Least Squares Support Vector Machine Research Articles

Data‐driven nonlinear state observation for controlled systems: A kernel method and its analysis

AbstractThis work proposes a data‐driven state observation algorithm for nonlinear dynamical systems, when the true state trajectory is not measurable and hence the states information needs to be reconstructed from input and output measurements. Such a reduction is formed by kernel canonical correlation analysis (KCCA), which (i) implicitly maps the available input–output data into a higher‐dimensional feature space, namely the reproducing kernel Hilbert space (RKHS); (ii) finds a projection of the past input–output data and a projection of the future input–output data with maximal correlation; and (iii) identifies the projected inputs and outputs, namely the canonical variates, as the observed states. We adopt a least squares support vector machine (LS‐SVM) formulation for KCCA, which imposes regularization on the vectors that specify the projections and is amenable to convex optimization. We prove theoretically that, based on the statistical consistency of KCCA, the observed states determined by the proposed state observer has a guaranteed correlativity with the actual states (when properly transformed). Furthermore, such observed states, when supplemented with the information of succeeding inputs, can be used to predict the succeeding outputs with guaranteed upper bound on the prediction error. Case studies are performed on two numerical examples and an exothermic continuously stirred tank reactor (CSTR).

A novel optimization rainfall coupling model based on stepwise decomposition technique

Traditional decomposition integration models decompose the original sequence into subsequences, which are then proportionally divided into training and testing periods for modeling. Decomposition may cause data aliasing, then the decomposed training period may contain part of the test period data. A more effective method of sample construction is sought in order to accurately validate the model prediction accuracy. Semi-stepwise decomposition (SSD), full stepwise decomposition (FSD), single model semi-stepwise decomposition (SMSSD), and single model full stepwise decomposition (SMFSD) techniques were used to create the samples. This study integrates Variational Mode Decomposition (VMD), African Vulture Optimization Algorithm (AVOA), and Least Squares Support Vector Machine (LSSVM) to construct a coupled rainfall prediction model. The influence of different VMD parameters α is examined, and the most suitable stepwise decomposition machine learning coupled model algorithm for various stations in the North China Plain is selected. The results reveal that SMFSD is relatively the most suitable tool for monthly precipitation forecasting in the North China Plain. Among the predictions for the five stations, the best overall performance is observed at Huairou Station (RMSE of 18.37 mm, NSE of 0.86, MRE of 107.2%) and Jingxian Station (RMSE of 24.74 mm, NSE of 0.86, MRE of 51.71%), while Hekou Station exhibits the poorest performance (RMSE of 25.11 mm, NSE of 0.75, MRE of 173.75%).

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.

Rapid classification of rice according to storage duration via near-infrared spectroscopy and machine learning

Rice is the most important staple crop for more than half of the world's population. As rice quality can deteriorate during storage, methods that can effectively classify rice according to its storage duration are essential. However, existing methods of assessing rice storage time are time-consuming, laborious, and incompatible with modern industrial processing technologies. Therefore, we investigated the ability of near-infrared spectroscopy combined with machine learning algorithms to distinguish rice storage duration. A total of 482 rice samples were analyzed, which included 74, 100, and 308 samples produced during 2015–2016, 2017–2018, and 2020–2021, respectively. Five pre-processing methods were initially applied to the spectra to enhance the accuracy of the discrimination model. Subsequently, two-dimensional correlation spectroscopy and competitive adaptive reweighted sampling (CARS) were used to extract the characteristic spectra associated with storage time. Finally, three pattern recognition methods (K-nearest neighbor analysis, linear discriminant analysis, and least squares support vector machine (LS-SVM)) were compared for their effectiveness in constructing classification models. The results indicated that the best model for identifying the storage duration of rice was established after spectral pre-processing with the standard normal variate and first derivative, using the CARS algorithm to select feature wavelengths, and applying the LS-SVM modeling method, which together yielded correct identification rates of 99.72% and 91.67% for the calibration and validation sets, respectively. Thus, we propose near-infrared spectroscopy coupled with machine learning algorithms as an effective approach for classifying rice according to storage duration, which can facilitate evaluations of rice freshness in the market.

Pipeline Leak Detection: A Comprehensive Deep Learning Model Using CWT Image Analysis and an Optimized DBN-GA-LSSVM Framework.

Detecting pipeline leaks is an essential factor in maintaining the integrity of fluid transport systems. This paper introduces an advanced deep learning framework that uses continuous wavelet transform (CWT) images for precise detection of such leaks. Transforming acoustic signals from pipelines under various conditions into CWT scalograms, followed by signal processing by non-local means and adaptive histogram equalization, results in new enhanced leak-induced scalograms (ELIS) that capture detailed energy fluctuations across time-frequency scales. The fundamental approach takes advantage of a deep belief network (DBN) fine-tuned with a genetic algorithm (GA) and unified with a least squares support vector machine (LSSVM) to improve feature extraction and classification accuracy. The DBN-GA framework precisely extracts informative features, while the LSSVM classifier precisely distinguishes between leaky and non-leak conditions. By concentrating solely on the advanced capabilities of ELIS processed through an optimized DBN-GA-LSSVM model, this research achieves high detection accuracy and reliability, making a significant contribution to pipeline monitoring and maintenance. This innovative approach to capturing complex signal patterns can be applied to real-time leak detection and critical infrastructure safety in several industrial applications.

Feature extraction method for ultrasonic pipeline defects based on fractional-order VMD

ABSTRACT Ensuring the safety of pipeline transportation is vital for societal well-being. Traditional methods for identifying defects in steel pipelines through ultrasonic echo signal pattern recognition often fail to extract comprehensive and effective features crucial for accurate defect detection. This study introduces an innovative feature extraction method employing a fractional Fourier transform variational modal decomposition (FRFT-VMD), hereafter referred to as the fractional-order VMD algorithm. This method utilises the fourth-order central moment and envelope entropy to optimise several key parameters: the fractional order in the Fourier transform, the number of decomposition layers, and the penalty factor in variational modal decomposition. To evaluate the effectiveness of the proposed method, ultrasonic echo signals from both finite element simulations and experimental platforms were analysed using the FRFT-VMD technique. The features extracted were then classified using a Least Squares Support Vector Machine (LSSVM) to determine defect depths. The results show a recognition accuracy of 95.2% in simulated signals and 89.1% in experimentally measured signals across various defect depths, indicating a significant improvement over existing feature extraction methodologies. The fractional-order VMD algorithm proves to be superior in extracting features that enhance the accuracy of defect identification in steel pipelines.

Dynamic internal resistance modeling and thermal characteristics of lithium-ion batteries for electric vehicles by considering state of health

Attempting to solve the problem of inconsistent dynamic thermal characteristics caused by transient changes in internal resistance of lithium-ion batteries (LIBs) for electric vehicles (EVs) under service conditions, taking a 9.4Ah prismatic LIB as the study object, the internal resistance data under different state of health (SOH), state of charge (SOC), temperature (T), charge/discharge rates of LIB are obtained through the mixed-rate hybrid pulse power characterization (MR-HPPC) test. Based on this, a dynamic internal resistance model (DIRM) considering the SOH is proposed by the prediction of the least squares support vector machines (LS-SVM) model. In this study, a thermoelectric coupling model and a resistance-thermal co-simulation of the LIB are established based on DIRM, and the temperature rise characteristics under constant rates and dynamic operating conditions are investigated at different SOH states. The maximum DIRM error (DIRME) between DIRM-based simulated maximum transient temperature (Tmax-tra) and test Tmax-tra is 0.88 °C at constant charge/discharge rate operating conditions, while the maximum DIRME between DIRM-based simulated Tmax-tra and test Tmax-tra is 0.21 °C under dynamic operating conditions. The results can provide a theoretical support for improving the modeling precision of the heat generation of LIBs with different aging levels for accurate thermal management design.

Optimization of PV module ash accumulation prediction based on an improved vulture algorithm

Abstract In this research, an ash accumulation prediction model based on the Improved Bald Eagle Algorithm (IBES) optimization is proposed, and a least-squares support vector machine (LSSVM) is used to investigate the correlation between climatic parameters and the quantity of ash deposition on PV panel surfaces. Ash deposit affects PV panel output power over time and is influenced by meteorological factors. Following a thorough selection procedure, meteorological variables like wind speed and rainfall are used in the model to forecast the amount of ash that will accumulate on the slab. The original condor method was prone to local optimum convergence and had a slow convergence rate. These weaknesses are addressed by the optimal selection of the next iteration, which introduces the Cauchy variation operator to mutate the population’s optimal individuals. The optimization parameters of the revised algorithm are incorporated into the model and results are compared to models of other optimization algorithms. The outcomes demonstrate that the IBES-LSSVM ash accumulation prediction model has a higher degree of fit and a reduced prediction error.

Rapid monitoring of the spatial distribution of soil organic matter using unmanned aerial vehicle imaging spectroscopy

ABSTRACT An existing technique for quickly obtaining the spatial distribution data of soil organic matter (SOM) involves combining an unmanned aerial vehicle (UAV) platform and imaging spectroscopy technology; this technique is suitable for precision agricultural management and real-time monitoring. In this study, the average spectral data were first extracted via circular regions of interest (ROIs) of different radii and modelled using the measured SOM to determine the optimal extraction range for the spectral data. Partial least-squares regression (PLSR) and support vector machine (SVM) models were constructed based on the raw spectra, standard normal transform spectra, multiple scattering-corrected spectra, and first-order differential spectra. The difference index, ratio index, and normalized index were calculated and analysed for their correlation with SOM content, and the spectral indices were screened to establish the SOM prediction model. Finally, the accuracy of the model was evaluated, and we selected the optimal model to map the spatial distribution of SOM. The results of our study show that 1) the radius of the ROI significantly affects the model’s accuracy; 2) the accuracy of the nonlinear SVM model is much higher than that of the linear PLSR model; 3) the prediction model based on spectral indices is better than full-band model. This study can serve as a model for the application of UAV imaging spectroscopy technology to field-scale SOM estimations and rapid monitoring, as well as provide technical support for precision agriculture and climate change studies.

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.

Effective approach to assess higher heating value of biomass from ultimate and proximate analysis

AbstractFor proper design and operation of biomass‐based energy systems, it is important to determine the higher heating value (HHV) of biomass. In this paper, two machine learning (ML) approaches, namely extra trees (ET) and least squares support vector machine (LSSVM), are used to predict the value of HHV associated with biofuels. The data required for HHV calculation, including proximate and ultimate analyses datasets, were collected from the literature. The performances of these two ML approaches for predicting biomass HHV were then compared with other smart models available in the literature. Even though the available empirical models can predict the biomass HHV with acceptable precision, it was found that our proposed ML techniques have a superior performance based on the error analysis; the proposed approaches also consider all key biomass characteristics in the developed models. In addition, the ET model proved to be slightly more accurate compared to the LSSVM model. Additionally, the developed proximate‐based ET model showed better performance compared to the ultimate‐based ET model. The most influential parameters in the developed ET models for the proximate and ultimate approaches were determined to be ash fraction and carbon fraction, respectively. Finally, it was concluded that the smart modelling techniques can be utilized as a robust and reliable alternative predictive methodology to replace direct laboratory measurement of the biomass HHV.

Numerical solutions to one dimensional linear Volterra–Fredholm integral equations based on LS-SVM model

This paper introduces a novel numerical approach using least squares support vector machine (LS-SVM) to handle one dimensional linear Volterra–Fredholm integral equations. This method can also handle weak singular kernel Fredholm/Volterra integral equations and linear systems of Volterra–Fredholm integral equations. By minimizing errors and utilizing least squares support vector machines, the approach derives continuous closed-form solutions to the origin problem. Ultimately, the method offers an efficient numerical approximation for solving Volterra–Fredholm integral equations through the resolution of linear equations. The paper includes multiple numerical examples that demonstrate the effectiveness and superiority of the proposed method.

Discrimination of New and Aged Seeds Based on On-Line Near-Infrared Spectroscopy Technology Combined with Machine Learning

The harvest year of maize seeds has a significant impact on seed vitality and maize yield. Therefore, it is vital to identify new seeds. In this study, an on-line near-infrared (NIR) spectra collection device (899–1715 nm) was designed and employed for distinguishing maize seeds harvested in different years. Compared with least squares support vector machine (LS-SVM), k-nearest neighbor (KNN), and extreme learning machine (ELM), the partial least squares discriminant analysis (PLS-DA) model has the optimal recognition performance for maize seed harvest years. Six different preprocessing methods, including Savitzky–Golay smoothing (SGS), standard normal variate transformation (SNV), multiplicative scatter correction (MSC), Savitzky–Golay 1 derivative (SG-D1), Savitzky–Golay 2 derivative (SG-D2), and normalization (Norm), were used to improve the quality of the spectra. The Monte Carlo cross-validation uninformative variable elimination (MC-UVE), competitive adaptive reweighted sampling (CARS), bootstrapping soft shrinkage (BOSS), successive projections algorithm (SPA), and their combinations were used to obtain effective wavelengths and decrease spectral dimensionality. The MC-UVE-BOSS-PLS-DA model achieved the classification with an accuracy of 88.75% using 93 features based on Norm preprocessed spectral data. This study showed that the self-designed NIR collection system could be used to identify the harvested years of maize seed.

Non-Destructive Detection of Cerasus Humilis Fruit Quality by Hyperspectral Imaging Combined with Chemometric Method

Cerasus Humilis fruit is susceptible to rapid color changes post-harvest, which degrades its quality. This research utilized hyperspectral imaging technology to detect and visually analyze the soluble solid content (SSC) and firmness of the fruit, aiming to improve quality and achieve optimal pricing. Four maturity stages (color turning stage, coloring stage, maturity stage, and fully ripe stage) of Cerasus Humilis fruit were examined using hyperspectral images (895–1700 nm) alongside data collection on SSC and firmness. These samples were divided into a calibration set and a validation set with a ratio of 3:1 by sample set partitioning based on the joint X-Y distances (SPXY) method. The original spectral data was processed by a spectral preprocessing method. Multiple linear regression (MLR) and nonlinear least squares support vector machine (LS-SVM) detection models were established using feature wavelengths selected by the successive projections algorithm (SPA), competitive adaptive reweighted sampling (CARS), uninformative variable elimination (UVE), and two combined downscaling algorithms (UVE-SPA and UVE-CARS), respectively. For SSC and firmness detection, the best models were the SNV-SPA-LS-SVM model with 18 feature wavelengths and the original spectra-UVE-CARS-LS-SVM model with eight feature wavelengths, respectively. For SSC, the correlation coefficient of prediction (Rp) was 0.8526, the root mean square error of prediction (RMSEP) was 0.9703, and the residual prediction deviation (RPD) was 1.9017. For firmness, Rp was 0.7879, RMSEP was 1.1205, and RPD was 2.0221. Furthermore, the optimal model was employed to retrieve the distribution of SSC and firmness within Cerasus Humilis fruit. This retrieved information facilitated visual inspection, enabling a more intuitive and comprehensive assessment of SSC and firmness at each pixel level. These findings demonstrated the effectiveness of hyperspectral imaging technology for determining SSC and firmness in Cerasus Humilis fruit. This paves the way for online monitoring of fruit quality, ultimately facilitating timely harvesting.

Non-destructive prediction of anthocyanin concentration in whole eggplant peel using hyperspectral imaging

Accurately detecting the anthocyanin content in eggplant peel is essential for effective eggplant breeding. The present study aims to present a method that combines hyperspectral imaging with advanced computational analysis to rapidly, non-destructively, and precisely measure anthocyanin content in eggplant fruit. For this purpose, hyperspectral images of the fruits of 20 varieties with diverse colors were collected, and the content of the anthocyanin were detected using high performance liquid chromatography (HPLC) methods. In order to minimize background noise in the hyperspectral images, five preprocessing algorithms were utilized on average reflectance spectra: standard normalized variate (SNV), autoscales (AUT), normalization (NOR), Savitzky–Golay convolutional smoothing (SG), and mean centering (MC). Additionally, the competitive adaptive reweighted sampling (CARS) method was employed to reduce the dimensionality of the high-dimensional hyperspectral data. In order to predict the cyanidin, petunidin, delphinidin, and total anthocyanin content of eggplant fruit, two models were constructed: partial least squares regression (PLSR) and least squares support vector machine (LS-SVM). The HPLC results showed that eggplant peel primarily contains three types of anthocyanins. Furthermore, there were significant differences in the average reflectance rates between 400–750 nm wavelength ranges for different colors of eggplant peel. The prediction model results indicated that the model based on NOR CARS LS-SVM achieved the best performance, with a squared coefficient of determination (R2) greater than 0.98, RMSEP and RMSEC less than 0.03 for cyanidin, petunidin, delphinidin, and total anthocyanin predication. These results suggest that hyperspectral imaging is a rapid and non-destructive technique for assessing the anthocyanin content of eggplant peel. This approach holds promise for facilitating the more effective eggplant breeding.

Multi-step carbon emissions forecasting model for industrial process based on a new strategy and machine learning methods

The rising industrial sector capacity increases carbon emissions, necessitating a low-carbon transformation for global sustainability. Accurate multi-step forecasting of industrial carbon emissions is crucial for optimizing production, reducing energy consumption, improving efficiency, and achieving decarbonization. However, current forecasting faces challenges like model uncertainty and low accuracy with multi forecasting steps. To address these issues, this study proposed a multi-step carbon emissions forecasting model for industrial processes. Firstly, a new multi-step forecasting strategy framework was proposed. Secondly, SHapley Additive exPlanations (SHAP) and lagged autocorrelation analysis were used to extract key features affecting industrial carbon emissions. On this basis, the grey model, autoregressive moving average (ARMA) model, and least squares support vector machine (LSSVM) method were used to build forecasting models separately. The weights of the three models were solved using the induced ordered weighted average operator and the Monte Carlo search tree (MCST) method. The final forecasting results were obtained by using the weighted summation method. The data collected from the real industry were used to validate the proposed model. The results showed that the proposed model could accurately forecast industrial carbon emissions within 12 steps and its MAPE is less than 10%. The proposed multi-step industrial carbon emissions forecasting model can provide data support for industrial energy saving, carbon reduction, and green and sustainable development.

Modeling and Optimization of an Enhanced Soft Sensor for the Fermentation Process of Pichia pastoris.

This paper proposes a novel soft sensor modeling approach, MIC-TCA-INGO-LSSVM, to address the decline in performance of soft sensor models during the fermentation process of Pichia pastoris, caused by changes in working conditions. Initially, the transfer component analysis (TCA) method is utilized to minimize the differences in data distribution across various working conditions. Subsequently, a least squares support vector machine (LSSVM) model is constructed using the dataset adapted by TCA, and strategies for improving the northern goshawk optimization (INGO) algorithm are proposed to optimize the parameters of the LSSVM model. Finally, to further enhance the model's generalization ability and prediction accuracy, considering the transfer of knowledge from multiple-source working conditions, a sub-model weighted ensemble scheme is proposed based on the maximum information coefficient (MIC) algorithm. The proposed soft sensor model is employed to predict cell and product concentrations during the fermentation process of Pichia pastoris. Simulation results indicate that the RMSE of the INGO-LSSVM model in predicting cell and product concentrations is reduced by 47.3% and 42.1%, respectively, compared to the NGO-LSSVM model. Additionally, TCA significantly enhances the model's adaptability when working conditions change. Moreover, the soft sensor model based on TCA and the MIC-weighted ensemble method achieves a reduction of 41.6% and 31.3% in the RMSE for predicting cell and product concentrations, respectively, compared to the single-source condition transfer model TCA-INGO-LSSVM. These results demonstrate the high reliability and predictive performance of the proposed soft sensor method under varying working conditions.

Double decomposition with enhanced least-squares support vector machine to predict water level

ABSTRACT As global climates undergo changes, the frequency of water-related disasters rises, leading to significant economic losses and safety hazards. During flood events, river water levels exhibit unpredictable fluctuations, introducing considerable noise that poses challenges for accurate prediction. A prediction of water level by using existing water level data makes a major contribution to forecasting flood. Enhanced least-squares support vector machine (ELSSVM) is utilized by integrating an additional extra bias error control term. In this study, least-squares support vector machine (LSSVM) and ELSSVM optimized by the genetic algorithm (GA) were chosen to be compared with the help of data decomposition methods to improve daily water level prediction accuracy. Double empirical mode decomposition (DEMD) will be integrated with LSSVM and ELSSVM. Thus, the models are named LSSVM-GA, ELSSVM-GA, empirical mode decomposition (EMD)-LSSVM-GA, EMD-ELSSVM-GA, DEMD-LSSVM-GA, and DEMD-ELSSVM-GA. The proposed models are used in forecasting the water level of Klang River in Sri Muda, Malaysia. The behavior proposed models are investigated and compared based on several performance metrics. The results demonstrated that the DEMD-ELSSVM-GA model outperformed the other models based on the performance analysis in forecasting the water level with RMSE = 0.2536 m and R2 = 0.8596 for testing data that indicate the forecasting accuracy.

Cutting-edge tool wear monitoring in AISI4140 steel hard turning using least square-support vector machine

ABSTRACT This research addresses the critical challenge of tool wear monitoring in AISI4140 steel hard turning through the innovative application of a Least Square-Support Vector Machine (LS-SVM) prediction model. While acknowledging the growing significance of hard turning over conventional grinding techniques, the background also recognizes the challenges posed by accelerated tool wear and decreased productivity. The main goal is to create a reliable tool wear prediction model that is tailored to harsh turning circumstances. Material selection, cutting force measurement, acceleration measurement, and accurate tool wear measurement are all included in the experimental procedures. Using time and frequency domain analyses, the research methodically examines how cutting force and acceleration affect tool wear. For feature selection, non-linear regression is used to determine which parameters have the greatest influence on wear. A comprehensive training and validation procedure, structural clarification, and a detailed mathematical foundation are used in the development of the LS-SVM-based tool wear prediction model. The presentation of the findings and related discussions explores the impact of acceleration and cutting force on wear. The LS-SVM model’s successful application for precise tool wear prediction in AISI4140 steel hard turning is highlighted in the conclusions, demonstrating the model’s potential to improve tool lifespan and manufacturing efficiency.

Forecasting ionospheric TEC using least squares support vector machine and moth-flame optimization methods in China

The total electron content (TEC) of the ionosphere is an important parameter to describe the ionosphere, and it is a great significance to monitor and predict it accurately. In this paper, a hybrid ionospheric TEC prediction model based on the least squares support vector machine (LSSVM) and the Moth-Flame Optimization (MFO) algorithm is proposed. The parameters of the LSSVM model are optimized by the MFO algorithm. We use observation data of 15 GNSS stations from the Crustal Movement Observation Network of China (CMONOC) to extract ionospheric TEC from 2012 to 2019. The ionospheric TEC is forecasted using solar and geomagnetic activity indices in both the low solar activity year (2019) and the high solar activity year (2015). The results show that the prediction performance of the MFO_LSSVM model is significantly better than that of the IRI model, SVM model, and LSSVM model. Compared with the other three models, there are more stable prediction results in the low and high solar activity years. At the same time, the predicted value of the MFO_LSSVM model has a good correlation with the measured value, and it also has good prediction potential in areas with active geomagnetic activity. The comparison with the Long Short-Term Memory (LSTM) model shows that the MFO_LSSVM model has better performance than the single LSTM model. In conclusion, the MFO_LSSVM model can accurately predict ionospheric TEC in China, and has better accuracy than traditional long-term and short-term models.