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.

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.

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.

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.

A Novel Method for Flatness Pattern Recognition via Least Squares Support Vector Regression

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.

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...

Rapid vision-based system for secondary copper content estimation

A vision-based color analysis system was developed for rapid estimation of copper content in the secondary copper smelting process. Firstly, cross section images of secondary copper samples were captured by the designed vision system. After the preprocessing and segmenting procedures, the images were selected according to their grayscale standard deviations of pixels and percentages of edge pixels in the luminance component. The selected images were then used to extract the information of the improved color vector angles, from which the copper content estimation model was developed based on the least squares support vector regression (LSSVR) method. For comparison, three additional LSSVR models, namely, only with sample selection, only with improved color vector angle, without sample selection or improved color vector angle, were developed. In addition, two exponential models, namely, with sample selection, without sample selection, were developed. Experimental results indicate that the proposed method is more effective for improving the copper content estimation accuracy, particularly when the sample size is small.

LS-SVR and AGO Based Time Series Prediction Method

Recently, fault or health condition prediction of complex systems becomes an interesting research topic. However, it is difficult to establish precise physical model for complex systems, and the time series properties are often necessary to be incorporated for the prediction in practice. Currently, the LS-SVR is widely adopted for prediction of systems with time series data. In this paper, in order to improve the prediction accuracy, accumulated generating operation （AGO） is carried out to improve the data quality and regularity of raw time series data based on grey system theory; then, the inverse accumulated generating operation （IAGO） is performed to obtain the prediction results. In addition, due to the reason that appropriate kernel function plays an important role in improving the accuracy of prediction through LS-SVR, a modified Gaussian radial basis function （RBF） is proposed. The requirements of distance functions-based kernel functions are satisfied, which ensure fast damping at the place adjacent to the test point and a moderate damping at infinity. The presented model is applied to the analysis of benchmarks. As indicated by the results, the proposed method is an effective prediction one with good precision.

A multiple-kernel LSSVR method for separable nonlinear system identifcation

In some nonlinear dynamic systems, the state variables function usually can be separated from the control variables function, which brings much trouble to the identification of such systems. To well solve this problem, an improved least squares support vector regression （LSSVR） model with multiple-kernel is proposed and the model is applied to the nonlinear separable system identification. This method utilizes the excellent nonlinear mapping ability of Morlet wavelet kernel function and combines the state and control variables information into a kernel matrix. Using the composite wavelet kernel, the LSSVR includes two nonlinear functions, whose variables are the state variables and the control ones respectively, in this way, the regression function can gain better nonlinear mapping ability, and it can simulate almost any curve in quadratic continuous integral space. Then, they are used to identify the two functions in the separable nonlinear dynamic system. Simulation results show that the multiple-kernel LSSVR method can greatly improve the identification accuracy than the single kernel method, and the Morlet wavelet kernel is more efficient than the other kernels.

Evaluation of the value of near infrared(NIR)spectromicroscopy for the analysis of glycyrrizhic acid in licorice

It has been reported that hyperspectral data could be employed to qualitatively elucidate the spatial composition of tablets of Chinese medicinal plants.To gain more insights into this technology,a quantitative profile provided by near infrared(NIR)spectromicroscopy was further studied by determining the glycyrrhizic acid content in licorice,Glycyrrhiza uralensis.Thirty-nine samples from twenty-four different origins were analyzed using NIR spectromicroscopy.Partial least squares,interval partial least square(iPLS),and least squares support vector regression(LS-SVR) methods were used to develop linear and non-linear calibration models,with optimal calibration parameters(number of interval numbers,kernel parameter,etc.) being explored.The root mean square error of prediction(RMSEP) and the coefficient of determination(R^2) of the iPLS model were 0.717 7% and 0.936 1 in the prediction set,respectively.The RMSEP and R^2 of LS-SVR model were 0.515 5%and 0.951 4 in the prediction set,respectively.These results demonstrated that the glycyrrhizic acid content in licorice could barely be analyzed by NIR spectromicroscopy,suggesting that good quality quantitative data are difficult to obtain from microscopic NIR spectra for complicated Chinese medicinal plant materials.

Timing decision-making method of engine blades for predecisional remanufacturing based on reliability analysis

A timing decision-making method for predecisional remanufacturing is presented.The method can effectively solve the uncertainty problem of remanufacturing blanks.From the perspective of reliability,this study analyzes the timing decision-making interval for predecisional remanufacturing of mechanical products during the service period and constructs an optimal timing model based on energy consumption and cost.The mapping relationships between time and energy consumption are predicted by using the characteristic values of performance degradation of products combined with the least squares support vector regression algorithm.Application of game theory reveals that when the energy consumption and cost are comprehensively optimal,this moment is the best time for predecisional remanufacturing.Used engine blades are utilized as an example to demonstrate the validity and effectiveness of the proposed method.

Adaptive online prediction method based on LS-SVR and its application in an electronic system

Health trend prediction has become an effective way to ensure the safe operation of highly reliable systems,and online prediction is always necessary in many real applications.To simultaneously obtain better or acceptable online prediction accuracy and shorter computing time,we propose a new adaptive online method based on least squares support vector regression(LS-SVR).This method adopts two approaches.One approach is that we delete certain support vectors by judging the linear correlation among the samples to increase the sparseness of the prediction model.This approach can control the loss of useful information in sample data,improve the generalization capability of the prediction model,and reduce the prediction time.The other approach is that we reduce the number of traditional LS-SVR parameters and establish a modified simple prediction model.This approach can reduce the calculation time in the process of adaptive online training.Simulation and a certain electric system application indicate preliminarily that the proposed method is an effective prediction approach for its good prediction accuracy and low computing time.