Data-driven computing in elasticity via kernel regression

This paper presents a simple nonparametric regression approach to data-driven computing in elasticity. We apply the kernel regression to the material data set, and formulate a system of nonlinear equations solved to obtain a static equilibrium state of an elastic structure. Preliminary numerical experiments illustrate that, compared with existing methods, the proposed method finds a reasonable solution even if data points distribute coarsely in a given material data set.

Nuclear charge radius predictions by kernel ridge regression with odd-even effects

The extended kernel ridge regression(EKRR)method with odd-even effects was adopted to improve the description of the nuclear charge radius using five commonly used nuclear models.These are:(i)the isospin-dependent A^(1∕3) formula,(ii)relativistic continuum Hartree-Bogoliubov(RCHB)theory,(iii)Hartree-Fock-Bogoliubov(HFB)model HFB25,(iv)the Weizsacker-Skyrme(WS)model WS*,and(v)HFB25*model.In the last two models,the charge radii were calculated using a five-parameter formula with the nuclear shell corrections and deformations obtained from the WS and HFB25 models,respectively.For each model,the resultant root-mean-square deviation for the 1014 nuclei with proton number Z≥8 can be significantly reduced to 0.009-0.013 fm after considering the modification with the EKRR method.The best among them was the RCHB model,with a root-mean-square deviation of 0.0092 fm.The extrapolation abilities of the KRR and EKRR methods for the neutron-rich region were examined,and it was found that after considering the odd-even effects,the extrapolation power was improved compared with that of the original KRR method.The strong odd-even staggering of nuclear charge radii of Ca and Cu isotopes and the abrupt kinks across the neutron N=126 and 82 shell closures were also calculated and could be reproduced quite well by calculations using the EKRR method.

Data-driven Transient Stability Assessment Model Considering Network Topology Changes via Mahalanobis Kernel Regression and Ensemble Learning

Transient stability assessment(TSA)is of great importance in power system operation and control.One of the usual tasks in TSA is to estimate the critical clearing time(CCT)of a given fault under the given network topology and pre-fault power flow.Data-driven methods try to obtain models describing the mapping between these factors and the CCT from a large number of samples.However,the influence of network topology on CCT is hard to be analyzed and is often ignored,which makes the models inaccurate and unpractical.In this paper,a novel data-driven TSA model combining Mahalanobis kernel regression and ensemble learning is proposed to deal with the problem.The model is a weighted sum of several sub-models.Each sub-model only uses the data of one topology to construct a kernel regressor.The weights are determined by both the topological similarity and numerical similarity between the samples.The similarities are decided by the parameters in Mahalanobis distance,and the parameters are to be trained.To reduce the model complexity,sub-models within the same topology category share the same parameters.When estimating CCT,the model uses not only the sub-model which the sample topology belongs to,but also other sub-models.Thus,it avoids the problem that there may be too few data under some topologies.It also efficiently utilizes information of data under all the topologies.Moreover,its decision-making process is clear and understandable,and an effective training algorithm is also designed.Test results on both the IEEE 10-machine 39-bus and a real system verify the effectiveness of the proposed model.

Data-driven Transient Stability Assessment Based on Kernel Regression and Distance Metric Learning

Transient stability assessment(TSA) is of great importance in power systems. For a given contingency, one of the most widely-used transient stability indices is the critical clearing time(CCT), which is a function of the pre-fault power flow.TSA can be regarded as the fitting of this function with the prefault power flow as the input and the CCT as the output. In this paper, a data-driven TSA model is proposed to estimate the CCT. The model is based on Mahalanobis-kernel regression,which employs the Mahalanobis distance in the kernel regression method to formulate a better regressor. A distance metric learning approach is developed to determine the problem-specific distance for TSA, which describes the dissimilarity between two power flow scenarios. The proposed model is more accurate compared to other data-driven methods, and its accuracy can be further improved by supplementing more training samples.Moreover, the model provides the probability density function of the CCT, and different estimations of CCT at different conservativeness levels. Test results verify the validity and the merits of the method.

Multi-view space object recognition and pose estimation based on kernel regression

The application of high-performance imaging sensors in space-based space surveillance systems makes it possible to recognize space objects and estimate their poses using vision-based methods. In this paper, we proposed a kernel regression-based method for joint multi-view space object recognition and pose estimation. We built a new simulated satellite image dataset named BUAA-SID 1.5 to test our method using different image representations. We evaluated our method for recognition-only tasks, pose estimation-only tasks, and joint recognition and pose estimation tasks. Experimental results show that our method outperforms the state-of-the-arts in space object recognition, and can recognize space objects and estimate their poses effectively and robustly against noise and lighting conditions.

Feature Extraction of Kernel Regress Reconstruction for Fault Diagnosis Based on Self-organizing Manifold Learning

The feature space extracted from vibration signals with various faults is often nonlinear and of high dimension.Currently,nonlinear dimensionality reduction methods are available for extracting low-dimensional embeddings,such as manifold learning.However,these methods are all based on manual intervention,which have some shortages in stability,and suppressing the disturbance noise.To extract features automatically,a manifold learning method with self-organization mapping is introduced for the first time.Under the non-uniform sample distribution reconstructed by the phase space,the expectation maximization(EM) iteration algorithm is used to divide the local neighborhoods adaptively without manual intervention.After that,the local tangent space alignment(LTSA) algorithm is adopted to compress the high-dimensional phase space into a more truthful low-dimensional representation.Finally,the signal is reconstructed by the kernel regression.Several typical states include the Lorenz system,engine fault with piston pin defect,and bearing fault with outer-race defect are analyzed.Compared with the LTSA and continuous wavelet transform,the results show that the background noise can be fully restrained and the entire periodic repetition of impact components is well separated and identified.A new way to automatically and precisely extract the impulsive components from mechanical signals is proposed.

Correlation between Combined Urinary Metal Exposure and Grip Strength under Three Statistical Models:A Cross-sectional Study in Rural Guangxi

Objective This study aimed to investigate the potential relationship between urinary metals copper(Cu),arsenic(As),strontium(Sr),barium(Ba),iron(Fe),lead(Pb)and manganese(Mn)and grip strength.Methods We used linear regression models,quantile g-computation and Bayesian kernel machine regression(BKMR)to assess the relationship between metals and grip strength.Results In the multimetal linear regression,Cu(β=−2.119),As(β=−1.318),Sr(β=−2.480),Ba(β=0.781),Fe(β=1.130)and Mn(β=−0.404)were significantly correlated with grip strength(P<0.05).The results of the quantile g-computation showed that the risk of occurrence of grip strength reduction was−1.007(95%confidence interval:−1.362,−0.652;P<0.001)when each quartile of the mixture of the seven metals was increased.Bayesian kernel function regression model analysis showed that mixtures of the seven metals had a negative overall effect on grip strength,with Cu,As and Sr being negatively associated with grip strength levels.In the total population,potential interactions were observed between As and Mn and between Cu and Mn(P_(interactions) of 0.003 and 0.018,respectively).Conclusion In summary,this study suggests that combined exposure to metal mixtures is negatively associated with grip strength.Cu,Sr and As were negatively correlated with grip strength levels,and there were potential interactions between As and Mn and between Cu and Mn.

Optimal decoupling control system using kernel method

A major difficulty in multivariable control design is the cross-coupling between inputs and outputs which obscures the effects of a specific controller on the overall behavior of the system. This paper considers the application of kernel method in decoupling multivariable output feedback controllers. Simulation results are presented to show the feasibility of the proposed technique.

Examination of machine learning for assessing physical effects:Learning the relativistic continuum mass table with kernel ridge regression

The kernel ridge regression(KRR)method and its extension with odd-even effects(KRRoe)are used to learn the nuclear mass table obtained by the relativistic continuum Hartree-Bogoliubov theory.With respect to the binding energies of 9035 nuclei,the KRR method achieves a root-mean-square deviation of 0.96 MeV,and the KRRoe method remarkably reduces the deviation to 0.17 MeV.By investigating the shell effects,one-nucleon and twonucleon separation energies,odd-even mass differences,and empirical proton-neutron interactions extracted from the learned binding energies,the ability of the machine learning tool to grasp the known physics is discussed.It is found that the shell effects,evolutions of nucleon separation energies,and empirical proton-neutron interactions are well reproduced by both the KRR and KRRoe methods,although the odd-even mass differences can only be reproduced by the KRRoe method.

GIS-based evaluation of landslide susceptibility using a novel hybrid computational intelligence model on different mapping units

Landslide susceptibility mapping is significant for landslide prevention.Many approaches have been used for landslide susceptibility prediction,however,their performances are unstable.This study constructed a hybrid model,namely box counting dimension-based kernel logistic regression model,which uses fractal dimension calculated by box counting method as input data based on grid cells mapping unit and terrain mapping unit.The performance of this model was evaluated in the application in Zhidan County,Shaanxi Province,China.Firstly,a total of 221 landslides were identified and mapped,and 11 landslide predisposing factors were considered.Secondly,the landslide susceptibility maps(LSMs) of the study area were obtained by constructing the model on two different mapping units.Finally,the results were evaluated with five statistical indexes,sensitivity,specificity,positive predictive value(PPV),negative predictive value(NPV) and Accuracy.The statistical indexes of the model obtained on the terrain mapping unit were larger than those based on grid cells mapping unit.For training and validation datasets,the area under the receiver operating characteristic curve(AUC) of the model based on terrain mapping unit were 0.9374 and 0.9527,respectively,indicating that establishing this model on the terrain mapping unit was advantageous in the study area.The results show that the fractal dimension improves the prediction ability of the kernel logistic model.In addition,the terrain mapping unit is a more promising mapping unit in Loess areas.

Received signal strength based indoor positioning algorithm using advanced clustering and kernel ridge regression

We propose a novel indoor positioning algorithm based on the received signal strength(RSS) fingerprint. The proposed algorithm can be divided into three steps, an offline phase at which an advanced clustering(AC) strategy is used, an online phase of approximate localization at which cluster matching is used, and an online phase of precise localization with kernel ridge regression. Specifically, after offline fingerprint collection and similarity measurement, we employ an AC strategy based on the K-medoids clustering algorithm using additional reference points that are geographically located at the outer cluster boundary to enrich the data of each cluster. During the approximate localization, RSS measurements are compared with the cluster radio maps to determine to which cluster the target most likely belongs. Both the Euclidean distance of the RSSs and the Hamming distance of the coverage vectors between the observations and training records are explored for cluster matching. Then, a kernel-based ridge regression method is used to obtain the ultimate positioning of the target. The performance of the proposed algorithm is evaluated in two typical indoor environments, and compared with those of state-of-the-art algorithms. The experimental results demonstrate the effectiveness and advantages of the proposed algorithm in terms of positioning accuracy and complexity.

Application of kernel ridge regression in predicting neutron-capture reaction cross-sections

This article provides the first application of the machine-learning approach in the study of the cross-sections for neutron-capture reactions with the kernel ridge regression(KRR)approach.It is found that the KRR approach can reduce the root-mean-square(rms)deviation of the relative errors between the experimental data of the Maxwellian-averaged(n,γ)cross-sections and the corresponding theoretical predictions from 69.8%to 35.4%.By including the data with different temperatures in the training set,the rms deviation can be further significantly reduced to 2.0%.Moreover,the extrapolation performance of the KRR approach along different temperatures is found to be effective and reliable.

Soft Sensing Modelling Based on Optimal Selection of Secondary Variables and Its Application

The composition of the distillation column is a very important quality value in refineries, unfortunately, few hardware sensors are available on-line to measure the distillation compositions. In this paper, a novel method using sensitivity matrix analysis and kernel ridge regression （KRR） to implement on-line soft sensing of distillation compositions is proposed. In this approach, the sensitivity matrix analysis is presented to select the most suitable secondary variables to be used as the soft sensor＇s input. The KRR is used to build the composition soft sensor. Application to a simulated distillation column demonstrates the effectiveness of the method.

Spider Monkey Optimization with Statistical Analysis for Robust Rainfall Prediction

Rainfall prediction becomes popular in real time environment due to the developments of recent technologies.Accurate and fast rainfall predictive models can be designed by the use of machine learning(ML),statistical models,etc.Besides,feature selection approaches can be derived for eliminating the curse of dimensionality problems.In this aspect,this paper presents a novel chaotic spider money optimization with optimal kernel ridge regression(CSMO-OKRR)model for accurate rainfall prediction.The goal of the CSMO-OKRR technique is to properly predict the rainfall using the weather data.The proposed CSMO-OKRR technique encompasses three major processes namely feature selection,prediction,and parameter tuning.Initially,the CSMO algorithm is employed to derive a useful subset of features and reduce the computational complexity.In addition,the KRR model is used for the prediction of rainfall based on weather data.Lastly,the symbiotic organism search(SOS)algorithm is employed to properly tune the parameters involved in it.A series of simulations are performed to demonstrate the better performance of the CSMO-OKRR technique with respect to different measures.The simulation results reported the enhanced outcomes of the CSMO-OKRR technique with existing techniques.

Stahel-Donoho kernel estimation for fixed design nonparametric regression models

This paper reports a robust kernel estimation for fixed design nonparametric regression models.A Stahel-Donoho kernel estimation is introduced,in which the weight functions depend on both the depths of data and the distances between the design points and the estimation points.Based on a local approximation,a computational technique is given to approximate to the incomputable depths of the errors.As a result the new estimator is computationally efficient.The proposed estimator attains a high breakdown point and has perfect asymptotic behaviors such as the asymptotic normality and convergence in the mean squared error.Unlike the depth-weighted estimator for parametric regression models,this depth-weighted nonparametric estimator has a simple variance structure and then we can compare its efficiency with the original one.Some simulations show that the new method can smooth the regression estimation and achieve some desirable balances between robustness and efficiency.

Short Term Wind Speed Prediction Using Multiple Kernel Pseudo Inverse Neural Network

An accurate short-term wind speed prediction algorithm based on the efficient kernel ridge pseudo inverse neural network （KRPINN） variants is proposed in this paper. The use of nonlinear kernel functions in pseudo inverse neural networks eliminates the trial and error approach of choosing the number of hidden layer neurons and their activation functions. The robustness of the proposed method has been validated in comparison with other models such as pseudo inverse radial basis function （PIRBF） and Legendre tanh activation function based neural network, i.e., PILNNT, whose input weights to the hidden layer weights are optimized using an adaptive firefly algorithm, i.e., FFA. However, since the individual kernel functions based KRPINN may not be able to produce accurate forecasts under chaotically varying wind speed conditions, a linear combination of individual kernel functions is used to build the multi kernel ridge pseudo inverse neural network （MK-RPINN） for providing improved forecasting accuracy, generalization, and stability of the wind speed prediction model. Several case studies have been presented to validate the accuracy of the short-term wind speed prediction models using the real world wind speed data from a wind farm in the Wyoming State of USA over time horizons varying from 10 minutes to 5 hours.

Semiparametric Model Averaging for Ultrahigh-Dimensional Conditional Quantile Prediction

In this paper,we develop a flexible semiparametric model averaging marginal regression procedure to forecast the joint conditional quantile function of the response variable for ultrahighdimensional data.First,we approximate the joint conditional quantile function by a weighted average of one-dimensional marginal conditional quantile functions that have varying coefficient structures.Then,a local linear regression technique is employed to derive the consistent estimates of marginal conditional quantile functions.Second,based on estimated marginal conditional quantile functions,we estimate and select the significant model weights involved in the approximation by a nonconvex penalized quantile regression.Under some relaxed conditions,we establish the asymptotic properties for the nonparametric kernel estimators and oracle estimators of the model averaging weights.We further derive the oracle property for the proposed nonconvex penalized model averaging procedure.Finally,simulation studies and a real data analysis are conducted to illustrate the merits of our proposed model averaging method.

Sex-specific and dose-response relationships of urinary cobalt and molybdenum levels with glucose levels and insulin resistance in U.S. adults

Growing studies have linked metal exposure to diabetes risk.However,these studies had inconsistent results.We used a multiple linear regression model to investigate the sexspecific and dose-response associations between urinary metals(cobalt(Co)and molybdenum(Mo))and diabetes-related indicators(fasting plasma glucose(FPG),hemoglobin A1c(HbA1c),homeostasis model assessment for insulin resistance(HOMA-IR),and insulin)in a cross-sectional study based on the United States National Health and Nutrition Examination Survey.The urinary metal concentrations of 1423 eligible individuals were stratified on the basis of the quartile distribution.Our results showed that the urinary Co level in males at the fourth quartile(Q4)was strongly correlated with increased FPG(β=0.61,95%CI:0.17–1.04),HbA1c(β=0.31,95%CI:0.09–0.54),insulin(β=8.18,95%CI:2.84–13.52),and HOMA–IR(β=3.42,95%CI:1.40–5.44)when compared with first quartile(Q1).High urinary Mo levels(Q4 vs.Q1)were associated with elevated FPG(β=0.46,95%CI:0.17–0.75)and HbA1c(β=0.27,95%CI:0.11–0.42)in the overall population.Positive linear dose-response associations were observed between urinary Co and insulin(Pnonlinear=0.513)and HOMA–IR(Pnonlinear=0.736)in males,as well as a positive linear dose-response relationship between urinary Mo and FPG(Pnonlinear=0.826)and HbA1c(Pnonlinear=0.376)in the overall population.Significant sex-specific and dose-response relationships were observed between urinary metals(Co and Mo)and diabetes-related indicators,and the potential mechanisms should be further investigated.

Background knowledge based privacy metric model for online social networks

The data of online social network （OSN） is collected currently by the third party for various purposes. One of the problems in such practices is how to measure the privacy breach to assure users. The recent work on OSN privacy is mainly focus on privacy-preserving data publishing. However, the work on privacy metric is not systematic but mainly focus on the traditional datasets. Compared with the traditional datasets, the attribute types in OSN are more diverse and the tuple is relevant to each other. The retweet and comment make the graph character of OSN notably. Furthermore, the open application programming interfaces （APIs） and lower register barrier make OSN open environment, in which the background knowledge is more easily achieved by adversaries. This paper analyzes the background knowledge in OSN and discusses its characteristics in detail. Then a privacy metric model faces OSN background knowledge based on kernel regression is proposed. In particular, this model takes the joint attributes and link knowledge into consideration. The effect of different data distributions is discussed. The real world data set from weibo.com has been adopted. It is demonstrated that the privacy metric algorithm in this article is effective in OSN privacy evaluation. The prediction error is 30% lower than that of the work mentioned above

On a Strategy to Develop Robust and Simple Tariffs from Motor Vehicle Insurance Data

Abstract The goals of this paper are twofold: we describe common features in data sets from motor vehicle insurance companies and we investigate a general strategy which exploits the knowledge of such features. The results of the strategy are a basis to develop insurance tariffs. We use a nonparametric approach based on a combination of kernel logistic regression and e-support vector regression which both have good robustness properties. The strategy is applied to a data set from motor vehicle insurance companies.