Assembly Algorithms for Seismic Vulnerability Estimation in Confined Masonry Dwellings

Seismic vulnerability is the susceptibility of a region, structure, or population to damage or loss from an earthquake [1]. It includes factors such as building quality, soil type, geographic location, seismic response capacity [2], type of material, structural system, workmanship [3], structural fragility, population density, and disaster response capability are pivotal factors that influence a community's resilience in the face of seismic events. These constituents permit nations susceptible to natural disasters to quantify fundamental aspects of vulnerability and delineate their capacities for national risk management [4, 5].

Confined masonry dwellings are widely used due to their low cost compared to other structural systems [6]. They are subjected to seismic movements of varying intensities caused by the movement of tectonic plates, resulting in human, economic, and material losses [7].

In Peru, most masonry constructions are self-built and do not adhere to the technical masonry standard (E.070) or the seismic design standard (E.030). Instead, they are based on the advice of a mason or master mason with empirical knowledge, resulting in structures that are vulnerable to seismic events. As a result, these houses do not ensure proper structural behavior or the safety of their inhabitants [8]. Several buildings in Arequipa (16 incidents), Ica (12 incidents), Tacna (9 incidents), and Ucayali (8 incidents) have suffered damage and structural deterioration due to frequent earthquakes with magnitudes greater than 5.0 on the Richter scale. This damage has been irreparable and has caused the collapse of the buildings [1]. Seismic events have occurred frequently, causing damage to masonry houses, such as cracks in walls, columns, and beams, leaving them vulnerable to future seismic events [9].

Determining seismic vulnerability involves both qualitative and quantitative methods, each requiring different approaches and data depending on factors such as the country [4], time, costs, and resources [10]. This presents a challenge for researchers and professionals involved in assessing and managing seismic vulnerability, as gaps in the literature must be identified. Ortega et al. [10], evaluated the seismic vulnerability of vernacular buildings using the SVIVA methodology; however, their research did not include the analysis of masonry dwellings. Firmansyah et al. [2] highlight the paucity of research on the impact of limited building data on the accuracy of large-scale vulnerability assessment models in low- and middle-income countries. Bektaş and Kegyes-Brassai [11] note that some studies rely on data collected from a single geographic location, which restricts the applicability of methods developed at a regional or global level. This generates the need for further improvement of seismic vulnerability assessment methods to achieve greater accuracy and applicability in different contexts.

Ensemble methods are effective strategies for improving the generalization and robustness of predictive models. They improve model predictive performance by individually training several models and integrating their predictions. This is achieved by integrating predictions from multiple base estimators, which are constructed using a specific learning algorithm or a combination of several algorithms [12].

The research proposes a new method for classifying large-scale seismic vulnerability using ensemble algorithms. It addresses gaps in the literature by extracting patterns from large databases to accurately identify factors that influence vulnerability to seismic events. Furthermore, this methodology aids in the creation of sturdy and dependable predictive models that can adjust to various forms of geographic and structural data, among others.

The research aimed to estimate the seismic vulnerability of confined masonry housing in the Pueblo Libre sector. Assembly algorithms were employed to estimate the level of vulnerability, categorizing it as low, medium, or high, as well as identifying potential damage scenarios that could ensue in the event of a seismic event.

The study implemented assembly algorithms to determine the seismic vulnerability of masonry houses. A database of 3760 masonry houses was compiled from various repositories in Peru. The variables were entered and the base models were trained, including Decision-Tree, Extra-Trees, Random-Forest, and Gradient-Boosting, using a 10-fold cross-validation with the Bayesian method. The process involved analyzing the relevance of each variable about seismic vulnerability. If the dimensionality was less than 5%, the variables were reduced from eleven to seven. Following this, a training (80%) and validation (20%) data set were created. Finally, five ensemble models were developed using the Stacking method, with the Random-Forest meta-classifier. This method integrates the forecasts from multiple base classifiers to enhance the final prediction accuracy. Once the model had been validated using the validation dataset, it was applied to assess the seismic vulnerability of confined masonry dwellings in the Pueblo Libre sector of Jaen, Cajamarca, Peru (see Figure 1).

3.1 Seismic vulnerability

The susceptibility of a building or structure to damage or collapse due to the action of an earthquake. This can be reduced by reinforcement or protection measures to better resist seismic forces [21]. In a building, this is contingent upon the absence of attributes that impact the structural components. These deficiencies can be attributed to a number of factors, including the effects of aging, inadequate maintenance, outdated design, material properties, construction site conditions, and natural phenomena [22].

There are different evaluation methods, with the vulnerability index being the most widely used to determine the seismic vulnerability of masonry buildings [23]. The Benedetti-Petrini vulnerability scale for masonry buildings was employed as a foundation for this study. The parameters were derived by applying a weighted sum of numerical values representing the "seismic quality" of each structural and nonstructural factor that affects the seismic behavior of masonry structures. Each parameter was assigned, during the technical visits (inspections), one of the four classes A, B, C, and D. The "A" rating is optimal with a numerical value Ki=0, while "D" is the most unfavorable with a numerical value Ki=45 [24], as shown in Tables 2 and 3. For example, if parameter number four "Building location and foundation" corresponds to a seismically unsafe configuration, it is assigned a rating of "D" and a numerical value of K4=45. Table 2 illustrates the 11 structural parameters utilized by Peruvian Standard E-0.70 (confined masonry), with the parameters assigned the attributes A, B, C, and D based on their compliance with the aforementioned structural parameters.

11111111111.jpg

Figure 1. Research flowchart

Table 2. Structural parameters for seismic vulnerability assessment

After evaluating each parameter, a weighted sum was performed using the weight factors to obtain the final vulnerability index using Eq. (1) [25, 26]:

$I v=\sum_{i=1}^{11} k i * W i$         (1)

where:

$I v$: Benedetti-Petrini vulnerability index.

$k i$: Numerical value of the vulnerability index of Benedetti-Petrini.

$W i$: Weight coefficient of the Benedetti-Petrini vulnerability index.

Table 3. Benedetti-Petrini vulnerability scale

After the evaluation of the Vulnerability Index ($I v$) corresponding to each confined masonry structure, whose values range from 0 to 382.5 according to the established methodology, the process of normalizing the Normalized Vulnerability Index ($I v n$) to a scale of 0 to 100 was initiated, see Eq. (2).

$I v n=\frac{I v * 100}{382.5}$       (2)

where:

$I v n$  = Normalized Vulnerability Index.

$I v $  = Vulnerability index.

After finding the normalized vulnerability index, which ranges from 0 to 100, it was classified according to the vulnerability ranges in Table 4.

Table 4. Vulnerability index ranges

3.2 Algorithms

3.2.1 Decision tree

It is a structure in which data is divided according to a criterion (test). Each node of the tree represents a distinct test on a specific attribute. Each branch represents the outcome of the test, while the leaves of the node indicate the classes or distributions of classes. Each data instance has several attributes, one of which (the target or class attribute) indicates the class to which each instance belongs. The ID3, C4.5, and J4.8 algorithms are some examples of commonly used decision trees. They also offer the benefit of generating comprehensible models with satisfactory accuracy across various application domains. Information gain is the difference in entropy before and after a change. Entropy represents the expected value of information, defined as -log2(xi) where xi is the frequency of the classification label in the sample set S recorded as p(xi) [27].

3.2.2 Extra tree

The algorithm, integrated within the Python sci-kit-learn module, is distinguished by its user-friendly interface, which requires minimal adjustment of meta-parameters, and its demonstrated computational efficiency. The algorithm is parameterized by three key aspects during the training phase. The first parameter determines the maximum number of features (K) that are considered for node splitting during the construction of decision trees. The second parameter specifies the minimum sample size required for node division. Finally, the third parameter indicates the number of trees (ntrees) included in the ensemble. Furthermore, the algorithm demonstrates a reduced susceptibility to overfitting in comparison to alternative techniques such as neural networks or individual decision trees. This reduced susceptibility to overfitting arises from the tendency of the algorithm to avoid capturing idiosyncratic features specific to the training data, including random noise, which may not generalize well to other samples from the same distribution. Conversely, ensemble learning methods are generally more resilient against this phenomenon. It is noteworthy that the Extra-Trees algorithm was specifically designed to address this concern [28].

3.2.3 Random forest

The algorithm is an integral component of the learning process. It employs multiple randomized decision trees, integrating their predictions through the averaging process. The algorithm is comprised of two principal phases: construction and prediction. In the construction phase, a number of decision trees are generated using different training sets. The objective is to create an accurate model while minimizing the risk of overfitting. In the subsequent prediction phase, the final result is obtained by averaging the predictions of each tree. The efficacy of the algorithm is gauged by a multitude of metrics, including the resilience of the classifier parameters to perturbation, the capacity to withstand noise, and fluctuations in the size of the training set [29]. Table 5 provides a detailed account of the algorithm, as presented by Sagi et al. [12], including a comprehensive overview of its inputs and outputs.

Table 5. Structure of the random forest

3.2.4 Gradient Boosting

The presented method is an ensemble learning approach that constructs a predictive model through the iterative incorporation of sequentially adjusted weak learners, as demonstrated in Eqs. (3)-(5). he general problem is to learn a functional mapping $y=F(X ; \beta)$ from data $\left\{x_i, y_i\right\}_{i=1}^n$ where is the set of parameters of F such that some cost function is minimized. Boosting assumes $F(x)$ follows an “additive” expansion form $F(x)=\sum_{m=0}^M p_m f\left(x, \tau_m\right)$, where, $f$ is called the weak or base learner with a weight $\rho$ and a parameter set $\mathcal{\tau}$ accordingly, $\left\{p_m, \tau_m\right\}_{m=1}^M$ compose the whole parameter set $\beta$. Gradient Boosting approximates with two steps. First, it fits $f\left(x ; \tau_m\right)$ by:

$\tau_m=\arg \min \sum_{i=1}^n\left(g_{i m}-f\left(x_i, \tau\right)\right)^2$       (3)

where,

$g_{i m}=\left[\frac{\partial \Phi\left(y_i, F\left(x_i\right)\right)}{\partial F\left(x_i\right)}\right]_{F(x)=F_{m-1(x)}}$       (4)

Second, it learns $\rho$ by:

$p_m=\arg \min \sum_{i=1}^n \Phi\left(y, F_{m-1}\left(x_i\right)+p f\left(x_i ; \tau_m\right)\right)$      (5)

Then, it updates $F_m(x)=F_{m-1}(x)+p_m f\left(x ; \tau_m\right)$  [30]. In practice, however, shrinkage is often introduced to control overfitting, and the update becomes $F_m(x)=F_{m-1}(x)+v p_m f\left(x ; \tau_m\right)$, where, $0<v \leq 1$. If the weak learner is the regression tree, the complexity of $f(x)$. The GBM's performance is influenced by tree depth and the minimum number of samples at end nodes. In addition to choosing appropriate parameters for shrinkage and tree structure, subsampling can further improve the model's performance [31]. The performance of the GBM can be improved by subsampling, which involves fitting each base learner to a random subset of the training data. This can help increase the diversity among trees and improve the predictive ability of the overall model.

3.3 Data matrix

A database was created using information from the National Institute of Civil Defense (INDECI), scientific articles, and theses related to the seismic vulnerability of masonry dwellings. The data was collected from various academic repositories in Peru between 2017 and 2023 using data collection sheets for 3827 masonry dwellings. The variables considered in this study include the building location and foundation, type and organization of the resistant system, quality of the resistant system, horizontal diaphragms, plan configuration, elevation configuration, maximum distance between walls, type of roof, nonstructural elements, state of preservation, conventional resistance, and seismic vulnerability. These variables are based on the Benedetti Petrini method [10, 32]. Table 6 displays the description, type, and range of variables A, B, C, and D, while Figure 2 shows their respective frequencies. Additionally, Table 7 presents the descriptive statistical analysis of the variables, including unique values and the frequency of the maximum class.

Table 6. Description, classification, and scope of the 12 variables collected

Table 7. Descriptive statistics of the variables

2222.jpg

Figure 2. Frequencies of each variable of the database

3.4 Study area

The masonry houses in Jaen, which are constructed in a traditional manner using handmade materials and without the guidance of a professional in the construction process (see Figure 3), were selected to apply the algorithm that had been trained and validated in the research. For this reason, the houses of the Pueblo Libre sector were studied, taking into account the seismic risk of the city of Jaén, which is located in seismic zone two according to the E.030 standard. The sector is situated in the province of Jaén, department of Cajamarca, Peru, at the following geographical coordinates: 5°42'12.06"S, 78°48'25.61"W (see Figure 4).

3333333333333.jpg

Figure 3. Confined masonry dwellings Jaen, Peru

3.5 Data processing

3.5.1 Selection of variables

Ensemble algorithms were used to estimate the seismic vulnerability of masonry houses in the Pueblo Libre sector of Jaen. A target dataset was selected for the discovery process. The Python programming language was used in this stage to select attributes based on the 'Random Forest Feature Importance' algorithm. This algorithm assigns weights to each variable based on its relevance to the output variable, which in this case is seismic vulnerability. After classifying the attributes, we reduced the dimensionality of the variables since their relative importance is less than 5%, resulting in a value of 1.8%. Consequently, we employed seven input variables that yielded the most information regarding the output variable, seismic vulnerability.

444444444.jpg

Figure 4. Map of the study area

3.5.2 Data standardization

The 'Label Encoding' technique was used to standardize variables in the dataset. This technique involves iterating over each column in the categorical dataset and creating a LabelEncoder object. The LabelEncoder class, which is part of the scikit-learn library, is used to transform categorical variables into numeric variables by assigning them a unique numeric value.

3.5.3 Pre-processing

To enhance data quality, we conducted a thorough data cleaning process to rectify anomalous data. Our cleaning procedures specifically targeted two main issues: missing values in certain records and duplicate data entries. The Python programming language, in conjunction with the Jupyter interface, was employed to achieve this objective. The pandas and NumPy data analysis libraries, which are both highly sophisticated and powerful, were leveraged to accomplish this task.

3.6 Ensemble combination

The study employed a hierarchical algorithm ensemble (SG) approach to enhance the performance of the model. This approach comprises two stages of learning. In the initial stage, a combination of machine learning algorithms, including CART, MARS, and Lasso, among others, is employed to generate a set of metadata from the original training set [33]. In the second stage, the meta-learner is employed to train the metadata set, resulting in the desired outcomes [34] (see Figure 5). The principles outlined by Sagi and Rokach [12] were followed to generate the ensemble models. Firstly, it was ensured that the base learners were as diverse as possible, in order to take advantage of multiple algorithms. Secondly, the objective was to achieve high predictive performance in the individual algorithms to avoid compromising the accuracy of the final model.

In accordance with the principles previously delineated, the study selected a machine learning (ML) ensemble algorithm in conjunction with four classical ML algorithms: The selected algorithms were Decision Tree, Extra Tree, Random Forest, and Gradient Impulse. Prior research has demonstrated the efficacy of these ML techniques in addressing the issue of algorithmic instability, which can result in the introduction of unintended errors. These methods have been validated for their robustness on diverse datasets, thereby contributing to the reduction of such errors. The stacking approach involves the combination of multiple base learners through a meta-learner. Consequently, the selection of a straightforward meta-learner is of paramount importance in order to prevent overfitting [35].

The parameters for each simple model were subsequently configured, including Gradient-Boosting, Random-Forest, Extra-Tree, and Decision-Tree. The Decision-Tree algorithm was configured with 'gini' node splitting, an undefined maximum tree depth (None), and specified minimum sample criteria required to split an internal node and form a leaf node. Similarly, the Extra-Tree and Random-Forest models were configured in detail. This entailed defining the number of trees in the ensemble, the node splitting criteria, The minimum sample threshold for a leaf node, and the number of features when searching for the optimal split, among other parameters. The Gradient-Boosting model was optimized concerning three parameters: the learning rate, the number of reinforcement stages, and the maximal tree depth.

The models CB_1, CB_2, CB_3, CB_4, and CB_5 were generated by combining the simple models using the Random-Forest metaclassifier with 10 folds for internal cross-validation. The predictions of the base models were combined (See Table 8).

55555555555.jpg

Figure 5. Types of distribution of each variable

Table 8. Parameters of simple and assembled models

3.7 Model evaluation

After training five models using the database, three models were selected for validation based on their high prediction percentage during training. The selected models were the simple Gradient Boosting model and the assembled models CB_3 and CB_4. To validate the models, 20% of the collected data was used to compare the results obtained using the Benedetti Petrini method and the proposed assembled models.

After estimating the seismic vulnerability, we evaluated the different models using a confusion matrix to assess the algorithms' performance during prediction (See Table 9).

Table 9. Confusion matrix

The matrix comprises four components: the true positive rate (TP) represents the correctly classified positive cases, while false negatives (FN) are instances that have been inaccurately classified. Likewise, the true negatives (TN) signify correctly identified negative cases, and the false positive rate (FP) indicates erroneously labeled positive instances. The aforementioned values can be utilized to compute the metrics described in Eqs. (6)-(9).

Precision $=\frac{T P}{T P+F P}$        (6)

Accuracy $=\frac{T P+T N}{T P+T N+F P+F N}$      (7)

Recall $=\frac{T P}{T P+F N}$    (8)

F-measure $=\frac{2 * \text { Precision } * \text { Recall }}{\text { Precision }+ \text { Recall }}$       (9)

Accuracy is a statistical metric that assesses the effectiveness of a classification model. It is frequently utilized in classification tasks. Recall, also known as true positive rate or sensitivity, is a metric that gauges the model's capability to identify pertinent instances. This is done by determining the proportion of instances with conditions AM or BM that are correctly identified by the model. Both metrics range from 0 to 1 and are often interrelated via the F-measure, which represents the harmonic mean of precision and recall [29, 36].

3.8 Seismic vulnerability map

The seismic vulnerability was estimated, and a representative map was created using ArcGIS software. The map was based on the spatial and non-spatial data collected from the Sub-Management of Urban Development and Cadastral of the Provincial Municipality of Jaen. The spatial reference system used was based on Datum WGS-84 and UTM projection in Zone 18. 67 polygons were generated to consolidate and systematize the characteristics of the houses in the sector, along with their respective level of seismic vulnerability estimated by the CB_4. A table of properties was created to display this information. A thematic map was generated using the symbology and design tools of ArcMap 10.8 to display the areas of seismic vulnerability of each house. ArcGIS is an effective tool for creating seismic vulnerability maps. By integrating geospatial data and statistical analysis, it is possible to generate maps that identify areas with greater susceptibility to earthquake damage. This allows for better planning and management of seismic risk, making it very useful for decision-making in risk reduction and mitigation planning [14].