Traditional Support Vector Regression Research Articles

Research on Sustainable Form Design of NEV Vehicle Based on Particle Swarm Algorithm Optimized Support Vector Regression

With the growing emphasis on eco-friendly and sustainable development concepts, new energy vehicles (NEVs) have emerged as a popular alternative to traditional fuel vehicles (FVs). Due to the absence of an internal combustion engine, electric vehicles (EVs) do not require a front air intake grille, allowing for a more minimalist and flexible design. Consequently, aligning EV styling with users’ visual cognition and emotional perception is a critical objective for automakers and designers. In this study, we establish the mapping relationship between users’ emotional cognition and NEV styling design based on experimental data. We introduce Particle Swarm Optimization Support Vector Regression (PSO-SVR) into the perceptual engineering (KE) research process to predict user emotions using Support Vector Regression (SVR). To optimize the three hyperparameters (penalty coefficient C, RBF kernel function parameter γ, and insensitivity loss coefficient ε) of the SVR model, we utilize the Particle Swarm Optimization (PSO) algorithm. The results indicate that the proposed PSO-SVR model outperforms traditional SVR and BPNN models in predicting NEV user emotions. This model effectively captures the nonlinear relationship between battery electric vehicle (BEV) morphological features and users’ emotional cognition, providing a novel method for enhancing NEV design. The results of this research are expected to drive design innovation and technological advancement in the new energy vehicle industry, contributing to the achievement of the ambitious goal of global eco-friendliness and sustainable development.

Research on the Development Height Prediction Model of Water-Conduction Fracture Zones under Conditions of Extremely Thin Coal Seam Mining

Addressing the difficult problem of predicting the height of water-conducting fracture zones in shallow and thin coal seams, a prediction model of water-conduction fracture zones based on a backpropagation (BP) neural network was developed by integrating theoretical analysis, field measurements, and algorithmic advancements. Firstly, through overburden migration analysis and correlation tests, the height index system of the water-conducting fracture zone was determined. This system includes mining height, buried depth, dip angle, working face width, and overburden rock lithology, with five groups of characteristic parameters. Then, 35 pairs of minefield-measured data were collected to establish the measured height data set of the water-conducting fracture zone. Secondly, a BP neural network prediction model and a traditional support vector regression (SVR) prediction model were constructed based on a Pytorch framework, and the models were trained and tested by selecting data sets. Thirdly, the optimal prediction model was determined by comparing the model with the empirical model and multiple regression model of mining regulations for coal pillar maintenance and pressure in buildings, water bodies, railways, and main shafts. Finally, a typical mine was selected for application to verify the suitability of the optimal model. The results show that: (1) the predicted value of the neural network model is consistent with the change trend of the measured value, which accords with the theoretical law; (2) compared with traditional forecasting methods, the error of the BP neural network prediction model is stable and the prediction effect is the best; (3) dropout can effectively mitigate mitigation training overfitting, achieve regularization, and improve prediction accuracy; (4) the field application further verified that the BP neural network model is the best for predicting the height of water-conducting fracture zones of extremely thin coal seams, and the research results can provide technical guidance for similar fragile coal seams.

A Novel Bézier LSTM Model: A Case Study in Corn Analysis

Accurate prediction of agricultural product prices is instrumental in providing rational guidance for agricultural production planning and the development of the agricultural industry. By constructing an end-to-end agricultural product price prediction model, incorporating a segmented Bézier curve fitting algorithm and Long Short-Term Memory (LSTM) network, this study selects corn futures prices listed on the Dalian Commodity Exchange as the research subject to predict and validate their price trends. Firstly, corn futures prices are fitted using segmented Bézier curves. Subsequently, the fitted price sequence is employed as a feature and input into an LSTM network for training to obtain a price prediction model. Finally, the prediction results of the Bézier curve-based LSTM model are compared and analyzed with traditional LSTM, ARIMA (Autoregressive Integrated Moving Average Model), VMD-LSTM, and SVR (Support Vector Regression) models. The research findings indicate that the proposed Bézier curve-based LSTM model demonstrates significant predictive advantages in corn futures price prediction. Through comparison with traditional models, the effectiveness of this model is affirmed. Consequently, the Bézier curve-based LSTM model proposed in this paper can serve as a crucial reference for agricultural product price prediction, providing effective guidance for agricultural production planning and industry development.

Bidirectional machine learning-assisted sensitivity-based stochastic searching approach for groundwater DNAPL source characterization.

In this study, we designed a machine learning-based parallel global searching method using the Bayesian inversion framework for efficient identification of dense non-aqueous phase liquid (DNAPL) source characteristics and contaminant transport parameters in groundwater. Swarm intelligence organized hybrid-kernel extreme learning machine (SIO-HKELM) was proposed to approximate the forward and inverse input-output correlation with a high accuracy using the DNAPL transport numerical simulation model. An adaptive inverse-HKELM was established for preliminary estimation of the source characteristics and contaminant transport parameters to correct prior information and generate high-quality initial starting points of parallel searching. A local accurate forward-HKELM surrogate of the numerical model was embedded in the searching system for avoiding repetitive CPU-demanding likelihood evaluations. A sensitivity-based Metropolis criterion (MC), incorporating the dynamic particle swarm optimization (SD-PSO) algorithm, was developed for improving the search ergodicity and realizing precise inversion of all the unknown variables with drastic variations in sensitivity to the likelihood function. Results showed that the generalization capability and robustness of SIO-HKELM were superior to those of the traditional machine learning methods, including KELM and support vector regression (SVR), and it sufficiently approximated the forward and inverse input-output mapping of the numerical model with testing determination coefficients of 0.9944 and 0.6440, respectively. With high-quality prior information and initial starting points generated by the adaptive inverse-HKELM feed approach, the uncertainty in the inversion outputs was reduced, and the searching process rapidly converged to reasonable posterior distributions in around 60 iterations. Compared with the widely used multichain Markov chain Monte Carlo (MCMC) approach, the parallel searching lines generated by SD-PSO-MC adequately covered the searching space, and the "equifinality" effect was more effectively restrained by reducing the relative errors of all the point estimations to less than 8%. Therefore, the real source information reflected by the statistical characteristics of the SD-PSO-MC inversion outputs was more precise than that obtained using the multichain MCMC approach.

Design and optimization of haze prediction model based on particle swarm optimization algorithm and graphics processor

With the rapid expansion of industrialization and urbanization, fine Particulate Matter (PM2.5) pollution has escalated into a major global environmental crisis. This pollution severely affects human health and ecosystem stability. Accurately predicting PM2.5 levels is essential. However, air quality forecasting currently faces challenges in processing vast data and enhancing model accuracy. Deep learning models are widely applied for their superior learning and fitting abilities in haze prediction. Yet, they are limited by optimization challenges, long training periods, high data quality needs, and a tendency towards overfitting. Furthermore, the complex internal structures and mechanisms of these models complicate the understanding of haze formation. In contrast, traditional Support Vector Regression (SVR) methods perform well with complex non-linear data but struggle with increased data volumes. To address this, we developed CUDA-based code to optimize SVR algorithm efficiency. We also combined SVR with Genetic Algorithms (GA), Sparrow Search Algorithm (SSA), and Particle Swarm Optimization (PSO) to identify the optimal haze prediction model. Our results demonstrate that the model combining intelligent algorithms with Central Processing Unit-raphics Processing Unit (CPU-GPU) heterogeneous parallel computing significantly outpaces the PSO-SVR model in training speed. It achieves a computation time that is 6.21–35.34 times faster. Compared to other models, the Particle Swarm Optimization-Central Processing Unit-Graphics Processing Unit-Support Vector Regression (PSO-CPU-GPU-SVR) model stands out in haze prediction, offering substantial speed improvements and enhanced stability and reliability while maintaining high accuracy. This breakthrough not only advances the efficiency and accuracy of haze prediction but also provides valuable insights for real-time air quality monitoring and decision-making.

Efficient Optimization of a Support Vector Regression Model with Natural Logarithm of the Hyperbolic Cosine Loss Function for Broader Noise Distribution

While traditional support vector regression (SVR) models rely on loss functions tailored to specific noise distributions, this research explores an alternative approach: ε-ln SVR, which uses a loss function based on the natural logarithm of the hyperbolic cosine function (lncosh). This function exhibits optimality for a broader family of noise distributions known as power-raised hyperbolic secants (PHSs). We derive the dual formulation of the ε-ln SVR model, which reveals a nonsmooth, nonlinear convex optimization problem. To efficiently overcome these complexities, we propose a novel sequential minimal optimization (SMO)-like algorithm with an innovative working set selection (WSS) procedure. This procedure exploits second-order (SO)-like information by minimizing an upper bound on the second-order Taylor polynomial approximation of consecutive loss function values. Experimental results on benchmark datasets demonstrate the effectiveness of both the ε-ln SVR model with its lncosh loss and the proposed SMO-like algorithm with its computationally efficient WSS procedure. This study provides a promising tool for scenarios with different noise distributions, extending beyond the commonly assumed Gaussian to the broader PHS family.

Research on Wind Power Prediction Model Based on Random Forest and SVR

Wind power generation is random and easily affected by external factors. In order to construct an effective prediction model based on wind power generation, a wind power prediction model based on principal component analysis (PCA) noise reduction, feature selection based on random forest model and support vector regression (SVR) algorithm is proposed. First, in the data preprocessing stage, PCA is used for sample data denoising; then the random forest model is used to calculate the importance evaluation value of each feature to optimize the selection of feature parameters; finally, The SVR algorithm is applied for training and prediction. Experiments show that the prediction effect of the model based on random forest and SVR is excellent, the root mean square error(RMSE) is 0.086, the average absolute percentage error(MAPE) is 23.47%, and the coefficient of determination(R2) is 0.991. Compared with the traditional SVR model, the root mean square error of the method proposed in this paper is reduced by 95.9%, and the prediction accuracy and the fit of the prediction curve are significantly improved.

Improving Electric Vehicle Structural-Borne Noise Based on Convolutional Neural Network-Support Vector Regression

In order to enhance the predictive accuracy and control capabilities pertaining to low- and medium-frequency road noise in automotive contexts, this study introduces a methodology for Structural-borne Road Noise (SRN) prediction and optimization. This approach relies on a multi-level target decomposition and a hybrid model combining Convolutional Neural Network (CNN) and Support Vector Regression (SVR). Initially, a multi-level target analysis method is proposed, grounded in the hierarchical decomposition of vehicle road noise along the chassis parts, delineated layer by layer, in accordance with the vibration transmission path. Subsequently, the CNN–SVR hybrid model, predicated on the multi-level target framework, is proposed. Notably, the hybrid model exhibits a superior predictive accuracy exceeding 0.97, surpassing both traditional CNN and SVR models. Finally, the method and model are deployed for sensitivity analysis of chassis parameters in relation to road noise, as well as for the prediction and optimization analysis of SRN in vehicles. The outcomes underscore the high sensitivity of parameters such as the dynamic stiffness of the rear axle bushing and the large front swing arm bushing influencing SRN. The optimization results, facilitated by the CNN–SVR hybrid model, align closely with the measured outcomes, displaying a negligible relative error of 0.82%. Furthermore, the measured results indicate a noteworthy enhancement of 4.07% in the driver’s right-ear Sound Pressure Level (SPL) following the proposed improvements compared to the original state.

A method based on improved ant colony algorithm feature selection combined with GWO-SVR model for predicting chlorophyll-a concentration in Wuliangsu Lake.

Chlorophyll-a (Chl-a) is an important parameter in water bodies. Due to the complexity of optics in water bodies, it is difficult to accurately predict Chl-a concentrations in water bodies by current traditional methods. In this paper, using Sentinel-2 remote sensing images as the data source combined with measured data, taking Wuliangsu Lake as the study area, a new intelligent algorithm is proposed for prediction of Chl-a concentration, which uses the adaptive ant colony exhaustive optimization algorithm (A-ACEO) for feature selection and the gray wolf optimization algorithm (GWO) to optimize support vector regression (SVR) to achieve Chl-a concentration prediction. The ant colony optimization algorithm is improved to select remote sensing feature bands for Chl-a concentration by introducing relevant optimization strategies. The GWO-SVR model is built by optimizing SVR using GWO with the selected feature bands as input and comparing it with the traditional SVR model. The results show that the usage of feature bands selected by the presented A-ACEO algorithm as inputs can effectively reduce complexity and improve the prediction performance of the model, under the condition of the same model, which can provide valuable references for monitoring the Chl-a concentration in Wuliangsu Lake.

Comparison of ethane recovery processes for lean gas based on a coupled model

Ethane recovery from natural gas is crucial for improving the economic efficiency of enterprises, saving energy and reducing emissions. This study analyses the characteristics of process parameters based on three lean gas ethane recovery processes. A prediction and multiobjective optimization model for ethane recovery and system energy consumption is established. Based on this framework, a new method for ethane recovery process comparison for lean gas is proposed. In the process analysis, two additional coolers are added to the cold residue recycling process to improve ethane recovery. Seven main process parameters are determined based on the three processes. According to the prediction results, support vector regression is the most effective model among the individual models. The prediction accuracy of the support vector regression model based on grey wolf optimization is the highest. Compared with traditional support vector regression, this approach yields average reductions in the mean absolute error, mean absolute percentage error and root mean square error of 63.95%, 64.21% and 47.98%, respectively, reflecting significantly improved prediction accuracy and stability. The multiobjective multiverse optimization algorithm displays the best optimization performance and the highest solution diversity among the optimization results. Additionally, it yields high-quality solutions at the shortest run time. Based on the optimization results, the supplemental rectification with compression process yields the lowest system energy consumption of any method considered and meets the ethane recovery requirements real projects.

Estimation of Lithium-Ion Battery State of Charge Based on Genetic Algorithm Support Vector Regression under Multiple Temperatures

In the energy crisis and post-epidemic era, the new energy industry is thriving, encompassing new energy vehicles exclusively powered by lithium-ion batteries. Within the battery management system of these new energy vehicles, the state of charge (SOC) estimation plays a pivotal role. The SOC represents the current state of charge of the lithium-ion battery. This paper proposes a joint estimation algorithm based on genetic algorithm (GA) simulating biogenetic properties and support vector regression (SVR) to improve the prediction accuracy of lithium-ion battery SOC. Genetic algorithm support vector regression (GASVR) is proposed to address the limitations of traditional SVR, which lacks guidance on parameter selection. The model attains notable accuracy. GASVR constructs a set of solution spaces, generating initial populations that adhere to a normal distribution using a stochastic approach. A fitness function calculates the fitness value for each individual. Based on their fitness, the roulette wheel method is employed to generate the next-generation population through selection, crossover, and mutation. After several iterations, individuals with the highest fitness values are identified. These top individuals acquire parameter information, culminating in the training of the final SVR model. The model leverages advanced mathematical techniques to address SOC prediction challenges in the Hilbert space, providing theoretical justification for handling intricate nonlinear problems. Rigorous testing of the model at temperatures ranging from −20 ∘C to 25 ∘C under three different working conditions demonstrates its superior accuracy and robustness compared to extreme gradient boosting (XGBoost), random forest regression (RFR), linear kernel function SVR, and the original radial basis kernel function SVR. The model proposed in this paper lays the groundwork and offers a scheme for predicting the SOC within the battery management system of new energy vehicles.

Forecasting DO of the river-type reservoirs using input variable selection and machine learning techniques - taking Shuikou reservoir in the Minjiang River as an example

Dissolved oxygen (DO) plays a significant role in maintaining the health of aquatic ecosystems. In this study, we propose a model that incorporates multiple machine learning methods for predicting DO. Firstly, the maximum information coefficient (MIC) was utilized to identify the key drivers of DO. Afterward, the particle swarm optimization (PSO) algorithm was used to enhance the traditional support vector regression (SVR) model, optimizing the penalty factor (c) and the width of the Gaussian kernel function (g). This resulted in the development of a MIC-PSO-SVR-based DO prediction model. As a case study, we analyzed three points (G1, G2, and Z1) located in the mainstem and tributaries of the Shuikou Reservoir in Fujian, China. The original dataset, encompassing various time scales and sample sizes, underwent reclassification. Key factors influencing DO were determined by calculating the MIC values between DO and each monitoring factor. The main findings of this study are as follows: (1) By assessing the correlation between candidate factors and DO, the MIC effectively eliminated irrelevant variables with low correlation, thereby reducing the dataset size. Furthermore, it was observed that the fluctuations in MIC values for each variable stabilized when the sample size exceeded 4000. (2) The model’s performance exhibited improvement with the reduced dataset. For instance, the mean absolute error (MAE) and root mean square error (RMSE) of the hybrid MIC-PSO-SVR model decreased by approximately 66% and 49%, respectively, whereas the R2 and Nash-Sutcliffe efficiency (NSE) are as high as 0.98 and 0.95, showing superior performance compared to the unreduced PSO-SVR model. (3) More importantly, the model successfully predicted sudden hypoxia events in the Shuikou reservoir area from October 11 to November 8, 2021. Additionally, the MIC-PSO-SVR model accurately captured DO changes in the point G2 in front of the Shuikou dam during a hypoxic event in the Shuikou reservoir. The prediction errors during hypoxia were as low as 0.23 mg·L-1 and 0.31 mg·L-1 for 1 h and 24 h, respectively.

Analysis and prediction of microbial fuel cell behaviour using MLP and SVR

BackgroundMicrobial fuel cell (MFC) is a device for simultaneous wastewater treatment and clean energy production. In this study, different amounts of yeast extract (1, 2, 3, 4, or 5 g/L) were varied and the MFC performance was measured in terms of power generation, COD removal and coulombic efficiency. MethodsThe first part of this study examined a dual chamber MFC with varying volumes of yeast extract for power output, COD removal, and coulombic efficiency. Soft computing approaches were utilized in the second part of the study to estimate MFC performance, and multilayer perceptron (MLP) with varied numbers of hidden layers was used to improve model accuracy. The method was next implemented in MATLAB software using 70% and 30% of the dataset for training and testing purposes of the system, which was validated with the traditional support vector regression (SVR) estimation method. FindingsThe experimental results have shown that the MFC4 (4 g/L yeast extract) had the highest catalytic activity and produced the maximum power (308 mW/m2). Comparing the experimental results and soft computing model proved that MFC behavior can be predicted 5.1819 times more accurately using MLP compared with traditional SVR.

Wavelet Support Vector Censored Regression

Learning methods in survival analysis have the ability to handle censored observations. The Cox model is a predictive prevalent statistical technique for survival analysis, but its use rests on the strong assumption of hazard proportionality, which can be challenging to verify, particularly when working with non-linearity and high-dimensional data. Therefore, it may be necessary to consider a more flexible and generalizable approach, such as support vector machines. This paper aims to propose a new method, namely wavelet support vector censored regression, and compare the Cox model with traditional support vector regression and traditional support vector regression for censored data models, survival models based on support vector machines. In addition, to evaluate the effectiveness of different kernel functions in the support vector censored regression approach to survival data, we conducted a series of simulations with varying number of observations and ratios of censored data. Based on the simulation results, we found that the wavelet support vector censored regression outperformed the other methods in terms of the C-index. The evaluation was performed on simulations, survival benchmarking datasets and in a biomedical real application.

Prediction method of pipe joint opening-closing deformation of immersed tunnel based on singular spectrum analysis and SSA-SVR

In order to predict the joint opening-closing deformation of immersed tunnel in operation, a comprehensive prediction model combining time series decomposition, least square method, sparrow search algorithm (SSA) and support vector regression (SVR) is proposed, which is verified by the monitoring data of E13-E14 and E17-E18 joints opening-closing deformation of immersed tunnel in Hong Kong-Zhuhai-Macao Bridge. Firstly, on the basis of summarizing and analyzing the characteristics of joint opening-closing deformation, the monitoring sequence of joint opening-closing is decomposed into trend component, periodic component and residual component by using time series decomposition singular spectrum analysis method, which clearly shows the composition of each component. Secondly, the least square method is used to fit and predict the trend component; Combining the commonly used RBF kernel function, Sigmoid kernel function and Ploy kernel function with SVR respectively, the SSA algorithm is used to globally optimize the penalty factors and kernel function parameters of the three models, and the optimized three coupling models are used to predict the periodic component and residual component. The results show that the prediction effect of the SVR model optimized by SSA algorithm is better than that of the traditional SVR model, The prediction result of SSA-SVR model constructed by RBF kernel function is the best. Finally, the time series addition model is applied to superimpose the optimal predicted values to obtain the predicted opening-closing amount. The mean square errors of the total predicted values of the opening-closing amount of the two joints are 0.1900mm and 0.2291mm respectively, the average errors are 0.1587mm and 0.2156mm respectively, and the correlation coefficients are 0.9792 and 0.9695 respectively. A satisfactory prediction effect is obtained, which proves the reliability and accuracy of this method, and provides a new way for the prediction of the opening-closing deformation of the pipe joint of immersed tunnel during the operation period.

Capillary water absorption values estimation of building stones by ensembled and hybrid SVR models

The absorption of capillary water is one of the most crucial factors in the flow of groundwater in rocks (CWA). Although meticulous experimental studies are needed to determine a rock’s CWA, predictive techniques might cut down on the expense and effort. There are various data mining methods for this purpose, but the considered algorithms in this study were not proposed so far for predicting the CWA. Different rock samples were taken for this purpose from various locations, yielding diverse rocks. For the prediction procedures, four support vector regression (SVR) models were created: a traditional SVR, two ensembled models, and a hybrid SVR model using the whale optimization technique (WOA - SVR). Results show that all models have acceptable performance in predicting the CWA with R2 larger than 0.797 and 0.806 for the training and testing data, respectively, representing the acceptable correlation between observed and predicted values. Regarding developed models, the conventional SVR model has the worst performance of all models. All statistical evaluation criteria were improved by assembling models, which present the ability of additive regression and bagging predictions in improving prediction processes. The hybrid WOA - SVR model has the best performance considering all indices. This hybrid model could also gain the lowest values of error indices between all SVR models, which leads to outperforming the WOA - SVR model compared to other methods.

Just-In-Time Learning Based Functional Spectral Data Modeling for In-Situ Measurement of Slurry Component Concentrations via Infrared Spectroscopy

For using the infrared spectroscopy to conduct in-situ measurement of slurry component concentrations during batch crystallization or fermentation process in engineering practice, a novel just-in-time learning (JITL) based functional modelling method is proposed for spectral data analysis in this paper to improve on-line measurement accuracy, by addressing engineering issues of very limited assay samples, spectral absorption nonlinearity and high-dimensional spectral variables. The traditional univariate or multivariate partial least-squares (PLS) model is subtly extended to the corresponding functional form for describing the relationship between the measured spectra and slurry component concentrations, such that the salient problem of only a small number of slurry component concentration samples available in practice for spectral data modeling could be effectively solved. The wavelet functions are adopted to properly approximate the measured spectral curves owing to their multi-scale and orthogonal properties. Accordingly, a functional spectral data model is established by wavelet functional PLS for on-line measurement of single and multiple component concentrations, respectively. Meanwhile, a JITL strategy is introduced to select the most representative samples for such modeling, which could efficiently handle the disparity issue involved with real-time samples and guarantee the model validity. Experimental results show that root mean square error of model prediction on the solution concentration during L-glutamic acid cooling crystallization process and multiple componts of ethanol fermentation process, could be evidently reduced over 40% and 50%, respectively, compared with the traditional PLS and support vector regression methods.

Support vector regression-bald eagle search optimizer-based hybrid approach for short-term wind power forecasting

AbstractWind power forecasting deals with the prediction of the expected generation of wind farms in the next few minutes, hours, or days. The application of machine learning techniques in wind power forecasting has become of great interest due to their superior capability to perform regression, classification, and clustering. Support vector regression (SVR) is a powerful and suitable forecasting tool that has been successfully used for wind power forecasting. However, the performance of the SVR model is extremely dependent on the optimal selection of its hyper-parameters. In this paper, a novel forecast model based on hybrid SVR and bald eagle search (BES) is proposed for short-term wind power forecasting. In the proposed model, the BES algorithm, which is characterized by a few adjustable parameters, a simplified search mechanism, and accurate results, is used to enhance the accuracy of the forecasted output by optimizing the hyper-parameters of the SVR model. To evaluate the performance of the developed wind power forecaster, a case study has been conducted on real wind power data from Sotavento Galicia in Spain. The developed model is compared to other forecasting techniques such as decision tree (DT), random forest (RF), traditional SVR, hybrid SVR, and gray wolf optimization algorithm (SVR–GWO) and hybrid SVR and manta ray foraging optimizer (SVR–MRFO). Obtained results uncovered that the proposed hybrid SVR−BES is more accurate than other methods.

Uncertain support vector regression with imprecise observations

Traditional support vector regression dedicates to obtaining a regression function through a tube, which contains as many as precise observations. However, the data sometimes cannot be imprecisely observed, which implies that traditional support vector regression is not applicable. Motivated by this, in this paper, we employ uncertain variables to describe imprecise observations and build an optimization model, i.e., the uncertain support vector regression model. We further derive the crisp equivalent form of the model when inverse uncertainty distributions are known. Finally, we illustrate the application of the model by numerical examples.

Hybrid machine learning model and Shapley additive explanations for compressive strength of sustainable concrete

The application of the traditional support vector regression (SVR) model to predict the compressive strength of concrete faces the challenge of parameter tuning. To this end, a hybrid machine learning model combines the SVR model and grid search (GS) optimization algorithm, namely the GS-SVR model was proposed and employed on 559 datasets with eight input variables to achieve the compressive strength prediction of sustainable concrete. Moreover, the prediction performance was compared with the original SVR model. Results showed that the GS-SVR model outperformed the original SVR with R2 = 0.93, R2 = 0.85, MAE = 3.52, MAE = 5.22, and RMSE = 4.89, RMSE = 7.01, respectively. The model proposed can be recommended as a reliable and accurate compressive strength prediction tool to assist or partially replace laboratory compression tests to save cost and time. Additionally, the Shapley additive explanation (SHAP) method was used to explain the importance and contribution of the input variables that influence the compressive strength.