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 t...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.展开更多
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 algorit...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.展开更多
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 w...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.展开更多
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 I2FS...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.展开更多
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 p...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.展开更多
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...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.展开更多
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 functiona...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...展开更多
The training algorithm of classical twin support vector regression (TSVR) can be attributed to the solution of a pair of quadratic programming problems (QPPs) with inequality constraints in the dual space.However,this...The training algorithm of classical twin support vector regression (TSVR) can be attributed to the solution of a pair of quadratic programming problems (QPPs) with inequality constraints in the dual space.However,this solution is affected by time and memory constraints when dealing with large datasets.In this paper,we present a least squares version for TSVR in the primal space,termed primal least squares TSVR (PLSTSVR).By introducing the least squares method,the inequality constraints of TSVR are transformed into equality constraints.Furthermore,we attempt to directly solve the two QPPs with equality constraints in the primal space instead of the dual space;thus,we need only to solve two systems of linear equations instead of two QPPs.Experimental results on artificial and benchmark datasets show that PLSTSVR has comparable accuracy to TSVR but with considerably less computational time.We further investigate its validity in predicting the opening price of stock.展开更多
To adapt to the new requirement of the developing flatness control theory and technology, cubic patterns were introduced on the basis of the traditional linear, quadratic and quartic flatness basic patterns. Linear, q...To adapt to the new requirement of the developing flatness control theory and technology, cubic patterns were introduced on the basis of the traditional linear, quadratic and quartic flatness basic patterns. Linear, quadratic, cubic and quartic Legendre orthogonal polynomials were adopted to express the flatness basic patterns. In order to over- come the defects live in the existent recognition methods based on fuzzy, neural network and support vector regres- sion （SVR） theory, a novel flatness pattern recognition method based on least squares support vector regression （LS-SVR） was proposed. On this basis, for the purpose of determining the hyper-parameters of LS-SVR effectively and enhan- cing the recognition accuracy and generalization performance of the model, particle swarm optimization algorithm with leave-one-out （LOO） error as fitness function was adopted. To overcome the disadvantage of high computational complexity of naive cross-validation algorithm, a novel fast cross-validation algorithm was introduced to calculate the LOO error of LDSVR. Results of experiments on flatness data calculated by theory and a 900HC cold-rolling mill practically measured flatness signals demonstrate that the proposed approach can distinguish the types and define the magnitudes of the flatness defects effectively with high accuracy, high speed and strong generalization ability.展开更多
Accurate load prediction plays an important role in smart power management system, either for planning, facing the increasing of load demand, maintenance issues, or power distribution system. In order to achieve a rea...Accurate load prediction plays an important role in smart power management system, either for planning, facing the increasing of load demand, maintenance issues, or power distribution system. In order to achieve a reasonable prediction, authors have applied and compared two features extraction technique presented by kernel partial least square regression and kernel principal component regression, and both of them are carried out by polynomial and Gaussian kernels to map the original features’ to high dimension features’ space, and then draw new predictor variables known as scores and loadings, while kernel principal component regression draws the predictor features to construct new predictor variables without any consideration to response vector. In contrast, kernel partial least square regression does take the response vector into consideration. Models are simulated by three different cities’ electric load data, which used historical load data in addition to weekends and holidays as common predictor features for all models. On the other hand temperature has been used for only one data as a comparative study to measure its effect. Models’ results evaluated by three statistic measurements, show that Gaussian Kernel Partial Least Square Regression offers the more powerful features and significantly can improve the load prediction performance than other presented models.展开更多
基金Supported by the Ministerial Level Advanced Research Foundation(3031030)the"111"Project(B08043)
文摘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.
基金supported by the National Natural Science Foundation of China (61074127)
文摘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.
基金Project(50675186) supported by the National Natural Science Foundation of China
文摘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.
基金Supported by the National Natural Science Foundation of China(51006052)
文摘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.
基金supported by the National Natural Science Foundation of China(50576033)
文摘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.
基金supported by the Science and Technology on Space Intelligent Control Laboratory for National Defense(KGJZDSYS-2018-08)。
文摘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.
基金National High-tech Research and Development Pro-gram (2006AA04Z405)
文摘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...
基金supported by the National Basic Research Program (973) of China(No.2013CB329502)the National Natural Science Foundation of China(No.61379101)the Fundamental Research Funds for the Central Universities,China(No.2012LWB39)
文摘The training algorithm of classical twin support vector regression (TSVR) can be attributed to the solution of a pair of quadratic programming problems (QPPs) with inequality constraints in the dual space.However,this solution is affected by time and memory constraints when dealing with large datasets.In this paper,we present a least squares version for TSVR in the primal space,termed primal least squares TSVR (PLSTSVR).By introducing the least squares method,the inequality constraints of TSVR are transformed into equality constraints.Furthermore,we attempt to directly solve the two QPPs with equality constraints in the primal space instead of the dual space;thus,we need only to solve two systems of linear equations instead of two QPPs.Experimental results on artificial and benchmark datasets show that PLSTSVR has comparable accuracy to TSVR but with considerably less computational time.We further investigate its validity in predicting the opening price of stock.
基金Sponsored by National Natural Science Foundation of China (50675186)
文摘To adapt to the new requirement of the developing flatness control theory and technology, cubic patterns were introduced on the basis of the traditional linear, quadratic and quartic flatness basic patterns. Linear, quadratic, cubic and quartic Legendre orthogonal polynomials were adopted to express the flatness basic patterns. In order to over- come the defects live in the existent recognition methods based on fuzzy, neural network and support vector regres- sion （SVR） theory, a novel flatness pattern recognition method based on least squares support vector regression （LS-SVR） was proposed. On this basis, for the purpose of determining the hyper-parameters of LS-SVR effectively and enhan- cing the recognition accuracy and generalization performance of the model, particle swarm optimization algorithm with leave-one-out （LOO） error as fitness function was adopted. To overcome the disadvantage of high computational complexity of naive cross-validation algorithm, a novel fast cross-validation algorithm was introduced to calculate the LOO error of LDSVR. Results of experiments on flatness data calculated by theory and a 900HC cold-rolling mill practically measured flatness signals demonstrate that the proposed approach can distinguish the types and define the magnitudes of the flatness defects effectively with high accuracy, high speed and strong generalization ability.
基金The National Natural Science Foundation of China(No.51978155)the Science and Technology Program of Ministry of Housing and Urban-Rural Development(No.2020-K-125).
文摘Accurate load prediction plays an important role in smart power management system, either for planning, facing the increasing of load demand, maintenance issues, or power distribution system. In order to achieve a reasonable prediction, authors have applied and compared two features extraction technique presented by kernel partial least square regression and kernel principal component regression, and both of them are carried out by polynomial and Gaussian kernels to map the original features’ to high dimension features’ space, and then draw new predictor variables known as scores and loadings, while kernel principal component regression draws the predictor features to construct new predictor variables without any consideration to response vector. In contrast, kernel partial least square regression does take the response vector into consideration. Models are simulated by three different cities’ electric load data, which used historical load data in addition to weekends and holidays as common predictor features for all models. On the other hand temperature has been used for only one data as a comparative study to measure its effect. Models’ results evaluated by three statistic measurements, show that Gaussian Kernel Partial Least Square Regression offers the more powerful features and significantly can improve the load prediction performance than other presented models.
