Remaining useful life prediction based on nonlinear random coefficient regression model with fusing failure time data

Remaining useful life(RUL) prediction is one of the most crucial elements in prognostics and health management(PHM). Aiming at the imperfect prior information, this paper proposes an RUL prediction method based on a nonlinear random coefficient regression(RCR) model with fusing failure time data.Firstly, some interesting natures of parameters estimation based on the nonlinear RCR model are given. Based on these natures,the failure time data can be fused as the prior information reasonably. Specifically, the fixed parameters are calculated by the field degradation data of the evaluated equipment and the prior information of random coefficient is estimated with fusing the failure time data of congeneric equipment. Then, the prior information of the random coefficient is updated online under the Bayesian framework, the probability density function(PDF) of the RUL with considering the limitation of the failure threshold is performed. Finally, two case studies are used for experimental verification. Compared with the traditional Bayesian method, the proposed method can effectively reduce the influence of imperfect prior information and improve the accuracy of RUL prediction.

The Minimax Estimator of Stochastic Regression Coefficients and Parameters in the Class of All Estimators

In this paper, the authors address the problem of the minimax estimator of linear combinations of stochastic regression coefficients and parameters in the general normal linear model with random effects. Under a quadratic loss function, the minimax property of linear estimators is investigated. In the class of all estimators, the minimax estimator of estimable functions, which is unique with probability 1, is obtained under a multivariate normal distribution.

Empirical Likelihood Test for Regression Coefficients in High Dimensional Partially Linear Models

This paper considers tests for regression coefficients in high dimensional partially linear Models.The authors first use the B-spline method to estimate the unknown smooth function so that it could be linearly expressed.Then,the authors propose an empirical likelihood method to test regression coefficients.The authors derive the asymptotic chi-squared distribution with two degrees of freedom of the proposed test statistics under the null hypothesis.In addition,the method is extended to test with nuisance parameters.Simulations show that the proposed method have a good performance in control of type-I error rate and power.The proposed method is also employed to analyze a data of Skin Cutaneous Melanoma(SKCM).

ADMISSIBILITY OF LINEAR ESTIMATORS OF REGRESSION COEFFICIENTS UNDER QUADRATIC LOSS

For the general fixed effects linear model: Y = X_T+ε, ε～N(0, V), V≥0, weobtain the necessary and sufficient conditions for LY +a to be admissible for a linear estimablefunction S_r in the class of all estimators under the loss function (d -- Sr)'D(d --Sr), whereD≥0 is known. For the general random effects linear model: Y = Xβ+ε,(βε)～N((Aα 0), (V_(11)V_(12)V_(21)V_(22))), ∧= XV_(11)X'+XV_(12)+ V_(21)X+V_(22)≥0, we also get the necessaryand sufficient conditions for LY+a to be admissible for a linear estimable function Sα+Qβin the class of all estimators under the loss function (d-Sα-Qβ)'D(d-Sα-Qβ).whereD≥0 is known.

Tests for p-regression Coefficients in Linear Panel Model When p is Divergent

This paper evaluates the performance of the FW-test for testing part of p-regression coefficients in linear panel data model when p is divergent.The asymptotic power of the F_W-statistic is obtained under some regular conditions.The theoretical development are challenging since the number of covariates increases as the sample size increases.It is worth noting that the inference approach does not require any specification of the error distribution.Some simulation comparisons are conducted and show that the simulated power coincide with theoretical power well.The method is also illustrated using a renal cancer data example.

LIMITING BEHAVIOR OF RECURSIVE M-ESTIMATORS IN MULTIVARIATE LINEAR REGRESSION MODELS AND THEIR ASYMPTOTIC EFFICIENCIES

Recursive algorithms are very useful for computing M-estimators of regression coefficients and scatter parameters. In this article, it is shown that for a nondecreasing ul （t）, under some mild conditions the recursive M-estimators of regression coefficients and scatter parameters are strongly consistent and the recursive M-estimator of the regression coefficients is also asymptotically normal distributed. Furthermore, optimal recursive M-estimators, asymptotic efficiencies of recursive M-estimators and asymptotic relative efficiencies between recursive M-estimators of regression coefficients are studied.

Comparing Land Degradation and Regeneration Trends in China Drylands

The aim of this paper is to offer a statistically sound method to make a precise account of the speed of land degradation and regeneration processes.Most common analyses of land degradation focus instead on the extent of degraded areas,rather than on the intensity of degradation processes.The study was implemented for the Potential Extent of Desertification in China(PEDC),composed by arid,semi-arid,and dry sub-humid regions and refers to the period 2002 to 2012.The metrics were standard partial regression coefficients from stepwise regressions,fitted using Net Primary Productivity as the dependent variable,and year number and aridity as predictors.The results indicate that:①the extension of degrading lands(292896 km 2 or 9.12%of PEDC)overcomes the area that is recovering(194560 km 2 or 6.06%of PEDC);and②the intensity of degrading trends is lower than that of increasing trends in three land cover types(grassland,desert,and crops)and in two aridity levels(semi-arid and dry sub-humid).Such an outcome might pinpoint restoration policies by the Chinese government,and document a possible case of hysteresis.

PSYCHOLOGICAL EVALUATION OF COLOR DESIGN

In this paper, a method of predicting psychological values of color design was performed by using random color patterns. The results were analyzed in terms of the Fourier transform of the color patterns, and it was found that the psychological values of the random color patterns depended not only on the zero frequency component but also on the dynamic components of the Fourier transform of the patterns. The application of the estimation method was discussed.

Mathematical Modeling of the Bulk Density Property of Knitted Fabrics

The paper focuses on the prediction of the volumetric density property of knitting fabrics using mathematical modeling. Based on the graphical analysis of the obtained mathematical models, the results of the raw material properties for the futer knitted fabric on the values of alternative indicators are presented.

B-spline estimation for varying coefficient regression with spatial data

This paper considers a nonparametric varying coefficient regression with spatial data. A global smoothing procedure is developed by using B-spline function approximations for estimating the coefficient functions. Under mild regularity assumptions,the global convergence rates of the B-spline estimators of the unknown coefficient functions are established. Asymptotic results show that our B-spline estimators achieve the optimal convergence rate. The asymptotic distributions of the B-spline estimators of the unknown coefficient functions are also derived. A procedure for selecting smoothing parameters is given. Finite sample properties of our procedures are studied through Monte Carlo simulations. Application of the proposed method is demonstrated by examining voting behaviors across US counties in the 1980 presidential election.

Two-stage Local Walsh Average Estimation of Generalized Varying Coefficient Models

In this paper we investigate the robust estimation of generalized varying coefficient models in which the unknown regression coefficients may change with different explanatory variables. Based on the B-spline series approximation and Walsh-average technique we develop an initial estimator for the unknown regression coefficient functions. By virtue of the initial estimator, the generalized varying coefficient model is reduced to a univariate nonparametric regression model. Then combining the local linear smooth and Walsh average technique we further propose a two-stage local linear Walsh-average estimator for the unknown regression coefficient functions. Under mild assumptions, we establish the large sample theory of the proposed estimators by utilizing the results of U-statistics and shows that the two-stage local linear Walsh-average estimator own an oracle property, namely the asymptotic normality of the two-stage local linear Walsh-average estimator of each coefficient function is not affected by other unknown coefficient functions. Extensive simulation studies are conducted to assess the finite sample performance, and a real example is analyzed to illustrate the proposed method.

On-line diagnosis method of crack behavior abnormality in concrete dams based on fluctuation of sequential parameter estimates

Research on on-line diagnosis method of crack behavior abnormality in concrete dams can provide support for timely grasping abnormality state of the crack itself and achieving real-time monitoring of the dam safety.Considering that samples of crack effects in concrete dams increase actually over monitoring time,a superiority criterion for the on-line diagnosis is determined so as to detect the abnormality moments timely and reliably.By integrating the safety monitoring statistical model of crack effect variable with change point theory,a fluctuation method of regression coefficients is established for the on-line diagnosis.In addition,each abnormality moment is detected by the cumulative sum of regression model residuals.Results indicate that abnormality of crack behavior in concrete dams can be characterized by structural instability of crack monitoring model.And causes of crack behavior abnormality can be analyzed by the established method,which will play an important role in dam safety monitoring.Further,taking the crack in a concrete gravity-arch dam as an example,the scientific rationality and validity of the established on-line diagnosis method are confirmed.

A statistical procedure to assess the significance level of barriers to gene flow

Although several methods are available to study the extent of isolation by distance （IBD） among natural populations, comparatively few exist to detect the presence of sharp genetic breaks in genetic distance datasets. In recent years, Monmonier＇s maximum-difference algorithm has been increasingly used by population geneticists. However, this method does not provide means to measure the statistical significance of such barriers, nor to determine their relative contribution to population differentiation with respect to IBD. Here, we propose an approach to assess the significance of genetic boundaries. The method is based on the calculation of a multiple regression from distance matrices, where binary matrices represent putative genetic barriers to test, in addition to geographic and genetic distances. Simulation results suggest that this method reliably detects the presence of genetic barriers, even in situations where IBD is also significant. We also illustrate the methodology by analyzing previously published datasets. Conclusions about the importance of genetic barriers can be misleading if one does not take into consideration their relative contribution to the overall genetic structure of species.

Optimization of vinegar-steaming process for Wuweizi (Fructus Schisandrae Chinensis) with response surface method

OBJECTIVE:To optimize the vinegar-steaming process of Wuweizi(Fructus Schisandrae Chinensis)using the response surface method(RSM)based on the Box-Behnken design.METHODS:A regression model was constructed with the response variables,the content of Deoxyschizandrin,and the three explanatory factors:length of steaming time,the quantity of vinegar and length of moistening time to evaluate the effects on the processing of Wuweizi(Fructus SchisandraeChinensis).RESULTS:There was a linear relationship between the content of Deoxyschizandrin and the three explanatory factors.When the steaming time was5.49 h,with 2.365 g of vinegar added and a moistening time of 4.13 h,the content of Deoxyschizandrin reached the maximum predicted value of0.1076%,and under the conditions the average content of Deoxyschizandrin was 0.1058%.CONCLUSION:The correlation coefficient of thenonlinear mathematical model was relatively high and the model matched the data well,potentially providing a method for the study of the steaming process.

Theoretical prediction and validation of global horizontal solar irradiance for a tropical climate in India

This paper aims to propose monthly models responsible for the theoretical evaluation of the global horizontal irradiance of a tropical region in India which is Sivagangai situated in Tamilnadu. The actual measured global horizontal irradiance hails from a 5 MW solar power plant station located at Sivagangai in Tamilnadu. The data were monitored from May 2011 to April 2013. The theoretical assessment was conducted differently by employing a programming platform called Microsoft Visual Basic 2010 Express. A graphical user interface was created using Visual Basic 2010 Express, which provided the evaluation of empirical parameters for model formulation such as daily sunshine duration （5）, maximum possible sunshine hour duration （S0）, extra terrestrial horizontal global irradiance （H0） and extra terrestrial direct normal irradiance （G0）. The proposed regression models were validated by the significance of statistical indicators such as mean bias error, root mean square error and mean percentage error from the predicted and the actual values for the region considered. Comparison was made between the proposed monthly models and the existing normalized models for global horizontal irradiance evaluation.