Introducing Methods for Analyzing and Detecting Concrete Cracks at the No. 3 Huaiyin Pumping Station in the South-to-North Water Diversion Project in China

Abstract

Concrete cracks pose significant threats to concrete structures, causing immediate strength loss and leading to gradual erosion that compromises structural integrity. Therefore, accurate and automatic detection and classification of concrete cracks, along with the evaluation of their effects on target structures, are critically important. This study focuses on the No. 3 Huaiyin pumping station, a large-scale hydraulic structure on the Eastern Route of the South-to-North Water Diversion Project in Jiangsu, China. First, relevant field test literature is reviewed, and the finite element method is applied to investigate the effects of an existing crack on the No. 2 supporting wall. Using thermomechanically coupled numerical simulations, the distribution of tensile stress in the supporting wall is reported in two cases: without a crack and with an existing crack. The findings indicate that the increase in tensile stress due to the existing crack is relatively small and can be considered negligible for the No. 2 supporting wall. Next, the pretrained YOLOX network for the detection and classification of three types of cracks is proposed and retrained using collected concrete crack datasets. The mean average precision of the retrained YOLOX network for all three types of cracks reaches 80%. Finally, the retrained YOLOX network is applied to detect and classify cracks at the No. 3 Huaiyin pumping station. This automatic detection and classification approach will enhance the high-quality management of the pumping station because it is labor-saving and easy to deploy.

1. Introduction

With the rapid economic development and population growth in China, there has been a significant increase in the construction of structures and infrastructure facilities, such as bridges, high-rise buildings, hydraulic structures, and tunnels. For example, the pumping station groups on the Eastern Route of the South-to-North Water Diversion Project in Jiangsu Province, China, were constructed in recent years to mitigate the water scarcity in Northern China. Concrete and reinforced concrete are predominantly used in these engineering constructions due to their excellent resistance to compressive stress and erosion, cost-effectiveness, and shape flexibility. However, one notable disadvantage of concrete and reinforced concrete is their brittleness under tensile stress. Consequently, if the tensile stress exceeds the tensile strength of the concrete, cracks will form. Several factors generally contribute to the formation of cracks in concrete, such as uneven settlement, the temperature difference between the exterior and interior of the concrete structure, the quality of the casting, and timely maintenance [1,2,3,4,5,6,7]. In this sense, a real-time health monitoring system is crucial to guaranteeing the safety of the structures [8,9,10]. For example, Arbaoui et al. [11] used an open-access crack database to detect the external cracks, whereas a customized wavelet technique was used to detect and monitor the internal cracks and crack initiation. The experimental study on crack monitoring using optical fiber sensors was carried out by Berrocal et al. [12] where the crack evolution was tracked and their location determined. Most errors in the location of cracks and crack width measurements were small, below 3 mm and 20 µm, respectively.

One primary cause of cracks in concrete structures is the temperature differential between the interior of the structures and their surroundings. It is well known that significant hydration heat accumulates in concrete at an early age, leading to a drastic increase in internal temperature. This local temperature differential results in increased tensile stress in the outer part of the concrete structure, which can eventually exceed the tensile strength of the concrete, leading to cracking. Other factors affecting the cracking of concrete include its shrinkage behavior and material properties such as surface heat insulation, and thermal expansion coefficient [13,14,15,16]. Additionally, the quality of the concrete during the casting procedure and the maintenance period afterward play a critical role. Poor control during casting can lower the tensile strength, increasing the risk of cracking even under normal environmental conditions [17,18]. Moccia et al. [19] investigated the effects of bleeding and plastic settlement of fresh concrete on the bond performance of reinforcement. They conducted 137 pull-out specimen tests under different casting conditions, clarifying the main influencing phenomena, including the potential presence of cracks and voids. In a separate study, Li et al. [20] addressed the penetrating cracking risk at an early age and the autogenous shrinkage problem in in situ cast underwater tunnels. Their research suggested that adopting a slight expansion mixture is an effective approach to preventing penetrating cracks and leakage in underwater tunnels. Similarly, a lack of timely and necessary maintenance after casting can also reduce the tensile strength of the concrete, making it more susceptible to cracking [21,22].

Cracks are harmful to concrete structures in several ways. For instance, they damage the integrity of the structure, leading to a loss of strength, reduced resistance capacity, and an increased risk of collapse. Moreover, cracks can shorten the lifespan of concrete structures due to gradual deterioration over time. Accurate and thorough evaluation of the effects of cracks on concrete structures is a complex and interdisciplinary challenge, warranting further investigation. In a study by Liu et al. [23], a multi-field coupling model was developed to assess the risk of shrinkage cracking in hardening concrete. The researchers also proposed three key technologies to mitigate thermal, autogenous, and drying shrinkage. The effectiveness of these technologies was demonstrated by their application in two engineering projects. Shen et al. [24] focused on the crack thermal resistance (CTR) effect using a thermomechanical coupled model. After validating the proposed model with a numerical uniaxial cyclic test of one element in ABAQUS, the model was applied to evaluate the CTR effect on a gravity dam. The findings showed little effect on the compressive stress state at the dam–foundation interface. As for the novel constitutive model development to account for the thermomechanical response of the concrete, Aidarov et al. [25] carried out an experiment and numerical study on fiber-reinforced concrete (FRC) to investigate the low-temperature effect on the mechanical behavior of the FRC. The results showed that the flexural strength of the FRC increases with a decrease in the surrounding temperature. The new constitutive model of steel fiber-reinforced concrete (SFRC), along with a temperature-dependent coefficient, was introduced by Wu et al. [26] to assess the mechanical behavior of the SFRC, taking into consideration the fiber dosage and fiber shape.

The shapes of cracks, such as vertical, lateral, and crossing cracks, can indicate different causes and have varying effects on concrete structures. Chourasia et al. [27] assessed building damage caused by land subsidence in Joshimath, India, and reported different crack patterns for various building types. For example, diagonal cracks were observed due to differential settlements in masonry buildings, while slide shear failures due to low vertical load appeared as lateral cracks. Kadiyan et al. [28] investigated the impact of the depletion-induced subsidence on local houses in the Mohali-Chandigarh area, India, and characterized the cracks into tensional cracks, compressional cracks, and shear cracks according to factors such as the shape, size, orientation, surface morphology, etc. In this context, it is significant to distinguish between different types of concrete cracks. However, there are few studies that detect and classify concrete cracks into multiple categories; most commonly, a binary classification strategy is adopted, i.e., crack images are simply classified as either crack images or non-crack images. For example, Qiu and Lau [29] investigated real-time crack detection using the You Only Look Once (YOLO) series via an unmanned aerial vehicle. They evaluated YOLOv2 to YOLOv4 and achieved over 90% accuracy under various harsh environmental conditions, but only for crack and non-crack detection. Khan et al. [30] reviewed the different image processing techniques for accurately detecting concrete cracks and highlighted the pros and cons of the used techniques.

This study is based on the large-scale hydraulic engineering structure of the No. 3 Huaiyin pumping station. The pumping station is a crucial component of the Eastern Route of the South-to-North Water Diversion Project (ERSNWDP) in China, with a total power capacity of 10,000 kW. Construction of the pumping station began in April 2007, and it became operational in October 2012. In July 2017, cracks were first discovered in the wing walls, piers, and supporting walls of the auxiliary equipment chambers. Subsequently, field tests were conducted, including the rebound hammer method to estimate the compressive strength of the reinforced concrete structures, drilling core samples of the concrete at the crack regions and inspecting and measuring the width of the cracks [31]. These field test results provide a foundation for further assessment of the damage trend in the concrete structures at the No. 3 Huaiyin pumping station. Additionally, this study proposes a method for the automatic detection and classification of cracks into multiple groups, aimed at reducing labor requirements.

Based on the above-mentioned background, the motivation for this study can be summarized into two main objectives. The first objective is to explore the impact of an existing crack on concrete structures over the coming years. To address this, the finite element method is applied to simulate the coupled thermomechanical behavior of the No. 2 supporting wall in the pumping station. The steady-state analysis step is carried out to accurately mirror the actual thermomechanical responses. The maximum tensile stress in the structures, both with and without cracks, is calculated, and the corresponding stress contours are illustrated under two scenarios: temperature increase and temperature decrease. Additionally, the stress states of the monitoring points near the designed crack are statistically analyzed to gain insights into the future cracking risks of the concrete structures. The second objective is to develop an effective method for the detection and classification of cracks on the surfaces of the concrete structures at the No. 3 Huaiyin pumping station in a labor-saving manner. This is crucial for the cost-effective and safe management of the pumping station as timely and efficient inspection of cracks ensures the station operates normally, economically, and safely. To achieve this, we employ the You Only Look Once X (YOLOX) detector, which balances accuracy and speed and can be conveniently deployed on mobile devices. The YOLOX network is retrained via transfer learning to the collected crack database to accurately detect and classify cracks on concrete surfaces, followed by validation and testing. The flowchart of this study is depicted in Figure 1 below.

The contributions of this study can be summarized into two main points. First, the study provides a numerical analysis of the stress states in the concrete structures under two conditions: without a crack and with a crack, in both temperature-increasing and temperature-decreasing scenarios. Additionally, the stress states of the seven monitoring points near the designed crack are analyzed statistically under the thermomechanical coupled condition. This analysis can serve as a reference for other research on similar engineering structures. Second, the cutting-edge YOLOX network is retrained, validated, and tested for potential use in detecting and classifying cracks on the surfaces of the concrete structures at the No. 3 Huaiyin pumping station. The advantages of YOLOX, including its lightweight, labor-saving, and accurate performance, can significantly improve the management quality of the pumping station and reduce maintenance burdens.

The rest of the paper is structured as follows: Section 2 introduces the methodologies adopted in this study, namely, the finite element method and the YOLOX detector based on the convolutional neural network (CNN). Section 3 presents the field test results and the numerical simulation results of the pumping station using the finite element method, including a brief background of the No. 3 Huaiyin pumping station. Section 4 details the retraining, validation, and testing processes of the YOLOX detector, along with its application to the No. 3 Huaiyin pumping station. Finally, conclusions are drawn in Section 5.

2. Methodology

2.1. Brief Introduction of the Finite Element Method

The finite element method is a widely used numerical technique that divides the domain of interest into finite subregions, or elements, and connects these elements with nodes. A group of partial differential equations is then formulated to solve the target problem. This process discretizes the continuous physical problem into adjacent elements with unknown nodal values. An approximating function based on these nodal values is sought, allowing for high precision through a piece-wise approximation approach achieved by increasing the number of elements. Additionally, the resolution of the resulting sparse equation system is relatively easier after discretization, giving the finite element method an advantage in handling a large number of nodal unknowns. The unknown values in the elements can be retrieved using an interpolation method that leverages the obtained nodal values. Commonly used techniques like the Galerkin method and variational formulation method are employed to transform the physical formulation of the problem into discretized forms, which are then assembled to solve the resulting algebraic equations [32,33,34]:

$$K_{ij}{u}_j=f_i$$

(1)

where u_j is the displacement at the jth node and f_i is the external force applied at the ith nodes; K_ij is called the global stiffness matrix, with a total assembly of stiffnesses.

The differential equation of heat conduction in concrete can be expressed as [35,36]:

$$\rho c_p{\displaystyle \frac{\partial T}{\partial t}}=k({\displaystyle \frac{{\partial }^{2}T}{{\partial }^{2}x}}+{\displaystyle \frac{{\partial }^{2}T}{{\partial }^{2}y}}+{\displaystyle \frac{{\partial }^{2}T}{{\partial }^{2}z}})+q_t$$

(2)

where ρ is density in units of kg/m³, c_p is specific heat in units of J/kg·K, and T denotes temperature in units of °C. The t is time in units of the hour, k is thermal conductivity in units of W/m·K, q_t is the rate of heat released in units of J/h·m³, while x, y, and z are position coordinates.

The boundary condition at the surface of the concrete structures that transfers heat from the concrete to the surrounding air can be considered as follows [35,37]:

$$q_c=h(Ts-Ta)$$

(3)

Here, q_c is a rate of heat transfer in units of W/m², Ts and Ta denote the surface temperature of the target structure and the surrounding air temperature, respectively, and h is a convention coefficient in units of W/m²·K.

Specifically, in this study, a total of 4080 continuum three-dimensional (3D) 8-node thermomechanical elements are used to simulate the actual No. 2 supporting wall at the No. 3 Huaiyin pumping station, utilizing an elastic constitutive model. The existing crack on the No. 2 supporting wall is simulated using the same elements but with a reduced value of the Young’s modulus parameter. To elaborate on the simulation process, a temperature-decreasing scenario is taken as an example. In this scenario, we set the predefined temperature field for the No. 2 supporting wall to 14.9 °C in the first analysis step. Then, a steady-state thermal-stress coupled analysis step, which is time-independent, is initiated. The boundary conditions of the model are set as follows: the front and back surfaces of the No. 2 supporting wall along the water flow direction are fixed in the x and y directions as well as the top surface because they are connected to adjacent structures (the Cartesian system is shown in the following corresponding figure). The bottom surface of the No. 2 supporting wall is fixed in the x, y, and z directions as the mechanical boundary condition. The left and right surfaces of the No. 2 supporting wall are free in the mechanical boundary condition, but the convection condition is considered. The temperature conditions on these two surfaces are set with a convection coefficient of 7.12 W/m²·K and an ambient temperature of −0.3 °C. The numerical task is then submitted to run, yielding the coupled thermal stress results. The detailed process and parameter settings in the simulation are presented in the following section.

2.2. A Brief Review of the YOLOX

The YOLO series has emerged as a powerful object detection tool widely utilized in recent industrial applications due to its real-time detection capabilities and relatively high precision. The relatively recent advancement in this series, YOLOX, introduced in 2021 [38], features an anchor-free and decoupled detection head. In their study, the decoupled head was found to expedite convergence and enhance the end-to-end strategy, while the anchor-free approach effectively reduced parameter counts and mitigated issues such as anchor clustering and grid sensitivity, simplifying the decoding phase. The architecture of YOLOX is schematically depicted in Figure 2.

The YOLOX network consists primarily of three components: the backbone network, the neck or feature pyramid network, and a decoupled detection head, as illustrated in Figure 2. At the core of the YOLOX network is a pretrained convolutional neural network called CSP-DarkNet-53, which has been trained on the Common Objects in Context (COCO) dataset. This backbone serves as the feature extractor, generating feature maps from the input images.

The neck component acts as a connector between the backbone and the head. It includes a feature pyramid network (FPN) that provides multi-scale feature maps and grids, along with a path aggregation network that merges both low-level and high-level features. The neck merges feature maps from the backbone layers and delivers them to the head at different scales.

The decoupled head processes the aggregated features into three feature channels, including classification scores, regression scores (indicating the location and dimensions of the bounding boxes), and objectness scores for intersection over union (IoU). YOLOX-Tiny is a lightweight version of YOLOX, containing 5.06 M parameters and achieving an average precision of 32.8% on COCO Train2017 [39].

In this study, the pretrained YOLOX network is retrained using the transfer learning technique. This technique makes the pretrained YOLOX network, based on a large database, feasible for use with a relatively small dataset. The first important step in the retraining process is to manually label all three types of concrete cracks in the collected images. Then, the dataset is split for training, validation, and testing. We will detail the process in the following section, including the split ratio and the training parameter settings.

3. Field Test and Numerical Simulation Results

3.1. Background of the No. 3 Huaiyin Pumping Station and Field Tests Conducted

The No. 3 Huaiyin pumping station, located in the suburbs of Huai’an City and adjacent to the No. 1 Huaiyin pumping station, is one of the key large-scale hydraulic structures on the Eastern Route of the South-to-North Water Diversion Project (ERSNWDP) in China, which aims to mitigate water scarcity in Northern China [40]. Construction of the pumping station began in April 2007, and it was put into operation in October 2012. The station is equipped with four horizontal axial-flow pump units, each powered by variable-frequency motors for electricity-saving purposes. Each pump unit has a rated flow of 34 m³/s and an impeller diameter of 3.3 m. One unit serves as a spare, while the others serve as main units. The designed total water flow of the No. 3 Huaiyin pumping station is 100 m³/s, and the total installed power capacity is 10,000 kW. Figure 3a provides a bird’s-eye view of the No. 3 Huaiyin pumping station, while Figure 3b offers a partial interior view.

Figure 3c presents a photo of the field tests conducted in July 2017. Some of the concrete core samples taken during the on-site test are illustrated in Figure 4. Figure 4a shows a concrete core sample taken from the No. 1 isolation pier, with a crack length of approximately 37 cm. Figure 4b displays a concrete sample taken from the No. 3 isolation pier where the crack extends almost from top to bottom along the longitudinal direction of the sample.

Figure 5a,b shows the distribution of cracks in the right part of the No. 1 isolation pier and the left part of the No. 3 isolation pier. Figure 5a reveals six cracks in the right part of the No. 1 isolation pier. For specific details about a particular crack, such as the lowest crack in Figure 5a, it is convenient to note that the location of the lowest crack is 0.3 m from the bottom and 3.1 m from the downstream edge of the isolation pier. Additionally, the width of the crack is measured at 0.41 mm, according to Figure 5a.

Figure 5c,d depicts measurements of the crack widths in the No. 1 and No. 3 isolation piers, respectively. The ZBL-F103 crack width observation instrument was utilized for these measurements. The crack with a width of 0.62 mm is the second crack in the right part of the No. 1 isolation pier from the top. Additionally, the crack with a width of 0.5 mm is the first crack shown in Figure 5b from the top.

3.2. The Numerical Simulation Results and Discussion

The whole finite element model of the No. 3 Huaiyin pumping station is established, as shown in Figure 6a. The target structure for analysis in this study is the No. 2 supporting wall of the auxiliary equipment chamber, as depicted in Figure 6b. Based on temperature data collected over the past ten years, the average local air temperature is approximately 14.9 °C, with the average minimum air temperature in winter around −0.3 °C and the average maximum air temperature in summer at about 27.4 °C [31]. Using these data, two scenarios have been defined:

• The temperature-increasing scenario simulates the concrete structure’s temperature change from 14.9 °C to 27.4 °C, similar to the transition from spring to summer.
• The temperature-decreasing scenario simulates the temperature change from 14.9 °C to −0.3 °C, resembling the transition from autumn to winter.

Additionally, seven monitoring points near the designed crack are set, as shown in Figure 6b, to record the evolution of tensile stress in two cases: without a crack and with a crack. The purpose of setting these two cases is to assess the effect of a crack on the concrete structure once it appears, specifically in terms of differences in tensile stress.

The No. 2 supporting wall is constructed using C25 concrete, with a measured tensile strength of approximately 1.78 MPa determined from field tests. The numerical model for this supporting wall adopts a linear elastic constitutive relationship, utilizing solid elements. The boundary conditions are set such that the surface of the supporting wall exposed to air follows a convection condition. The parameters of the finite element model are detailed in

Table 1. Parameters of the finite element model of the No. 2 supporting wall.

Parameter	Value	Parameter	Value
Density (kg/m3)	2400	Tensile strength (MPa)	1.78
Young’s modulus (MPa)	2.8 × 104	Thermal conductivity (W/m·K)	1.65
Poisson’s ratio	0.167	Convection coefficient (W/m2·K)	7.12

.

Some of the numerical simulation results are illustrated in Figure 6c,d, representing the temperature-increasing scenario. Figure 6c shows the principal stress contour of the No. 2 supporting wall without a crack, with a maximum tensile stress of 0.539 MPa, well below the specified tensile strength of 1.78 MPa. Figure 6d depicts the principal stress contour of the No. 2 supporting wall with a designed crack, showing maximum tensile stress of 0.676 MPa, which remains below the specified tensile strength. It can be observed from Figure 6c,d that the difference in maximum tensile stress in the No. 2 supporting wall is negligible. This suggests that even with the presence of a crack, the induced tensile stress in the future can be disregarded. Similar numerical results were also obtained in the temperature-decreasing scenario although they are not reported here due to limited space.

The seven monitoring points near the crack are also investigated in this study. Figure 7a displays a statistical diagram of the tensile stress distribution at the monitoring points along the x-axis, comparing cases with and without a designed crack under the temperature-increasing scenario. It can be observed that the tensile stress is generally lower in the presence of a crack. This trend is similarly depicted in Figure 7b, which illustrates the tensile stress distribution along the y-axis under the same scenario. The reason for this distribution pattern may be attributed to the increased flexibility of the No. 2 supporting wall with a crack, allowing for more deformation. This flexible deformation results in the redistribution of induced tensile stress in the concrete, leading to lower tensile stress in the concrete structure with a crack compared with the intact one.

Figure 7c shows the tensile stress distribution at the seven monitoring points along the x-axis under the temperature-decreasing scenario. It can be seen from Figure 7c that there is a marginal difference in tensile stress in the No. 2 supporting wall between the two cases: without a crack and with a crack. However, the tensile stress distribution near the crack along the x-axis differs significantly between the two scenarios, as depicted in Figure 7d. The tensile stresses in the temperature-decreasing scenario, whether the supporting wall has a crack or not, are generally larger than those in the temperature-increasing scenario. However, it should be noted that the results presented in Figure 7 are only validated and applicable to the concrete structures in the No. 3 Huaiyin pumping station and should be generalized with caution.

4. Classification and Detection of Concrete Cracks in the No. 3 Huaiyin Pumping Station Using Transfer Learning

4.1. Image Data Augmentation and Training Process

The crack image data used in this study for training the YOLOX network are collected from several crack image databases [41,42] and combined into a new mixed image database. Three types of cracks are categorized in general: the crossing crack, the vertical crack, and the lateral crack, and all selected images are labeled before training. There are a total of 120 images evenly distributed across the three classes for training, validation, and testing. However, the labeled boxes are unevenly distributed, as shown in

Table 2. Three types of training datasets.

No.	Label	Label Count	Image Count
1	Crossing	70	58
2	Lateral	56	52
3	Vertical	53	51

. Table 2 indicates that there are 106 labeled boxes for the crossing crack, 41 labeled boxes for the lateral crack, and 40 labeled boxes for the vertical crack. The size of all images is uniformly transformed into 227 × 227 × 3.

Figure 8 shows twenty example images of cracks. Among them, six images depict crossing cracks, seven images depict vertical cracks, and seven images depict lateral cracks. The image data are split into training, validation, and test sets following a ratio of 0.7:0.15:0.15. Due to the relatively small size of the image dataset, we allocate more images for training. Before initiating the training process, the data allocated for training and validation are augmented using three strategies: random horizontal flipping, random resizing by a factor in the range of [1, 1.3], and random translation horizontally or vertically by −30 to 30 pixels.

The pretrained YOLOX-tiny model is retrained using the augmented crack data mentioned above through the transfer learning process. The training options are defined and listed in

Table 3. Training parameters specified.

Parameters	Value
Input size	227 × 227 × 3
Initial learning rate	0.001
Learning rate drop factor	0.99
Batch size	50
Epoch	120

. The output network is selected based on the minimum validation loss observed during the training process. The hardware used for this training process includes a Lenovo laptop with the following specifications:

Operating System: Windows 10;

CPU: Intel Core i7-7700HQ at 2.80 GHz;

GPU: NVIDIA GeForce GTX 1060;

This laptop was manufactured by Lenovo in Shanghai, China.

Intel Core i7-7700HQ CPU at 2.80 GHz, and one NVIDIA GeForce GTX 1060 GPU, The training process is illustrated in Figure 9.

4.2. Results and Discussion

To evaluate the performance of the retrained YOLOX-tiny detector, several metrics are utilized, including precision, recall, average precision (AP), and mean AP (mAP). It is important to first clarify the definitions of true positive (TP), true negative (TN), false positive (FP), and false negative (FN). The TP refers to an image with cracks being successfully detected, while the TN indicates the detector successfully classifying an image without any cracks. FP occurs when the detector falsely detects cracks in an image where there are none, and FN signifies the detector’s failure to detect cracks in an image. By using the above definitions, the other metrics can be defined as follows [43,44,45,46]:

$$Precision={\displaystyle \frac{TP}{TP+FP}}$$

(4)

$$Recall={\displaystyle \frac{TP}{TP+FN}}$$

(5)

$$mAP={\displaystyle \frac{{\displaystyle \sum _1^{N}AP}}{N}}={\displaystyle \frac{{\displaystyle \sum _1^N{\displaystyle {\int }_0^{1}P(R)dR}}}{N}}$$

(6)

Precision quantifies the ability of the retrained detector to classify objects correctly, while recall evaluates its ability to identify all relevant objects in a class. By applying the retrained detector to the desired test dataset, the recall–precision curves for all three types of cracks are presented in Figure 10.

Figure 10a clearly shows that the retrained detector performs exceptionally well in detecting vertical cracks, achieving an AP of 100%. The performance on lateral cracks, depicted in Figure 10b, is also high-precision, with an AP of 99%. However, as shown in Figure 10c, the performance for detecting crossing cracks is deemed lower, with an AP value of only 41%. We will delve into the reasons for this later. Consequently, the mAP of the retrained YOLOX-tiny detector across all three types of cracks is calculated to be 80%. In total, the performance of the retrained YOLOX is acceptable for crack detection.

In addition, the pretrained YOLOv4-tiny network is also employed in this study and retrained using the same concrete crack dataset for comparison. The training parameters set are the same as those of the YOLOX network for fairness. The obtained recall–precision curves for all three types of cracks by using YOLOv4 are illustrated in Figure 11.

It can be observed from Figure 11a that the AP for vertical cracks is 100%, the same as that obtained using the YOLOX model. However, the APs for lateral and crossing cracks plummet dramatically when using the YOLOv4 network. Specifically, the AP for lateral cracks drops from 99% to 51%, and the AP for crossing cracks decreases from 41% to 26%. As a result, the mAP for all cracks plummets from 80% using YOLOX to only 59% using YOLOv4. Combining the results from Figure 10 and Figure 11, it is evident that the YOLOX network has a stronger ability to detect and classify concrete cracks compared with YOLOv4.

Another significant aspect explored in this section is the correlation between mAP and object sizes. It is well known that smaller objects are more challenging to detect accurately, but is it easier to detect larger targets? To validate this in our case, we evaluated object size using the labeled bounding box area, categorizing them into small, medium, and large groups. The distribution of object sizes in the test set is illustrated in Figure 12.

It can be seen from Figure 11 that the distribution of the object sizes is near normal, indicating more objects with a relatively medium size and a few objects with either too-large or too-small object size. Note that here the total area of each image is 227 × 227, i.e., approximately 5.15 × 10⁴ square pixels. The detailed information on the object size is listed in

Table 4. The mAP of detection in relation to the object size.

No.	Area Range		Number of Objects	mAP
	Minimum	Maximum
1	0	7.107 × 103	10	0.523
2	7.107 × 103	1.204 × 104	9	0.806
3	1.204 × 104	Inf	10	0.667

.

The object size ranges are defined based on the percentiles of the bounding box areas, specifically the 33rd and 66th percentiles of the distribution. The results are summarized in Table 4. It is evident from Table 4 that objects in the small group have the lowest mAP value of 0.523, those in the medium group exhibit the highest mAP value of 0.806, while objects in the large group demonstrate a mAP value of 0.679, lower than that of the medium group, which is not consistent with expectations. The low detection precision for small areas aligns with the common recognition that small objects are more difficult to detect. However, this does not imply that large objects are easier to detect in this case. Upon inspecting the labeled bounding boxes, it is observed that the small bounding boxes are mostly related to crossing cracks. In this sense, the results in Figure 10 and Figure 12, and Table 4 are consistent.

Lastly, some detected samples from the test dataset are illustrated in Figure 13. Figure 13a demonstrates that the retrained detector correctly identified a crossing crack with a confidence score of 0.602, while Figure 13b shows the successful detection of a vertical crack. Two lateral cracks are successfully identified with confidence scores of 0.673 and 0.775, as shown in Figure 13c, while Figure 13d depicts the detection of one lateral crack.

As previously mentioned, we aim to understand the reason for the lowest precision in detecting crossing cracks. Moreover, it is worth noting here that a misclassified crossing crack is shown in Figure 13e. As can be seen, it was falsely classified as a lateral crack due to its relatively long horizontal part. Table 4 and Figure 12 and Figure 13e provide a reasonable explanation for why the retrained detector performs poorly for crossing cracks, and this issue will be addressed in our future work.

4.3. Application in the No. 3 Huaiying Pumping Station

The fine-tuned YOLOX network is applied for the detection and classification of cracks in the concrete structures of the No. 3 Huaiyin pumping station. The crack images include old cracks with measured widths from previous field tests and newly observed cracks from regular inspections after the field test. Some of the detected crack images using the retrained YOLOX are illustrated in Figure 14. Figure 14a depicts newly found cracks on the surface of the pumping station concrete structures, while Figure 14b shows old cracks with measured widths detected and classified by the retrained YOLOX network. It is evident in Figure 14 that YOLOX can accurately detect and classify cracks in the No. 3 Huaiyin pumping station. This is beneficial for maintaining high-quality management of the pumping station due to its labor-saving and easy deployment features.

5. Conclusions

The study on concrete crack detection, classification, and evaluation of the effects on the structure was conducted based on the large-scale hydraulic structure—No. 3 Huaiyin pumping station. The field test conducted in 2017 served as a reference. The finite element method was used to gain insights into the effect of cracks on the tensile stress distribution in the No. 2 supporting wall of the auxiliary equipment chamber. Two scenarios were defined—the temperature-increasing scenario and the temperature-decreasing scenario—to investigate the effect of ambient temperature changes on the induced tensile stress distribution. Two cases, the supporting wall without a crack and the same wall with a designed crack, were considered for evaluating the effect of an existing crack on the induced tensile stress in the concrete structure. Key conclusions were drawn from this study for the No. 3 Huaiyin pumping station, which should be generalized with caution.

The first conclusion is that the difference in tensile stress is negligible between the No. 2 supporting wall without a crack and the same wall with a designed crack. Although the maximum principal stress in the supporting wall with a designed crack is slightly larger than that in the same structure without an existing crack, the tensile stress value remains far below the tensile strength for C25 concrete, which has a tensile strength of 1.78 MPa. This minor difference between the two cases may be attributed to the presence of only one crack in the supporting wall. The second noteworthy conclusion is that ambient temperature has a more significant impact on tensile stress than a crack does. However, this conclusion requires more similar case studies and further investigation.

The YOLOX network was retrained, validated, and tested for crack detection and classification, achieving an acceptable mean average precision of 80%. The retrained YOLOX detector was successfully used for detecting and classifying both newly found cracks and old cracks with measured crack widths in the actual concrete structures of the No. 3 Huaiyin pumping station. It should be mentioned that the retrained YOLOX network in this study lacks the ability to measure crack width, which will be addressed in future research. However, implementing this cutting-edge technique inevitably improves the management of the pumping station due to its labor-saving characteristics and convenient deployment.