Least Squares Support Vector Machine Model Research Articles

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.

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.

Research on blasting vibration prediction based on BFO-LSSVM and its engineering application

In order to realize the accurate prediction of blasting vibration, the LS-SVM optimization model based on BFO algorithm is constructed with the help of bacterial foraging algorithm (BFO) and least squares support vector machine (LS-SVM) theory. 30 groups of blasting data are used as training samples to test the prediction accuracy of the model, and the main factors affecting the propagation of blasting vibration are selected as the input factors, such as single shot charge, blasting center distance, elevation difference, blockage, hole depth and other factors as the input factors, and blasting vibration as the output factor of the prediction model. The results show that the prediction accuracy of BFO-LSSVM model is higher than that of LS-SVM model under the same sample size. Taking the measured vibration data of excavation blasting of Wuqiangxi power station as an example, the average error of BFO-LSSVM model is 5.57%, which verifies the feasibility and practicability of the prediction model.

Sparse L0-norm least squares support vector machine with feature selection

Least squares support vector machine (LSSVM) is a powerful classification tool based on hyperplanes. But the classical LSSVM does not perform well on small sample size data sets (SSS) because it lacks feature selection capability. To address this issue, we introduce an L0-norm regularization term into the objective function of LSSVM, and propose a new sparse LSSVM model called L0-LSSVM. However, the introduction of the L0-norm makes the resulting optimization problem nonconvex and nonsmooth. To overcome these challenges, instead of using the traditional convex or non-convex approximation of the L0-norm, we design an efficient algorithm for L0-LSSVM based on alternating direction method of multipliers (ADMM) where the L0-norm is handled by employing the proximity operator. Numerical results demonstrate that L0-LSSVM not only exhibits excellent generalization performance and feature selection capability but also offers a substantial improvement in computational speed.

Crater-Spectrum Feature Fusion Method for Panax notoginseng Cadmium Detection Using Laser-Induced Breakdown Spectroscopy.

Panax notoginseng (P. notoginseng) is a valuable herbal medicine, as well as a dietary food supplement known for its satisfactory clinical efficacy in alleviating blood stasis, reducing swelling, and relieving pain. However, the ability of P. notoginseng to absorb and accumulate cadmium (Cd) poses a significant environmental pollution risk and potential health hazards to humans. In this study, we employed laser-induced breakdown spectroscopy (LIBS) for the rapid detection of Cd. It is important to note that signal uncertainty can impact the quantification performance of LIBS. Hence, we proposed the crater-spectrum feature fusion method, which comprises ablation crater morphology compensation and characteristic peak ratio correction (CPRC), to explore the feasibility of signal uncertainty reduction. The crater morphology compensation method, namely, adding variables using multiple linear regression (MLR) analysis, decreased the root-mean-square error of the prediction set (RMSEP) from 7.0233 μg/g to 5.4043 μg/g. The prediction results were achieved after CPRC pretreatment using the calibration curve model with an RMSEP of 3.4980 μg/g, a limit of detection of 1.92 μg/g, and a limit of quantification of 6.41 μg/g. The crater-spectrum feature fusion method reached the lowest RMSEP of 2.8556 μg/g, based on a least-squares support vector machine (LSSVM) model. The preliminary results suggest the effectiveness of the crater-spectrum feature fusion method for detecting Cd. Furthermore, this method has the potential to be extended to detect other toxic metals in addition to Cd, which significantly contributes to ensuring the quality and safety of agricultural production.

Underwater Sound Speed Field Forecasting Based on the Least Square Support Vector Machine

Underwater sound speed is one of the most significant factors that affects high-accuracy underwater acoustic positioning and navigation. Due to its complex temporal variation, the forecasting of the underwater sound speed field (SSF) becomes a challenging task. Taking advantage of machine learning methods, we propose a new method for SSF forecasting based on the least square support vector machine (LSSVM) and a multi-parameter model, aiming to enhance the forecasting accuracy of underwater SSF with hourly resolution. We first use a matching extension method to standardize profile data and train the LSSVM with the parameters of observation time, temperature, salinity, and depth. We then employ radial basis function kernels to construct the forecasting model of SSF. We validate the feasibility and effectiveness of the LSSVM model by comparing it with the polynomial fitting (PF) and back propagation neural network (BPNN) methods, using hourly data obtained from the measured data and open data. The results show that the means of the root mean square for the LSSVM based on the observation time parameter and the LSSVM based on the multi-parameter model achieve 0.51 m/s and 0.45 m/s, respectively, presenting a significant improvement compared with the PF (0.82 m/s) and BPNN (0.76 m/s) methods.

Improved prediction of groundwater depth in urban areas using the EWT-S–G-GRU and LSSVM model: a case study of Xinxiang City

ABSTRACT The improvement in predicting groundwater depth accuracy has significant implications for the management, ecological environment protection, and economic and social development of regional water resources. Employing empirical wavelet transform (EWT) for nonlinear processing, Savitzky–Golay (S–G) filtering to reduce high-frequency noise, gate recurrent unit (GRU) neural network for linear feature signal processing, and least squares support vector machine (LSSVM) for nonlinear signal handling, we established a comprehensive model combining EWT-S–G-GRU and LSSVM. The results demonstrate that the proposed model exhibits superior accuracy in groundwater depth prediction, with an average relative error of only 2.14% and Nash–Sutcliffe efficiency (NSE) of 0.93. This outperforms the other four models, with average relative errors of 12.88%, 11.90%, 7.07%, and 11.10%, and NSE values of 0.58, 0.56, 0.71, and 0.73, respectively. The superiority of the model established in this study is attributed to its effective handling of both nonlinear and linear features of groundwater, thereby enhancing predictive accuracy. The EWT-S–G-GRU and LSSVM model proves to be more reliable in revealing the spatial distribution and dynamic changes of future groundwater, providing a robust reference for the rational development and utilization of groundwater in the urban area of Xinxiang City.

Prediction of Energy Consumption in a Coal-Fired Boiler Based on MIV-ISAO-LSSVM

Aiming at the problem that the energy consumption of the boiler system varies greatly under the flexible peaking requirements of coal-fired units, an energy consumption prediction model for the boiler system is established based on a Least-Squares Support Vector Machine (LSSVM). First, the Mean Impact Value (MIV) algorithm is used to simplify the input characteristics of the model and determine the key operating parameters that affect energy consumption. Secondly, the Snow Ablation Optimizer (SAO) with tent map, adaptive t-distribution, and the opposites learning mechanism is introduced to determine the parameters in the prediction model. On this basis, based on the operation data of an ultra-supercritical coal-fired unit in Xinjiang, China, the boiler energy consumption dataset under variable load is established based on the theory of fuel specific consumption. The proposed prediction model is used to predict and analyze the boiler energy consumption, and a comparison is made with other common prediction methods. The results show that compared with the LSSVM, BP, and ELM prediction models, the average Relative Root Mean Squared Errors (aRRMSE) of the LSSVM model using ISAO are reduced by 2.13%, 18.12%, and 40.3%, respectively. The prediction model established in this paper has good accuracy. It can predict the energy consumption distribution of the boiler system of the ultra-supercritical coal-fired unit under variable load more accurately.

Prediction of the Harvest Time of Cabernet Sauvignon Grapes Using Near-Infrared Spectroscopy

Harvest time assessment during the grape-ripening process can provide meaningful information for vineyard harvest scheduling. The purpose of this study was to investigate the identification of the harvest time of grape clusters using near-infrared (NIR) spectroscopy. During the harvest season from September to October 2019, bunches of Cabernet Sauvignon grapes were examined. Before establishing two classification models, namely partial least-squares discriminant analysis (PLS-DA) and support vector machine (SVM) models, raw spectra were processed by different pre-processing methods, including multiplicative signal correction (MSC), mean-centering, the standard normal variable (SNV), and the Savitzky-Golay method. Competitive adaptive weighted sampling (CARS) and the successive projections algorithm (SPA) were employed to select the optimal wavenumbers. The results indicate that NIR spectroscopy is a potentially promising approach for the rapid identification of different harvest times of Cabernet Sauvignon grapes, and the proposed technique is helpful for the prediction of ripened and over-ripened Cabernet Sauvignon grapes during the harvest time.

Short-term wind speed forecasting based on a hybrid model that integrates PSO-LSSVM and XGBoost

Abstract A groundbreaking method is proposed to mitigate the impact of unpredictable fluctuations in wind velocity on wind power generation. This innovative approach integrates the particle swarm optimization (PSO)-least squares support vector machine (LSSVM) and XGBoost models in a harmonious manner. Initially, the raw wind speed data is subjected to wavelet threshold denoising to reduce noise and volatility. For short-term wind speed prediction, a PSO-LSSVM-XGBoost model is introduced. After the initial wind speed sequence undergoes wavelet threshold denoising, the enhanced sequence is forecasted using the LSSVM model, with its hyperparameters optimized through the PSO algorithm. The errors, obtained by subtracting the predicted values from the original data, are compensated using XGBoost. The final forecast results combine the rectified error data with the initial projected results. Experimental findings demonstrate the model’s remarkable capability to enhance prediction performance and accuracy.

Short-term PV power prediction based on VMD-CNN-IPSO-LSSVM hybrid model

Abstract This article discusses the significance and obstacles of short-term power prediction in photovoltaic systems and introduces a hybrid model for photovoltaic short-term power prediction technology based on variational mode decomposition (VMD), convolutional neural network (CNN), improved particle swarm optimization (IPSO) and least squares support vector machine (LSSVM). In the initial stage, the photovoltaic generation signal is decomposed into multiple Intrinsic mode functions (IMFs) using VMD to enhance the extraction of signal time–frequency characteristics. Subsequently, CNN is utilized for feature learning and extraction of each IMF, modeling the nonlinear and non-stationary features. Following this, the IPSO-LSSVM optimization algorithm is employed to establish and optimize multiple LSSVM models, predicting power fluctuations at different time scales. Finally, the predictions from each model are synthesized to obtain the final photovoltaic short-term power forecast. Through validation with actual photovoltaic generation data, this hybrid model demonstrates high accuracy and reliability in short-term power prediction, showing an average relative error and root mean square error reduction of 15.23 and 53.60%, respectively, compared to a certain comparative model. This proposed method based on VMD-CNN-IPSO-LSSVM hybrid model for photovoltaic power prediction holds promising prospects and practical value in the operation and scheduling of photovoltaic generation systems.

A dual-scale hybrid prediction model for UAV demand power: Based on VMD and SSA optimization algorithm

The prediction of power demand for unmanned aerial vehicles (UAV) is an essential basis to ensure the rational distribution of the energy system and stable economic flight. In order to accurately predict the demand power of oil-electric hybrid UAV, a method based on variational mode decomposition (VMD) and Sparrow Search Algorithm (SSA) is proposed to optimize the hybrid prediction model composed of long-short term memory (LSTM) and Least Squares Support Vector Machine (LSSVM). Firstly, perform VMD decomposition on the raw demand power data and use the sample entropy method to classify the feature-distinct mode components into high-frequency and low-frequency categories. Then, each modality component was separately input into the mixed model for rolling prediction. The LSSVM model and LSTM model were used to process low-frequency and high-frequency components, respectively. Finally, the predicted values for each modal component are linearly combined to obtain the final predicted value for power demand. Compared with the current models, the prediction model constructed in this paper stands out for its superior ability to track the changing trends of power demand and achieve the highest level of prediction accuracy.

Research on Production Prediction Method of Multi-stage Fractured Shale Gas Horizontal Well

Abstract Shale gas is a crucial component of unconventional energy. Productivity evaluation of gas wells is essential to ensure efficient and stable production. However, predicting productivity has been challenging due to the complex characteristics of shale gas reservoirs and the use of multi-stage fractured horizontal wells (MFHW) technology in the development process. This study compares traditional production prediction methods with an optimized least squares support vector machine model (LSSVM). The traditional productivity prediction method involves establishing a mathematical model of the MFHW in a fully enclosed rectangular shale formation. The model considers the effects of shale gas adsorption, diffusion, and pressure sensitivity. The model’s analytical solution is obtained using Duhamel’s principle, Laplace transform, and inverse transform. An independent production data analysis software is developed based on the analytical solution of bottom-hole pressure to predict production. To implement the LSSVM model, the model’s input parameters must be determined first. The LSSVM model’s regularization parameters and kernel parameters are obtained through the particle swarm optimization (PSO) algorithm, and the prediction model is established. The model’s matching is evaluated by calculating the coefficient of determination (R2) and the normalized root mean square error (NRMSE). The results indicate that the traditional production capacity prediction method is suitable for stable production in terms of applicability. However, the LSSVM model does not have this limitation and generally provides more accurate predictions throughout the entire production process. For complex shale gas reservoirs that frequently switch wells and use multi-stage fracturing technology, the LSSVM model is more suitable for predicting shale gas well productivity.

Integrative analysis of multi machine learning models for tetracycline photocatalytic degradation with MOFs in wastewater treatment

This study focuses on the utilization of connectionist models, specifically Independent Component Analysis (ICA), Genetic Algorithm (GA), Particle Swarm Optimization (PSO), and Genetic Algorithm-Particle Swarm Optimization (GAPSO) integrated with a least-squares support vector machine (LSSVM) to forecast the degradation of tetracycline (TC) through photocatalysis using Metal-Organic Frameworks (MOFs). The primary objective of this study was to evaluate the viability and precision of these connectionist models in estimating the efficiency of TC degradation, particularly within the context of wastewater treatment. The input parameters for these models cover essential MOF characteristics, such as pore size and surface area, along with critical operational factors, such as pH, TC concentration, catalyst dosage, and illumination duration, all of which are linked to the photocatalytic performance of MOFs. Sensitivity analysis revealed that the illumination duration is the primary influencer of TC photodegradation with MOF photocatalysts, while the MOFs’ surface area is the second crucial parameter shaping the efficiency and dynamics of the TC-MOF photocatalytic system. The developed LSSVM models display impressive predictive capabilities, effectively forecasting the experimental degradation of TC with high accuracy. Among these models, the GAPSO-LSSVM model excels as the top performer, achieving notable evaluation metrics, including STD, RMSE, MSE, MRE, and R2 at values of 3.09, 3.42, 11.71, 5.95, and 0.986, respectively. In comparison, the PSO-LSSVM, ICA-LSSVM, and GA-LSSVM models yield mean relative errors of 6.18%, 7.57%, and 11.37%, respectively. These outcomes highlight the exceptional predictive capabilities of the GAPSO-LSSVM model, solidifying its position as the most accurate and dependable model for predicting TC photodegradation in this study. This study contributes to advancing photocatalytic research and effectively reinforces the importance of leveraging machine learning methodologies for tackling environmental challenges.

Thermal error modeling of servo axis based on optimized LSSVM with gray wolf optimizer algorithm

Thermal error of a CNC machine tool has a serious effect on its machining accuracy. In order to reduce the thermal error, establishing an accurate and robust thermal error model is necessary. A new data-driven thermal error model is proposed based on gray wolf optimizer (GWO) and least squares support vector machine (LSSVM). While, three temperature-sensitivity points (TSPs) were picked by grouping search method. With optimizing the hyperparameters γ and σ2 by GWO algorithm, LSSVM is applied to thermal error modeling, which has advantages in dealing with small samples and nonlinear data. The experiments were conducted, and the results showed that the error prediction model constructed by GWO-LSSVM achieved an accuracy of 94.39 % meeting the requirements for error compensation. Then, the stability of the proposed error model is verified. Finally, the LSSVM model is compared with MLR and BP models commonly used in error modeling, and the advantages and applicable occasions are analyzed through experiments.

A Cotton Leaf Water Potential Prediction Model Based on Particle Swarm Optimisation of the LS-SVM Model

Frequent monitoring of crop moisture levels can significantly improve crop production efficiency and optimise water resource utilisation. The aim of the present study was to generate moisture status maps using thermal infrared imagery, centring on the development of a predictive model for the cotton leaf water potential. The model was constructed using particle swarm optimisation (PSO) in conjunction with the least squares support vector machine (LS-SVM). Traditional SVM models suffer from high computational complexity, long training times, and inequality constraints in predicting leaf water potential. To address such issues, the PSO algorithm was introduced to improve the performance of the LS-SVM model. The PSO-optimised LS-SVM model exhibited notable improvements in performance when evaluated on two distinct test datasets (Alaer and Tumushuke). The research results indicate that the predictive accuracy of the PSO-LS-SVM model significantly improved, as evidenced by an increase of 0.05 and 0.04 in the R2 values, both of which reached 0.95. This improvement is reflected in the corresponding RMSE values, which were reduced to 0.100 and 0.103. Furthermore, a model was established based on data from three cotton growth stages, achieving high predictive accuracy even with fewer training samples. By using the PSO-LS-SVM model to predict leaf water potential information, the predicted data were mapped onto drone images, enabling the transformation of the leaf water potential from a point to an area. The present findings contribute to a more comprehensive understanding of the cotton leaf water potential by visually representing the spatial distribution of crop water status on a large scale. The results hold substantial significance for the improvement of crop irrigation management.

Improved fuzzy sparse multi-class least squares support vector machine

The classification problem is a key area of research in machine learning. The Least Squares Support Vector Machine (LSSVM) is an important classifier that is commonly used to solve classification problems. Its widespread use stems from its replacement of the inequality constraint in the Support Vector Machine (SVM) with the equality constraint, which transforms the convex quadratic programming (QP) problem of SVM into the solution of linear equations. However, when dealing with multi-class classification problems, LSSVM faces the challenges of lack of sparsity and sample noises, which can negatively impact its performance. Based on the modeling characteristics and data distribution of the multi-class LSSVM model, this paper proposes two improvements and establishes an improved fuzzy sparse multi-class least squares support vector machine (IF-S-M-LSSVM). The first improvement adopts a non-iterative sparse algorithm, which can delete training sample points to different degrees by adjusting the sparse ratio. The second improvement addresses the impact of sample noise on determining the optimal hyperplane by adding a fuzzy membership degree based on sample density. The advantages of the new model, in terms of training speed and classification accuracy, are verified through UCI machine learning standard data set experiments. Finally, the statistical significance of the IF-S-M-LSSVM model is tested using the Friedman and Bonferroni-Dunn tests.

Concentration Prediction of Multi-component Gases Based on Improved Sparrow Search Algorithm

The electronic nose consists of a sensor array and software algorithms, which can be used for gas identification and concentration prediction. The least-squares support vector machine (LSSVM) is often used for gas concentration prediction. However, the effectiveness of its performance is largely influenced by the chosen parameters. Hence, it is essential to integrate efficient optimization algorithms to enhance the predictive capabilities of LSSVM. This work introduces an improved sparrow search algorithm (ISSA) to enhance the precision of gas concentration prediction by LSSVM. The ISSA approach is evaluated against the particle swarm optimization algorithm (PSO) and the sparrow search algorithm (SSA). Response data of different concentrations of CH4, CO, H2 and their binary gases mixture have been measured using an electronic nose composed of six gas sensors. After processing feature extraction and principal component analysis (PCA) on the original data, it is used as a training and test dataset for prediction models. The results demonstrate that ISSA can significantly enhance the precision of the LSSVM model for gas concentration prediction.

Modeling of Monthly Rainfall–Runoff Using Various Machine Learning Techniques in Wadi Ouahrane Basin, Algeria

Rainfall–runoff modeling has been the core of hydrological research studies for decades. To comprehend this phenomenon, many machine learning algorithms have been widely used. Nevertheless, a thorough comparison of machine learning algorithms and the effect of pre-processing on their performance is still lacking in the literature. Therefore, the major objective of this research is to simulate rainfall runoff using nine standalone and hybrid machine learning models. The conventional models include artificial neural networks, least squares support vector machines (LSSVMs), K-nearest neighbor (KNN), M5 model trees, random forests, multiple adaptive regression splines, and multivariate nonlinear regression. In contrast, the hybrid models comprise LSSVM and KNN coupled with a gorilla troop optimizer (GTO). Moreover, the present study introduces a new combination of the feature selection method, principal component analysis (PCA), and empirical mode decomposition (EMD). Mean absolute error (MAE), root mean squared error (RMSE), relative RMSE (RRMSE), person correlation coefficient (R), Nash–Sutcliffe efficiency (NSE), and Kling Gupta efficiency (KGE) metrics are used for assessing the performance of the developed models. The proposed models are applied to rainfall and runoff data collected in the Wadi Ouahrane basin, Algeria. According to the results, the KNN–GTO model exhibits the best performance (MAE = 0.1640, RMSE = 0.4741, RRMSE = 0.2979, R = 0.9607, NSE = 0.9088, and KGE = 0.7141). These statistical criteria outperform other developed models by 80%, 70%, 72%, 77%, 112%, and 136%, respectively. The LSSVM model provides the worst results without pre-processing the data. Moreover, the findings indicate that using feature selection, PCA, and EMD significantly improves the accuracy of rainfall–runoff modeling.