Kernel Function Method Research Articles

A novel time-domain dynamic load identification numerical algorithm for continuous systems

Structural design and optimization are inseparable from the load acting on the structure. However, a direct measurement of the input loads is very difficult, especially dynamic loads on the large coupled continuous systems. Hence, having an accurate algorithm for the dynamic load identification for continuous systems is critical for solving many vibration problems. In this paper, we propose a novel time-domain algorithm based on the Newmark-β method, which is first attempt to solve the problems of dynamic load identification for continuous systems. By means of modal coordinate transformation and modal truncation method, the algorithm transforms the continuous system with infinite degrees of freedom into a discrete system with multi-degrees of freedom. The conventional implicit Newmark-β method is transformed into an explicit form for the solution of the Y=HF equation, and then the load F can be obtained by inverse solution. The Tikhonov regularization is adopted to overcome the ill-posedness in the inverse problem. Simulated results demonstrate the better accuracy of the proposed algorithm against Green’s kernel function method (GKFM) in the identification of sinusoidal, impact and random loads. To further verify the performance of the proposed algorithm in practical application, experimental studies of dynamic load identification are conducted on a simply supported beam system, and the results show that the algorithm is effective and robust against noises as well.

A morphometric analysis for investigation climate impact on settlement in Lengkiti, Ogan Komering Ulu Regency, Indonesia

The change in morphological patterns upstream of Ogan River were investigated to analyze land-use and climate change impact on the river meandering. This study aimed to investigate morphological changes of Ogan River in Lengkiti area between 1996 and 2019. Two sets of Landsat areal (1990 and 2016) were used to identify the morphological changes during flood periods. Data analysis used the maximum likelihood approach, t-test and Spearman correlation analysis. The morphometric indicators such as river width (W), meander neck length (L), axis length (A), curvature radius (R), water flow and sinuosity of meander (C) were extracted to identify the morphological pattern of river meandering. Analysis of land-use change used Support Vector Machine (SVM) and kernel function method to interpret the meander parameter change. Ogan River in Lengkiti, such as Batu Kuning and Marga Jaya segments, which have rice field and settlement cover from 1996 to 2019, had been cut off. Cut-off occurred due to landslides that entered river’s body and narrowed riverbed. This fasted river flow even though river discharge was same, caused intensive erosion and sedimentation. The increase in water velocity increased flow power, shortened flow distance and cut-off caused reduced meander’s sinuosity (C).

Social emotion classification of Japanese text information based on SVM and KNN

How to model multi-modal data and rich context information under the same model framework has become the key to user sentiment analysis in social media. This research uses SVM and KNN to build models for Japanese social sentiment classification and proposes a topic model for user sentiment analysis based on SVM and KNN. Moreover, taking TE process data as an example, this paper selects radial basis kernel function and grid search method for the construction of SVM classifier. In addition, by introducing the correlation variable between the sentiment of the comment and the sentiment of the tweet, the comment is related to the original tweet. Based on the establishment of the model, this research proposes a parameter estimation algorithm for model solving based on the idea of SVM-KNN, and uses the Twitter real data set as the experimental data set to verify the effectiveness of the user sentiment analysis model proposed in this paper. The research results show that the method proposed in this paper has a certain effect.

A novel mathematical model for predicting landslide displacement

Landslide displacement evolution is important for predicting landslide geological disasters. Because landslide displacement monitoring data are limited, in this paper we propose a novel model for predicting landslide displacement, namely the kernel grey model with fractional operators (FKGM). By combining the advantages of fractional modeling, kernel function methods and grey models, we derived the theoretical framework of FKGM. The parameters of FKGM were obtained using particle swarm optimization algorithm. Then, FKGM was applied in a case study of a landslide in Hubei, China. The engineering geological characteristics of the landslide were analyzed, and seven factors including rainfall and the rate of the reservoir water-level change were selected as inputs. The results show that the mean absolute percentage error and mean square error of FKGM are smaller than those of the least square support vector machine (LSSVM) and the classical grey prediction model—GM(1,1). The influence of the FKGM parameters was investigated. Our results indicate that FKGM can be applied to reliably predict large deformation of landslides.

Time Domain Identification Method for Random Dynamic Loads and its Application on Reconstruction of Road Excitations

A time domain method for identifying random dynamic loads is proposed based on spectral decomposition and regularization, which to some extent makes up for the deficiency of frequency domain methods. The random dynamic loads are descripted with their time domain mean functions and covariance matrix, which can intuitively reflect the statistical characteristics of the loads. Therein the random dynamic load identification is transformed into the load mean function identification and covariance matrix reconstruction. The forward identification models are mainly established based on Green’s kernel function method, and then spectral decomposition is conducted to transform the identification of load covariance matrix into a series of identifications of eigenvectors. To overcome the ill-posedness in the inverse process, the least-square QR iterative regularization is adopted. Two numerical examples and an application on the reconstruction of road excitations acting on a vehicle are studied to verify the effectiveness of the proposed method.

Sparse identification of time-space coupled distributed dynamic load

A novel and efficient method utilizing blind source separation and orthogonal matching pursuit is proposed in this paper to identify the time-space coupled distributed dynamic loads. By using proper orthogonal decomposition, the time-space coupled distributed dynamic load can be decomposed into the form of series of independent spatial distribution functions and time history functions. Considering the influences of the load distribution functions and time history functions on the structural responses are different, the non-uniqueness of distributed dynamic load identification is analyzed. The modal loads can be regarded as the weighted mixtures of the unknown independent time history functions and are identified by Green’s kernel function method and regularization. Then, the blind source separation technique is introduced to realize the identification of load time history functions, and the orthogonal matching pursuit algorithm is adopted to achieve the unique sparse solutions for load distribution functions. Finally, the distributed dynamic load is sparsely identified and equivalently represented as several concentrated dynamic loads acting on the appropriate positions. This proposed method is capable to deal with the time-space coupled distributed dynamic load on complicated structures, and to realize its spatial distribution representation and time history reconstruction separately. The results of the numerical examples demonstrate the reasonability and effectiveness of the method.

A time-domain method for load identification using moving weighted least square technique

Based on the thought of Green’s kernel function method (GKFM), an improved time-domain load identification method using moving weighted least square technique (MWLST) which can accurately fit dynamic load is proposed. Better than the traditional shape function method using moving least square fitting (SFM_MLSF), the proposed method considers continuity and correlation of dynamic load between two adjacent sampling points, and involves the weighted contribution of sampling points to the fitting point. In numerical examples, Gauss, Cubic and Quartic spline weight functions are utilized in the proposed method to realize the reconstruction of kernel matrix. It is found that the accuracies of load identification are almost same when their optimum supported domain radii are adopted. Furthermore, the numerical results illustrate that the proposed method can identify dynamic load more accurately and smoothly than GKFM and SFM_MLSF significantly by the same regularization method for ill-posedness, and the proposed method has excellent stability and robustness. Additionally, a special technique combining both the whole identification and the truncated-processing identification is proposed to identify external dynamic loads during hoisting process, which solves the oscillation problem caused by using inversing methods directly.

Privacy-Preserving Recommendation Based on Kernel Method in Cloud Computing

The application field of the Internet of Things (IoT) involves all aspects, and its application in the fields of industry, agriculture, environment, transportation, logistics, security and other infrastructure has effectively promoted the intelligent development of these aspects. Although the IoT has gradually grown in recent years, there are still many problems that need to be overcome in terms of technology, management, cost, policy, and security. We need to constantly weigh the benefits of trusting IoT products and the risk of leaking private data. To avoid the leakage and loss of various user data, this paper developed a hybrid algorithm of kernel function and random perturbation method based on the algorithm of non-negative matrix factorization, which realizes personalized recommendation and solves the problem of user privacy data protection in the process of personalized recommendation. Compared to non-negative matrix factorization privacy-preserving algorithm, the new algorithm does not need to know the detailed information of the data, only need to know the connection between each data; and the new algorithm can process the data points with negative characteristics. Experiments show that the new algorithm can produce recommendation results with certain accuracy under the premise of preserving users’ personal privacy.

A Novel DDoS Attack Detection Method Using Optimized Generalized Multiple Kernel Learning

Distributed Denial of Service (DDoS) attack has become one of the most destructive network attacks which can pose a mortal threat to Internet security. Existing detection methods cannot effectively detect early attacks. In this paper, we propose a detection method of DDoS attacks based on generalized multiple kernel learning (GMKL) combining with the constructed parameter R. The super-fusion feature value (SFV) and comprehensive degree of feature (CDF) are defined to describe the characteristic of attack flow and normal flow. A method for calculating R based on SFV and CDF is proposed to select the combination of kernel function and regularization paradigm. A DDoS attack detection classifier is generated by using the trained GMKL model with R parameter. The experimental results show that kernel function and regularization parameter selection method based on R parameter reduce the randomness of parameter selection and the error of model detection, and the proposed method can effectively detect DDoS attacks in complex environments with higher detection rate and lower error rate.

A novel two-dimensional NMR relaxometry pulse sequence for petrophysical characterization of shale at low field.

Low field two-dimensional nuclear magnetic resonance (2D-NMR) relaxometry is a powerful probe for the characterization of heterogenous, porous media and provides geometrical, physical and chemical information about samples at a molecular level and has been widely used in shale studies. However, NMR signals of shale decay so rapidly, dry sample for particular, that the conventional two-dimensional pulse sequence is either not sensitive enough to short relaxation components or takes too much measurement time. In this paper, 2D-NMR relaxometry correlation based on partial inversion recovery CPMG (PIR-CPMG) pulse sequence is proposed and illustrated to improve the contrast over saturation recovery CPMG (SR-CPMG) and reduces the T1 encoding time of inversion recovery CPMG (IR-CPMG) for petrophysical characterization of shale. Subsequently, the kernel function and inversion method of this sequence are presented and the reliability of the inversion method is testified by numerical simulation. Next, theoretical analysis is conducted to validate the advantages of PIR-CPMG. Ultimately, experiments on copper sulfate solution, artificial sandstone, and shale samples are performed, respectively, to verify the feasibility and effectiveness of the proposed pulse sequence. The results demonstrate that the PIR-CPMG sequence is time-saving and high-contrast, especially for the short relaxation components. This pulse sequence can be utilized in bench-top NMR core analyzer and downhole well logging, potentially, to achieve integrated petrophysical characterization of shale.

A novel inverse procedure for load identification based on improved artificial tree algorithm

This paper presents an accurate and effective method, namely, the improved artificial tree algorithm based on the Green’s kernel function method (IAT-GKFM), to identify the load in time domain. The forward problem of load identification is constructed by using the Green’s kernel function method. The forward problem is discretized using the time domain Galerkin method, where a matrix form for load identification is formed. The IAT algorithm is proposed to solve the inverse multi-dimensions problem in the inverse stage, which aims to minimize the measuring dispersion between the calculated response and the actual response. Several numerical examples are conducted. It is demonstrated that the IAT with high performance can provide more optimum results than those of other compared algorithms. Using this optimized strategy, the loads acting on a simple plate and a vehicle roof are reconstructed successfully. The superiority of IAT-GKFM may motivate the improvement of the other inverse problems.

Simultaneous upscaling of two properties of reservoirs in one dimension using adaptive bandwidth in kernel function method

Abstract Upscaling of primary geological models with huge cells, especially in porous media, is the first step in fluid flow simulation. Numerical methods are often used to solve the models. The upscaling method must preserve the important properties of the spatial distribution of the reservoir properties. An grid upscaling method based on adaptive bandwidth in kernel function is proposed according to the spatial distribution of property. This type of upscaling reduces the number of cells, while preserves the main heterogeneity features of the original fine model. The key point of the paper is upscaling two reservoir properties simultaneously. For each reservoir feature, the amount of bandwidth or optimal threshold is calculated and the results of the upscaling are obtained. Then two approaches are used to upscaling two properties simultaneously based on maximum bandwidth and minimum bandwidth. In fact, we now have a finalized upscaled model for both reservoir properties for each approach in which not only the number of their cells, but also the locations of the cells are equal. The upscaling error of the minimum bandwidth approach is less than that of the maximum bandwidth approach.

Density Peak clustering algorithm based on t-SNE Optimization

Aiming at the defect that the fast peak search clustering does not adapt to high-dimensional data sets, a T-DPC optimization algorithm is proposed. The algorithm is based on the t-SNE dimensionality reduction method, and also optimizes the calculation method of Gaussian kernel function, using a uniform metric when solving the density. Finally, the T-DPC algorithm and the DPC algorithm are compared in the artificial data set and the UCI standard data set, respectively, The experimental results show that the T-DPC algorithm not only adapts to the high dimensional dataset, but also improves the efficiency of the DPC algorithm.

Dynamic Force Identification Problem Based on a Novel Improved Tikhonov Regularization Method

The main purpose of this paper is to identify the dynamic forces between the conical pick and the coal-seam. According to the theory of time domain method, the dynamic force identification problem of the system is established. The direct problem is described by Green kernel function method. The dynamic force is expressed by a series of functions superposed by impulses, and the dynamic response of the structure is expressed as a convolution integral form between the input dynamic force and the response of Green kernel function. Because of the ill-conditioned characteristics of the structure matrix and the influence of measurement noise in the process of dynamic force identification, it is difficult to deal with this problem by the usual numerical method. In present content, a novel improved Tikhonov regularization method is proposed to solve ill-posed problems. An engineering example shows that the proposed method is effective and can obtain stable approximate solutions to meet the engineering requirements.

Dual possibilistic regression analysis using support vector networks

This study proposes a novel and efficient dual regression model for possibilistic regression analysis that incorporates the principles of support vector machine (SVM) theory. The dual regression model, which comprises an upper model and a lower model, approximates the observed fuzzy phenomena from the outside and inside directions, respectively, such that the inclusion relationship between those two models holds. The proposed dual regression model better explains the inherent vagueness that exists in a given dataset. It provides the outer and inner bounds for the estimated vagueness region, and allows an estimation of the degree of confidence in the predicted fuzzy output. Using the principles for a twin support vector machine (TSVM), the upper- and lower models are estimated by solving two smaller SVM-type quadratic programming problems (QPPs), instead of a single larger QPP. This strategy significantly increases the learning speed for the proposed algorithm. The structural risk minimization principle of SVM makes the proposed method to yield better generalization ability. The kernel function method offers a model-independent framework for the proposed dual regression model. This paper focuses on the class of radial kernels, which enables the proposed method to conquer the problem of increasing spreads. The radial kernel also gives the proposed method a unified framework that allows both crisp and fuzzy inputs. The experimental results verify the effectiveness and efficiency of the proposed method. In comparison with previous SVM-based dual regression model, the proposed approach significantly improves the sparsity, prediction speed, and training speed.

An active learning reliability method with multiple kernel functions based on radial basis function

Surrogate models combined with Monte Carlo simulation (MCS) are effective ways to address failure probability problems, which involve time-consuming computer codes, in structural reliability analysis. Recently, many active learning functions based on the Kriging model have been developed to conduct adaptive sequential sampling due to its predicted value and variance. However, effective methods for learning functions based on other surrogate models to address failure probability problems remain sparse. Hence, this paper presents a new adaptive sampling function that combines the radial basis function (RBF) approximate model with MCS to calculate the failure probability of structures. The new learning function is named the active RBF method with multiple kernel functions and Monte Carlo simulation (ARBFM-MCS). It uses several RBF kernel functions to estimate the local uncertainty of the predicted values based on interquartile range (IQR) to formulate the active learning function. This method can establish several surrogate models simultaneously for application to different problems. The stopping criterion of this method is that if one of the errors calculated by the various RBF models meets the demand, the learning process stops automatically. Furthermore, the method is also compared with the k-fold cross-validation approach based on a single RBF kernel function and some other approaches presented in the literature. Six numerical examples are considered to verify the accuracy and the efficiency of the proposed method. The results reveal that the multiple kernel function method is effective and has the same accuracy level as other methods. Moreover, for these examples, the method often calls the limit state function in fewer times to obtain accurate failure probabilities.

Statistical inference for the accelerated failure time model under two-stage generalized case–cohort design

In this article, we propose a two-stage generalized case–cohort design and develop an efficient inference procedure for the data collected with this design. In the first-stage, we observe the failure time, censoring indicator and covariates which are easy or cheap to measure, and in the second-stage, select a subcohort by simple random sampling and a subset of failures in remaining subjects from the first-stage subjects to observe their exposures which are different or expensive to measure. We derive estimators for regression parameters in the accelerated failure time model under the two-stage generalized case–cohort design through the estimated augmented estimating equation and the kernel function method. The resulting estimators are shown to be consistent and asymptotically normal. The finite sample performance of the proposed method is evaluated through the simulation studies. The proposed method is applied to a real data set from the National Wilm’s Tumor Study Group.

Automatic seizure detection based on kernel robust probabilistic collaborative representation.

Visual inspection of electroencephalogram (EEG) recordings for epilepsy diagnosis is very time-consuming. Therefore, much research is devoted to developing a computer-assisted diagnostic system to relieve the workload of neurologists. In this study, a kernel version of the robust probabilistic collaborative representation-based classifier (R-ProCRC) is proposed for the detection of epileptic EEG signals. The kernel R-ProCRC jointly maximizes the likelihood that a test EEG sample belongs to each of the two classes (seizure and non-seizure), and uses the kernel function method to map the EEG samples into the higher dimensional space to relieve the problem that they are linearly non-separable in the original space. The wavelet transform with five scales is first employed to process the raw EEG signals. Next, the test EEG samples are collaboratively represented on the training sets by the kernel R-ProCRC and they are categorized by checking which class has the maximum likelihood. Finally, post-processing is deployed to reduce misjudgment and acquire more stable results. This method is evaluated on two EEG databases and yields an accuracy of 99.3% for interictal and ictal EEGs on the Bonn database. In addition, the average sensitivity of 97.48% and specificity of 96.81% are achieved from the Freiburg database. Graphical abstract Visual inspection of EEG recordings for epilepsy diagnosis is very time-consuming. Therefore, many researchers are devoted to developing a computer-assisted diagnostic system to relieve the workload of neurologists. In this paper, a kernel version of the robust probabilistic collaborative representation based classifier (R-ProCRC) is proposed for the detection of epileptic EEG signals. The kernel R-ProCRC jointly maximizes the likelihood that a test EEG sample belongs to each of the two classes, i.e., seizure and non-seizure, and uses the kernel function method to map the EEG samples into the higher dimensional space to relieve the problem that they are linearly non-separable in the original space. The main procedures of the proposed method are exhibited in the two figures as following, Fig. 1 The main procedures of the proposed method. (a) The schematic diagram of EEG classification based on the Freiburg database. (b) The detailed procedures of the kernel R-ProCRC This method has been evaluated on two different types of EEG databases and shows superior performance.

Data inversion methods to determine sub-3 nm aerosol size distributions using the particle size magnifier

Abstract. Measuring particle size distribution accurately down to approximately 1 nm is needed for studying atmospheric new particle formation. The scanning particle size magnifier (PSM) using diethylene glycol as a working fluid has been used for measuring sub-3 nm atmospheric aerosol. A proper inversion method is required to recover the particle size distribution from PSM raw data. Similarly to other aerosol spectrometers and classifiers, PSM inversion can be deduced from a problem described by the Fredholm integral equation of the first kind. We tested the performance of the stepwise method, the kernel function method (Lehtipalo et al., 2014), the H&A linear inversion method (Hagen and Alofs, 1983), and the expectation–maximization (EM) algorithm. The stepwise method and the kernel function method were used in previous studies on PSM. The H&A method and the expectation–maximization algorithm were used in data inversion for the electrical mobility spectrometers and the diffusion batteries, respectively (Maher and Laird, 1985). In addition, Monte Carlo simulation and laboratory experiments were used to test the accuracy and precision of the particle size distributions recovered using four inversion methods. When all of the detected particles are larger than 3 nm, the stepwise method may report false sub-3 nm particle concentrations because an infinite resolution is assumed while the kernel function method and the H&A method occasionally report false sub-3 nm particles because of the unstable least squares method. The accuracy and precision of the recovered particle size distribution using the EM algorithm are the best among the tested four inversion methods. Compared to the kernel function method, the H&A method reduces the uncertainty while keeping a similar computational expense. The measuring uncertainties in the present scanning mode may contribute to the uncertainties of the recovered particle size distributions. We suggest using the EM algorithm to retrieve the particle size distributions using the particle number concentrations recorded by the PSM. Considering the relatively high computation expenses of the EM algorithm, the H&A method is recommended for preliminary data analysis. We also gave practical suggestions on PSM operation based on the inversion analysis.

Probability density forecasting of wind power using quantile regression neural network and kernel density estimation

Owing to the increasingly serious social energy crisis nowadays, wind power and other renewable energy are paid more attention. However, penetration of wind power prominently enhances the degree of complexity and difficulty in planning and dispatching of electric power systems. High-precision and more-information short term wind power forecasting (STWPF) results can effectively alleviate the uncertainly of wind power and balance the electrical power. Kernel function and bandwidth selection method have significant impact on the results of STWPF. A hybrid wind power probability density prediction method based on quantile regression neural network and Epanechnikov kernel function using Unbiased cross-validation (QRNNE-UCV) is presented. The wind power predicting results at different conditional quantiles are used as the input of kernel density estimation (KDE), which is capable of estimating the comprehensive wind power probability density forecasting information at any time in the future. In order to evaluate the wind power prediction results, the paper constructs two evaluation criteria, including evaluation metrics of point prediction results and evaluation metrics of prediction interval (PI). As a point prediction result, the probability mean is first constructed in the paper. Two real datasets of wind power from Ontario, Canada, are used to verify the QRNNE-UCV method. Moreover, by comparing with the probability density results at various confidence levels, the influence of confidence level on STWPF is investigated in this article. Experiment results show that the QRNNE-UCV method can construct more accurate PI and probability density curves, and the calculated probability mean is superior to the other point predictions. Meanwhile, the quality of PICP and PINAW improves with the increase of confidence level. The above prediction results have the ability to validly quantify the indeterminacy of wind power generation in contrast to existing support vector quantile regression (SVQR) and quantile regression neural network and triangle kernel function (QRNNT) probability density forecasting methods.