Least Squares Support Vector Machine Algorithm Research Articles

A LS-SVM method for CMM geometric error identification based on spatially integrated measurement

The measurement and identification of geometric errors are important for improving the accuracy of CMM(Coordinate Measuring Machine). Since measurement instruments cannot simultaneously identify all geometric errors, multiple installations for measurements will lead to repeated installation errors between systems, low measurement efficiency, and low identification accuracy. To obtain geometric error of CMM accuractly and conveniently, this paper proposes a method for CMM geometric error identification based on spatially integrated measurement. Specifically, the identification model is determined through the transformation of the spatial comprehensive error model. Then, the LS-SVM(least squares support vector machine) algorithm is adopted for identifying geometric errors. The validity of the proposed method is verified through simulation and experiments. Compared with the ridge regression and least squares methods, the accuracy of the proposed identification method is improved by 35.53% and 46.53%, respectively. The applicability of the proposed method is also verified by setting up another set of experiments.

Inversion Study on Landslide Seepage Field Based on Swarm Intelligence Optimization Least-Square Support Vector Machine Algorithm

The permeability coefficient of landslide mass, a key parameter in the study of reservoir landslides, is commonly obtained through in situ and laboratory tests; however, the tests are costly and subject to high variability, leading to potential biases. In this paper, a new method was proposed to inversely estimate the permeability coefficient of landslide layers using monitoring data of groundwater level (GWL). First, the landslide transient seepage simulation was conducted to generate sample data for permeability coefficients and GWL during a reservoir operation cycle. Second, using GWL data as input and permeability coefficient data as output, the least-square support vector machine (LSSVM) was trained with two optimization algorithms, the particle swarm optimization (PSO) algorithm and the whale optimization algorithm (WOA), to construct the nonlinear mapping relationship between simulated GWL and permeability coefficients. Third, the accurate permeability coefficients for landslide seepage simulation were inverted or predicted based on the monitored GWL. Finally, using the inverted permeability coefficients for landslide seepage simulation, we compared simulation results with actual monitored GWL and achieved good consistency. In addition, this paper compared the inversion effects of three different algorithms: the standard LSSVM, PSO-LSSVM, and WOA-LSSVM. This study showed that these three algorithms had good nonlinear fitting effects in studying landslide seepage fields. Among them, using the inversion values from PSO-LSSVM for landslide seepage simulation resulted in the smallest relative error compared to actual monitoring data. Within a single reservoir operation cycle, the simulated water level changes were also largely consistent with the monitored water level changes. The results could provide a reference to determine landslide permeability coefficients and seepage.

A Realistic Method for Diagnosing Bearing Faults of Three-Phase Induction Motor using Advanced Support Vector Machine Algorithm

Bearings are one of the most crucial components of any induction motor. The faults or failure of bearings can lead to high maintenance and operational costs. To ensure the induction motor operates consistently, it is crucial to identify and diagnose bearing faults at an early stage. In this perspective, this manuscript presents a method based on least square support vector machine (LSSVM) to identify the bearing defects of an induction motor. The IM parameters, such as stator currents, input voltage, and rotor speed, were extracted using experimental setup at different loads and health conditions of bearing. Then these parameters were used to train and validate the LSSVM algorithm in MATLAB to diagnose the bearing defects. The proposed method provides 97.14% fault prediction accuracy with an RBF kernel.

Prediction of the Productivity Ratio of Perforated Wells Using Least Squares Support Vector Machine with Particle Swarm Optimization

The productivity ratio is a vital metric for assessing the efficiency of perforated completions. Accurate and rapid prediction of this ratio is essential for optimizing the perforation design. In this study, we propose a novel approach that combines three-dimensional finite element numerical simulation and machine learning techniques to predict the productivity ratio of perforated wells. Initially, we obtain the productivity ratio of perforated wells under various perforation parameters using three-dimensional finite element numerical simulation. This generates a sample set for machine learning. Subsequently, we employ the least squares support vector machine (LSSVM) algorithm to establish a prediction model for the productivity ratio of perforated wells. To optimize the parameters of the LSSVM algorithm, we utilize the particle swarm optimization (PSO) algorithm. We compare our proposed PSO-LSSVM model with that established based on other parameter optimization methods and machine learning algorithms, such as Grid search-LSSVM, PSO-ANN, and PSO-RF. Our results demonstrate that the PSO-LSSVM model exhibits rapid convergence, high prediction accuracy, and strong generalization ability in predicting the productivity ratio of perforated wells. This research provides a valuable reference and guidance for optimizing perforation design. Additionally, it offers new insights into predicting the productivity of complex completions.

A New Method for Erosion Prediction of 90° Elbow Based on Non-Axisymmetric Ultrasonic-Guided Wave and the PSO-LSSVM Algorithm.

The non-axisymmetric exciting guided wave can detect the thinning section of the elbow, and the time domain energy value of the signal collected at the outer arch position of the receiving end displays a downward trend as the remaining thickness of the erosion area decreases. To address the difficulty in detecting the erosion degree of the elbow with high accuracy, this paper uses the linear frequency modulation (LFM) signal to excite a non-axisymmetric guided wave that propagates in the 90° elbow and collects signals through four PZT receivers. To predict the erosion degree, the corresponding relationship between the energy value of the four signals after fractional Fourier filtering and the degree of elbow erosion is established through the particle swarm optimization (PSO)-least squares support vector machine (LSSVM) algorithm. The results show that the method proposed has an average accuracy rate of 98.1864%, 94.7167%, 99.119%, and 99.9593% for predicting the erosion degree of four elbow samples, and 94.0039%. and 81.2976% for two new erosion degrees, which are higher than the nonlinear regression model, LSSVM algorithm, and BP neural network algorithm. This study has guiding significance for real-time monitoring of elbow erosion.

Spectroscopic studies on thermal degradation and quantitative prediction on acid value of edible oil during frying by Raman spectroscopy

The health risks posed by harmful substances resulting from the thermal degradation of frying oils are of great concern. Characteristic peak intensity ratios (PIRs) screened from Raman spectra were used to characterize the thermal degradation. High correlation coefficients between PIRs and acid values (AVs) of 0.972 (linear fitting), 0.984 (logarithmic function fitting), and 0.954 (linear fitting) for fried soybean oil, canola oil, and palm oil, were obtained at the PIRs of I1267/I1749, I1267/I1659, and I1267/I1749, respectively. The highly correlated PIRs common to the three oils were determined by Pearson’s correlation coefficient combined with heat maps. To accommodate both linear and nonlinear features, a global model for predicting AVs of multi-varieties frying oils was constructed using a least-squares support vector machine algorithm, and the results performed well with a root mean square error of prediction of 0.016 and a ratio of prediction to deviation of 11.351. The whole results demonstrate that Raman spectroscopy could characterize the thermal degradation and has excellent quantitative analysis ability for food control based on AV in frying oils, thus providing a new approach to quality control of frying oils.

Comfort Prediction of Office Chair Surface Material Based on the ISSA-LSSVM

This study serves the purpose of assisting users in selecting a comfortable seat surface material for office chairs and enhancing users' comfort while using office chairs. To address the issue that the selection of traditional seat surface material is too subjective and that the prediction effect is poor, an improved sparrow search algorithm (ISSA) optimized least squares support vector machine (LSSVM) method for office chair seat surface material comfort prediction has been proposed. Sparrow Search Algorithm (SSA) was optimized with Sobol sequences, nonlinear inertial weights, and a crisscross optimization algorithm to produce the Improved Sparrow Search Algorithm (ISSA), and then the relevant parameters of the LSSVM algorithm were optimized with the modified algorithm to improve its prediction performance. The prediction accuracy of the ISSA-LSSVM model is as high as 95.75% by combining the body pressure distribution experiments; the root mean square error (RMSE) is 0.29; the goodness of fit (R2) is 0.92; the mean absolute error (MAE) is 0.24; the standard deviation (RSD) is 5.99%. The ISSA-LSSVM model predicts seat surface material comfort more accurately and reliably. This strategy can assist consumers to narrow down their seat surface material choices and even suggest an optimal selection. In this way, it can boost users' pleasure with office chairs, which has great potential for wide application.

Lithological classification by PCA-QPSO-LSSVM method with thermal infrared hyper-spectral data

To improve the accuracy and operation efficiency of lithological classification using a thermal infrared airborne hyper-spectral imager (TASI) data, an innovative combinatorial algorithm (PCA-QPSO-LSSVM) based on principal component analysis (PCA), quantum-behaved particle swarm optimization (QPSO), and least-squares support vector machines (LSSVM) is proposed. After pre-processing, the emissivity data was extracted from TASI data, and 27 types of lithological units were selected in comparison with the measured spectrum and Johns Hopkins University spectrum library. The PCA was used for statistical analysis, and the appropriate n principal components were selected instead of the original 32 bands of TASI emissivity data. Based on the LSSVM classification algorithm, the improved QPSO algorithm was used to optimize the regularization parameter γ and the kernel function σ2 in the classification process. Finally, test samples selected from TASI data were classified by PCA-QPSO-LSSVM. The results show that, compared with the traditional LSSVM algorithm, PCA-QPOS-LSSVM has a higher recognition accuracy and greater operation efficiency. The field verification of the study area was carried out in LiuYuan town, GanSu province, China, and the accuracy of the field verification was 74.36% for the classification result, which is more consistent with the actual lithological distribution compared with the LSSVM algorithm. However, there are some flaws in this paper, such as the low classification accuracy in Moyite and plauenite. In general, The PCA-QPSO-LSSVM algorithm is a practical algorithm for lithological classification of TASI data.

Evolving application of machine learning in the synthesis of CHA/ZrO2 nanocomposite for the microhardness prediction

• An efficient approach of machine learning in the field of materials science. • Prediction of CHA/ZrO 2 nanocomposites microhardness using of LS-SVM and GWOA. • High-precision models (R 2 = 0.9986) were presented using the machine learning. • Variables that affect the microhardness of CHA/ZrO 2 nanocomposites are identified. Nanocomposites containing ZrO 2 and HA have been considered in various fields due to their unique mechanical properties. The principal purpose of this paper is to select the models with the maximum accuracy for the prediction of microhardness of CHA/ZrO 2 nanocomposite. For this purpose, three models, including gene expression programming (GEP), gray wolf optimization algorithm (GWOA), and least squares support vector machine (LS-SVM), were implemented to predict and optimize the microhardness of the CHA/ZrO 2 nanocomposite. Finally, the results showed that the data obtained from the LS-SVM model were closer to the preliminary data than the others. According to the results, the LS-SVM could predict the microhardness by R 2 = 0.9986, MSE = 0.0086, MAPE = 4.3, MSE = 0.018, and RRSE = 0.0143. Therefore, it seems that the LS-SVM algorithm and preliminary data are completely utilitarian to predict the microhardness of CHA/ZrO 2 nanocomposites, accurately.

Predicting the yield of stepped corrugated solar distiller using kernel-based machine learning models

• Stepped solar still with corrugated basin was designed and constructed. • Maximum distillate improvement was 255% for stepped still over conventional one. • A two machine learning models were developed for predicting both still performances. • Five kernel functions were used to find the optimum structure of each model. • Radial basis function (RBF) was the most appropriate kernel function. • Support vector machine combined RBF had a superior accuracy in predicting the still yield. Recently, accurate prediction of the distilled productivity is a decisive issue to assess and compare the ability of these designs of solar stills to provide distilled water to a certain application without carrying out time-consuming and more costly field experiments. Machine learning techniques have become powerful alternatives to conventional modeling approaches in different engineering disciplines. In this study, two improved machine learning models, namely relevance vector machine (RVM) and least squares support vector machine (LSSVM), are proposed to predict the productivity of two solar distillers. The two solar distillers are a conventional single slope single basin solar still (SSSS) and a modified stepped corrugated solar still (SCSS). Initially, the experimental energetic and exergetic performance of the SCSS is compared with that of SSSS. The experimental results showed that the water yield, energy efficiency, and exergy efficiency of the SCSS are improved by about 255 %, 239%, and 379%, respectively, compared with that of the SSSS. Then, the proposed RVM and LSSVM models are used to predict the productivity of two solar stills. During the simulation, different kernel functions, such as Laplace, linear, spline, Gaussian (G), and radial basis function (RBF), are embedded in both models to obtain the optimal function that maximizes the model accuracy. The simulated results showed that Gaussian and radial basis functions are the most appropriate kernel functions for RVM and LSSVM algorithms, respectively. Particularly, the LSSVM-RBF and RVM-G models predict the distilled production of the SCSS with determination coefficient values of 0.999 and 0.982, and root mean square error values of about 6.646 e-06, and 0.002, respectively Consequently, the LSSVM-RBF model is recommended as a promising prediction tool in predicting the production of both solar distillers.

Study on Model Evolution Method Based on the Hybrid Modeling Technology With Support Vector Machine for an SOFC-GT System

Abstract The mechanism models of solid oxide fuel cell–gas turbine (SOFC-GT) systems are very useful to analyze the thermodynamic performance details, including the internal complex transfers of mass, heat, and electrochemical processes. However, several physical-property parameters in the mechanism model are unmeasurable and difficult to accurately quantify from the operation data when the inevitable degradation occurs. As a result, it is difficult for the mechanism model to accurately capture the SOFC electrochemical characteristic during the full operating cycle. In this paper, a model evolution method based on hybrid modeling technology is proposed to address this problem. A hybrid modeling framework of a SOFC-GT system is designed by combining a least squares-support vector machine algorithm (LS-SVM) electrochemical model with our previous mechanism model. The electrochemical characteristic of SOFC is easily identified and evolved by re-training the LS-SVM model from operating data, no longer needing a mechanism electrochemical model. The validated full-mechanism model from our previous work is taken to simulate a physical SOFC-GT system to generate the operating data. Various LS-SVM models are trained by different data sets. The comparison results demonstrate that the LS-SVM model trained by large-size data set 3 performs the highest accuracy in predicting the local current density. The maximum absolute error of prediction is only about 1.379 A/m2, and the prediction mean square error of the normalized test data reaches 4.36 × 10−9. Then, the LS-SVM hybrid model is applied to evaluate the thermodynamic performance of a SOFC-GT system. The comparison results between the hybrid model and our previous full-mechanism model show that the hybrid model can accurately predict the SOFC-GT system performance. The maximum error is 1.97% at the design condition and 0.60% at off-design conditions. Therefore, the LS-SVM hybrid model is significant for accurately identifying the real electrochemical characteristic from operation data for a physical SOFC-GT system during the full operation cycle.

Estimating the distribution of chlorophyll content in CYVCV infected lemon leaf using hyperspectral imaging

Yellow vein clearing disease of lemon caused by the citrus yellow vein clearing virus (CYVCV) is a new devastating disease in lemon. Chlorophyll contents and distributions are critical biochemical parameters to assess this new disease. The objective of this study was to develop an efficient method for detecting chlorophyll contents and distributions in lemon leaves infected with CYVCV. Spectral reflectance and chlorophyll content data of healthy, nitrogen deficient, pesticide-damaged and the corresponding CYVCV-infected leaves were obtained. Successive projections algorithm, random frog, competitive adaptive reweighted sampling (CARS), synergy interval partial least squares and synergy interval partial least squares combined with successive projections algorithm were applied for reducing data dimension, respectively. Prediction models were built by applying least squares-support vector machine algorithm (LS-SVM). The results showed that the characteristic wavelengths were basically located in “green peak” (near 550 nm), “red valley” (near 680 nm), and “red edge” (680–750 nm). Prediction model based on the wavelengths extracted by CARS achieved the optimal prediction results with determination coefficient of 0.94, relative prediction deviation of 3.91 and root mean square error of 0.10 in testing set. Thus, the CARS algorithm combined with LS-SVM was applied for distributions of chlorophyll contents. The chlorophyll content of each pixel of the six types of leaves were displayed, and significantly reduced in the mesophyll tissue near the veins of CYVCV-infected leaves. These results suggest that the hyperspectral imaging coupled with CARS and LS-SVM can be used to efficiently measure the distribution of chlorophyll content in CYVCV infected lemon leaf, which provides a reference for a better understanding of the symptoms of disease.

A comparative analysis of hybrid SVM and LS‐SVM classification algorithms to identify dried wolfberry fruits quality based on hyperspectral imaging technology

A very common preservation method used in food processing is the drying method. Hence it is necessary to properly examine and ascertain how the fruit's quality is affected after drying. Hyperspectral imaging (HSI) technology is one of the advanced technologies adopted for assessing food quality. This study explored the impact of standard normalization variate (SNV) and Savitsky–Golay (SG) data preprocessing and optimization methods on spectral data of dried wolfberry fruits’ quality taken in a range of 400.680–1001.612 nm wavelength. Thus, this research demonstrated that using HSI technology and integrating SG-SVN preprocessing methods to the least square-support vector machine (LS-SVM) model could accurately predict dried wolfberry fruit quality. The prediction accuracy of the LS-SVM algorithm coupled with SG-SVN achieved 96.66%, which was the highest classification accuracy. The study results demonstrated that HSI technology combined with the LS-SVM model is feasible for dried wolfberry fruit quality classification. Novelty impact statement Conventional methods of classifying wolfberry fruit quality rely mainly on appearance and human sensory, which is time consuming and lacks accuracy. In this study, hyperspectral imaging technology with the LS-SVM algorithm is used for precise rapid nondestructive classification of wolfberry fruit dried under different temperatures and time frames, respectively.

Modeling the effects of biodiesel chemical composition on iodine value using novel machine learning algorithm

Biodiesel is a promising renewable energy the use of which facilitates the goals of carbon neutrality and timely carbon peak. The iodine value (IV), one of the major properties of biodiesel, denotes the degree of unsaturation and correlates with the chemical composition of biodiesel. In this work, a novel approach based on random forest (RF) and least squares support vector machine (LSSVM) algorithms optimized by whale optimization algorithm (WOA) is proposed for estimating the IV of biodiesel as a function of fatty acid methyl ester profiles. In doing so, the compositions and IVs of 52 biodiesel/binary biodiesel blends were determined by gas chromatography mass spectrometry and EN14111 standard. Then, LSSVM algorithm was assessed as the most appropriate predictive method compared to the adaptive neuro fuzzy inference system, multi-layer perceptron neural network, and decision tree algorithms. Continuously, four feature selection approaches (Pearson’s correlation coefficient, principal component analysis, ReliefF algorithm, and RF) were utilized to choose the most influencing fatty acid methyl ester combination as input. The RF-LSSVM model was found to be superior to other Ⅰ hybrid models. Then, WOA was incorporated into the modeling process and the RF-WOA-LSSVM model achieved a high performance with a root mean square error and correlation coefficient of 1.1893 and 0.9977, respectively. The accuracy and error of the RF-WOA-LSSVM model have been validated. Comparison with previous biodiesel IV machine learning models and application of other new experimental datasets from the literature prove the feasibility of the proposed hybrid RF-WOA-LSSVM model for estimating the IV of different biodiesels types.

Predictability of carcass traits in live Tan sheep by real-time ultrasound technology with least-squares support vector machines.

This study aimed to investigate the performance of least-squares support vector machines to predict carcass characteristics in Tan sheep using noninvasive in vivo measurements. A total of 80 six-month-old Tan sheep (37 rams and 43 ewes) were examined. Back fat thickness and eye muscle area between the 12th and 13th ribs were measured using real-time ultrasound in live Tan sheep. All carcasses were dissected to hind leg, longissimus dorsi muscle, lean meat, fat, and bone to determine carcass composition. Multiple linear regression (MLR), partial least squares regression (PLSR), and least-squares support vector machines (LSSVM) were applied to correlate the live Tan sheep characteristics with carcass composition. The results showed that the LSSVM model had a better efficacy for estimating carcass weight, longissimus dorsi muscle weight, lean meat weight, fat weight, lean meat, and fat percentage in live lambs (R =0.94, RMSE = 0.62; R =0.73, RMSE = 0.02; R =0.86, RMSE = 0.47; R =0.78, RMSE = 0.63; R =0.73, RMSE = 0.02; R =0.65, RMSE = 0.03, respectively). LSSVM algorithm was a potential alternative to the conventional MLR method. The results demonstrated that LSSVM model might have great potential to be applied to the evaluation of sheep with superior carcass traits by combining with real-time ultrasound technology.

The effect of self-absorption compensation methods on the quantitative analysis of soil samples using Laser-induced breakdown spectroscopy

When the detection of heavy metal elements in the soil was conducted using Laser-induced breakdown spectroscopy (LIBS), the accuracy of the calibration model can be affected by the self-absorption effect. In this work, the piecewise fitting and the least square support vector machine (LSSVM) were used to reduce the influence of self-absorption effect on quantitative analysis of the Cr element in the soil. With the increase of the Cr element content, the increased rate of the Cr element emission intensity decreases using internal standard method under the best conditions. The non-linear relationship exists between the content of the Cr element and the emission intensity of the Cr element, which reduces the accuracy of the quantitative analysis. Hence, the self-absorption coefficient (SA) was evaluated. The results showed that the self-absorption effect becomes more and more serious with the increase of element content. Therefore, the piecewise fitting and the LSSVM algorithm were used to establish calibration model. The correlation coefficients of the calibration model based on piecewise fitting were 0.9918, 0.9787 and 0.9655, respectively. The root mean square error (RMSE) and mean relative error (MRE) of the calibration model of piecewise fitting were 1.2853 wt% and 15.64%, respectively. Compared with the piecewise fitting calibration model, the LSSVM calibration model performed best, with an overall correlation coefficient of 0.9902, RMSE and MRE of 0.3878 wt% and 8.9926%, respectively. The results indicated that the LSSVM algorithm can be used as a method of reducing the influence of the self-absorption effect on the calibration model.

Optimization of vacuum assisted heat reflux extraction process of radix isatidis using least squares-support vector machine algorithm

• An improved vacuum assisted heat reflux extraction (VAHRE) technique was proposed and applied to extract Radix isatidis . • The least-squares support vector machine (LS-SVM) algorithm was introduced to improve the optimization's predictive accuracy. • VAHRE is a promising technique for improving extraction yield of other thermally sensitive resources. An improved vacuum-assisted heat reflux extraction (VAHRE) technique was proposed and applied to extract Radix Isatidis. The extraction parameters of VAHRE, including the boiling temperature, extraction cycles, extraction time, soak time, and liquid-solid ratio, were carefully optimized with a single factor experiment. The least-squares support vector machine (LS-SVM) novel machine learning algorithm was introduced to improve the optimization's predictive accuracy. The results indicated that the LS-SVM model had better performance, with a higher R 2 and lower RMSE value than those of the conventional quadratic polynomial model (QPM). Compared with conventional reference extraction methods, the VAHRE method gave a higher extraction yield due to indirubin's reduced for volatile loss and more efficient release from the plant matrix with the aid of a vacuum. This is the first study on optimizing the extraction process of Radix Isatidis using VAHRE and LS-SVM algorithms. The present findings also demonstrated that VAHRE was a promising procedure for extracting indirubin from Radix Isatidis, which shows great potential for becoming an alternative system for industrial scale-up applications.

Classification of Electronic Nose Data Using the Least Squares Support Vector Machine

In this study, the response signals of three kinds of dry alfalfa volatile odors were collected by an electronic nose (E-nose), and the collected data were processed by principal component analysis (PCA) and linear discriminant analysis (LDA). A least squares support vector machine (LS-SVM) model was established to classify and evaluate the data. For the combined E-nose algorithm, the classification accuracies of the PCA-LS-SVM and LDA-LS-SVM models are 85% and 100%, respectively. LDA as the input model has better classification accuracy than the PCA-based model. The results show that the combination of the LDA and LS-SVM algorithms using an E-nose signal is effective in identifying different drying alfalfa. The performance of the LDA-based LS-SVM model is slightly higher than that of the PCA-based LS-SVM model. It can be concluded that the E-nose system combined with the LDA-based model has great potential to distinguish different dry alfalfa.

Development of computational methods for estimation of current efficiency and cell voltage in a Chlor-alkali membrane cell

ABSTRACT This work presents proposing two artificial intelligence methods including Least squares support vector machine (LSSVM) and Adaptive neuro fuzzy inference system (ANFIS) for the prediction of caustic current efficiency (CCE) and cell voltage as a function of pH, current density, brine concentration, electrolyte velocity, operating temperature, and run time. The predictions of LSSVM and ANFIS models were evaluated by the experimental values of this process graphically and statistically. The overall R-squared values of LSSVM and ANFIS for prediction of CCE were 0.999 and 0.972, respectively. On the other hand, these values for cell voltage prediction were 1 and 0.998. According to the CCE and cell voltage predictions results, LSSVM algorithm has great performance in prediction of chlor-alkali membrane cell processes. Furthermore, artificial intelligence methods can have wide use in electrolytic processes to enhance power consumption.

Regional Zenith Tropospheric Delay Modeling Based on Least Squares Support Vector Machine Using GNSS and ERA5 Data

The meteorological reanalysis data has been widely applied to derive zenith tropospheric delay (ZTD) with a high spatial and temporal resolution. With the rapid development of artificial intelligence, machine learning also begins as a high-efficiency tool to be employed in modeling and predicting ZTD. In this paper, we develop three new regional ZTD models based on the least squares support vector machine (LSSVM), using both the International GNSS Service (IGS)-ZTD products and European Centre for Medium-Range Weather Forecasts Reanalysis 5 (ERA5) data over Europe throughout 2018. Among them, the ERA5 data is extended to ERA5S-ZTD and ERA5P-ZTD as the background data by the model method and integral method, respectively. Depending on different background data, three schemes are designed to construct ZTD models based on the LSSVM algorithm, including the without background data, with the ERA5S-ZTD, and with the ERA5P-ZTD. To investigate the advantage and feasibility of the proposed ZTD models, we evaluate the accuracy of two background data and three schemes by segmental comparison with the IGS-ZTD of 85 IGS stations in Europe. The results show that the overall average Root Mean Square Errors (RMSE) value of all sites is 30.1 mm for the ERA5S-ZTD, and 10.7 mm for the ERA5P-ZTD. The overall average RMSE is 25.8 mm, 22.9 mm, and 9 mm for the three schemes, respectively. Moreover, the overall improvement rate is 19.1% and 1.6% for the ZTD model with ERA5S-ZTD and ERA5P-ZTD, respectively. In order to explore the reason of the lower improvement for the ZTD model with ERA5P-ZTD, the loop verification is performed by estimating the ZTD values of each available IGS station. In actuality, the monthly improvement rate of estimated ZTD is positive for most stations, and the biggest improvement rate can even reach about 40%. The negative rate mainly comes from specific stations, these stations are located on the edge of the region, near the coast, as well as the lower similarity between the individual verified station and training stations.