Improved adaptive pruning algorithm for least squares support vector regression

As the solutions of the least squares support vector regression machine （LS-SVRM） are not sparse, it leads to slow prediction speed and limits its applications. The defects of the ex- isting adaptive pruning algorithm for LS-SVRM are that the training speed is slow, and the generalization performance is not satis- factory, especially for large scale problems. Hence an improved algorithm is proposed. In order to accelerate the training speed, the pruned data point and fast leave-one-out error are employed to validate the temporary model obtained after decremental learning. The novel objective function in the termination condition which in- volves the whole constraints generated by all training data points and three pruning strategies are employed to improve the generali- zation performance. The effectiveness of the proposed algorithm is tested on six benchmark datasets. The sparse LS-SVRM model has a faster training speed and better generalization performance.

Flatness intelligent control via improved least squares support vector regression algorithm

To overcome the disadvantage that the standard least squares support vector regression(LS-SVR) algorithm is not suitable to multiple-input multiple-output(MIMO) system modelling directly,an improved LS-SVR algorithm which was defined as multi-output least squares support vector regression(MLSSVR) was put forward by adding samples' absolute errors in objective function and applied to flatness intelligent control.To solve the poor-precision problem of the control scheme based on effective matrix in flatness control,the predictive control was introduced into the control system and the effective matrix-predictive flatness control method was proposed by combining the merits of the two methods.Simulation experiment was conducted on 900HC reversible cold roll.The performance of effective matrix method and the effective matrix-predictive control method were compared,and the results demonstrate the validity of the effective matrix-predictive control method.

Fault diagnosis of power-shift steering transmission based on multiple outputs least squares support vector regression

A method of multiple outputs least squares support vector regression （LS-SVR） was developed and described in detail, with the radial basis function （RBF） as the kernel function. The method was applied to predict the future state of the power-shift steering transmission （PSST）. A prediction model of PSST was gotten with multiple outputs LS-SVR. The model performance was greatly influenced by the penalty parameter γ and kernel parameter σ2 which were optimized using cross validation method. The training and prediction of the model were done with spectrometric oil analysis data. The predictive and actual values were compared and a fault in the second PSST was found. The research proved that this method had good accuracy in PSST fault prediction, and any possible problem in PSST could be found through a comparative analysis.

A sparse algorithm for adaptive pruning least square support vector regression machine based on global representative point ranking

Least square support vector regression(LSSVR)is a method for function approximation,whose solutions are typically non-sparse,which limits its application especially in some occasions of fast prediction.In this paper,a sparse algorithm for adaptive pruning LSSVR algorithm based on global representative point ranking(GRPR-AP-LSSVR)is proposed.At first,the global representative point ranking(GRPR)algorithm is given,and relevant data analysis experiment is implemented which depicts the importance ranking of data points.Furthermore,the pruning strategy of removing two samples in the decremental learning procedure is designed to accelerate the training speed and ensure the sparsity.The removed data points are utilized to test the temporary learning model which ensures the regression accuracy.Finally,the proposed algorithm is verified on artificial datasets and UCI regression datasets,and experimental results indicate that,compared with several benchmark algorithms,the GRPR-AP-LSSVR algorithm has excellent sparsity and prediction speed without impairing the generalization performance.

Improved Scheme for Fast Approximation to Least Squares Support Vector Regression

The solution of normal least squares support vector regression(LSSVR)is lack of sparseness,which limits the real-time and hampers the wide applications to a certain degree.To overcome this obstacle,a scheme,named I2FSA-LSSVR,is proposed.Compared with the previously approximate algorithms,it not only adopts the partial reduction strategy but considers the influence between the previously selected support vectors and the willselected support vector during the process of computing the supporting weights.As a result,I2FSA-LSSVR reduces the number of support vectors and enhances the real-time.To confirm the feasibility and effectiveness of the proposed algorithm,experiments on benchmark data sets are conducted,whose results support the presented I2FSA-LSSVR.

Improved scheme to accelerate sparse least squares support vector regression

The pruning algorithms for sparse least squares support vector regression machine are common methods, and easily com- prehensible, but the computational burden in the training phase is heavy due to the retraining in performing the pruning process, which is not favorable for their applications. To this end, an im- proved scheme is proposed to accelerate sparse least squares support vector regression machine. A major advantage of this new scheme is based on the iterative methodology, which uses the previous training results instead of retraining, and its feasibility is strictly verified theoretically. Finally, experiments on bench- mark data sets corroborate a significant saving of the training time with the same number of support vectors and predictive accuracy compared with the original pruning algorithms, and this speedup scheme is also extended to classification problem.

Improved IMM algorithm based on support vector regression for UAV tracking

With the development of technology, the relevant performance of unmanned aerial vehicles(UAVs) has been greatly improved, and various highly maneuverable UAVs have been developed, which puts forward higher requirements on target tracking technology. Strong maneuvering refers to relatively instantaneous and dramatic changes in target acceleration or movement patterns, as well as continuous changes in speed,angle, and acceleration. However, the traditional UAV tracking algorithm model has poor adaptability and large amount of calculation. This paper applies support vector regression(SVR)to the interacting multiple model(IMM) algorithm. The simulation results show that the improved algorithm has higher tracking accuracy for highly maneuverable targets than the original algorithm, and can adjust parameters adaptively, making it more adaptable.

Modeling personalized head-related impulse response using support vector regression

A new customization approach based on support vector regression （SVR） is proposed to obtain individual headrelated impulse response （HRIR） without complex measurement and special equipment. Principal component analysis （PCA） is first applied to obtain a few principal components and corresponding weight vectors correlated with individual anthropometric parameters. Then the weight vectors act as output of the nonlinear regression model. Some measured anthropometric parameters are selected as input of the model according to the correlation coefficients between the parameters and the weight vectors. After the regression model is learned from the training data, the individual HRIR can be predicted based on the measured anthropometric parameters. Compared with a back-propagation neural network （BPNN） for nonlinear regression, better generalization and prediction performance for small training samples can be obtained using the proposed PCA-SVR algorithm.

Prediction of Henry Constants and Adsorption Mechanism of Volatile Organic Compounds on Multi-Walled Carbon Nanotubes by Using Support Vector Regression

Support vector regression （SVR） combined with particle swarm optimization for its parameter optimization is employed to establish a model for predicting the Henry constants of multi-walled carbon nanotubes （MWNTs） for adsorption of volatile organic compounds （VOCs）. The prediction performance of SVR is compared with those of the model of theoretical linear salvation energy relationship （TLSER）. By using leave-one-out cross validation of SVR test Henry constants for adsorption of 35 VOCs on MWNTs, the root mean square error is 0.080, the mean absolute percentage error is only 1.19~, and the correlation coefficient （R2） is as high as 0.997. Compared with the results of the TLSER model, it is shown that the estimated errors by SVR are ali smaller than those achieved by TLSER. It reveals that the generalization ability of SVR is superior to that of the TLSER model Meanwhile, multifactor analysis is adopted for investigation of the influences of each molecular structure descriptor on the Henry constants. According to the TLSER model, the adsorption mechanism of adsorption of carbon nanotubes of VOCs is mainly a result of van der Waals and interactions of hydrogen bonds. These can provide the theoretical support for the application of carbon nanotube adsorption of VOCs and can make up for the lack of experimental data.

Support vector regression-based operational effectiveness evaluation approach to reconnaissance satellite system

As one of the most important part of weapon system of systems(WSoS),quantitative evaluation of reconnaissance satellite system(RSS)is indispensable during its construction and application.Aiming at the problem of nonlinear effectiveness evaluation under small sample conditions,we propose an evaluation method based on support vector regression(SVR)to effectively address the defects of traditional methods.Considering the performance of SVR is influenced by the penalty factor,kernel type,and other parameters deeply,the improved grey wolf optimizer(IGWO)is employed for parameter optimization.In the proposed IGWO algorithm,the opposition-based learning strategy is adopted to increase the probability of avoiding the local optima,the mutation operator is used to escape from premature convergence and differential convergence factors are applied to increase the rate of convergence.Numerical experiments of 14 test functions validate the applicability of IGWO algorithm dealing with global optimization.The index system and evaluation method are constructed based on the characteristics of RSS.To validate the proposed IGWO-SVR evaluation method,eight benchmark data sets and combat simulation are employed to estimate the evaluation accuracy,convergence performance and computational complexity.According to the experimental results,the proposed method outperforms several prediction based evaluation methods,verifies the superiority and effectiveness in RSS operational effectiveness evaluation.

Inverse Model Control for a Quad-rotor Aircraft Using TS-fuzzy Support Vector Regression

An inverse model control based on TS-fuzzy support vector regression( TS-fuzzy SVR) for a quadrotor aircraft is developed. The TS-kernel is the product of linear combination of input and a cluster of output corresponding to a cluster of TS-type fuzzy rules. The output of TS-fuzzy SVR is a linear weighted sum of the TSkernels. The dynamical model of the quad-rotor aircraft is derived. A new control scheme combined with TSfuzzy SVR inverse model control and PID control is presented so that the TS-fuzzy SVR inverse model control enhances capabilities of disturbance rejection and the robustness while the PID control enhances fast responsiveness and reliability of the system. Simulation results show the capabilities of the developed control for the attitude system of quad-rotor aircraft.

SUPPORT VECTOR REGRESSION VIA MCMC WITHIN EVIDENCE FRAMEWORK

This paper proposes a novel approach, Markov Chain Monte Carlo (MCMC) sampling approximation, to deal with intractable high-dimension integral in the evidence framework applied to Support Vector Regression (SVR). Unlike traditional variational or mean field method, the proposed approach follows the idea of MCMC, firstly draws some samples from the posterior distribution on SVR's weight vector, and then approximates the expected output integrals by finite sums. Experimental results show the proposed approach is feasible and robust to noise. It also shows the performance of proposed approach and Relevance Vector Machine (RVM) is comparable under the noise circumstances. They give better robustness compared to standard SVR.

State of Health Estimation of Lithium-Ion Batteries Using Support Vector Regression and Long Short-Term Memory

Lithium-ion batteries are the most widely accepted type of battery in the electric vehicle industry because of some of their positive inherent characteristics. However, the safety problems associated with inaccurate estimation and prediction of the state of health of these batteries have attracted wide attention due to the adverse negative effect on vehicle safety. In this paper, both machine and deep learning models were used to estimate the state of health of lithium-ion batteries. The paper introduces the definition of battery health status and its importance in the electric vehicle industry. Based on the data preprocessing and visualization analysis, three features related to actual battery capacity degradation are extracted from the data. Two learning models, SVR and LSTM were employed for the state of health estimation and their respective results are compared in this paper. The mean square error and coefficient of determination were the two metrics for the performance evaluation of the models. The experimental results indicate that both models have high estimation results. However, the metrics indicated that the SVR was the overall best model.

Application of Least Squares Support Vector Machine for Regression to Reliability Analysis

In order to deal with the issue of huge computational cost very well in direct numerical simulation, the traditional response surface method (RSM) as a classical regression algorithm is used to approximate a functional relationship between the state variable and basic variables in reliability design. The algorithm has treated successfully some problems of implicit performance function in reliability analysis. However, its theoretical basis of empirical risk minimization narrows its range of applications for...

基于LS-SVR岩石爆破块度预测

为了准确预测小样本条件下露天矿山岩石的爆破块度,并得到小样本条件下预测露天矿山爆破块度的有效方法,借助最小二乘支持向量机工具(LS-SVMlab)构建基于最小二乘支持向量机回归(LS-SVR)预测模型并合理优化模型参数。分别使用15组露天矿山爆破数据和35组爆破数据作为小样本容量和正常样本容量,对模型的预测精度进行检验。结果表明:两种样本容量下LS-SVR预测模型的预测结果精度都比同样本容量下人工神经网络(ANN)回归预测的结果精度更高,说明所提出的LS-SVR模型适用于预测露天矿山爆破块度,并且在小样本条件下更具优势。

基于新息的多参量混沌时间序列LS-SVR加权预测

复杂系统常常依赖于通过观测所获得的多参量混沌时间序列进行预测分析。论文借鉴单参量混沌时间序列预测的思路,考虑全部相关参量混沌时间序列中的信息,以实现多参量混沌时间序列的相空间重构。同时,基于新息优先原理和支持向量机理论,结合混沌时间序列发展变化的规律,提出分别利用相空间重构后长期多样本和近期少样本构建2个自适应最小二乘支持向量回归预测模型进行加权预测的观点,并给出了以预测均方根误差最小为目标函数的模型参数混沌优化方法。论文以某飞机转子部件磨损故障的3个相关参量的仿真混沌时间序列为例进行了预测实验,结果表明文中方法有较好的预测精度,是一种有效的预测方法。

基于LS-SVR的机器人空间4DOF无标定视觉定位

研究了基于智能算法的机器人无标定视觉伺服问题,提出了一种新的基于最小二乘支持向量回归的机器人无标定视觉免疫控制方法.利用最小二乘支持向量回归学习机器人位姿变化和观测到的图像特征变化之间的复杂非线性关系,其中最小二乘支持向量回归的参数由自适应免疫算法加5折交叉检验优化确定,在此基础上利用免疫控制原理设计了视觉控制器.六自由度工业机器人空间4DOF视觉定位实验结果表明了该方法的有效性.

基于特征量重要度LS-SVR的WSN定位方法

针对无线传感器网络（WSN）节点定位方法中采用粗测距技术时，节点间较大的测距误差导致定位准确度不足的问题，提出一种基于特征量重要度最小二乘支持向量回归（LS-SVR）的定位方法．该方法把未知节点到锚节点的距离作为特征量，依据特征量的重要度进行特征提取，通过对探测区域网格化采样得到训练样本集，使用LS-SVR学习得到定位模型；在定位阶段，将未知节点的特征向量输入定位模型，利用LS—SVR良好的泛化能力实现对未知节点的准确定位．对均匀分布和C形区域随机分布的100个节点的定位实验表明，文中提出的定位方法能有效地降低测距误差对定位准确度的影响，减小平均定位误差；与采用相同测距技术的DV—Hop方法相比，均匀分布情况下该方法的平均定位误差减小7．5％～14．0％，C形区域随机分布情况下显著减小36．5％～55．2％．

基于LS-SVR的图像噪声去除算法研究

通过对最小二乘支持向量机(Least squares support vector regression,LS-SVR)滤波特性的分析,给出了LS-SVR用于图像滤波的卷积模板构造方法,解决了LS-SVR在应用中需要求解的问题,在此基础上,提出了基于LS-SVR的开关型椒盐噪声滤波算法.滤波算法中以Maximum-minimum算子作为椒盐噪声检测器,利用滤波窗口内非噪声点构成LS-SVR的输入数据,使用事先构造出的LS-SVR滤波算子,对滤波窗口进行简单的卷积运算,实现了被椒盐噪声污染点数据的有效恢复,实验表明,本文提出的方法具有较好的细节保护能力和较强的噪声去除能力.