Minimax Probability Machine Regression Research Articles

Dynamic Soil-Structure Interaction of Multi-Story Buildings using the Finite Element Method and Minimax Probability Machine Regression

Soil-Structure Interaction (SSI) issues are some of the most critical problems encountered in the design of structures prone to earthquake shaking. The damage caused by an earthquake mainly depends on the interaction between soil and structure. In this study, the effect of dynamic SSI on a multi-story building is examined using two methods, Finite Element Method (FEM) and Minimax Probability Machine Regression (MPMR). The MPMR was used to develop a model based on the input and output database generated from the FEM model. The performance comparison of these two models shows a good correlation. The MPMR model significantly reduced the computational time and can thus be utilized as a substitute for determining the response quantities.

Soft-Computing Techniques for Predicting Seismic Bearing Capacity of Strip Footings in Slopes

In this study, various machine learning algorithms, including the minimax probability machine regression (MPMR), functional network (FN), convolutional neural network (CNN), recurrent neural network (RNN), and group method of data handling (GMDH) models, are proposed for the estimation of the seismic bearing capacity factor (Nc) of strip footings on sloping ground under seismic events. To train and test the proposed machine learning model, a total of 1296 samples were numerically obtained by performing a lower-bound (LB) and upper-bound (UB) finite element limit analysis (FELA) to evaluate the seismic bearing capacity factor (Nc) of strip footings. Sensitivity analysis was performed on all dimensionless input parameters (i.e., slope inclination (β); normalized depth (D/B); normalized distance (L/B); normalized slope height (H/B); the strength ratio (cu/γB); and the horizontal seismic acceleration (kh)) to determine the influence on the dimensionless output parameters (i.e., the seismic bearing capacity factor (Nc)). To assess the performance of the proposed models, various performance parameters—namely the coefficient of determination (R2), variance account factor (VAF), performance index (PI), Willmott’s index of agreement (WI), the mean absolute error (MAE), the weighted mean absolute percentage error (WMAPE), the mean bias error (MBE), and the root-mean-square error (RMSE)—were calculated. The predictive performance of all proposed models for a bearing capacity factor (Nc) prediction was compared by using the testing dataset, and it was found that the MPMR model achieved the highest R2 values of 1.000 and 0.957 and the lowest RMSE values of 0.000 and 0.038 in both the training and testing phases, respectively. The parametric analyses, rank analyses, REC curves, and the AIC showed that the proposed models were quite effective and reliable for the estimation of the bearing capacity factor (Nc).

Broad Minimax Probability Learning System and its Application in Regression Modeling

Broad learning system (BLS), a novel incremental learning algorithm, has attracted more and more attention and application. BLS achieves a perfect balance between learning performance and modeling efficiency based on the mean square error (MSE) criterion. However, MSE assumes that a random error between an observed value and real value is a Gaussian distribution, which may be inconsistent to the real-world situation. Moreover, the distributional assumptions may cast doubt on the generalization and validity of the built BLS model. In this article, we propose a novel distribution-free BLS for regression analysis, called broad minimax probability learning system (BMPLS). Learning from the idea of minimax probability machine regression, BMPLS builds a regression model by maximizing the worst probability of the regression function being within the allowed error range. It adequately utilizes the mean and covariance information of the hidden-space feature without making any distributional assumptions of the random error. In order to further improve the learning performance of the model, a regularized BMPLS (RBMPLS) is proposed by applying elastic-net regularization term to BMPLS. The corresponding optimization algorithm is also designed for calculating the output weights of the model. Multiple experiments based on public datasets were carried out to demonstrate the feasibility of the proposed algorithms.

Machine Learning Approach for Prediction of Lateral Confinement Coefficient of CFRP-Wrapped RC Columns

Materials have a significant role in creating structures that are durable, valuable and possess symmetry engineering properties. Premium quality materials establish an exemplary environment for every situation. Among the composite materials in constructions, carbon fiber reinforced polymer (CFRP) is one of best materials which provides symmetric superior strength and stiffness to reinforced concrete structures. For the structure to be confining, the region jeopardizes seismic loads and axial force, specifically on columns, with limited proportion of ties or stirrups implemented to loftier ductility and brittleness. The failure and buckling of columns with CFRP has been studied by many researchers and is ongoing to determine ways columns can be retrofitted. This article symmetrically integrates two disciplines, specifically materials (CFRP) and computer application (machine learning). Technically, predicting the lateral confinement coefficient (Ks) for reinforced concrete columns in designs plays a vital role. Therefore, machine learning models like genetic programming (GP), minimax probability machine regression (MPMR) and deep neural networks (DNN) were utilized to determine the Ks value of CFRP-wrapped RC columns. In order to compute Ks value, parameters such as column width, length, corner radius, thickness of CFRP, compressive strength of the unconfined concrete and elastic modulus of CFRP act as stimulants. The adopted machine learning models utilized 293 datasets of square and rectangular RC columns for the prediction of Ks. Among the developed models, GP and MPMR provide encouraging performances with higher R values of 0.943 and 0.941; however, the statistical indices proved that the GP model outperforms other models with better precision (R2 = 0.89) and less errors (RMSE = 0.056 and NMBE = 0.001). Based on the evaluation of statistical indices, rank analysis was carried out, in which GP model secured more points and ranked top.

Application of Artificial Intelligence Techniques in Slope Stability Analysis

Artificial intelligence (AI) techniques have become a trusted methodology among researchers in the recent decades for handling a variety of geotechnical and geological problems. Machine learning (ML) algorithms are distinguished by their superior feature learning and expression capabilities as compared to traditional approaches, attracting researchers from a variety of domains to their growing number of applications. Different ML models are extensively used in the field of geotechnical engineering to accounting for the inherent spatial variability of soils in slope stability assessments. This study presents a brief overview of the application of several AI techniques in the area of slope stability, including adaptive neuro-fuzzy inference system, artificial neural network, extreme learning machine, functional network, genetic programming, Gaussian process regression, least-square support vector machine, multivariate adaptive regression spline, minimax probability machine regression, relevance vector machine, and support vector machine. Additionally, a summary containing published literature, the corresponding reference cases with the type of input soil parameters, and the implemented ML algorithms was compiled. Recent applications of various hybrid ML models in slope stability assessment are also discussed. Furthermore, the challenges and future prospects of AI techniques development in solving slope stability problems are presented and discussed.

Stress intensity factor prediction on offshore pipelines using surrogate modeling techniques

This study aims to predict the accurate stress intensity factor (SIF) of a crack propagating in offshore piping, which is one of the crucial factors used to assess the remaining fatigue life (RFL) of offshore pipelines. Four soft computing techniques are examined and evaluated in the modeling of SIF of a crack propagating in topside piping, as an inexpensive alternative to the finite element methods (FEM). In the training and testing stages, developed models of Functional Network (FN), Emotional Neural Network (ENN), Relevance Vector Machine (RVM), and minimax probability machine regression (MPMR) for SIF prediction were used and compared. Also, a comparative study was conducted for the developed models with the Adaptive Gaussian Process Regression Model (AGPRM). The load, crack depth, and half crack length have been adopted as input variables of the models, and the output variable is the SIF. All variables were simulated and determined based on the flat-plate FEM model. The analysis confirms that the RVM and MPMR models are superior to FN and ENN models for SIF prediction in the training and testing stages. In addition, the RVM and MPMR models show better than AGPRM for the prediction of pipe SIF in the testing stage. The MPMR accurately outperforms all models within 1.31% prediction error, and the majority of its error values at 99% confidence level fall within ±29.64 MPamm.

Soft computing approaches towards tensile strength estimation of GFRP rebars subjected to alkaline-concrete environment

The rising demand for coastal infrastructure has led to seawater and sea sand concrete which is highly alkaline in nature. Glass-fibre reinforced polymer (GFRP) bars are a durable alternative to conventional steel rebars; however, they are susceptible to degradation in a harsh alkaline concrete environment. This study aims to develop three soft computing techniques, namely minimax probability machine regression (MPMR), deep neural network (DNN), and integrated adaptive neuro-fuzzy inference system with genetic algorithm (ANFIS-GA), to estimate accurate tensile strength retention (TSR) of conditioned GFRP rebars in the aggressive alkaline concrete environment. The sensitivity of production parameters of GFRP rebars and environmental factors in estimating TSR is also discussed. Statistical analyses, e.g. root mean square error (RMSE) and determination coefficient (R2), are used to assess the proposed models' accuracy. The predictions from the developed models manifested a reliable agreement to the experimental results.In comparison, the developed DNN and hybrid ANFIS-GA algorithms outperformed MPMR. The RMSE and R2 are (8.16% and 78.22), (7.42% and 76.04), and (7.53% and 75.00) for the ANFIS-GA, DNN, and MPMR, respectively. The DNN and ANFIS-GA were also compared with the previous approaches developed in the literature. The superior performance of DNN and ANFIS-GA was observed with a maximum model error approach of 10.71%. Furthermore, the sensitivity of temperature and pH of the conditioning environment significantly affect the TSR of GFRP bars. The diameter of GFRP bars and volume fraction of fibres are essential attributes in the degradation of GFRP rebars and shall be considered in the design of concrete structures.

Regularized twin minimax probability machine for pattern classification and regression

As an excellent discriminant classifier based on generating prior knowledge, the minimax probability machine (MPM) has been widely used and deeply researched in many fields. The core idea of minimax probability machine is to directly estimate probability accuracy bound by minimizing the maximum probability of misclassification. However, minimax probability machine does not include a regularization term for the construction of the separating hyperplane, and it needs to solve a large-scale second-order cone programming problem in the solution process, which greatly limits it development and application. In this paper, to improve the performance of minimax probability machine, we propose a novel binary classification method called regularized twin minimax probability machine classification (TMPMC). The TMPMC constructs two non-parallel hyperplanes for final classification by solving two smaller second-order cone programming problems to improve the performance of the MPM. For each hyperplane, our method is theoretically well grounded on the idea of minimizing the worst case (maximum) probability of misclassification of a class of samples while the distance to the other class is as large as possible. Our approach was first derived as linear methods, and subsequently extended as kernel-based strategies for nonlinear classification. Additionally, we extend TMPMC to the regression problem and propose a new regularized twin minimax probability machine regression (TMPMR). Experimental results on several datasets show that our methods are competitive in terms of generalization performance compared to other algorithms.

Smart phase behavior modeling of asphaltene precipitation using advanced computational frameworks: ENN, GMDH, and MPMR

Asphaltene precipitation is the reason behind some of the most destructive issues in the oil industry such as wettability alteration, formation plugging, and reduction of the relative permeability. There are different experimental and modeling methods to study the asphaltene phase behavior. However, those approaches are either time-consuming or costly. In addition, the prediction of asphaltene precipitation is challenging due to the nonlinear dependence. Therefore, in this study, three advanced computational algorithms including group method of data handling (GMDH), emotional neural network (ENN), and minimax probability machine regression (MPMR) are developed and applied to the comprehensive dataset to estimate the amount of asphaltene precipitation as the function of temperature, dilution ratio, and the molecular weight of the n-alkanes. Many different performance metrics are used to evaluate the predictive performance of intelligent algorithms. Obtained results of the modeling reveal that intelligent computational algorithms have a great ability to mimic the nonlinear relationships between the target variable and its influential variables. The results indicate MPMR as the best predictive model with the highest R-squared value on both training and testing datasets with values of R 2 = 0.992 and R 2 = 0.991, respectively. In addition, MPMR is compared and outperformed empirical correlations.

Improving accuracy of local geoid model using machine learning approaches and residuals of GPS/levelling geoid height

This study aims to use GPS/Levelling data and machine learning techniques (MLs) to model a high precision local geoid for Kuwait. To improve the accuracy of a local geoid the global geopotential model and local terrain effect should be incorporated. The geoid model was improved based on the modelling of geoid residuals using three MLs. Minimax Probability Machine Regression (MPMR), Gaussian Process Regression (GPR), and Multivariate Adaptive Regression Splines (MARS) MLs were developed for modelling the calculated geoid residuals. The results show that the accuracy of the three MLs was improved compared to previous studies, and the accuracy of the GPR model was better than the other models. The standard deviations of Kuwait geoid undulation determined by GPS/Levelling, gravimetric, and developed GPR models were 1.377, 1.375, 1.375 m, respectively. Thus, the developed GPR model has successfully predicted an accurate geoid height of Kuwait with maximum variation approaches ±0.02 m.

Soft computing techniques for the prediction of concrete compressive strength using Non-Destructive tests

This study presents a comparative assessment of conventional soft computing techniques in estimating the compressive strength (CS) of concrete utilizing two non-destructive tests, namely ultrasonic pulse velocity and rebound hammer test. In specific, six conventional soft computing models namely back-propagation neural network (BPNN), relevance vector machine, minimax probability machine regression, genetic programming, Gaussian process regression, and multivariate adaptive regression spline, were used. To construct and validate these models, a total of 629 datasets were collected from the literature. Experimental results show that the BPNN attained the most accurate prediction of concrete CS based on both ultrasonic pulse velocity and rebound number values. The results of the employed MARS and BPNN models are significantly better than those obtained in earlier studies. Thus, these two models are very potential to assist engineers in the design phase of civil engineering projects to estimate the concrete CS with a greater accuracy level.

Predicting concrete compressive strength using hybrid ensembling of surrogate machine learning models

This study aims to implement a hybrid ensemble surrogate machine learning technique in predicting the compressive strength (CS) of concrete, an important parameter used for durability design and service life prediction of concrete structures in civil engineering projects. For this purpose, an experimental database consisting of 1030 records has been compiled from the machine learning repository of the University of California, Irvine. The database was used to train and validate four conventional machine learning (CML) models, namely Artificial Neural Network (ANN), Linear and Non-Linear Multivariate Adaptive Regression Splines (MARS-L and MARS-C), Gaussian Process Regression (GPR), and Minimax Probability Machine Regression (MPMR). Subsequently, the predicted outputs of CML models were combined and trained using ANN to construct the Hybrid Ensemble Model (HENSM). It is observed that the proposed HENSM produces higher predictive accuracy compared to the CML models used in the present study. The predictive performance of all models for CS prediction was compared using the testing dataset and it is found that the HENSM model attained the highest predictive accuracy in both phases. Based on the experimental results, the newly constructed HENSM model is very potential to be a new alternative in handling the overfitting issues of CML models and hence, can be used to predict the concrete CS, including the design of less polluting and more sustainable concrete constructions.

Reliability Analysis of Pile Foundation Using Soft Computing Techniques: A Comparative Study

Uncertainty and variability are inherent to pile design and consequently, there have been considerable researches in quantifying the reliability or probability of failure of structures. This paper aims at examining and comparing the applicability and adaptability of Minimax Probability Machine Regression (MPMR), Emotional Neural Network (ENN), Group Method of Data Handling (GMDH), and Adaptive Neuro-Fuzzy Inference System (ANFIS) in the reliability analysis of pile embedded in cohesionless soil and proposes an AI-based prediction method for bearing capacity of pile foundation. To ascertain the homogeneity and distribution of the datasets, Mann–Whitney U (M–W) and Anderson–Darling (AD) tests are carried out, respectively. The performance of the developed soft computing models is ascertained using various statistical parameters. A comparative study is implemented among reliability indices of the proposed models by employing First Order Second Moment Method (FOSM). The results of FOSM showed that the ANFIS approach outperformed other models for reliability analysis of bearing capacity of pile and ENN is the worst performing model. The value of R2 for all the developed models is close to 1. The best RMSE value is achieved for the training phase of the ANFIS model (0 in training and 2.13 in testing) and the poorest for the ENN (2.03 in training and 31.24 in testing) model. Based on the experimental results of reliability indices, the developed ANFIS model is found to be very close to that computed from the original data.

Determination of reliability index of cantilever retaining wall by RVM, MPMR and MARS

Overturning criterion is an important parameter for designing cantilever retaining wall. This study adopts relevance vector machine (RVM) based first order second method (FOSM), minimax probability machine regression (MPMR) based FOSM and multivariate adaptive regression spline (MARS) based FOSM for determination of reliability index of cantilever retaining wall based on overturning criterion. RVM, MPMR and MARS have been used to overcome the limitations of the FOSM method. An example is illustrated how the proposed RVM based FOSM, MPMR based FOSM and MARS based FOSM analysis can be carried out. A comparative study has been carried out between the developed techniques. The results demonstrate that the developed techniques have ability to overcome the limitations of FOSM. This article describes new methods based on RVM, MPMR and MARS for determination of reliability index of retaining wall. The adopted methods eliminate the limitation of FOSM.

Predicting longitudinal dispersion coefficient in natural streams using minimax probability machine regression and multivariate adaptive regression spline

This article employs minimax probability machine regression (MPMR) and multivariate adaptive regression spline (MARS) for prediction of longitudinal dispersion coefficient in natural streams. The variables of hydraulic features such as channel width (B), flow depth (H), flow velocity (U), shear velocity (u*) and geometric features such as channel sinuosity (σ) and channel shape parameter (β) were taken as the input. The dispersion coefficient Kx was the decision parameter for the proposed machine learning models. MARS does not assume any functional relationship between inputs and output. The MARS model is a non-parametric regression model that splits the data and fits each interval into a basis function. MPMR is a probabilistic model which maximises the minimum probability of predicted output. MPMR also provides output within some bound of the true regression function. The proposed study gives an equation for prediction of longitudinal dispersion coefficient based on the developed MARS. The developed MARS has been compared with proposed MPMR. Finally, the performances of the models have been measured by different performance metrics.

Predicting longitudinal dispersion coefficient in natural streams using minimax probability machine regression and multivariate adaptive regression spline

This article employs minimax probability machine regression (MPMR) and multivariate adaptive regression spline (MARS) for prediction of longitudinal dispersion coefficient in natural streams. The variables of hydraulic features such as channel width (B), flow depth (H), flow velocity (U), shear velocity (u*) and geometric features such as channel sinuosity (σ) and channel shape parameter (β) were taken as the input. The dispersion coefficient Kx was the decision parameter for the proposed machine learning models. MARS does not assume any functional relationship between inputs and output. The MARS model is a non-parametric regression model that splits the data and fits each interval into a basis function. MPMR is a probabilistic model which maximises the minimum probability of predicted output. MPMR also provides output within some bound of the true regression function. The proposed study gives an equation for prediction of longitudinal dispersion coefficient based on the developed MARS. The developed MARS has been compared with proposed MPMR. Finally, the performances of the models have been measured by different performance metrics.

Prediction of Young’s modulus of weathered igneous rocks using GRNN, RVM, and MPMR models with a new index

Young’s modulus (YM) of intact rock is an important parameter in the assessment of engineering behaviours of rock masses, and it cannot always be obtained in an economical and practical manner in laboratory experiments. The main purpose of this study is to examine the capability of the minimax probability machine regression (MPMR), relevance vector machine (RVM), and generalised regression neural network (GRNN) models for the prediction of YM. The other aim is to determine the usefulness of a new index, the n-durability index (ndrb), which is based on porosity and the slake durability index. According to the regression analysis performed in this study, the n-durability index as an explanatory parameter performs better than the P-wave velocity (Vp), porosity, and slake durability index in the models, considering the results herein as well as the existing literature. According to regression error characteristic curves, Taylor diagrams, and performance indices, the best prediction model is MPMR, while the worst is the GRNN model. Although GRNN is the worst of the soft computing models, its performance is slightly better than that of the multiple linear regression (MLR) model. According to the results of the study, the MPMR and RVM models with ndrb and Vp are successful tools that can predict the YM of igneous rock materials to different degrees.

Reliability Analysis of Circular Footing by Using GP and MPMR

Circular footings are designed to bear a load of super structures. Studies have been done on the influence of soil properties on bearing capacity of shallow foundations. The use of circular foundation is practical in geotechnical engineering. During the design of circular footing, bearing capacity of soil is taken into consideration, and cohesion (c), unit weight (γ), and angle of internal friction (ϕ) are the most variable parameters. Reliability analysis is used frequently for the design of circular footing. Most of the authors have used first order second moment methods (FOSM). However, FOSM is a time-consuming method. Drawbacks of FOSM have been overcome by genetic programming (GP), minimax probability machine regression (MPMR). This article gives a distinct analysis between the developed MPMR based FOSM and GP-based FOSM.

Estimating Slump Flow and Compressive Strength of Self-Compacting Concrete Using Emotional Neural Networks

The characteristics of fresh and hardened self-compacting concrete (SCC) are an essential requirement for construction projects. Moreover, the sensitivity of admixture contents of SCC in these properties is highly impacted by that cost. The current study investigates to estimate the slump-flow (S) and compressive strength (CS), as fresh and hardened properties of SCC, respectively. Four developed soft-computing approaches were proposed and compared, including the group method of data handling (GMDH), Minimax Probability Machine Regression (MPMR), emotional neural network (ENN), and hybrid artificial neural network-particle swarm optimization (ANN-PSO), to estimate the S and 28-day CS of SCC, which comprises fly ash (FA), silica fume (SF), and limestone powder (LP) as part of cement by mass in total powder content. In addition, the impact of eight admixture components is investigated and evaluated to assess the sensitivity of admixture contents for the modelling of S and CS of SCC. The results demonstrate that the performance prediction of ENN model is more significant than other models in estimating S and CS characteristics of SCC. The overall of Pearson correlation coefficient, r, and root mean square error (RMSE) of ENN model are 97.80% and 20.16 mm, respectively, for the S. These are 96.07% and 2.59 MPa, respectively, for the CS. Furthermore, the sensitivity of the powder content of fly ash is shown to have a high impact on the estimated S and CS values of SCC.

Newly explored machine learning model for river flow time series forecasting at Mary River, Australia.

Hourly river flow pattern monitoring and simulation is the indispensable precautionary task for river engineering sustainability, water resource management, flood risk mitigation, and impact reduction. Reliable river flow forecasting is highly emphasized to support major decision-makers. This research paper adopts a new implementation approach for the application of a river flow prediction model for hourly prediction of the flow of Mary River in Australia; a novel data-intelligent model called emotional neural network (ENN) was used for this purpose. A historical dataset measured over a 4-year period (2011-2014) at hourly timescale was used in building the ENN-based predictive model. The results of the ENN model were validated against the existing approaches such as the minimax probability machine regression (MPMR), relevance vector machine (RVM), and multivariate adaptive regression splines (MARS) models. The developed models are evaluated against each other for validation purposes. Various numerical and graphical performance evaluators are conducted to assess the predictability of the proposed ENN and the competitive benchmark models. The ENN model, used as an objective simulation tool, revealed an outstanding performance when applied for hourly river flow prediction in comparison with the other benchmark models. However, the order of the model, performance wise, is ENN > MARS > RVM > MPMR. In general, the present results of the proposed ENN model reveal a promising modeling strategy for the hourly simulation of river flow, and such a model can be explored further for its ability to contribute to the state-of-the-art of river engineering and water resources monitoring and future prediction at near real-time forecast horizons.