Parameter selection of support vector machine for function approximation based on chaos optimization

The support vector machine （SVM） is a novel machine learning method, which has the ability to approximate nonlinear functions with arbitrary accuracy. Setting parameters well is very crucial for SVM learning results and generalization ability, and now there is no systematic, general method for parameter selection. In this article, the SVM parameter selection for function approximation is regarded as a compound optimization problem and a mutative scale chaos optimization algorithm is employed to search for optimal paraxneter values. The chaos optimization algorithm is an effective way for global optimal and the mutative scale chaos algorithm could improve the search efficiency and accuracy. Several simulation examples show the sensitivity of the SVM parameters and demonstrate the superiority of this proposed method for nonlinear function approximation.

Piezoelectric transducer parameter selection for exciting a single mode from multiple modes of Lamb waves

Excitation and propagation of Lamb waves by using rectangular and circular piezoelectric transducers surface- bonded to an isotropic plate are investigated in this work. Analytical stain wave solutions are derived for the two transducer shapes, giving the responses of these transducers in Lamb wave fields. The analytical study is supported by a numericM simulation using the finite element method. Symmetric and antisymmetric components in the wave propagation responses are inspected in detail with respect to test parameters such as the transducer geometry, the length and the excitation frequency. By placing only one piezoelectric transducer on the top or the bottom surface of the plate and weakening the strength of one mode while enhancing the strength of the other modes to find the centre frequency, with which the peak wave amplitude ratio between the SO and A0 modes is maximum, a single mode excitation from the multiple modes of the Lamb waves can be achieved approximately. Experimental data are presented to show the validity of the analyses. The results are used to optimize the Lamb wave detection system.

Parameter selection and model research on remote sensing evaluation for nearshore water quality

Using remote sensing technology for water quality evaluation is an inevitable trend in marine environmental monitoring. However, fewer categories of water quality parameters can be monitored by remote sensing technology than the 35 specified in GB3097-1997 Marine Water Quality Standard. Therefore, we considered which parameters must be selected by remote sensing and how to model for water quality evaluation using the finite parameters. In this paper, focused on Leizhou Peninsula nearshore waters, we found N, P, COD, PH and DO to be the dominant parameters of water quality by analyzing measured data. Then, mathematical statistics was used to determine that the relationship among the five parameters was COD〉DO〉P〉N〉pH. Finally, five-parameter, fourparameter and three-parameter water quality evaluation models were established and compared. The results showed that COD, DO, P and N were the necessary parameters for remote sensing evaluation of the Leizhou Peninsula nearshore water quality, and the optimal comprehensive water quality evaluation model was the four- parameter model. This work may serve as a reference for monitoring the quality of other marine waters by remote sensing.

TV/L2-based image denoisingalgorithm with automaticparameter selection

In order to improve the adaptiveness of TV/L2-based image denoising algorithm in differ- ent signal-to-noise ratio （SNR） environments, an iterative denoising method with automatic parame- ter selection is proposed. Based upon the close connection between optimization function of denois- ing problem and regularization parameter, an updating model is built to select the regularized param- eter. Both the parameter and the objective function are dynamically updated in alternating minimiza- tion iterations, consequently, it can make the algorithm work in different SNR environments. Mean- while, a strategy for choosing the initial regularization parameter is presented. Considering Morozov discrepancy principle, a convex function with respect to the regularization parameter is modeled. Via the optimization method, it is easy and fast to find the convergence value of parameter, which is suitable for the iterative image denoising algorithm. Comparing with several state-of-the-art algo- rithms, many experiments confirm that the denoising algorithm with the proposed parameter selec- tion is highly effective to evaluate peak signal-to-noise ratio （PSNR） and structural similarity

Parameter selection in time series prediction based on nu-support vector regression

The theory of nu-support vector regression (Nu-SVR) is employed in modeling time series variationfor prediction. In order to avoid prediction performance degradation caused by improper parameters, themethod of parallel multidimensional step search (PMSS) is proposed for users to select best parameters intraining support vector machine to get a prediction model. A series of tests are performed to evaluate themodeling mechanism and prediction results indicate that Nu-SVR models can reflect the variation tendencyof time series with low prediction error on both familiar and unfamiliar data. Statistical analysis is alsoemployed to verify the optimization performance of PMSS algorithm and comparative results indicate thattraining error can take the minimum over the interval around planar data point corresponding to selectedparameters. Moreover, the introduction of parallelization can remarkably speed up the optimizing procedure.

Convolution Neural Network-based Load Model Parameter Selection Considering Short-term Voltage Stability

The recently proposed ambient signal-based load modeling approach offers an important and effective idea to study the time-varying and distributed characteristics of power loads.Meanwhile,it also brings new problems.Since the load model parameters of power loads can be obtained in real-time for each load bus,the numerous identified parameters make parameter application difficult.In order to obtain the parameters suitable for off-line applications,load model parameter selection(LMPS)is first introduced in this paper.Meanwhile,the convolution neural network(CNN)is adopted to achieve the selection purpose from the perspective of short-term voltage stability.To begin with,the field phasor measurement unit(PMU)data from China Southern Power Grid are obtained for load model parameter identification,and the identification results of different substations during different times indicate the necessity of LMPS.Meanwhile,the simulation case of Guangdong Power Grid shows the process of LMPS,and the results from the CNNbased LMPS confirm its effectiveness.

Novel linear search for support vector machine parameter selection

Selecting the optimal parameters for support vector machine (SVM) has long been a hot research topic. Aiming for support vector classification/regression (SVC/SVR) with the radial basis function (RBF) kernel, we summarize the rough line rule of the penalty parameter and kernel width, and propose a novel linear search method to obtain these two optimal parameters. We use a direct-setting method with thresholds to set the epsilon parameter of SVR. The proposed method directly locates the right search field, which greatly saves computing time and achieves a stable, high accuracy. The method is more competitive for both SVC and SVR. It is easy to use and feasible for a new data set without any adjustments, since it requires no parameters to set.

Scaling parameters selection principle for the scaled unscented Kalman filter

The paper deals with the state estimation of the widely used scaled unscented Kalman filter（UKF）. In particular, the stress is laid on the scaling parameters selection principle for the scaled UKF. Several problems caused by recommended constant scaling parameters are highlighted. On the basis of the analyses, an effective scaled UKF is proposed with self-adaptive scaling parameters,which is easy to understand and implement in engineering. Two typical strong nonlinear examples are given and their simulation results show the effectiveness of the proposed principle and algorithm.

Novel Method for Selection of Regularization Parameter in the Near-field Acoustic Holography

Because of the ill-posedness of the near-field acoustic holography（NAH）,the regularization method is required to stabilize the computational process of NAH.The regularization effect is related to how to select the parameter correctly and effectively.However the L-curve method commonly used for the selection of regularization parameters has the disadvantages of wrong selection and incorrect selection,which influences the application of NAH.For the purpose of solving the problems existed in the L-curve method,the （？）-curve method is introduced into the field of NAH,and the performance applied to NAH directly is analyzed on the basis of equivalent source method-based NAH.However,it is found out via investigations that the（？）-curve method in NAH also has the problem of wrong selection and is unable to choose the regularization parameter correctly.In order to select the parameter correctly and effectively,a novel method for selecting regularization parameters is proposed based on the original（？）-curve method,which can be called improved （？）-curve method.In the proposed method the regularization parameters are discretized linearly between the largest singular value and the smallest singular value,and the solution norm and the residual norm corresponding to these regularization parameters are also described in a linear coordinate instead of in a lg-lg coordinate,which are the two main differences compared with the L-curve and with the original（？）-curve method.In linear coordinate and using the linearly discretized regularization parameters,the solution norm is a monotonically decreasing function of the residual norm as the increase of the regularization parameter,moreover the curve is convex everywhere.So the regularization parameters can be selected correctly and effectively based on the improved（？）-curve method.Then a numerical simulation is done with a simply supported plate to verify the validity of the proposed method.Experiments with two actual sources,a clamped plate and the double speakers,are carried out to do a further demonstration.The simulation result as well as the experimental result shows that the improved（？）-curve method is efficacious and has some advantages over the L-curve method and the original（？）-curve method.The proposed novel method is able to avoid the problem of wrong selection and to select the regularization parameter correctly even if the curve is smooth.

Optimal choice of parameters for particle swarm optimization

The constriction factor method (CFM) is a new variation of the basic particle swarm optimization (PSO), which has relatively better convergent nature. The effects of the major parameters on CFM were systematically investigated based on some benchmark functions. The constriction factor, velocity constraint, and population size all have significant impact on the per- formance of CFM for PSO. The constriction factor and velocity constraint have optimal values in practical application, and im- proper choice of these factors will lead to bad results. Increasing population size can improve the solution quality, although the computing time will be longer. The characteristics of CFM parameters are described and guidelines for determining parameter values are given in this paper.

Numerical estimation of choice of the regularization parameter for NMR T2 inversion

Nuclear Magnetic inversion is the basis of NMR Resonance （NMR） T2 logging interpretation. The regularization parameter selection of the penalty term directly influences the NMR T2 inversion result. We implemented both norm smoothing and curvature smoothing methods for NMR T2 inversion, and compared the inversion results with respect to the optimal regular- ization parameters （（Xopt） which were selected by the dis- crepancy principle （DP）, generalized cross-validation （GCV）, S-curve, L-curve, and the slope of L-curve methods, respectively. The numerical results indicate that the DP method can lead to an oscillating or oversmoothed solution which is caused by an inaccurately estimated noise level. The （Xopt selected by the L-curve method is occa- sionally small or large which causes an undersmoothed or oversmoothed T2 distribution. The inversion results from GCV, S-curve and the slope of L-curve methods show satisfying inversion results. The slope of the L-curve method with less computation is more suitable for NMR T2 inversion. The inverted T2 distribution from norm smoothing is better than that from curvature smoothing when the noise level is high.

Individualization of Data-Segment-Related Parameters for Improvement of EEG Signal Classification in Brain-Computer Interface

In electroencephalogram (EEG) modeling techniques, data segment selection is the first and still an important step. The influence of a set of data-segment-related parameters on feature extraction and classification in an EEG-based brain-computer interface (BCI) was studied. An auto search algorithm was developed to study four datasegment-related parameters in each trial of 12 subjects’ EEG. The length of data segment (LDS), the start position of data (SPD) segment, AR order, and number of trials (NT) were used to build the model. The study showed that, compared with the classification ratio (CR) without parameter selection, the CR was increased by 20% to 30% with proper selection of these data-segment-related parameters, and the optimum parameter values were subject-dependent. This suggests that the data-segment-related parameters should be individualized when building models for BCI.

Parameter selecting and quality predicting of spot welding based on artificial neural networks

This paper proposes a procedure for using artificial neural networks (ANN) in spot welding , and establishes spot welding parameter selecting ANN systems and spot welding joint quality predicting ANN systems . It has been proved that the ANN systems have high prediction precision , providing a new way of parameter selecting and quality predicting in spot welding .

Deep Learning-Based Stacked Auto-Encoder with Dynamic Differential Annealed Optimization for Skin Lesion Diagnosis

Intelligent diagnosis approaches with shallow architectural models play an essential role in healthcare.Deep Learning(DL)models with unsupervised learning concepts have been proposed because high-quality feature extraction and adequate labelled details significantly influence shallow models.On the other hand,skin lesionbased segregation and disintegration procedures play an essential role in earlier skin cancer detection.However,artefacts,an unclear boundary,poor contrast,and different lesion sizes make detection difficult.To address the issues in skin lesion diagnosis,this study creates the UDLS-DDOA model,an intelligent Unsupervised Deep Learning-based Stacked Auto-encoder(UDLS)optimized by Dynamic Differential Annealed Optimization(DDOA).Pre-processing,segregation,feature removal or separation,and disintegration are part of the proposed skin lesion diagnosis model.Pre-processing of skin lesion images occurs at the initial level for noise removal in the image using the Top hat filter and painting methodology.Following that,a Fuzzy C-Means(FCM)segregation procedure is performed using a Quasi-Oppositional Elephant Herd Optimization(QOEHO)algorithm.Besides,a novel feature extraction technique using the UDLS technique is applied where the parameter tuning takes place using DDOA.In the end,the disintegration procedure would be accomplished using a SoftMax(SM)classifier.The UDLS-DDOA model is tested against the International Skin Imaging Collaboration(ISIC)dataset,and the experimental results are examined using various computational attributes.The simulation results demonstrated that the UDLS-DDOA model outperformed the compared methods significantly.

Local Radial Basis Function Methods: Comparison, Improvements, and Implementation

Radial Basis Function methods for scattered data interpolation and for the numerical solution of PDEs were originally implemented in a global manner. Subsequently, it was realized that the methods could be implemented more efficiently in a local manner and that the local approaches could match or even surpass the accuracy of the global implementations. In this work, three localization approaches are compared: a local RBF method, a partition of unity method, and a recently introduced modified partition of unity method. A simple shape parameter selection method is introduced and the application of artificial viscosity to stabilize each of the local methods when approximating time-dependent PDEs is reviewed. Additionally, a new type of quasi-random center is introduced which may be better choices than other quasi-random points that are commonly used with RBF methods. All the results within the manuscript are reproducible as they are included as examples in the freely available Python Radial Basis Function Toolbox.

Parameter value selection strategy for complete coverage path planning based on the Lüsystem to perform specific types of missions

We propose a novel parameter value selection strategy for the Lüsystem to construct a chaotic robot to accomplish the complete coverage path planning(CCPP)task.The algorithm can meet the requirements of high randomness and coverage rate to perform specific types of missions.First,we roughly determine the value range of the parameter of the Lüsystem to meet the requirement of being a dissipative system.Second,we calculate the Lyapunov exponents to narrow the value range further.Next,we draw the phase planes of the system to approximately judge the topological distribution characteristics of its trajectories.Furthermore,we calculate the Pearson correlation coefficient of the variable for those good ones to judge its random characteristics.Finally,we construct a chaotic robot using variables with the determined parameter values and simulate and test the coverage rate to study the relationship between the coverage rate and the random characteristics of the variables.The above selection strategy gradually narrows the value range of the system parameter according to the randomness requirement of the coverage trajectory.Using the proposed strategy,proper variables can be chosen with a larger Lyapunov exponent to construct a chaotic robot with a higher coverage rate.Another chaotic system,the Lorenz system,is used to verify the feasibility and effectiveness of the designed strategy.The proposed strategy for enhancing the coverage rate of the mobile robot can improve the efficiency of accomplishing CCPP tasks under specific types of missions.

Extrapolated Tikhonov method and inversion of 3D density images of gravity data

Tikhonov regularization（TR） method has played a very important role in the gravity data and magnetic data process. In this paper, the Tikhonov regularization method with respect to the inversion of gravity data is discussed. and the extrapolated TR method（EXTR） is introduced to improve the fitting error. Furthermore, the effect of the parameters in the EXTR method on the fitting error, number of iterations, and inversion results are discussed in details. The computation results using a synthetic model with the same and different densities indicated that. compared with the TR method, the EXTR method not only achieves the a priori fitting error level set by the interpreter but also increases the fitting precision, although it increases the computation time and number of iterations. And the EXTR inversion results are more compact than the TR inversion results, which are more divergent. The range of the inversion data is closer to the default range of the model parameters, and the model features and default model density distribution agree well.

Notes on the forest soil respiration measurement by a Li-6400 system

The correct method used in forest soil respiration measurement by Li-6400 is a premise of data quality control. According to the study in a larch plantation, collars should be inserted at 12 hours in advance to efficiently reduce the influence of CO2 spring-out.Moreover, collar insertion depth substantially affected soil respiration measurement, i.e. when collar was shallowly inserted into soil,transversal gas diffusion and the CO2 re-spring-out caused by unstable collars in the measurement could lead to overestimating soil respiration rate; however, when collar was deeply inserted into soil, root respiration decline caused by root-cut and the most active respiratory of the surface soil separated by the inserted collars could lead to underestimating soil respiration rate. Furthermore, an error less than 5% could be guaranteed in typical sunny day if the target [CO2] was set to the mean value of ambient [CO2] in most time of the day, but it should be carefully set in early morning and late afternoon according to changing ambient [CO2]. This protocol of measurement is useful in real measurement.

Partition region-based suppressed fuzzy C-means algorithm

Aimed at the problem that the traditional suppressed fuzzy C-means clustering algorithms ignore the real needs of different objects, applying the same suppressed parameter for modifying membership degrees of all the objects, a novel partition region-based suppressed fuzzy C-means clustering algorithm with better capacity of adaptability and robustness is proposed in this paper. The model based on the real needs of different objects is built, making it clear to decide whether to proceed with further determination; in addition, the external user-defined suppressed parameter is automatically selected according to the intrinsic structural characteristic of each dataset, making the proposed method become robust to the fluctuations in the incoming dataset and initial conditions. Experimental results show that the proposed method is more robust than its counterparts and overcomes the weakness of the original suppressed clustering algorithm in most cases.

A modeling method of microburst based on multiple vortex ring

Microburst is a special kind of low-level wind shear, which may do great damage to aircrafts. Modelling of a microburst is significant for flight simulations. In this paper we adopt multiple vortex ring principle to model microburst and propose a new parameter selection method of multiple vortex ring model. We treat the parameters selection as an optimization problem, and introduce the differential evolution algorithm into it. A nested differential evolution algorithm is proposed to complete the two optimization process, objective optimization and intermediate optimization. The simulation results show that this method can flexibly generate microburst with any maximum wind velocity.