Determination of Steel Area in Reinforced Concrete Beams Using Data Mining Techniques

Most Latin American countries have a "housing problem" [1]. In Peru, 70% are informal and have no structural design, causing material losses. These problems become evident when seismic events occur, causing the collapse of structural elements because they have not been designed by a civil or structural engineer, do not comply with technical standards, and the personnel is not qualified for construction [2]. Generating demolition and reconstruction of structures, with rehabilitation and strengthening being a more cost-effective alternative [3]. This affects most of the self-built houses in Peru, making them uninhabitable and vulnerable to structural collapse [4]. In addition, structural deformation must be controlled to ensure the safety of concrete structures [5]. These are designed primarily for strength, using standards such as the American Concrete Institute (ACI) and Technical Standard E.060 (Reinforced Concrete), where the structure can reach a limited state of damage based on the loss of compressive strength capacity of the concrete [6].

Reinforced concrete structures are exposed to various factors that can cause functional and structural damage over time [7]. Understanding the cracking behavior and failure load of reinforced beams is crucial for designing robust and strong structures [8]. Cracking may occur in the early stages, followed by a possible decrease in yield strength and ultimate load capacity [9]. This is because they have not been designed to withstand loads according to their use [10]. Reinforced concrete beams are subjected to loads and their design must ensure ultimate load capacity, stiffness, ductility, and energy absorption capacity [11], being destined to fail typically by steel creep followed by concrete failure [12]. In addition, increasing the reinforcement ratio can reduce deflection and deformation while maintaining the same stiffness. However, increasing the reinforcement ratio will also cause the tensile strength to be underutilized, resulting in economic waste and brittle failure [13]. Mohammed [14] recommends reinforcing beams with a composite section by reusing the beam web and reinforcing it with epoxy, but in Peru, they are not compatible with design standards, have construction errors, or are exposed to unforeseen loads [15]. The most common beam failures are critical cracks, diagonal cracks in the web [16], out-of-limit deflections, and multiaxial stress states [17].

Proper design of beams is of great importance because it ensures the safety, stability, durability, and economy of structures by distributing loads along their length, avoiding excessive concentration of stresses at certain points on other elements, controlling structural deformations, is resistant and the materials used for its manufacture are low cost compared to steel beams [18].

The method used to calculate the steel in the beams is based on the ACI and Technical Standard E-0.60 (Reinforced Concrete), which uses several iterative processes. The beam section is pre-dimensioned according to the free span and the dead load is determined. Then, the nominal moment is calculated and checked if it is greater than or equal to the bending moment divided by the load factor (Ø). This process is repeated until a sufficient steel area is obtained, which makes it difficult to match the section's resisting moment with the ultimate applied moment due to the beam's weight. Therefore, the design process is slow and has no economic analysis [19]. Other methods used in the design of reinforced concrete beams are serviceability limit state design and fire resistance design using bar diameter, camber, and loading regime. Here, increasing the beam diameter or decreasing the camber thickness is an effective method to reduce the maximum crack width [20]. These methods are complex and require the use of specialized seismic and structural analysis software, which requires time and effort to learn how to use them correctly. Faced with this problem, data mining algorithms have been used to discover patterns, trends, and relationships in large data sets due to their applications in structural data management, helping engineers to organize, store, and analyze large amounts of information about existing structures. This facilitates the design of structural elements, monitoring of structural health, and informed maintenance and repair decisions.

3.1 Data matrix

The information was collected from technical files hosted on the SEACE (Electronic State Contracting System) website, using a total of 593 reinforced concrete beam designs obtained from 2019 to 2022; forming a data matrix of 593 instances and 8 variables. The variables collected were: Ultimate moment, length, width, height, effective camber, concrete strength, steel creep, and reinforcing steel (see Figure 1).

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Figure 1. Descriptive statistics of the variables

The reinforcing steel present in the data matrix includes 9.5 mm, 12.7 mm, 15.9 mm, 19.1 mm, and 25.4 mm bars corresponding to bars #3, #4, #5, #6, and #8 according to the "Standard Specification for Deformed and Plain Carbon-Steel Bars for Concrete Reinforcement" (ASTM A-615), placed in one and two layers. The design with the highest percentage was 2 Ø #5 +3 Ø #6 and the lowest was 3 Ø #4, with a total of 38 different combinations (see Figure 2). The description, unit, and type of variables are shown in Table 1.

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Figure 2. Types of reinforcing steel contained in the database

Table 1. Description, type, and range of variables collected

3.2 Methodology for employing data mining

The Knowledge Discovery Databases (KDD) approach was used, which is characterized by automatically obtaining a deep knowledge of the rules implicit in the information [33]. This process includes data preparation, statistical analysis, the algorithm used for data mining, and the evaluation and interpretation of the data, resulting in knowledge, which is a non-trivial process of identifying valid, novel, potentially useful, and understandable patterns from the data [34].

3.2.1 Selection

The need to determine the reinforcing steel in rectangular reinforced concrete beams was identified through data mining. A data set was created on which the discovery process was performed. For this stage, the Weka software was used, using the "InfoGainAttributeEval" algorithm for the selection of variables, due to its ability to evaluate and classify the characteristics of the data set through information gain, for the assignment of weights to each variable by calculating the entropy, which measures the degree of "impurity". The closer it is to 0, the fewer impurities there are in the data set, therefore a good attribute contains the most information, reducing the entropy to the maximum [35].

After classifying the attributes, variables with entropy greater than 0.5 were selected to filter out those variables that do not have a significant influence on the determination of the steel area in reinforced concrete beams, reducing the complexity of the model in terms of relevant variables to improve efficiency. We worked with five input variables (see Table 2), which are those that provide the most information to the output variable (reinforcing steel).

Table 2. Selected variables that provide the most information

3.2.2 Pre-processing

It ensures the quality and suitability of the data for classification. It includes data cleaning, integration, normalization, and transformation to improve the quality and relevance of training the classification algorithm [36]. The cleaning tasks are aimed at solving two common problems: the absence of values in some datasets and the existence of duplicate data [37]. Data cleaning was applied to improve data quality by eliminating anomalous data. This was done by replacing missing values using the average, median, and regression algorithms, as well as eliminating duplicate data using Python's Set (Data) command and anomalous data using the Panda library's boxplot, which allows visualization of the distribution and detection of outliers by identifying points outside the boundaries of the graph.

3.2.3 Transformation

Characteristics were sought to represent the data as a function of the steel to be used. Dimensionality reduction methods include principal component analysis, which transforms a set of correlated variables into uncorrelated variables called principal variables. It allows dimensionality reduction by projecting the data into a lower dimensional subspace that preserves most of the variability of the data [38], Linear Discriminant Analysis maximizes the separation between classes in a labeled data set, taking into account class information where samples are separated, is useful when the goal is to reduce dimension while maintaining discrimination between classes [39], Singular value decomposition divides a matrix into three matrices, allowing important features to be extracted and the data to be represented in a lower dimensional subspace [40], Feature selection is based on obtaining a subset of relevant features and discarding irrelevant or redundant ones, using statistical techniques such as significance or correlation tests, as well as methods based on machine learning algorithms such as genetic algorithms [41]. In this sense, the feature selection method was used to reduce variables according to the statistical analysis to maximize the separation between classes and the data set, taking into account the labels and the effective number of variables under consideration to find representations in the data, see Table 3.

Table 3. Variables that make up each group

3.2.4 Data mining

WEKA 3.9.4 software, written in Java and developed by the University of Waikato for machine learning and data mining, was used. Through the graphical interface, the "Explorer" function and the "Classify" tool were used, using the k-folds cross-validation k=15 test recommended by Sunyani et al. [42], because it provides a better estimation in the model accuracy, reducing the variance by dividing the dataset into more folds to improve random partitions of the data in the final results.

The decision tree algorithms used were Decision Stump, which constructs a single-level binary decision tree applied to either nominal or numeric data sets. Hoeffding Tree is an incremental decision tree induction algorithm that can learn from massive data streams at any point in time, assuming that the examples used to generate the distribution do not change over time. Hoeffding trees take advantage of the fact that a small sample may be sufficient to choose an optimal partitioning attribute. J48 is an algorithm that provides the ability to stop before reaching the leaves in each subtree; this results in less refined trees and avoids overfitting. LMT is a classifier algorithm for constructing logistic model trees with logistic regression functions on the leaves. The algorithm can handle binary and multiclass target variables, numeric attributes, and nominal and missing values. Random Tree, an algorithm that constructs a tree that considers K randomly selected attributes at each node, does not perform pruning. In addition, it has the ability to perform class probability estimation based on a holdout set (back-fitting) [43]. These algorithms were used for their simplicity and ability to build decision trees that consider nominal and numeric data, allowing efficient and adaptive learning in situations where data arrive in stream form, combining logistic regression features in the leaves of the tree, being able to handle binary and multi-class target variables, as well as numeric and nominal attributes.

3.2.5 Data evaluation

After training the five models with the database, three for validation, the groups of variables were selected that showed the highest percentage of prediction during training, namely GP_1, GP_2, GP_3, GP_4, and GP_5. The collected data and the proposed data mining models were used for validation.

After determining the steel area, the different models are evaluated through the confusion matrix according to Zambrano et al. [30], which allowed us to evaluate the algorithms during prediction, see Table 4 and Eqs. (1) to (4).

Table 4. Confusion matrix

Correctly classified instances (CCI): The proportion of correctly classified instances divided by the total number of instances.

$\mathrm{CCI}=\frac{P V+N V}{P V+N F+N V+P F}$      (1)

Incorrectly classified instances (ICI): The proportion of incorrectly classified instances divided by the total number of instances.

$\mathrm{ICI}=\frac{P F+N F}{P V+N F+N V+P F}$      (2)

PV Rate (TPV): The rate of positive cases that are correctly identified or the proportion of cases that test positive and are positive.

$\mathrm{TPV}=\frac{P V}{P V+N F}$     (3)

Accuracy (AC): The ratio of the total number of correct positive predictions over the total number of instances classified as that class.

$\mathrm{AC}=\frac{P V}{P V+P F}$     (4)

The RamdomTree algorithm used in GP_04 was the one that best estimated the steel area in reinforced concrete beams with an accuracy of 88.98%, for its application in the design of structural elements that guarantee the structural safety of buildings. This was the result of the evaluation of the 5 groups (GP_1, GP_2, PL_3, GP_4, GP_5) conformed by 3 different variables, and trained with 5 decision tree algorithms in Weka with which an accuracy of 87.72, 88.56, 88.14, and 87.71% was obtained.

The selected algorithms were DecisionStump because it captures linear relationships or simple rules of beam geometry and strength, HoeffdingTree because of its ability to adapt to massive data streams and its efficiency in memory usage and processing time, J48 because of its ability to handle numeric and nominal attributes, perform pruning, and avoid overfitting, LMT because of its ability to handle binary and multiclass target variables as well as numeric, nominal, and missing value attributes. RandomTree was used because it randomly builds decision trees to improve accuracy and avoid overfitting, as they best represent the patterns of a data set, according to Leon Atiquipa [44], who used DecisionStump, HoeffdingTree, J48, LMT, Random Forest, Random Tree, and REPtree algorithms in his research to select the best algorithm applied to the same data set.

The results obtained in the research were superior to the results of Mataei et al. [25] of 72.44, 81.29, and 80.66% of correctly classified instances, respectively. We contributed to the existing literature by evaluating and comparing classification algorithms in the field of civil engineering and construction in the accurate classification of reinforcing steel in beams to ensure the safety and efficiency of structures through proper material selection.