematically incorporating smartphone-captured images and degradation-based augmentation strategies.

In addition, to compare CNN-based prediction using cross-sectional images with conventional regression using only mix-design parameters, we established several regression baselines that take mix-design variables as inputs, including XGBoost, MLP, SVR, and RF. These models were evaluated under the same metric system as the proposed BLS-Xception, and the test-set results are shown in Figure 11. Overall, mix-design–driven regression models can capture the general trend of strength variation, but their predictive capability is clearly limited. Among them, XGBoost performs best (R² = 0.70236, RMSE = 0.542, MAPE = 0.0891), followed by MLP (R² = 0.516, RMSE = 0.691, MAPE = 0.104), while SVR and RF show weaker fitting performance. In contrast, the image-based BLS-Xception achieves higher overall accuracy (R² = 0.9534, RMSE = 0.6073, MAPE = 0.0586). Using XGBoost as the strongest parameter baseline, BLS-Xception increases the test-set R² from 0.70236 to 0.9534 (a relative improvement of 35.74%) and reduces MAPE from 0.0891 to 0.0586 (a relative reduction of 34.23%). For RMSE, BLS-Xception yields 0.6073, which is slightly higher than that of XGBoost (0.542, by about 12%). Nevertheless, the higher R² and lower MAPE indicate more consistent fitting and better control of relative errors when image information is introduced. These results suggest that cross-sectional images provide additional and critical cues, such as pore structure and EPS particle distribution, which are difficult to characterize using mix-design parameters alone. Therefore, the comparison quantitatively demonstrates the contribution of image-based learning to compressive-strength prediction for EPS concrete.

To compare the prediction consistency of different models across material regimes defined by EPS content and particle size, Figure 12 presents the relative error distributions for each group. The relative errors of different models across EPS-content and particle-size groups generally fall within ±20%. With respect to EPS content, the EPS = 80% group exhibits the largest dispersion, featuring both overestimation points of around +10% and underestimation points approaching −10% or even lower; in contrast, the EPS = 70% and EPS = 85% groups show more concentrated error distributions and better overall stability. Regarding particle size, errors in the small-size range (1.18–2.36) fluctuate mostly around 0%, whereas the large-size range (4.75–6.3) contains more negative-error points, indicating a tendency toward systematic underestimation. This suggests that larger particle sizes may introduce greater bias or reduce the discriminative information in cross-sectional texture features. Overall, BLS-Xception yields errors closer to 0 with smaller fluctuations across all content and size ranges, demonstrating more consistent generalization across different material regimes.

4.3. Evaluation of Prediction Speed for BLS-DCNN Models

Figure 13 compares the average training time per image between the baseline models and their corresponding BLS-optimized versions across different DCNN architectures. Overall, the introduction of the BLS optimization strategy leads to a consistent reduction in per-image training time for all models. Among the evaluated networks, VGG19 exhibits the most pronounced reduction, with a decrease of approximately 27.1%, indicating that the BLS architecture is particularly effective in improving computational efficiency for models with a large number of parameters and fully connected layers. In comparison, more moderate reductions are observed for ResNet101, InceptionV3, InRN-V2, and Xception, with decreases of 6.2%, 7.1%, 12.6%, and 11.4%, respectively. This variation can be attributed to differences in network structure and feature extraction mechanisms. Models with heavier parameter dependence and deeper feature aggregation stages benefit more from the BLS framework, which reduces redundant parameter updates and simplifies feature mapping. In contrast, architectures such as Inception and Xception already employ efficient convolutional designs, limiting the relative gain achievable through BLS optimization. Nevertheless, the overall reduction in per-image training time demonstrates that the BLS-based approach can effectively enhance computational efficiency while maintaining prediction accuracy, thereby providing practical support for rapid and near-real-time strength assessment in engineering applications.

4.4. Ablation Study on Mechanism Contribution

To rigorously evaluate the contributions of each component in the BLS-Xception framework, we conducted a series of ablation experiments. In each experiment, we systematically removed Xception, BLS and compared them with BLS-Xception. All experiments were conducted under the same data partition, training strategy, and evaluation metrics.

As shown in

Table 5. Ablation Study Results of BLS-Xception.

Model Variant	R2	RMSE	MAPE	Per-Image Time (s)
Xception	0.9237	0.6441	0.0665	2.3
BLS	0.9019	0.6627	0.0691	1.7
BLS-Xception	0.9465	0.6073	0.0586	1.9

, the performance differences between the three models highlight the advantages of Xception and BLS. Specifically, Xception outperforms BLS in image feature extraction, particularly in capturing microscopic structural features, with an R² of 0.9237 and an RMSE of 0.6441. In contrast, using BLS alone results in a decrease in performance: R² drops to 0.9019 and RMSE increases to 0.6627, but the training speed improves, from 2.3 s to 1.7 s, indicating that BLS has a natural advantage over Xception in terms of running speed. The high accuracy of Xception is due to its deep feature extraction architecture, which leverages deep convolutional layers and Separable Convolution techniques to extract rich local features around each pixel in the image, enabling the model to achieve high prediction accuracy when handling complex surface texture structures. However, this inevitably leads to longer training times. On the other hand, BLS simplifies the learning process by avoiding the need for extensive training in complex fully connected layers, thus significantly improving training speed. Especially in controlling parameter redundancy, BLS reduces unnecessary computations through local learning strategies, enhancing both training and inference efficiency.

Further, the prediction accuracy of BLS-Xception improves to 0.9465, with the error further reduced, and the training time slightly increased compared to BLS. This indicates that by combining Xception deep feature extraction capabilities with BLS efficient learning mechanism, the BLS-Xception model achieves a balance between accuracy and efficiency. The rich image features captured by Xception allow the model to make more precise predictions, while the fast learning capability of BLS ensures that the model maintains efficient training on large-scale data, demonstrating outstanding performance in both accuracy and training efficiency, and fully leveraging the complementary advantages of the two mechanisms.

5. Conclusions

In this study, the effects of different cementitious material replacement rates, polystyrene particle sizes, and polystyrene particle contents on the compressive strength of EPS concrete. Furthermore, by introducing the BLS to enhance the traditional Convolutional Neural Network, a predictive modelcombining image analysis was proposed (BLS-Xception). The incorporation of BLS represents a critical advancement, effectively improving predictive performance by addressing the discrepancies between experimental and predicted results, significantly enhancing the model’s accuracy. Based on the results obtained from cubic experimental tests, the compressive strength predictions made using this model were highly correlated with the actual test results. The model was capable of automatically extracting features and demonstrated high reliability and accuracy after systematic training, testing, and validation. These findings indicated that this model could be used as a method for onsite detection of the compressive strength of EPS concrete in real engineering projects. Based on the experimental and predicted results, the following conclusions can be drawn:

• The training time of the EPS concrete compressive strength prediction model was successfully optimized by introducing the mechanisms of BLS. The experimental results showed that these mechanisms significantly reduced the training time by approximately 15%. Among all models, the BLS-Xception model had the shortest training time, with each image taking only 1.9 s.
• Based on the combined evaluation of R2, MAE, MSE, MAPE and RMSE, the BLS-Xception model performed optimally. It achieved the highest R2 value of 0.95, along with the best performance in the other metrics, indicating superior prediction accuracy compared with the other models.
• The study demonstrates that as the polystyrene content increases, the compressive strength shows a progressive decline, with smaller EPS particles exhibiting better performance. The choice of cementitious materials significantly influences the compressive strength of concrete, with mineral powder showing the most pronounced enhancement effect for small-particle EPS. Silica fume performs better with larger EPS particles. The proposed BLS-Xception model effectively captures the impact of particle size, cementitious material type, and content on the mechanical properties, showcasing its practical application potential in EPS concrete strength prediction.