Least Squares Support Vector Regression Model Research Articles

Enhancing Unconfined Compressive Strength prediction in geotechnical engineering: a novel approach using LSZO and LSWG optimization

ABSTRACT The Unconfined Compressive Strength (UCS) measures a rock’s ability to withstand axial loads without lateral support, crucial for engineering applications. Accurate prediction of UCS is critical for the stability and safety of various civil engineering projects, such as foundation design, mining, and tunneling. The ability to predict UCS reliably ensures better project planning and execution, ultimately enhancing the safety and efficiency of engineering applications. The paper aims to develop an innovative method for predicting the UCS of rocks using a combination of the Zebra Optimisation Algorithm (ZOA) and the Wild Geese Algorithm (WGA) integrated with the Least Square Support Vector Regression (LSSVR) predictive model. The novelty of the paper lies in the integration of ZOA and WGA optimizers with the LSSVR model to address the limitations of conventional methods, which often face challenges like slow achieving convergence and being stuck in local minima. The combination of these advanced algorithms results in significantly improved accuracy and convergence speed in UCS predictions, demonstrating a robust and reliable approach that advances the field of geotechnical engineering. The results show that combining ZOA and WGA optimizers with LSSVR enhances UCS prediction accuracy and speed convergence. The LSZO models achieve a high level of precision, with a low RMSE value of 2.206 and an R2 value of 0.993. The safety and effectiveness of civil engineering projects are improved by this model, which provides a strong and trustworthy method for UCS prediction.

Prediction of Geometric Characteristics of Laser Cladding Layer Based on Least Squares Support Vector Regression and Crested Porcupine Optimization.

The morphology size of laser cladding is a crucial parameter that significantly impacts the quality and performance of the cladding layer. This study proposes a predictive model for the cladding morphology size based on the Least Squares Support Vector Regression (LSSVR) and the Crowned Porcupine Optimization (CPO) algorithm. Specifically, the proposed model takes three key parameters as inputs: laser power, scanning speed, and powder feeding rate, with the width and height of the cladding layer as outputs. To further enhance the predictive accuracy of the LSSVR model, a CPO-based optimization strategy is applied to adjust the penalty factor and kernel parameters. Consequently, the CPO-LSSVR model is established and evaluated against the LSSVR model and the Genetic Algorithm-optimized Backpropagation Neural Network (GA-BP) model in terms of relative error metrics. The experimental results demonstrate that the CPO-LSSVR model can achieve a significantly improved relative error of no more than 2.5%, indicating a substantial enhancement in predictive accuracy compared to other methods and showcasing its superior predictive performance. The high accuracy of the CPO-LSSVR model can effectively guide the selection of laser cladding process parameters and thereby enhance the quality and efficiency of the cladding process.

Research on hyperspectral timely monitoring model of green tea processing quality based on PSO-LSSVR

To monitor the processing status and content of the main components of tea leaves during green tea processing timely, a monitoring model for the contents of green tea processing based on hyperspectral imaging is established in this paper. The aim of this model is to improve the quality of finished green tea products by addressing the shortcomings of existing methods that cannot achieve timely, non-destructive, and accurate detection. Initially, hyperspectral and biochemical data were collected across four processing procedures of green tea. Following the exclusion of abnormal samples, preprocessing techniques including Savitzky-Golay, multiple scatter correction, and 2nd derivative were compared and selected. Subsequently, feature wavelengths extracted through correlation analysis, principal component analysis, and successive projections algorithm were utilized to construct least squares support vector regression (LSSVR) prediction models, determining the optimal feature extraction method. Finally, particle swarm optimization (PSO) was employed to refine LSSVR model parameters, resulting in the PSO-LSSVR model. Post-optimization, the determination coefficient (R2) exceeded 0.9, the root means square error remained around 0.005, and the residual prediction deviation surpassed 3. The PSO-LSSVR model exhibited better predictive capabilities compared to the LSSVR model, offering a method reference for timely monitoring of green tea processing inclusions.

Random projection enhancement: A Novel method for improving performance of surrogate models

Surrogate models serve as powerful tools for engineering application but constructing highly accurate models with limited samples remains a challenge. Inspired by this, this paper proposes a general random projection enhancement method (RPE) aimed at improving surrogate model performance. Taking least squares support vector regression (LSSVR) as an example, we conducted numerical experiments to evaluate the feasibility of the RPE method. The RPE-enhanced LSSVR demonstrates superior predictive accuracy and robustness compared to the unenhanced model and other benchmark models. The results show that the RPE method can not only enhance the predictive accuracy of the model but also improve the robustness of the model. Meanwhile, analysis of optimization experiments indicated that the enhanced LSSVR model obtained better solutions compared to the unenhanced LSSVR model. Even when extended to high-dimensional problems, the RPE method remains effective. Furthermore, the applicability of RPE method extends from the LSSVR model to other models, as demonstrated by the enhancement of the extreme learning machine, regression kriging, and radial basis function neural network. More importantly, the feasibility of the RPE method is also verified in engineering problems, obtaining the same results. This method offers a reliable alternative for real-world engineering optimization problems.

On Least Squares Support Vector Regression for Predicting Mechanical Properties of Steel Rebars

Aiming at ensuring the quality of the product and reducing the cost of steel manufacturing, an increasing number of studies have been developing nonlinear regression models for the prediction of the mechanical properties of steel rebars using machine learning techniques. Bearing this in mind, we revisit this problem by developing a design methodology that amalgamates two powerful concepts in parsimonious model building: (i) sparsity, in the sense that few support vectors are required for building the predictive model, and (ii) locality, in the sense that simpler models can be fitted to smaller data partitions. In this regard, two regression models based on the Least Squares Support Vector Regression (LSSVR) model are developed. The first one is an improved sparse version of the one introduced in a previous work. The second one is a novel local LSSVR-based regression model. The task of interest is the prediction of four output variables (the mechanical properties YS, UTS, UTS/YS, and PE) based on information about its chemical composition (12 variables) and the parameters of the heat treatment rolling (6 variables). The proposed LSSVR-based regression models are evaluated using real-world data collected from steel rebar manufacturing and compared with the global LSSVR model. The local sparse LSSVR approach was able to consistently outperform the standard single regression model approach in the task of interest, achieving improvements in the average R2 from previous studies: 5.04% for UTS, 5.19% for YS, 1.96% for UTS/YS, and 3.41% for PE. Furthermore, the sparsification of the dataset and the local modeling approach significantly reduce the number of SV operations on average, utilizing 34.0% of the total SVs available for UTS estimation, 44.0% for YS, 31.3% for UTS/YS, and 32.8% for PE.

Quantitative determination of cadmium content in peanut oil using microwave detection method combined with multivariate analysis

This research introduced an innovative application of microwave detection technology to quickly and precisely quantify cadmium concentration in peanut oil. Using the principle of free space measurement, a compact microwave detection device was fabricated, and obtain a transmission index with a frequency range of 2.5 GHz to 11.5 GHz and a step size of 10 MHz. Firstly, the preprocessed transmission index is selected by using three feature extraction algorithms: competitive adaptive reweighting sampling (CARS) algorithm, boot­strapping soft shrinkage (BOSS) algorithm, and iteratively variable subset optimization (IVSO) algorithm, and quantified them with the least square support vector regression (LSSVR) model. Then, two intelligent optimization algorithms, sine cosine algorithm (SCA) and firefly algorithm (FA) were used to optimize the parameters of the LSSVR model. Compared with the original LSSVR model, the coefficient of determination (RP2) is improved after three feature extraction algorithms and two parameter optimization algorithms, and the root average square error (RMSEP) is also decreased. Among these algorithms, feature extraction algorithm CARS and parameter optimization algorithm FA have the best prediction results. When the two are coupled, the CARS-FA-LSSVR model shows the best generalization performance, with RP2 of 0.9944 and RMSEP of 1.3075 mg∙kg-1. Through this research, it can be seen that high-precision detection of heavy metal cadmium content in peanut oil can be achieved by using microwave detection method combined with the stoichiometric model and can be extended to the detection of heavy metal content in other foods, providing a new way of idea for food safety detection.

Least Squares Generalization-Memorization Regression

Generalization-Memorization learning endeavors to minimize empirical risk while simultaneously reducing expected risk. Although we often do not pay attention to whether the training samples are accurately memorized during regression, improving generalization performance with better memory is always a goal pursued by regression. To tackle this issue, we introduce two new regression models, Least Squares Generalization-Memorization Regression (LSGMR) and Soft Least Squares Generalization-Memorization Regression (SLSGMR), by introducing the memory kernel learning on Least Squares Support Vector Regression (LSSVR). We conduct tests on these models using synthetic dataset and showcase that the LSSVR model can be viewed as a special case of our proposed model. Our experiments highlight that, for numerous problems, the models incorporating the employed memory mechanisms, LSGMR and SLSGMR, prove highly effective in yielding superior results compared to LSSVR on noise regression.

The least-square support vector regression model for the dyes and heavy metal ions removal prediction

Wastewater treatment plants are typically complex because they involve physical, chemical, and biological processes. Meanwhile, the efficiency of the removal of pollutants such as auramine (AO), methylene blue (MB), and ion Cadmium (Cd (II)) from the wastewater are difficult to be measured directly in real-time, as this measurement requires laboratory instruments that are time-consuming. The soft sensors could be the solution to perform the real-time prediction of the AO, MB, and Cd (II) removals’ capability. Hence, this study investigates the performances of a soft sensor, namely least-square support vector regression (LSSVR) to estimate the AO, MB, and Cd (II) removals’ ability. In this study, two wastewater-related case studies involving AO, MB, and Cd (II) removals were used to evaluate the predictive performance of the LSSVR. Additionally, its results were compared and analyzed with other soft sensors. For both case studies, notice that LSSVR gives the best results for AO, MB, and Cd (II) removals as compared to other soft sensor models where its root means square errors, mean absolute errors, and the approximate error, are lowered by 83% to 1,756%. Moreover, its coefficients of determination, denoted R 2 are the highest which are all more than or close to 0.9 for all the AO, MB, and Cd (II) removals even for the testing data for the case studies that were not used to develop the LSSVR model. In conclusion, LSSVR is more suitable for evaluating the effectiveness of the AO, MB, and Cd (II) removals at present.

Uncertainty analysis of discharge coefficient predicted for rectangular side weir using machine learning methods

Abstract The present study used three machine learning models, including Least Square Support Vector Regression (LSSVR) and two non-parametric models, namely, Quantile Regression Forest (QRF) and Gaussian Process Regression (GPR), to quantify uncertainty and precisely predict the side weir discharge coefficient (Cd) in rectangular channels. So, 15 input structures were examined to develop the models. The results revealed that the machine learning models used in the study offered better accuracy compared to the classical equations. While the LSSVR and QRF models provided a good prediction performance, the GPR slightly outperformed them. The best input structure that was developed included all four dimensionless parameters. Sensitivity analysis was conducted to identify the effective parameters. To evaluate the uncertainty in the predictions, the LSSVR, QRF, and GPR were used to generate prediction intervals (PI), which quantify the uncertainty coupled with point prediction. Among the implemented models, the GPR and LSSVR models provided more reliable results based on PI width and the percentage of observed data covered by PI. According to point prediction and uncertainty analysis, it was concluded that the GPR model had a lower uncertainty and could be successfully used to predict Cd.

Quantitative prediction of AFB1 in various types of edible oil based on absorption, scattering and fluorescence signals at dual wavelengths

This study aims to address the challenge of matrix interference of various types of edible oils on intrinsic fluorescence of aflatoxin B1 (AFB1) by developing a novel solution. Considering the fluorescence internal filtering effect, the absorption (μa) and reduced scattering (μ’s) coefficients at dual wavelengths (excitation: 375 nm, emission: 450 nm) were obtained by using integrating sphere technique, and were used to improve the quantitative prediction results for AFB1 contents in six different kinds of edible oils. A research process of “Monte Carlo (MC) simulation - phantom verification - actual sample validation” was conducted. The MC simulation was used to determine interference rule and correction parameters for fluorescence, the results indicated that the escaped fluorescence flux nonlinearly decreased with the μa, μ’s at emission wavelength (μa,em, μ’s,em) and μa at excitation wavelength (μa,ex), however increased with the μ’s at excitation wavelength (μ’s,ex). And the required optical parameters to eliminate the interference of matrix on fluorescence intensity are: effective attenuation coefficients at excitation and emission wavelengths (μeff,ex, μeff,em) and μ’s,ex. Phantom verification was conducted to explore the feasibility of fluorescence correction based on the identified parameters by MC simulation, and determine the optimal machine learning method. The modelling results showed that least squares support vector regression (LSSVR) model could reach the best performance. Three kinds of edible oil (peanut, rapeseed, corn), each with two brands were used to prepare oil samples with different AFB1 contamination. The LSSVR model for AFB1 based on μeff,ex, μeff,em, μ’s,ex and fluorescence intensity at 450 nm was calibrated, both correlation coefficients for calibration (Rc) and the validation (Rv) sets could reach 1.000, root mean square errors for calibration (RMSEC) and the validation (RMSEV) sets were as low as 0.038 and 0.099 respectively. This study proposed a novel method which is based solely on the absorption, scattering, and fluorescence characteristics at excitation and emission wavelengths to achieve accurate prediction of AFB1 content in different types of vegetable oils.

Dynamic nonlinear soft sensor modelling method using linear slow feature analysis and least squares support vector regression for batch processes

AbstractData‐driven soft sensor models have been extensively utilized in industrial processes. Batch processes are usually employed to manufacture low‐volume and high value‐added products in chemical, materials, and pharmaceutical industries. The most distinctive features of batch process lie in nonlinear, repetition, and slow time varying characteristics. In this paper, a data‐driven soft sensor modelling method based on linear slow feature analysis (LSFA) and least squares support vector regression (LSSVR) is proposed. In this method, LSFA was used to effectively capture the driving force behind the data features that change as slowly as possible. Then, a LSSVR model was constructed between the extracted slow feature variables and quality variables. Finally, a numerical example, industrial penicillin fermentation processes, and cobalt oxalate synthesis process were utilized to confirm the prediction accuracy and model reliability of the proposed approach.

Influence of phase change material and nano silica aerogel aggregates on the characteristics of cementitious composite: An experimental and predictive study

This paper studies the influence of two high-performance thermal insulating materials including aerogel and phase change materials (PCM) aggregates, on the key characteristics of cementitious composites in experimental and predictive aspects. Thermal conductivity (ThC), rapid chloride migration test (RCMT), permeable pore volume, compressive strength, dry density, and microstructural analysis were performed for the mechanical properties. Moreover, Least Squares Support Vector Regression (LSSVR) as a machine learning method was introduced to evaluate and provide a proper method for non-destructive evaluation of parameters. The results of experiments indicated that both aerogel and PCM aggregates were highly effective although the aerogel showed more efficiency in enhancing the thermal insulation property of cementitious mixtures. In addition, the compressive strength of the mixtures with PCM composites was higher than the aerogel aggregates, where the compressive strength of the mixture containing 20 % paraffin was 50 % higher than the aerogel mixture with similar incorporation levels. Moreover, the mixtures with PCM aggregates had significantly lower water and chloride permeability compared to those of plain mixtures, and mixtures consisted of aerogel aggregates. The scanning electron microscope (SEM) analyses, also, revealed that the use of the aerogel aggregates led to an open and porous structure of the mixtures; however, PCM aggregates had a weak interfacial transition zone (ITZ) in the vicinity of cement paste. Furthermore, LSSVR model provided a close prediction of the effective parameters with an acceptable accuracy in capturing the influences of important parameters.

Application of soft computing and evolutionary algorithms to estimate hydropower potential in multi-purpose reservoirs

Hydropower is a clean and efficient technology for producing renewable energy. Assessment and forecasting of hydropower production are important for strategic decision-making. This study aimed to use machine learning models, including adaptive neuro-fuzzy inference system (ANFIS), gene expression programming, random forest (RF), and least square support vector regression (LSSVR), for predicting hydroelectric energy production. A total of eight input scenarios was defined with a combination of various observed variables, including evaporation, precipitation, inflow, and outflow to the reservoir, to predict the hydroelectric energy produced during the experimental period. The Mahabad reservoir near Lake Urmia in the northwest of Iran was selected as a study object. The results showed that a combination of hydroelectric energy produced in the previous month, evaporation, and outflow from the dam resulted in the highest prediction performance using the RF model. A scenario that included all input variables except the precipitation outperformed other scenarios using the LSSVR model. Among the models, LSSVR exerted the highest prediction performance for which RMSE, MAPE, and NSE were 442.7 (MWH), 328.3 (MWH), and 0.85, respectively. The results showed that Harris hawks optimization (HHO) (RMSE = 0.2 WMH, MAPE = 10 WMH, NSE = 0.90) was better than particle swarm optimization (PSO) (RMSE = 0.2 WMH, MAPE = 10 WMH, NSE = 0.90) in optimizing ANFIS during the prediction. The results of Taylor’s diagram indicated that the ANFIS-HHO model had the highest accuracy. The findings of this study showed that machine learning models can be used as an essential tool for decision-making in sustainable hydropower production.

Optimization and prediction of the cotton fabric dyeing process using Taguchi design-integrated machine learning approach

The typical textile dyeing process calls for a wide range of operational parameters, and it has always been difficult to pinpoint which of these qualities is the most important in dyeing performance. Consequently, this research used a combined design of experiments and machine learning prediction models’ method to offer a sustainable and beneficial reactive cotton fabric dyeing process. To be more precise, we built a least square support vector regression (LSSVR) model based on Taguchi's statistical orthogonal design (L27) to predict exhaustion percentage (E%), fixation rate (F%), and total fixation efficiency (T%) and color strength (K/S) in the reactive cotton dyeing process. The model's prediction accuracy was assessed using many measures, including root mean square error (RMSE), mean absolute error (MAE), and the coefficient of determination (R2). Principal component regression (PCR), partial least square regression (PLSR), and fuzzy modelling were some of the other types of regression models used to compare results. Our findings reveal that the LSSVR model greatly outperformed competing models in predicting the E%, F%, T%, and K/S. This is shown by the LSSVR model's much smaller RMSE and MAE values. Overall, it provided the highest possible R2 values, which reached 0.9819.

Synchronously Predicting Tea Polyphenol and Epigallocatechin Gallate in Tea Leaves Using Fourier Transform-Near-Infrared Spectroscopy and Machine Learning.

Tea polyphenol and epigallocatechin gallate (EGCG) were considered as key components of tea. The rapid prediction of these two components can be beneficial for tea quality control and product development for tea producers, breeders and consumers. This study aimed to develop reliable models for tea polyphenols and EGCG content prediction during the breeding process using Fourier Transform-near infrared (FT-NIR) spectroscopy combined with machine learning algorithms. Various spectral preprocessing methods including Savitzky-Golay smoothing (SG), standard normal variate (SNV), vector normalization (VN), multiplicative scatter correction (MSC) and first derivative (FD) were applied to improve the quality of the collected spectra. Partial least squares regression (PLSR) and least squares support vector regression (LS-SVR) were introduced to establish models for tea polyphenol and EGCG content prediction based on different preprocessed spectral data. Variable selection algorithms, including competitive adaptive reweighted sampling (CARS) and random forest (RF), were further utilized to identify key spectral bands to improve the efficiency of the models. The results demonstrate that the optimal model for tea polyphenols calibration was the LS-SVR with Rp = 0.975 and RPD = 4.540 based on SG-smoothed full spectra. For EGCG detection, the best model was the LS-SVR with Rp = 0.936 and RPD = 2.841 using full original spectra as model inputs. The application of variable selection algorithms further improved the predictive performance of the models. The LS-SVR model for tea polyphenols prediction with Rp = 0.978 and RPD = 4.833 used 30 CARS-selected variables, while the LS-SVR model build on 27 RF-selected variables achieved the best predictive ability with Rp = 0.944 and RPD = 3.049, respectively, for EGCG prediction. The results demonstrate a potential of FT-NIR spectroscopy combined with machine learning for the rapid screening of genotypes with high tea polyphenol and EGCG content in tea leaves.

Forecasting by Combining Chaotic PSO and Automated LSSVR

An automatic least square support vector regression (LSSVR) optimization method that uses mixed kernel chaotic particle swarm optimization (CPSO) to handle regression issues has been provided. The LSSVR model is composed of three components. The position of the particles (solution) in a chaotic sequence with good randomness and ergodicity of the initial characteristics is taken into consideration in the first section. The binary particle swarm optimization (PSO) used to choose potential input characteristic combinations makes up the second section. The final step involves using a chaotic search to narrow down the set of potential input characteristics before combining the PSO-optimized parameters to create CP-LSSVR. The CP-LSSVR is used to forecast the impressive datasets testing targets obtained from the UCI dataset for purposes of illustration and evaluation. The results suggest CP-LSSVR has a good predictive capability discussed in this paper and can build a projected model utilizing a limited number of characteristics.

Integration Vis-NIR Spectroscopy and Artificial Intelligence to Predict Some Soil Parameters in Arid Region: A Case Study of Wadi Elkobaneyya, South Egypt

Understanding and determining soil properties is reflected in improving farm management and crop production. Soil salinity, pH and calcium carbonate are among the factors affecting the soil’s physical and chemical properties. Hence, their estimation is very important for agricultural management, especially in arid regions (Wadi Elkobaneyya valley, located in the northwest of Aswan Governorate, Upper Egypt). The study objectives were to characterize and develop prediction models for soil salinity, pH and calcium carbonate (CaCO3) using integration soil analysis and spectral reflectance vis-NIR spectroscopy. To achieve the study objectives, three multivariate regression models: Partial Least Squares Regression (PLSR), Multivariate Adaptive Regression Splines (MARS) and Least Square-Support Vector Regression (LS-SVR)); and two machine learning algorithms, Random Forest (RF) and Artificial Neural Networks (ANN) were used. Ninety-six surface soil samples were collected from the study area at depths 0–5 cm. The data were divided into a calibration dataset (70% of the total) and a validation dataset (30% of the total dataset). The obtained results represent that the PLSR model was the best model for soil pH parameters where R2 of calibration and validation predictability = 0.68 and 0.52, respectively. The LS-SVR model was the best model to predict soil Electrical Conductivity (EC) and soil Calcium Carbonate (CaCO3) content, with R2 0.70 and 0.74 for calibration and R2 0.26 and 0.47 for validation, respectively. On the other hand, the results of the implemented machine learning algorithm model showed that RF was the best model to predict soil pH and CaCO3, as the R2 was 0.82 for calibration and 0.57 for validation, respectively. Nevertheless, the best model for predicting soil EC was ANN, with an R2 of 0.96 for calibration and 64 for validation. The results show the advantages of machine learning models for predicting soil EC, pH and CaCO3 by Vis-NIR spectroscopy. Therefore, Vis-NIR spectroscopy is considered faster and more cost-efficient and can be further used in environmental monitoring and precision farming.

Regional modeling and forecasting of precipitable water vapor using least square support vector regression

We propose a new model for spatio-temporal modeling and forecasting of precipitable water vapor (PWV) using least square support vector regression (LS-SVR) method. The LS-SVR uses simple linear equations. As a result, the complexity of the computational algorithm is reduced. In addition, the convergence speed and accuracy of the results increase. The evaluation of the new method has been done with the observations of the GPS networks at north-west and central Alborz in Iran. In the north-west GPS network, observations of 23 GPS stations in the period of 27 October to 10 November 2011 are used. However, in central Alborz network, the observations of 11 GPS stations in the period of 10 to 24 June 2016 have been used. The north-west GPS network is in the mountainous region and its observations are for the winter season. But, the second network is near the coastal area and summer season measurements are used. The latitude, longitude and height of GPS stations, DOY, time, relative humidity, temperature and pressure are considered as an input of the LS-SVR model. The output of the new model is the PWV (LS-SVRPWV). After the training step, the new model is used to estimate the spatio-temporal variation of PWV. The results of the LS-SVR model are compared and evaluated with the standard neural network (SNN), adaptive neuro-fuzzy inference system (ANFIS), support vector regression (SVR), Saastamoinen, global pressure and temperature 3 (GPT3), voxel-based tomography (VBT) models, as well as with radiosonde measurements. Error evaluation of models has been done in control stations as well as by precise point positioning (PPP) method. For LS-SVR model, the averaged RMSE in the control stations of the north-west GPS network is 1.69 mm, while for the central Alborz GPS network, 1.88 mm is calculated. Also, the averaged relative error of LS-SVR model calculated in the Tabriz and Tehran radiosonde stations are 4.66 % and 6.12 %, respectively. The results of this paper show that the LS-SVR model has a very high capability in forecasting the spatio-temporal variation of PWV at the GPS network territory. The new model can be used for accurate estimation of PWV, meteorological applications and flood forecasting.

A comparison study between different kernel functions in the least square support vector regression model for penicillin fermentation process

Soft sensors are becoming increasingly important in our world today as tools for inferring difficult-to-measure process variables to achieve good operational performance and economic benefits. Recent advancement in machine learning provides an opportunity to integrate machine learning models for soft sensing applications, such as Least Square Support Vector Regression (LSSVR) which copes well with nonlinear process data. However, the LSSVR model usually uses the radial basis function (RBF) kernel function for prediction, which has demonstrated its usefulness in numerous applications. Thus, this study extends the use of non-conventional kernel functions in the LSSVR model with a comparative study against widely used partial least square (PLS) and principal component regression (PCR) models, measured with root mean square error (RMSE), mean absolute error (MAE) and error of approximation (Ea) as the performance benchmark. Based on the empirical result from the case study of the penicillin fermentation process, the Ea of the multiquadric kernel (MQ) is lowered by 63.44% as compared to the RBF kernel for the prediction of penicillin concentration. Hence, the MQ kernel LSSVR has outperformed the RBF kernel LSSVR. The study serves as empirical evidence of LSSVR performance as a machine learning model in soft sensing applications and as reference material for further development of non-conventional kernels in LSSVR-based models because many other functions can be used as well in the hope to increase the prediction accuracy.

FCDT-IWBOA-LSSVR: An innovative hybrid machine learning approach for efficient prediction of short-to-mid-term photovoltaic generation

The short-term photovoltaic (PV) power prediction is mainly used to prevent photovoltaic power generation fluctuations, grid overvoltage, reverse current, and islanding effects. At the same time, the mid-term PV power forecast is of great significance to improving the availability of PV power generation and the benefit of PV grid connection. Because of the significant differences in time scales between mid-term and short-term power prediction, the short-term power prediction model or method cannot be directly applied to mid-term power prediction. Therefore, few scholars have developed effective short-to-mid-term power forecasting strategies for photovoltaics. As a result, this research proposes a prediction model based on a fast cull outlier algorithm (FC), a decision tree (DT), least squares support vector regression (LSSVR), and an improved whale bat optimization algorithm (IWBOA), which is used for the prediction of the short-to-mid-term photovoltaic power on different time scales, one day and one month in advance. The FC algorithm is used to analyze the difference between the overall data and the abnormal data in the local density and distance to remove the outliers in the original data set. The revised DT model differentiates the data according to climate characteristics to obtain different input data subsets with the best correlation and constructs an independent LSSVR-based model corresponding to the data subsets. The WOA algorithm is improved by independently designing the Chebyshev chaotic initialization strategy, chaotic adaptive inertia weight and BOA algorithm, and the kernel function width and penalty factor of each short-to-mid-term independent sub-PV power prediction model are optimized by IWBOA, thereby improving the computational speed and prediction accuracy of the LSSVR model. Finally, the effectiveness of the proposed strategy is evaluated using actual data from photovoltaic power plants in China. The regression coefficient (R2), mean square error (MSE), root mean square error (RMSE), and mean absolute error (MAE) of short-term forecasting ability of the FCDT-IWBOA-LSSVR model established in this paper are 0.99657, 0.22009, 0.32515, and 0.20959, respectively, while the R2, MSE, RMSE, and MAE of medium-term forecasting ability are 0.98374, 1.91371, 1.38336, and 0.6256. The calculation results show that the prediction accuracy of the FCDT-IWBOA-LSSVR model is higher than that of the WOA-LSSVR, PSO-LSSVR, PSO-BP, I-ACO-SVR, ANN, EMS-DSM-RT, 5 ML, and ELM models.