Introduction

Liquefaction is one of the most important, interesting, complex, and controversial topics in geotechnical engineering. The great destruction caused by liquefaction in the Alaska earthquakes (Mw = 9.2) and Niigata (Ms = 7.5) that occurred in 1964 increased the interest of geotechnical engineers in this phenomenon. The term liquefaction describes a set of soil deformations that occur when saturated cohesionless soils are disturbed in undrained conditions in static, temporary, or cyclical ways (Kramer 1996). Although liquefaction was thought to occur only in sandy soils for many years, studies and observations have shown that liquefaction may occur in low-cohesive silts (Ishihara 1984, 1985) and gravelly soils (Evans and Seed 1987; Yegian et al. 1994). The emergence of liquefaction in the soil layers in earthquakes can cause considerable damage to structures on the ground and underground structures. Therefore, determining the factors that cause liquefaction in soils, liquefaction hazards, and predicting possible harmful effects are considered among important research topics in geotechnical earthquake engineering.

Local ground conditions significantly affect the structural damage that can occur during earthquakes. Thus, it is important to predict the behavior of soils under cyclic loads and their static strength after earthquakes. It is possible to determine the stress–strain behavior of soils during and after earthquakes with various laboratory test systems. In particular, the liquefaction potentials and the post-liquefaction behavior of saturated sandy soils under cyclic loads can be investigated in the laboratory with dynamic test systems such as dynamic simple shear, dynamic triaxial, dynamic torsion test, and shaking table (Das 1993; Youd and Idriss 2001; Xue and Xiao 2016; Rahbarzare and Azadi 2019; Erzin and Tuskan 2019; Alizadeh Mansouri and Dabiri 2021; Pham 2021; Zhou et al. 2022b). However, obtaining undisturbed samples from soils whose liquefaction risk is investigated, and the modeling of the field conditions in laboratory experiments may present some difficulties. Therefore, it is widely preferred to perform liquefaction risk analyses using methods based on field tests, such as the standard penetration test (SPT), cone penetration test (CPT), and measurement of shear wave velocity (Vs). The most significant advantage of field tests is that they allow evaluating the soil in its natural state. Experiments and identification can be made at the desired depth from the surface. However, since seismic activity is difficult to demonstrate in the field, soil parameters related to liquefaction strength cannot be obtained in experiments to determine the liquefaction potential. To reach the evaluation criteria, empirical relations have been developed by examining past earthquakes where liquefaction has occurred (Law and Wang 1994).

Methods based on SPT test results are widely used to determine the liquefaction potential among field tests (Ghani and Kumari 2022a; Ghani et al. 2022; Yılmaz et al. 2022). The most important of these is the “Simplified Method” published in 1971 (Seed and Idriss 1971) and has also been accepted as the standard in liquefaction analysis. This method is based on the principle of obtaining a factor of safety (FSL) by dividing the ratio of cyclic resistance to liquefaction (CRR) by the earthquake-induced cyclic stress (CSR). If the factor of safety is less than 1, liquefaction is expected. If it is greater than 1, there is no risk of liquefaction.

On the other hand, the fact that the SPT test contains many uncertainties in the application procedure necessitates correction in the obtained SPT-N values (Youd et al. 2001; Idriss and Boulanger 2010; Alizadeh Mansouri and Dabiri 2021). In addition to those that can be determined by laboratory and field tests, many parameters, such as earthquake magnitude and peak horizontal ground acceleration, are used in liquefaction analyses based on the SPT test. Although CSR and CRR parameters can be determined using empirical expressions developed based on past earthquakes (Youd et al. 2001; Cetin et al. 2004; Idriss and Boulanger 2008, 2010; Boulanger and Idriss 2014) and field observations, it is difficult to obtain a single appropriate empirical expression due to the need for many parameters and uncertainties (Cai et al. 2022; Zhou et al. 2022b). Although the deterministic methods mentioned above are still widely used in the evaluation of liquefaction, as they are simple and practical, they might contain significant uncertainties due to the variables used in these methods. In addition to the uncertainties related to the anisotropy and non-uniform properties resulting from the heterogeneous structure of the soils, the uncertainties in the seismic parameters caused by earthquakes are the major ones. Although some researchers propose reliability methods for deterministic approaches used in liquefaction evaluations to overcome these uncertainties (Baecher and Christian 2005; Ghani and Kumari 2022b; Golmoghani Ebrahimi et al. 2023; Jha and Suzuki 2009; Johari et al. 2012; Juang et al. 2009; Kwak and Lee 1987), some researchers have also emphasized that it is inevitable to use reliable, simple, and predictable flexible calculation techniques to evaluate the liquefaction potential of any piece of soil, as in many fields of engineering science (Xue and Yang 2013, 2016; Xue and Xiao 2016; Juang et al. 2022).

Examining the literature in question, it is seen that different researchers have used different types of artificial intelligence (AI) and machine learning (ML) techniques, such as artificial neural network (ANN) (Hanna et al. 2007; Ramakrishnan et al. 2008; Mughieda et al. 2009; Xue and Liu 2017; Alizadeh Mansouri and Dabiri 2021; Kurnaz et al. 2023), adaptive neuro-fuzzy inference system (ANFIS) (Rahman and Wang 2002; Chern et al. 2008; Xue and Yang 2013), support vector machine (SVM) and relevance vector machine (RVM) (Samui and Sitharam 2011; Samui and Karthikeyan 2013; Rahbarzare and Azadi 2019) to overcome the uncertainties in the assessment of soil liquefaction risk. Additionally, optimization techniques have started to be used in liquefaction risk evaluations to improve the generalization ability of ML models and overcome limitations in recent years (Rahbarzare and Azadi 2019; Zhang et al. 2021; Zhao et al. 2021; Cai et al. 2022; Ghani and Kumari 2022a; Ghani et al. 2022; Umar et al. 2022; Zhou et al. 2022a), have been implemented in most complex geotechnical engineering problems with high success (Díaz et al. 2022; Li et al. 2022; Rehman et al. 2022; Wang et al. 2022).

Classification-based estimation studies also have a major role in the liquefaction phenomenon with AI and ML. Using historical case datasets, researchers have successfully used classifiers of different methods to predict the liquefaction potential. Ahmad et al. (2019) focused on case histories with Bayesian belief network (BBN) and C4.5 decision tree (DT) models to assess the liquefaction potential. They achieved satisfactory results, especially with the BBN model. Alobaidi et al. (2019) used ensemble models to predict the liquefaction potential and compared them with ML models. They have claimed that the ensemble models perform better in overcoming the uncertainties and predicting. Rahbarzare and Azadi (2019) studied CPT-based field cases and proposed a fuzzy support vector machine (FSVM) classifier supported by optimization algorithms for liquefaction prediction, and they achieved satisfactory results. Zhao et al. (2021) studied two case history databases. They proposed a hybrid ML model that includes particle swarm optimization and kernel extreme learning machine (PSO-KELM) to evaluate the liquefaction potential. They emphasized that the proposed model has achieved better results than the various ML models. Ahmad et al. (2021) used different BBN models in CPT field cases to assess the liquefaction potential, and gave the results comparatively. Zhang et al. (2021) focused on the addition of the Vs parameter to the prediction models of the liquefaction potential based on the SPT field cases. They used a multi-layer fully connected network model optimized by the deep neural network (ML-FCN DNN). Thus, they stated that they achieved higher accuracy prediction success. Kumar et al. (2021) proposed a deep learning (DL) model for the prediction of classification-based liquefaction, and the results they achieved were compared with the emotional backpropagation neural network (EmBP), and highlighted the success of the proposed DL model. Zhang et al. (2021) proposed an SVM model optimized by gray wolf optimization (GWO) to present a prediction model of the liquefaction potential and suggested that GWO improved the prediction success. Zhang and Wang (2021) used three different datasets. They proposed an ensemble model that combined the predictions of the seven base classifiers in the prediction of liquefaction and achieved reliable results. Zhou et al. (2022a) proposed SVM models optimized by GWO and genetic algorithm (GA) using three historical datasets. The results indicated that GWO and GA have increased SVM performance; however, GWO was slightly more successful. Zhou et al. (2022b) used three historical datasets to propose random forest (RF) models optimized by GWO and GA. The results showed that the optimization of GWO and GA has improved the performance of the single RF model. Additionally, GWO-RF was more successful in two datasets and GA-RF was more successful in one. Demir and Sahin (2023) presented Adaptive Boosting (AdaBoost), Gradient Boosting Machine (GBM) and eXtreme Gradient Boosting (XGBoost) ensemble algorithms to evaluate soil liquefaction potential in SPT-based dataset. The results suggest that the proposed ensemble models obtained reliable results in liquefaction prediction. Kumar et al. (2022) used XGBoost, RF, GBM, support vector regression (SVR), and group method of data handling models in the prediction of soil liquefaction using a SPT-based database. Although all models were successful, the XGBoost model showed the best prediction performance for the liquefaction potential.

This study focused on a thorough investigation of the potential of ML algorithms, particularly classifiers, in accurately predicting soil liquefaction. In this regard, the dataset containing 620 SPT-based historical cases presented by Hanna et al. (2007) was used. It is seen that a significant part of the soil types in the dataset presented by Hanna et al. (2007) are classified as fine-grained soils. However, the dataset includes only the parameters used in coarse-grained soil liquefaction analysis methods based on SPT as input parameters. Nevertheless, the input parameters in the database do not include parameters that reflect the physical properties of soils that are known to be effective in the liquefiability of fine-grained soils. Since the development of the pore water pressure of clay–silt mixtures during cyclic loads is quite different from that of sand soils, the liquefaction criteria developed for sands will not function efficiently for fine-grained soils. In terms of stress–strain behavior, the behavior of sands depends significantly on confining stress and relative density, while the behavior of clays depends on plasticity, consolidation stress, and stress history. Therefore, Boulanger and Idriss (2006) separated fine-grained soils into categories such as "sand-like" and "clay-like" according to their behavior. Over time, many criteria have been developed to determine the susceptibility to liquefaction of fine-grained soils based on the physical properties of the soil. Early on, the criteria proposed to separate liquefiable and non-liquefiable fine-grained soils were based on the percentage of clay (C%), liquid limit (LL), and the ratio of natural water content to liquid limit (wn/LL) (Wang et al. 2022; Seed and Idriss 1971; Andrews and Martin 2000). In the following years, the average grain size (D50) (Bol et al. 2010), and the soil plasticity index (PI) (Bray and Sancio 2006; Ghani and Kumari 2021; Seed et al. 2003) were used for liquefaction sensitivity.

The dataset presented by Hanna et al. (2007) has been widely used in many studies that propose prediction models on liquefaction evaluation (Gandomi et al. 2013; Hoang and Bui 2018; Kayadelen 2011; Kurnaz and Kaya 2019; Zhang and Wang 2021; Zhang et al. 2021; Zhao et al. 2021; Zhou et al. 2022a, 2022b). In the mentioned studies, the performance results of the models were obtained by performing analyzes with parameters affecting the liquefaction behavior of coarse-grained soils, without considering the presence of fine-grained soil types in the dataset. Considering that this situation may affect the performance of the proposed forecasting models, in addition to the entire dataset, the dataset was divided into fine and coarse-grained soils, and three different datasets were analyzed in the current study. A variety of powerful ML ensemble algorithms were used in the analysis, including XGBoost, AdaBoost, Extra Trees Algorithm (EXT), Bagging Classifier (Bagging), Light Gradient Boosting (LightGBM), and Random Forest (RF).

The main contribution of this paper is highlighted as follows:

  1. (a)

    Unlike previous studies that used the dataset presented by Hanna et al. (2007), prediction models were developed for different variations considering the difference in soil type within the dataset, and it is emphasized that grouping the dataset according to soil type positively affects the prediction model performance results.

  2. (b)

    The ML models’ performance was enhanced through the utilization of optimization techniques, including random search (RS), grid search (GS), and GA.

  3. (c)

    By integrating ensemble methods and fine-tuning the hyperparameters, this study aims to provide valuable insights into the practical application of these robust algorithms and their unparalleled effectiveness in precisely classifying the liquefaction potential across various soil types.

Dataset description

In this study, the dataset presented by Hanna et al. (2007), which contains a total of 620 SPT-based case records of two major earthquakes that occurred in 1999 in Türkiye (Mw = 7.4) and Taiwan (Mw = 7.6), was used in three different variations. Since the whole dataset contains different soil types, as mentioned in the Introduction part of this paper, the dataset was divided into two categories: fine-grained and coarse-grained soils. Three different datasets were analyzed in this study. The first dataset (A) consists of fine-grained soils only, the second dataset (B) consists of coarse-grained soils only, and the third dataset (C) consists of all samples. Among the case records in the entire dataset, 406 data are classified as fine-grained soil (dataset A) and 214 data are classified as coarse-grained soil (dataset B). All three datasets consist of 12 input parameters and a single output parameter. The input parameters are the depth of the analyzed layer (z), the corrected SPT blow numbers (N1,60), the percentage of fine content less than 75 µm (FC (%)), the depth of the groundwater table (dw), total and effective overburden stresses (σv, σv’), threshold acceleration (at), cyclic stress ratio (CSR), shear wave velocity (vs), internal friction angle of the soil (ϕ), earthquake magnitude (Mw), maximum ground acceleration (amax). The output parameter of the binary classification problem is the liquefaction potential. The descriptive statistics for the dataset used in this study are presented in Table 1.

Table 1 Descriptive statistics for variables related to soil liquefaction
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Additionally, Table 2 presents the correlation coefficients between the distinctive characteristics analyzed. The values range from -1 to 1, with higher absolute values indicating stronger correlations. As expected, σv and σv’ exhibit a high correlation, with a coefficient of 0.98. \({N}_{\mathrm{1,60}}\) also shows a positive correlation with ϕ, with a coefficient of 0.84. Furthermore, CSR exhibits a positive correlation with amax, with a coefficient of 0.90. The presented correlations can help identify important relationships between distinctive features and can be utilized in predicting the values of certain variables based on others.

Table 2 Correlation matrix of input and output parameters
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Background of ensemble learning methods

The basic working mechanism of ensemble learning methods (ELM) is based on multiple learning models rather than the individual learning model in ML. ELM combines predictive values obtained with multiple learners to produce a single predictive value. In this way, ELM reduces variance and bias in estimation results compared to individual ML, which are mostly divided into boosting, bagging, and stacking (Mienye and Sun 2022). Boosting methods use data from the wrong test results of the learning model as input in the next stage until a successful prediction is obtained. The stages continue until a certain stopping condition is satisfied. However, methods that prefer the bagging approach obtain predictions with the learning model by taking different subsets from the training set. These estimation results are aggregated as a result of a single estimation by taking max voting or average (Dietterich 2000). The final predictions are obtained through a meta-model using different learning models’ predictions in stacking. Under the heading of boosting, bagging, and stacking, many different methods have been developed so far, and their applications in various fields, such as landslide assessment, predicting water quality, have been compared and discussed (Dou et al. 2020; Almadani and Kheimi 2023). In this part of the study, the methods of XGBoost, AdaBoost, EXT, Bagging, LightGBM, and RF, which achieved satisfactory results in the application phase for the estimation of soil liquefaction classification, are explained.

Extreme gradient boosting

XGBoost is an improvised version of the gradient boosting algorithm, and the working procedure for both is the same. Its implementation of parallel processing at the node level makes it more powerful and faster than the gradient boosting algorithm (Walia 2021). XGBoost is used for supervised learning problems that try to predict the yi variable from a xi multi-feature training set. The objective function consists of two parts, the training loss L(θ) and the regulation term Ω(θ) (Eq. 1):

$$obj \left( \theta \right) = L\left( \theta \right) + \Omega \left( \theta \right).$$
(1)

\(L\left(\theta \right)\) represents how predictive the model is based on the training data. Several types of loss functions can be used. The regulation term \(\Omega (\theta )\) controls the complexity of the model. It helps to make predictions with high accuracy by simplifying the model. In this way, it ensures that the model avoids overfitting. The trade-off between the training loss \(L\left(\theta \right)\) Moreover, the regulation term \(\Omega (\theta )\) is also called the bias-variance trade-off in ML (Chen and Guestrin 2016). In the study, the hyperparameters of XGBoost, including the step size shrinkage (eta), minimum loss reduction (gamma), maximum depth of a tree (max_depth), minimum sum of instance weight (min_child_weight), maximum delta step (max_delta_step), subsample ratio (subsample), and the number of runs XGBoost will try to learn (n_estimators), were identified as the parameters to be optimized. Some recent studies have emphasized that the various parameters of the XGBoost algorithm give superior results when optimized and adjusted for different problems (Abdu-Aljabar and Awad 2022; Janizadeh et al. 2022).

Adaptive boosting

AdaBoost’s main difference from other ELM is that it adaptively adjusts the errors of weak hypotheses returned by weak learners (WeakLearn) (Freund and Schapire 1997). WeakLearn predictions are combined using a weighted majority vote (or sum) to produce the final prediction. In each successful iteration, the weights (w1, w2, …, wN) assigned to the training samples are modified, and the learning algorithm is applied again. The weights of the incorrectly predicted training samples in the previous step are increased in the boosted model. Thus, WeakLearn is forced to guess correctly the wrongly guessed examples (Pedregosa et al. 2011). According to research by Rajasekar et al. (2022) and Amini et al. (2023), AdaBoost has shown promising performance in predicting problems compared to other algorithms, particularly when hyperparameterized.

Extra-trees algorithm

EXT is named after Extremely Randomized Trees. It is an ELM based on DTs. It acts randomly like RF while making certain decisions. It is similar to RF in creating multiple trees and splitting nodes using random subsets of features. However, it does not bootstrap the observations. It also randomly splits the nodes instead of the best ones (Geurts et al. 2006). This method applies a meta-estimator that fits a set of random DTs (a.k.a. EXT) to various sub-samples of the dataset. It uses averaging to improve prediction accuracy and overfitting (Pedregosa et al. 2011). Few studies emphasize that if the EXT algorithm is hyperparameterized in different application areas, it can greatly affect the results. One of these studies, Cuocolo et al. (2020), emphasized that the hyperparametric EXT classifier can achieve good results in predicting the surgical consistency of pituitary adenoma. In this study, max_depth, the number of trees in the forest (n_estimators), the minimum number of samples required to split (min_samples_split), the minimum number of samples required to be at a leaf node (min_samples_leaf), whether bootstrap samples are used when building trees (bootstrap), and the function to measure the quality of a split (criterion) parameters are tuned.

Bagging classifier

Bagging methods work well with powerful and complex models, such as advanced DTs, compared to boosting methods. Bagging methods use the randomness of an ensemble to reduce the variance of the weak estimator. It is a class of ensemble algorithms that obtain individual predictions from random subsets of the original training set via a black-box estimator and aggregate them to form the final prediction. It performs this aggregation using voting or averaging and generates the final prediction. This algorithm also includes several studies in the literature known as Pasting, Random Subspaces, and Random Patches (Pedregosa et al. 2011). Few studies in the literature use the bagging classifier for hyperparameterization. Sari and Maki (2023) emphasized that they obtained superior results using the face mask detection dataset over the Kaggle face mask detection on Kaggle by optimizing the bagging classifier using a hybrid bat algorithm. In this study, the Bagging method’s hyperparameters were optimized, which involved tuning the parameters such as the number of samples to draw (max_samples), the number of base estimators in the ensemble (n_estimators), whether samples are drawn with replacement (bootstrap), and whether features are drawn with replacement (bootstrap_features).

Light gradient boosting

Many boosting tools use pre-sort-based algorithms for DT learning, while LightGBM uses histogram-based algorithms. The main advantages of using histogram-based algorithms are that it reduces the amount of memory usage in calculation processes and shortens the training time (Ke et al. 2017). This situation increases the usefulness of the LightGBM technique, especially in problems where the number of features is high, and the data volume is high. The LightGBM method uses gradient-based one-sided sampling (GOSS) and exclusive feature bundle (EFB) approaches to overcome the performance degradation of other methods in problems with many features and large data sizes. With GOSS, most data samples with small gradients are not used, focusing on a specific part of the dataset. With EFB, mutually exclusive features are bundled to reduce the number of features (Ke et al. 2017). These two techniques significantly reduce the solution time and processor requirements. Numerous studies emphasize that satisfactory results are obtained when the LightGBM method is hyperparametrized for different problems (Dhar 2022; Pei et al. 2022). In this study, the hyperparameters of the LightGBM method, including learning_rate, the complexity of the tree model (num_leaves), max_depth, minimum number of data points needed in a child node (min_child_samples), subsample, and column sample by tree (colsample_bytree), were optimized.

Random forest

In RF, each tree in the ensemble is generated from a bootstrap sample taken with replacement from the training set. Additionally, when each node is constructed during the tree, the best split is determined from all the input features or a random subset of the features. Similarly, to other classifiers, the RF classifier utilizes two types of dataset that store the attributes and target values of the training samples. It uses randomness in generating classifiers, and the ensemble is estimated by combining the average predictions of the individual classifiers. The primary purpose of incorporating randomness is to mitigate the variance within the forest estimator. However, this effort to reduce variance might slightly increase bias (Pedregosa et al. 2011). It has been emphasized that using the RF method and population-based algorithms such as the GA and Harris Hawks optimization algorithm can obtain satisfactory results in various estimation problems if its parameters are tuned (Daviran et al. 2023; Ge et al. 2023). In this study, the hyperparameters of the RF algorithm, including max_depth, min_samples_split, min_samples_leaf, bootstrap, and criterion, were optimized.

Performance evaluation criteria for ensemble learning methods

Performance evaluation is a crucial step in developing and deploying machine learning models and algorithms. It allows us to assess the effectiveness and reliability of our models, determine their strengths and weaknesses, and make informed decisions about their performance in real world scenarios. Performance evaluation quantitatively measures how well a machine learning model or algorithm performs on a given task or dataset. Various performance metrics are available to evaluate a model’s performance, and the choice depends on the nature of the task and the type of model. Common metrics include accuracy, representing the ratio of correct predictions to the total; precision, measuring the proportion of true positives among positive predictions; recall, indicating the ratio of true positives to all actual positives; and F1 score, a harmonic mean of precision and recall for balanced assessment. It is crucial to select the appropriate metric based on the task at hand and interpret the results contextually for an effective model assessment (Gong et al. 2023).

In our study, we evaluate the performance of the classification models mentioned using commonly accepted metrics, namely accuracy, which is a very basic and intuitive performance measure. During binary classification, some samples may be misclassified into the opposite class. The accuracy score indicates how well the model classifies both positive and negative samples. Accuracy is calculated as the proportion of true predictions, both true positives (TP) and true negatives (TN), from the total number of samples, which are given below:

$${\text{Accuracy}} = \frac{TP + TN}{{TP + TN + FP + FN}},$$
(2)

where TP are correctly predicted positive samples, TN are correctly predicted negative samples, FP are negative samples incorrectly predicted as positive, and FN are positive samples predicted as negative. High accuracy indicates that the model is effective in classifying samples into the right classes overall. However, precision and recall provide more detailed information on how well it identifies positive classes. We use these standard evaluations to evaluate the different models developed for our binary classification task and identify the most suitable approach.

Hyperparameter optimization and traditional methods

The performance of ML algorithms in terms of variance can vary depending on the parameters used. Although some parameters are determined internally by the algorithm during the training process, others are set by the user (Agrawal 2021). This multiplicity of parameters poses an optimization problem known as hyperparameter optimization, which is separate from the core problem being solved. Hyperparameter optimization is a challenging task that requires users to explore different parameter values through trial and error. To address this, various methods have been developed. Two commonly used methods in the field are GS and RS, which are considered traditional methods (Lim 2022). GS involves systematically evaluating all combinations of parameter values, which can be time-consuming and resource-intensive. On the other hand, RS reduces solution time and resource consumption by randomly sampling parameter values. However, this randomness can sometimes lead RS to deviate from the optimal solution compared to GS.

Genetic algorithm

GA is a widely used AI technique to deliver satisfactory results in a short time frame. It was initially developed by Holland in 1975 (Holland 1992) and is based on the principles of Darwin’s theory of evolution. The algorithm follows a solution generation and evaluation mechanism to improve results by favoring well-performing individuals. GA incorporates crossover and mutation operators to create new individuals. The process continues iteratively until a specific stopping condition is met. Through the use of these operators, poor-performing individuals in the initial population and among the newly generated individuals can be identified and, if necessary, removed or improved upon, contributing to the refinement of the population. GA has demonstrated success in numerous domains, including energy, health, industry, and earth science, and has been applied to a wide range of problem types, such as estimation, optimization, and classification (Jalal et al. 2021; De and Kundu 2022; Sharma et al. 2022; Kummer et al. 2023).

Given the complexity and multidimensionality of the optimization problem at hand, GAs were selected as the primary optimization method due to their qualities, such as versatility, effectiveness, and efficiency. GAs have inherent robustness to noise and outliers in the data, ensuring stable performance even under challenging conditions. Moreover, their parallelizability allows for significant acceleration of the optimization process, particularly for large-scale problems or computationally expensive fitness functions. Additionally, GAs can seamlessly handle a mix of categorical, continuous, and integer parameters, making them well suited for optimizing machine learning (ML) models with diverse parameter types. The combination of robustness, parallelizability, and the ability to handle various parameter types makes GAs an ideal choice for optimizing ML models in the context of this study.

Results

In this study, an Intel(R) Core(TM) i7-5600U CPU @ 2.60 GHz and a suite of Python libraries, encompassing numpy for efficient mathematical computations, pandas for seamless data manipulation, matplotlib and seaborn for informative data visualization, sklearn for comprehensive ML tasks, xgboost and lightgbm for boosting algorithms, and sklearn_genetic and hyperopt for hyperparameter optimization, were employed to augment soil liquefaction prediction in geotechnical engineering. The overall study workflow is depicted in Fig. 1.

Fig. 1
figure 1

General flow diagram of the study

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Data preprocessing and model training strategy

The dataset utilized in this study was robustly scaled using the robust scaling technique. This scaling approach is highly suitable for datasets characterized by outliers or a non-normal distribution. By employing the Robust Scaler, the data were transformed by subtracting the median and dividing it by the interquartile range, effectively capturing the data’s spread. Furthermore, to manage categorical data, the Mw and amax features re-encoded using one-hot encoding, which allows for the representation of categorical information in a format that machine learning algorithms can readily interpret. The algorithms can capture the inherent patterns and relationships associated with each category by converting the categorical variables into binary columns, enabling more comprehensive analysis and prediction.

To ensure the reliability and generalizability of the models, the dataset was divided into a training set, comprising 70% of the samples, and a test set, which constituted the remaining 30%. To avoid potential biases and objectively assess the models’ performance, a tenfold cross-validation was conducted on the training set. The StratifiedKFold technique was used to select the validation sets, ensuring that the class distribution remained balanced throughout the cross-validation process. This rigorous evaluation methodology helps assess effectiveness and mitigate the risk of overfitting. In addition, the models’ hyperparameters were fine-tuned to optimize their performance. To achieve high success in cross-validation results, searching in the hyperparameter space is a recommended and possible process. It is common for searching on a small subset of its parameters to have a large impact on the model’s predictive and computational performance, while other parameters can be left at their default values (Pedregosa et al. 2011). In this study, a comparable strategy was employed, aligning with similar approaches found in the literature that have demonstrated successful outcomes (Abdu-Aljabar and Awad 2022; Amini et al. 2023; Cuocolo et al. 2020; Dhar 2022; Ge et al. 2023; Janizadeh et al. 2022; Sari and Maki 2023). These studies utilized parameters and parameters ranges similar to those outlined in Table 3. A range of values, as presented in Table 3, were explored and adjusted to identify the optimal configuration for each algorithm. By carefully tuning these hyperparameters, the predictive capabilities were enhanced, improving accuracy and reliability in predicting soil liquefaction potential.

Table 3 Hyperparameters for different ML models
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Hyperparameter optimization using GA

To investigate the classification of soil types, a grain size partitioning technique was used to analyze the soil samples. This process revealed two discernible categories of soil: fine-grained and coarse-grained soils. A comprehensive understanding of the different soil types was achieved by identifying and segregating the samples based on their grain size, facilitating a subsequent classification analysis. To assess the performance of the learning models, three distinct datasets were constructed, namely, as mentioned earlier, datasets A, B, and C, were constructed. Each dataset corresponded to a specific soil type, and the learning models were independently evaluated using these datasets. This approach allowed for meticulous examination of the effectiveness in accurately classifying the respective soil types. Therefore, a comprehensive and robust analysis was performed, allowing for a more nuanced understanding of the classification capabilities of the models.

In addition, this study used GAs as a hyperparameter optimization technique for ML algorithms. GA employs a population size parameter which determines the number of chromosomes within the population utilized in the algorithm. The population size plays a crucial role in the efficiency and efficacy of the GA. A larger population size has the potential to enhance diversity within the population, increasing the chances of discovering the optimal global solution. However, this advantage comes at the expense of longer run times for each generation. Conversely, a smaller population size can lead to faster convergence but also increases the risk of premature convergence, where the algorithm may become trapped in a local optimum and fail to reach the global optimal solution. Choosing the most appropriate population size is thus crucial for the success of the GA and is often determined through experimentation and testing. This study evaluated the performance of ML algorithms using GA with different population sizes. The GA was implemented with different configurations. The population size varied between 10, 15, 20, and 30 individuals, while the number of generations was set to 100. A cross-over probability of 0.6 and a mutation probability of 0.2 were utilized. The tournament size for selection was set to 4, and the algorithm used for optimization was eaMuPlusLambda, that implements the (\(\mu +\lambda\)) evolutionary algorithm, utilizing a provided population, toolbox of evolution operators, and various parameters to iteratively generate offspring, evaluate their fitness, and select the next generation for a specified number of generations, returning the final population and a logbook of evolution statistics. The GA was executed 20 times with a different random seed to mitigate the influence of randomness. The results of the experiment are presented in Fig. 2, which shows a comparison of the GA performance for varying population sizes. Based on the provided data, the highest average accuracy is achieved by Dataset B, while the lowest average accuracy is observed in Dataset C. Changes in population size do not appear to significantly affect the overall performance across datasets.

Fig. 2
figure 2

Comparison of GA performance across different population sizes (Dataset A, B, and C, respectively)

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After tuning the population size and other parameters of the GA, we applied ensemble learning algorithms, such as bagging and boosting, to further enhance the learning performance. However, to achieve optimal results with these algorithms, it is crucial to fine-tune their hyperparameters through experimental studies. To accomplish this, we leveraged the power of GA for hyperparameter optimization. The objective was to obtain the optimal set of hyperparameters for the ML algorithm, ensuring the best possible performance. This approach offers several benefits, including automating the hyperparameter tuning process and effectively handling non-linear and non-convex optimization problems with numerous hyperparameters. Using GA for hyperparameter optimization, our objective was to streamline and optimize the ensemble learning process, improving the overall performance of ML algorithms.

Tables 4 and 5 comprehensively evaluate the performance of ML accuracy and CPU times for different population sizes on three datasets. The values highlighted in bold indicate the highest performance metrics in each category: train accuracy, test accuracy, and CPU times, thereby aiding in the identification of the most effective ML algorithm per metric. Our experimental study showed that Dataset B achieved the highest performance, with a test accuracy of 0.9231 and a training accuracy of 0.9230. Dataset A exhibited a training accuracy of 0.8821 and a test accuracy of 0.8402, while Dataset C had a training accuracy of 0.8782 and a test accuracy of 0.8667.

Table 4 Comparison of ML accuracy performance for different population sizes (Dataset A, B, C)
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Table 5 CPU times (seconds) for different classification algorithms on three datasets
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Tables 4, 5 and Fig. 3 compare the performance of multiple ML algorithms. LightGBM consistently emerges as the leading algorithm in accuracy across all three datasets. It presents robust performance, particularly in predicting soil liquefaction potential, which is critically important in geotechnical engineering. AdaBoost and XGBoost also demonstrate strong accuracy results, making them viable alternatives. However, it is essential to consider computational efficiency, as some algorithms may have a longer CPU. As can be observed, training time generally increases with the population size of the dataset. Among the algorithms, Bagging consistently exhibits the highest training time, while LightGBM has the lowest training time across all datasets.

Fig. 3
figure 3

Comparison of ML algorithms test accuracy performances across different models

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Comparison of genetic algorithm performances with other search algorithms

In the subsequent phase of our study, we compared the performance of the GA with other traditional search algorithms such as GS and RS. Details of the experimental setup and hyperparameters used for each algorithm are provided in the methodology section. The results showed that GA outperformed the other search algorithms mainly in terms of the mean and standard deviation of the results. It is important to note that the best results were obtained in dataset B. Figure 4 compares the performance of different search algorithms with respect to their ability to optimize hyperparameters for ML models. Regarding the standard deviation of the test precision, GS generally has the lowest standard deviation across the three datasets, indicating that its performance is more consistent compared to GA and RS. GA has a slightly higher standard deviation in Dataset A but performs better in Datasets B and C. RS has the highest standard deviation on Dataset B, suggesting that its performance is more variable on this particular dataset.

Fig. 4
figure 4

Test accuracy performance comparisons of search algorithms (Dataset A, B, and C, respectively)

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Figure 4 and Table 6 compare performance metrics for three search algorithms: GA, GS, and RS. The metrics evaluated include the average test accuracy, the average train accuracy, standard deviation of the test accuracy, the standard deviation of the train accuracy, and average CPU time. Based on the comparison, the GA algorithm achieves the highest average test and train accuracy, indicating its effectiveness in optimizing the model performance. Furthermore, the GA algorithm exhibits lower standard deviations, indicating more consistent performance across different trials. However, the GS and RS algorithms also show promising performance, although with slightly lower accuracy and varying standard deviations. Regarding computational efficiency, RS consistently achieves the lowest average CPU time across all datasets, suggesting its advantage in faster execution.

Table 6 Performance comparison of search algorithms
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Discussion

This study evaluated the effectiveness of a GA approach for hyperparameter tuning of ML algorithms and compared it with traditional methods such as GS and RS. The study was divided into two parts. In the first part, the performance of six different ML algorithms was compared, with LightGBM showing the best performance. In the second part, the GA approach was evaluated, and it outperformed both GS and RS in terms of the average test and training accuracy. These findings suggest that GA is a promising method for hyperparameter tuning of ML algorithms. Overall, the study highlights the importance of selecting the appropriate population size for ML algorithms to achieve optimal performance and could be expanded further to evaluate the performance of GA on a larger set of ML algorithms and datasets.

While the GA may perform better in optimizing hyperparameters, it is important to consider that it can be computationally expensive and time-consuming, especially for large datasets. This aspect can be seen as a disadvantage when dealing with large datasets. Due to the nature of GA, which involves evaluating multiple individuals within a population over multiple generations, the computational cost increases as the dataset size grows. The time required to search the hyperparameter space and converge to the optimal solution can become a limiting factor, particularly when dealing with large datasets. In scenarios where computational efficiency is a priority, the time-consuming nature of GA may present a drawback. In such cases, alternative approaches that offer faster hyperparameter optimization methods, such as GS or RS, might be more suitable.

The choice of the hyperparameter optimization method should consider the trade-off between performance gains and computational time, considering the specific characteristics of the dataset and the available computational resources.

In addition to the findings related to hyperparameter optimization, the study also made significant contributions to soil mechanics and geotechnical engineering. Specifically, the study explored the use of ML algorithms to predict soil liquefaction potential based on particle size. Soil liquefaction is a phenomenon that occurs when saturated soil loses its strength and stiffness during an earthquake, leading to the inability of the soil to support structures such as buildings and bridges. Accurate prediction of soil liquefaction potential is critical to assess the safety and stability of structures in earthquake-prone regions.

As explained in the “Dataset Description” section of this study, the main dataset used in the study includes historical liquefaction cases on fine- and coarse-grained soils exposed to the 1999 Turkey and Taiwan earthquakes. When the data on the soil layers whose liquefaction status is given are examined, it is seen that all of them are data that affect the liquefaction sensitivity of coarse-grained soils and are used to determine their liquefaction risk (Table 1). It is known that liquefaction does not occur in all layers of the soil. Therefore, it is important to examine whether there are the necessary conditions for liquefaction in hazard assessments. The type of soil has a key place among these conditions. For years, it has been thought that soil liquefaction is a behavior peculiar only to water-saturated loose sands and that fine-grained soils cannot produce an excessive pore water pressure that causes liquefaction. However, it has been determined by research that low plasticity silty soils can liquefy easily, such as sands, and plasticity properties have been revealed to be important in affecting the liquefaction sensitivity of fine-grained soils (Ishihara 1984, 1985, 1996). The parameters and approaches used in the evaluation of liquefaction in fine- and coarse-grained soils are different from each other. When liquefaction in fine-grained soils, the decision is made mainly by examining the physical properties of the soil or based on laboratory test results. In the literature, there are many criteria based on the physical properties of the relevant soil to determine the liquefaction potential of fine-grained soils.

The physical properties of soils, particularly fine-grained soils, are important factors that can affect the liquefaction behavior of soils. The missing parameters in the dataset, such as soil grain size distribution, plasticity index, liquid limit and water content, can have a significant impact on the accuracy of the models. For example, Ghani et al. (2022) conducted a study in which physical properties such as wn/LL and PI were used as an input parameter in addition to seismic properties to examine the liquefaction behavior of fine-grained soils under seismic conditions. They integrated artificial intelligence to enhance accuracy and reduce uncertainties associated with traditional deterministic approaches. A hybrid method combining optimization algorithms and the adaptive neuro-based fuzzy inference system (ANFIS) was introduced to determine the safety factor against earthquake-induced liquefaction. The ANFIS firefly hybrid model demonstrated high predictive capabilities, with R2 values of 0.976 and 0.982 in the training and testing phases, respectively. Moreover, it is important to consider the broader context of soil properties, particularly in fine-grained soils, which significantly influence the behavior of liquefaction. Ozsagir et al. (2022) emphasized the importance of incorporating comprehensive datasets, including parameters such as grain size distribution, plasticity index, and specific gravity, to enhance model accuracy. They achieved remarkable success in predicting soil liquefaction for fine-grained soils using machine learning models, with an accuracy of nearly 90%. Their findings highlighted the mean grain size (D50) as a critical physical property that influences the performance of machine learning models.

Therefore, considering a range of physical properties in fine-grained soils is crucial to improving the predictive capabilities of models. On the other hand, in evaluating the liquefaction of sandy soil layers, the degree of firmness of the ground and the stress state are considered. The simplified method proposed by Seed and Idriss (1971) is the most widely used approach. The authors conducted the study by dividing the dataset into three groups according to the type of soil, with the foresight that the parameters used as input data in estimating the state of liquefaction could lead to erroneous interpretations, since they are only used for coarse soils. However, the cases of fine- and coarse-grained soils are combined in the dataset. Dataset A represented fine-grained soils, while Dataset B represented the coarse-grained soils, and Dataset C included all 620 soil cases. The ML algorithms applied in this study were evaluated on all three datasets. The best prediction performances were obtained with the LightGBM algorithm for the three datasets. Based on the test sets, these were calculated as 0.9231 for coarse-grained soils, 0.8402 for fine-grained soils, and 0.8667 for all soils.

As a result, the models used in the study could classify the soil liquefaction potential of fine-grained or coarse-grained soils with high accuracy. The best predictions were obtained for coarse-grained soils, while the lowest prediction performance was obtained for fine-grained soils. Taking into account the susceptibility to liquefaction of soils, the best prediction performance was obtained in coarse-grained soils, and the lowest prediction performance in fine-grained soils supported the authors’ approach in this study to separate the main dataset according to the soil type. With the effect of including parameters used in the assessment of sandy soils in the input layer of all models, the best estimation performance was achieved for the dataset representing coarse-grained soils. However, although none of the parameters given in this dataset are used in the calculations for the evaluation of fine-grained soils in the literature, they have provided a good prediction performance on fine-grained soils with ML methods. This evidence shows that the classification-based prediction models applied and proposed in this study can be useful in evaluating a complex phenomenon such as liquefaction.

Limitations of the study

Although this study has achieved significant learning outcomes, it is important to acknowledge certain limitations and challenges encountered during the research. Machine learning, in general, is limited by the availability and quality of data. Overfitting and underfitting are common challenges that can arise when training machine learning models. Overfitting happens when a model learns the specific details of the training data too well and starts to make predictions that are too closely tied to the training data, which can lead to poor performance on new, unseen data. On the other hand, this occurs when a model is too simple to capture the complexity of the data, resulting in poor predictions.

In the context of geotechnical engineering, the data used for training machine learning models often come from complex and multidimensional datasets. This can make it challenging to develop models that can accurately depict the underlying relationships in the data. Additionally, geotechnical problems often involve multiple interacting factors, which can make it difficult to identify the most important features for model training.

Genetic algorithm-optimized machine learning algorithms can be computationally costly, especially for large datasets. Especially the large number of populations and increasing the number of individuals that will undergo mutation and crossover can significantly increase the solution time and the amount of resource usage. This is true not only for GA, but also for other soft computing techniques with a wide choice of parameters. Although having many options may seem to increase uncertainty, it also creates an opportunity to improve the quality of the solution. A second hyperparameter optimization process can be applied to find the most suitable parameters. Or, initial parameter values can be created with the parameter values of good results obtained by examining similar studies in the literature. This can limit the practical applicability of these algorithms, particularly for real-time applications or for problems with a large number of input features.

In addition, in hyperparameter-based studies, choosing wide search ranges and choosing continuous variables instead of discrete and categorical variables has the chance to increase the solution quality, but may increase the calculation time and amount of resource usage.

Finally, machine learning models can suffer from generalization issues, meaning that they may not perform as well on new data that are different from the data used for training. This is a common challenge in machine learning, and it is important to carefully evaluate the performance of models on a variety of datasets to ensure that they are able to generalize well to new data.

In conclusion, while this study has demonstrated the potential of genetic algorithm-optimized machine learning for geotechnical engineering applications, it is important to be aware of the limitations and challenges associated with these methods. Future research should focus on addressing these limitations, such as developing more efficient algorithms, improving the generalization of models, and exploring new approaches to handling complex and multidimensional geotechnical data.

Conclusions

In this study, we investigate hyperparameter optimization techniques for ML algorithms, focusing on their application to prediction of soil liquefaction. By applying our approach, we were able to accurately predict soil liquefaction potential, highlighting the importance of utilizing artificial intelligence to improve the accuracy and reliability of these predictions. Our findings indicate that LightGBM emerged as the most effective among the ML algorithms evaluated. This observation underscores the importance of using sophisticated algorithms to improve understanding and prediction of soil liquefaction. Accurate prediction of soil liquefaction is crucial in preventing or mitigating the potential damage caused by this natural disaster. On the other hand, our study also draws attention to the effect of soil type on the performance results obtained in studies for the prediction of liquefaction.

In this study, it is emphasized that the input parameters to be selected based on the type of soil to estimate the liquefaction potential in coarse and fine-grained soils have an effect on increasing performance in prediction studies. Since there is no input parameter for the susceptibility to liquefaction of fine-grained soils in the dataset used in the study, the authors divided the dataset according to the type of soil and the best performance results were obtained with the dataset containing coarse-grained soils (Dataset B). This situation is explained by the fact that all input parameters in the dataset are parameters used to determine the liquefaction sensitivity of coarse-grained soils (especially sands). However, although there are no parameters to evaluate the liquefaction potential of fine-grained soils in the dataset, high precision was achieved in the prediction of fine-grained soil liquefaction. This observation is another detail that reflects the success of the prediction performances of the methods used in this study.

Class redundancy in any dataset negatively affects the performance of prediction techniques. Poor performance in one class also reduces the success of the other class. By dividing the dataset into classes and applying the methods separately, the individual prediction performance is higher than when considering all classes as a whole. The main reason for this is that the parameters are determined specifically for each dataset class. In particular, machine learning algorithms based on learning have the opportunity to adjust the parameters with less complexity in the training processes by dividing the dataset into classes, allowing one to obtain high-accuracy results in a shorter time. As emphasized in this study, when machine learning algorithms are hyperparameterized using successful artificial intelligence techniques such as GA, the quality of the solution is positively affected.

Soil liquefaction is a critical geotechnical issue that poses significant risks, including physical damage and loss of life. Additionally, due to the heterogeneous characteristics of soils and the participation of many factors that affect the occurrence of liquefaction due to an earthquake, the determination of the liquefaction potential is considered one of the most complex problems in geotechnical engineering. This study contributes to the field by providing information on GA for hyperparameter optimization of ML algorithms, specifically in the prediction of soil liquefaction in geotechnical engineering. The successful application of the GA highlights its potential for broader applications in this domain.