Least Squares Support Vector Regression Model Research Articles

Rapid prediction of multiple wine quality parameters using infrared spectroscopy coupling with chemometric methods

Infrared spectroscopy (IRs) coupling with chemometric methods were used to predict principal quality parameters in wine. A new strategy of variable (wavelength) selection named as Fisher Discriminant-Variable Selection (FD-VS) model was constructed. Characteristic variables were selected from Infrared spectra based on the absolute values of eigenvector obtained by Fisher Discriminant Function. The FD-VS method was combined with quantitative models including Principal Component Regression (PCR), Partial Least Squares (PLS) and Least Squares Support Vector Regression (LSSVR), which were utilized for prediction of multiple principal quality parameters of red wine. It is shown that FD-VS method obviously improves the performances of PCR, PLS and LSSVR models. Then four variable selection methods based on PLS regression including Competitive Adaptive Reweighted Sampling (CARS)-PLS, Uninformative Variable Elimination (UVE)-PLS, Interval Partial Least Squares (IPLS) and Moving Windows Partial Least Squares (MWPLS) were also compared. The results also show good performance of FD-VS-LSSVR in terms of prediction accuracy or robustness. Therefore, the FD-VS method provides an effective and credible variable selection way for IR spectrum to predict quality parameters of wine.

Using the Least Squares Support Vector Regression to Forecast Movie Sales with Data from Twitter and Movie Databases

Due to the rapid prominence and popularity of social media, social broadcasting networks with voluntary information sharing have become one of the most powerful ways to spread word-of-mouth opinions, and thus, have influence on consumers’ preferences toward products. Therefore, sentiment analysis data from social media have become more important in forecasting product sales. For the movie industry, the opinions expressed on social media have increasing impacts on movie sales. In addition, some databases, such as the Box Office Mojo and Internet Movie Database (IMDb), contain structured data for predicting movie sales. Thus, three categories of data—data of movie databases, data of tweets, and hybrid data including movies databases and tweets—are employed symmetrically in this study. The aim of this study is to employ the least squares support vector regression (LSSVR) to forecast movie sales worldwide according to these three forms of data. In addition, three other forecasting techniques—namely, the back propagation neural network (BPNN), the generalized regression neural network (GRNN), and the multivariate linear regression (MLR) model—were used to forecast movie sales with the three types of data. The empirical results show that the LSSVR model with hybrid data can obtain more accurate results than the other forecasting models with all data types. Thus, forecasting movie sales using the LSSSVR model with data containing movie databases and tweets is a feasible and prospective method to forecast movie sales.

Hybrid machine learning for predicting strength of sustainable concrete

Foamed concrete material is a sustainable material which is widely used in the construction industry due to their sustainability. Accurate prediction of their compressive strength is vital for structural design. However, empirical methods are limited to consider simultaneously all influencing factors in predicting the compressive strength of foamed concrete materials. Thus, this study proposed a novel hybrid artificial intelligence (AI) model which couples the least squares support vector regression (LSSVR) with the grey wolf optimization (GWO) to consider effectively the influencing factors and improve the predictive accuracy in predicting the foamed concrete’s compressive strength. Performance of the proposed model was evaluated using a real-world dataset. Comparison results confirm that the proposed GWO–LSSVR model was superior than the support vector regression, artificial neural networks, random forest, and M5Rules with the improvement rate of 144.2–284.0% in mean absolute percentage error (MAPE). Notably, the evaluation results show that the GWO–LSSVR model showed the good agreement between the actual and predicted values with the correlation coefficient of 0.991 and MAPE of 3.54%. Thus, the proposed AI model was suggested as an effective tool for designing foamed concrete materials.

Comparative assessment on smart pre-processing methods for extracting information in FT-NIR measured data

Fourier transform near infrared (FT-NIR) spectroscopy is a rapid and straightforward technology to analyse soil properties. However, FT-NIR measurement of soil is always accompanied with latent noises coming from masking and overlaps because of systematic bias and manual errors. Several pre-processing methods were investigated as smart pre-modelling modes for extracting data information and getting rid of the noises. Using least squares support vector regression (LSSVR), the FT-NIR calibration models were established for predicting target nutrients (nitrogen, phosphorus and potassium). With the combined investigation on noise-sensing pre-processing methods, the LSSVR models were automatically optimized by tuning its kernel parameters. Results show that the pre-processing methods were optimized in smart ways of polynomial modifications or function derivatives on quasi-continuous data. The effective pre-processing methods for the three target nutrients were originated from optical path length estimation and correction (OPLEC) and Whittaker smoother (WTK), switched to modification of the regulation polynomials and 1st- or 2nd- order derivatives, respectively. Thus we concluded that the modified OPLEC and the derivative WTK had strong potentials to replace the traditional pre-processing methods in FT-NIR analysis of soil nutrients.

Online Multiple Outputs Least-Squares Support Vector Regression Model of Ship Trajectory Prediction Based on Automatic Information System Data and Selection Mechanism

Existing maritime trajectory prediction models are faced with problems of low accuracy and inability to predict ship tracks in real time. To solve the above problem, an online multiple outputs Least-Squares Support Vector Regression model based on selection mechanism was proposed: (a) converting the traditional Least-Squares Support Vector Regression’s single output to multiple outputs, aiming at the problem that the single-output of the traditional Least-Squares Support Vector Regression model is difficult to apply to complex multiple features prediction scenarios, (b) reducing the high computational complexity of matrix inversion calculations using an iterative solution, in order to solve the problem of poor real-time performance, (c) determining whether to use online model based on the characteristics of different trajectories, and (d) removing initial samples least affecting the model to alleviate the impact of large increases in the number of new samples on computational complexity. The model was simulated using the automatic identification system tracks of Tianjin port in March 2015. The calculation accuracy and efficiency of this model was verified by comparing the predicted results of the proposed model with the recurrent neural network–long short-term memory, back propagation neural network, and traditional Least-Squares Support Vector Regression models. In sum, the proposed model is highly accurate in online and real-time prediction of a target ship’s trajectory when sailing at sea. In particular, it can sustain high prediction accuracy in the case of smaller data samples. The real-time predicted trajectory can assist the generation of ship collision avoidance decision-making.

Soft sensor design based on phase partition ensemble of LSSVR models for nonlinear batch processes.

Traditional single model based soft sensors may have poor performance on quality prediction for batch processes because of the strong nonlinearity, multiple-phase, and time-varying characteristics. Therefore, a phase partition based ensemble learning framework upon least squares support vector regression (LSSVR) is proposed for soft sensor modeling. Firstly, multiway principal component analysis (MPCA) is employed to handle high-dimensional datasets and extract essential correlation information. Then, different operation phases of the process can be identified by the phase partition strategy based on Gaussian mixture model (GMM) method. Meanwhile, the optimal Gaussian component number is determined by Bayesian information criterion (BIC) technique. Further, multiple localized LSSVR models are constructed to characterize the various dynamic relationships between quality and process variables for local regions, while the grid search (GS) and ten-fold cross-validation methods are introduced to parameter optimization for each local model. Finally, the posterior probability for each test sample with respect to different phases can be estimated by Bayesian inference strategy, and local outputs are integrated to produce the final quality prediction results. Feasibility and superiority of the proposed soft sensor are validated through a case study for penicillin fermentation process. It can achieve satisfactory prediction accuracy and effectively tackle nonlinear and multi-phase modeling problems in chemical and biological processes.

Multi-objective combustion optimization based on data-driven hybrid strategy

In order to reduce pollutant discharge and improve boiler efficiency, data-driven hybrid strategy is proposed to solve the problem of multi-objective combustion optimization. First, massive historical operation data of a coal-fired power station are preprocessed (including resampling, steady-state detection, data cleaning and cluster analysis), so as to divide the whole boiler working condition into different partitions. Next, combustion association rules based multi-objective optimal strategy is applied to extract a combustion optimal rule from every partition, and a combustion optimal rule-base is built up by merging all the rules, so that the preliminary combustion optimization can be quickly finished based on the combustion optimal rule-base. Meanwhile, combustion mathematical model based multi-objective optimal strategy is applied to develop the LSSVR (least square support vector regression) model of boiler combustion process for every partition, and a combustion optimal model-base, which contains all the LSSVR models, is built up. After that, an improved multi-objective particle swarm optimization algorithm is presented to calculate Pareto optimal solutions depend on the corresponding LSSVR model with the constraint of real-time boiler working condition. To achieve further combustion optimization, the method of multiple attribute decision making is used to determine the unique solution from all the Pareto optimal solutions. Data-driven hybrid strategy is to combine the above two strategies. Simulation experiments verified the validity and feasibility of data-driven hybrid strategy on multi-objective test function ZDT1. Taking advantage of data-driven hybrid strategy, the comprehensive average of NOx emissions dropped by 29.63% and the comprehensive average of boiler efficiency increased by 0.69% in the application experiments with historical operation data under some boiler working conditions. Data-driven hybrid strategy based multi-objective combustion optimization makes the integration of instantaneity and effectiveness, so that it is suitable for online application.

A Fuzzy Optimization Strategy for the Implementation of RBF LSSVR Model in Vis–NIR Analysis of Pomelo Maturity

Spectral analysis is a practical technology used for rapid analysis of fruit maturity. Least-squares support vector regression (LSSVR) with radial basis function (RBF) kernel is an effective nonlinear method for the quantitative calibration in the visible–near-infrared (Vis–NIR) spectral region. However, the nonlinear effect and high-dimensional spectrum data influence the prediction accuracy and complexity of modeling procedures. This article presents a fuzzy optimization strategy to improve the performance of the RBF LSSVR model in Vis–NIR quantitative determination of pomelo maturity. In the proposed strategy, a linguistic iterative mode is introduced for optimizing RBF kernel parameters. The input variables of the model are the informative features extracted through fuzzy transform principal component analysis algorithm, and the output was a polynomial equation of the inputs. In this article, pomelo maturity is recorded using the quantitative indices of L *, a *, and b *. The Vis–NIR spectral data of Pomelo samples are first converted to a set of fuzzy-transformed principal components and inputted into a fuzzy-optimized LSSVR model for calibration, validation, and test. Parameter uncertainty is evaluated to verify the effectiveness of the proposed strategy. Experimental results show that the proposed fuzzy optimization strategy is feasible for reducing the computational complexity of the BRF LSSVR model, and the predictions on L *, a *, and b * are much appreciable. The proposed fuzzy optimization strategy based on the linguistic iteration mode is considered as the effective implementation for calibration models in the spectroscopy technology for rapid prediction of fruit maturity.

A Glucose Prediction Model based on Variational Mode Decomposition and Least Squares Support Vector Regression

Online prediction of subcutaneous glucose concentration plays a critical role in glucose management for type 1 diabetes. In this work, a new method combining Variational Mode Decomposition (VMD) and Least Squares Support Vector Regression (LSSVR) is proposed with three main stages to improve the prediction accuracy. Firstly, the time series of blood glucose are decomposed into different frequency series by VMD method. Secondly, the LSSVR model is trained to predict each subsequence. Finally, the predicted sequences are reconstructed to obtain the overall glucose predictions. The experimental results demonstrate the effectiveness and accuracy of the proposed model for short term glucose prediction.

A pre-warning system of abnormal energy consumption in lead smelting based on LSSVR-RP-CI

The pre-warning of abnormal energy consumption is important for energy conservation of industrial engineering. However, related studies on the lead smelting industries which usually have a huge energy consumption are rarely reported. Therefore, a pre-warning system was established in this study based on the intelligent prediction of energy consumption and the identification of abnormal energy consumption. A least square support vector regression (LSSVR) model optimized by the adaptive genetic algorithm was developed to predict the energy consumption in the process of lead smelting. A recurrence plots (RP) analysis and a confidence intervals (CI) analysis were conducted to quantitatively confirm the stationary degree of energy consumption and the normal range of energy consumption, respectively, to realize the identification of abnormal energy consumption. It is found the prediction accuracy of LSSVR model can exceed 90% based on the comparison between the actual and predicted data. The energy consumption is considered to be non-stationary if the correlation coefficient between the time series of periodicity and energy consumption is larger than that between the time series of periodicity and Lorenz. Additionally, the lower limit and upper limit of normal energy consumption are obtained.

Evaluating the performance of four different heuristic approaches with Gamma test for daily suspended sediment concentration modeling.

Accurate prediction of suspended sediment concentration (SSC) carried by a river or watershed basin is essential for understanding the hydrology of basin in terms of water quality, river bed sustainability and aquatic habitats. In this study, four heuristic methods, namely, radial basis neural network (RBNN), self-organizing map neural network (SOMNN), least square support vector regression (LSSVR), and multivariate adaptive regression spline (MARS) were employed for daily SSC modeling at Ashti, Bamini, and Tekra stations located in Godavari River basin, Andhra Pradesh, India. The Gamma test (GT) was utilized for identifying the most significant input variables for the applied heuristic approaches. The results obtained by RBNN, SOMNN, LSSVR, and MARS models were compared with those of the traditional sediment rating curve (SRC). The performance of the models was evaluated based on the root mean square error (RMSE), coefficient of efficiency (COE), Pearson correlation coefficient (PCC), Willmott index (WI), and pooled average relative error (PARE) indices, as well as the visual inspection using line diagram, scatter diagram, and Taylor diagram (TD). The results of comparison revealed that the four heuristic methods gave higher accuracy than the SRC model. Among the heuristic models, the RBNN-3 (RMSE = 0.045, 0.062, 0.131g/l; COE = 0.884, 0.883, 0.914; PCC = 0.955, 0.961, 0.958; and WI = 0.970, 0.963, 0.976) outperformed the other models in simulating daily SSC records in the studied stations.

Molecular docking and receptor-based QASR studies on pyrimidine derivatives as potential phosphodiesterase 10A inhibitors

In the present work, molecular docking methodology in combination with quantitative structure–activity relationship (QSAR) was employed to predict the inhibition activity of 87 structurally diverse pyrimidine-based derivatives as phosphodiestrae10A (PDE10A) inhibitors due to their potential in the treatment of schizophrenia. In this method, compounds in their preferred enzyme-docked conformations were utilized to derive interaction-based quantitative descriptors in order to explain reported PDE10A inhibitory activities. Multiple linear regression (MLR), artificial neural network (ANN), and least square support vector regression (LS-SVR) were exploited to developing the structure-based quantitative structure–activity relationship models. Among these models, LS-SVR model showed more satisfactory statistical parameters with regard to both internal (Rtrain = 0.951, Q2 = 0.804, RMSEtrain = 0.494) and external validation (Rtest = 0.941, RMSEtest = 0.549) test results. Information from the most relevant descriptors suggests that incorporating steric effect, electronegativity, and the number of substituted aromatic carbon correlate the activity with structural features of the studied compounds. Molecular docking analysis of the most potent inhibitor explored that hydrogen bond formation and hydrophobicity participated in the binding interaction of PDE10A complex active pocket which these findings are in line with those obtained from QSAR model. The reliability assessment of compounds predictions was checked by model applicability domain (AD) analysis.

Fast estimation of optical properties of pear using a single snapshot technique combined with a least-squares support vector regression model based on spatial frequency domain imaging.

Spatial frequency domain imaging has great potential in agricultural produce quality control due to its advantage of wide-field mapping of absorption (μa) and reduced scattering (μs') parameters. However, it is not widely adopted in real applications due to the large time cost during image acquisition and inversion calculation processes. In this study, a single snapshot technique was used to obtain ac and dc components (Rd_ac, Rd_dc) of diffuse reflectance of turbid media (phantoms and pears). The validation results for the snapshot method indicate that at the spatial frequency of 1000/3 m-1, it achieved the optimal demodulation, by comparison with the results obtained by the commonly used time-domain amplitude demodulation method. Diffusion approximation, artificial neural network, least-squares support vector machine regression (LSSVR), and LSSVR combined with a genetic algorithm (LSSVR+GA) were then used to predict μa and μs' from the obtained Rd_ac, Rd_dc at the fx of 1000/3 m-1. Validation results indicated that the LSSVR method took the least time to calculate μa and μs' with high performance. The proposed imaging system and algorithm were implemented for the inspection of a pear bruise. Results indicated that the bruise, which is not obviously distinguishable in original gray maps, can show obvious contrast in calculated μa and μs' maps, especially in μa maps. Further, the contrast becomes more obvious with the passage of time. In summary, this study developed a low-cost spatial frequency imaging system and matching software that could realize fast detection of optical properties for a pear with the proposed snapshot and LSSVR algorithms.

Predicting ultimate bond strength of corroded reinforcement and surrounding concrete using a metaheuristic optimized least squares support vector regression model

The ultimate bond strength of corroded steel reinforcement and surrounding concrete critically affects the load carrying capacity and eventually serviceability of the reinforced concrete structures. This study constructs and verifies a data-driven method for estimating ultimate bond strength. The proposed method is a hybridization of least squares support vector regression (LSSVR) and differential flower pollination (DFP) computational intelligence approaches. Since the problem of ultimate bond strength prediction involves nonlinear and multivariate data modeling, the LSSVR is employed to infer the mapping function between ultimate bond strength and its influencing factors of concrete compressive strength, concrete cover, steel type, diameter of steel bar, bond length, and corrosion level. Moreover, in order to overcome the very challenging task of fine-tuning the LSSVR model training, the DFP algorithm, as a population-based metaheuristic, is utilized to optimize the performance of the LSSVR prediction model. A dataset including 218 experimental tests has been collected from the literature to construct and verify the proposed hybrid method. Experimental results supported by the Wilcoxon signed-rank test point out that the hybridization of LSSVR and DFP can deliver predictive results (root-mean-square error = 2.39, mean absolute percentage error = 33.82%, and coefficient of determination = 0.84) superior to those of benchmark models including the artificial neural network, the multivariate adaptive regression splines, and the regression tree. Additionally, a software program based on the LSSVR model and the DFP optimization result has also been developed and compiled in Visual C#.Net to ease the model implementation. Hence, the hybrid model of DFP and LSSVR can be a promising alternative to assist engineers in the task of evaluating the health of reinforced concrete structures.

Development of multivariate adaptive regression spline integrated with differential evolution model for streamflow simulation

Among several components of the hydrology cycle, streamflow is one of the essential process necessarily needed to be studied. The establishment of an accurate and reliable forecasting soft computing model for this process is highly vital for water resource planning and management. The influence of the climatological environment on streamflow is central and studying its influence is very significant from the hydrology perspective. It has been noticed that the application of machine learning models considerably become predominant in solving and capturing the complexity of hydrological applications. This research presents the implementation of a novel hybrid model called Multivariate Adaptive Regression Spline integrated with Differential Evolution (MARS-DE) to forecast streamflow pattern in semi-arid region. To achieve this, monthly time series streamflow data at Baghdad station, coordinated at Tigris River, Iraq, is inspected. For the model validation, Least Square Support Vector Regression (LSSVR) and standalone MARS models are conducted. To demonstrate the analysis of the undertaken models, several statistical indicators are computed to verify the modeling accuracies. Based on the achieved results, the MARS-DE model exhibited an excellent hybrid predictive modeling capability for monthly time scale streamflow in semi-arid region. Quantitatively; MARS-DE, LSSVR and MARS models achieved the minimum root mean square error (RMSE) and mean absolute error (MAE) values of 46.64–35.25 m3/s, 57.50–49.20 m3/s and 78.01–62.65 m3/s, respectively. In conclusion, several perspectives are suggested for further studies to enhance the forecasting capability of the model.

Sliding-window metaheuristic optimization-based forecast system for foreign exchange analysis

The forecasting of exchange rates has become a challenging area of research that has attracted many researchers over recent years. This work presents a sliding-window metaheuristic optimization-based forecast (SMOF) system for one-step ahead forecasting. The proposed system is a graphical user interface, which is developed in the MATLAB environment and functions as a stand-alone application. The system integrates the novel firefly algorithm (FA), metaheuristic (Meta) intelligence, and least squares support vector regression (LSSVR), namely MetaFA-LSSVR, with a sliding-window approach. The MetaFA automatically tunes the hyperparameters of the LSSVR to construct an optimal sliding-window LSSVR prediction model. The optimization effectiveness of the MetaFA is verified using ten benchmark functions. Two case studies on the daily Canadian dollar-USD exchange rate (CAN/USD) and the 4-h closing EUR-USD rates (EUR/USD) were used to confirm the performance of the system, in which the mean absolute percentage errors are 0.2532% and 0.169%, respectively. The forecast system has an 89.8–99.7% greater predictive accuracy than prior work when applied to the currency pair CAN/USD. With respect to the EUR/USD exchange rate, the error rates obtained using the proposed system were 20.8–23.9% better than those obtained by the baseline sliding-window LSSVR model. Therefore, the SMOF system is potentially useful for decision-makers in financial markets.

Bi-sparse optimization-based least squares regression

For forecasting by regression, more and more instances and features are collected and added to the regression models. When there are many noisy and redundant instances and features, these models often give the poor predictive accuracy and interpretability owing to overfitting and computational complexity. Besides, least squares support vector regression (LSSVR) can hardly obtain sparse solutions and identify important instances and features from data. In this paper, a novel bi-sparse optimization-based least squares regression (BSOLSR) method is proposed in the framework of LSSVR. Based on the new row and column kernel matrices, the ℓ0-norm sparsification function is introduced to the LSSVR model. By alternatively solving two unconstrained quadratic programming problems or two systems of linear equations, BSOLSR can predict output values for given input points and provide interpretable results by simultaneous selecting relevant and important instances and features. As shown in the experimental results on real data sets and comparison with SVR, ℓ1-norm SVR (L1SVR), LSSVR, and multiple kernel learning SVR (MKLSVR), the proposed BSOLSR can effectively increase predictive accuracy, discover representative instances and important features, and gain the interpretable results, which are very critical for many real-world applications.

Comparison of LSSVR, M5RT, NF-GP, and NF-SC Models for Predictions of Hourly Wind Speed and Wind Power Based on Cross-Validation

Accurate predictions of wind speed and wind energy are essential in renewable energy planning and management. This study was carried out to test the accuracy of two different neuro fuzzy techniques (neuro fuzzy system with grid partition (NF-GP) and neuro fuzzy system with substractive clustering (NF-SC)), and two heuristic regression methods (least square support vector regression (LSSVR) and M5 regression tree (M5RT)) in the prediction of hourly wind speed and wind power using a cross-validation method. Fourfold cross-validation was employed by dividing the data into four equal subsets. LSSVR’s performance was superior to that of the M5RT, NF-SC, and NF-GP models for all datasets in wind speed prediction. The overall average root-mean-square errors (RMSE) of the M5RT, NF-GP, and NF-SC models decreased by 11.71%, 1.68%, and 2.94%, respectively, using the LSSVR model. The applicability of the four different models was also investigated in the prediction of one-hour-ahead wind power. The results showed that NF-GP’s performance was superior to that of LSSVR, NF-SC, and M5RT. The overall average RMSEs of LSSVR, NF-SC, and M5RT decreased by 5.52%, 1.30%, and 15.6%, respectively, using NF-GP.

Evaluation of mechanical properties of concretes containing coarse recycled concrete aggregates using multivariate adaptive regression splines (MARS), M5 model tree (M5Tree), and least squares support vector regression (LSSVR) models

This paper investigates the application of three artificial intelligence methods, including multivariate adaptive regression splines (MARS), M5 model tree (M5Tree), and least squares support vector regression (LSSVR) for the prediction of the mechanical behavior of recycled aggregate concrete (RAC). A large and reliable experimental test database containing the results of 650 compressive strength, 421 elastic modulus, 152 flexural strength, and 346 splitting tensile strength tests of RACs with no pozzolanic admixtures assembled from the published literature was used to train, test, and validate the three data-driven-based models. The results of the model assessment show that the LSSVR model provides improved accuracy over the existing models in the prediction of the compressive strength of RACs. The results also indicate that, although all three models provide higher accuracy than the existing models in the prediction of the splitting tensile strength of RACs, only the performance of the LSSVR model exceeds those of the best-performing existing models for the flexural strength of RACs. The results of this study indicate that MARS, M5Tree, and LSSVR models can provide close predictions of the mechanical properties of RACs by accurately capturing the influences of the key parameters. This points to the possibility of the application of these three models in the pre-design and modeling of structures manufactured with RACs.

Non‐linear MIMO identification of a Phantom Omni using LS‐SVR with a hybrid model selection

Here, a multiple-input-multiple-output (MIMO) Phantom Omni robot made by SensAble Technologies Inc. is identified by using a least-square support vector regression (LS-SVR). To this end, a two-stage hybrid optimisation strategy combining coupled simulated annealing as a priori optimisation strategy and a derivative-free Simplex method as a complementary stage is proposed to solve the LS-SVR model selection problem. This extra step is a fine-tuning procedure to enhance the optimal tuning parameters and hence lead LS-SVR to a better performance. Generalised v -fold cross-validation is considered as the criterion of LS-SVR model selection problem. The Phantom robot model is implemented via OPAL-RT to assess the performance of the proposed algorithm compared with firefly algorithm and adaptive particle swarm optimisation in solving LS-SVR model selection in practical application of the Phantom robot modelling. Finally, the proposed approach is validated and implemented in the hardware-in-the-loop based on OPAL-RT to integrate the fidelity of physical simulation as well as the flexibility of numerical simulations.