Weighted Least Squares Support Vector Machine Research Articles

Early prediction of lithium-ion battery cycle life based on voltage-capacity discharge curves

Accurately predicting the lifetime of lithium-ion batteries is critical for accelerating technological advancements and applications. Nevertheless, the complex aging mechanisms and dynamic operating conditions of lithium-ion batteries have remained major challenges. This paper proposes a method for early predicting lithium-ion batteries cycle life based on weighted least squares support vector machine (WLS-SVM) with health indicators (HIs) as input. The HIs are extracted from lithium-ion batteries voltage-capacity discharge curves, since these curves are easy to measure and strongly correlate to battery cycle life. Taking into account the nonlinearity of batteries cycle life, a support vector machine (SVM) that is capable of strong generalization is used to predict cycle life. As a solution to the problem of misleading results from outlier data in SVM, error square term combined with weight functions is used in this study to improve robustness and prediction accuracy. The datasets of 41 cells are used to verify the proposed early prediction method. The results show that the root mean square error (RMSE) and mean absolute error (MAE) of cycle life prediction results by the proposed method are much lower, and the cycle life early prediction errors of the test cells are all <9 %, which notes that the proposed method is accurate and valid for cycle life early prediction.

Investigation of the Solubility of Elemental Sulfur (S) in Sulfur-Containing Natural Gas with Machine Learning Methods

Some natural gases are toxic because they contain hydrogen sulfide (H2S). The solubility pattern of elemental sulfur (S) in toxic natural gas needs to be studied for environmental protection and life safety. Some methods (e.g., experiments) may pose safety risks. Measuring sulfur solubility using a machine learning (ML) method is fast and accurate. Considering the limited experimental data on sulfur solubility, this study used consensus nested cross-validation (cnCV) to obtain more information. The global search capability and learning efficiency of random forest (RF) and weighted least squares support vector machine (WLSSVM) models were enhanced via a whale optimization-genetic algorithm (WOA-GA). Hence, the WOA-GA-RF and WOA-GA-WLSSVM models were developed to accurately predict the solubility of sulfur and reveal its variation pattern. WOA-GA-RF outperformed six other similar models (e.g., RF model) and six other published studies (e.g., the model designed by Roberts et al.). Using the generic positional oligomer importance matrix (gPOIM), this study visualized the contribution of variables affecting sulfur solubility. The results show that temperature, pressure, and H2S content all have positive effects on sulfur solubility. Sulfur solubility significantly increases when the H2S content exceeds 10%, and other conditions (temperature, pressure) remain the same.

Modeling the Solubility of Sulfur in Sour Gas Mixtures Using Improved Support Vector Machine Methods.

The study of sulfur solubility is of great significance to the safe development of sulfur-containing gas reservoirs. However, due to measurement difficulties, experimental research data on sulfur solubility thus far are limited. Under the research background of small samples and poor information, a weighted least-squares support vector machine (WLSSVM)-based machine learning model suitable for a wide temperature and pressure range is proposed to improve the prediction accuracy of sulfur solubility in sour gas. First, we use the comprehensive gray relational analysis method to extract important factors affecting sulfur solubility as the model input parameters. Then, we use the whale optimization algorithm (WOA) and gray wolf optimizer (GWO) intelligence algorithms to find the optimal solution of the penalty factor and kernel coefficient and bring them into three common kernel functions. The optimal kernel function is calculated, and the final WOA-WLSSVM and GWO-WLSSVM models are established. Finally, four evaluation indicators and an outlier diagnostic method are introduced to test the proposed model’s performance. The empirical results show that the WOA-WLSSVM model has better performance and reliability; the average absolute relative deviation is as low as 3.45%, determination coefficient (R2) is as high as 0.9987, and the prediction accuracy is much higher than that of other models.

Online State-of-Health Estimation for Second-Use Lithium-Ion Batteries Based on Weighted Least Squares Support Vector Machine

Online state-of-health (SOH) estimation is critical for second-use retired lithium-ion batteries. However, the SOH of retired batteries is highly nonlinear, and the existing degradation trend data are limited. Consequently, achieving accurate and effective SOH estimation remains a challenge. To address the above problem, an online SOH estimation based on a weighted least squares support vector machine (WLS-SVM) is proposed in this paper. In this work, the health features (HFs) are first extracted from the partial charging curves of retired batteries, and the Pearson correlation coefficient is applied to select the important HFs that are strongly correlated to the SOH. These selected HFs are used as the estimation model inputs for characterizing the aging procedure of the retired battery effectively. Then, to enhance the accuracy and robustness of SOH estimation, the standard support vector machine (SVM) is improved by a weighting function and linear equations. Last, the online SOH estimation is conducted by using the test data sets of second-use batteries with different battery materials and under different conditions. The results show that compared with the most popular methods, such as the back-propagation neural network (BPNN)-based method, the Gaussian process regression (GPR)-based method, and the standard SVM-based method, the performance of the WLS-SVM-based method is superior. The root mean square error (RMSE) for the SOH estimation with the WLS-SVM-based method for all the test cells is less than 1.85% at different aging paths and levels, whereas the RMSEs of the BPNN-based method, GPR-based method, and standard SVM-based method are within 3.6%, 5.7%, and 7.6%, respectively. The proposed WLS-SVM-based method can thus provide highly robust and accurate online SOH estimation.

An Interval Forecasting Model Based on Phase Space Reconstruction and Weighted Least Squares Support Vector Machine for Time Series of Dissolved Gas Content in Transformer Oil

Transformer state forecasting and fault forecasting are important for the stable operation of power equipment and the normal operation of power systems. Forecasting of the dissolved gas content in oil is widely conducted for transformer faults, but its accuracy is affected by data scale and data characteristics. Based on phase space reconstruction (PSR) and weighted least squares support vector machine (WLSSVM), a forecasting model of time series of dissolved gas content in transformer oil is proposed in this paper. The phase spaces of time series of the dissolved gas content sequence are reconstructed by chaos theory, and the delay time and dimension are obtained by the C-C method. The WLSSVM model is used to forecast time series of dissolved gas content, the chemical reaction optimization (CRO) algorithm is used to optimize training parameters, the bootstrap method is used to build forecasting intervals. Finally, the accuracy and generalization ability of the forecasting model are verified by the analysis of actual case and the comparison of different models.

Data Processing Method of Multibeam Bathymetry Based on Sparse Weighted LS-SVM Machine Algorithm

In this paper, on the basis of the sparse weighted least-squares support vector machine (LS-SVM) algorithm, the sparse weighted LS-SVM surface is established and the corresponding steps are given. Then, multibeam bathymetric anomalies can be detected using the sparse weighted LS-SVM surface. The construction of the sparse weighted LS-SVM surface requires four aspects: selection of kernel function, parameters calculation of sparse weighted LS-SVM, selection of support vectors, calculation of weight coefficients. Finally, to verify the validity of sparse weighted LS-SVM surface in multibeam bathymetric anomalies detection, the measured multibeam bathymetric data are selected to calculate and analyze. The conclusion of the experiment is introduced, that is, the sparse weighted LS-SVM surface has a better performance compared to the traditional polynomial surface function, and the sparse weighted LS-SVM surface is more capable of reflecting the overall change of seabed topography. Compared with the combined uncertainty and bathymetry estimator surface, the proposed method utilizes the raw soundings rather than the nodes, so the sparse weighted LS-SVM surface can better reflect the detailed information of seabed topography.

A general method for thermal error measurement and modeling in CNC machine tools’ spindle

To improve the machining accuracy of the CNC machine tools, it is essential to establish a high-precision and strong-robustness thermal error model for further thermal error compensation work. In this paper, it presents a new method of thermal error measurement and modeling in CNC machine tools’ spindle. In order to measure the thermal deformation of the machine tools’ spindle more conveniently and efficiently, a five-point measurement method is proposed in this paper. The sensitive temperature points are identified by using the theory of partial correlation analysis and it has successfully reduced 12 raw temperature variables to 2~3 sensitive temperature variables. The thermal error model of the machine tools’ spindle is exactly figured out based on the regression theory of weighted least squares support vector machine (WLS-SVM). This paper proposes a method of gene expression programming (GEP) algorithm to optimize the penalty parameter c and kernel function parameter σ involved in WLS-SVM. The parameter υ of the weighting value contained in WLS-SVM is to be optimized with the method of an improved normal distribution weighting rule (INDWR). The measurement and modeling experiments are carried out on i5M1 CNC machining center and its modeling accuracy reaches 0.7664 μm in the axial direction of the spindle. That the prediction accuracy under the variable working condition reaches 0.8168 μm proves that the model is still of high precision and robustness. Compared with other modeling methods, the experimental results have shown that this GEP-WLSSVM modeling method is superior to PSO-LSSVM and GA-LSSVM method.

An effective fault diagnosis approach based on optimal weighted least squares support vector machine

Fault diagnosis is always a vital technology in the chemical industry and is influenced by a large number of process variables in the practical manufacturing process. Thus, an effective diagnosis method is crucial in practical chemical processes. A novel fault diagnosis method is proposed based on the weighted least squares support vector machine (WLSVM) to deal with the small sample and non‐linear partition data. It provides the strong potential in predicting faults, especially by further employing a suitable particle swarm optimization (PSO) algorithm to determine the most important parameters of the punishment factor and the Gaussian RBF kernel, which has the advantages of high accuracy and low false alarm rate. PSO‐WLSSVM is further accomplished with the data from the classic benchmark test set Tennessee Eastman (TE) process. Also, the models SVM, PSO‐SVM, and PSO‐LSSVM are employed on the TE process to compare the performance of PSO‐WLSSVM. The results show the validity of the proposed approach on the TE process.

Soft Measurement of the Purity of the Synthetic Edible Pigment Powder Using Fluorescence Spectroscopy Combined with SVM

The feature compression algorithm which was reformed from the original Moment method was used for the pre-processing of the fluorescence spectral data, then combined the data and the Weighted Least Squares Support Vector Machine(WLS-SVM) algorithm to establish a robust regression model, which is used for forecasting the purity of edible pigment powder. In this paper, brilliant blue and ponceau 4R served as an example to discuss the method of forecasting effect of edible pigment powder purity. The emission fluorescence spectra of two edible pigment at the optimal excitation wavelength were measured by FLS920 fluorescence spectrometer. The compression and transformation of the fluorescence spectral data was acquired by the feature compression algorithm reformed from the Original Moment method. On the one hand the feature compression algorithm shortened the operation time, on the other hand it improved the prediction accuracy of the model. Then, the concentration prediction model was established after inputting the fluorescence spectral data pre-processed into the Weighted Least Squares Support Vector Machine. The model gave anastomotic predicted spectral data with the actual experiments of the brilliant blue and ponceau 4R, and the average coefficient of determination in the half peak width was 0.700 and 0.930 respectively. There was a good linear relationship between the predicted and the nominal concentration of the brilliant blue and ponceau 4R, and the correlation coefficients were 0.997 and 0.992 respectively. It can be concluded that, the predicted concentration of the brilliant blue and ponceau 4R powder were got the results of 61.0% and 72.3% respectively.

A New Algorithm to Improve Efficiency of Resource Scheduling in Clouding Computing Based on Extended Support Vector Machine

A high effective scheduling in cloud computing environment is significant to guarantee quality of cloud service. In this paper, Weighted Least Squares Support Vector Machine (WLS-SVM) is introduced to reflect finished time and cost of assignments in cloud computing and can obtain robust estimates for regression through the limited observation. There is a simple and efficient approach to model parameters selection. Some significant parameters of support vector machine are defined to further improve convergence performance of algorithm. Moreover, high effective scheduling will be acquired and service cost may be generated in cloud computing environment. Through the simulation experiment, the validity of the proposed model is demonstrated. The results show that the method has more superior performance than other methods like Least Squares Support Vector Machine (LS-SVM).

A robust regression based on weighted LSSVM and penalized trimmed squares

Least squares support vector machine (LS-SVM) for nonlinear regression is sensitive to outliers in the field of machine learning. Weighted LS-SVM (WLS-SVM) overcomes this drawback by adding weight to each training sample. However, as the number of outliers increases, the accuracy of WLS-SVM may decrease. In order to improve the robustness of WLS-SVM, a new robust regression method based on WLS-SVM and penalized trimmed squares (WLSSVM–PTS) has been proposed. The algorithm comprises three main stages. The initial parameters are obtained by least trimmed squares at first. Then, the significant outliers are identified and eliminated by the Fast-PTS algorithm. The remaining samples with little outliers are estimated by WLS-SVM at last. The statistical tests of experimental results carried out on numerical datasets and real-world datasets show that the proposed WLSSVM–PTS is significantly robust than LS-SVM, WLS-SVM and LSSVM–LTS.

Analysis of Ammonia Nitrogen Content in Water Based on Weighted Least Squares Support Vector Machine (WLSSVM) Algorithm

Determination of ammonia nitrogen content in water is the basic item of the environmental water pollution, and is the key index to evaluate the water quality. This article designs a water quality monitoring system based on the on-line automatic ammonia nitrogen monitoring system, and establishes a forecasting model based on the weighted least squares support vector machine algorithm. The weighted least squares support vector machine algorithm increases the weight parameter setting, improves the speed and accuracy of prediction learning, and improves the robustness. In this article, a comparison between neural network model and weighted least square support vector machine model is made, which shows that the weighted least squares support vector machine model has better prediction accuracy.

Optimal design of homogeneous earth dams by particle swarm optimization incorporating support vector machine approach

The main aim of this study is to introduce optimal design of homogeneous earth dams with oblique and horizontal drains based on particle swarm optimization (PSO) incorporating weighted least squares support vector machine (WLS-SVM). To achieve this purpose, the upstream and downstream slopes of earth dam, the length of oblique and horizontal drains and angle among the drains are considered as the design variables in the optimization problem of homogeneous earth dams. Furthermore, the seepage through dam body and the weight of dam as objective functions are minimized in the optimization process simultaneously. In the optimization procedure, the stability coefficient of the upstream and downstream slopes and the seepage through dam body as the hydraulic responses of homogeneous earth dam are required. Hence, the hydraulic responses are predicted using WLS-SVM approach. The optimal results of illustrative examples demonstrate the efficiency and computational advantages of PSO with WLS-SVM in the optimal design of homogeneous earth dams with drains.

Hybridizing two-stage meta-heuristic optimization model with weighted least squares support vector machine for optimal shape of double-arch dams

A two-stage meta-heuristic optimization model is introduced to find the optimal shape of double-arch concrete dams. The main aim is that computational merits of the continuous ant colony optimization (ACOR) and the particle swarm optimization (PSO) be integrated. This proposed method called ACOR–PSO can accelerate the capability of exploitation and convergence of PSO. To achieve this, a preliminary optimization is accomplished using ACOR in the first stage of ACOR–PSO. In the second phase ACOR–PSO, PSO is utilized by using the optimal initial swarm of the first phase results. The weighted least squares support vector machine (WLS-SVM) is considered as the most reliable method for predicting the dynamic responses of dams. To testify the robustness and efficiency of the proposed ACOR–PSO, first, the well-known benchmark functions in literatures are optimized using the proposed ACOR–PSO, and provides comparisons with ACOR and PSO. Then, a real world double-arch dam is presented to demonstrate the effectiveness and practicality of the ACOR–PSO. The numerical results reveal that ACOR–PSO not only converges to better solutions but also provides faster convergence rate in comparison with ACOR and PSO.

A robust least squares support vector machine for regression and classification with noise

Least squares support vector machines (LS-SVMs) are sensitive to outliers or noise in the training dataset. Weighted least squares support vector machines (WLS-SVMs) can partly overcome this shortcoming by assigning different weights to different training samples. However, it is a difficult task for WLS-SVMs to set the weights of the training samples, which greatly influences the robustness of WLS-SVMs. In order to avoid setting weights, in this paper, a novel robust LS-SVM (RLS-SVM) is presented based on the truncated least squares loss function for regression and classification with noise. Based on its equivalent model, we theoretically analyze the reason why the robustness of RLS-SVM is higher than that of LS-SVMs and WLS-SVMs. In order to solve the proposed RLS-SVM, we propose an iterative algorithm based on the concave–convex procedure (CCCP) and the Newton algorithm. The statistical tests of the experimental results conducted on fourteen benchmark regression datasets and ten benchmark classification datasets show that compared with LS-SVMs, WLS-SVMs and iteratively reweighted LS-SVM (IRLS-SVM), the proposed RLS-SVM significantly reduces the effect of the noise in the training dataset and provides superior robustness.

A hybrid approach based on an improved gravitational search algorithm and orthogonal crossover for optimal shape design of concrete gravity dams

A hybrid approach based on an improved gravitational search algorithm (IGSA) and orthogonal crossover (OC) is proposed to efficiently find the optimal shape of concrete gravity dams. The proposed hybrid approach is called IGSA-OC. The hybrid of IGSA and the OC operator can improve the global exploration ability of the IGSA method, and increase its convergence rate. To find the optimal shape of concrete gravity dams, the interaction effects of dam–water–foundation rock subjected to earthquake loading are considered in this study. The computational cost of the optimal shape of concrete gravity dams subjected earthquake loads is usually high. Due to this problem, the weighted least squares support vector machine (WLS-SVM) regression as an efficient metamodel is utilized to considerably predict dynamic responses of gravity dams by spending low computational cost. To testify the robustness and efficiency of the proposed IGSA-OC, first, four well-known benchmark functions in literatures are optimized using the proposed IGSA-OC, and provides comparisons with the standard gravitational search algorithm (GSA) and the other modified GSA methods. Then, the optimal shape of concrete gravity dams is found using IGSA-OC. The solutions obtained by the IGSA-OC are compared with those of the standard GSA, IGSA and particle swarm optimization (PSO). The numerical results demonstrate that the proposed IGSA-OC significantly outperforms the standard GSA, IGSA and PSO.

Reliability-based design optimization of reinforced concrete structures including soil–structure interaction using a discrete gravitational search algorithm and a proposed metamodel

A new discrete gravitational search algorithm (DGSA) and a metamodelling framework are introduced for reliability-based design optimization (RBDO) of reinforced concrete structures. The RBDO of structures with soil–structure interaction (SSI) effects is investigated in accordance with performance-based design. The proposed DGSA is based on the standard gravitational search algorithm (GSA) to optimize the structural cost under deterministic and probabilistic constraints. The Monte-Carlo simulation (MCS) method is considered as the most reliable method for estimating the probabilities of reliability. In order to reduce the computational time of MCS, the proposed metamodelling framework is employed to predict the responses of the SSI system in the RBDO procedure. The metamodel consists of a weighted least squares support vector machine (WLS-SVM) and a wavelet kernel function, which is called WWLS-SVM. Numerical results demonstrate the efficiency and computational advantages of DGSA and the proposed metamodel for RBDO of reinforced concrete structures.

Melt Index Prediction by Fuzzy Functions and Weighted Least Squares Support Vector Machines

AbstractThe melt index (MI) is considered as one of the most important quality variables to determine propylene product specifications. Reliable prediction of the MI is significant in practical propylene polymerization (PP) processes. This paper presents novel predictive fuzzy functions (FF), combining the particle swarm optimization (PSO) algorithm and weighted least squares support vector machines (WLS‐SVM) to infer MI from real PP process variables, where the FF utilize WLS‐SVM for regression models to calculate the parameters and the PSO algorithm further optimizes the model. Research on the proposed FF model is carried out with the data from a real PP plant and the results are compared among the standard SVM, FF‐LS‐SVM, FF‐WLS‐SVM, and PSO‐FF‐WLS‐SVM models. The results show that the model developed here can be a powerful tool for online MI prediction.

Non-linear dependency between spiking response and gamma-band power of local field potentials in the human auditory cortex

Recent advancement in recordings of extracellular potentials from multiple sites in the human brain [1] has allowed us to simultaneously record spiking activity and local field potentials (LFP) to examine the brain's response to experimental stimuli. Various mechanisms have been suggested for the generation of the LFP. A point of special interest is that LFP reflects not only the inputs to the tissue, but also local processing. For example, spike contribution to the high-frequency LFP through increased spike rate or increased synchrony has been suggested [2]. Subjects (n = 19 ) were epilepsy patients who needed intracranial electrode implantation and chronic monitoring of for diagnostic and treatment purposes. Protocols were approved by University of Iowa IRB. Recordings were made from micro contacts implanted in the Heschl's gyri during pure tone presentations. Single-trial gamma-band responses were extracted using band-pass filters (40-150 Hz). Spike trains at the same contacts were analyzed with Poisson generalized linear models (GLM) with coded stimulus convolved with finite impulse-response (FIR) function which was estimated from the data, as well as spiking history (up to 80 ms duration, determined by minimum BIC criterion) as covariates. We treated the system as a time-invariant black box and the relationship between spiking activity (rates) and gamma-band LFP power was analyzed with Volterra kernel expansion (memory length of 200 ms) up to the second-order to examine potentially non-linear dependencies [3] (Figure ​(Figure1A).1A). Estimated discharge rates were used as the inputs and gamma LFP power was used as the outputs of the system. Weighted least-squares support-vector machines were utilized for estimating the regression coefficients [4], and the kernels were expanded using Laguerre orthogonal basis. First order kernel (linear filter) typically decreased toward zero within 150 ms lag time (Figure ​(Figure1A1A and ​and1B),1B), and 2nd -order kernels typically contain negative components, indicating non-linear suppressive effect on the gamma. (Figure ​(Figure1B).1B). A separate correlation analysis between spike count and gamma-band power within post-stimulus 200 ms shows strong positive correlation (Figure ​(Figure1C1C). Figure 1

Predictive modeling of human operator cognitive state via sparse and robust support vector machines

The accurate prediction of the temporal variations in human operator cognitive state (HCS) is of great practical importance in many real-world safety-critical situations. However, since the relationship between the HCS and electrophysiological responses of the operator is basically unknown, complicated and uncertain, only data-based modeling method can be employed. This paper is aimed at constructing a data-driven computationally intelligent model, based on multiple psychophysiological and performance measures, to accurately estimate the HCS in the context of a safety-critical human-machine system. The advanced least squares support vector machines (LS-SVM), whose parameters are optimized by grid search and cross-validation techniques, are adopted for the purpose of predictive modeling of the HCS. The sparse and weighted LS-SVM (WLS-SVM) were proposed by Suykens et al. to overcome the deficiency of the standard LS-SVM in lacking sparseness and robustness. This paper adopted those two improved LS-SVM algorithms to model the HCS based solely on a set of physiological and operator performance data. The results showed that the sparse LS-SVM can obtain HCS models with sparseness with almost no loss of modeling accuracy, while the WLS-SVM leads to models which are robust in case of noisy training data. Both intelligent system modeling approaches are shown to be capable of capturing the temporal fluctuation trends of the HCS because of their superior generalization performance.