Prediction Of Peak Particle Velocity Research Articles

Data-driven machine learning approaches for simultaneous prediction of peak particle velocity and frequency induced by rock blasting in mining

The vibrations generated by rock blasting are a serious and hazardous outcome of these activities, causing harmful effects on the surrounding environment as well as the nearby residents. Both the local ecology and human communities suffer from the consequences of these vibrations. Assessing the severity of blasting vibrations necessitates a thorough evaluation of Peak Particle Velocity (PPV) and frequency, which are essential parameters for measuring vibration velocity. Accurate prediction of vibration occurrence is critically important. Therefore, this study employs five machine learning models for predicting the PPV and frequency resulting from quarry blasting. This work compares five machine learning models (XGBoost, Catboost, Bagging, Gradient Boosting, and Random Forest Regression) to choose the most efficient performance model. The performance evaluation of each five machine learning models demonstrates each model achieved a performance of more than 0.90 during the testing phase, there was a strong correlation observed between the actual and the predicted ones. The analysis of performance metrics shows Catboost regression model demonstrate better performance prediction comparing with the other models with R2 = 0.983, MSE = 0.000078, RMSE = 0.008, NRMSE = 0.019, MAD = 0.004, MAPE= 35.197 in the PPV prediction, and R2 = 0.975, MSE = 0.000243, RMSE = 0.015, NRMSE = 0.031, MAD = 0.008, MAPE = 37.281 for the frequency prediction. This study will help mining engineers and blasting experts to select the best machine learning model and its hyperparameters in estimating ground vibration, and frequency. In the context of the mining and civil industry, the application of this study offers significant potential for enhancing safety protocols and optimizing operational efficiency. By employing machine learning models, this research aims to accurately predict and assess ground vibrations with frequency resulting from rock blasting.

Prediction of Ground Vibration Velocity Induced by Long Hole Blasting Using a Particle Swarm Optimization Algorithm

Obtaining accurate basic parameters for long hole blasting is challenging, and the resulting vibration damage significantly impacts key surface facilities. Predicting ground vibration velocity accurately and mitigating the harmful effects of blasting are crucial aspects of controlled blasting technology. This study focuses on the prediction of ground vibration velocity induced by underground long hole blasting tests. Utilizing the fitting equation based on the US Bureau of Mines (USBM) formula as a baseline for predicting peak particle velocity, two machine learning models suitable for small sample data, Support Vector Regression (SVR) machine and Random Forest (RF), were employed. The models were optimized using the particle swarm optimization algorithm (PSO) to predict peak particle velocity with multiple parameters specific to long hole blasting. Mean absolute error (MAE), mean Squared error (MSE), and coefficient of determination (R2) were used to assess the model predictions. Compared with the fitting equation based on the USBM model, both the Support Vector Regression (SVR) and Random Forest (RF) models accurately and effectively predict peak particle velocity, enhancing prediction accuracy and efficiency. The SVR model exhibited slightly superior predictive performance compared to the RF model.

Research on prediction of PPV in open-pit mine used RUN-XGBoost model

The drill-blasting method is a commonly used mining technique in open-pit mines, and the peak particle velocity (PPV) caused by blasting vibrations is an important indicator for evaluating the rationality of blasting mining design parameters. To develop an effective PPV prediction model, a parameter self-optimizing RUN-XGBoost prediction model is implemented using the Runge-Kutta optimization algorithm (RUN) combined with extreme gradient boosting (XGBoost). The factors affecting the prediction of PPV, including maximum explosive (ME), total explosive (TE), blast center distance (BCD), blast hole depth (BHD), and height difference between the measurement location and the blast location (DH), are selected as the influencing indicators. 188 pieces of blasting operation data were measured at the RK open pit copper-cobalt mine. Then, the RUN-XGBoost prediction model for PPV is studied and compared with the Sadovsky empirical formula, traditional XGBoost model, PSO-XGBoost model, and some traditional machine learning models (Ridge, LASSO, SVM, and SVR) using R2, RMSE, VAF, MAE, and MBE as evaluation indicators for model prediction results. Finally, the Shapley Additive Explanations (SHAP) method is used to evaluate the contribution of different influencing indicators to the PPV prediction results. The results show that the RUN-XGBoost prediction model is significantly better than other machine learning models and the Sadovsky empirical formula in the prediction of PPV, further demonstrating that the RUN-XGBoost prediction model can handle the nonlinear features of multiple factors and provide a reliable, simple, and effective PPV prediction model, forming a rapid prediction and evaluation method for blasting vibrations in open-pit mining.

Study on blast-induced vibration of single-hole cylindrical charge

It is essential to study the blast-induced vibration of cylindrical charge so as to reduce ground vibration level and protect the surrounding environment. In this paper, the Heelan model is used to study the generation and propagation mechanisms of blasting vibration induced by single-hole cylindrical charge. It shows that the superposition of vibration waves induced by explosives in different positions of the cylindrical charge causes the increase of peak particle velocity ( PPV) in the region along the propagation direction of detonation waves. The vector peak particle velocity ( VPPV) versus distance for different stemming lengths ( SL) indicates that the linear attenuation between the VPPV and the exponential of distance appears only over a certain distance. Hence, the traditional formula for PPV prediction is suitable just in the middle and far field, not in the near field. The influences of charge length, detonation velocity and initiation pattern on the blast vibration are also investigated. The generation of Mach waves is determined by the relationship of scale between velocity of detonation ( VoD), P-wave velocity, and S-wave velocity. Over a certain value, the charge length doesn’t affect maximum VPPV, but affects the range of VPPV with relatively large values. Moreover, the bottom and top detonator positions have similar consequences on vibration control in the far field as the influence of limited charge length on blast vibration can be ignored. The VPPV of the middle initiating is almost twice as much as the other two detonator positions in the far field. Thus, in practical blasting, the middle initiating needs to be avoided.

Experimental and numerical investigation of badarpur sand subjected to air-blast loading

In the present study, the results of experimental and numerical investigation of Badarpur sand subjected to air-blast loading generated from a laboratory-scale blast simulator are presented. The air-blast loading on the sand specimen is simulated experimentally using a vertical shock tube test facility to investigate the stress wave attenuation and vibrational characteristics of the Badarpur sand. The peak stress wave pressure and peak particle acceleration are recorded using the synchronized pressure transducers and triaxial accelerometers embedded inside the sand specimen. A stress enhancement of about 1.25-2.69 times the peak over-pressure is observed at the top one-third layer of the sand due to its compaction by the stress wave generated upon the blast wave impact. The stress wave intensity first increases and then rapidly decreases with the depth of the sand specimen. The amplitude of the peak particle acceleration is also observed to attenuate with the depth of the sand specimen. Further, based on the experimental results, the empirical equations are developed to predict peak particle velocity against the scaled distance with a power law index of 3.9, 2.5, and 3.0 for dense-coarse, dense-fine, and medium-dense fine sand, respectively. The numerical model of the vertical shock tube and sand specimens are also developed based on the Arbitrary Lagrangian-Eulerian formulation, commercially available in finite element simulation package LS DYNA and the results are validated with the experimental data.

Urban Quarry Ground Vibration Forecasting: A Matrix Factorization Approach

Blasting is routinely carried out in urban quarry sites. Residents or houses around quarry sites are affected by the ground vibrations induced by blasting. Peak Particle Velocity (PPV) is used as a metric to measure ground vibration intensity. Therefore, many prediction models of PPV using experimental methods, statistical methods, and Artificial Neural Networks (ANNs) have been proposed to mitigate this effect. However, prediction models using experimental and statistical methods have a tendency of poor prediction accuracy. In addition, while prediction models using ANNs can produce a highly accurate prediction results, a large amount of measured data is necessarily collected. In an urban quarry site where the number of blastings is limited, it is difficult to collect a lot of measured data. In this study, a new PPV prediction method using Weighted Non-negative Matrix Factorization (WNMF) is proposed. WNMF is a method that approximates a non-negative matrix (including missing data) to the product of two low-dimensional matrices and predicts the missing data. In addition, WNMF is one of the unsupervised learning methods, so it can predict PPV regardless of the amount of data. In this study, PPV was predicted using measured data from 100 sites at the Mikurahana quarry site in Japan. As a result, the proposed method showed higher accuracy when using measured data at 60 sites rather than 100 sites, and the root mean square error for PPV prediction decreased from 0.1759 (100 points) to 0.1378 (60 points).

A method for predicting blast-induced ground vibration based on Mamdani Fuzzy Inference System

Blast-induced ground vibration is highly possible to result in serious losses such as destroyed buildings. The crucial parameter of the mentioned vibration is peak particle velocity (PPV). Many equations have been developed to predict PPV, however, worse performance has been reported by multiple literatures. This paper developed a method for predicting PPV based on Mamdani Fuzzy Inference System. Firstly, Minimum Redundancy Maximum Relevance was employed to identify the blasting design parameters which significantly contribute to the PPV induced by blasting. Secondly, K-means method was applied to determine the value ranges of the selected parameters. The selected parameters and corresponding value ranges were combined to input into Mamdani Fuzzy Inference System for obtaining predicted PPV. Totally, 280 samples were collected from a blasting site. 260 out of them were used to train the proposed method and 20 were assigned for test. The proposed method was tested in the comparison with empirical equation USBM, multiple linear regression analysis, pure Mamdani Fuzzy Inference System in terms of the difference between predicted PPV and measured PPV, coefficient of correlation, root-mean-square error, and mean absolute error. The results from that showed that the proposed method has the better performance in PPV prediction.

Prediction of ground vibration due to mine blasting in a surface lead–zinc mine using machine learning ensemble techniques

Ground vibration due to blasting is identified as a challenging issue in mining and civil activities. Peak particle velocity (PPV) is one of the blasting undesirable consequences, which is resulted during emission of vibration in blasted bench. This study focuses on the PPV prediction in the surface mines. In this regard, two ensemble systems, i.e., the ensemble of artificial neural networks and the ensemble of extreme gradient boosting (EXGBoosts) were developed for PPV prediction in one of the largest lead–zinc open-pit mines in the Middle East. For ensemble modeling, several ANN and XGBoost base models were separately designed with different architectures. Then, the validation indices such as coefficient determination (R2), root mean square error (RMSE), mean absolute error (MAE), the variance accounted for (VAF), and Accuracy were used to evaluate the performance of the base models. The five top base models with high accuracy were selected to construct an ensemble model for each of the methods, i.e., ANNs and XGBoosts. To combine the outputs of the top base models and achieve a single result stacked generalization technique, was employed. Findings showed ensemble models increase the accuracy of PPV predicting in comparison with the best individual models. The EXGBoosts was superior method for predicting of the PPV, which obtained values of R2, RMSE, MAE, VAF, and Accuracy corresponding to the EXGBoosts were (0.990, 0.391, 0.257, 99.013(%), 98.216), and (0.968, 0.295, 0.427, 96.674(%), 96.059), for training and testing datasets, respectively. However, the sensitivity analysis indicated that the spacing (r = 0.917) and number of blast-holes (r = 0.839) had the highest and lowest impact on the PPV intensity, respectively.

Effects of Vibration on Adjacent Pipelines under Blasting Excavation

Exploring a pipeline’s response to blast vibration during tunnel excavation is critical for ensuring the safety of the pipeline. In this paper, the vibration monitoring and numerical simulation methods are used to evaluate the dynamic response of ground soil and pipelines to blasts. The attenuation law of peak particle velocity (PPV) and the distribution characteristics of peak effective stress (PES) in pipe sections under different working conditions are studied. The following findings are recorded: (1) A three-dimensional model considering in situ stress is established, and it is found the triangular equivalent load simulation blast effect method used in this paper can effectively reflect the impact of blasting on pipelines. The simulation error is controlled at 7.69%. (2) The ground PPV of each monitoring point decays continuously with the increase in horizontal and axial distance, and the cavity enlargement effect is exhibited above the excavation area. The oncoming blast side PPV of the pipe section is more significant than that behind the blast side. (3) When the blast vibration is transmitted to the pipe, there are differences in the PPV and PES distribution characteristics across the pipe cross-section. The PPV is greater in the lower part of the pipe section, while the PES value is greater in the upper part of the pipe section. The maximum PES of 1.53 MPa is significantly lower than the safety threshold (≤4.6 MPa) at the hazardous-section-monitoring point. (4) A pipeline PPV prediction model is proposed to guide subsequent blasting program development. An empirical formula for the safety criterion applicable to this study is proposed for the scientific implementation of safety assessments for subsequent construction. This safety evaluation framework can be used as a reference for similar projects.

Prediction of Peak Particle Velocity of Blast-induced Ground Vibrations using Boosted Regression Trees Authored

Loosening of rockmass during its excavation in an infrastructure project is carried by rock blasting. The blast-induced ground vibrations pose a major challenge to the blasting engineers, whose main objective is to control their potential to cause any damage to the buildings in the vicinity. The research reported in this paper explains how the error in the prediction of the Peak Particle Velocity (PPV) by the United States Bureau of Mines (USBM)-based approach can be minimised using machine learning techniques. The complex correlation between the blast parameter and the PPV value has been modelled using the least square boosted decision tree approach after the selection of the best suitable feature has been selected based on the correlation matrix. The proposed model automatically maps the input blast feature (SD) with the target PPV values by aggregating the decision of various weak learners. The generalization of the proposed model has been validated through a 5-fold cross-validation approach using a dataset comprising of two hundred blast records generated by monitoring the blasts at International airport site, Navi Mumbai, India. The assessment of the prognostic ability of the proposed model demonstrates that it has outperformed the USBM-based approach for PPV prediction. The results establish that the predictions by the proposed model are closer to the measured values than the other regression models.

Study on influencing factors and prediction of peak particle velocity induced by roof pre-split blasting in underground

Blasting technology is widely used to prevent coal bursts by presplitting the overburden in underground coal mines. The control of blasting intensity is important in achieving the optimal pre-split effectiveness and reducing the damage to roadway structures that are subjected to blasting vibrations. As a critical parameter to measure the blasting intensity, the peak particle velocity (PPV) of vibration induced by blasting, should be accurately predicted, and can provide a useful guideline for the design of blasting parameters and the evaluation of the damage. In this paper, various factors that influence PPV, induced by roof pre-split blasting, were analyzed using engineering blasting experiments and numerical simulations. The results showed that PPV was affected by many factors, including charge distribution design (total charge and maximum charge per hole), spacing of explosive centers, as well as propagation distance and path. Two parameters, average charge coefficient and spatial discretization coefficient were used to quantitatively characterize the influences of charge distribution and spacing of explosive centers on the PPV induced by roof pre-split blasting. Then, a model consisting of the combination of artificial neural network (ANN) and genetic algorithm (GA) was adopted to predict the PPV that was induced by roof pre-split blasting. A total of 24 rounds of roof pre-split blasting experiments were carried out in a coal mine, and vibration signals were collected using a microseismic (MS) monitoring system to construct the neural network datasets. To verify the efficiency of the proposed GA-ANN model, empirical correlations were applied to predict PPV for the same datasets. The results showed that the GA-ANN model had superiority in predicting PPV compared to empirical correlations. Finally, sensitivity analysis was performed to evaluate the impacts of input parameters on PPV. The research results are of great significance to improve the prediction accuracy of PPV induced by roof pre-splitting blasting.

A Short Overview of Soft Computing Techniques in Tunnel Construction

Tunnel construction is a complex technology, with a huge number of effective parameters, which cannot be accurately analyzed/designed using empirical or theoretical methods. With the rapid development of computer technologies, Soft Computing (SC) approaches have been widely used in tunnel construction. Typically, the two common tunneling methods, blasting and mechanical excavation (e.g., tunnel boring machine, shield, pipe jacking method), have been used in conjunction with some SC techniques to solve specific problems and have shown a good fit. On this basis, this paper first summarizes the current research on the application of SC techniques in the field of tunnel construction methods. For example, in the case of blasting, the application of SC techniques is focusing on the environmental problems induced by blasting, such as the prediction of peak particle velocity and over-break. As for mechanical tunnel construction, the SC techniques were used to analyze the boring characteristics of the machine, such as the estimation of penetration rate and advance rate. Additionally, an important aspect for the application of SC techniques is the identification of the influencing factors for each of the study subjects, i.e. the necessary input parameters for the SC. Finally, this paper elaborates on the working process of the supervised learning models, highlights the points that need to be taken care of in each step, and points out that the SC technique, which is synergistic with the physical process, is more useful to explain the actual phenomenon.

A Short Overview of Soft Computing Techniques in Tunnel Construction

Tunnel construction is a complex technology, with a huge number of effective parameters, which cannot be accurately analyzed/designed using empirical or theoretical methods. With the rapid development of computer technologies, Soft Computing (SC) approaches have been widely used in tunnel construction. Typically, the two common tunneling methods, blasting and mechanical excavation (e.g., tunnel boring machine, shield, pipe jacking method), have been used in conjunction with some SC techniques to solve specific problems and have shown a good fit. On this basis, this paper first summarizes the current research on the application of SC techniques in the field of tunnel construction methods. For example, in the case of blasting, the application of SC techniques is focusing on the environmental problems induced by blasting, such as the prediction of peak particle velocity and over-break. As for mechanical tunnel construction, the SC techniques were used to analyze the boring characteristics of the machine, such as the estimation of penetration rate and advance rate. Additionally, an important aspect for the application of SC techniques is the identification of the influencing factors for each of the study subjects, i.e. the necessary input parameters for the SC. Finally, this paper elaborates on the working process of the supervised learning models, highlights the points that need to be taken care of in each step, and points out that the SC technique, which is synergistic with the physical process, is more useful to explain the actual phenomenon.

Improvement in the prediction of peak particle velocity of blast-induced ground vibrations using K-means clustering

Improvement in the prediction of peak particle velocity of blast-induced ground vibrations using K-means clustering

Prediction of BlastInduced Ground Vibration (BIGV) of Metro Construction Using Difference Evolution AlgorithmOptimized Gaussian Process (DE-GP)

Rock blasting often has an irreversible impact on the surrounding environment and threatens the safety of life and property. Therefore, accurate prediction of blast-induced ground vibration (BIGV) is a prerequisite for safe construction. In view of the fact that traditional blasting peak particle velocity (PPV) empirical formulas cannot be accurately predicted, this study selected 88 sets of blasting monitoring data, based on distance from the blast-face, maximum charge per delay, total charge, hole depth, spacing, burden, stemming length, and powder factor being used as input variables and PPV being used as output variable to characterize BIGV. First, a nonlinear mapping relationship between input variables and output variable is established through the Gaussian process (GP). The differential evolution algorithm (DE) is used to optimize the hyperparameters σf, σn, and l of the GP, and a blasting PPV model based on the DE-GP is constructed. The proposed model is compared with the empirical formulas, least square support vector machine (LSSVM), artificial neural network (ANN), and GP model, and its prediction performance is evaluated by statistical indicators such as root mean square error (RMSE). Finally, the cosine amplitude method (CAM) is used to analyze the sensitivity of blasting parameters. The results show that the DE-GP algorithm for blasting vibration velocity prediction has higher precision and accuracy, which is significantly better than other models, and is the closest to the measured PPV. Distance from the blast-face, total charge, and maximum charge per delay have a greater impact on the prediction of PPV, while stemming length and powder factor have a smaller impact on the prediction of PPV. The DE-GP model proposed by this research has certain reference value for the prediction and control of PPV in blasting construction.

Developing a hybrid model of Jaya algorithm-based extreme gradient boosting machine to estimate blast-induced ground vibrations

Blasting is still being considered to be one the most important applicable alternatives for conventional excavations. Ground vibration generated due to blasting is an undesirable phenomenon which is harmful for the nearby structures and should be prevented. In this regard, a novel intelligent approach for predicting blast-induced PPV was developed. The distinctive Jaya algorithm and high efficient extreme gradient boosting machine (XGBoost) were applied to obtain the goal, called the Jaya-XGBoost model. Accordingly, 150 sets of data composed of 13 controllable and uncontrollable parameters are chosen as input independent variables and the measured peak particle velocity (PPV) is chosen as an output dependent variable. Also, the Jaya algorithm was used for optimization of hyper-parameters of XGBoost. Additionally, six empirical models and several machine learning models such as XGBoost, random forest, AdaBoost, artificial neural network and Bagging were also considered and applied for comparison of the proposed Jaya-XGBoost model. Accuracy criteria including determination coefficient (R2), root-mean-square error (RMSE), mean absolute error (MAE), and the variance accounted for (VAF) were used for the assessment of models. For this study, 150 blasting operations were analyzed. Also, the Shapley Additive Explanations (SHAP) method is used to interpret the importance of features and their contribution to PPV prediction. Findings reveal that the proposed Jaya-XGBoost emerged as the most reliable model in contrast to other machine learning models and traditional empirical models. This study may be helpful to mining researchers and engineers who use intelligent machine learning algorithms to predict blast-induced ground vibration.

Blasting Vibration Control Using an Improved Artificial Neural Network in the Ashele Copper Mine

Blasting is currently the most important method for rock fragmentation in metal mines. However, blast-induced ground vibration causes many negative effects, including great damage to surrounding rock masses and projects and even casualties in severe cases. Therefore, prediction of the peak particle velocity (PPV) caused by blasting plays an important role in reducing safety threats. In this paper, a genetic algorithm (GA) and an artificial neural network (ANN) algorithm were jointly used to construct a neural network model with a 4-5-1 topology to predict the PPV. For this model, the ANN parameters were optimized using the GA, and the deviating direction, horizontal distance, vertical distance, Euclidean distance, explosive type, burden, hole spacing, and maximum charge per delay were used as input information. Moreover, principal component analysis (PCA) was used to extract the first four principal components from the eight input factors as the four inputs of the ANN model. The model was successfully applied to protect an underground crushing cave from blasting vibration damage by adjusting the blasting parameters. Compared with several widely used empirical equations, the GA-ANN PPV prediction model produced significantly better results, while the Ambraseys–Hedron method was the best of the empirical methods. Therefore, the improved GA-ANN model can be used to predict the PPV on site and provide a reference for the control of blasting vibration in field production.

Prediction of Peak Particle Velocity Caused by Blasting through the Combinations of Boosted-CHAID and SVM Models with Various Kernels

This research examines the feasibility of hybridizing boosted Chi-Squared Automatic Interaction Detection (CHAID) with different kernels of support vector machine (SVM) techniques for the prediction of the peak particle velocity (PPV) induced by quarry blasting. To achieve this objective, a boosting-CHAID technique was applied to a big experimental database comprising six input variables. The technique identified four input parameters (distance from blast-face, stemming length, powder factor, and maximum charge per delay) as the most significant parameters affecting the prediction accuracy and utilized them to propose the SVM models with various kernels. The kernel types used in this study include radial basis function, polynomial, sigmoid, and linear. Several criteria, including mean absolute error (MAE), correlation coefficient (R), and gains, were calculated to evaluate the developed models’ accuracy and applicability. In addition, a simple ranking system was used to evaluate the models’ performance systematically. The performance of the R and MAE index of the radial basis function kernel of SVM in training and testing phases, respectively, confirm the high capability of this SVM kernel in predicting PPV values. This study successfully demonstrates that a combination of boosting-CHAID and SVM models can identify and predict with a high level of accuracy the most effective parameters affecting PPV values.

PPV distribution of sidewalls induced by underground cavern blasting excavation

The peak particle velocity (PPV) is an important indicator for predicting blasting excavation disturbances. However, the PPV distribution in the deep underground space is significantly different from that on the outdoor ground. Therefore, it is difficult to predict the underground PPV by Sadovsky’s vibration formula. The PPV sidewall distribution characteristics were studied during site blasting in an underground cavern in the Taohuazui mine in China, and a similar numerical model was used to verify the site test data. We derived a PPV prediction formula for the underground cavern sidewall surrounding rock using a mechanical analysis model of a simply supported plate and beam in combination with dimensional analysis. The model considered derived boundary constraints, comparison with site measured data, the value predicted by Sadovsky’s vibration formula, and numerical simulation results. The results showed that the PPV distribution on the middle 1/3 section of the underground cavern sidewall showed a “platform” or “bulge” different from the curve from Sadovsky’s vibration formula. The PPV amplification coefficient in this section was distributed in a drum shape. The PPV prediction formula for the middle section of the sidewall derived in this paper was highly consistent with the data measured on-site and the numerical simulation results. The mechanical analysis model with a simply supported plate and beam included an underground cavern sidewall length–height ratio of 5 and effectively supplemented the PPV prediction formula for the middle section of the traditional underground cavern sidewall.

Prediction of ground vibration intensity in mine blasting using the novel hybrid MARS–PSO–MLP model

The present paper's primary goal is to propose a novel hybrid model with high reliability to predict peak particle velocity (PPV)—a ground vibration evaluation unit in mine blasting. This model is based on the coupling of the multivariate adaptive regression splines (MARS), particle swarm optimization (PSO), and multi-layer perceptron neural networks (MLP). To this end, a strategy of stacking the MARS models was applied. Multiple MARS models were developed first with different hyper-parameters. Subsequently, the outcome predictions from these MARS models were merged as a new data set. The MLP model was then developed based on the newly generated data set, called the MARS–MLP model. To improve the accuracy and reduction of the MARS–MLP model's error, the PSO algorithm was applied in terms of optimization of the MARS–MLP's weights, called the MARS–PSO–MLP model. The proposed MARS–PSO–MLP model was then compared with the stand-alone MARS, MLP, empirical models, and the hybrid PSO–MLP model (without stacking MARS models) using the same data set. The results revealed that the proposed strategies could significantly boost the MARS and MLP models' performance with the PSO algorithm's effective help. The proposed MARS–PSO–MLP model yielded the highest accuracy and reliability with a root-mean-squared error (RMSE) of 1.569, mean absolute error (MAE) of 1.017, and squared-correlation (R2) of 0.902. In comparison, the stand-alone models (i.e., MARS and MLP) and the hybrid model of PSO–MLP provided lower performances with an RMSE of 1.582 to 1.704, MAE of 0.941 to 1.427, and R2 of 0.871 to 0.891. In contrast, poor performance with an RMSE of 5.059, MAE of 3.860, and R2 of 0.127 was found for the empirical model, and it is not a reliable method to predict PPV in this study. This work's findings also indicated that explosive charge per delay, monitoring distance, spacing, powder factor, and burden have significant effects on PPV, the incredibly explosive charge per delay, and monitoring distance. Remarkable, the stemming variable has a minimal impact on PPV, and its role in the modeling of PPV is not exact.