Remaining useful life prediction of aircraft lithium-ion batteries based on F-distribution particle filter and kernel smoothing algorithm

As an emergency and auxiliary power source for aircraft,lithium(Li)-ion batteries are important components of aerospace power systems.The Remaining Useful Life(RUL)prediction of Li-ion batteries is a key technology to ensure the reliable operation of aviation power systems.Particle Filter(PF)is an effective method to predict the RUL of Li-ion batteries because of its uncertainty representation and management ability.However,there are problems that particle weights cannot be updated in the prediction stage and particles degradation.To settle these issues,an innovative technique of F-distribution PF and Kernel Smoothing(FPFKS)algorithm is proposed.In the prediction stage,the weights of the particles are dynamically updated by the F kernel instead of being fixed all the time.Meanwhile,a first-order independent Markov capacity degradation model is established.Moreover,the kernel smoothing algorithm is integrated into PF,so that the variance of the parameters of capacity degradation model keeps invariant.Experiments based on NASA battery data sets show that FPFKS can be excellently applied to RUL prediction of Liion batteries.

Study of formation boundary and dip attribute extraction based on edge detection technology

In the seismic profile interpretation process,as the seismic data are big and the small geological features are difficult to identify,improvement of the efficiency is needed. In this study,structure tensor method in computer image edge detection processing is applied into the 2D seismic profile. Coherent attribute is used to extract formation edge. At the same time,extracting the eigenvalues and eigenvectors to calculate the seismic geometric properties which include dip and apparent dip,automatic identification is achieved. Testing the Gaussian kernel function with synthetic models and comparing the coherent attribute and dip attribute extraction results before and after,the conclusion that Gaussian filter can remove the random noise is obtained.

A Note on the Optimality of Generalized Cross-validation Bandwidth Selection in Partially Linear Models with Kernel Smoothing Estimator

The issue of selection of bandwidth in kernel smoothing method is considered within the context of partially linear models, hi this paper, we study the asymptotic behavior of the bandwidth choice based on generalized cross-validation （CCV） approach and prove that this bandwidth choice is asymptotically optimal. Numerical simulation are also conducted to investigate the empirical performance of generalized cross-valldation.

The Application of Kernel Smoothing to Time Series Data

There are already a lot of models to fit a set of stationary time series, such as AR, MA, and ARMA models. For the non-stationary data, an ARIMA or seasonal ARIMA models can be used to fit the given data. Moreover, there are also many statistical softwares that can be used to build a stationary or non-stationary time series model for a given set of time series data, such as SAS, SPLUS, etc. However, some statistical softwares wouldn＇t work well for small samples with or without missing data, especially for small time series data with seasonal trend. A nonparametric smoothing technique to build a forecasting model for a given small seasonal time series data is carried out in this paper. And then, both the method provided in this paper and that in SAS package are applied to the modeling of international airline passengers data respectively, the comparisons between the two methods are done afterwards. The results of the comparison show us the method provided in this paper has superiority over SAS＇s method.

Influence Diagnostics for the Cross－Validated Smoothing Parameter in Kernel Smoothing

In this paper, we present influence analysis that can identify observations: which locally infulence the choice of smoothing parameter by cross-validation method when fitting a kelnel regnssion model. The diagnostic methods are illustrated with examples.

Training Robust Support Vector Machine Based on a New Loss Function

To reduce the influences of outliers on support vector machine(SVM) classification problem,a new tangent loss function was constructed.Since the tangent loss function was not smooth in some interval,a smoothing function was used to approximate it in this interval.According to this loss function,the corresponding tangent SVM(TSVM) was got.The experimental results show that TSVM is less sensitive to outliers than SVM.So the proposed new loss function and TSVM are both effective.

Numerical Discretization-Based Kernel Type Estimation Methods for Ordinary Differential Equation Models

We consider the problem of parameter estimation in both linear and nonlinear ordinary differential equation（ODE） models. Nonlinear ODE models are widely used in applications. But their analytic solutions are usually not available. Thus regular methods usually depend on repetitive use of numerical solutions which bring huge computational cost. We proposed a new two-stage approach which includes a smoothing method（kernel smoothing or local polynomial fitting） in the first stage, and a numerical discretization method（Eulers discretization method, the trapezoidal discretization method,or the Runge–Kutta discretization method） in the second stage. Through numerical simulations, we find the proposed method gains a proper balance between estimation accuracy and computational cost.Asymptotic properties are also presented, which show the consistency and asymptotic normality of estimators under some mild conditions. The proposed method is compared to existing methods in term of accuracy and computational cost. The simulation results show that the estimators with local linear smoothing in the first stage and trapezoidal discretization in the second stage have the lowest average relative errors. We apply the proposed method to HIV dynamics data to illustrate the practicability of the estimator.

Model-averaging-based semiparametric modeling for conditional quantile prediction

In real data analysis,the underlying model is frequently unknown.Hence,the modeling strategy plays a key role in the success of data analysis.Inspired by the idea of model averaging,we propose a novel semiparametric modeling strategy for the conditional quantile prediction,without assuming that the underlying model is any specific parametric or semiparametric model.Due to the optimality of the weights selected by leaveone-out cross-validation,the proposed modeling strategy provides a more precise prediction than those based on some commonly used semiparametric models such as the varying coefficient and additive models.Asymptotic properties are established in the proposed modeling strategy along with its estimation procedure.We conducted extensive simulations to compare our method with alternatives across various scenarios.The results show that our method provides more accurate predictions.Finally,we applied our approach to the Boston housing data,yielding more precise quantile predictions of house prices compared with commonly used methods,and thus offering a clearer picture of the Boston housing market.

Semi-parametric estimation for the Box-Cox transformation model with partially linear structure

The Box-Cox transformation model has been widely used in applied econometrics, positive accounting, positive finance and statistics. There is a large literature on Box-Cox transformation model with linear structure. However, there is seldom seen on the discussion for such a model with partially linear structure. Considering the importance of the partially linear model, in this paper, a relatively simple semi-parametric estimation procedure is proposed for the Box-Cox transformation model without presuming the linear functional form and without specifying any parametric form of the disturbance, which largely reduces the risk of model misspecification. We show that the proposed estimator is consistent and asymptotically normally distributed. Its covariance matrix is also in a closed form, which can be easily estimated. Finally, a simulation study is conducted to see the finite sample performance of our estimator.

Mapping Seismic Hazard for Canadian Sites Using Spatially Smoothed Seismicity Model

The estimated seismic hazard based on the delineated seismic source model is used as the basis to assign the seismic design loads in Canadian structural design codes.An alternative for the estimation is based on a spatially smoothed source model.However,a quantification of differences in the Canadian seismic hazard maps(CanSHMs)obtained based on the delineated seismic source model and spatially smoothed model is unavailable.The quantification is valuable to identify epistemic uncertainty in the estimated seismic hazard and the degree of uncertainty in the CanSHMs.In the present study,we developed seismic source models using spatial smoothing and historical earthquake catalogue.We quantified the differences in the estimated Canadian seismic hazard by considering the delineated source model and spatially smoothed source models.For the development of the spatially smoothed seismic source models,we considered spatial kernel smoothing techniques with or without adaptive bandwidth.The results indicate that the use of the delineated seismic source model could lead to under or over-estimation of the seismic hazard as compared to those estimated based on spatially smoothed seismic source models.This suggests that an epistemic uncertainty caused by the seismic source models should be considered to map the seismic hazard.

Smoothed Estimator of Quantile Residual Lifetime for Right Censored Data

It is of great interest to estimate quantile residual lifetime in medical science and many other fields. In survival analysis, Kaplan-Meier（K-M） estimator has been widely used to estimate the survival distribution. However, it is well-known that the K-M estimator is not continuous, thus it can not always be used to calculate quantile residual lifetime. In this paper, the authors propose a kernel smoothing method to give an estimator of quantile residual lifetime. By using modern empirical process techniques, the consistency and the asymptotic normality of the proposed estimator are provided neatly.The authors also present the empirical small sample performances of the estimator. Deficiency is introduced to compare the performance of the proposed estimator with the naive unsmoothed estimator of the quantile residaul lifetime. Further simulation studies indicate that the proposed estimator performs very well.

The Proportional Mean Residual Life Regression Model with Cure Fraction and Auxiliary Covariate

As biological studies become more expensive to conduct,it is a frequently encountered question that how to take advantage of the available auxiliary covariate information when the exposure variable is not measured.In this paper,we propose an induced cure rate mean residual life time regression model to accommodate the survival data with cure fraction and auxiliary covariate,in which the exposure variable is only assessed in a validation set,but a corresponding continuous auxiliary covariate is ascertained for all subjects in the study cohort.Simulation studies elucidate the practical performance of the proposed method under finite samples.As an illustration,we apply the proposed method to a heart disease data from the Study of Left Ventricular Dysfunction.

A class of weighted estimating equations for additive hazards models with covariates missing at random

Missing covariate data arise frequently in biomedical studies.In this article,we propose a class of weighted estimating equations for the additive hazards regression model when some of the covariates are missing at random.Time-specific and subject-specific weights are incorporated into the formulation of weighted estimating equations.Unified results are established for estimating selection probabilities that cover both parametric and non-parametric modelling schemes.The resulting estimators have closed forms and are shown to be consistent and asymptotically normal.Simulation studies indicate that the proposed estimators perform well for practical settings.An application to a mouse leukemia study is illustrated.

Data-driven modeling and simulation of complex multistation manufacturing process for dimensional variation analysis

Dimensional variation analysis in multistation manufacturing processes(MMPs)is a challenging research topic with great practical significance.Researchers have been focused on constructing various mathematical models to identify the correlations among the huge amounts of collected production data.However,current models have achieved insufficient insights into the variation correlation laws due to the complexity of the data’s mutual relations.In this study,a data-driven modeling method is developed for deep data-mining and dimensional variation analysis.The proposed initial mathematical expression originates from practical engineering knowledge.Through a mathematical treatment,the mathematical expression is transformed into a first-order AR(1)model format,which contains multiple dimensional variations’interstation and temporal correlating information.To obtain this information,the estimation of the proposed model is discussed in detail.A simulation case involving two key product characteristics of a grinding process is used to demonstrate the effectiveness and accuracy of the proposed method for dimensional variation analysis in MMPs.