Anisotropic diffusion dynamics in vector models for liquid crystal

Vector-based continuous models for nematic liquid crystals such as the Oseen-Frank model and the Ericksen model are relatively simpler compared with tensor-based models such as the Landau-de Gennes model.However,these vector models do not respect head-to-tail symmetry.As a result,they cannot predict configurations corresponding to non-orientable line fields,particularly the half-integer defects.This paper confirms a significant discrepancy between the transition dynamics predicted by the Oseen-Frank vector model and Landau-de Gennes tensor model for liquid crystals confined in a two-dimensional square well.The so-called inner product weighted Laplacian operator is introduced as an anisotropic diffusion operator to evolve the Euler-Lagrange equations corresponding to the modified Oseen-Frank model.Numerical results show that both the predicted equilibrium configurations and the transition dynamics from one equilibrium states to another satisfies head-to-tail symmetry and can accommodate half-integer defects.The connections of anisotropic diffusion operator to the graph Laplacian and the discrete Lebwohl-Lasher model are also discussed.The numerical trick proposed in this paper can be considered a simple remedy to restore head-to-tail symmetry in vector models of liquid crystals,making them more applicable in situations such as systems containing half-integer defects where the traditional numerical approach would fail.

A Composite Approach of Radar Echo Extrapolation Based on TREC Vectors in Combination with Model-Predicted Winds

Extending the lead time of precipitation nowcasts is vital to improvements in heavy rainfall warning, flood mitigation, and water resource management. Because the TREC vector （tracking radar echo by correlation） represents only the instantaneous trend of precipitation echo motion, the approach using derived echo motion vectors to extrapolate radar reflectivity as a rainfall forecast is not satisfactory if the lead time is beyond 30 minutes. For longer lead times, the effect of ambient winds on echo movement should be considered. In this paper, an extrapolation algorithm that extends forecast lead times up to 3 hours was developed to blend TREC vectors with model-predicted winds. The TREC vectors were derived from radar reflectivity patterns in 3 km height CAPPI （constant altitude plan position indicator） mosaics through a cross-correlation technique. The background steering winds were provided by predictions of the rapid update assimilation model CHAF （cycle of hourly assimilation and forecast）. A similarity index was designed to determine the vertical level at which model winds were applied in the extrapolation process, which occurs via a comparison between model winds and radar vectors. Based on a summer rainfall case study, it is found that the new algorithm provides a better forecast.

Small-time scale network traffic prediction based on a local support vector machine regression model

In this paper we apply the nonlinear time series analysis method to small-time scale traffic measurement data. The prediction-based method is used to determine the embedding dimension of the traffic data. Based on the reconstructed phase space, the local support vector machine prediction method is used to predict the traffic measurement data, and the BIC-based neighbouring point selection method is used to choose the number of the nearest neighbouring points for the local support vector machine regression model. The experimental results show that the local support vector machine prediction method whose neighbouring points are optimized can effectively predict the small-time scale traffic measurement data and can reproduce the statistical features of real traffic measurements.

SOFT SENSING MODEL BASED ON SUPPORT VECTOR MACHINE AND ITS APPLICATION

Soft sensor is widely used in industrial process control. It plays animportant role to improve the quality of product and assure safety in production. The core of softsensor is to construct soft sensing model. A new soft sensing modeling method based on supportvector machine (SVM) is proposed. SVM is a new machine learning method based on statistical learningtheory and is powerful for the problem characterized by small sample, nonlinearity, high dimensionand local minima. The proposed methods are applied to the estimation of frozen point of light dieseloil in distillation column. The estimated outputs of soft sensing model based on SVM match the realvalues of frozen point and follow varying trend of frozen point very well. Experiment results showthat SVM provides a new effective method for soft sensing modeling and has promising application inindustrial process applications.

Nonlinear Model Predictive Control Based on Support Vector Machine with Multi-kernel

Multi-kernel-based support vector machine （SVM） model structure of nonlinear systems and its specific identification method is proposed, which is composed of a SVM with linear kernel function followed in series by a SVM with spline kernel function. With the help of this model, nonlinear model predictive control can be transformed to linear model predictive control, and consequently a unified analytical solution of optimal input of multi-step-ahead predictive control is possible to derive. This algorithm does not require online iterative optimization in order to be suitable for real-time control with less calculation. The simulation results of pH neutralization process and CSTR reactor show the effectiveness and advantages of the presented algorithm.

A new magneto-cardiogram study using a vector model with a virtual heart and the boundary element method

A cardiac vector model is presented and verified, and then the forward problem for cardiac magnetic fields and electric potential are discussed based on this model and the realistic human torso volume conductor model, including lungs. A torso-cardiac vector model is used for a 12-lead electrocardiographic （ECG） and magneto-cardiogram （MCG） simulation study by using the boundary element method （BEM）. Also, we obtain the MCG wave picture using a compound four-channel HTc.SQUID system in a magnetically shielded room. By comparing the simulated results and experimental results, we verify the cardiac vector model and then do a preliminary study of the forward problem of MCG and ECG. Therefore, the results show that the vector model is reasonable in cardiac electrophysiology.

Numerical Analysis of Stochastic Vector Borne Plant Disease Model

We are associating the solutions of stochastic and deterministic vector borne plant disease model in this manuscript.The dynamics of plant model depends upon threshold number P^(∗).If P^(∗)<1 then condition helpful to eradicate the disease in plants while P^(∗)>1 explains the persistence of disease.Inappropriately,standard numerical systems do not behave well in certain scenarios.We have been proposed a structure preserving stochastic non-standard finite difference system to analyze the behavior of model.This system is dynamical consistent,positive and bounded as defined by Mickens.

Support vector machine based nonlinear model multi-step-ahead optimizing predictive control

A support vector machine with guadratic polynomial kernel function based nonlinear model multi-step-ahead optimizing predictive controller was presented. A support vector machine based predictive model was established by black-box identification. And a quadratic objective function with receding horizon was selected to obtain the controller output. By solving a nonlinear optimization problem with equality constraint of model output and boundary constraint of controller output using Nelder-Mead simplex direct search method, a sub-optimal control law was achieved in feature space. The effect of the controller was demonstrated on a recognized benchmark problem and a continuous-stirred tank reactor. The simulation results show that the multi-step-ahead predictive controller can be well applied to nonlinear system, with better performance in following reference trajectory and disturbance-rejection.

Support Vector Machine active learning for 3D model retrieval

In this paper, we present a novel Support Vector Machine active learning algorithm for effective 3D model retrieval using the concept of relevance feedback. The proposed method learns from the most informative objects which are marked by the user, and then creates a boundary separating the relevant models from irrelevant ones. What it needs is only a small number of 3D models labelled by the user. It can grasp the user＇s semantic knowledge rapidly and accurately. Experimental results showed that the proposed algorithm significantly improves the retrieval effectiveness. Compared with four state-of-the-art query refinement schemes for 3D model retrieval, it provides superior retrieval performance after no more than two rounds of relevance feedback.

Robustly stable model predictive control based on parallel support vector machines with linear kernel

Robustly stable multi-step-ahead model predictive control (MPC) based on parallel support vector machines (SVMs) with linear kernel was proposed. First, an analytical solution of optimal control laws of parallel SVMs based MPC was derived, and then the necessary and sufficient stability condition for MPC closed loop was given according to SVM model, and finally a method of judging the discrepancy between SVM model and the actual plant was presented, and consequently the constraint sets, which can guarantee that the stability condition is still robust for model/plant mismatch within some given bounds, were obtained by applying small-gain theorem. Simulation experiments show the proposed stability condition and robust constraint sets can provide a convenient way of adjusting controller parameters to ensure a closed-loop with larger stable margin.

Semi-supervised Support Vector Regression Model for Remote Sensing Water Quality Retrieving

This paper proposed a semi-supervised regression model with co-training algorithm based on support vector machine, which was used for retrieving water quality variables from SPOT 5 remote sensing data. The model consisted of two support vector regressors (SVRs). Nonlinear relationship between water quality variables and SPOT 5 spectrum was described by the two SVRs, and semi-supervised co-training algorithm for the SVRs was es-tablished. The model was used for retrieving concentrations of four representative pollution indicators―permangan- ate index (CODmn), ammonia nitrogen (NH3-N), chemical oxygen demand (COD) and dissolved oxygen (DO) of the Weihe River in Shaanxi Province, China. The spatial distribution map for those variables over a part of the Weihe River was also produced. SVR can be used to implement any nonlinear mapping readily, and semi-supervis- ed learning can make use of both labeled and unlabeled samples. By integrating the two SVRs and using semi-supervised learning, we provide an operational method when paired samples are limited. The results show that it is much better than the multiple statistical regression method, and can provide the whole water pollution condi-tions for management fast and can be extended to hyperspectral remote sensing applications.

A Multiple Model Approach to Modeling Based on Fuzzy Support Vector Machines

A new multiple models(MM) approach was proposed to model complex industrial process by using Fuzzy Support Vector Machines(F -SVMs). By applying the proposed approach to a pH neutralization titration experiment, F -SVMs MM not only provides satisfactory approximation and generalization property, but also achieves superior performance to USOCPN multiple modeling method and single modeling method based on standard SVMs.

FAULT DIAGNOSIS APPROACH BASED ON HIDDEN MARKOV MODEL AND SUPPORT VECTOR MACHINE

Aiming at solving the problems of machine-learning in fault diagnosis, a diagnosis approach is proposed based on hidden Markov model （HMM） and support vector machine （SVM）. HMM usually describes intra-class measure well and is good at dealing with continuous dynamic signals. SVM expresses inter-class difference effectively and has perfect classify ability. This approach is built on the merit of HMM and SVM. Then, the experiment is made in the transmission system of a helicopter. With the features extracted from vibration signals in gearbox, this HMM-SVM based diagnostic approach is trained and used to monitor and diagnose the gearbox＇s faults. The result shows that this method is better than HMM-based and SVM-based diagnosing methods in higher diagnostic accuracy with small training samples.

Stability of GM(1,1) power model on vector transformation

The morbidity problem of the GM（1,1） power model in parameter identification is discussed by using multiple and rotation transformation of vectors. Firstly we consider the morbidity problem of the special matrix and prove that the condition number of the coefficient matrix is determined by the ratio of lengths and the included angle of the column vector, which could be adjusted by multiple and rotation transformation to turn the matrix to a well-conditioned one. Then partition the corresponding matrix of the GM（1,1） power model in accordance with the column vector and regulate the matrix to a well-conditioned one by multiple and rotation transformation of vectors, which completely solve the instability problem of the GM（1,1） power model. Numerical results show that vector transformation is a new method in studying the stability problem of the GM（1,1） power model.

A novel excitation controller using support vector machines and approximate models

This paper proposes a novel excitation controller using support vector machines （SVM） and approximate models. The nonlinear control law is derived directly based on an input-output approximation method via Taylor expansion, which not only avoids complex control development and intensive computation, but also avoids online learning or adjustment. Only a general SVM modelling technique is involved in both model identification and controller implementation. The robustness of the stability is rigorously established using the Lyapunov method. Several simulations demonstrate the effectiveness of the proposed excitation controller.

Support Vector Machine-Based Nonlinear System Modeling and Control

This paper provides an introduction to a support vector machine, a new kernel-based technique introduced in statistical learning theory and structural risk minimization, then presents a modeling-control framework based on SVM. At last a numerical experiment is taken to demonstrate the proposed approach's correctness and effectiveness.

Study on Vector Magnetic Properties of Magnetic Materials Using Hybrid Hysteresis Model

This paper presents a method to study the vector magnetic properties of magnetic materials under alternating and rotational magnetic field using 2-D vector hybrid hysteresis model.Combining Preisach model and Stoner-Wohlfarth(S-W)model,the vector hybrid hysteresis model is established for magnetic materials.The alternating and rotational hysteresis properties are calculated under different excitation frequency,respectively.And the computed results are compared with the experimental measurement ones.It is shown that the vector model can simulate the alternating and rotational magnetic properties effectively under low magnetization fields and low excitation frequency.

Vector modeling of robotic helical milling hole movement and theoretical analysis on roughness of hole surface

To avoid the machine problems of excessive axial force, complex process flow and frequent tool changing during robotic drilling holes, a new hole-making technology (i.e., helical milling hole) was introduced for designing a new robotic helical milling hole system, which could further improve robotic hole-making ability in airplane digital assembly. After analysis on the characteristics of helical milling hole, advantages and limitations of two typical robotic helical milling hole systems were summarized. Then, vector model of helical milling hole movement was built on vector analysis method. Finally, surface roughness calculation formula was deduced according to the movement principle of helical milling hole, then the influence of main technological parameters on surface roughness was analyzed. Analysis shows that theoretical surface roughness of hole becomes poor with the increase of tool speed ratio and revolution radius. Meanwhile, the roughness decreases according to the increase of tool teeth number. The research contributes greatly to the construction of roughness prediction model in helical milling hole.

Support vector regression-based internal model control

This paper proposes a design of internal model control systems for process with delay by using support vector regression(SVR).The proposed system fully uses the excellent nonlinear estimation performance of SVR with the structural risk minimization principle.Closed-system stability and steady error are analyzed for the existence of modeling errors.The simulations show that the proposed control systems have the better control performance than that by neural networks in the cases of the training samples with small size and noises.

Nonlinear model predictive control based on support vector machine and genetic algorithm

This paper presents a nonlinear model predictive control(NMPC) approach based on support vector machine(SVM) and genetic algorithm(GA) for multiple-input multiple-output(MIMO) nonlinear systems.Individual SVM is used to approximate each output of the controlled plant Then the model is used in MPC control scheme to predict the outputs of the controlled plant.The optimal control sequence is calculated using GA with elite preserve strategy.Simulation results of a typical MIMO nonlinear system show that this method has a good ability of set points tracking and disturbance rejection.